CORRESPONDENCE BETWEEN PROF. BARTOCCI
AND ARDESHIR MEHTA

The following is the exact text of e-correspondence between
Prof. Umberto Bartocci of the University of Perugia, Italy,
and myself, regarding Relativity (especially my "Simple
Challenge"). The correspondence is complete and unedited,
translated by me when necessary from Italian into English;
and the only other changes that have been made are the
elimination of typographical errors, and reformatting to fit all
messages into the same margins (for the sake of legibility).

From the following, any rational person should be able to
judge between Prof. Bartocci and myself, and see who is right
from a logical and mathematical point of view.

Comments regarding the correspondence may be sent via e-
mail to us at:

     ardeshirmehta@myself.com

and

      bartocci@dipmat.unipg.it
 
 

_____________________________________________________
 
 

Subject: Argomento Contro la Teoria della Relativita Speciale
         [Translation: Argument Against the Special Theory of Relativity]
Date: Thu, 14 Jun 2001 17:26:19 -0400
From: "Ardeshir Mehta, N.D." <ardeshir@sympatico.ca>
To: bartocci@dipmat.unipg.it
 
 

[TRANSLATED FROM THE ITALIAN BY ARDESHIR MEHTA]
 
 

Dear Professor:
 
 

Having read your Web page:

<http://www.dipmat.unipg.it/~bartocci/quest.htm>

... I have decided to write my argument against the Special Theory
of Relativity -- at least the one I consider to be the best and simplest.

You can read it at my Home Page, and at the following URL:

<http://homepage.mac.com/ardeshir/RelativityDebunked.html>
 

Regards,
 
 

Ardeshir Mehta
Ottawa, Canada

Home Page: <http://homepage.mac.com/ardeshir/education.html>
 

______________________________________________________
 
 

Subject: Re: Argomento Contro la Teoria della Relativita Speciale
             [Translation: Argument Against the Special Theory of Relativity]
Date: Fri, 15 Jun 2001 08:59:57 +0200
From: umberto bartocci <bartocci@dipmat.unipg.it>
To: "Ardeshir Mehta, N.D." <ardeshir@sympatico.ca>
References: 1
 

Dear Dr Mehta,

thank you very much for your attention. I shall read your argument with
great interest, and possibly I shall then send to you some comments.

Best wishes,

Umberto Bartocci

(How it happens that you know so well Italian?)

(Are you a relative of the famous Indian conductor Zubin Mehta?)
 

--
Umberto Bartocci
Dipartimento di Matematica
Universita' di Perugia
06100 - Italy
http://www.dipmat.unipg.it/~bartocci
 

______________________________________________________
 
 

Subject: Re: Argomento Contro la Teoria della Relativita Speciale
             [Translation: Argument Against the Special Theory of Relativity]
Date: Sat, 16 Jun 2001 13:49:26 -0400
From: "Ardeshir Mehta, N.D." <ardeshir@sympatico.ca>
To: umberto bartocci <bartocci@dipmat.unipg.it>
References: 1 , 2
 

Hello Professor:
 
 

You wrote:

> Dear Dr Mehta,
> thank you very much for your attention. I shall read your
> argument with great interest, and possibly I shall then send
> to you some comments.

I shall await your comments and read them with interest.
I am in touch with Dr. Al Kelly of Ireland, and Prof. Paul
Marmet of Ottawa, both of whom, I understand, you know
also. (In fact I became acquainted with your Web site after
reading Prof. Marmet's work, and then read about Dr Kelly
on your site, whereupon I contacted him.)

By the way: Please call me "Ardeshir"! The "N.D." after
my name stands for "No Degrees".  :-)  I am so ashamed
of the way the academic world has distorted twentieth
century physics and mathematics, that I would personally
take no pride at all in being called "Doctor."

> (How it happens that you know so well Italian?)

I lived in Italy three years, from 1964 to '67. Infatti, sono
stato anche a' Perugia, nell'anno '65, ed a volte ho mangiato
nella mensa degli studenti all'università. (In quei giorni ero
molto più giovane!) Per di più, ricordo benissimo il mio
soggiorno a' Perugia, e mi piacerebbe molto ritornarci un di'.

> (Are you a relative of the famous Indian conductor Zubin
> Mehta?)

No, I am afraid not; however, both he and I belong to a very
small ethnic group called "Parsis", less than 80,000 in number,
who fled Iran after Islam became the dominant religion there,
and found refuge in India. We are Zoroastrians, followers of
the Persian Prophet Zarathushtra.

As a result of intermarriage within such a small community,
which took place over many centuries, it is quite possible
that a few of my genes and the conductor's are from the same
source!

Saluti,
 
 

Ardeshir <http://homepage.mac.com/ardeshir/education.html>
 
 

___________________________________________________
 
 

Subject: Re: Argomento Contro la Teoria della Relativita Speciale
             [Translation: Argument Against the Special Theory of Relativity]
Date: Fri, 27 Jul 2001 13:42:18 +0200
From: umberto bartocci <bartocci@dipmat.unipg.it>
To: "Ardeshir Mehta, N.D." <ardeshir@sympatico.ca>
References: 1
 
 

Dear Mehta,

I have at last found some time for reading your "best
argument". I do not know if you are interested in my
comments/help, in case let me know. Anyway, I must tell you
in short that it is "obvious" that once more I did not find any
good argument against relativity. As a matter of fact, it is
simply NOT true that "the Lorentz transformation requires that
the stop watch should show a lesser time for this event if it is
calculated under the assumption that A is moving and B is
stationary, than it would if the time were calculated under the
assumption that B is moving and A is stationary. Thus the
Lorentz transformation requires the readings on the stop watch
to be calculated to be different, depending on whether A is
assumed to be moving or stationary...". If you do the
computation correctly, you find a unique answer to your
question.

In any case, you should be much more clear since the
beginning, in the description of the physical situation you
propose to analyze. I presume that you imagine to have A and
B BOTH moving with respect to a THIRD (inertial) observer
C. Which is then their speed with respect to a Lorentzian
coordinate system associated with C? And when you ask "how
much time should it take for A to pass by the spot X marked
on B, as measured by a stop watch carried on board A?", you
should specify carefully which is the STARTING POINT of
the time interval you intend to compute (in A "proper time",
namely, with regard to the time marked by a watch carried by
A).

If you do all things correctly, all "troubles" will disappear.
Unfortunately, relativity cannot be defeated with such simple
arguments: one needs some (strong) experimental evidence, for
instance of the non-validity of the "principle of relativity" for
electromagnetic phenomena...

Molti cordiali saluti da Perugia,

dal suo  Umberto Bartocci
 
 

--
Umberto Bartocci
Dipartimento di Matematica
Universita' di Perugia
06100 - Italy
http://www.dipmat.unipg.it/~bartocci
 
 

_______________________________________________________
 
 

Subject: Re: Argomento Contro la Teoria della Relativita Speciale
             [Translation: Argument Against the Special Theory of Relativity]
Date: Mon, 30 Jul 2001 11:38:49 -0400
From: "Ardeshir Mehta, N.D." <ardeshirmehta@myself.com>
To: umberto bartocci <bartocci@dipmat.unipg.it>
References: 1 , 2
 
 

Caro Professore:
 
 

With the utmost respect, I think you are *completely* wrong.

And there is a *simple* test to prove it. Try to take my
challenge, given towards the end of my paper as follows:

       "I hereby challenge *anyone* to give a consistent answer
       to the above question -- one that does not contradict
       either the Principle of Relativity or the Lorentz transfor-
       mation equations."

You will see that you cannot give any *consistent* answer to
the question, "exactly what should the snapshots show?" No
one has ever been able to do so, not even the most respected
physicists in the world.

You write:

       If you do the computation correctly, you find a unique
       answer to your question.

Well, here is your chance to prove that you mean what you
say! Please do the computation, omitting no detail, and try
your best to prove yourself right. I am 100% sure I will be
able to find *specific* mathematical and / or logical errors in
any such computation.

BTW: There is no need for a "third (inertial) observer C". It is
the *snapshots* taken of the stop watches carried on board A
and B that count. All observers, wherever they are, and even if
they are not in inertial frames, will see the *same* snapshots -
- it would be impossible for them to see different ones!

You see, I do not even *need* to "defeat relativity" -- I only
have to show that the relativists cannot *support* relativity by
computations of their own, when I am allowed to set up the
*Gedankenexperimente* myself! That suffices to show that
they have not proved their own case.
 
 

Auguri e saluti,
 
 

Ardeshir <http://homepage.mac.com/ardeshir/education.html>
 

************************************************************
 

PS: Shall we consult with my good cyber-friend Al Kelly of Ireland? Or
Dr Christoph von Mettenhem, author of the book *Popper vs. Einstein*?
 
 

************************************************************
 
 

________________________________________________________
 
 

Subject: Re: Argomento Contro la Teoria della Relativita Speciale
             [Translation: Argument Against the Special Theory of Relativity]
Date: Mon, 13 Aug 2001 19:23:43 -0400
From: "Ardeshir Mehta, N.D." <ardeshirmehta@myself.com>
To: umberto bartocci <bartocci@dipmat.unipg.it>
CC: "Ardeshir Mehta, N.D." <ardeshir@sympatico.ca>
References: 1 , 2
 
 

Caro professore:
 
 

Thinking that perhaps you did not understand my paper, I have condensed
my argument into a one-page challenge, which can be found at:

<http://homepage.mac.com/ardeshir/SimpleChallenge-Relativity.html>

Se vuole, potrei anche tradurre la mia sfida in italiano!
[If you wish, I can even translate my challenge into Italian!]
 
 

Molti saluti,
 
 

Ardeshir <http://homepage.mac.com/ardeshir/education.html>
 
 

________________________________________________________
 
 

Subject: Re: Argomento Contro la Teoria della Relativita Speciale
             [Translation: Argument Against the Special Theory of Relativity]
Date: Tue, 14 Aug 2001 07:25:33 +0200
From: umberto bartocci <bartocci@dipmat.unipg.it>
To: "Ardeshir Mehta, N.D." <ardeshirmehta@myself.com>
References: 1 , 2 , 3
 
 

Dear Mehta,

I did not forget you, and I was preparing a detailed answer (no need to
translate), but I have got too many things to carry on simultaneously (either
in the classical or in the relativistic sense!), and I am getting old and with
less resources every day which goes...

Always best wishes,  UB
 

Umberto Bartocci
Dipartimento di Matematica
Universita' di Perugia
06100 - Italy
http://www.dipmat.unipg.it/~bartocci
 
 

_______________________________________________________
 
 

Subject: Re: Argomento Contro la Teoria della Relativita Speciale
             [Translation: Argument Against the Special Theory of Relativity]
Date: Wed, 15 Aug 2001 23:32:22 -0400
From: "Ardeshir Mehta, N.D." <ardeshirmehta@myself.com>
To: umberto bartocci <bartocci@dipmat.unipg.it>
References: 1 , 2 , 3 , 4
 
 

Caro Prof. Bartocci,
 
 

Thank you for your response!

You wrote:

>    Dear Mehta,
>
> I did not forget you, and I was preparing a detailed answer (no need to
> translate), but I have got too many things to carry on simultaneously (either
> in the classical or in the relativistic sense!), and I am getting old and with
> less resources every day which goes...
>
>    Always best wishes,  UB

I think, from a picture of you I saw on the Web, that you
must be quite a bit older than I am (I am 58 now.) So I shall
understand if you cannot reply immediately -- just so long as
you reply eventually!

I would like you to recall your own words in the Web page
entitled <ANSWERS TO "BARTOCCI INQUIRY">:

     Remember as scientists the duty to answer to criticism.

I find that you had also written there:

    There are no mathematical contradictions in SR, which
    is quite a coherent theory.

It is to counter this second statement that I have devised a
simple one-page mathematical challenge to supporters of
Special Relativity, available at:

<http://homepage.mac.com/ardeshir/SimpleChallenge-Relativity.html>

Of course I realise that you are not a supporter of SR, but
perhaps you still think that SR is *mathematically* correct. It
is definitely not.

If you *do* the mathematics, which should not take you more
than twenty minutes at the most, you will find that there are
absolutely NO correct mathematical answers to the problem I
have posed in my challenge -- i.e., answers which are ALSO
consistent with the Special Theory of Relativity.

No one to whom I have put the challenge has been able to
answer me. And indeed I think no one ever will, because SR,
despite your claim, is both logically and mathematically
flawed!

Remember that Einstein was not a good mathematician. But
you are, so you should be able to see the mathematical flaw --
that is, if you actually *do* the mathematics.

I suspect that the problem with SR is that the flaws are TOO
SIMPLE, and that is why they has not been widely discovered
till now. I have written yet another short *reductio-ad-
absurdum* refutation of SR -- this time logical in nature -- at:

<http://homepage.mac.com/ardeshir/ShortestRefutatnRelativity.html>.

This is so short that it takes almost no time at all to read! It
is, as I say, a logical argument, not mathematical; but it is
still devastating to SR.

But of course the mathematical argument is even more
conclusive in this regard.

And naturally, it is impossible to properly answer a
mathematical challenge unless the mathematical calculations
are actually *done*!

Tanti saluti,
 
 

Ardeshir <http://homepage.mac.com/ardeshir/education.html>
 
 

_______________________________________________________
 
 

Subject: Re: Argomento Contro la Teoria della Relativita Speciale
             [Translation: Argument Against the Special Theory of Relativity]
Date: Sun, 19 Aug 2001 10:24:35 +0200
From: umberto bartocci <bartocci@dipmat.unipg.it>
To: "Ardeshir Mehta, N.D." <ardeshirmehta@myself.com>
References: 1 , 2 , 3 , 4 , 5
 
 

Dear Mehta,

here it is at last my answer, which I shall divide in various
steps. I shall be VERY FRANK with you, after all it is you
who makes a "challenge", and I always believe that "amicus
Plato, sed magis amica veritas" (I hope that you already know
these words, or that you can be able to understand their
meaning in force of the Italian you can remember).

A - First of all, let me say that I had to change this message at
least twice, since in the meantime I received two more mails
from you! For instance, I was trying to argue [1 - footnote]
that I AM NOT A SUPPORTER OF RELATIVITY, but then
I acknowledge with pleasure that you wrote in your last mail:

> Of course I realise that you are not a supporter of SR, but
> perhaps you still think that SR is *mathematically* correct.

Yes, I am definitively NOT a supporter of relativity, since I
believe (and I hope it, too) that it can be shown wrong in the
EXPERIMENTAL SIDE, but of course I still obviously think
that SR is *mathematically* correct.

I would be indeed the HAPPIEST man in the world if it was
true that your argument (just to quote one between many
similar, like Dingle's, or Kelly's, etc.) is correct, and that I am
*completely* wrong"! UNFORTUNATELY IT IS NOT SO,
and  there is no doubt about it.

I can say it, I must say it, with no arrogance at all, but in
mathematics THERE IS NO FREEDOM OF OPINIONS: an
assertion is either right or wrong, and we must consider (both
special and general) relativity as "simple" mathematical
theories (which does NOT mean that they are in agreement
with the ORDINARY CATEGORIES  of space and time!).
Special relativity, for instance, is just the theory of the
Minkowski space-time (a flat space-time). In this space the
"principle of relativity" for Lorentzian coordinate systems
(inertial observers - observers are not "people", but precisely
defined mathematical entities!) simply holds in force of the
definition of the space itself; the Lorentz transformations are
just the automorphisms of this space, no problems at all. If it
was true, as you claim, that:

> SR, despite your claim, is both logically and
> mathematically flawed!

then the WHOLE MATHEMATICS would be affected by
contradictions, and I hope  that you will agree that this is
rather impossible, unbelievable (Goedel theorems apart)!

I really cannot understand how is it possible that there is
always a lot of people (the most famous was perhaps Dingle,
with his notorious, but "stupid", "Dingle syllogism") which
believes that simple "paradoxes" can show that relativity is
wrong! As I wrote in a whole paper about
"Misunderstandings..." (which is available in point N. 2 of
my web page on the Foundations of Physics), the origin of
ALL of them is in some MISUNDERSTANDING of the
theory. As a matter of fact, these misconceptions are
sometimes "interesting", because to find where is the
"mistake" can be amusing, or fruitful for deeper understanding
of the theory, sometimes they are of no value at all. They
show in any case how ordinary space and time (which means
even ORDINARY LANGUAGE) differ from the relativistic
correspondents!

Of course, SR is even a "physical theory", which means that
the mathematical theory is equipped with a code, a set of
rules, which allow to transform real situations into
mathematical ones, and conversely. That is to say, relativity
pretends to describe in some sense REALITY, at least in
certain well defined conditions, and we could indeed contest
THIS claim, but nothing more.

This is why I can assert what I assert, and why I am able to
"answer" to all questions you ask, even if I am not a supporter
of relativity. The fact is that I understand relativity, which is
one thing that many "classical physicists" seem unable to
achieve.

B - After this general introduction, I come to the special case
of your "challenge". There are many ways to make
"comments" to it, but there is no way to give a "strict answer"
to your question, since it is ILL POSED (in other words, it is
not well formulated; in Italian: MAL POSTA)! I am not
surprised at all that:

> No one to whom I have put the challenge has been able to
> answer me.

I have just stated which is the first possible reason for this
fact. It is as if you said: two men are going together for a
walk, one of them is tall x meters, the weight of the other is y
kilo, which is their age?

I shall PROVE immediately that this is (of course only in
some sense) the case with your "question", but I wish to add
two more remarks.

B1 - I am well aware that to show where are the "flaws" in the
simple statement of your question does not finish the
discussion, and that it could be the "duty" of a teacher to do
something more. For instance, a good teacher should even
show how one could correct the flaws, posing then a good
question, and then answer to it. I shall try to do even this for
you, but only for friendship, and not because I think that this
discussion can have some scientific interest, I think sincerely
that this is not the case

B2 - What I have just said could be another reason why you
did not get until now a reply to your question. Did really any
"competent" physicist assert that your problem was difficult,
and that he was not able to give an answer? I do not believe
that. I just believe that other people to whom you have sent
your challenge simply did not reply because they did not
intend to waste their time in a discussion which they
immediately judged unproductive.

B3 - As far as the previous point is concerning, let me tell
you something which has been said to me by a colleague here
in Perugia - one of the most competent expert in relativity, I
believe. He told me that he cannot understand why people
understands that they have to pay lawyers, physicians, etc., in
order to have their opinion, even for matters which require less
knowledge, time and commitment than scientific ones, but
then the same people suppose instead that scientists should
loose their time in answering to amateurish ill-posed
questions. He added that a teacher could do this work only for
the benefit of his own students, but if a student insists in not
understanding then he gets fired (in Italian: BOCCIATO).

C - I see with pleasure that you have changed, simplified,
your previous question*, seeming to have appreciated the
objections contained in one of my last mails. Now the
physical situation about which you require an explanation is
defined rather more clearly, but all the same it needs some
correction, if you want to formulate a question which has
some meaning from a relativistic point of view, and then "can
be answered".

You say that one has a spaceship A in empty space, L metres
in length (why do you introduce numbers instead than simple
letters, parameters?! There is no need at all of numbers in
mathematics, even if I understand which is your strategy, as I
shall soon argue!), and first of all:

- what do you mean by this length?

You know very well that in relativity there is not the
possibility to define an absolute length for any "object", so
you could say for instance that L is the proper length of the
spaceship, namely the length with respect to some coordinate
system in which the ship stands still. Or otherwise you could
say that L is the length of the ship with respect to the buoy,
but then you have to deal with DIFFERENT lengths, as far as
relativity is concerning. You must decide which is the
meaning of this L . The same objection holds for the
definition of the buoy's length, which I shall call M . I shall
assume from now on that both  L  and  M  are PROPER
LENGTHS. You then assume that the relative speed between
the spaceship A and the buoy B is some percentage v of the
speed of light (in relativity, one says that in this case he is
measuring speeds in "geometrical unities", c = 1, OK), etc.,
and here we have not problems.

D - In your words this spaceship is "passing rectilinearly just
centimetres past a small spherical capsule or buoy B" (avoid
please that "small", it has not an absolute meaning at all!).

Then you claim:

> that some suitable mechanism (which can easily be devised)
> causes both the stop watches to measure the time interval
> taken for the spaceship A to pass the buoy B.

THIS IS EXACTLY THE POINT WHICH HAS LESS
MEANING, for more than  one reason, and which requires
greater attempts of correction, in comparison with what  I did
before in the case of the lengths!

D1 - First of all, what does it precisely mean this "time
interval"? You did not define it enough well in order to
identify it exactly. You use a generic expression which could
have a meaning in rough ordinary language, but not in a
physical problem like the one we are now dealing with. I shall
try to explain the situation with more detail.

A time interval measured by some SINGLE clock can be
defined as the DIFFERENCE of two values  t2 - t1  marked
by this clock, where  t2  is the time corresponding to some
SECOND EVENT in the clock's "life", in some given space-
time coordinate system, and  t2  the time corresponding to
some FIRST EVENT. Which are precisely the EVENTS you
wish to introduce for defining your time interval?

Let us assume for instance THAT THE BUOY IS
POINTLIKE, namely that M = 0 (I understand very well that
you have said 1 meter in length, with respect to 259,627,884 ,
exactly because you were looking for a "clever" way to avoid
complications, and then to say that 1 is "almost" zero with
respect to  259,627,884 !  The point is that one must be very
precise in mathematics, no ad hoc approximations at all, when
they are not needed, and above all when one is trying to hide
with them exactly the point which on the contrary one should
have to bring to the light!), and that there is only one clock in
the buoy. Then we could ask indeed the following question:

- the clock which is in the buoy marks  t1  when the "bow" of
the spaceship is in front of it; this same clock marks  t2  when
the "stern" of the spaceship is in front of it (let us introduce
bow and stern with respect to the buoy, first the bow, then the
stern are passing in front of the buoy), and then we take t2 - t1
(which, after all, does not depend from the choice of the origin
of times for this clock). Well, we could then ask: how much
is this difference?

The answer is very easy: it is L'/v , where L' is the length of
the spaceship WITH RESPECT TO THE BUOY, which in
relativity is NOT the same  L  we introduced before. But let
me draw a picture, as I can, with the purpose of being more
clear:

  S ____________ B    ----->  (vector velocity v)         °

the spaceship has a bow                                   the pointlike
and a stern S with respect                                buoy, with a
to the buoy                                                      clock B
 

If you ask for a comparison which is the time which is needed
in this case for the buoy to pass the spaceship, from the point
of view of clocks which are in the spaceship, it is obviously
L/v , and it is a time interval GREATER than the other I have
indicated before:

L/v > L'/v .

D2 - Having said that, what happens if the buoy is not
supposed pointlike, and it has too a bow and a stern with
respect to the spaceship (it would be much more "honest" to
speak of TWO SPACESHIPS, with possibly different
lengths!)?

  S ____________ B     -----> (vector velocity v)   B° ___S°

       spaceship                                                     buoy

Do you wish to compute the time interval which is needed for
the two external points of the spaceship in order to pass in
front of the SAME POINT in the buoy, a point in which there
is a clock? Or do you suppose to want to compute for instance
the time which goes from the bow B being in front of the
other bow B° of the buoy, and then the stern S being in front
of the other stern S° of the buoy? (if you object that these
remarks are too much "pedantic", since you have introduced a
buoy of only 1 meter, and a much "longer" spaceship, think
what happens when you try to do the converse: namely, to
measure this investigated time interval from the point of view
of the spaceship! In any case, I repeat it, in mathematics there
are not long and small, there are only precise computations,
and possibly, AT THE END, when we are doing physics, we
can make APPROXIMATIONS, but not at the very
beginning).

D3 - In truth, I understand that you have foreseen this
objection, and that you have tried to cleverly avoid it, by
introducing that "suitable mechanism (which can easily be
devised)" etc.! But where is this mechanism? In B, or in S, or
in B°, in S°, or elsewhere? And where is the clock (or better,
where are the clocks) you use for the measure of time?

If they are at some distance from the "mechanism", in any case
you have to deal with the time which is needed for a signal
sent by this instrument in order to arrive to the clock. All
your efforts notwithstanding, you cannot avoid the relativistic
speculations in this matter, which claim that no signal can
travel faster than light, etc., and then assuming that exactly c
is the "better speed" (faster) which is required for
"communications" between your "mechanism" and the clock!

D4 - I try to explain the problems in yet another way. At last
you propose to compare TWO measures, with apparently only
two clocks, but this is simply impossible. If it is possible to
suppose (or to approximate, if you prefer) the buoy as
pointlike, and to make the measurement you require with only
one clock in this case, how can you do the same measurement
from the spaceship? If there is only one clock in the spaceship,
say for instance in the bow, then this clock shows some time
when the bow of the spaceship is in front of the buoy (or of
the clock which is the buoy), but how can you get a second
value for the time measured by this clock, the second value
which is needed in order to compute the required difference?

YOU NEED FOR INSTANCE ANOTHER CLOCK IN THE
STERN, or even - if you think  that it is a different thing (but
it isn't!) - you need a signal going from the stern to the bow,
in order to know where the stern WAS in front of the buoy.
Here it is exactly where relativity comes in, with all his
stories about the synchronization of distant clocks etc.. If the
clock you are talking about was placed instead in the stern of
the spaceship, it could register only the time when the stern is
in front of the buoy, but he cannot "know" when the bow was
in front of the buoy! Summing up, you need TWO
synchronized clocks in order to do the measurement you wish,
both in the spaceship and in the buoy, and you must be more
precise in specifying which is the time interval you wish to
compute, and most of all HOW...

E - Now that it has become clear, I hope, how your question
SHOULD HAVE BEEN FORMULATED, let us go on,
choosing (between many), one possibility, namely ask to
measure the time which passes - either from the point of view
of the buoy, or of the spaceship (in both cases you need a
whole space-time coordinate system associated with the two
objects: there is no difference at all with the attempt of
introducing only TWO objects, clock and mechanism!) - from
the two events which correspond to the coincidences:
bow/bow, stern/stern. In other words, I say that you have to
pose your question for instance in the following way, and that
then there is an easy not contradictory answer to it:

- One has an inertial spaceship, with some proper length L,
and ANOTHER ONE, of some proper length M , the relative
speed is v. One has synchronized clocks on both spaceships [I
repeat that it is really enough to have TWO of them for each
spaceship, so FOUR in all], and one asks how much time is
needed, from the point of view of both spaceships, for
completely passing one the other.

Now we have at last a WELL POSED question, and an easy
answer. The two time intervals are:

L/v + M'/v (from the point of view of the first spaceship -
with obvious notation)

L'/v + M/v (from the point of view of the second spaceship,
the "old" buoy) ,

where of course it is L' = L*sqr(1-v^2/c^2) , and M' =
M*sqr(1-v^2/c^2) (in force of the so called length contraction
- we do not even need to introduce Lorentz transformations,
even if of course the length contraction is one of their
consequences).

In order to decide which time interval is bigger than the other,
one has just to decide which length is bigger between L and
M . If one supposes that the first spaceship is longer than the
second (the ex-buoy), then one has:

(L+M')/v > (L'+M)/v ,

no doubt at all about that, the second time interval is smaller
than the first.

If one supposes instead COMPLETE SYMMETRY, namely
L = M (in other words,  TWO EQUAL SPACESHIPS), one
gets at last TWO EQUAL TIME INTERVALS.

As you see, everything is very simple, much more simple for
instance than introducing a coordinate system with respect to an
accelerated observer, like one must do when discussing the twin
paradox (see for instance the paper in the point 4 in the above
quoted web page, which is unfortunately only written in Italian,
but there is some comment to this problem even in the fifth
section of the aforesaid paper about "Misunderstandings...").

The question is always the same, which after all is not even
too much difficult to overcome: it is to understand the
counterintuitive (but mathematically precise, and then
"logically possible") relativistic treatment of space and time
(not to have an "intuition" of it with the common thought
space and time categories, which would be of course rather
impossible)...

F - I have talked too much - and with my bad English this is
perhaps harmful for a better understanding - yet I have not said
everything I could have said. For instance, in some lecture to
students, I could have shown even how one could have
connected length contraction and time dilation in the proposed
exercise.

In any case I hope:

F1 - first of all, to not have made mistakes (which should
have to be considered my personal mistakes, and not
mistakes/contradictions in the theory!);

F2 - that you have understood where are the mistakes in your
posing the question;

F3 - that you have understood how could one pose a good
question, between many possible of the "same nature";

F4 - that you will not require to me endless discussions, as it
happened many times to me with people not willing to
understand relativity (there is an example of such useless
discussions in my web site, with Percival, or Galeczki, etc.,
all people who do not know enough well relativity);

F5 - to have been useful to you at least from an ethical point
of view, showing that one could indeed answer to all people,
even when one believes that the required effort of writing will
not produce anything "useful".

I am at your disposal with sincere friendship for a possible
next round, but please only one, no more (and please spare to
me a comment about your new "logical" "Short Reductio-ad-
Absurdum Refutation of Special Relativity", which is no
better "idea" than the one I have discussed until now); time is
indeed a precious thing, mostly at the end of one's life, and
there are better, most productive, ways to spend it...

Once again best wishes, from yours most sincerely

correspondent perugino  UB

[1] There were even other things which I started to discuss in
my preliminary attempts of answer, for instance about what
you have said in one of yours intermediate mails:

> There is no need for a "third (inertial) observer C"...

I do agree about that, and as a matter of fact you avoided to do
it in the second formulation of your "challenge", but it was
you that in the first formulation of it had written:

> Imagine two objects, A and B, in rectilinear motion past
> one another.

In order to "imagine" this situation, one needed to introduce
the point of view of a third observer! The fact is that there are
always many different manners to describe in mathematical
terms the "same" physical situation, since the "code" which
translates from "reality" to mathematics is rather flexible, but
in any case the answers must always be the same!
 

--
Umberto Bartocci
Dipartimento di Matematica
Universita' di Perugia
06100 - Italy
http://www.dipmat.unipg.it/~bartocci
 

__________________________________________________
 
 

Subject:  Re: Argomento Contro la Teoria della Relativita Speciale
Date: Fri, 24 Aug 2001 14:24:44 -0400
From: "Ardeshir Mehta, N.D." <ardeshirmehta@myself.com>
To: umberto bartocci <bartocci@dipmat.unipg.it>
 References: 1 , 2 , 3 , 4 , 5 , 6
 
 

Caro Prof. Bartocci:
 
 

Saluti!

Thank you for your detailed response. I am especially glad to
see that you have given philosophical arguments against my
views also!

But I am very, very sorry to see that you have made a BIG
MISTAKE -- namely, you have *completely* ignored time
dilation!

As you yourself have pointed out, in mathematics one must
be ABSOLUTELY PRECISE; and as you yourself also say,
"with no arrogance at all, ... in mathematics THERE IS NO
FREEDOM OF OPINIONS: an assertion is either right or
wrong".

So if we get *one* answer using length contraction *alone*,
and *another* answer using both length contraction *and*
time dilation, then *both* answers cannot possibly be correct!
Only ONE of them can be correct.

And then the question arises: Which one? Obviously, if one
accepts the Lorentz transformations, the right answer can only
be the one using BOTH length contraction AND time
dilation!

SO YOUR ANSWER, CALCULATED *WITHOUT* USING
TIME DILATION, CANNOT POSSIBLY BE CORRECT!

There is no freedom of opinion: you HAVE to be wrong!

Do you see my point? Am I not right? And are you not
wrong? Be honest, now.

Also, as you would have seen had you carefully read my first
article "The Single Best Argument Against Relativity", my
entire "Challenge" is based on Dingle's observation that time
dilation, on the one hand, and the principle of all rectilinear
motion being relative, on the other, are contradictory to one
another.

Thus time dilation is AN INTEGRAL PART of my
Challenge! By not mentioning time dilation you have not
answered my Challenge at all.

I am moreover also sorry to see that you did not read my two
articles *carefully*. All the points you have raised have
already been answered in them. None of the objections you
have raised are new to me, and I have foreseen and taken care
of *all* of these objections.

(Did you imagine you were entering into a Challenge with
some first-year university student? My dear Sir, you are
carrying on a mathematical discussion with someone who has
written a 110-page book entitled "Critique of Goedel's
Theorem"! Trust me, if I can find mistakes as subtle as those
made by Kurt Goedel in his most celebrated theorem, I can
find mistakes in anything YOU can write -- that is, if any
mistakes exist in what you write, and especially if they are
*blatant* mistakes.)

Now I shall describe your mistakes in detail. I shall reply in
the beginning to the mistake in mathematical part of your
answer, and then the mistakes arising from the fact that you
did not read my articles carefully; and I shall tackle the
philosophical part at the end.

You wrote:

> You say that one has a spaceship A in empty space, L metres in
> length (why do you introduce numbers instead than simple letters,
> parameters?! There is no need at all of numbers in mathematics,
> even if I understand which is your strategy, as I shall soon argue!),
> and first of all:
>
> - what do you mean by this length?

I meant, of course, the so-called "rest length". Even in
discussions concerning Relativity, when one speaks of
"length" *without* any qualifications, one normally means
"rest length" or "length as measured by a rod which is at rest
with respect to the object being measured." If I remember
correctly, Einstein himself in his book *Relativity: the
Special and General Theory* does this.

(But I think you know this fact already!)

By the way, I could easily have used "length L" instead of
precise numbers; but I used precise numbers so that the
calculations become easy. The numbers I have used allow the
Lorentz <gamma> factor to be exactly 2.00, which simplifies
calculations, especially for precise numbers. This is for those
who are not professional mathematicians, like many
philosophers I know, who are interested in Relativity from a
philosophical point of view.

Also, in physics, measurements cannot be performed with
ABSOLUTE perfection. With every measurement there is
associated a MARGIN OF ERROR. If we take the margin of
error to be +/- 10^(-10) -- which is reasonable -- then my
numbers make perfect sense from the point of view of physics.
(After all, it is the APPLICATION of mathematics that we are
discussing, not PURE mathematics!)

> You know very well that in relativity there is not the
> possibility to define an absolute length for any "object", so
> you could say for instance that L is the proper length of the
> spaceship, namely the length with respect to some coordinate
> system in which the ship stands still. Or otherwise you could
> say that L is the length of the ship with respect to the buoy,
> but then you have to deal with DIFFERENT lengths, as far as
> relativity is concerning. You must decide which is the
> meaning of this L . The same objection holds for the
> definition of the buoy's length, which I shall call M . I shall
> assume from now on that both  L  and  M  are PROPER
> LENGTHS.

Right. (But the length M is not necessary, as I shall show
below.)

> You then
> assume that the relative speed between the spaceship A and the
> buoy B is some percentage v of the speed of light (in relativity,
> one says that in this case he is measuring speeds in "geometrical
> unities", c = 1, OK), etc., and here we have not problems.

Right again.

> D - In your words this spaceship is "passing rectilinearly just
> centi-metres past a small spherical capsule or buoy B" (avoid
> please that "small", it has not an absolute meaning at all!).

Okay: one can assume that there is a point marked "X" on the
buoy which is the point past which the spaceship A must
pass. (I already wrote that in my longer, first article entitled
"Single Best Argument Against Relativity", which, if you had
read carefully, you would have seen clearly. Indeed it is
mentioned in the Abstract at the very *beginning* of the
article.)

And as I said also, if we take the margin of error to be +/-
10^(-10), as specified by me in my first article, then even this
"X" is not necessary.

So the buoy's length M is NOT NECESSARY AT ALL.

> Then you claim:
>
> > that some suitable mechanism (which can easily be devised)
> > causes both the stop watches to measure the time interval
> > taken for the spaceship A to pass the buoy B.
>
> THIS IS EXACTLY THE POINT WHICH HAS LESS
> MEANING, for more than  one reason, and which requires
> greater attempts of correction, in comparison with what  I did
> before in the case of the lengths!
>
> D1 - First of all, what does it precisely mean this "time
> interval"? You did not define it enough well in order to
> identify it exactly. You use a generic expression which could
> have a meaning in rough ordinary language, but not in a
> physical problem like the one we are now dealing with. I shall
> try to explain the situation with more detail.
>
> A time interval measured by some SINGLE clock can be
> defined as the DIFFERENCE of two values  t2 - t1  marked
> by this clock, where  t2  is the time corresponding to some
> SECOND EVENT in the clock's "life", in some given space-
> time coordinate system, and  t2  the time corresponding to
> some FIRST EVENT. Which are precisely the EVENTS you
> wish to introduce for defining your time interval?

I thought it was obvious that the two events are:

t1 = the time corresponding to the event of the "bow" of the
spaceship A coming to its closest possible distance compared
to the spot marked "X" on the buoy B, and

t2 = the time corresponding to  the event of the "stern" of the
spaceship A coming to its closest  possible distance compared
to the spot marked "X" on the buoy B.

> Let us assume for instance THAT THE BUOY IS POINTLIKE,
> namely that M = 0 (I understand very well that you have said 1 meter
> in length, with respect to 259,627,884, exactly because you were
> looking for a "clever" way to avoid complications, and then to say
> that 1 is "almost" zero with respect to 259,627,884!)

Yes. The difference would have been negligible, indeed zero
when calculated to ten decimal places (which is the level of
accuracy I have specified in my first article entitled "Single
Best Argument Against Special Relativity".)

I also did not say the buoy was pointlike because then there
would be a problem of how, from a *practical* point of view,
one could put a clock *inside* the buoy.

But both these problems can be avoided by saying there is a
spot on the buoy marked "X" past which the spaceship passes.
(As I said above, in my earlier article entitled "Single Best
Argument Against Relativity" I have already mentioned this.)

> The point is that one must be very precise in mathematics, no ad
> hoc approximations at all, when they are not needed, and above all
> when one is trying to hide with them exactly the point which on the
> contrary one should have to bring to the light!), and that there is only
> one clock in the buoy.

Yes, I agree fully. But as I said, I already explained this in
my first article.

And in physics there is ALWAYS a margin of error.

> Then we could ask indeed the following question:
>
> - the clock which is in the buoy marks t1 when the "bow" of
> the spaceship is in front of it; this same clock marks t2
> when the "stern" of the spaceship is in front of it (let us
> introduce bow and stern with respect to the buoy, first the
> bow, then the stern are passing in front of the buoy), and
> then we take t2 - t1 (which, after all, does not depend from
> the choice of the origin of times for this clock). Well, we
> could then ask: how much is this difference?
>
> The answer is very easy: it is L'/v , where L' is the length
> of the spaceship WITH RESPECT TO THE BUOY, which in
> relativity is NOT the same L we introduced before.
>
> But let me draw a picture, as I can, with the purpose of being
> more clear:
>
>  S ____________ B     -----> (vector velocity v)         °
>
> the spaceship has a bow                                   the pointlike
> and a stern S with respect                                buoy, with a
> to the buoy                                                      clock B
>
> If you ask for a comparison which is the time which is needed in
> this case for the buoy to pass the spaceship, from the point of view
> of clocks which are in the spaceship, it is obviously L/v , and it is
> a time interval GREATER than the other I have indicated before:
>
> L/v > L'/v.

Now do you not SEE your mistake? You have
COMPLETELY IGNORED TIME DILATION in your above
calculation!

In that case, HOW can your calculation be correct? If the
answer *using* time dilation *and* length contraction is
different from your above answer, then your answer cannot
possibly be correct!

And there is NO WAY the answer *using* time dilation
*and* length contraction is NOT going to be different from
your above answer!

If I have understood you correctly, you say that the stop watch
on the buoy would show t2 - t1 =  L'/v, while the stop watch
in the spaceship would show t2 - t1 = L/v where L/v > L'/v.
Right?

So WHERE is the time dilation calculation here? It does not
show up ANYWHERE in your calculations! ALL YOU
HAVE APPLIED IS THE LENGTH CONTRACTION.

Maybe you are trying to side-step my Challenge -- which is
based, as I wrote in my first article, on Dingle's argument
about two clocks each ticking slower than the other -- by
*avoiding* all mention of time dilation? If so, then your
calculations contain an error -- and a very simple, elementary
and blatant error at that!

You see, you are NOT applying the Lorentz transformation
equations properly. The Lorentz transformations absolutely
and categorically *require* time dilation. Length contraction
alone, *without* time dilation, IS NOT PERMITTED BY
THE LORENTZ TRANSFORMATIONS!

If two DIFFERENT answers are obtained -- one when using
*only* length contraction and another when using *both*
length contraction *and* time dilation -- then only ONE of
the answers can be correct: namely, the one calculated using
both length contraction *and* time dilation.

It is not a matter of opinion: YOU ARE
MATHEMATICALLY WRONG!

(But why is it that I have to EXPLAIN all this to you, who
are a senior professor of mathematics? Surely this should have
been obvious to you from the start!)

And as for time dilation, one CANNOT have two clocks, each
of which ticks slower than the other. That is *logically*
impossible.

Suppose however we DO take time dilation into account.
Then we would have to say that the MOVING stop watch
ticks SLOWER than the one which is NOT moving.

(N.B.: It is IMPOSSIBLE to calculate the time dilation
without specifying WHICH stop watch is moving and which
one is NOT.

If you think it IS possible, please show exactly HOW -- for I
do not think you will be able to do so, ever!)

Let me finish doing your calculations the way you SHOULD
have finished doing them.

Suppose we assume the buoy to be MOVING. Then the time
recorded by its stop watch would *not* be L'/v, but
(L'/v)/<gamma> (where <gamma> = 1/sqrt.[1-(v^2/c^2)], and
which as a consequence must always be greater than 1)!

And since L' = L/<gamma>, this equals
[(L/<gamma>)/v]/<gamma>, which is (L/v)/<gamma>^2
(and again, <gamma> is greater than 1)!

And so it is clear that (L'/v)/<gamma> =/= L'/v   !

Or suppose we take the SPACESHIP to be moving. Then the
time recorded by *its* stop watch would *not* be L/v, but
(L/v)/<gamma>  (where <gamma> is once again greater than
1) !

And again it is clear that (L/v)/<gamma> =/= L/v   !

So your answers are wrong, wrong, WRONG!!! It is NOT a
matter of opinion. ANY mathematical judge will say so.

Now remember the words of my Challenge: "exactly what
should the snapshots [of the stop watches' readouts] show?"

Suppose you say that the snapshots would show that the
buoy's stop watch would show (L'/v)/<gamma> and the stop
watch on the spaceship would show L/v.

Aha! But then WE CAN DETERMINE THAT THE BUOY
WAS MOVING AND THE SPACESHIP WAS
STATIONARY!

For if the buoy was NOT moving, the readout of its stop
watch would NOT be (L'/v)/<gamma>, but rather, according
to your calculations, L'/v, which is not the same as
(L'/v)/<gamma>   !

Or suppose you say that the snapshots would show that the
spaceship's stop watch would show (L/v)/<gamma>   and the
stop watch on the spaceship would show L'/v.

Then WE CAN DETERMINE THAT THE SPACESHIP
WAS MOVING AND THE BUOY WAS STATIONARY!

For if the spaceship was NOT moving, the readout of its stop
watch would NOT be (L/v)/<gamma>, but rather, according to
your calculations, L/v, which is not the same as
(L/v)/<gamma>   !

So depending on the snapshots before us, we can determine
which of the two -- buoy or spaceship -- was stationary and
which was moving.

But according to Relativity there should be NO WAY to
determine which of the two -- spaceship or buoy -- was
moving! For Relativity (both Special and General) denies that
there is such a thing as absolute motion.

Thus even *your own answer* above, when PROPERLY
calcu- lated, disproves Relativity -- both the Special and
General Theories, both of which require that there can be *no*
such thing as absolute motion!

On the other hand, if you claim that MY CORRECTION IS
WRONG, and that  your calculations are correct AS THEY
STAND, then the Lorentz time dilation CANNOT have
occurred in either of the stop watches!

This TOO would disprove the Theory of Relativity, for
Special Relativity absolutely and categorically DEMANDS
time dilation.

Again, it is NOT a matter of opinion. Either Relativity
demands time dilation or it does not! And ALL the books on
Relativity demand time dilation: it is NOT optional!

So EITHER WAY the Theory of Relativity is
*mathematically* disproved ... whether by YOUR OWN
answers above, or by MY CORRECTIONS to them.
 
 

Do you now admit that this is so? Am I not right? HAVE I
NOT WON MY CHALLENGE?
 
 

If you still claim to be right, prove it! Prove that the time
dilation *has* been applied by you, or else prove that time
dilation does *not* have to be applied in Special Relativity!

Or prove that even if you apply the time dilation, you will get
the SAME results you gave me above.

But I am virtually certain you can NEVER do any of the
above.

So here I rest my case. Any impartial mathematical judge
would rule in my favour!

(My wife is a lawyer, so I am used to arguing my case -- and
let me tell you that I often end up winning, even against her!)

The rest of this e-mail is now superfluous; but for the sake of
being thorough, I shall reply in detail to your other specific
comments.

You have added all the following material to your e-mail,
which is absolutely and completely unnecessary, since if you
had read my articles carefully you will have seen that I have
taken care of all the objections you raise:

> D2 - Having said that, what happens if the buoy is not supposed
> pointlike, and it has too a bow and a stern with respect to the
> spaceship (it would be much more "honest" to speak of TWO
> SPACESHIPS, with possibly different lengths!)?
>
> S ____________ B   ----->   (vector velocity v)      B° ___  S°
>
>       spaceship                                                       buoy

This needlessly complicates the problem, since all that is
required is for the spaceship to pass a specific point *on* the
buoy.

And as I said, it we have a buoy of 1 m diameter, and accept
the margin of error to be +/- 10^(-10), then the calculations in
*precise numbers* (i.e., in arithmetic and not in algebra) also
remain the same.

> Do you wish to compute the time interval which is needed for
> the two external points of the spaceship in order to pass in
> front of the SAME POINT in the buoy, a point in which there
> is a clock? Or do you suppose to want to compute for instance
> the time which goes from the bow B being in front of the
> other bow B° of the buoy, and then the stern S being in front
> of the other stern S° of the buoy? (if you object that these
> remarks are too much "pedantic", since you have introduced a
> buoy of only 1 meter, and a much "longer" spaceship, think
> what happens when you try to do the converse: namely, to
> measure this investigated time interval from the point of view
> of the spaceship! In any case, I repeat it, in mathematics there
> are not long and small, there are only precise computations,
> and possibly, AT THE END, when we are doing physics, we
> can make APPROXIMATIONS, but not at the very
> beginning).

Of COURSE in mathematics one must be precise; but all that
needs to be done is to make it clear that the spaceship is
required to pass a specified point *on* the buoy.

And it is necessary to specify the margin of error in
PRACTICE.

I can re-word the "Challenge" appropriately -- though as I said,
I have already mentioned both in my earlier, longer article: the
point marked "X" is mentioned, in fact, right in the first para-
graph of the Abstract.

> D3 - In truth, I understand that you have foreseen this objection,
> and that you have tried to cleverly avoid it, by introducing that
> "suitable mechanism (which can easily be devised)" etc.! But
> where is this mechanism? In B, or in S, or in B°, in S°, or else-
> where? And where is the clock (or better, where are the clocks)
> you use for the measure of time?

I have, as you say, already foreseen this difficulty, and have
*described in some detail* all the above, including the
mechanism, in my first article "Single Best Challenge to
Special Relativity".

But I see that you have not read the article carefully enough to
understand what I have written (or perhaps I should have
translated the article?)

In any case, here are the details for you, here in this very e-
mail, and expressed simply and in words that are easy to
understand:

1. The stop watch in the spaceship is exactly at the
*midpoint* of the spaceship. (Nota bene: it is *not* a "clock"
but a *stop watch*, which can be made to *start* and *stop*
by signals. The reason for this will be explained below.)

2. The stop watch in the buoy is at the spot marked "X" on
the buoy.

3. The mechanism for activating the stop watches is as
follows:

A blue laser light shines from the spot "X" on the buoy B, the
direction of this light being at *right angles* to the direction
of relative motion between A and B.

This light is so aimed that when the bow of A passes by B,
the light will begin to shine on A.

As soon as the blue laser light impinges upon the hull of A,
light sensors located all over the hull of A sense this blue
laser light as long as it continues to shine on A.

As soon as it begins shining on A, these sensors send a signal
to activate a stop watch carried on board A -- the stop watch
being located, as mentioned above, exactly at the mid-point of
A.

(The exact nature of the signal will also be described below).

And as soon as the sensors detect that NO blue laser light is
shining on A any more, they send ANOTHER signal to the
stop watch to STOP ticking.

All the sensors send all their signals to the stop watch carried
on board A *at a fixed and known speed*.

This could be accomplished -- just as an example -- by a
system of electrical wires, as follows:

An electrical wire of rest length L/2 connects the sensor at the
bow of the spaceship to the stop watch at the mid-point of the
spaceship, and an identical electrical wire of identical rest
length connects the sensor at the stern of the spaceship to the
same stop watch. (Nota bene: there is only ONE stop watch
on board the spaceship!)

And electrical wires of rest lengths shorter than L/2 connect all
the other sensors along the hull of the spaceship to the stop
watch.

Note that the wires are all *inside* the spaceship, and thus
they are all *stationary with respect to the spaceship*. If the
spaceship contracts, they contract along with it! But they all
contract in equal proportion, so the time taken (in the IFR of
the spaceship) for the signal to travel the length of the wire
from the bow to the stop watch is still identical to the time
taken for the signal to travel the length of the wire from the
stern to the stop watch.

(N.B.: "IFR" = "Inertial Frame of Reference".)

And the time taken for the signals to travel from the other
sensors to the stop watch is always less than the time taken
for the signal to travel from the bow and the stern to the stop
watch.

Thus while the spaceship is passing the buoy, one or another
sensor on the spaceship is always sending a signal to the stop
watch, and the stop watch is always receiving it, and therefore
continues to tick until the blue light stops shining on A.

So when A moves past B, the stop watch located at the
midpoint of A records a time interval *exactly equal* to the
time interval t2 - t1.

Of course the stop watch carried at the mid point of A starts
ticking with a fixed *delay* after the bow of A passes by the
spot "X" marked on B, because the sensor at the bow of A
takes a precise amount of time to send its signal, at the speed
at which electrical signals travel, to the mid-point of A, so as
to get the stop watch starting to tick.

But then again, this is *exactly compensated* by the fact that
the signal from the sensor at the stern of A takes exactly an
*identical* amount of time to reach the stop watch, and
inform it that the laser light from B has *stopped* shining on
A's hull, and thereby to get the stop watch to stop ticking!

And thus the amount of time recorded by the stop watch on A
will be *exactly* equal to the time it takes for A to pass by
the spot "X" marked on B.

All this, of course, is to be taken as in the IFR of the
spaceship.

(It is because of this *delay* that I changed the timepieces in
my Challenge from "clocks" to *stop watches*. What matters
here is to record the specific time *interval*, and not the
*time*!)

And furthermore, as the front end of A passes by the spot "X"
marked on B, an AMBER laser light emanating from the front
end of A, pointed at right angles to the direction of relative
motion between A and B, shines on a light sensor on B
located at the spot marked "X", activating a stop watch on
board B, which is also located at the spot marked "X", just
behind the sensor.

And as the rear end of A passes by the spot "X" marked on B,
a GREEN laser light, similarly pointed at right angles to the
direction of the relative motion between A and B,  shines on a
light sensor carried aboard B at  the spot marked "X", and as
soon as this sensor on B detects this green laser light, it sends
a signal causing the stop watch on B to stop ticking.

Thus both the stop watches record the very *same* time
interval, namely t2 - t1. The only difference is that the stop
watch on the spaceship records it with a slight *delay*, that
delay being exactly measurable and even calculable; and thus
for this delay, allowances can be *precisely* made.

You see, there is NO PROBLEM AT ALL.

> If they are at some distance from the "mechanism", in any case
> you have to deal with the time which is needed for a signal sent by
> this instrument in order to arrive to the clock. All your efforts not-
> withstanding, you cannot avoid the relativistic speculations in this
> matter, which claim that no signal can travel faster than light, etc.,
> and then assuming that exactly c is the "better speed" (faster) which
> is required for "communications" between your "mechanism" and
> the clock!

Ah, but if the *delay* for the signal to reach the stop watch is
*identical*, regardless of whether the signal is sent from the
bow or the stern, the time interval t2 - t1 will *still* be
accurately recorded by the stop watch on the spaceship!

(Did you seriously imagine that I had not already thought of
this problem?)

Note also that the signals can be of *any* kind, however slow
or fast -- within reason, of course. (In my earlier article I have
described an OPTICAL mechanism to perform the same
function.)

Even SOUND TRAVELLING IN A RIGID ROD can attain
the same objective. As long as the rods are carried *inside*
the spaceship, and as long as the time it takes for the signal to
reach from sensor to stopwatch is the same in both the rods, it
would still be possible to have the stop watch record a time
interval EQUAL EXACTLY to the time interval t2 - t1.

(Note that it is not necessary to record the time interval t2 - t1
ITSELF, but only a time interval exactly EQUAL to it!)

And *even* if the time it takes for the signal to reach from
sensor to stopwatch is *not* the same in both the rods, as
long as the time to for the signal to travel in *each* rod is
known, it is still possible to make the necessary adjustments,
by CALCULATION! The calculations would be a little more
complex, of course, but it is still possible to perform them
fairly easily.

Thus it is ALWAYS POSSIBLE to know the time interval t2
- t1, REGARDLESS of the kind of signal used to trigger the
stop watch on board the spaceship. Even if the signal has
different speeds in different parts of the spaceship, as long as
what the speed is, and where, is known with precision, it is
possible to precisely compen- sate for the signal's delay in
reaching the stop watch.

Indeed we may locate the stop watch *anywhere* in the
spaceship: as long as the speed of the signal each way is
known with precision, allowances can be precisely made for
the delay(s)!

I did not insult your intelligence by explaining all this,
thinking that you, being a professor, would easily understand
that this can be done. I am surprised, indeed, that you raise
this objection!

> D4 - I try to explain the problems in yet another way. At last
> you propose to compare TWO measures, with apparently only
> two clocks, but this is simply impossible. If it is possible to
> suppose (or to approximate, if you prefer) the buoy as
> pointlike, and to make the measurement you require with only
> one clock in this case, how can you do the same measurement
> from the spaceship? If there is only one clock in the spaceship,
> say for instance in the bow, then this clock shows some time
> when the bow of the spaceship is in front of the buoy (or of
> the clock which is the buoy), but how can you get a second
> value for the time measured by this clock, the second value
> which is needed in order to compute the required difference?
>
> YOU NEED FOR INSTANCE ANOTHER CLOCK IN THE
> STERN, or even - if you think  that it is a different thing (but
> it isn't!) - you need a signal going from the stern to the bow, in
> order to know where the stern WAS in front of the buoy.

As I have explained above, measuring the time interval t2 - t1
with  one single stop watch is NOT AT ALL IMPOSSIBLE,
as you claim,  and has been taken care of by the above
mechanism.

And I can describe many other mechanisms to do the same
thing. (I am also an engineer, with over thirty registered
inventions to my credit, many of them in aerospace
technology: so it is very easy for me to do this!)

Perhaps you are not an engineer: in which case, please take my
description to any competent engineer and ask him or her!
ANY competent engineer -- and not necessarily one working
in aerospace technology -- will definitely confirm what I say.

I think that Einstein, not being an engineer, did not
understand how the measurement of an exact time interval
between events that occur in different widely-separated
locations using one single clock could be done. That is HIS
mistake. But WE, having good engineering skills (or at least
having access to good engineers in our midst), do not have to
make the same mistake HE made!

> Here it is exactly
> where relativity comes in, with all his stories about the synchro-
> nization of distant clocks etc. If the clock you are talking about was
> placed instead in the stern of the spaceship, it could register only the
> time when the stern is in front of the buoy, but he cannot "know"
> when the bow was in front of the buoy! Summing up, you need
> TWO synchronized clocks in order to do the measurement you wish,
> both in the spaceship and in the buoy, and you must be more precise
> in specifying which is the time interval you wish to compute, and
> most of all HOW...

The absolute and utter nonsense about synchronisation of
clocks in Relativity is just that: ABSOLUTE AND UTTER
NONSENSE!

ANY competent engineer knows how to synchronise clocks
that are merely separated (but not MOVING relative to one
another): *he simply allows for the time a signal takes to go
from one to the other* !!!

And it can be ANY kind of signal, as long it has a measurable
and constant speed!

Perhaps, as I said, you are not an engineer, but I assure you it
can easily be done. Please ask any competent engineer in Italy:
he or she will confirm what I say.

As I wrote to a friend of mine only yesterday, criticising Max
Born's famous book "Einstein's Theory of Relativity":

[QUOTE]

     On pages 228 and 229, Max Born writes:

          "From this it follows that absolute simultaneity can likewise
          be ascertained in no way whatsoever."

     ... and:

          "THERE IS NO SUCH THING AS ABSOLUTE
          SIMULTANEITY." [His emphasis, no less!]

     I mean, *come ON*. Did we not read *Born's own* words on page
     225 of his book -- just a few pages before! -- that "the velocity of
     light is independent of the state of motion of the observer and has
     always the same value c"? If this is indeed the case, what is the
     difficulty in making the necessary correction, using the equation
     {time = distance / velocity}?

     There are *numerous* ways to measure distance [in any particular
     IFR]: for example, one can use a ruler, or use triangulation, or use
     the time taken to send a signal -- such as electrical, or sound
     travelling in a rigid rod -- whose speed is actually known. Once the
     distance between two objects is known, and the speed of the signal
     is also known, one can calculate the *time* it takes for the signal
     to get from one clock to the other using the above formula! One
     expects even Grade 6 students to be able to do this.

     Just *what* is Max Born's -- and Einstein's -- difficulty here?
     (Maybe they didn't pass their mathematics exams in grade school?)

     And even if the speed of light were *not* constant, but changed
     depending on the conditions (such as for example the direction in
     which it travels), as long as the different velocities were known for
     the different conditions, the requisite adjustments could *still* be
     made! (Maybe not in Grade 6, but at least in Grade 9.)

     ...

     For instance, even if the time it takes for the signal to go one way is
     different from the time it takes to go the other way, the difference
     can be measured by sending the signal both ways along the very
     same route.

     Heck, astronomers have known since long before Max was born
     that they can calculate the exact positions of *all* the planets --
     and their satellites as well -- at *any* given instant. Not, mind you,
     where the planets *appear* to be, but where they actually *are* at
     that instant. It is *so-o-o-o-o-o* very easy: *one simply allows for
     the time it takes for the signal (which in this case is light) to reach
     us from them!*

[END QUOTE]

As you can see, the very fact that the planets' actual positions
can be calculated proves that there *can be* simultaneity all
throughout the Solar System. (This was known even
BEFORE Relativity!)

I simply do not understand why Relativists keep on repeating
*ad nauseam* that simultaneity is impossible, when
astronomers have known for so long that not only it IS
possible, but is ROUTINELY USED in their calculations.
(Otherwise we would never calculate when eclipses, or
alignments of the planets, would occur!)

You see now, your objection to measuring the time interval t2
- t1 with the help of a single stop watch carried on the
spaceship is completely cleared up by simple but competent
reasoning.

> E - Now that it has become clear, I hope, how your question
> SHOULD HAVE BEEN FORMULATED, let us go on,
> choosing (between many), one possibility, namely ask to
> measure the time which passes - either from the point of view
> of the buoy, or of the spaceship (in both cases you need a
> whole space-time coordinate system associated with the two
> objects: there is no difference at all with the attempt of
> introducing only TWO objects, clock and mechanism!) - from
> the two events which correspond to the coincidences:
> bow/bow, stern/stern. In other words, I say that you have to
> pose your question for instance in the following way, and that
> then there is an easy not contradictory answer to it:
>
> - One has an inertial spaceship, with some proper length L, and
> ANOTHER ONE, of some proper length M , the relative speed is
> v. One has synchronized clocks on both spaceships [I repeat that it
> is really enough to have TWO of them for each spaceship, so
> FOUR in all], and one asks how much time is needed, from the
> point of view of both spaceships, for completely passing one the
> other.

All this is not needed at all. (I do wish you had read my
articles more carefully! And I do hope that you will read THIS
e-mail carefully: I select all my words with great care, and
seldom use a word when a more precise one is available.)

As I have shown in my articles and also shown above, *two*
stop watches -- one in the buoy B and one in the spaceship A
-- are QUITE sufficient to measure the time interval t2 - t1;
and a single spot marked "X" on the buoy is ALSO quite
sufficient to represent the point past which the spaceship
passes.

And if the margin of error in measurement is 10^(-10), then
the length M is also not needed.

And as explained also, it IS possible to precisely measure the
interval t2 - t1 by using a *single* stop watch carried on the
spaceship.

So all the rest of your so-called "WELL POSED question" is
totally unnecessary!

> Now we have at last a WELL POSED question, and an easy
> answer. The two time intervals are:
>
> L/v + M'/v (from the point of view of the first spaceship -
> with obvious notation)
>
> L'/v + M/v (from the point of view of the second spaceship,
> the "old" buoy) ,
>
> where of course it is L' = L*sqr(1-v^2/c^2) , and M' =
> M*sqr(1-v^2/c^2) (in force of the so called length contraction
> - we do not even need to introduce Lorentz transformations,
> even if of course the length contraction is one of their
> consequences).
>
> In order to decide which time interval is bigger than the other,
> one has just to decide which length is bigger between L and
> M . If one supposes that the first spaceship is longer than the
> second (the ex-buoy), then one has:
>
> (L+M')/v > (L'+M)/v ,
>
> no doubt at all about that, the second time interval is smaller
> than the first.
>
> If one supposes instead COMPLETE SYMMETRY, namely
> L = M (in other words,  TWO EQUAL SPACESHIPS), one
> gets at last TWO EQUAL TIME INTERVALS.
>
> As you see, everything is very simple, much more simple for
> instance than introducing a coordinate system with respect to
> an accelerated observer, like one must do when discussing the
> twin paradox (see for instance the paper in the point 4 in the
> above quoted web page, which is unfortunately only written in
> Italian, but there is some comment to this problem even in the
> fifth section of the aforesaid paper about
> "Misunderstandings...").
>
> The question is always the same, which after all is not even
> too much difficult to overcome: it is to understand the
> counterintuitive (but mathematically precise, and then
> "logically possible") relativistic treatment of space and time
> (not to have an "intuition" of it with the common thought
> space and time categories, which would be of course rather
> impossible)...

I hope you have understood by now that all this is COM-
PLETELY unnecessary.

> F - I have talked too much - and with my bad English this is
> perhaps harmful for a better understanding - yet I have not said
> everything I could have said. For instance, in some lecture to stu-
> dents, I could have shown even how one could have connected
> length contraction and time dilation in the proposed exercise.

But it is not an *optional* matter to connect length
contraction and time dilation! In Relativity it is absolutely
*necessary* to do so.

The Lorentz transformations are nothing WITHOUT time
dilation. By ignoring time dilation you have ignored the
Lorentz transfor- mation equations.

Please excuse my being blunt, but in science one can be a
respecter only of the Truth, and not of persons. If anything
anyone tells me is untrue -- even if it be you who are older
than I am -- then I shall not mince words in condemning what
is said!

For like you, I also believe that "amicus Plato, sed magis
amica veritas".

But I have great respect for all persons *qua* persons, as also
for you. If I am blunt and contemptuous, it is only towards
the untruth: not towards the person in whose mind it may
temporarily reside ... because, of course, everyone is at liberty
to change his or her mind!

And please feel free to reciprocate: for I am never afraid or
reluctant to change my mind when the truth is clearly shown
to me!

> In any case I hope:
>
> F1 - first of all, to not have made mistakes (which should
> have to be considered my personal mistakes, and not
> mistakes/contradictions in the theory!);
>
> F2 - that you have understood where are the mistakes in your
> posing the question;
>
> F3 - that you have understood how could one pose a good
> question, between many possible of the "same nature";
>
> F4 - that you will not require to me endless discussions, as it
> happened many times to me with people not willing to
> understand relativity (there is an example of such useless
> discussions in my web site, with Percival, or Galeczki, etc.,
> all people who do not know enough well relativity);
>
> F5 - to have been useful to you at least from an ethical point
> of view, showing that one could indeed answer to all people,
> even when one believes that the required effort of writing will
> not produce anything "useful".

Firstly, and most importantly, I hope you understand that you
have made a BIG MISTAKE in your calculations in ignoring
the time dilation. I hope that you now UNDERSTAND and
ACCEPT your mistake in answering the question -- as the
honest person I am sure you are.

Or else can you show me with what justification time dilation
*may* be left out of the calculations when calculating a
problem in Special Relativity? I doubt very much that you can
do so.

Also I hope that you now understand and accept that your
criticism of my posing of my question is totally unfounded,
because you did not read my articles carefully before
answering me.

But as I said, even though you did not read my two articles
carefully enough, YOUR OWN WORDS ABOVE HAVE
DISPROVED SPECIAL RELATIVITY: for you did not
apply the Lorentz time dilation, which is *absolutely
REQUIRED* by Special Relativity.

And even if the time dilation IS applied, it *still* disproves
Relativity, for then it becomes possible to determine which of
the two -- spaceship and buoy -- must have been moving and
which must have been at rest! And this contradicts the
principle according to which all rectilinear motion must be
relative and not absolute.

So either way your answer -- as it stands, OR as corrected by
me -- disproves the Special Theory of Relativity.

I hope you see this clearly now?

If you still do not see, I can explain it in even greater detail.

As for an ongoing discussion, there is never a need for
discussion between NON-scientists, all of whom are entitled
to their own views, however irrational; but as you yourself
have written, it is the absolute obligation of any *scientist* to
answer criticism -- for science *must* be rational and logical.

Thus in science, discussion cannot, unfortunately, be avoided.
No one who claims to be a scientist can avoid answering to
criticism.

But if you do have the courage of your convictions to discuss
Relativity with me further, let us have no more silly mistakes,
okay? Please make sure that you have thoroughly gone over
everything I have written, and also over your reply; and
remove from your reply *all* the mistakes that you are able to
remove.

Please also do not insult my intelligence: I am not a first-year
university student, but a person almost 60 years old, well-
travelled and well read, and extremely highly educated, with
several first-rate books and many papers and inventions -- and
that too, in several different disciplines -- to my credit.

> I am at your disposal with sincere friendship for a possible next
> round, but please only one, no more (and please spare to me a com-
> ment about your new "logical" "Short Reductio-ad-Absurdum Refu-
> tation of Special Relativity", which is no better "idea" than the one
> I have discussed until now); time is indeed a precious thing, mostly
> at the end of one's life, and there are better, most productive, ways to
> spend it...

Surely there is no better or more productive way to spend
one's time on earth -- at whatever stage in one's life one may
be -- than seeking the Truth, and clearing one's mind of
untruth?

If even on my death-bed I am able to learn something new, or
to find out that something I had thought of as truth was
untruth, I would be very, very happy.

And as to these following words of yours:

> ... let me tell you something which has
> been said to me by a colleague here in Perugia - one of the most com-
> petent expert in relativity, I believe. He told me that he cannot
> understand why people understands that they have to pay lawyers,
> physicians, etc., in order to have their opinion, even for matters which
> require less knowledge, time and commitment than scientific ones, but
> then the same people suppose instead that scientists should loose their
> time in answering to amateurish ill-posed questions. He added that a
> teacher could do this work only for the benefit of his own students, but
> if a student insists in not understanding then he gets fired (in Italian:
> BOCCIATO).

... direi ch'è *Lei* chi sta bocciato qui! [Translation: "I'd say
it is YOU  who have failed the exam here!]

In any case, I have approached you, NOT as a student, but as a
Challenger: an adversary. I would approach a lawyer in a law
court likewise! I do not have to PAY my opposing lawyer in a
law court -- on the contrary, it is expected either that my
challenge be fully and satisfactorily answered, or else that the
opponent concede defeat -- that is, if my opponent has any
self-respect and honour at all (as I hope and believe you have!)

So: give me your counter-arguments against my arguments
here -- if you have any -- OR ELSE CONCEDE DEFEAT!

(But please, no more silly mistakes like you have made
above! And no more misreading or non-reading of my clearly-
written words!)

>Once again best wishes, from yours most sincerely
>
> correspondent perugino UB
>
> [1] There were even other things which I started to discuss in my
> preliminary attempts of answer, for instance about what you have
> said in one of yours intermediate mails:
>
> > There is no need for a "third (inertial) observer C"...
>
> I do agree about that, and as a matter of fact you avoided to do it
> in the second formulation of your "challenge", but it was you that
> in the first formulation of it had written:
>
> > Imagine two objects, A and B, in rectilinear motion past one another.

Yes, this was a small mistake in my first article. I shall
correct it. (In English, one sometimes says "Imagine" when
one intends to say "Suppose that there is". But as you
indicate, this is a bit imprecise.)

> In order to "imagine" this situation, one needed to introduce the point
> of view of a third observer! The fact is that there are always many different
> manners to describe in mathematical terms the "same" physical situation,
> since the "code" which translates from "reality" to mathematics is rather
> flexible, but in any case the answers must always be the same!

Right.

But as you have seen from the above, it does not matter in the
present case, because the calculations above have shown that if
length contraction *and* time dilation are accepted as valid, it
*is* possible to distinguish between the two -- spaceship or
buoy -- as to which of them was moving and which was
stationary.

In other words, time dilation, on the one hand, and the
principle of all rectilinear motion being relative, on the other,
are contradictory to one another. This, essentially, is what
Dingle says too. What I have done is to provide a
mathematical PROOF of Dingle's argument.

Philosophically, however, there is an EVEN MORE FUNDA-
MENTAL objection to the Lorentz transformation: namely,
that they CANNOT be derived from the axioms of
mathematics and the propositions and postulates of Euclidean
geometry!

The *only* transformations that can be derived for *Euclidean
space* from the axioms of mathematics -- such as those of
Peano, or those expounded by Zermelo and Fraenkel (later
extended by John von Neumann) -- and the propositions and
postulates of Euclidean geometry, are the GALILEAN
transformations. The Lorentz transformations CONTRADICT
the Galilean, and therefore *cannot* be a part of mathematics
and Euclidean geometry.

(Nota bene: the Lorentz transformations refer to *Euclidean*
space, and so there is no need to include non-Euclidean
geometry in this argument!)

You being a mathematician should understand that *every
mathematical theorem must be constructed from previously-
proven theorems, or from the axioms.* And *every
geometrical theorem in Euclidean geometry must be
constructed from the propositions and postulates of Euclidean
geometry, or from previously proven geometrical theorems*.
These are absolute and SINE-QUA-NON conditions in
mathematics and Euclidean geometry.

But there is *no* way the Lorentz-Fitzgerald transformations
can be constructed from either previously-proven mathematical
and geometrical theorems, or from the axioms of mathematics
and the propositions and postulates of Euclidean geometry.
But there *is* a way to construct the Galilean transformations
therefrom!

Therefore the Lorentz-Fitzgerald transformations MUST be
*mathematically* and *geometrically* invalid, at least from
the point of view of Euclidean geometry (and that is the only
kind of geometry used in Special Relativity, strictly
speaking).

This, too, would disprove Special Relativity from a mathe-
matical point of view -- contrary to your claim that Special
Relativity is "mathematically quite a consistent theory".

Indeed I intend to write a second Challenge -- of course not a
"Simple" one, and understandable only by mathematicians --
viz., to try and derive the Lorentz-Fitzgerald transformations
from the axioms of mathematics and the definitions, axioms
and postulates of Euclidean geometry. This is *impossible*,
because the Galilean transformations *can* be derived
therefrom, and they *contradict* the Lorentz transformations!

By the way, this would not, as you say, result in the
conclusion that "then the WHOLE MATHEMATICS would
be affected by contradictions" -- it would just mean that the
LORENTZ TRANSFORMATIONS must affected by
contradictions!

Yours always in sincere friendship,
 
 

Ardeshir <http://homepage.mac.com/ardeshir/education.html>.
 
 

____________________________________________________
 
 

Subject: Re: Argomento Contro la Teoria della Relativita Speciale
             [Translation: Argument Against the Special Theory of Relativity]
Date: Sun, 26 Aug 2001 09:25:03 +0200
From: umberto bartocci <bartocci@dipmat.unipg.it>
To: "Ardeshir Mehta, N.D." <ardeshirmehta@myself.com>
References: 1 , 2 , 3 , 4 , 5 , 6 , 7
 
 

Dear Mehta,

thanks for your long and warm ("appassionata") answer, to
which I answer immediately, at least in connection with the
most important part, just one piece at a time. But let me say
that your mail shows that we have got a kind of intellectual
friendship, since we share a common dislike for the work of
some "great" scientists which the whole world, quite on the
contrary, worships.

SO, MAY I PLEASE ASK YOU TO LET ME HAVE A
COPY OF YOUR "CRITIQUE  OF GOEDEL'S
THEOREM"?

I am very interested about it, because I think that one MUST
criticise Goedel, even if until now I did not know of any one
who attempted to do it, and I would not even know  where to
start from in order to do that!

As far as the case against relativity is concerning, from a quite
HONEST point of view, there is unfortunately no doubt at all
about who is right and who is wrong. After all, if you were
right, there would be no question to discuss between each
other, and you should have to discuss with the greatest experts
in the field of theoretical physics (and, believe me, I would be
very happy to see relativity down, even if I had to consider
myself "bocciato"!).

As a matter of fact, your objection:

> But I am very, very sorry to see that you have made a BIG
> MISTAKE -- namely, you have *completely* ignored
> time dilation!

is wrong. I must say sincerely that these words show to me
that you have not got a full understanding of relativity, as I
said does indeed happen with ALL the pseudo-arguments
against relativity (and this does not mean that one is not
clever enough, but just that unfortunately he has to study
more).

As you know very well, Minkowski said since the beginning,
that space and time "are doomed to fade away into mere
shadows, and only a kind of UNION of the two will preserve
an independent reality". In your criticism to my simple answer
to your easy challenge, you "separate" in some sense space and
time, while in relativity there exists ONLY ONE space-time
interval, and the SAME phenomenon could be explained - as I
shall soon prove - FROM A  RELATIVE POINT OF VIEW
once with a length contraxtion, another with a time dilation.

I shall try to explain better all these assertions, after all I am a
professor, and I have explained these things many times to
students, even if writing them, and in English, is rather
difficult for me, and it takes too much time. I shall analyze
your objection, splitting it in order to find that it is grounded
on the following assumptions:

1 - you point out the existence in relativity of one "length
contraction" and of one "time dilation" (which is in some
sense correct);

2 - you pretend to see BOTH of them at work in the situation
we are studying (which is in some sense correct);

3 - you see that in "my" computation there is only one of the
two, WRONG, and you pretend to see even the other, RIGHT.

The fact is that it is you who sees only one of it, and not the
two together! In the computation that your challenge required
from me, and which I have fully satisfied, THERE ARE
BOTH length contraction and time dilation, DEPENDING
FROM THE POINTS OF VIEW.  One must simply be able
to interpret the result which is the only one possibly correct. I
shall try  to show you where you have to look for finding the
time dilation in the same and one formula.

Now that we have made a complete understanding of the
physical situation, we must say that we have only one
phenomenon to study in Minkowski space-time, namely we
have three different world lines, two of which are parallel,
which intersect, something of the following kind:
 

              /          /     !
            /           /      !
          /            /       !
        /            /         !
      /             /          !

  stern S    bow B   buoy X

(the time orientation is from top to down).
 The world lines of the bow of the spaceship and of the buoy,
let us call it in the order B  and X , thought of as single
points (no worry for instance about the fact that a "real clock"
is not pointlike, we are doing simple "theory"!), intersect in
some event  E1 ; the lines of the stern  S  of the spaceship and
of the buoy  X  intersect in some event  E2 . We do not need
to introduce more than that.

Then one can ask which is the proper time elapsed WITH
RESPECT TO  X  from E1  to  E2 . The situation is like that
from  X's  point of view:
______________              ------->                      °
S                        B      vector velocity                  X
    the spaceship                                         the buoy is "still"
     is "moving"

and the computation is very easy, I repeat it. If the proper
length  of the spaceship is L, then  L' = L*sqr(1-v^2/c^2)
(the star * stands  for product) is the length of the spaceship
with respect to  X , and the  required time is (MUST BE!):

(1)  L'/v

(here  v  is the scalar speed, the "module" of the vector velocity).

Conversely, from the point of view of the spaceship, we
have a  physical situation like the following one:

______________              <-------                       °
S                        B      vector velocity                  X
    the spaceship                                         the buoy is "moving"
     is "still"

and WE CANNOT ASK EXACTLY the same question as
before, since  E1  is an event in the life of B , and E2 is an
event in the life of  S ! So, there is no possibility to ask a
difference between proper times of anybody!!

But we can of course suppose to have synchronized clocks
aboard of the spaceship (this is exactly the meaning of the
words in my last mail, about the role of your "mechanism"),
and we can ask which is the time which is needed for the buoy
to pass the spaceship, FROM THE POINT OF VIEW OF
THE SPACESHIP, which means from the point of view of a
coordinate system associated with the spaceship (we could
better think of  X  as a meteorite). Well, since the length of
the ship is  L , and the module of the velocity does not
change, this time MUST BE now equal to:

(2)  L/v .

Let me remark that relativity is not so stupid to give different
answers from these ones which I have given to you!

In conclusion, once again, you have got the two times that
you challenged me to compute. The second time, (2), is surely
GREATER than the first time (1), at least if v is not zero.
Now you have got all the answers to all your questions. Try
to ask to do these easy computations to any other good
physicist, and you will obviously get the same answers (if
not, he is not a good physicist - or at least he does not know
enough relativity).

Now you object: I see length contraction at work in (1) -
CORRECT - so you must be wrong, because you forgot the
time dilation. This is WRONG, since in (1) there is even a
time dilation. As a matter of fact, I said it already at the end
of my previous mail:

"I have talked too much - and with my bad English this is
perhaps harmful for a better understanding - yet I have not said
everything I could have said. For instance, in some lecture to
students, I COULD HAVE SHOWN EVEN HOW ONE
COULD HAVE  CONNECTED LENGTH CONTRACTION
AND TIME DILATION IN THE  PROPOSED EXERCISE."

In order to show that, let us put the thing in the following
terms. The people aboard of the spaceship measure the time
needed for the meteorite to pass, and they claim that it is L/v ,
good. Somebody aboard of the meteorite says that this time is
not  L/v , but it is LESS than that, because he measures  L'/v ,
good once again. Well, this assertion from the point of view of
the time elapsed for the meteorite is exactly what the crew of
the spaceship would interpret as the time dilation occurring
"aboard of the meteorite"!

The proper time of some phenomenon (between any two
events  E1  and  E2  in the world line of some "observer") is
defined as the LEAST value of this time with respect to all
inertial observer, in the same way as the proper length is, on
the contrary, the GREATEST value etc. etc.. This proper time
is connected to the measure of the "same time-interval" with
respect to other coordinate times by the well known relation:

  proper time interval = sqr(1-v^2/c^2) * coordinate time interval

while the corresponding formula for lengths is the "inverse":

  proper length * sqr(1-v^2/c^2) = coordinate (or "apparent") length.

Well, in (1) you have got exactly the first formula at work:

proper time of the phenomenon we are studying, namely the
passing of the meteorite  X = sqr(1-v^2/c^2) * coordinate time
interval of the same event = sqr(1-v^2/c^2) * (L/v) .

As a matter of fact, the coordinate time interval of this
phenomenon is L/v , as we said in formula (2) , and if you
write the previous formula "associating" differently (a shifting
of parentheses), you find exactly (L*sqr(1-v^2/c^2))/v , and
the numerator of this fraction (ratio) is L' , the "contracted
length"...

That is to say, in (1) time dilation and length contraction
THERE ARE BOTH PRESENT, I hope that you will be
satisfied by that, since this is the simple easy truth.

I could say even more, showing how one could explain even
the "time dilation" which happens (must happen!) in the time
of spaceship as "seen" from the point of view of the meteorite
(until now we had only a "time dilation" in the meteorite from
the point of view of the spaceship).This is just a bit more
difficult exercise for students, which requires a little attention,
and an explicit use of Lorentz transformations. I avoid to do
that, thinking that I have answered enough to your criticism,
but if you want I can send to you the complete "solution" - it
is one argument that I have experienced most amateur people
do not know precisely, and then they get in other "paradoxes",
because they are not able (for instance Dingle was unable to
see it, and he was not even an amateur!) to see the
COMPLETE SYMMETRY which is now at work (of course,
there is no possibility to see even the length contraction of  X
, which we have supposed pointlike).

Ciao, I HOPE TO READ SOON YOUR OBJECTIONS
AGAINST GOEDEL, perhaps  they are more useful than the
ones against relativity (I am sympathetic with these attempt to
show that relativity is wrong, at least they show that one has
understood that to do this is a  most important task, but one
must not underestimate the problems), one never knows,

I return the expression of a sincere friendship,

UB
 
 

--
Umberto Bartocci
Dipartimento di Matematica
Universita' di Perugia
06100 - Italy
http://www.dipmat.unipg.it/~bartocci
 
 

________________________________________________________
 
 

Subject: Re: Argomento Contro la Teoria della Relativita Speciale
             [Translation: Argument Against the Special Theory of Relativity]
Date: Mon, 27 Aug 2001 20:53:22 -0400
From: "Ardeshir Mehta, N.D." <ardeshirmehta@myself.com>
To: umberto bartocci <bartocci@dipmat.unipg.it>
References: 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8
 
 

Caro Professore:
 
 

Grazie tanto per la Sua risposta!

Però potrà vedere dal sottoscritto che ANCORA una volta Lei sbaglia.

[Translation:

Thank you very much for your answer.

However, you will be able to see from what is written below
that ONCE AGAIN you are mistaken.]

(By the way: If you prefer to write in Italian, and if you accept my answers in
English, I am quite agreeable, if it will make your life easier!)

You wrote:

> Dear Mehta,
>
> thanks for your long and warm ("appassionata") answer, to
> which I answer immediately, at least in connection with the
> most important part, just one piece at a time. But let me say
> that your mail shows that we have got a kind of intellectual
> friendship, since we share a common dislike for the work of
> some "great" scientists which the whole world, quite on the
> contrary, worships.

Indeed! The more "dogmatic" the theory, the more it SHOULD
be criticised, because if it cannot meet strict and logical criticism,
it must have been false!

> SO, MAY I PLEASE ASK YOU TO LET ME HAVE A
> COPY OF YOUR "CRITIQUE  OF GOEDEL'S
> THEOREM"?
>
> I am very interested about it, because I think that one MUST
> criticise Goedel, even if until now I did not know of any one
> who attempted to do it, and I would not even know  where to
> start from in order to do that!

Anyone can download my book in PDF format (i.e., *Adobe
Acrobat* format) from my Home Page

     <http://homepage.mac.com/ardeshir/education.html>,

... and print it out on a printer.

The same file is also available at my Web site from the following
URL: <http://homepage.mac.com/ardeshir/Critique_Of_Goedel.pdf>.

Unfortunately it is not possible to publish this book in
HTML format because of the way Goedel has written his
formulae, which requires elaborate type- setting. (Even then I
have had to modify the formulae for typesetting with
Microsoft Word, which does not allow them to be typeset
EXACTLY the way Goedel does in his original German
Paper.)

I warn you, however, that since it is a full book, it is a LONG
download -- almost 1 MB. And it takes a long time to read
also. (Part 1 is fairly short and easy, however, and contains
most of the more important arguments against the Theorem.
But the entire book is one SINGLE download, unfortunately.)

One reason why the book is long is that I have quoted almost
all of Goedel's *own words* verbatim, and criticised them,
sometimes sentence by sen- tence, and often paragraph by
paragraph, so as to make sure that there is NO
misunderstanding as to WHAT I am criticising and WHY I
am criticising it. So my book includes almost the FULL text
of Section 1 and Section 2 of Goedel's 1931 paper entitled
"On Formally Undecidable Propositions of Principia
Mathematica and Related Systems", which is more popularly
known as "Goedel's Theorem" or sometimes as "Goedel's First
Incomplete- ness Theorem".

But I have to admit that the ideas were not ORIGINALLY
mine. I first read them on the Web, written in not very good
English, by Ferdinand Romero, who at present lives in
Argentina, and who later became my colleague and good
friend. He does not write English very well, and although he
does write it, it is somewhat hard for most English-speaking
readers to understand from his English words exactly what he
is trying to say.

Still, as a LOGICIAN he is superb: indeed the very BEST I
have ever known.

And since I know Italian, and for that reason can to some
extent understand Spanish also, I re-wrote, for my own
benefit, Ferdinand's arguments, using better English, trying to
understand what he might have been thinking in Spanish as he
tried to write in English. And from re-reading his arguments
in better English, I easily understood that he MUST be right.

So we two collaborated to write our book, using good English
-- I have had many years of experience as a writer and editor in
English, and of course Ferdinand checked to see that there
were no logical mistakes in what I wrote.

The book took about 8 months to write, and was finished -- or
almost finished -- this past winter. (There are still a few
mistakes of mine that need to be corrected, according to
Ferdinand's comments, but they are comparatively minor. You
may say that the presently-available edition is the "pre-press"
edition!)

In fact originally I thought I would do the same thing with
Relativity, quoting Einstein's OWN words and disproving
them. Perhaps I shall do so some day.

But Special Relativity (not General) is TEN TIMES MORE
EASY to disprove than Goedel's Theorem! So I thought I
would simply write a few short articles against Relativity
first, and publish them on my Home Page.

But I see that many people -- including your good self -- are
not able to understand even my simple arguments. So one day
I shall DEFINITELY disprove Special Relativity IN EVERY
SINGLE DETAIL, quoting EVERY WORD of Einstein's
1905 paper and disproving what he says sentence by sentence
or at least paragraph by paragraph, as Ferdinand and I have
done with Goedel.

(For his information, I am separately sending to Ferdinand a
copy of this first part of my e-mail to you.)

So now on to Relativity. As I said, you are AGAIN mistaken,
as follows:

> As far as the case against relativity is concerning, from a quite
> HONEST point of view, there is unfortunately no doubt at all
> about who is right and who is wrong. After all, if you were
> right, there would be no question to discuss between each
> other, and you should have to discuss with the greatest experts
> in the field of theoretical physics (and, belive me, I would be
> very happy to see relativity down, even if I had to consider
> myself "bocciato"!).
>
> As a matter of fact, your objection:
>
> > But I am very, very sorry to see that you have made a BIG
> > MISTAKE -- namely, you have *completely* ignored
> > time dilation!
>
> is wrong. I must say sincerely that these words show to me
> that you have not got a full understanding of relativity, as I
> said does indeed happen with ALL the pseudo-arguments
> against relativity (and this does not mean that one is not
> clever enough, but just that unfortunately he has to study
> more).
>
> As you know very well, Minkowski said since the beginning,
> that space and time "are doomed to fade away into mere
> shadows, and only a kind of UNION of the two will preserve
> an independent reality". In your criticism to my simple answer
> to your easy challenge, you "separate" in some sense space and
> time, while in relativity there exists ONLY ONE space-time
> interval, and the SAME phenomenon could be explained - as I
> shall soon prove - FROM A RELATIVE POINT OF VIEW
> once with a length contraction, another with a time dilation.
>
> I shall try to explain better all these assertions, after all I am a
> professor, and I have explained these things many times to
> students, even if writing them, and in English, is rather
> difficult for me, and it takes too much time. I shall analyze
> your objection, splitting it in order to find that it is grounded
> on the following assumptions:
>
> 1 - you point out the existence in relativity of one "length
> contraction" and of one "time dilation" (which is in some
> sense correct);
>
> 2 - you pretend to see BOTH of them at work in the situation
> we are studying (which is in some sense correct);
>
> 3 - you see that in "my" computation there is only one of the
> two, WRONG, and you pretend to see even the other, RIGHT.
>
> The fact is that it is you who sees only one of it, and not the
> two together! In the computation that your challenge required
> from me, and which I have fully satisfied, THERE ARE
> BOTH length contraction and time dilation, DEPENDING
> FROM THE POINTS OF VIEW.

Parenthetically, this is a mere ASSERTION on your part: there
is no DEMONSTRATION of it anywhere in your e-mail.

(See also below.)

One must simply be able
> to interpret the result which is the only one possibly correct. I
> shall try  to show you where you have to look for finding the
> time dilation in the same and one formula.
>
> Now that we have made a complete understanding of the
> physical situation, we must say that we have only one
> phenomenon to study in Minkowski space-time, namely we
> have three different world lines, two of which are parallel,
> which intersect, something of the following kind:
>
>             /             /     !
>            /             /      !
>           /             /       !
>          /             /        !
>         /             /         !     >
>   stern S     bow B   buoy X
>
> (the time orientation is from top to down).
>
>  The world lines of the bow of the spaceship and of the buoy,
> let us call it in the order B  and X , thought of as single
> points (no worry for instance about the fact that a "real clock"
> is not pointlike, we are doing simple "theory"!), intersect in
> some event  E1 ; the lines of the stern  S  of the spaceship and
> of the buoy  X  intersect in some event  E2 . We do not need
> to introduce more than that.

Now here you have cunningly shifted the argument from the
Lorentz transformation to Minkowski space-time, which is
NOT a part of Einstein's ORIGINAL 1905 formulation of the
Special Theory of Relativity -- for note that Minkowski
published his first paper on Relativity only in 1908, three
years LATER. (You are playing the part of the *advocatus
diaboli* very diabolically!)

But never mind: I can show you how you are mistaken HERE
TOO.

I am indeed sorry to see that it is YOU who do not have a full
understanding of Relativity. If you had, you would know that
for the scenario described in my challenge, there is not just
ONE possible Minkowski diagram, but at least TWO (or more
accurately, one can have an INFINITE NUMBER of
Minkowski diagrams, depending on which IFR is used for the
orthogonal axes -- x horizontal and ct vertical -- in the
diagram!)

In particular, you should also know that in a Minkowski
diagram the PRIMED axes -- i.e., those SLANTED format,
for ct' and x' respectively -- are ALWAYS those of the
MOVING IFR, and the UN-PRIMED axes -- i.e., those in in
exact ORTHOGONAL format -- are ALWAYS those of the
STATIONARY IFR. (If this is NOT done the time dilation
solutions come out wrong -- the moving clocks tick *faster*
than the stationary ones!)

So ALTHOUGH it is true that in a Minkowski diagram one
can show BOTH time dilation AND length contraction
SIMULTANEOUSLY, because we are using space-time
combined, and not space and time separately, the primed co-
ordinates once gain indicate WHICH of the two IFRs was
moving!

So the question STILL remains: WHICH Minkowski diagram
is the one according to which the two stop watches will read?
Because depending on which diagram you use, YOU WILL
GET DIFFERENT TIME DILATION RESULTS!

If you draw a Minkowski diagram using the IFR of the
BUOY for the ortho- gonal x and t axes, then YOUR diagram
is certainly ONE of the possible correct ones.

But if you draw a Minkowski diagram using the IFR of the
SPACESHIP for the orthogonal x and t axes, then the
diagram CHANGES, and becomes something like this:

       !                        !        \
       !                        !         \
       !                        !          \
       !                        !           \
       !                        !            \                             <
   stern S              bow B    buoy X    direction of velocity vector

Note that according to *this* diagram, if you WORK OUT
THE TIME INTERVALS  which should be indicated by the
readouts of the TWO snapshots, THOSE two readouts would
be DIFFERENT from the two readouts computed from the
Minkowski diagram given by you!

Indeed in the two diagrams even the DIRECTION of the
velocity vector is reversed.

So AGAIN we can determine, if we agree as to which diagram
is the one which will determine the readouts of the two stop
watches, which of the two -- spaceship or buoy --  was
moving and which was not -- and also IN WHICH
DIRECTION the movement was taking place! But this, as I
said, contradicts the Principle of Relativity.

So one way or the other --  <Lei sta "bocciato">.

Have I not made you very HAPPY, though? For this
PROVES that Relativity IS mathematically flawed!

***

And one more thing: you have not actually USED the
Minkowski diagram to demonstrate clearly just WHAT the
two readouts should show!

Instead you have used the LORENTZ TRANSFORMATIONS
for calculating this -- and you have NOT shown the LINK
between the Lorentz transformations and the Minkowski
diagram for doing this!

So in the matter of THOROUGHNESS of showing DETAILS
of your mathematics also, you are very, VERY lacking.

Indeed if a STUDENT of yours showed you an answer like
you have shown me, WITHOUT giving details of his
calculations, you would definitely have him "bocciato"!

So you are TWICE "bocciato": first, for giving the wrong
answer, and the second time for giving an answer without
giving FULL DETAILS as to how you reached your
conclusions!

You then added:

> Then one can ask which is the proper time elapsed WITH
> RESPECT TO  X  from E1  to  E2 . The situation is like that
> from  X's  point of view:
> ______________              ------->                      °
> S                        B      vector velocity              X
>     the spaceship                                           the buoy
>          is "still"                                           is "moving"
>
>
> and the computation is very easy, I repeat it. If the proper
> length of the spaceship is L, then  L' = L*sqr(1-v^2/c^2) (the star *
> stands for product) is the length of the spaceship with respect to  X ,
> and the required time is (MUST BE!):
>
> (1)  L'/v
>
> (here  v  is the scalar speed, the "module" of the vector
> velocity).

Now you RE-INTRODUCE the Lorentz transformations into
the picture. But then WHY did you give the MINKOWSKI
DIAGRAM above, if as you say about your Minkowski
diagram: "We do not need to introduce more than that"?

You see, you HAVE NOT shown how a SINGLE Minkowski
diagram is used to compute the TWO time interval readouts
which should be photo- graphed by the cameras -- the one in
the spaceship and the one in the buoy.

Although it is possible, certainly, you have not shown it --
maybe because to show it in an e-mail is very hard: we do not
have graph paper.

But since the same results can be obtained using the Lorentz
transformations, which are easy to show without graph paper,
why should we not use them?

So forget the Minkowski diagrams: they were never a part of
the ORIGINAL Theory of Special Relativity anyway.
Remember that in the ORIGINAL 1905 Special Theory of
Relativity ONLY the Lorentz-Fitzgerald transformation is
used. Don't confuse the issue by using in one single argument
both the Lorentz-Fitzgerald transformations *and* the
Minkowski world-lines!

You should be CONSISTENT in your argument. You should
use the Minkowski world-lines *alone*, OR the Lorentz-
Fitzgerald transformations *alone*. But you should use
ONLY ONE OF THEM. Otherwise you will be confusing the
issue: not only in MY mind, but more importantly, ALSO IN
YOURS.

(And THAT, I suspect, must have been your mistake ALL
THESE YEARS.)

That is because ANY Minkowski diagram shows BOTH time
dilation AND length contraction, whereas EACH Lorentz
transformation equation shows only ONE  of the two:
EITHER length contraction  OR time dilation!

You added:

> Conversely, from the point of view of the spaceship, we have
> a physical situation like the following one:
>
>______________              <-------                       °
>  S                        B      vector velocity               X
>      the spaceship                                    the buoy is "moving"
>          is "still"
>
> and WE CANNOT ASK EXACTLY the same question as before,
> since E1 is an event in the life of B , and E2 is an event in the life
> of S ! So, there is no possibility to ask a difference between proper
> times of anybody!!

Now here is ANOTHER one of your mistakes: because even
though E1 is an event in the life of B and E2 is an event in
the life of S, since B and S are NON-MOVING WITH
RESPECT TO ONE ANOTHER, it IS possible to know the
exact TIME DIFFERENCE (in the IFR of the spaceship)
between the "life" of the bow B and the "life" of the stern S!

So if the time difference between the "life" of the bow B and
the "life" of the stern S is, say, t seconds -- i.e., if any event
occurs in the "life" of the stern S t seconds after it occurs in
the life of the bow B, and vice versa -- then if the event E2
occurred in the "life" of the stern S occurred at a time of T
seconds, then in the IFR of the spaceship, that event will have
occurred in the "life" of the bow B at a time of (T-t) seconds!

Thus it IS possible to ask what is the difference between E2
and E1 in the life of the bow B compared with the same
interval in  the life of the stern S.

Do you STILL not see how this is accomplished? If not, I can
explain even further. (Or else, as I wrote earlier, you could ask
an engineer.)

O forse sarà meglio se scriverò in italiano?

Anche se E1 è un evento nella "vita" di B, ed E2 è un evento
nella "vita" di S, per causa che B ed S non stanno muovendo
fra loro, è certamente POSSIBILE di sapere qual'è l'intervallo
temporale (nel'IFR dello 'spaceship') fra la "vita" di B e la
"vita" di S!

E' vero o no, questo che ho scritto?

E si è vero, possiamo sempre SAPERE l'intervallo temporale
fra E2 ed E1, nell'IFR dello 'spaceship'!

Infatti, come Lei ha scritto, è possibile avere due orologi
sincronizzati nel IFR dello spaceship, l'uno a B e l'altro a S --
il quale risolve tutti i problemi.

[TRANSLATION:

Or perhaps it might be better if I were to write in Italian?

Even if E1 is an event in the "life" of B, and E2 is an event in
the "life" of S, since B and S are not moving relative to one
another, it is certainly POSSIBLE to know the time interval
(in the IFR of the spaceship) between the "life" of B and the
"life" of S!

Is this not true?

And if it is, we can always KNOW the time interval between
E1 and E2, in the IFR of the spaceship!

In fact, as you have written, it is possible to have two
synchronised clocks in the IFR of the spaceship, one at B and
the other at S -- which resolves all problems.

END OF TRANSLATION]

> But we can of course suppose to have synchronized clocks
> aboard of the spaceship (this is exactly the meaning of the
> words in my last mail, about the role of your "mechanism"),
> and we can ask which is the time which is needed for the buoy
> to pass the spaceship, FROM THE POINT OF VIEW OF
> THE SPACESHIP, which means from the point of view of a
> coordinate system associated with the spaceship (we could
> better think of  X  as a meteorite). Well, since the length of
> the ship is  L , and the module of the velocity does not
> change, this time MUST BE now equal to:
>
> (2)  L/v .
>
> Let me remark that relativity is not so stupid to give different
> answers from these ones which I have given to you!

(I see you have changed the nomenclature, saying "meteorite
X" instead of "buoy B", and have used the letter "B" for
"Bow" -- i.e., of the spaceship A. Let it be so from now on --
though it would be best in a SINGLE argument to stick to a
SINGLE nomenclature and a SINGLE set of alphabetic letters
throughout.)

Now as I pointed out there must be at least TWO Minkowski
diagrams, depending on which IFR is used, and each of them
give two DIFFERENT answers to what the snapshots should
show!

Indeed, as I said, there must be an INFINITE NUMBER of
solutions to the challenge --  and this is logically impossible.

And EVEN if you use the Lorentz transformations ALONE,
what you claim above, namely (2) L/v as being the interval E2
- E1 in the IFR of the spaceship, is correct ONLY if the
spaceship is considered to be NON-MOVING.

Note: L is the *rest-length* of the spaceship. And v is always
the same. So the rest-length divided by v gives the time
between E2 and E1 as observed by a stop watch in a NON-
MOVING IFR!

But the spaceship is MOVING relative to the "meteorite"!

If the spaceship is considered on the contrary to be MOVING,
the time given by its stop watch CANNOT be L/v, as you
claim, but LESS than that, because of the TIME DILATION
which that movement causes to appear on the readout of its
stop watch, and also because its LENGTH will have
contracted!

But note that a meteorite moving past a stationary spaceship
cannot affect the stop watch on board the meteorite! It is only
if the spaceship is *actually* moving (i.e., moving in an
*absolute* sense) that its stop watch will show a dilated time.

So your remarks are ONCE AGAIN IN ERROR. (Why is it
you cannot see this simple error you have made? Perhaps you
are not paying attention?)

As for the following, namely:

> In conclusion, once again, you have got the two times that
> you challenged me to compute. The second time, (2), is surely
> GREATER than the first time (1), at least if v is not zero.
> Now you have got all the answers to all your questions. Try
> to ask to do these easy computations to any other good
> physicist, and you will obviously get the same answers (if
> not, he is not a good physicist - or at least he does not know
> enough relativity).
>
> Now you object: I see length contraction at work in (1) -
> CORRECT - so you must be wrong, because you forgot the
> time dilation. This is WRONG, since in (1) there is even a
> time dilation. As a matter of fact, I said it already at the end
> of my previous mail:
>
> "I have talked too much - and with my bad English this is
> perhaps harmful for a better understanding - yet I have not said
> everything I could have said. For instance, in some lecture to
> students, I COULD HAVE SHOWN EVEN HOW ONE
> COULD HAVE  CONNECTED LENGTH CONTRACTION
> AND TIME DILATION IN THE  PROPOSED EXERCISE."
>
> In order to show that, let us put the thing in the following
> terms. The people aboard of the spaceship measure the time
> needed for the meteorite to pass, and they claim that it is L/v ,
> good. Somebody aboard of the meteorite says that this time is
> not  L/v , but it is LESS than that, because he measurs  L'/v ,
> good once again. Well, this assertion from the point of view
> of the time elapsed for the meteorite is exactly what the crew
> of the spaceship would interpret as the time dilation occurring
> "aboard of the meteorite"!

Now PLEASE: why do you EQUIVOCATE?

At first you say that according to the IFR of the "meteorite"
X, the LENGTH of the spaceship has CONTRACTED, and
THAT is why the elapsed time is shorter: L'/v rather than L/v
(as required by the Galilean transformation.)

And you also specify that "L' = L*sqr(1-v^2/c^2) (the star *
stands for product)"!

And NOW you say that the shorter time recorded by the stop
watch on board the "meteorite" is due to the TIME
DILATION    !!!

P L E A S E     ---     M A K E      U P      Y O U R
M I N D    ! ! !

Just WHAT is the lesser time recorded by the stop watch on
the meteorite DUE TO: time dilation or length contraction?

I am beginning to think that you do not even UNDERSTAND
my objection.

Let me explain in more detail.

Note that if the meteorite is NOT considered to be moving,
there can be NO time dilation of ITS stop watch! But the
LENGTH CONTRACTION OF THE SPACESHIP, as
observed from the IFR of the meteorite, remains unaffected!

Whereas if the meteorite IS considered to be moving, then it
observes the LENGTH of the spaceship as CONTRACTED
(because each is moving relativistically compared with the
other), AND it observes the TIME of its OWN stop watch --
i.e., the one on the METEORITE -- to be DILATED!

If, in other words, the meteorite is considered to be moving,
BOTH length contraction AND time dilation have to be
applied to obtain the final readout of its stop watch: the length
contraction is applied to the SPACESHIP, and the time
dilation to its OWN STOP WATCH.

Whereas if the meteorite is considered to be stationary, ONLY
the length contraction of the spaceship is applied to obtain the
final readout of its stop watch, since its stop watch can NOT
show a dilated time!

Why is it that you cannot see this SIMPLE mistake you have
made?

I think it is because you do not give full DETAILS of your
argument.

Or perhaps because you confuse in your own mind the two
methods of calculation: Minkowski diagrams or Lorentz
transformations.

That, I think, must be the reason why YOU DO NOT
UNDERSTAND RELATIVITY FULLY!

If you wish to prove that you are NOT wrong, show me the
EXACT DETAILS of your calculations, USING ONLY
O  N  E       OF THE TWO METHODS: Minkowski
diagrams or Lorentz transformation equations (preferably the
latter).

You will see if you do the calculations IN DETAIL, you
WILL  get more than one set of two readouts -- whichever
method you use: Minkowski diagrams or Lorentz
transformations.

(But of course if you use BOTH Minkowski diagrams and
Lorentz transformation equations TOGETHER, you will
CONFUSE everyone, including yourself; so restrict yourself
to only ONE of the two: Minkowski diagrams or Lorentz
transformation equations.

Select one, but select only ONE, of the two methods.

Preferably, select the Lorentz transformation equations,
because they are the ONLY ones used by Einstein in his
original 1905 Paper on Special Relativity.)

Then also, you have added all the following nonsense about
"proper times". Please note: I have NOT ASKED about
"proper times": I have only asked, "What should the
SNAPSHOTS show?" Proper or improper, ALL that is
required is the time intervals recorded by the two stop watches
as photo- graphed by the two cameras.

So all this you have written below is irrelevant:

> The proper time of some phenomenon (between any two
> events  E1  and  E2  in the world line of some "observer") is
> defined as the LEAST value of this time with respect to all
> inertial observer, in the same way as the proper lenght is, on
> the contrary, the GREATEST value etc. etc.. This proper time
> is connected to the measure of the "same time-interval" with
> respect to other coordinate times by the well known relation:
>
>      proper time interval = sqr(1-v^2/c^2) * coordinate time interval
>
> while the corresponding formula for lengths is the "inverse":
>
>      proper length * sqr(1-v^2/c^2) = coordinate (or "apparent") length .
>
> Well, in (1) you have got exactly the first formula at work:
>
> proper time of the phenomenon we are studying, namely the
> passing of the meteorite  X = sqr(1-v^2/c^2) * coordinate time
> interval of the same event = sqr(1-v^2/c^2) * (L/v) .
>
> As a matter of fact, the coordinate time interval of this
> phenomenon is L/v , as we said in formula (2) , and if you
> write the previous formula "associating" differently (a shifting
> of parentheses), you find exactly (L*sqr(1-v^2/c^2))/v , and
> the numerator of this fraction (ratio) is L' , the "contracted
> length"...

And as for the following:

> That is to say, in (1) time dilation and length contraction
> THERE ARE BOTH PRESENT, I hope that you will be
> satisfied by that, since this is the simple easy truth.

Again, it is the simple and easy-to-understand FALSEHOOD,
and a mathematical JUDGE will easily be able to see that this
is the case.

And in addition, in your referred to (1) above, you have NOT
introduced the *Lorentz* time dilation. Let me repeat (1) for
your convenience, and for the convenience of any
mathematical JUDGE who might happen in future to see
copies of this correspondence between us:

[QUOTE]

    > Then one can ask which is the proper time elapsed WITH
    > RESPECT  TO X from  E1 to E2 . The situation
    > is like that from X's point of view:
    >
    >  ______________              -------    >                      °
    >  S                        B      vector velocity              X
    >      the spaceship                                    the buoy is "still"
    >       is "moving"
    >
    > and the computation is very easy, I repeat it.
    > If the proper length of the spaceship is L, then
    > L' = L*sqr(1-v^2/c^2) (the star * stands for product)
    > is the length of the spaceship with respect to
    > X , and the required time is (MUST BE!):
    >
    > (1) L'/v
    >
    > (here is the scalar speed, the "module" of the vector velocity).

[END QUOTE]

Now show me just WHERE is the time dilation calculation
here ? ? ? ? ? ? ?

Indeed, if as you write, the buoy is "still", the time of the
stop watch carried at X *cannot* be dilated!

And even you yourself admit that the time interval between
E2 and E1 in the IFR of the SPACESHIP is L/v, not L'/v!

THERE IS NO LORENTZ TIME DILATION IN (1). Any
mathematically competent judge will be able to see this.

> I could say even more, showing how one could explain even
> the "time dilation" which happens (must happen!) in the time
> of spaceship as "seen" from the point of view of the meteorite
> (until now we had only a "time dilation" in the meteorite from
> the point of view of the spaceship).This is just a bit more
> difficult exercise for students, which requires a little attention,
> and an explicit use of Lorentz transformations. I avoid to do
> that, thinking that I have answered enough to your criticism,
> but if you want I can send to you the complete "solution" - it
> is one argument that I have experienced most amateur people
> do not know precisely, ...

It is precisely the COMPLETE SOLUTION that will prove to
you that you are wrong. So please DO send me the complete
solution, omitting absolutely no detail! In the very process of
doing so, you will PROVE to YOURSELF that you are
wrong.

Actually, I have an even better idea, if you will agree to it: let
us publish the FULL AND UNEDITED TEXT of our
correspondence on the Web -- at my Home Page if you wish,
or at your Web site, or better still, at both of them -- for
public review! Then ANY competent mathematician will be
able to judge who is right and who is wrong: you or I.

Do you agree to this?

If so, then I shall definitely claim -- and that too with
COMPLETE justification -- that you have NOT answered my
Challenge satisfactorily! And ANYONE with competence in
the field of physics and mathematics who reads our
correspondence will be able to SEE that this is so.

In other words, I will have proved not only to YOU, but to
THE ENTIRE WORLD OF SCIENCE AND
MATHEMATICS, that you are wrong and I am right.

For as I answer to Del Larson when he says:

[QUOTE]

     > Dear Mr. Mehta,
     >
     > I read the first half of the lengthy correspondence you had with
     > Umberto Bartocci.  It was, unfortunately, quite clear from your
     > writings that you simply do not understand the theory of relativity.
     >
     > There are many in the alternative space time community that share
     > your disability.  Relativity is not the easiest thing to understand.
     > Many make claims about the "common sense" inaccuracies in the special
     > theory, and think from those claims alone they have disproved it.
     > But that is wrong.  Special relativity is not illogical.  Rather it
     > has a different logic than what prevails as "common sense".
     >
     > All of this is highly unfortunate.  Since there is a small army
     > making inaccurate claims without sufficient prior study and
     > understanding, it makes it even harder for the few competent relativity
     > critics to be heard.
     >
     > Please take the time to study and understand relativity.  I would
     > suggest contacting your closest quality university and seeking out
     > a mentor.  Once you understand relativity I would hope that you could
     > join the battle against it.
     >
     > But fighting an intellectual battle without an understanding of its
     > underpinnings is simple folly.
     >
     > Sincerely, and with Best Hopes and Intentions,
     >
     > Del Larson

[END QUOTE]

... to this I answer very simply:

[QUOTE]

Dear Sir:

I am sorry to say that your answer clearly shows that YOU do
not understand SCIENCE.

If you did, you would know that science does not consist of
mere ASSERTIONS such as "You do not understand
Relativity", but rather demands logical, and if possible also
mathematical, ARGUMENTS!

Your complete lack of any ARGUMENT against my words
shows that either you HAVE none, or else that you do not
know even the first principles of science.

In fact, do you HAVE THE COURAGE OF YOUR OWN
CONVICTIONS to agree to my publishing the full and
unedited text of our brief correspondence on the Web for all to
see and judge who is a true scientist: you or I?

For I think your present response would indicate to ALL who
read it that your words in our correspondence do not even
allow you to merit the title "scientist".

Sincerely, and with Best Hopes and Intentions of turning a
promising human being from a dogmatist -- even if an anti-
Relativity dogmatist -- to a TRUE scientist,

Ardeshir Mehta.

(Let me add that I am not so much anti-Relativity as anti-
humbug, no matter what its source.)

[END QUOTE]

> and then they get in other "paradoxes",
> because they are not able (for instance Dingle was unable to
> see it, and he was not even an amateur!) to see the
> COMPLETE SYMMETRY which is now at work (of course,
> there is no possibility to see even the length contraction of  X
> , which we have supposed pointlike).

Your argument becomes completely INVALID as soon as you
are reminded of the SECOND Minkowski diagram!

And indeed, as I said, there are an infinite number of such
diagrams possible for the scenario of my Challenge ... which
proves that there is NO mathematically consistent solution
possible for the question I have posed which is ALSO
consistent with the Theory of Special Relativity.

Anyway, you should realise by now that you have NOT been
able to satisfactorily answer my Challenge, whether with the
help of the Lorentz transformation equations OR with the help
of the Minkowski diagrams -- and ANY competent
mathematical judge should be able to see that too.

> Ciao, I HOPE TO READ SOON YOUR OBJECTIONS
> AGAINST GOEDEL, perhaps  they are more useful than the
> ones against relativity (I am sympathetic with these attempt to
> show that relativity is wrong, at least they show that one has
> understood that to do this is a  most important task, but one
> must not underestimate the problems), one never knows,

I hope you have seen from the above at least that you have
YOURSELF not been able to understand Relativity until now
-- !

Or else, if you do understand my arguments, you should
realise by now that it is VERY EASY to refute Relativity -- at
any rate if one restricts oneself to Special Relativity alone!
(General Relativity is not being addressed here by me
properly, except for being mentioned once in a while, mostly
in passing.)

Goedel is a much  more difficult matter than Special
Relativity. If you cannot even understand my arguments
against Special Relativity I don't think you will be able to
understand the arguments against Goedel, whose own
arguments in his 1931 Paper are MUCH more subtle than
those in Special Relativity.

I also don't think you are up to the job of tackling Goedel's
Theorem because you have not given me an answer to my
PHILOSOPHICAL argument against the Lorentz
transformations: namely that they contradict the Galilean ones,
and thus they *cannot* possibly be deduced in a step-by-step
mathematical fashion from the axioms of mathematics and the
propositions and postulates of Euclidean geometry, whereas
the Galilean transformations CAN be so deduced.

(Why did you not answer my philosophical argument? Maybe
you did not read my e-mail carefully enough ... AGAIN?
Don't say I didn't warn you.)

This philosophical argument is MUCH stronger than the one
in my Simple Challenge ... and of course it is not a SIMPLE
one either. If you are not a philosopher versed in the
philosophy of mathematics, however -- as for example
Bertrand Russell was -- it may be best for you to avoid
responding to my argument: you may not even understand it.

(Of course if you DO claim to understand it, I shall willingly
debate your counter-arguments -- and that too, very
thoroughly.)

But by all means TRY to understand my Critique of Goedel's
Theorem: and who knows? Maybe I shall be proven mistaken
in my opinion, and you WILL understand it after all! -- In
which case no one will be happier than I.

In any case, I remain always your sincere friend in our
common battle against dogma and humbug, whether in
mathematics or in science.

Tanti saluti,
 

Ardeshir.

Home Page: <http://homepage.mac.com/ardeshir/education.html
 
 

_______________________________________________________
 
 

Subject: Re: Argomento Contro la Teoria della Relativita Speciale
                 (addendum molto breve)
                 [Translation: Argument Against the Special Theory of
                 Relativity (very brief addendum)]
Date: Tue, 28 Aug 2001 02:56:22 -0400
From: "Ardeshir Mehta, N.D." <ardeshirmehta@myself.com>
To: umberto bartocci <bartocci@dipmat.unipg.it>
References: 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8
 
 

Caro Prof. Bartocci:
 
 

Here is an absolutely clinching argument that you are
DEFINITELY wrong.

You had written:

> But we can of course suppose to have synchronized clocks
> aboard of the spaceship (this is exactly the meaning of the
> words in my last mail, about the role of your "mechanism"),
> and we can ask which is the time which is needed for the buoy
> to pass the spaceship, FROM THE POINT OF VIEW OF
> THE SPACESHIP, which means from the point of view of a
> coordinate system associated with the spaceship (we could
> better think of  X  as a meteorite). Well, since the length of
> the ship is  L , and the module of the velocity does not
> change, this time MUST BE now equal to:
>
> (2)  L/v .

Now let us give some hard figures, and let us exaggerate
GREATLY (and you will see how useful this is!).

Let us say, just hypothetically, that L = 1 light-second, and v
= 0.9999 ... 999 c (with ONE BILLION 9's after the decimal
point).

Then according to your calculation, which as you say MUST
be right, the time which is needed for the buoy to pass the
spaceship, from the point of view of a co-ordinate system
associated with the spaceship, ACCURATE TO FIFTY
DECIMAL PLACES, should be L/v = (1/0.9999 ... 999)
seconds or 1.0000 ... 000 second (with fifty 0's after the
decimal point). Right?

And let us assume that it is impossible to measure
ANYTHING with an accuracy GREATER than fifty decimal
places -- i.e., that this is the allowable margin of error in our
measuring instruments.

But according to Relativity it should make NO
DIFFERENCE to the readout of the stop watch (or of the stop
watches, if there are more than one) on board the spaceship,
whether the spaceship passes the buoy, or the buoy passes the
spaceship!

Right?

So according to you, the time which is needed for the
SPACESHIP to pass the BUOY, again from the point of view
of a co-ordinate system associated with the spaceship, and
again accurate to fifty decimal places, should ALSO be
1.0000 ... 000 second.

Right?

Now let us suppose that this spaceship is passing, not a buoy,
but the axis of the Sun -- i.e., the axis around which the Sun
rotates every so many hours -- so that this axis lies at right
angles to the relative motion between the spaceship and the
Sun's axis of rotation. (The axis has only one dimension, and
this takes care of the problem created by the finite size of a
buoy or a meteorite.)

(And for the purposes of THIS calculation, a stop watch on
the buoy is not at all required: only the stop watch(es) in the
spaceship is/are taken into consideration.)

And let us suppose the spaceship passes the Sun at a distance
of 200 million kilometres from the Sun's centre, so it misses
the Sun's heat by a great distance.

Now if Relativity is correct, according to the TIME
DILATION which the stop watch in the spaceship must be
undergoing, time should be running SO very slowly on board
the spaceship that its stop watch (or stop watches, if there are
more than one) should register NO TIME AT ALL -- i.e.,
0.0000 ... 000 seconds, when measured with an accuracy of
fifty decimal places -- for the spaceship to pass the Sun's axis!

(And this is EVEN if we ignore the spaceship's length
contraction; for if its length contraction IS also taken into
account, the time registered by the stop watches in the
spaceship's co-ordinate system would be even less ... if that
were at all possible!)

Do you now see the VAST difference? Observe--

1.  According to your calculation:  the spaceship's stop watch
reads 1.0000 ... 000 second.

2.  According to Relativity:  the spaceship's stop watch reads
0.0000 ... 000 seconds.

And 1.0000 ... 000 second is NOT equal to 0.0000 ... 000
seconds!

So either your calculation is wrong or the Theory of Relativity
is wrong!

Are you NOW satisfied that you are ABSOLUTELY, COM-
PLETELY and CATEGORICALLY mistaken?
 
 

Best wishes,

Ardeshir.
 

_______________________________________________________
 
 

Subject: Come si deve fare la matematica
             [How Mathematics Should be Done]
Date: Thu, 30 Aug 2001 01:26:21 -0400
From: "Ardeshir Mehta, N.D." <ardeshirmehta@myself.com>
To: umberto bartocci <bartocci@dipmat.unipg.it>
References: 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8
 
 

Caro Professore:
 
 

Le faccio vedere come si deve fare i calcoli matematici,
piano-piano, senza fare delle "balze" intellettuali, sicché
si ritiene tutti i legamenti fra le idee:

[TRANSLATION]

I show you how mathematical calculations should be done,
slowly, without making intellectual "jumps", so as to retain
all the connections between the ideas:

[END OF TRANSLATION]

[1] Let the rest length of the spaceship be L, and the velocity
between spaceship and buoy be v; and let all these
expressed, for the sake of convenience in making the
calculations, in units in which the speed of light, c, equals 1.

[2] Let the event of the front end -- i.e., the "bow" -- of the
spaceship passing the buoy be denoted as E1, and the event
of the rear end of the spaceship -- its "stern" -- passing the
buoy be denoted as E2. (Note that E1 and E2 are events
common to the "lives" of both, the co-ordinate system
associated with the buoy AND the co-ordinate system
associated with the spaceship.)

[3] Let the primed co-ordinates in the calculations below be
those pertaining to the spaceship, and let the un-primed co-
ordinates be those pertaining to the buoy.

[4] The Lorentz time dilation formula is
<delta>t' = <delta>t*(sqrt.(1-v^2/c^2))^-1.

[5] The Lorentz length contraction formula is
<delta>x' = <delta>x*(sqrt.(1-v^2/c^2))^-1.

[6] The Lorentz transformation equations are as follows:
x' = (x - vt)/(sqrt.(1-v^2/c^2)),
y' = y,
z' = z,
t' = (t - vx/c^2)/(sqrt.(1-v^2/c^2)).

[7] Let E1 occur in the co-ordinate system associated with the
buoy at t1= 0.

[8] Then by the Lorentz transformation equation for time, E1
will also occur in the co-ordinate system associated with the
spaceship at t'1=0. (Note that at E1, x = 0, and thus
vx/c^2 also equals zero.)

[9] According to the Lorentz length contraction formula, in the
co-ordinate system associated with the buoy, the length of
the spaceship will not be L but L', where
L' = L*(sqrt.(1-v^2/c^2))^-1.

[10] Thus E2 will occur, in the co-ordinate system associated
with the buoy, at t2 = L'/v where L' = L*sqrt.(1-v^2/c^2).

[11] Let 1/(sqrt.(1-v^2/c^2)) be denoted by the conventional
term [<gamma>].

[12] Then E2 will occur in the co-ordinate system associated
with the buoy at t2 = L'/v, where L' = L*[<gamma>^-1].

[13] Using the Lorentz time dilation formula, we calculate that
E2 will occur in the co-ordinate system associated with the
spaceship at t'2 = t2*[<gamma>^-1]. (Note: The same
result is attained if we use the Lorentz transformation
equation t' = (t - vx/c^2)/(sqrt.(1-v^2/c^2)), since at E2, x
is zero, and thus vx/c^2 is also zero.)

[14] Since t2 = L'/v and L'=L*[<gamma>^-1],
t'2 = t2*[<gamma>^-1]
= (L'/v)* [<gamma>^-1]
= ((L*[<gamma>^-1])/v) )* [<gamma>^-1]
= ((L*[<gamma>^-1])*v^-1) )* [<gamma>^-1]
= L*v^-1*[<gamma>^-2].

[15] E1 will occur at t1 = 0.00 and t'1 = 0.00 -- i.e., in both co-
ordinate systems E1 will occur at time 0.00.

[16] Since both t1 and t'1 are zero, and E2 will occur at time
t2 = L'/v (according to [10] and [12] above), the time
registered by the stop watch aboard the buoy at event E2
will be T = (t2 - t1) = (t2 - 0) = t2; and the time registered by
the stop watch aboard the spaceship at the same event E2 will
be equal to T' = (t'2 - t'1) = (t'2 - 0) = L*v^-1*[<gamma>^-2]
(according to [14] above).

[17] These will be the times registered by the two stop watches
when photographed -- that is, IF the primed co-ordinates
are those of the SPACESHIP.

[18] But if the primed co-ordinates are those of the BUOY, then
the situation will be as follows:

[19] E1 will again occur at t = 0.00 and t' = 0.00.

[20] E2 will occur in the un-primed co-ordinate system -- i.e.,
the one associated with the spaceship -- at t2 = L/v: or in
other words, at t2 = L*v^-1.

[21] According to the Lorentz time dilation formula, E2 will
occur in the primed co-ordinate system -- the one
associated with the buoy -- at t'2 = t2*[<gamma>^-1].
(Again, the same result is obtained if we use instead the
Lorentz transformation t' = (t - vx/c^2) / (sqrt.(1-v^2/c^2)),
since at E2, x is zero, and thus vx/c^2 is also zero.)

[22] Since t2 = L/v, by the Lorentz time dilation formula
t'2 = t2*[<gamma>^-1] = (L/v)*[<gamma>^-1].

[23] And since L' = L*[<gamma>^-1],
(L/v)*[<gamma>^-1] = L'/v.

[24] So the time recorded by the stop watch aboard the buoy
will be L'/v in EITHER case -- no matter which co-ordinate
system is represented by the primed letters.

[25] BUT the time recorded by the stop watch aboard the
spaceship will be EITHER L*v^-1 OR
L*v^-1*[<gamma>^-2], depending on which co-ordinate
system is represented by the primed letters!

So WHICH figure correctly represents the time recorded by the
stop watch of the co-ordinate system associated with the
spaceship: L*v^-1*[<gamma>^-2] or L*v^-1?

According to the above calculations, which are done using the
Lorentz transformation equations, BOTH figures must be
correct!

But this is mathematically IMPOSSIBLE.

Therefore the Lorentz transformation equations cannot be
MATHEMATICALLY valid.
 
 

Tanti saluti,
 
 

Ardeshir <http://homepage.mac.com/ardeshir/education.html>
 
 

_______________________________________________________
 
 

Subject: Re: Come si deve fare la matematica
             [How Mathematics Should be Done]
Date: Fri, 31 Aug 2001 14:53:31 +0200
From: umberto bartocci <bartocci@dipmat.unipg.it>
To: "Ardeshir Mehta, N.D." <ardeshirmehta@myself.com>
References: 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 , 9
 
 

[I wish to reply to you immediately, I hope not to have made
mistakes...]

Dear Mehta,

thanks even for your last mails, even if they confirm my
opinion: you make too many mistakes, not knowing
accurately enough relativity. So for friendship, and even for
"duty" as a teacher (which cannot last at "infinity"!), I send to
you a list of the new mistakes you have made in one of these
mails, but let me say once again very frankly that I have no
more time for this kind of discussion.

As a matter of fact, there is a kind of "small" mistakes, which
can be corrected, and do not change the value of some
argument; there are instead "big" mistakes, which reduce the
value of some argument to zero. If you are not convinced that
you are making BIG mistakes, you can ask to some other
competent professor, and please let me know if there exists
even ONE which will appreciate these same objections against
relativity (of course in some point you are right, for instance
when you remark that the 1905 Einstein's paper is not so good
- but nowadays relativity is simply the Minkowski space-time
physics, and it is rather useless to express criticism which
would be as best accepted as possessing only some
HISTORICAL value)...

Always best wishes,

from yours  UB  (I took the file of your work on Goedel, and
I shall try to study the whole matter in the following months,
I hope...)

- - - - -

> [2] (Note that E1 and E2 are events common to the "lives" of
> both, the co-ordinate system associated with the buoy AND the
> co-ordinate system associated with the spaceship.)

- This is not entirely correct. We have got three "observers", in
the language of relativity, X the buoy, B the bow, S the stern,
and E1 is an event which is common to X and B, while E2 is
an event which is common to X and S. So E1 and E2 are both
in the "life" ONLY of X, and not of B and S. This is in some
sense a source of error in what follows.

> [4] The Lorentz time dilation formula is
> <delta>t' = <delta>t*(sqrt.(1-v^2/c^2))^-1.
> [5] The Lorentz length contraction formula is
> <delta>x' = <delta>x*(sqrt.(1-v^2/c^2))^-1.

- This is the major source of misunderstanding. If this was true,
then you would simply get immediately a contradiction like the
following one:

1 - <delta>t' = <delta>t*(sqrt.(1-v^2/c^2))^-1

2 - there is no difference whatsoever between t and t', Lorentz
transformations have a group structure, the situation is SYM-
METRIC,
so one must have even:

<delta>t = <delta>t'*(sqrt.(1-v^2/c^2))^-1

3 - from 1 and 2 it follows for instance:

<delta>t' = <delta>t'*(sqrt.(1-v^2/c^2))^-2

[as a matter of fact, this is precisely what happens in your
point 16]

whence:

(sqrt.(1-v^2/c^2))^-1 = 1 which implies  v = 0 .

I HAVE SEEN THIS MISTAKE HUNDRED OF TIMES
IN MY LIFE...

The true formulae, which one must "understand", are the ones
which I gave to you in my last mail, namely:

A - (proper length of some object)*sqr(1-v^2/c^2) =
coordinate (or "apparent") length of this same object in an
(inertial) reference frame in which the object is moving with
speed v

B - proper time of some phenomenon IN THE LIFE OF ONE
OBSERVER = sqr(1-v^2/c^2)*(coordinate time interval of the
same event)  [meaning as before]

> [9] According to the Lorentz length contraction formula, in the
> co-ordinate system associated with the buoy, the length of the
> spaceship will not be L but L', where L' = L*(sqrt.(1-v^2/c^2))^-1.

- WRONG, the exponent ^-1 is wrong, the truth is:

L' = L*sqr(1-v^2/c^2) . As a matter of fact, you write that
correctly  in your point N. 10, which is GOOD:

[10] Thus E2 will occur, in the co-ordinate system associated
 with the buoy, at t2 = L'/v where L' = L*sqrt.(1-v^2/c^2).

> [13] Using the Lorentz time dilation formula, we calculate that E2
> will occur in the co-ordinate system associated with the spaceship at
> t'2 = t2*[<gamma>^-1]. (Note: The same result is attained if we use the
> Lorentz transformation equation t' = (t - vx/c^2)/(sqrt.(1-v^2/c^2)),
> since at E2, x is zero, and thus vx/c^2 is also zero.)

- This is WRONG. True that x = 0, but if you make the com-
putation:

t'2 = t2/sqr(1-v^2/c^2) ,

by using the formula which you write above in your point 10,
which
I said is correct, then you get

t'2 = (L'/v)/sqr (1-v^2/c^2) = (L*sqr(1-v^2/c^2)/v)/sqr(1-v^2/c^2)
= L/v

(as I already wrote to you in my previous mail!)

which implies:

t'2 = t2*gamma [and not gamma^-1!!]
 

REMARK 1 - It is not enough to give t'2, since in order to
give an event we must specify even the SPACE
COORDINATE, which in this case is -L , as it MUST BE
because, with the actual hypotheses, it happens in the stern of
the spaceship. As a matter of fact, Lorentz transformations
rightly give:

-v*t2/sqr(1-v^2/c^2) ,

and since t2 is L'/v , we have:

-L'/sqr(1-v^2/c^2) = - L*sqr(1-v^2/c^2)/sqr(1-v^2/c^2) = -L !!
GOOD.
 

REMARK 2 - The formula t'2 = t2*gamma SEEMS at odd
with B, namely with:

proper time of some phenomenon IN THE LIFE OF ONE
OBSERVER = sqr(1-v^2/c^2)*(coordinate time interval of
the same event) which we could indeed "tentatively" write as:

Dt' = Dt*(gamma^-1)

but the point one has to understand is that UNTIL NOW
THERE IS NOT A PROPER TIME in the primed coordinates
of the spaceship, since E1 and E2 belong to DIFFERENT
OBSERVERS (or, if you prefer, they happen in DIFFERENT
SPACES), so you CANNOT make use of the previous
formula in this case.

On the contrary, one has such a proper time in the life of X ,
so one could have indeed said immediately that, since  L'/v  is
the proper time for X , then this time is, in the primed
coordinate of the spaceship, equal to:

coordinate time = (proper time)*(gamma) = (L'/v)/sqr(1-v^2/c^2)
                      = ((L*sqr(1-v^2/c^2))/v)/sqr(1-v^2/c^2)
                      = L/v

AND EVERYTHING GOES WELL.

> [14] Since t2 = L'/v and L'=L*[<gamma>^-1],
> t'2 = t2*[<gamma>^-1]
> = (L'/v)* [<gamma>^-1]
> = ((L*[<gamma>^-1])/v) )* [<gamma>^-1]
> = ((L*[<gamma>^-1])*v^-1) )* [<gamma>^-1]
> = L*v^-1*[<gamma>^-2].

- WRONG, WRONG, I hope you will start to get persuaded
of this! Everything which follows from now on is wrong.
 

FINAL REMARK 3 (for "students" - one can be "student" a
lot of time in his life, every time he studies something he
does not know yet, even if he is a "professor" in some other
matter: for instance, I shall now become a student about that
Goedel affair...)

The event E1 is (0,0) (first space, second time) for the
coordinate system of the buoy, and then it is (0,0) even for the
coordinate system of the spaceship. The event E2 is (0,L'/v)
for the buoy, and it is (-L,L/v) for the spaceship. So the time
which is needed for the spaceship to pass the buoy, FROM
THE POINT OF VIEW OF THE BUOY, is L'/v , while this
"same" time, FROM THE POINT OF VIEW OF THE
SPACESHIP, is L/v . This means that S "knows" that at the
time 0 of the spaceship the buoy was in front of the bow, and
at L/v of its clock it SEES the buoy in front of it. He sees
that the buoy's clock marks in this event L'/v < L/v , while he
knows that it marked 0 when it was in front of the bow. S
then describes this phenomenon as a DILATION OF TIME
occurred to the buoy's clock. From the point of view of the
buoy, instead, the time measured L'/v was simply less of that
time L/v because this was due to the "contraction of the
length" L . [By the way, why do you say: "Parenthetically,
this is a mere ASSERTION on your part: there is no
DEMONSTRATION of it anywhere in your e-mail"? THIS IS
THE DEMONSTRATION, and it is exactly the same which I
have given before]. But we can ask: where is the TIME
DILATION that the buoy MUST see, according to relativity,
aboard of the spaceship? When the two clocks of X and of S
meet, the clock of X marks LESS than the clock of S , no
doubt about it. Is this then a real ASYMMETRY? Does this
mean that X DOES NOT see a time dilation occurring aboard
of the spaceship, but a TIME CONTRACTION? The answer
is simply NO, because in order to understand HOW THE
CLOCK OF S HAS GONE, slower or faster than its own, X
cannot assert that the time elapsed for S, from X's point of
view, is L/v. As a matter of fact, X should compute the
difference between L/v , the time marked in front of it, at the
unique meeting of the two clocks, AND THE TIME WHICH
THIS SAME CLOCK MARKED, IN THE REFERENCE
FRAME ASSOCIATED WITH THE BUOY, at t = 0 , when
X had in front of it the bow of the spaceship, with a clock
marking 0, exactly as its own: but it does not know anything
DIRECTLY about the clock of the stern, which was
SOMEWHERE ELSE. If this time, let us call T , was zero,
then we would have got problems, but this time is not zero.
In order to compute this value T , we must realize that by
definition of the length of a moving object, at t = 0
(remember that the unprimed coordinates are relative to the
buoy), the observer associated with the buoy which had the
stern S in front of it, was exactly -L' (event (-L',0) )
[ATTENTION, one should be careful not to make confusion:
with our assumptions, L would "belong" in some sense to the
primed coordinates, and L' to the unprimed!]. Well, which is
the event corresponding to (-L',0) in the primed coordinates? It
is:

x' = (-L')/sqr(1-v^2/c^2) = -L

(AS WE COULD HAVE SAID IMMEDIATELY, it must be
the stern S!), plus:

t' = vL'/c^2*sqr(1-v^2/c^2) = vL/c^2 = T .

Now that we have T , we must compute, as we have said, the
difference:

L/v - T = L/v - v*L/c^2 = (L/v)*(1 - v^2/c^2) .

THIS IS THE TIME WHICH, FROM THE POINT OF VIEW
OF THE BUOY (of the system associated to the buoy),
OCCURRED TO S's CLOCK IN ORDER TO ARRIVE IN
FRONT OF IT, when it marked the time L/v .

The previous formula implies that the buoy sees exactly a
time dilation aboard of the spaceship, as it must be according
to relativity, exactly in the same quantitative form which is
foreseen by the theory.

As a matter of fact this time interval (L/v - T) , WHICH IS
NOW A PROPER TIME OF ONE SINGLE OBSERVER,
namely  S , is equal to:

the time elapsed for the buoy, L'/v, namely a "coordinate
time" (which is even a proper time), multiplied by the factor
sqr(1-v^2/c^2) , and so at last:

(L'/v)*sqr(1-v^2/c^2) = ((L*sqr(1-v^2/c^2))/v)*sqr(1-v^2/c^2)
= (L/v)*(1 - v^2/c^2) .

EVERYTHING IS ALRIGHT ONCE MORE, AS IT OB-
VIOUSLY HAD TO BE.

- - - - -

This is the promised FULL solution of this rather simple
exercise in relativity. I am not playing the part of the
ADVOCATUS DIABOLI in a very diabolically way, but the
truth is the truth. Pretending to have shown that "the Lorentz
transformation equations cannot be MATHEMATICALLY
valid", as you claim, with such wrong arguments, is counter-
productive with respect to all serious attempts to criticize
relativity...

--
Umberto Bartocci
Dipartimento di Matematica
Universita' di Perugia
06100 - Italy
http://www.dipmat.unipg.it/~bartocci
 
 

________________________________________________________
 
 

Subject: Re: Come si deve fare la matematica - Addendum
             [How Mathematics Should be Done - Addendum]
Date: Sat, 01 Sep 2001 09:19:45 +0200
From: umberto bartocci <bartocci@dipmat.unipg.it>
To: "Ardeshir Mehta, N.D." <ardeshirmehta@myself.com>
References: 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 , 9
 
 

Short addendum to my previous "final" comment...

Dear Mehta,

since I have understood from the correspondence between you
and Del Larson that our discussion is going to be made public
in Internet, it is perhaps better to add some "public remark" to
my last mail, in order to be even more clear.

Remark I - I could have explained better to "students" the
situation we were discussing, by using more simple words as
conclusion. But first let me sum up what I have said,
answering to your question. A buoy X is passing in front of a
spaceship, long L (proper length), from bow B to stern S, and
with some speed  v (spaceship and buoy are equipped with
Lorentz coordinates etc.). Here it is the "picture" in the
reference frame associated with the ship:

______________              <-------                       °
S                        B      vector velocity               X
    the spaceship                                    the buoy is "moving"
       "is still"

When B and X are one in front of the other, the clock of B marks
0 as the clock of X. When X is in front of S, the clock of X marks:

(1) L'/v = [L*sqr(1-v^2/c^2)]/v

while the clock of S (synchronized with the clock of B) marks
(quite OBVIOUSLY!):

(2) L/v .

Since (2) > (1) , one has indeed something "strange" from the
point of view of common sense. From aboard of the
spaceship, one must acknowledge that the clock of X is going
SLOWER, since it shows LESS time as it should have to.
This is called "time dilation". From the point of view of X, it
has needed less time in order to pass the spaceship, because
the spaceship was not long L , but less, namely  L' = L*sqr(1-
v^2/c^2) , and to pass a shorter spaceship obviously requires
less time. This is called "length contraction". In the previous
formulae (1) and (2) , and in their comparison  (2) > (1) , there
are simultaneously at work both time dilation and length
contraction.

Remark II - Since the situation is quite symmetric, according
to the theory of relativity, X must even "see" a time dilation
in the clocks aboard of the spaceship, exactly in the same
amount as before, that is to say it must see two different rate
of times connected by the ratio sqr(1-v^2/c^2) . This is more
difficult to be understood, but it can be done (see the Remark
3 in my previous message). Of course, there is no possibility
to notice an "inverse" symmetric length contraction, since one
has supposed the buoy to be "pointlike". If one introduces
even a (proper) length for the buoy, let us call it M , then the
situation is FULLY SYMMETRIC. With the necessary
specifications (see one of my previous mails), the formulae (1)
and (2) become:

(1a)  L'/v + M/v

(2a)  L/v + M'/v .

Remark III - There is no doubt that the relativistic description
of the "phenomenon" which Mr Mehta challenged to discuss
is exactly the previous one, and that THERE IS NO "logical
contradiction" at all in the relativistic treatment of spaces and
times. On the contrary, one has a great and still alive
discussion about the "physical interpretation" of the formulae
above. These contractions and dilations are in some sense
REAL, or they just depend on the assumptions introduced by
Einstein, and followers, in order to synchronize clocks (using
the II postulate of special relativity), to measure lengths of
moving objects, and so on? This is why some people talk of
"apparent phenomena", but I rather believe that in this case
relativity IS MAKING SOME PRECISE PHYSICAL
ASSERTION, which could be put to test (of course, from an
"ideal", if today not yet "practical", point of view). One way
of doing it, it is to use the famous "twin paradox": when an
inertial clock and another accelerated clock (in this case, NO
SYMMETRY AT ALL, Herbert Dingle famous "syllogism"
notwithstanding!) meet again, then, according to relativity, the
accelerated clock MUST show less time then the inertial one,
in the prescribed quantitative amount. Physicists claim that
this is so, after experiments made with particles in their
accelerators, but I think: first, that one could provide for
different interpretations (see for instance in Bartocci's website
the "cup-model" explained in point 4ter in the page
Foundations of Physics) of these observations, which I "must"
assume to be correct; second, that one could try to check the
whole matter MORE DIRECTLY. One famous trial is the
celebrated Hafele-Keating experiment, but it seems to meet the
strong criticism of Dr Kelly (see again in Bartocci's website
the point 18bis in the page Foundations of Physics).
Moreover, this experiment has to deal even with rather
complicated gravitational effects. For these reasons, I believe
that it would be convenient to perform this kind of
experimental tests, and it does not seem impossible to
imagine a Gedanken-Experiment with rotating clocks in some
Earth's laboratory. Supposing that the Earth's laboratory is
(with good approximation) an inertial one, it is rather funny to
observe that even some ether theory would foresee a
SLOWING DOWN of spinning "light-clocks", but with a
different ratio than the relativistic one, namely by (1 -
v^2/c^2) , with no square root in front of this term (this
would even imply that the well known modification in the
mean-life of particles WOULD NOT obey the same
quantitative law than the slowing down of light clocks!). So,
at least "in principle", all what we have said above is physics,
and not only mathematics (which of course cannot be
contradictory!).

[Remark IV (less important) - When I have said at the end of
my last mail that:

> the time elapsed for the buoy, L'/v, namely a "coordinate
> time" (which is even a proper time)...

I was not quite correct, since the words between parentheses
could give rise to some misunderstanding. As a matter of fact,
we were using in that case the formula connecting a proper
time (in the life of S), which was  L/v - T , with a coordinate
time, which was  L'/v  (computed as the difference of the two
"corresponding" times  L'/v and 0 , which were observed by
TWO DIFFERENT observers in the reference frame associated
with X ). So the fact that  L'/v  is even a proper time for X is
(obviously) true, but it is a useless, if not worst, remark, in
the context I was discussing...]
 
 

--
Umberto Bartocci
Dipartimento di Matematica
Universita' di Perugia
06100 - Italy
http://www.dipmat.unipg.it/~bartocci
 
 

_______________________________________________________
 
 

Subject: Re: Come si deve fare la matematica (reply in English)
             [How Mathematics Should be Done (reply in English)]

Date: Thu, 13 Sep 2001 23:36:10 -0400
From: "Ardeshir Mehta, N.D." <ardeshirmehta@myself.com>
To: umberto bartocci <bartocci@dipmat.unipg.it>
References: 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 , 9 , 10
 
 

Caro Professore:
 
 

(I am separately sending you a copy of this e-mail translated
into Italian, because I think you have not understood properly
some important points in my preceding e-mails. I hope I
haven't made too many serious linguistic mistakes! Here is the
original e-mail in English.)

(Le spedisco in un altro e-mail una copia di questo e-mail
tradotto in italiano, perché penso che Lei non ha capito bene
dei punti importanti nei miei e-mails precedenti. Spero di non
aver fatto grandi sbagli linguistici! Le spedisco qui l'originale
di questo e-mail in inglese.)

Thank you very much for your two last replies, but I am sorry
to say that although I did indeed make what you call SMALL
mis- takes in my previous e-mail to you (with the subject line
"Come si deve fare la matematica"), I did not make any BIG
mistakes which can reduce my argument to zero.

On the contrary, it is YOU who did that! And I shall show
you hereunder just how your calculations result in
contradictions. (I have pointed out seven contradictions
hereunder, but essentially an infinite number of contradictions
can result from the fact that there is a fundamental
contradiction between the Lorentz transformation equations,
on the one hand, and on the other, the axioms of mathe-
matics and the propositions and postulates of Euclidean
geometry.)

And I am certainly willing to show what I have written to
other competent people well versed in logic, mathematics and
physics, and I am sure that if they actually read -- and
consequently, understand -- my arguments, they WILL
appreciate and agree with what I am saying. (Try Dr Al Kelly
of Ireland or Clarence Dulaney of Texas, or Mrs Gertrude
Walton of England -- an excellent mathematician if ever there
was one! -- or for that matter try my fellow- citizen of Ottawa,
Prof. Paul Marmet of the National Research Council of
Canada, who does not even agree with my philosophical
views on the nature of Reality! Indeed try ANYONE with an
open and clear mind. Maybe there are even people among your
own students or assistants who would be interested in our
discussion -- perhaps Dr. Macri'?)

And I am also exceedingly sorry to see that you say you "have
no more time for this kind of discussion." It smacks of what
the kind of remark the Church Cardinals might have made to
Galileo. People who think they already KNOW the truth, and
think they do not have to listen to any reason why they might
NOT know it, often say such things. But SEEKERS after the
truth -- as all scientists should be -- cannot say such things
and still claim to be seekers and scientists.

There is not -- and never has been, and probably never will be
-- ANY scientific  theory so completely true that it can
NEVER be refuted by an intelligence clever enough to find a
flaw in it! And I claim to have found just that in the Theory
of Relativity.

But to grasp my arguments you must first *read carefully and
digest thoroughly what I am saying*: which I am sorry to see
you continue to neglect doing. THIS IS THE MOST
IMPORTANT POINT IN ALL OUR DISCUSSIONS. Unless
it is resolved there can be no agreement between us, because
you will not GRASP what I am saying!

BUT FIRST OF ALL --

Let me see if *I* have understood YOU correctly. (It would be
wrong of me to point the finger while making the same
mistake you do!)

A-i.

You say that if the spaceship is supposed to be MOVING,
while the buoy is NOT supposed to be moving, the stop
watch in the spaceship will record the time interval [E2 - E1]
as L/v  -- right?

A-ii.

You say that if the buoy is NOT supposed to be moving,
while the spaceship IS supposed to be moving, the stop watch
in the buoy will record the time interval [E2 - E1] as L'/v  --
right?

A-iii.

You say that if the spaceship is NOT supposed to be moving,
while the buoy IS supposed to be moving, the stop watch in
the spaceship will record the time interval [E2 -= E1] as L/v
-- right?

A-iv.

You say that if the buoy is supposed to be MOVING, while
the spaceship is NOT supposed to be moving, the stop watch
in the buoy will record the time interval [E2 - E1] as L'/v  --
right?

Have I understood your answers correctly?

A-v.

If so, then you would have to be saying, when comparing A-i
to A-iii, that the stop watch in the spaceship will show the
SAME reading whether it is supposed to be moving or not!

(Note that the interval [E2 - E1] is the SAME interval in both
A-i and A-iii. If they were not the same, it WOULD be
possible to tell when the spaceship was moving and when it
wasn't!)

But A-v contradicts the Theory of Relativity, according to
which a stop watch which is MOVING must run slower than
the SAME stop watch when it is STATIONARY!
(Remember, we are speaking here about the very SAME stop
watch measuring the SAME time interval.)

This proves that your answer, if I have understood it correctly,
contradicts the Theory of Relativity.
 
 

[I] -- THIS IS THE FIRST CONTRADICTION WHICH
RESULTS FROM YOUR CALCULATIONS.
 
 

Or else, if you say I do not understand the Theory of
Relativity, please explain how, according to the Theory of
Relativity, a stop watch which is carried in a MOVING object
can run at the SAME rate as the SAME stop watch carried in
the SAME object when the latter is STATIONARY?
Specifically, if that is so, where would be the length
contraction and the time dilation that should take place for a
moving object, and for any clock or stop watch in such an
object, in comparison for the SAME object -- and for its clock
or stop watch -- when said object is NOT in motion?

For example, let's say the spaceship and the buoy are both
equipped with powerful rocket engines, capable of accelerating
and decelerating each of them to speeds of +v or - v. Let's say
the reading of the stop watch in the spaceship which given in
A-i is measured when the buoy passes the spaceship, the buoy
during this pass travelling along the x axis in the positive
direction at velocity v. Then let's say the buoy is caused to
decelerate, using its rocket engine, to the same speed as the
spaceship, so that they are now motionless relative to one
another: and at this point the engine on the buoy is shut off.
Now let's say the spaceship fires ITS rocket engine,
accelerating to speed v along the x axis in the positive
direction, at which speed ITS engine is shut off. So now it is
the spaceship which passes the buoy at speed v: and during
this pass, we obtain the reading of the stop watch in the space-
ship given in A-iii. Both the readings, according to your
calculations, must be the same: namely, L/v. SO WHERE IS
THE TIME DILATION WHICH OUGHT TO BE PRESENT,
ACCORDING TO THE THEORY OF RELATIVITY FOR
THE SPACE- SHIP'S STOP WATCH IN A-iii?

If you say that the length contraction and the time dilation of
the spaceship and of its stop watch can only be observed by a
hypo- thetical observer on the buoy, but never by a
hypothetical obser- ver on board the spaceship itself, then the
length contraction and the time dilation must exist merely *in
appearance* and not in *reality*.

Right?

But if that is the case, the Theory of Relativity must be
dealing only with *appearances*, and not with *reality*!

If THAT is what you are saying, then I am in complete
AGREEMENT with you.

But in that case the Theory of Relativity cannot be a truly
*physi- cal* theory, which must deal with *reality* and not
mere *appear- ances*! (Perhaps it would be more correct to
say, in that case, that the Theory of Relativity is a
PSYCHOLOGICAL theory  :-)  ... !

(See also below, wherein I show that this is indeed the case.)

NOW NEXT --

Let me get MY few small mistakes in my previous e-mail out
of the way.

B.

I admit that I made a careless mistake in [4], in which I wrote:

> [4] The Lorentz time dilation formula is
> <delta>t' = <delta>t*(sqrt.(1-v^2/c^2))^-1.

I should have written instead:

> [4] The Lorentz time dilation formula is
> <delta>t' = <delta>t*(sqrt.(1-v^2/c^2)).

(See equations 11.5 and 11.6 given at the following Web
Page: <http://theory.uwinnipeg.ca/mod_tech/node135.html>.
Note that this Web page is part of a Physics Course written by
Dr. Randy Kobes and Prof. Gabor Kunstatter of the Physics
Department, University of Winnipeg, Canada, in September,
1999 -- in other words, a course given by a professor much
like your good self, and his assistant!)

But as you see from my e-mail, I CORRECTED this mistake
in the first part of my [13] *et seq.*: so my conclusion in [14]
and [16] IS correct!

Note also that THIS is the formula that is actually
RELEVANT to my argument, since if you read the text of the
Web article above, you will see that this formula refers to the
rate at which moving clocks tick at different rates. In my
Challenge I have only TWO stop watches, so if Relativity is
correct, the stationary stop watch must tick <gamma> times
faster than the moving stop watch!

Now I anticipate that you may claim that THIS formula is just
as wrong as the PREVIOUS one, because we can always
obtain a contradiction like the one you had already noted
earlier, in the following manner (I quote your own words,
with a small change):

> If this was true, then you would simply get
> immediately a contradiction like the following one:
>
> 1 - <delta>t' = <delta>t*(sqrt.(1-v^2/c^2))
>
> 2 - there is no difference whatsoever between t and t', Lorentz
> transformations have a group structure, the situation is SYM-
> METRIC, so one must have even:
>
> <delta>t = <delta>t'*(sqrt.(1-v^2/c^2))
>
> 3 - from 1 and 2 it follows for instance:
>
> <delta>t' = <delta>t'*(sqrt.(1-v^2/c^2))^2
>
> ...
>
> whence:
>
> (sqrt.(1-v^2/c^2)) = 1 which implies  v = 0 .
 
 

[II] -- THIS IS THE SECOND CONTRADICTION WHICH
          RESULTS FROM YOUR CALCULATIONS.
 
 

IT IS PRECISELY BECAUSE SUCH CONTRADICTIONS
ARE DERIVED that I claim that the Lorentz transformation
equations cannot be mathematically valid! (Note that the
Lorentz transformation equations can only be constructed
using such equations as Eq. 11.5 and 11.6 of the above-
mentioned Web page, which as you rightly point out above,
result in mathematical contradictions.)

C.

I also made another careless mistake in saying at [5]:

> [5] The Lorentz length contraction formula is
<delta>x' = <delta>x*(sqrt.(1-v^2/c^2))^-1.

I should instead have written:

> [5] The Lorentz length contraction formula is
<delta>x' = <delta>x*(sqrt.(1-v^2/c^2)).

(See equation 11.7 at

    <http://theory.uwinnipeg.ca/mod_tech/node136.html>.)

And I made a similar careless mistake in [9] -- which you
have already pointed out -- wherein I mistakenly wrote:

> [9] According to the Lorentz length contraction formula, in the
> co-ordinate system associated with the buoy, the length of the
> spaceship will not be L but L', where L' = L*(sqrt.(1-v^2/c^2))^-1.

But as you yourself noted, I CORRECTED both these
mistakes in [10] *et seq.* -- which AGAIN makes my
conclusion in [14] and [16] quite correct.

Note also that with THIS formula ALSO one can obtain a
contradiction such as:

> If this was true, then you would simply get
> immediately a contradiction like the following one:
>
> 1 - <delta>x' = <delta>x*(sqrt.(1-v^2/c^2))
>
> 2 - there is no difference whatsoever between x and x', Lorentz
> transformations have a group structure, the situation is SYM-
> METRIC, so one must have even:
>
> <delta>x = <delta>x'*(sqrt.(1-v^2/c^2))
>
> 3 - from 1 and 2 it follows for instance:
>
> <delta>x' = <delta>x'*(sqrt.(1-v^2/c^2))^2
>
> ...
>
> whence:
>
> (sqrt.(1-v^2/c^2)) = 1 which implies  v = 0 .

In any case, you surely cannot claim the equation <delta>x' =
<delta>x*(sqrt.(1-v^2/c^2)) to be wrong -- when written as "L'
= L*sqr(1-v^2/c^2)", as expressed in your e-mails -- because
you YOURSELF use this equation in calculating the length of
the spaceship as when it is in movement L' -- as opposed to
L !

So if you YOURSELF have used the above equation to
calculate the length of the spaceship when in movement, how
is it that this very equation can give a contradiction such as
the one described above?

Either you yourself must have used an equation, namely "L' =
L*sqr(1-v^2/c^2)", in your calculation of the contracted length
of the spaceship, which you must claim is wrong; or else if
you claim it is RIGHT, then your own words (as slightly
changed above for the sake of the context) prove that such an
equation results in a mathematical contradiction!
 
 

[III] -- THIS IS THE THIRD CONTRADICTION WHICH
           RESULTS FROM YOUR CALCULATIONS.
 
 

SURELY NOW YOU MUST ADMIT THAT YOUR OWN
EQUATION CONTRADICTS MATHEMATICS AS WE
HUMAN BEINGS KNOW IT!

And if again you say that the length contraction of the
spaceship can only be observed by a hypothetical observer on
the buoy, but never by a hypothetical observer on board the
spaceship itself, then the length contraction must be merely
*apparent* and not *real*.

And if that is the case, then again, as I said, the Theory of
Relativity must be dealing only with *appearances*, and not
*reality*!

And in that case, as I said earlier,  the Theory of Relativity
cannot be a truly *physical* theory, which must deal with
*reality* and not mere *appearances*!

D.

I did NOT make a mistake -- careless or otherwise! -- in the
FIRST part of [13], as you imply in the following words of
yours (in which you also quote my [13] for ease of reference):
On the contrary, it is YOU who made the mistake!

Note that I had written:

> > [13] Using the Lorentz time dilation formula, we calculate
> > that E2will occur in the co-ordinate system associated with
> > the spaceship at t'2 = t2*[<gamma>^-1]. (Note: The same
> > result is attained if we use the Lorentz transformation
> > equation t' = (t - vx/c^2)/(sqrt.(1-v^2/c^2)),since at E2,
> > x is zero, and thus vx/c^2 is also zero.)

To which you had replied:

> - This is WRONG. True that x = 0, but if you make the
> computation:
>
> t'2 = t2/sqr(1-v^2/c^2) ,
>
> by using the formula which you write above in your point
> 10, which I said is correct, then you get
>
> t'2 = (L'/v)/sqr (1-v^2/c^2) = (L*sqr(1-v^2/c^2)/v)/sqr(1-v^2/c^2)
> = L/v
>
> (as I already wrote to you in my previous mail!)
>
> which implies:
>
> t'2 = t2*gamma [and not gamma^-1!!]

Here -- look carefully, now! -- it is YOU who made a mistake!

For on the one hand you say that (i) t'2 = t2/sqr(1-v^2/c^2) --
which is ESSENTIALLY THE SAME as my ORIGINAL [4] --
is WRONG (and which I ADMIT is wrong), and yet (ii) you
make USE of my WRONG original [4] to arrive at YOUR
answer "t'2 = t2*gamma [and not gamma^-1!!]"!

How then can your answer NOT be wrong?

YOUR OWN WORDS prove that YOU MUST BE WRONG
in what you have written above, and that I was actually RIGHT
in the FIRST part of my [13] !
 
 

[IV] -- THIS IS THE FOURTH CONTRADICTION WHICH
           RESULTS FROM YOUR CALCULATIONS.
 
 

E.

I DID make a somewhat more serious, but still not fatal,
mistake in the SECOND part of [13], which I quote once
again in full for ease of reference:

> [13] Using the Lorentz time dilation formula, we calculate that
> E2 will occur in the co-ordinate system associated with the
> spaceship at t'2 = t2*[<gamma>^-1]. (Note: The same result is
> attained if we use the Lorentz transformation equation
> t' = (t - vx/c^2)/(sqrt.(1-v^2/c^2)),since at E2, x is zero, and
> thus vx/c^2 is also zero.)

The SECOND part, between the parentheses after the word
"(Note: ...)", does not agree with the FIRST part. I made a
mistake in saying that it does.

But the important question is, WHY does the second part of
[13] not agree with the first part of [13], which is based on my
COR- RECTED [4], and which in turn is based on Equations
11.5 and 11.6 of the above-noted Web site, and which in *its*
turn is based on a simple *Gedankenexperimente* conducted
on the postulate of the constancy of the speed of light?

For it is to be noted that if the result obtained by ME using
my corrected [4] -- which is based on equations 11.5 and 11.6
of the above-noted Web site -- is *different* from the result
obtained by YOU using the Lorentz transformation equation
for time, then there must be a CONTRADICTION between
the Lorentz trans- formation equation for time on the one
hand, and the postulate of the constancy of the speed of light,
on the other!

But how can that be, if the Lorentz transformation equations
are THEMSELVES obtained by using the postulate of the
constancy of the speed of light?

The answer is to be found in YOUR mistake -- and this is the
BIG one, which reduces the value of your ENTIRE argument
to zero! -- namely, to consider the so-called "proper" time as
being the time RECORDED by the two stop watches -- the
one on the buoy and the one at the mid-point of the spaceship.
THIS IS JUST NOT THE CASE.

(Remember I had written earlier that I had NOT asked for any
such thing as "proper time" in my Challenge? I think it is fair
to say -- and I am sure you would agree! -- that anyone who
does not actu- ally READ my Challenge before ANSWERING
it will not have TRULY answered it at all!!)

I NEVER asked for "proper time", and your introducing this
notion into your answer is the source of your BIG mistake.

But if you INSIST on bringing the notion of "proper time"
into the argument, then please note that the DEFINITION of
"proper time" is as follows:

     "... the time which is measured by an observer who is
     present at the same location as the events which mark the
     beginning and the ending of the event. Another way to
     say this is that the proper time is measured in a reference
     frame in which the events occur at the same spatial point.
     ... Time intervals as measured by any other inertial
     observers are always greater than the proper time."

(See < http://aci.mta.ca/Courses/Physics/4701/EText/Proper.html>.
This is from Mount Allison University of New Brunswick, Canada .)

Now this term "proper time" is really the source of one HUGE
problem -- among several -- in the Special Theory of
Relativity. Even the TERM "proper time" is a misnomer: it
should instead be called "IMproper time". Because according
to this definition -- which I would call a very stupid
definition! --  a clock observed from a great distance would
not be ticking at a rate that indicates the "proper time" at all!

A clock observed from a great distance -- say, a gigantic clock
on the moon observed through a very powerful telescope on
earth -- does not *really* show a different time from an
identical clock on earth which is synchronised with the
former: it only *appears* to the earthly observer to show a
different time (ticking about two seconds slow compared to
the identical and synchronised clock on earth.) That is simply
because it takes light from the clock on the moon about two
seconds to each the earth, whereas it takes light almost no
time at all to reach the observer from the clock on earth!

But to grasp this, one has to truly understand what the term
"synchronised clocks" means. When two clocks are *really*
(or *actually*) synchronised, it means they are *actually* or
*really* displaying the same reading simultaneously. They do
not, however, always have to *appear* to be displaying the
same reading simultaneously! If the clocks are at different
distances from the observer, then the clock which is farther
away from the observer will *appear* to be displaying its time
with a delay compared to the display observed on the other
clock. And the magnitude of this delay will depend on the
difference in the distances of each of the clocks from the
observer

But that will only be an *apparent* difference in the two
displays, not a *real* one! It will be due to the TIME
DIFFERENCE THE SIGNAL TAKES TO REACH THE
OBSERVER FROM EACH CLOCK -- much like in the case
of lightning and thunder, which *appear* not to be
simultaneous, though everyone knows that they *are*, and
indeed MUST BE and cannot be otherwise.

Now the Lorentz transformation equations I had given at [6],
which I mistakenly applied in the second part of [13], are
obtained not ONLY by applying a *Gedankenexperimente* to
the postulate of the constancy of the speed of light, but ALSO
a second *Gedankenexperimente*: the one on which the
argument that "proper time" REALLY exists is based! This,
as I said, is Einstein's well-known "Train *Gedanken-
experimente*" regarding the lack of simultaneity of lightning
flashes for different inertial observers. The logic of this
*Gedankenexperimente*, when examined carefully,  can only
prove that the famous (or maybe we should say, infamous!)
"lack of simultaneity for different inertial observers" can only
*apparently* exist, and not *really*.

And why is this? It is because the two observers in this
*Gedankenexperimente* do not observe the lightning flashes
at the precise LOCATIONS at which they occur, but at a
DISTANCE from those locations!

And to arrive at the conclusion that the two observers do not
observe the lightning flashes simultaneously, Einstein forgets
to take into account the ACTUAL and CALCULABLE
difference in time it takes for the light from each flash to reach
each of the observers!

He pretends that since one of the two observers *perceives*
the lightning flashes simultaneously while the other does not,
that the flashes *are* in fact simultaneous for one observer and
not for the other. But that is absolute nonsense. It is almost as
bad as arguing that since we do not *perceive* the thunder at
the same time as we perceive the lightning, the lightning and
thunder are in *reality* not simultaneous. Just because light
travels much faster than sound doesn't mean that light takes
absolutely NO TIME AT ALL to travel from one location to
the other!

Indeed in the same *Gedankenexperimente* Einstein could
also argue -- and validly -- that the fellow on the platform
would hear the two THUNDERCLAPS simultaneously, while
the fellow on the train would hear them non-simultaneously!
And yet the difference in time between the two thunderclaps
for the fellow on the train would be GREATER than the
difference in time for the two lightning flashes! Would
Einstein be so stupid as to claim, as a result, that the
thunderclap from one side occurred *before* the lightning
flash that gave rise to it, and/or that the thunderclap from the
other end occurred *after* the lightning flash that gave rise to
IT?

No, of course, not. Any reasonable and realistic person would
argue that it was absolutely necessary, in order to know at pre-
cisely what instant in time the flashes and the thunderclaps
ACTUALLY occurred, to take into account NOT ONLY the
time at which each of them was *observed* to have occurred,
but ALSO the speeds of the signals -- whether light or sound -
- which conveyed the relevant information to the observer, as
well as the distances over which these signals had to travel!

(But of course Einstein was neither reasonable nor realistic, so
he actually *might* have argued that the thunderclaps occurred
at a time different from the lightning flashes that gave rise to
them ... ! ;-) And then we could have all had a huge laugh at
his expense, and at Relativity as well.)

The fact is that Einstein developed this half-baked idea in
order to remove what he called "the apparent" incompatibility
of the law of propagation of light with the principle of
relativity. It is not an *apparent* incompatibility at all, but a
very *real* one!

And as for Einstein's even more stupid remarks in Chapter
VIII of his well-known book "Relativity: The Special and
General Theory", viz.:

     After thinking the matter over for some time you then offer
     the following suggestion with which to test simultaneity.
     By measuring along the rails, the connecting line AB should
     be measured up and an observer placed at the mid-point M
     of the distance AB. This observer should be supplied with
     an arrangement (e.g. two mirrors inclined at 90 deg.) which
     allows him visually to observe both places A and B at the
     same time. If the observer perceives the two flashes of
     lightning at the same time, then they are simultaneous.

     I am very pleased with this suggestion, but for all that I
     cannot regard the matter as quite settled, because I feel
     constrained to raise the following objection: "Your defi-
     nition would certainly be right, if I only knew that the
     light by means of which the observer at M perceives the
     lightning flashes travels along the length A --> M with the
     same velocity as along the length B --> M. But an exami-
     nation of this supposition would only be possible if we
     already had at our disposal the means of measuring time.
     It would thus appear as though we were moving here in a
     logical circle."

... does Einstein forget that we have plenty of ways of
measuring time that have nothing to do with the speed of
light? What then are pendulums, tuning forks or caesium
atoms? The "examination of the proposal" he speaks of is
eminently possible! There is absolutely NO logical circle here
at all.

Besides, his entire objection in his second paragraph quoted
above deals with the speed of a LIGHT signal. But is it not
necessary to use a LIGHT signal in order to judge whether two
events occur simultaneously! One could use sound, or a
rolling ball-bearing ball, or any other signal whose speed -- or
even rate of change of speed over time or over distance -- is
unchanging and actually known with precision.

For instance, if the two lightning bolts were arranged to each
set a ball-bearing ball rolling down an inclined and polished
steel groove towards the observer, then by measuring the time
difference between the two times when the two balls arrive at
the observer, and if the rate at which they roll down their
respective inclined groove were also known with precision, the
observer could STILL make the necessary calculations to
judge whether the two lightning flashes *actually* occurred
simultaneously or not!

(Note also that in the above case the balls would not even be
rolling at the same speed throughout their trips! And neither
would they be required to both reach the observer at the same
instant in time, even if the two lightning flashes WERE in
fact simultaneous! All that would be needed would be to
know with precision how MUCH time it takes any GIVEN
ball to roll down any GIVEN length of any GIVEN groove.
And of course one should remember that this method would
not be too accurate, because the margin of error might be too
great to judge simultaneity any better than with optical means.
But it just illustrates that ANY signal may be used for the
purpose. A quite adequately accurate signal, as already
described in my previous e-mails, could be an electrical one in
a wire of known length. Of course NO signal would ever be
100% accurate, but that's beside the point: absolute accuracy
in judging simultaneity impossible even when events occur
right in front of the observer's nose!)

The whole problem lies in EINSTEIN'S definition of
simultaneity, namely "If the observer PERCEIVES the two
flashes of lightning at the same time, then they ARE
simultaneous." (His own words, no less!) This essentially
implies that "Perception IS Reality" -- which idea, when thus
expressed, does not even pass the laugh test, at least in
physics.

(Of course in ADVERTISING he is right: and Einstein,
though a lousy physicist and mathematician, was indeed a
great PR man and an advertising genius: witness his hairstyle,
which I have myself adopted, and which has made him
famous even among government bureaucrats, who haven't the
foggiest idea what he actually wrote!)

You see now: it is not *I* who do not understand
RELATIVITY well enough: rather it is *you* -- and Einstein
-- who do not under- stand REALITY well enough! (As I said,
you should have asked any competent engineer about this.)

And when Relativity contradicts Reality, it is Relativity that
must give way and not Reality! For Reality mocks, not just at
Relativity, but at ALL so-called "theories" which do not
conform to it!

So the difference between my [4] and the Lorentz
transformation equation for time is that the former is derived
ONLY from the postulate of the constancy of the speed of
light, while the latter is derived from BOTH, (i) the postulate
of the constancy of the speed of light AND (ii) the argument
used by Einstein in his above- mentioned "Train *Gedanken-
experimente*" to try and show that simultaneity at a distance
is impossible. (To see how the Lorentz transformation
equations is derived using not just one, but BOTH, of these
hypotheses, see the Web article entitled "Construction of the
Lorentz Transformation" which can be found at the URL
<http://origins.Colorado.EDU/~ajsh/sr/construction.html> .)

In my Challenge I have got RID of this nonsense of "proper
time" which is derived from the notion of "lack of
simultaneity-at-a- distance" -- and which in turn implies that
an *apparent* lack of simultaneity is in fact a *real* one. I
have done this by insisting that there be only ONE stop watch
in the spaceship (note again, this is not a "clock" but a *stop
watch*), placed exactly at the MID-POINT between the ends
of the spaceship. And I have insisted that the signals to start
and to stop the stop watch both travel from the relevant sensor
to the stop watch at the SAME speed (whatever that speed
may be) over the SAME distance (whatever that distance may
be) in the SAME Inertial Frame of Reference or IFR (once
again, whatever that IFR may be)!

So THIS stop watch does not measure the "proper time" of
ANYTHING! Instead it measures the *actual* time interval
between the events E1 and E2. The actual time interval
recorded by this stop watch is NOT the so-called "proper
time" at all.

As I already wrote in previous e-mails, this stop watch at the
mid- point of the spaceship measures the time interval with a
DELAY compared to the stop watch on board the buoy, for it
will take the signal indicating that E1 has occurred a FINITE
AMOUNT OF TIME (as measured in the Inertial Frame of
Reference -- or IFR -- of the spaceship) to reach the stop watch
from the bow. But since the signal that E2 has occurred will
also take the exact SAME amount of time (as measured in the
same IFR) to reach the stop watch from the stern, these two
delays will CANCEL EACH OTHER OUT!

So if -- to illustrate -- the speed of the signal (in the IFR of
the spaceship) is u, and the length it has to travel (again in the
IFR of the spaceship) is l, then the stop watch on board the
spaceship will START ticking with a delay of l/u compared
with the stop watch at X on the buoy. But the stop watch on
the spaceship will also STOP ticking with a delay of l/u
compared with the stop watch at X on board the buoy! So the
time INTERVAL which the two stop watches will record will
be the *real* or *actual* time interval which the spaceship
takes to pass the X marked on the buoy.

You STILL haven't grasped this ELEMENTARY point,
which I have repeated many times. You do not even
MENTION it in your replies! But THAT is where one of your
major mistakes lies. You apparently do not read, or give any
indication that you understand, my arguments.

Of course, if we use this method of measuring the time
interval [E2 - E1] in the system of co-ordinates associated
with the spaceship, my calculation given in the second part of
[13] is NOT correct, because the single stop watch at the mid-
point of the spaceship cannot be at E1 when it takes place, nor
can it be at E2 when IT takes place. Thus it cannot measure
the "proper time" of E1 *or* of E2. The second part of [13] is
a formula based on the notion of "proper time", and since
there IS no proper time in this case, this notion and this
formula is not applicable at all here.

(I DID make a mistake in thinking initially that it IS
applicable: I admit that. And it was a serious mistake. But
even so, it does NOT vitiate my conclusions in [14] and [16]!)

But as an alternative -- as you also note -- I could also have
per- formed the same calculation by putting two
SYNCHRONISED clocks (N.B.: this time, it is *not* stop
watches), one at the bow and the second at the stern. I would
arrange to have them photo- graphed automatically on two
different occasions: first, when the bow of the spaceship
passes the X marked on the buoy, a photo- graph would be
taken of the clock at the bow; and the second time, when the
stern of the spaceship passes the X marked on the buoy, a
photograph would be taken of the clock at the stern.
Subtracting the reading of the photograph of the stern clock
from that of the photograph of the bow clock will also give
the time interval exactly as calculated by me.

But before you even START to object, please, please, P L E
A S E note that to conduct such an experiment correctly, these
two clocks have got to be SYNCHRONISED. Since in your
e-mails YOU do not give a way to synchronise clocks which
are not moving relative to one another, I shall do so myself.
In order to synchronise such clocks, one sends a SIGNAL
whose speed is KNOWN from one clock to the other along a
distance whose length is KNOWN, and by dividing the latter
by the former, calculates the time interval it takes for the
signal to go from one clock to the other: and one ALLOWS
FOR THAT TIME INTERVAL WHEN SETTING THE TWO
CLOCKS!

For example, if from the stern of the spaceship one observes,
say through a telescope, the clock at the bow reading 0.00
seconds, the clock at the stern should be set to read at that
moment -(L/c) seconds! Then although a hypothetical observer
at the stern will not *observe* the two clocks ticking
simultaneously, they will in fact *actually* and *really* be
ticking simultaneously.

It is THAT simple. No need for Special Relativity at all!

(I have already written much of this in previous e-mails and
given several details from which the above can easily be
deduced, and so I won't repeat myself here any further: I have
already said more than enough.)

So you are COMPLETELY WRONG when you write in your
"FINAL REMARK 3":

> ...
> it [i.e., the clock at X in the buoy] does not know anything
> DIRECTLY  about the clock of the stern, which was SOME-
> WHERE ELSE. If this time, let us call T , was zero, then we
> would have got problems, but this time is not zero. ...

As a matter of fact the time which you have called "T" IS zero,
and there are     N O     P R O B L E M S  ! ! !

None WHATSOEVER. (If you can think of any, let me know!)
 
 

[V] -- SO THIS IS THE FIFTH CONTRADICTION. It results
          more from Einstein's thinking than from yours, but since you
          are supporting Einstein in the nonsensical  notion of "proper
          time", it is yours also.
 
 

But again, it is of course true that to a hypothetical observer at
X, for example, or at the bow of the spaceship, it will not
*appear* that the two clocks in the spaceship -- the one at the
bow and the one at the stern -- are synchronised with each
other at time t = 0.00. But that will only be an *apparent*
lack of synchronicity, because of the time it takes for the light
to reach the observer at the bow from the stern -- not a *real*
lack of synchronicity, any more than there is indeed a *real*
lack of synchronicity between thunder and lightning, even
though we see the lightning a short time before we hear the
thunder.

(Heck, I figured this out from the very first time I read
Einstein's argument, over forty years ago, when I was still in
my teens! I just didn't make an "waves" about it until now
because I always thought that Einstein, being a certified
genius, must surely have had some additional argument up his
sleeve to counter what I had figured out. Only this year, when
I made a serious effort to study the Theory of Relativity in
every single detail, did I find out that the genius did NOT
have any such argument!)

But note that a hypothetical observer at the MID-POINT of
the SPACESHIP will, if he uses a telescope and a simple
system of mirrors to see both clocks together, OBSERVE
them both as being synchronised -- though of course this
observation will take place with some DELAY from the
ACTUAL or REAL time that the ticks do take place.

F.

Indeed you have hit the nail on the head with your remark in
your "addendum":

> ... one has a great and still alive discussion about the "physical
> of interpretation"the formulae above. These contractions and dilations
> are in some sense REAL, or they just depend on the assumptions
> introduced by Einstein, and followers, in order to synchronize
> clocks (using the II postulate of special relativity), to measure
> lengths of moving objects ...

... but you are mistaken when you continue on by saying:

> but I rather believe that in this case relativity IS MAKING SOME
> PRECISE PHYSICAL ASSERTION ...

... which is wrong.

But I see that you are open-minded enough about it to say:

> ... which could be put to test (of course, from an "ideal", if today
> not yet "practical", point of view).

However, I would like to point out that there is ALREADY
today a physical test and a PROOF that Relativity is wrong
about this: namely the possibility -- which astronomers have
known since before Einstein was even born -- that the EXACT
POSITIONS of ALL the planets can ALL be calculated with
GREAT PRECISION: so great a precision indeed that we can
now even land spacecraft on a precise predetermined location
on Mars! This would be impossible if we could not calculate
just WHERE Mars would be at any given time as measured
on earth, EVEN THOUGH WE CANNOT OBSERVE
EITHER MARS OR OUR SPACECRAFT AT THAT
PRECISE TIME, namely the moment when they are
ACTUALLY at the location where they meet!

Therefore there must be the true or real simultaneity possible
ALL THROUGHOUT THE SOLAR SYSTEM, even though
all the planets are separated by many light-minutes and even
light-hours.

So the fact that the Theory of Relativity is contradicted by
this very elementary fact is ALREADY a physical test
disproving it, which should satisfy your longing for a
PHYSICAL proof of the falsity of the Theory of Relativity.
 
 

[VI] -- SO THIS SIXTH CONTRADICTION CONTRADICTS
           THE NOTION OF "PROPER TIME", according to which
           the time which is measured by an observer who is NOT
           present at the same location as the events which mark the
           beginning and the ending of the event does NOT measure the
           "proper time".
 
 

And the fact that Special Relativity is MATHEMATICALLY
self-contradictory is proven by my arguments in my previous
e- mails, and also above.

G.

And if anyone is interested enough to discuss my PHILOSO-
PHICAL argument against the postulate of the constancy of
the speed of light regardless of the speed of the source of the
light or of the observer thereof, I can also do that: namely that
such a postulate cannot be part of mathematics and geometry
as we know them, since it contradicts the Galilean
transformations which *are* a part of mathematics and
geometry as we know them, and since mathematics -- and
geometry -- cannot be self-contradictory. (I see that you have
avoided mentioning anything against THIS argument of mine
in any of your e-mails, though I consider it to be even
stronger than my "Challenge" as an argument against Special
Relativity.)
 
 

[VII] -- AND THIS IS THE SEVENTH CONTRADICTION:
             BETWEEN THE AXIOMS AND THEOREMS OF
             MATHEMATICS AND THE LORENTZ
             TRANSFORMATIONS.
 
 

Now it is up to you, of course, whether you wish to reply to
this e-mail or not: but I for one am so confident that I am
right and you are wrong, that I am willing to put all of our e-
mail correspondence regarding Relativity on the Web, so that
any persons with competence in the fields of physics, logic
and mathematics -- in ALL of these fields, of course, not in
just one or two of them -- who might find themselves reading
our correspondence can judge who is right and who is wrong!

But in closing let me assure you that I remain always your
friend in our search for a strong argument against Relativity.
The only difference between us is that I am pretty sure (not
100% sure, of course, but *almost* sure!) that I have FOUND
it, and anyone who actually reads and understands my
arguments will see that this is so; while you STILL do not
understand just HOW I have found it, and so you THINK I
have NOT found it!

So, in friendship, as always, I remain,

Yours
 
 

Ardeshir <http://homepage.mac.com/ardeshir/education.html>.
 
 

______________________________________________________
 

Subject: Re: Come si deve fare la matematica (Your reply in
             Italian, including errata, translated by me into English)
Date: Sat, 29 Sep 2001 16:33:40 -0400
From: "Ardeshir Mehta, N.D." <ardeshirmehta@myself.com>
To: umberto bartocci <bartocci@dipmat.unipg.it>
References: 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 , 9 , 10 , 11 , 12
 
 

Dear Mehta,

Here quickly is my reply to some of your claims.

> There is not -- and never has been, and probably never will be --
> ANY scientific  theory so completely true that it can NEVER be
> refuted by an intelligence clever enough to find a flaw in it! And I
> claim to have found just that in the Theory of Relativity.

NO!

>  But to grasp my arguments you must first *read carefully and
> digest thoroughly what I am saying*: which I am sorry to see you
> continue to neglect doing.

You surely know very well that there are thousands of people
who write thousands of pages, claiming that they contain
marvellous things capable of advancing knowledge, and claim
to be read by everyone, accusing others of treating them like
Galileo in case they are not! But before dedicating one's time
to the study of something one should have a fair hope that the
time will be well spent, OR ELSE ACCORDING TO YOU,
NO,  and one must read EVERYTHING that arrives?
(extravagant arguments regarding perpetual motion,
demonstration that the Greek "pi" is a rational number, etc.).
There are in fact some of my colleagues who after having read
some lines such as these throw them into the trash-can right
away (one must also admit that there are competent persons
who write nonsense, but a competent person can tell that
quickly), or do not even take them up in hand. I instead read
you in general with great attention, but NOT INFINITE. I
have already told you frankly that I think that you, as a
student, should be "failed" for what you have written, but
naturally you may refute my judgement in this case, even if it
does harm, and it would be better to study further certain
questions before asserting that scientists commit the errors
you accuse them of committing. Incidentally, I have read at
your site the material concerning Cantor's Theorem on the
denumerability of real numbers, but it is possible that no one
has ever told you that what you have written in this case is
without any sense, even worse than what you have sent me
concerning Relativity? You can try sending these reflections to
ANY mathematician in the world and see what he replies. You
write in fact a natural number with an INFINITE number of
digits!

>  Now consider the natural number X = x1x2x3x4x5 ... xk ... ,
> where x1 is any digit other than d11; x2 is different from d22;
> x3is not equal to d33; x4 is not d44; and so on. Now, X is
> a natural number, so it should be in our list. But where is it?

- Obviously your X is NOT a natural number - it is not even
any number!, and you should address to yourself your
conclusion that: "One wonders where their authors' and
editors' heads are at!"

Returning to the preceding discussion, though it is true that
one risks in some cases ignoring, or persecuting in certain
cases, a person such as Galileo, it is also necessary to defend
oneself from those who make so many errors and do not wish
to admit them, do not wish to recognise them with an
incredible and presumptuous obstinacy. Or are you not in
agreement with my words? What other attitude would it
suggest to a professor in front of students who SHOULD be
failed?

Now I come without further delay to the subject of Relativity,
saying once again that you obviously are mistaken in all your
considerations, despite having some merit in having
understood that there is something that does not seem right.
But we are dealing with a problem much more complicated
than you think, which can be confronted only from an
experimental point of view, not logical and mathematical, a
problem which can be quickly solved with a very simple
argument, but all the same INVALID,  and which as a result
does nothing but increase the strength of the Relativists, who
have good reason to say: See, those who are not in agreement
with us are not only not those who do not understand science,
and make huge errors ...

> Let me see if *I* have understood YOU correctly. (It would
be wrong > of me to point the finger while making the same
mistake you do!)

In all that follows you report correctly enough what I have
indicated should be the right result, but you seem not to
understand that all the expressions you use, such as " if the
spaceship is supposed to be MOVING", have no exact
meaning. They have meaning only to introduce special co-
ordinate systems, in which certain objects can be in motion or
not, but these co-ordinate systems are only AUXILIARY,  for
the purposes of being able to perform the calculations better. If
the calculations are performed in ONE system, one knows that
the result obtained must be the same in ALL systems, I could
for example use a SINGLE system in which BOTH bodies,
the spaceship and the buoy, ARE MOVING, and all the same
I would get the same result. When the clock is in the rear (the
poop), of the spaceship, and the one on board the buoy are
next to one another, they indicate different times, to be exact,
the one in the spaceship L/v , the one on board the buoy L'/v ,
period, there cannot be any doubt, and it is quite obvious that
it is so.

The fact is that to you this conclusion still seems
contradictory to other things such as time dilation, but which
you know only imprecisely (a contradiction in a claim can be
revealed only along with other elements, the claim by itself
not enough), despite my preceding efforts to explain. In fact
you write:

> But A-v contradicts the Theory of Relativity, according to which
> a stop watch which is MOVING must run slower than the SAME
> stop watch when it is STATIONARY! (Remember, we are speak-
> ing here about the very SAME stop watch measuring the SAME
> time interval.)

And with these words you demonstrate once again that you
have not understood the Theory of Relativity, like thousands
of people like you. In Minkowski space-time a clock is neither
in movement nor is it not in movement: it "is", and that's all:
a clock is a geometrical CURVE of a particular type, which
can be a (geodesic) straight line or not, and the proper time is
nothing more than a certain "length" of this curve between two
of its points (events). The clock is in movement or not only
in respect to other clocks, in other curves, (it would be
different if one were to think for example of the ether, but that
would be quite another discussion.) But what can one do? I
cannot explain better than I have already done. I have already
told you that the preceding result demonstrates in an obvious
manner that time in the spaceship seems to go more slowly
relative to a clock situated in the buoy, because clearly L/v >
L'/v , and it is a little less easy to understand that, according
to the Theory of Relativity, without any contradiction, TIME
IN THE BUOY ALSO SEEMS TO GO MORE SLOWLY,
and by the same factor, relative to a clock in the spaceship!
The fact is that the preceding inequality is undoubtedly valid -
it is ONE only, and cannot be reversed - and does NOT mean
anything, because it is not necessary to see in ONE SINGLE
INSTANT that a clock indicates less than another to say that
this clock runs more quickly (I speak from the point of view
of the "poop" of the spaceship, which sees the clock in the
buoy indicating a lesser time than its own.) That clock
perhaps goes more slowly! The fact is that it is necessary to
calculate the DIFFERENCE between TWO different
INSTANTS , as I have demonstrated in my preceding e-mail
(which I can re- send to enable you to study it better), and one
finds that the spaceship also finds the clock in the buoy going
more slowly, as it must according to Einstein's Theory! (and
note that we are not speaking of EXPERIMENTS, but only of
a purely mathematical theory of space-time, whose fault, if
any, is to claim to describe "reality".) I can anticipate a less-
perspicacious student's doubt: How is it that in the first case,
that is to say in the conclusion that there is a time dilation in
the spaceship as seen from the buoy, we haven't spoken of the
these TWO instants which are necessary? But THE FACT IS
THAT we have spoken about it implicitly when we have
supposed that the clock in the buoy and the clock in the
FRONT (that is, the prow) of the spaceship indicated the same
time, for example zero, when they are next to one another, and
there you are, the whole "mystery" is explained to him who
succeeds in understanding it, or has the necessary humility to
exert himself to learn it ...

I wish to emphasise at this point in our correspondence (this
file dedicated to you has come to 156 pages) that you will
NOT  remain persuaded what I have said, even though perhaps
it is owing to some problems due to the language, and due to
the fact that writing continuously I could have made some
mistake or confused something. But on one point I would be
curious to get a non-scientific comment from you: WOULD
YOU ADMIT, OR WOULD YOU NOT, THAT IT IS RIGHT
FOR A PROFESSOR SOMETIMES TO FAIL SOMEONE?
(obviously one can always be mistaken.) Or do you think that
all should be promoted?

I hope you won't find my frankness offensive if I add sincerely
that I do not consider our discussion to be between peers, just
as I don't feel when I explain things to students (who can be
of any age, I am myself a student in many things) that the
discussion is between peers. In certain cases it is I who know
and the other who must learn, from me or from books, at least
up to a certain point, until it is demonstrated that they have
arrived at a peer level, or superior, and then can request
attention to suggest something of possible interest. This
discussion instead is NOT INTERESTING, except as an
didactic exercise for me, and as an eventual help for you to
learn and correct your evident errors, but it does not seem to
me that you are disposed to do that ...

Always in friendship, yours, UB

(If you wish, I can give you addresses of professors who are
certainly more expert in the matter than myself, to whom you
can address yourself to verify if they do not say the same
things I do: but you will have to write to them in extreme
synthesis, otherwise they will not read it ...)

Short Errata Corrige:

I had written:

> I have already told you that the preceding result demonstrates
> in obvious manner that time in the spaceship seems to go more
> slowly relative to a clock situated in the buoy, because clearly
> easy L/v > L'/v , and it is a little less to understand that,
> according to the Theory of Relativity, without any contradiction,
> TIME IN THE BUOY ALSO SEEMS TO GO MORE SLOWLY,
> and by the same factor, relative to a clock in the spaceship!

I should have written the opposite instead! L/v > L'/v
demonstrates in fact that the clock in the buoy seems to be
SLOWER with respect to THOSE in the spaceship, precisely
because L'/v is smaller, and that is to say less time has passed
in the buoy than in the spaceship, which is to say, for the
slower clock. Vice versa, it is more difficult to understand that
the clocks in the spaceship also seem to be slower than the
one in the buoy, DESPITE the fact that when the clock in the
poop of the spaceship encounters the one on board the buoy,
the one in the spaceship indicates MORE time than the one on
board the buoy (which would make one believe, as in fact you
say, that the clocks in the spaceship are FASTER than the one
on board the buoy) ...

I wish to emphasise the word "THOSE " (plural)! There have
to be in fact TWO distinct clocks in two distinct positions to
verify the phenomenon of which we speak, and your entire
"paradox" is in fact based on a sort of ASYMMETRY: in the
spaceship there are TWO clocks, while in the buoy there is
ONE only. If we leave things thus, then certainly the buoy
cannot experience the time dilation which takes place on the
spaceship, and the fact that it does not experience it does not
mean it doesn't take place!

Cordially as always, and excuse me for the mistake,

UB
 
 

_______________________________________________________
 
 
 

Subject: Re: Come si deve fare la matematica (reply in English)
             [How Mathematics Should be Done (reply in English)]
Date: Sat, 29 Sep 2001 16:10:09 -0400
From: "Ardeshir Mehta, N.D." <ardeshirmehta@myself.com>
To: umberto bartocci <bartocci@dipmat.unipg.it>
References: 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 , 9 , 10 , 11 , 12
 
 

Dear Professor:
 
 

I am making an effort to write concisely.

I.

As regards Galileo, etc.: as Bernard Shaw says, it is true that a
lot of people speak nonsense, but that doesn't mean that ALL
people speak nonsense. But to know who does and who
doesn't, one has to listen to them all!

(And besides, as you yourself say, one should always suspect
that even professors and so-called "experts" sometimes do
speak and write nonsense.)

I have already specified several contradictions in your
preceding words, to which you do not seem disposed to reply
to me. Well, okay -- but I cannot see how, in that case, you
can claim to know more than I do in this matter. (Perhaps you
do not know that in mathematics, not even ONE single
contradiction is permitted?)

Besides, I am not your STUDENT but your INTELLEC-
TUAL ADVERSARY -- a FRIENDLY adversary, of course,
but an adversary nevertheless. I have CHALLENGED you
intellectually: and in such a challenge, I have to exercise rather
forcefully my intellectual ability, and I must NOT accept
everything you say -- at least not unless you can PROVE what
you say.

(You do not seem to understand the difference between an
intellectual challenge and an instruction. In a challenge,
especially one which involves mathematics, if I contradict
myself, I'd have "failed" and you'd have won, while if you
contradict yourself, you would have "failed" and I'd have won!
This is what is called the "failure criterion" of the challenge.
And I have already pointed out several contradictions in your
words, so it is obvious that you have failed, at least
mathematically.)

Moreover, although you are certainly at liberty to IGNORE
my challenge, ignoring an intellectual challenge seems to me
to demonstrate a clear lack of intellectual courage!

In any case, if you think I have NOT won my challenge
already, we can ask the world community of rational people to
judge between us: as indicated by me before, we should
publish our entire correspondence on the Web! I am sure that
ANY rational person who actually reads and understands all
that I have written will agree that I am in the main right, and
that you have contradicted yourself. (I might have made one or
two small mistakes here and there, but they would not nullify
everything I have said.)

II.

Incidentally, as regards the idea of perpetual motion, which
you ridicule: your words made me smile. Every physicist
knows full well that there are MANY systems in existence
which are clearly in perpetual motion! In the microcosm some
of them are called "atoms". Aside from the obvious fact that
EVERY atom possesses electrons in perpetual motion, even
the atoms THEMSELVES  cannot CEASE  to be in perpetual
motion -- it is precisely because of this perpetual motion of
atoms that we cannot solidify Helium, even at a temperature
of absolute zero (i.e., at 0 degrees Kelvin)!

And if we are to speak of the macrocosm, the Universe itself
is a system in perpetual motion. Ever since the Universe
began (whether with a "Big Bang" or otherwise), everything in
it has been in motion, and will remain in motion till the very
end of time.

And this means that all these things will be moving for ALL
time -- i.e., in PERPETUAL motion!

It is in fact perpetual REST that is impossible, not perpetual
MOTION.

In any case, whoever finds arguments about perpetual motion
"extravagant" cannot be living in the real world!

III.

Also incidentally, as regards my critique of Cantor's theorem
at:

(<http://homepage.mac.com/ardeshir/ArgumentAgainstCantor.html>)

... you are mistaken when you say that I write "a natural
number with an INFINITE number of digits". Or to be more
accurate, you are mistaken in not specifying WHAT KIND of
infinity you are talking about: potential or completed.

You being a mathematician must surely know that according
to Aristotle's and Kant's arguments, there cannot be a
COMPLETED infinity, only a POTENTIAL one. It is
certainly true that a natural number cannot have a
COMPLETED  infinity of digits, for the simple reason that a
completed infinity cannot exist! But for the SAME reason,
neither can a real number possess a COMPLETED infinity of
digits. Both natural numbers AS WELL AS real numbers can
have only a POTENTIALLY  infinite number of digits.

If natural numbers can have only a POTENTIALLY infinite
number of digits, it is certainly possible to construct a table
using natural numbers, exactly in the same manner as Cantor
has constructed a table using real numbers!

As I wrote recently to Allan Gillis, who teaches mathematics
at the Faculty of Mathematics, Ryerson University, Toronto,
Canada (and who incidentally is in complete AGREEMENT
with me!):

     Essentially, Cantor tries to make his argument by confusing
     a POTENTIAL  infinity -- that is, an infinity according to which
     there can always be one digit more than the digits actually
     specified -- with a COMPLETED  infinity, that is to say one
     according to which all the infinite number of digits are actually
     SPECIFIED. As Aristotle and Kant pointed out, while the former
     is possible, the latter is impossible.

 As you can see, there ARE mathematicians who are in
agreement with me in this regard: in fact I am not even the
first person in the world to have described this argument
against Cantor's theorem, and I have already discussed my
article with several other people who know mathematics very
well -- and who know also that in mathematics it is not
permissible to have even one single contradiction, which you
don't seem to have understood. (Remember that you had
written: "You can try sending these reflections to ANY
mathematician in the world and see what he replies.")

IV.

Now regarding the Theory of Relativity: as I said, I see that
you do not wish to discuss some of the contradictions in your
previous e-mail, the ones which I have indicated in MY
previous e-mail by the numbers [II] to [VII].

Now in science as in mathematics, even a SINGLE
contradiction suffices to invalidate a mathematical theorem or
a scientific theory.

So if you do not reply to the contradictions which I have
pointed out, I must assume that you do not contest them.
(Certainly it is your right to NOT respond to my arguments --
but NOT TO RESPOND to an argument is certainly not the
same thing as REFUTING it!)

On the other hand if you do contest my above-mentioned
points, how can you deny all the contradictions I have pointed
out in them? I see no RATIONAL way for you to do that.

V.

As regards the ONLY point to which you HAVE responded,
you are mistaken once again. Note that you had written:

> A clock is not in movement or at rest, in Minkowski space-time: it
> "is", and that's all: a clock is a geometrical CURVE of a particular
> type, which can be a (geodesic) straight line or not, and the proper
> time is nothing other than a certain "length" of this curve between
> two of its points (events). The clock is in movement or not only
> in respect to other clocks ...

This is certainly FALSE, and in fact I believe you know so
too!

ANY Minkowski space-time can be represented by a
Minkowski diagram.

And in ANY Minkowski diagram one can ALWAYS
represent at least ONE object which is NOT in motion
according to that diagram. In such a diagram this object would
be represented by a VERTICAL STRAIGHT LINE -- i.e., a
line parallel to the time axis.

If after a period of time this SAME object were to be set in
motion, the line in the Minkowski diagram would not remain
parallel to the time axis any more!

A clock which is NOT in motion, and THE SAME CLOCK
when it is moving, can thus be represented in the SAME
Minkowski diagram: TWO diagrams are not needed.

Which proves without any doubt that it is NOT true, as you
claim, that "A clock is not in movement or at rest, in
Minkowski space-time" or a clock "is in movement or not
only in respect to other clocks" -- since in such a SINGLE
Minkowski diagram, there is ONLY one clock, which can be
EITHER in movement OR at rest ... and there ARE no other
clocks!

Nor can one argue that acceleration is not part of Special
Relativity, but only of General Relativity -- because
acceleration can be represented perfectly well in such a
Minkowski diagram in FLAT space-time. There is no NEED
for General Relativity here, which deals with CURVED space-
time.

You remember I had written:

     For example, let's say the spaceship and the buoy are both
     equipped with powerful rocket engines, capable of accelerating
     and decelerating each of them to speeds of +v or - v. Let's say the
     reading of the stop watch in the spaceship which is given in A-i is
     measured when the buoy passes the spaceship, the buoy during
     this pass travelling along the x axis in the positive direction at
     velocity v. Then let's say the buoy is caused to decelerate, using
     its rocket engine, to the same speed as the spaceship, so that they
     are now motionless relative to one another: and at this point the
     engine on the buoy is shut off. Now let's say the spaceship fires
     ITS rocket engine, accelerating to speed v along the x axis in the
     positive direction, at which speed ITS engine is shut off. So now
     it is the spaceship which passes the buoy at speed v: and during
     this pass, we obtain the reading of the stop watch in the space-
     ship given in A-iii. Both the readings, according to your calcula-
     tions, must be the same: namely, L/v.

Surely one cannot claim that according to the Theory of
Relativity, after having reached velocity v from its initial
velocity -- which was zero -- the stop watch in the spaceship
does NOT experience a time dilation!

Remember that Einstein himself writes in his book
"Relativity -- The Special and General Theory" (1920):

           As a consequence of its motion the clock
           goes more slowly than when at rest.

(Clearer and more unambiguous -- and briefer -- words cannot
be found! See paragraph 6 of Chapter XII of the above-
mentioned book).

Nor can you say that EINSTEIN himself, in the year 1920,
did not adequately understand the Theory of Relativity! (So
let's hear no more of this claim of yours made several times,
saying to me: "You do not understand Relativity well
enough", okay? If I don't, neither did Einstein.)

According to you, the stop watch in the spaceship would
indicate the interval [E2 - E1] as L/v equally when the
spaceship is stationary as when it is in motion at speed v ;
and according to Einstein's above-mentioned words, the
moving stop watch must go slower than when the stop watch
is stationary. (And what possible meaning can there be to the
phrase "goes slower" than that the clock indicates a lesser
reading for the same time interval, or for an equivalent time
interval?)

This means that:

(a) According to you, the stop watch in the spaceship must
indicate the interval [E2 - E1] when the spaceship is motion as
L/v -- and equally, it must indicate L/v also when the
spaceship is at rest. (We observe clearly that L/v = L/v .)

(b) But according to Einstein, in measuring the interval [E2 -
E1], the stop watch in the spaceship must indicate a time
period -- let us call it T' -- which is SMALLER than the time
period, which we may call T ,  indicated by it for an
equivalent interval when the spaceship is at rest. (We clearly
see that T > T' .)

But (a) and (b) CONTRADICT one another, even if either of
the time periods indicated, T or T' , equals L/v ! For if T =
L/v, then T' cannot equal L/v ; while if T' = L/v, then T
cannot equal L/v  -- for T is not equal to T' .

In that case, it is so very obvious that from a mathematical
point of view, one of you two -- yourself or Einstein -- must
be mistaken! (I can't understand how you cannot see this
utterly clear contradiction, which even a high school student
should be able to see.)

Moreover, it is unimportant in our discussion which of the
two of you is mistaken -- yourself or Einstein. If you are
mistaken there must be an error in the Lorentz
transformations, while if Einstein is mistaken there must be
an error in the Theory of Relativity!

So the rest of your argument cannot be valid, since we have
already found a contradiction in your above-quoted words.

VI.

As regards your TWO clocks in the spaceship, I have
ALREADY told you several times that it is not necessary to
have TWO  clocks: ONE stop watch, situated at the mid-point
of the spaceship, is quite enough to precisely measure the
interval [E2 - E1] !

(And as I had already said, if you don't believe me you can
consult an engineer.)

VII.

As regards the 156 pages of our correspondence: I do not
know how much effort YOU wish to dedicate to the pursuit of
the truth, but as for myself, I am willing to dedicate my
ENTIRE LIFE to it. The number of pages is altogether
irrelevant.

VIII.

As regards your following question:

> WOULD YOU ADMIT, OR NOT, THAT IT IS RIGHT  FOR A
> PROFESSOR SOMETIMES TO FAIL SOMEONE? (obviously
> one can always be mistaken.) Or do you think that all should
> be promoted?

... I would say that sometimes a professor himself can have failed
a test!

(What determines who fails or passes depends only on who
says what's true and who doesn't -- and not on who is a
professor or isn't. And what you say can't POSSIBLY be true,
because you keep on contradicting yourself -- or else you
contradict Einstein, as above!)

IX.

The rest of your e-mail doesn't seem to me to be relevant to
the present discussion. Even if you BELIEVE yourself to be
right it doesn't mean that you ARE. On the contrary, when
you make statements that result in clear contradictions, which
I point out, and you do not respond to the contradictions, it is
abundantly clear that you must be WRONG.

Rather than send my arguments in "extreme synthesis" to
those who are -- according to you -- "even more expert" than
you are, I'd rather publish our ENTIRE correspondence on the
Web, so that EVERYONE who is interested will be able to
read it, and moreover will be able to judge personally and
independently who between the two of us is right and who is
wrong! I think that even if students or colleagues of yours read
our correspondence they will be able to see that it is you who
are in error and not I.

For such publication purposes I have translated this e-mail, as
well as your preceding e-mail, into English (since most
scientists in the world read English.) I am sending you a copy
of the translation of your preceding e- mail for approval, so
that you can personally judge whether I have translated your
words correctly.

If anyone sends me comments on our e-mail I can forward
them to you, along with any reply I might send them, so that
you can see for yourself what the world is saying about your
intellectual position regarding the Theory of Relativity.

But let me assure you that our correspondence should be taken
-- and IS taken by me -- only as a LOGICAL and
INTELLECTUAL challenge, and not at all personal.

So I remain yours always in friendship,
 
 

Ardeshir <http://homepage.mac.com/ardeshir/education.html>.
 
 

_______________________________________________________
 
 
 

Subject: Re: Come si deve fare la matematica (reply in English)
             [How Mathematics Should be Done (reply in English)]
Date: Sun, 30 Sep 2001 10:49:33 +0200
From: umberto bartocci <bartocci@dipmat.unipg.it>
To: "Ardeshir Mehta, N.D." <ardeshirmehta@myself.com>
References: 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 , 9 , 10 , 11 , 12 , 13
 
 

Dear Mehta,

Your knowledge of Italian is indeed excellent,  and this
enables me to reply to you immediately, even if not as
exhaustively as you would have liked, but now I do not have
much time for correspondence, whether because tomorrow the
classes at the university begin, or whether because, as I already
explained to you, I sincerely consider the question completely
resolved.

I do not wish to hurt anyone's susceptibility, but I am
convinced that it is necessary always to note that "amicus
Plato sed magis amica veritas" ("Plato is a friend, but truth is
a greater friend"). When you write:

> Besides, I am not your STUDENT but your
> INTELLECTUAL ADVERSARY -- a FRIENDLY
> adversary, of course, but an adversary nevertheless. ...

I cannot be in agreement. It is obvious that you aren't one of
my students (otherwise I would have other duties with respect
to your challenges, seeking to better explain things, as much
as is possible*), but your level of knowledge of physics and
mathematics seems to me that of a student (or if you prefer, an
"amateur"), and as a result I cannot comport myself towards
you other than as a professor. It is not a question of age, when
I go to study music or Arabic I am at my age of 60 a student
in respect of the youngsters who teach me. I cannot in
frankness consider your challenge as one BETWEEN PEERS.

Other comments on your words:

> As regards Galileo, etc.: as Bernard Shaw says, it is true
> that a lot of people speak nonsense, but that doesn't mean that
> ALL people speak nonsense. But to know who does and who
> doesn't, one has to listen to them all!

- And I do listen to all (or almost), but one should also agree
that often/sometimes it is possible to become aware right
away when someone is speaking inappropriately of things that
he does not know at all, having not understood them well (I
maintain that even in respect to your observations on Cantor's
Theorem.) I always remember a colleague who teaches music,
who used to say that one could tell AFTER A FEW
SECONDS whether a person could play the piano well or not:
I find that this is true also in the field of science (taking into
consideration that we are talking of a high level, a university
level, of scientific knowledge, and not of simple chatting
between friends, even though it is true that at times even
professors can be in error.)

> (And besides, as you yourself say, one should always
> suspect that even professors and so-called "experts"
> sometimes do speak and write nonsense.)

Very true, but that does not mean that anyone who writes
nonsense is a professor!

> I have already specified several contradictions in your
> preceding words, to which you do not seem disposed to
> reply to me.

- Because there are no contradictions in my words, or at least I
am not convinced that you have revealed them, on a question
so simple, and completely understood, on which it is not
possible to add anything (I have never claimed to be
"original": I have only explained  things as they stand, as a
"good" professor should). Your comments are without
foundation and demonstrate that you do not understand certain
questions as you should (before desiring to speak of certain
levels): you have still to study a bit more, as Dr Larson has
invited you to do, and this is friendly advice, not an insult.

> (What determines who fails or passes depends only on who
> says what's true and who doesn't -- and not on who is a
> professor or isn't. And what you say can't POSSIBLY be
> true, because you keep on contradicting yourself -- or
> else you contradict Einstein, as above!)

- Here I am obviously completely in agreement with you! But
how can one get out of the dilemma of knowing who is right
and who is wrong? If the one who is wrong continues not to
admit it, and to exclaim stridently that he is being persecuted
like Galileo was, what can one do? I do not have a
prescription in that regard. As regards Einstein, I admit that I
do not know his writings well, nor have I ever claimed the
contrary (besides, as you well know, I do not like Einstein nor
his theory). I can SUPPOSE many things, that perhaps the
"great" scientist had not understood the consequences of his
theory, as undoubtedly have understood mathematicians such
as Hilbert, Minkowski, Weyl, etc. (remember that Hilbert said
that physics was too important to be left to the physicists, and
perhaps he was at least a little right!), or in certain writings
(certainly the "popular" ones, which could even be the ones he
himself wrote) his words can be interpreted in more than one
way, etc. Even if this is an interesting question, I personally
don't find it essential to dedicate my time to it (nowadays
even less so!) I think Relativity can be combated only in the
experimental field, and to this task I dedicate much (though
indeed not all, there are many other important things, I don't
know if you have had a chance to see my review "Episteme"
...) of my now scarce intellectual resources. You ought to
study Relativity from a modern well-written book, as for
example the book written by O'Neill which I cite several times
in my Site.

> In any case, if you think I have NOT won my challenge
> already, we can ask the world community of rational people to
> judge between us: as indicated by me before, we should
> publish our entire correspondence on the Web! I am sure that
> ANY rational person who actually reads and understands all
> that I have written will agree that I am in the main right, and
> that you have contradicted yourself. (I might have made one or
> two small mistakes here and there, but they would not nullify
> everything I have said.)

If you want to lose time in this manner I certainly cannot
prevent you. As far as I am concerned these are mere worthless
people who do not know things well: why don't you follow
my advice and turn to true experts in Relativity? Certainly
there may be a consensus on the part of those who do not
understand Relativity, I know people who have studied the
question for years together and yet do not succeed in
understanding the essence of the theory, and claim to refute it
with banal/simple pseudo-logical arguments. Unfortunately
such people are numerous, even among my own anti-
Relativistic friends -- but as usual, not everything they say is
in error, and from some of them one can understand, all the
same, many interesting things. Do therefore as you wish, I
shall be grateful if you would keep me informed of any
comments received as a result.

Always and in friendship,

yours UB,

* For example, I could add to what I have already said this
regard, that one should really be aware of a certain
ASYMMETRY in the example which you propose for
analysis, the one which according to you would put Relativity
into a crisis. When the spaceship and the buoy cross each
other, or shall we say also, as is more "usual", a train and a
passenger who is on the station platform, people who are on
the train (let's say two people, on in the front end of the train
and the other in the rear end) observe ONE SINGLE CLOCK -
the one of the passenger on the platform - during two different
events (spatially and temporally) and can thereupon decide
whether this clock goes slower or not comparing their TWO
DISTINCT observations. The gentleman who sees the train
passing in front of him, sees TWO DISTINCT CLOCKS, and
not one SINGLE one, during events which are temporally
distinct though not spatially. From this knowledge one
CANNOT deduce at all whether these clocks tick more slowly
or more rapidly: there is a need for him too to have a
"companion", who can furnish some further information on
these clocks!

--  Prof. Umberto Bartocci Dipartimento di Matematica -
Universita' Via Vanvitelli 06100 PERUGIA (ITALY)

http://www.dipmat.unipg.it/~bartocci
 
 

_________________________________________________
 
 

Subject: Re: Come si deve fare la matematica (reply in
English)
             [How Mathematics Should be Done (reply in English)]
Date: Sat, 06 Oct 2001 12:16:08 -0400
From: "Ardeshir Mehta, N.D." <ardeshirmehta@myself.com>
To: umberto bartocci <bartocci@dipmat.unipg.it>
References: 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 , 9 , 10 , 11 , 12 , 13 ,
14
 
 

Dear Professor:
 
 

I was indeed surprised to learn that, as you put it,

> there are no contradictions in my words, or at least I am
> not convinced that you have revealed them, on a question
> so simple, and completely understood, on which it is not
> possible to add anything ...

Is it really possible that you do not see your extraordinarily
simple contradictions -- which, as I had said, even a high
school student can see? (And I describe below only two of the
SEVERAL contra- dictions in your e-mails -- and note that
these are purely MATHEMATICAL contradictions, and have
nothing to do with ANY understanding of Relativity, whether
good or otherwise):
 

FIRST CONTRADICTION:

You said my formula [4] (in my e-mail dated August 30,
2001), namely:

     <delta>t' = <delta>t*(sqrt.(1-v^2/c^2))^-1

... is WRONG, and then you yourself USED the formula
t'2 = t2/sqrt.(1-v^2/c^2) -- which is essentially the SAME as
<delta>t*(sqrt.(1-v^2/c^2))^-1 -- to obtain your answer, as
follows:

t2 = L'/v (from my Point No. [10], which you said is correct)

...

t'2 = (L'/v)/sqrt.(1-v^2/c^2)
= (L*sqrt.(1-v^2/c^2)/v)/sqrt.(1-v^2/c^2)
= L/v

So you must have used a formula which according to you
yourself is wrong, in order to obtain your conclusion! How
then can your conclusion NOT be wrong?

(In this case you CLEARLY contradict yourself -- and that too
not just once but TWICE: see your e-mail of 31 August 2001,
and Section B as well as Section D in my e-mail of
September 13, 2001. In Section B in fact you contradict
yourself in a manner similar to what is written below):
 
 

SECOND CONTRADICTION.

You yourself have USED the formula L' = L*sqrt.(1-v^2/c^2)
-- see your e-mail dated August 19, 2001 -- but then you
imply (in your e-mail dated August 31) that if this formula
were correct, one could get a contradiction of the following
type (and I quote your own words, which were written in
English):

     1 - L' = L*sqrt.(1-v^2/c^2)
 
     2 - there is no difference whatsoever between L and L', Lorentz
     transformations have a group structure, the situation is
     SYMMETRIC, so one must have even:
 
     L = L'*sqrt.(1-v^2/c^2)
 
     3 - from 1 and 2 it follows for instance:
 
     L' = L'*sqrt.(1-v^2/c^2)^2
 
     whence:
 
     sqrt.(1-v^2/c^2) = 1 which implies  v = 0 .

(See Section C in my e-mail of 13 September 2001. In
Section B thereof you contradict yourself in a similar manner,
using t and t' instead of L and L'.)

This proves that the formula you have used in your e-mail of
August 19, namely

     L' = L*sqrt.(1-v^2/c^2)

... CANNOT be mathematically valid, because from it one can
arrive at a contradiction, as you yourself have pointed out
above!
 
 

You doubtless know that even ONE mathematical
contradiction suffices to completely negate the validity of the
entire mathematical theorem in which it appears.

The rest of your previous e-mail is irrelevant, having nothing
to do with contradictions, and therefore with the truth or
falsehood of your claims.

The above-mentioned contradictions in your e-mails -- even if
we do not speak of the others which I have pointed out in my
e-mail of September 13 -- suffice to prove to any independent
and impartial mathematician that you must be MATHE-
MATICALLY mistaken, and indeed quite REGARDLESS  of
any understanding the mathematician may or may not have of
the Theory of Relativity.

How can you possibly NOT see these contradictions? I am
truly surprised that you do not see them.

In friendship, as always,

Yours,
 

Ardeshir <http://homepage.mac.com/ardeshir/education.html>.
 

________________________________________________
 
 

Subject: Re: Come si deve fare la matematica (Reply in Italian)
             [How Mathematics Should be Done (reply in English)]
Date: Thu, 11 Oct 2001 19:51:01 +0200
From: umberto bartocci <bartocci@dipmat.unipg.it>
To: "Ardeshir Mehta, N.D." <ardeshirmehta@myself.com>
References: 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 , 9 , 10 , 11 , 12 , 13 , 14 , 15
 

Dear Mehta,

I thank you as always for your kind consideration, even if, as I
have told you, the lessons having started again, I do not have
much time to dedicate to correspondence. However I reply at
once, because it seems to me that it is possible to quickly
clarify an ambiguity in which you seem to me to have fallen.
You write in fact things such as the following:

>You have said that the formula ... is WRONG, and then you
> yourself have USED the formula ...

but the fact is that all these formulae have full significance or
are radically wrong depending on the meaning of the terms
with which one wishes to describe them. I had said for
example that it is wrong to claim, as you had done:

> [4] The Lorentz time dilation formula is
> <delta>t' = <delta>t*(sqrt.(1-v^2/c^2))^-1.
> [5] The Lorentz length contraction formula is
> <delta>x' = delta>x*(sqrt.(1-v^2/c^2))^-1.

where you had specified the meaning of the terms involved in
the following way:

> Let the primed co-ordinates in the calculations below be those
> pertaining to the spaceship, and let the un-primed co-ordinates be
> those pertaining to the buoy.

If these are the terms, the preceding formulae are WRONG, by
virtue of the absolute symmetry between the "primed" and
"un-primed" co-ordinates, to which in fact I had referred in the
following words:

- This is the major source of misunderstanding. If this was true,
then you would simply get immediately a contradiction like the
following one:

1 - <delta>t' = <delta>t*(sqrt.(1-v^2/c^2))^-1

2 - there is no difference whatsoever between t and t', Lorentz
transformations have a group structure, the situation is
SYMMETRIC, so one must have even:

<delta>t = <delta>t'*(sqrt.(1-v^2/c^2))^-1

3 - from 1 and 2 it follows for instance:

<delta>t' = <delta>t'*(sqrt.(1-v^2/c^2))^-2

[as a matter of fact, this is precisely what happens in your point 16]

whence:

(sqrt.(1-v^2/c^2))^-1 = 1 which implies v = 0 .

I HAVE SEEN THIS MISTAKE HUNDRED OF TIMES IN MY
LIFE...

I had done my best to explain to you what ought to be the
meaning given to the length contraction and time dilation
formulae:

- The true formulae, which one must "understand", are the
ones  which I gave to you in my last mail, namely:

A - (proper length of some object)*sqr(1-v^2/c^2) =
coordinate (or  "apparent") length of this same object in an
(inertial) reference  frame in which the object is moving with
speed v

B - proper time of some phenomenon IN THE LIFE OF ONE
OB- SERVER = sqr(1-v^2/c^2)*(coordinate time interval of
the same  event) [meaning as before]

You see, one can say that the formulae ARE THE SAME, but
it is necessary to pay close attention to how they are used:
there is NO connection between primed and un-primed co-
ordinates, which cannot be other than symmetric, but rather a
connection between proper and apparent measurements in the
above-specified sense. If one uses the formulae in this sense,
NO CONTRADICTIONS ARISE. Which is to say that, once
again (and I do not take any pleasure in this), I have to repeat
that you are wrong when you sustain that:

> How can you NOT see these contradictions? I am truly
> surprised that you do not see them.

I could say that it is I who am truly surprised that you do not
understand how one should treat space and time -- which are
"relative" -- in the Theory of Relativity: a manner which is
certainly not in consonance with common sense, but not
impossible to understand. Because instead of trying to find
contradictions, WHICH DO NOT EXIST, in my theory, why
don't you try to study and understand it well, so as to be able
to direct thereby your efforts to refute it which are effectively
refutable? (These aspects could be the EXPERIMENTAL
aspects: for example, if one could find an electromagnetic
phenomenon which does not satisfy Maxwell's equations, and
which are not Lorentz invariant, then Einstein's theory would
be in a crisis, but certainly not with INFANTILE mistakes -
and that is the correct word! - manipulations in your
fundamental conceptions ...)

I exchange friendly greetings, hoping that you can soon
understand the root of your errors, and overcome them once
and for all,

Yours, UB

-- Prof. Umberto Bartocci
Mathematics Department
University
Via Vanvitelli
06100 PERUGIA (ITALY)

http://www.dipmat.unipg.it/~bartocci
 
 

________________________________________________
 
 
 

Subject: Your Own Words Refute the Theory of Relativity!
Date: Fri, 19 Oct 2001 13:17:30 -0400
From: "Ardeshir Mehta, N.D." <ardeshirmehta@myself.com>
To: umberto bartocci <bartocci@dipmat.unipg.it>
References: 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 , 9 , 10 , 11 , 12 , 13 , 14 , 15 , 16
 
 

Dear Professor:
 
 

I just noted that YOUR OWN WORDS are sufficient to mathe-
matically refute the Theory of Relativity!

Note that the formulae which you said were "true" were as
follows:

> - The true formulae, which one must "understand", are the ones
> which I gave to you in my last mail, namely:
>
> A - (proper length of some object)*sqr(1-v^2/c^2)  = coordinate
> (or "apparent") length of this same object in an (inertial) reference
> frame in which the object is moving with speed v
>
> B - proper time of some phenomenon IN THE LIFE OF ONE OB-
> SERVER = sqr(1-v^2/c^2)*(coordinate time interval of the same
> event) [meaning as before]

I presume you mean by your sentence B above as follows (I
have replaced your words "meaning as before" by your EXACT
WORDS from your sentence A above):

> B - proper time interval of some phenomenon IN THE LIFE OF
> ONE OBSERVER = sqrt.(1-v^2/c^2)*(coordinate time interval of
> the same phenomenon) in an (inertial) reference frame in which
> another observer is moving with speed v

This completely and absolutely DISPROVES the so-called
Relativistic "loss of simultaneity between clocks moving rela-
tive to one another". You see:

[1] If two events -- let's call them F and G -- are SIMULTANE-
     OUS in the life of ONE observer, that means that according to
     THAT observer's clock, they occur at the SAME TIME.
     (After all, that is the very DEFINITION of the word "simul-
     taneity".)

[2] Let us call the times at which they occur, as indicated by that
     observer's clock, t(F) and t(G) : where t(F) = t(G) . Then obvi-
     ously [t(G) - t(F)] must be absolutely ZERO. In other words,
     the "proper" time interval between them in the life of THAT
     observer must be absolutely ZERO.

[3] And since in mathematics, zero multiplied by ANY number
     whatsoever -- even by [1/sqrt.(1-v^2/c^2)] -- is STILL zero,
     this means that the CO-ORDINATE time interval between
     events F and G in ANY other (inertial) reference frame in which
     ANY other observer is moving with ANY speed whatsoever
     must ALSO be absolutely zero!

[4] And this in turn means that if two the events F and G are si-
     multaneous in ONE (inertial) reference frame, they must be
     simultaneous in ALL (inertial) reference frames.

Thus if what you say is true, the famous Einsteinian argument
about the "loss of simultaneity" in reference frames moving
relative to one another must be MATHEMATICALLY IN-
CORRECT -- and in that case, ALL the other mathemati-
cal/logical arguments against the Special Theory of Relativity
become superfluous, be- cause as Einstein himself says in his
book *Relativity: The Special and General Theory* (1920):

     Now before the advent of the theory of relativity it had
     always tacitly been assumed in physics that the statement
     of time had an absolute significance, i.e. that it is inde-
     pendent of the state of motion of the body of reference.
     But we have just seen that this assumption is incompatible
     with the most natural definition of simultaneity; if we
     discard this assumption, then the conflict between the law
     of the propagation of light in vacuo and the principle of
     relativity (developed in Section VII) disappears.

But as we have seen above, the so-called "loss of simultaneity
for different inertial frames" argued by Einstein cannot be
logically valid.

Thus it is abundantly clear that time can no longer be
considered to be relative, but instead must be regarded as
absolute (for if simultaneity must be the same for ALL clocks,
wherever they may be and however they may be moving, then
one can always synchronise all the clocks in the universe with
a SINGLE clock situated, for example, at Greenwich in
England, using the method given by Einstein himself in his
above-quoted book.)

As a result, what Einstein calls above "the conflict between
the law of the propagation of light in vacuo and the principle
of relativity" does NOT disappear -- and this logical conflict
cannot be overcome.

So the rest of my present e-mail becomes, as I said,
superfluous; but if you want to see how one can still get
contradictions from your previous arguments, EVEN IF what
you said were true, you can find them below.

I hope you are happy now ... ? It should be clear now to all
who read the above that Relativity cannot be a mathematically
and logically sound theory. (And as I have already explained,
we are not dealing here with an understanding -- good or bad -
- of the Theory of Relativity, but only of mathematics and of
logic.)

I remain, as always, yours in friendship,
 
 

Ardeshir <http://homepage.mac.com/ardeshir/education.html>.
 

****************************************************

P.S.: Nor can one argue -- as do certain people, among them Dr
Tom Van Flandern -- that according to the Theory of Relativity
there can be NO simultaneity between two events if these events are
separated spatially. According to the above-mentioned book, the
Theory of Relativity claims no such thing. Quoting Einstein's own
words:

     Note 1. We suppose further that, when three events A, B
     and C take place in different places in such a manner that,
     if A is simultaneous with B, and B is simultaneous with C
     (simultaneous in the sense of the above definition), then the
     criterion for the simultaneity of the pair of events A, C is
     also satisfied.

Note the words "in different places".
 

****************************************************

To reveal the contradictions that arise in the Theory of Relativity
even if what you say is true, I repeat what you had written, for
ease of reference:

> - The true formulae, which one must "understand", are the ones
> which I gave to you in my last mail, namely:
>
> A - (proper length of some object)*sqr(1-v^2/c^2)  = coordinate
> (or "apparent") length of this same object in an (inertial) reference
> frame in which the object is moving with speed v
>
> B - proper time of some phenomenon IN THE LIFE OF ONE OB-
> SERVER = sqr(1-v^2/c^2)*(coordinate time interval of the same
> event) [meaning as before]

If this is correct, then if the symbols L and T represent the
proper length and time, respectively, and L' and T' the co-
ordinate length and time, then with respect to the spaceship
mentioned in my "Challenge", we can say that:

A - L*sqrt.(1-v^2/c^2) = L' < L ,

... and

B - T = T'*sqrt.(1-v^2/c^2) < T' .

Suppose now that in my "Challenge" there IS an observer on
board the spaceship and another on the buoy. The
"phenomenon" under consideration in my "Challenge" is, of
course, the spaceship passing the buoy: that is, as you had
written, the time interval (E2 - E1).

Now there are ONLY TWO POSSIBILITIES here, as follows:

I.

The proper time interval between E1 and E2 is the time
interval observed by the observer on the BUOY -- in which
case the co- ordinate time interval corresponding to that proper
time interval is the one observed by the observer on board the
spaceship;

... or

II.

The proper time interval between E1 and E2 is the time
interval observed by the observer on board the SPACESHIP --
in which case the co-ordinate time interval corresponding to
that proper time interval is the one observed by the observer
on the buoy.

Let us consider each of these in turn. Both of them will result
in contradictions -- though different ones.

I.

In the first case, if we claim that the proper time interval for
this phenomenon is the one observed by the hypothetical
observer on the buoy, and the co-ordinate time interval for the
same phenomenon is the one observed by the hypothetical
observer in the space- ship, then we get the following
contradiction.

Your B above can be now expressed as:

> B - proper time interval of the phenomenon of the spaceship
> passing the buoy IN THE LIFE OF THE OBSERVER ON
THE > BUOY = sqrt.(1-v^2/c^2)*(coordinate time interval of
the same > phenomenon) in the (inertial) reference frame of the
spaceship, in > which the buoy is moving with speed v .

This means that if the proper time interval of the phenomenon
of the spaceship passing the buoy in the life of the observer on
the buoy is T, then the co-ordinate time interval of the
phenomenon of the spaceship passing the buoy in the life of
the observer on the spaceship must be T', where T = sqrt.(1-
v^2/c^2)*T' .

And since sqrt.(1-v^2/c^2) < 1 , we get T < T' .

However:

(1) In the IRF of the buoy, the spaceship -- and its stop watch -- is
     moving with speed v.

(2) According to Relativity, if in any (inertial) reference frame --
     which we shall abbreviate as IRF -- a timepiece C[mov.] (of any
     nature) is moving with speed v , time passing in the timepiece
     C[mov.] must be dilated in comparison with time passing ac-
     cording to another timepiece C[stat.] which is NOT moving in
     that same IRF. (See also footnote 1.)

(3) Therefore according to Relativity, in the IRF of the buoy, any
     timepiece in the spaceship -- which spaceship, in the IRF of
     the buoy, is moving with speed v -- ought to experience its time
     dilated in comparison with any timepiece on board the buoy,
     which is NOT moving in the IRF of the buoy. (See also foot-
     note 2.)

(4) This means that for every unit of time -- say, for every nano-
     second -- indicated by a stop watch on the buoy, the stop
     watch on the spaceship must indicate LESS than one unit of
     time (so in the above example, the stop watch on the spaceship
     will indicate LESS than one nanosecond for every nanosecond
     indicated by the stop watch on the buoy.)

(5) This in turn means that if the stop watch on the buoy indicates
     a time interval equal to T nanoseconds for (E2 - E1), then the
     stop watch on the spaceship, which is moving in the IRF of the
     buoy, must indicate for (E2 - E1) a time interval of T' nanosec-
     onds, where T' < T .

(6) This contradicts your B above, according to which T < T' .
     (Note that this is a purely mathematical contradiction, and not
     a physical one.)

II.

On the other hand, if the proper time interval is the one observed
by an observer on the spaceship and the co-ordinate time interval is
the one observed by the observer on the buoy, then we get another
(and even simpler) contradiction, as follows:

1. The relative velocity between the spaceship and the buoy must
     be the SAME, regardless of which of the two above-mentioned
     observers calculates it.

2. Thus v = L/T = L'/T' .

3. By A above, L > L' .

4. So L/v > L'/v .

5. From 2, 3 and 4 above, we get T > T' .(See footnote 3.)

6. But according to your B above, T < T' , which contradicts 5
     above.

Either way -- whether by argument I above or by argument II above
-- we get a MATHEMATICAL contradiction: which proves that
the theory of Relativity must be MATHEMATICALLY self-
contradictory.
 

****************************************************
 

(Footnote 1):

Otherwise the postulate of the constancy of the speed of light
would be violated. For a theoretical proof of this, see for example:

     <http://www.btinternet.com/~j.doyle/SR/sr7/sr7.htm>.

Many other Web sites on Relativity argue in much the same way.

(Of course the argument must be WRONG, because the postulate
of the constancy of the velocity of light -- regardless of the velocity
of the source of light or of the observer -- is mathematically inad-
missible, since it contradicts the theorem of the addition of veloci-
ties which, being a THEOREM (that is, a mathematical statement
already possessing proof) may not be contradicted; but it cannot be
denied that this IS what Relativity TRIES to argue.)
 
 

(Footnote 2):

It cannot mathematically be argued that BOTH the following are
correct (although Relativity tries it also):

(i) In the IRF of the buoy, any clock in the spaceship -- which in
     the IRF of the buoy, is moving with speed v -- ought to have
     its time dilated in comparison with any clock on board the
     buoy, which is NOT moving in the IRF of the buoy;

... AND

(ii) In the IRF of the spaceship, any clock in the buoy -- which in
     the IRF of the spaceship, is moving with speed v -- ought to
     have ITS time dilated in comparison with any clock on board
     the spaceship, which is NOT moving in the IRF of the space-
     ship.

But that is mathematically impossible: for if (i) and (ii) above
were BOTH true, then by (i) above, ANY time interval of,
say, T(b) nanoseconds indicated by the stop watch on board
the buoy would correspond to a time interval of T(s) nano-
seconds indicated by a stop watch on board the spaceship,
where T(s) < T(b), while by (ii) above, ANY interval of T(b)
nanoseconds indicated by the stop watch on board the buoy
would correspond to a time interval of T(s) nanoseconds
indicated by a stop watch on board the spaceship -- but in this
case T(s) > T(b). So (i) above contradicts (ii) above.
 
 

(Footnote 3):

The calculation is simple:

     L/v = L/(L/T) > L'/v = L'/(L'/T')

So cancelling out the two L s on the left of the inequality sign and
the two L' s on its right, we get  T > T' .
 
 

______________________________________________________
 
 

Subject: Re: Your Own Words are Sufficient to Refute the Theory of Relativity!
Date: Sun, 21 Oct 2001 09:42:28 +0200
From: umberto bartocci <bartocci@dipmat.unipg.it>
To: "Ardeshir Mehta, N.D." <ardeshirmehta@myself.com>
References: 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 , 9 , 10 , 11 , 12 , 13 , 14 , 15 , 16 , 17
 

Dear Mehta,
 
 

Despite the fact that I have told you several times that I
sincerely  consider this discussion a MERE LOSS OF TIME,
I reply at once  in friendship because it is very easy to do so,
and basically you al- ready know the answer! In fact VAN
FLANDERN IS RIGHT ,   according to your words:

     Nor can one argue -- as do certain people, among them Dr
     Tom Van Flandern -- that according to the Theory of Relativity
     there can be NO simultaneity between two events if these events are
     separated spatially.

In fact this is the argument which one CAN MAKE, and
MUST  MAKE (properly explaining all the concepts), and
this resolves all  the usual mistakes made by beginners-
amateurs. In my opinion it is  not worth wasting time to see
if Einstein explained himself well or  not in one or another
place  (in reality it is much easier to explain  oneself badly, IT
MUST HAVE HAPPENED TO ME TOO IN  OUR
CORRESPONDENCE, because one speaks in a hurry, does
not lay out all the hypotheses, etc. as you say: "According to
...." I  don't know, but strictly speaking Relativity is not
what Einstein  has written, in different times in his life, and
which different "rigor"  depending on the readers he was
addressing, but rather  Minkowski's theory of space-time, and
every mathematician can  create it himself without "copying"
it off anyone.

Here is the complete explanation. If two events are NOT
separated  from a spatial point of view with respect to an
observer, and are  also not separated from a temporal point of
view with respect to  the same observer, then it IS THE
SAME EVENT, whether for  that observer or for any other, an
d is in effect one part, BUT  ONLY ONE PART, of your
following reasoning is correct, but  also obvious, and thus
useless.
 

[1] If two events -- let's call them F and G -- are SIMULTANE-
     OUS in the life of ONE observer, that means that according to
     THAT observer's clock, they occur at the SAME TIME.
     (After all, that is the very DEFINITION of the word "simul-
     taneity".)

- CORRECT, but it is well to understand what it means to
say "in  the life of an observer". In this case, the two events
which you  speak of are MORE THAN SIMULTANEOUS,
they are in fact  COINCIDENT, F = G . Thus everything that
follows is unimportant, superfluous! One should not confuse
simultaneity, which the  observer registers in the Relativistic
sense between events which  are NOT in his "life", and events
which are in his life, for which  simultaneity is in fact
coincidence.  To understand it better, would  you say that the
event that you read this e-mail there where you  are is an event
in MY life as an observer? NO, I can however try to  say that
this event is simultaneous with some other event in my  life,
or in the life of anyone else that I am "observing".
 

[2] Let us call the times at which they occur, as indicated by that
     observer's clock, t(F) and t(G) : where t(F) = t(G) . Then obvi-
     ously [t(G) - t(F)] must be absolutely ZERO. In other words,
     the "proper" time interval between them in the life of THAT
     observer must be absolutely ZERO.

- OBVIOUS.
 

[3] And since in mathematics, zero multiplied by ANY number
     whatsoever -- even by [1/sqrt.(1-v^2/c^2)] -- is STILL zero,
     this means that the CO-ORDINATE time interval between
     events F and G in ANY other (inertial) reference frame in which
     ANY other observer is moving with ANY speed whatsoever
     must ALSO be absolutely zero!

- OBVIOUS.
 

[4] And this in turn means that if two the events F and G are si-
     multaneous in ONE (inertial) reference frame, they must be
     simultaneous in ALL (inertial) reference frames.

- MISTAKEN. You forget that in the preceding point [1], the
two  events were supposed to have belonged to one single
observer,  were not any two events, which were "observed
from a distance"!  This is a FUNDAMENTAL
HYPOTHESIS, without which con- clusion [4] (which in the
correct hypothesis only means F = G ,  and not in general "F
is simultaneous with G", a circumstance  which is in general
quite "relative") mistaken.

I repeat, if you make the hypothesis that two events are NOT
spatially separated (or in other words, are spatially coincident))
for  a certain observer, they your conclusion would be correct,
because  if two events have a difference of proper time equal to
zero, then  they ARE THE SAME EVENT, and it is obvious
that if they are  the same event in an IFR, they must be the
same event in any  IFR.

The strange aspect of Relativistic time is not this, but is
instead  that two events SPATIALLY SEPARATED in an
IFR can have  the same temporal co-ordinate in that same IFR
(being that is to  say relatively "simultaneous") and not
having the same temporal  co-ordinate in another IFR (being
that is to say not simultaneous.)  That is to say, in
Minkowski space-time, simultaneity is relative to  a given
observer, and not "absolute", just as I imagine Einstein has
already well said, who has forgotten to explain the simple and
particular case of two events in the life of one single observer,
but I repeat that I don't think it very interesting to test if it
truly is or not, or whether in one sense yes and in another not.

I could add, for a "student", that it should not be forgotten
that an  "observer" is a special CURVE (a straight line in an
inertial case),  and that if two events are points on such a
special curve then they  are not any two events. If one does
not exert oneself to understand  these things one will never
understand Relativity, not even the  most simple, that is the
restricted. Given two events in Minkowski  space-time one
can calculate the ds^2 of the vector which joins  them, and it
makes a great difference whether the value one obtains  is
positive, negative or zero (for what follows I underline that I
am  using the so-called "geometrical unities", that is, c=1). If
two events  are separated and spatially separated in an IFR,
this ds^2 is  positive, and vice versa, in the sense that if ds^2
is positive then  there exists and IFR for which the two events
belong to a single  space of simultaneity (the square root of
this ds^2 expresses their  spatial distance, and is "relative").
On the other hand, if the two  events have a negative ds^2,
this means that there exists an IFR in  which they occur in the
same position, but in different times, calculated with respect
to an inertial observer who "lives" both of  them (in purely
geometrical terms, this observer is simply the  straight line
which joins them: if we take another observer who  "lives"
both of them, this time will be less, and this is the essence  of
the "twin paradox" which is asymmetric because in one case
we  have a straight line, aa geodesic, and in the other, no.)

Finally, I can ask once more, with a sincere spirit of
friendship:  why, instead of seeking stupid contradictions that
do not exist, do  you not seek to study/understand the theory
better? Basically it is  not difficult ...

Salutations, yours UB
 
 

-- Prof. Umberto Bartocci Dipartimento di Matematica - Universi-
ta' Via Vanvitelli 06100 PERUGIA (ITALY)

http://www.dipmat.unipg.it/~bartocci
 
 

_________________________________________________
 
 
 

Subject: If you wish, let us end this correspondence here
Date: Sat, 27 Oct 2001 15:43:06 -0400
From: "Ardeshir Mehta, N.D." <ardeshirmehta@myself.com>
To: umberto bartocci <bartocci@dipmat.unipg.it>
References: 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 , 9 , 10 , 11 , 12 , 13 , 14 , 15 , 16 , 17 , 18
 
 

Dear Professor,
 
 

If you wish to terminate this correspondence, believing it to
be a "mere waste of time" (as you put it), then let us end it
here, and let us publish it, as it stands up to and including
this e-mail, on the Web, so that anyone -- among them even
your own students and colleagues -- may judge who is right:
you or I.

And hereunder I explain your errors -- in a way which any
rational and well-educated person should be able to understand
-- one last time.

You claim that I do not understand Relativity, but I on the
contrary think that not only do I understand it, but I
understand it even better than you do yourself. What I do
understand, and what you do not, is that the "Minkowski
space-time" is ITSELF a concept which is in- valid from a
logical and mathematical point of view -- and the proof of that
is clearly laid out by me here in this e-mail.

Of course WITH the concept of Minkowski space-time one can
"explain" the twin paradox, and refute Dingle; but one cannot
prove that the VERY CONCEPT of Minkowski space-time is
a part of mathematics, because in order to FORMULATE this
concept, one must ADD an postulate to those of mathematics:
the additional postulate being that of the constancy of the
velocity of light! So Minkowski space-time ITSELF
CANNOT FORM A PART OF MATHEMATICS (as we
know it).

Try to formulate the concept of Minkowski space-time as a
series of mathematical theorems, WITHOUT the postulate of
the constancy of the velocity of light, and I am certain that
you will not be able to do so! But all the REST of
mathematics CAN be developed perfectly well using only the
axioms, propositions and postulates of mathematics itself:
namely, those of Peano, or those enunciated by Zermelo,
Fraenkel and John von Neumann, and the propositions and
postulates of Euclid (at least his first four postulates) -- that is
to say, WITHOUT the postulate of the constancy of the
velocity of light.

So that what YOU do not understand is what mathematics IS.
Mathematics -- including geometry -- is a series of theorems
obtained from a limited number of given axioms, propositions
and postulates, to which are applied a limited number of rules
of inference. And one cannot add to the existing axioms,
propositions or postulates another postulate, nor another rule
to the existing rules of inference, without going outside the
bounds of mathematics itself.

Therefore Minkowski space-time, and the Lorentz
transformation equations, formulated with the help of an
ADDITIONAL postulate to those of mathematics as we know
it, are only a kind of "pseudo- mathematics", and cannot be
part of the rest of mathematics known to humanity.

What I do not accept, therefore, is the FUNDAMENTAL
BASIS of what you accept uncritically: namely, the very
concept of Minkowski space-time. Besides, it results -- and
MUST result, due to the postulate of the constancy of the
velocity of light, which is illogical -- in contradictions ...
despite your efforts at explaining them away: for your
explanations only cause other contradictions to arise,
endlessly, for every one you succeed in explaining away. And
this is once again clear from what I have written below.

I remain always,

Yours in friendship,
 
 

Ardeshir <http://homepage.mac.com/ardeshir/education.html>.
 

*****************************************************
 

The proof that you are mistaken, and that I am right, is given
here below in the form of a *reductio ad absurdum* type of
proof.

Note that I have NEVER spoken of events which are NOT
separated spatially. One should not forget in fact that there
must ALWAYS be a distance -- and for that very reason, a
time interval -- between the occurrence of an event and the
observation of the same event: because of the distance, which
must exist, even if it be a very tiny one, between any event
and its observer. So that strictly speaking, absolutely NO
event is EVER observed at the exact SAME moment and at
the exact SAME location at which it occurs.

So that if you define "proper time" as the interval between two
events when observed at the EXACT LOCATION AT
WHICH THEY OCCUR, that itself is strictly speaking an
impossibility from a practical point of view. In fact strictly
speaking, EVERY time interval must be a "co-ordinate" one,
and can never be a "proper" one.

But there can always be two events at a distance from one
another, which are nevertheless simultaneous in the life of an
observer. It doesn't matter whether we call the (zero) interval
between them the "proper time" or not; what matters is that
the interval between them, according to THAT particular
observer, must be ZERO.

Then the interval between them must be zero ALSO according
to any OTHER observer. And the proof is as follows:

Let us suppose that the Theory of Relativity, and the concept
of "Minkowski space-time", are NOT mistaken.

Then it is obvious that:

1.  If two events F and G were to occur, according to any observer
     O , at a distance D from one another,

2.  and if the observer O , with a clock C in his hand, were to ob-
     serve the two events, the event F being at a distance d from O
     and the event G being at an equal distance d from O , so that
     the points O , F and G form, in the IRF of the observer O , an
     isosceles triangle, in such a manner that the line OF = d and the
     line GO also equals d , while the line FG = D ,

3.  and if the observer O were to observe the event F at a moment
     t(F) and the event G at a moment t(G) -- both moments indi-
     cated, of course, by his SINGLE clock C ,

4.  and if the moments t(G) and t(F) were THE SAME -- which is
     to say, according to the clock C in the hands of the observer O ,
     t(F) = t(G) = t ,

5.  then the OBSERVATION of the two events F and G must have
     been SIMULTANEOUS in the life of the observer O , because
     the observation of BOTH events must have occurred in his life at
     the SAME moment, i.e., at the precise moment t = t(F) = t(G) .

6.  But this is only the moment at which F and G are OBSERVED in
     the life of the observer O -- not the moment at which the events
     F and G OCCURRED in his life. The moment at which the event
     F OCCURRED would be T(F) , where clearly T(F) = [t-(d/c)] --
     and the moment at which the event G occurred must have been
     the moment T(G) , where clearly T(G) = [t-(d/c)] also: so that
     obviously T(F) = T(G) = T ... and so of course the moment
     T = [t-(d/c)] (according to the clock C ).

7.  And if the moments when F and G OCCURRED *in the life of
     the observer O* -- that is to say, according to his SINGLE
     clock C -- are T(F) and T(G) , when clearly T(F) = T(G) = T ,
     this means that the time interval between T(F) and T(G) ,
     which we may call <theta>, must, in the life of O , be absolutely
     ZERO.

8.  And this in turn means that *in the life of the observer O* --
     that is according to his single clock C -- the events F and G
     must certainly have been SIMULTANEOUS, but at the same
     time certainly NOT COINCIDENT (because of the distance
     D between them.)

9.  And additionally, according to the Lorentz transformation equa-
     tions, and according to my point No. 7 above, the time interval
     indicated by ANY other clock C' , which may even be in motion
     relative to the clock C -- which interval we may call <tau> -- for
     the occurrence of the events F and G must also be zero, because
     of the mathematical fact that zero multiplied by any other num-
     ber is still zero ... so that quite clearly <theta> = <tau> = zero.

10. And this means that in the life of ANY other observer O' --
     which is to say according to HIS clock C' -- who may even be
     moving relative to O , the events F and G must ALSO have
     occurred simultaneously.

And this completely refutes your statement:

> One should not confuse simultaneity, which the observer regis-
> ters in the Relativistic sense between events which are NOT in his
> "life", and events which are in his life, for which simultaneity is in
> fact coincidence.

As you can see above, the events F and G are
SIMULTANEOUS in the life of the observer O , but NOT
COINCIDENT (since they are separated by a distance D ,
which can be enormous: even many kilometres) -- and which
are also simultaneous in the life of any other observer O' ,
who may even be in motion relative to the observer O .

(Of course another observer might not actually OBSERVE the
events F and G simultaneously, unless he too happens to be
equi- distant from them at the moment when the observation
takes place; but the events themselves must nevertheless
OCCUR simultaneously for the observer O' as for the observer
O , because of the fact that the moment of the
OBSERVATION of an event can never be the same as the
moment of its OCCURRENCE.)

And the above-described conclusion, arrived at PURELY
LOGICALLY AND MATHEMATICALLY, completely
contradicts the notion of "Minkowski space-time" according to
which -- as you yourself have explained -- there can be
simultaneity between two (or more) events as indicated by a
clock in one particular IFR, and yet NOT according to a clock
which is in motion relative to the first-mentioned clock.

Thus it is clear that the very notion of "Minkowski space-
time" is contrary to logic and to mathematics, since it
contradicts a conclusion arrived at under the assumption that it
is NOT mistaken.

Q.E.D.
 
 

______________________________________________________
 
 

Subject:  Re: Se vuole, terminiamo questa corrispondenza qui
              [If you wish, let us end this correspondence here]
Date:  Sun, 28 Oct 2001 09:46:49 +0100
From:  umberto bartocci <bartocci@dipmat.unipg.it>
To:  "Ardeshir Mehta, N.D." <ardeshirmehta@myself.com>
References:  1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 , 9 , 10 , 11 , 12 , 13 , 14 ,
15 , 16 , 17 , 18 , 19
 

[TRANSLATED FROM THE ITALIAN BY ARDESHIR MEHTA]
 

Dear Mehta,

I thank you once again for your constant kindness and con-
sideration, but it is obvious that, despite all the good inten-
tions and education, I cannot change my opinion on that
which  I consider a fact, and that is, that your reasoning is
completely  erroneous, and demonstrates a lack of knowledge
of the fundamentals of Relativity. I have tried to help you a
little to  correct your numerous misunderstandings, but it is
clear that  at such a distance it is difficult to do so, and seeing
as how  I have not yet been able to convince you of anything,
it is  preferable to end the discussion here. The "story" which
you would recount if you were to succeed in convincing  the
world of claims such as "the concept of 'Minkowski  space-
time' is itself contrary to mathematics" (we are  looking at a
simple example of variety of Lorentzian geometry: to say that
it is "contrary to logic" is to say that  Euclidean geometry too
is contrary to logic).

The only thing that I can repeat, in all sincerity and
friendship, is the well-meaning suggestion Dr Larson has
already given you: "Please take the time to study and
understand relativity. I would suggest contacting your closest
quality university and seeking out a mentor. Once you
understand relativity I would hope that you could join the
battle against it. But fighting an intellectual battle without an
understanding of its underpinnings is simple folly".
 
 

Always very cordially,

from your UB

 -- Prof. Umberto Bartocci
Dipartimento di Matematica
- Universita'
Via Vanvitelli 06100
PERUGIA (ITALY)

http://www.dipmat.unipg.it/~bartocci

 
________________________________________________
 
 

Subject: Ho spiegato tutto nel mio ultimo articlo Web
          [I have explained everything in my latest Web article]
Date:  Sun, 11 Nov 2001 14:44:38 -0500
From:  "Ardeshir Mehta, N.D." <ardeshirmehta@myself.com>
References: 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 , 9 , 10 , 11 , 12 , 13 , 14 , 15 ,
16 , 17 , 18 , 19 , 20
 

[TRANSLATED FROM THE ITALIAN BY ARDESHIR MEHTA]
 

Dear Professor:
 
 

I see once more that you do not carefully read what I write.

In any case I have explained everything in my latest Web article,
entitled 'The "Mathematics" of Relativity, which can be found at:

     <http://homepage.mac.com/ardeshir/RelativityMath.html>

And our entire correspondence has now been published on the
Web at:

   <http://homepage.mac.com/ardeshir/BartocciComments.html>

Best wishes,
 
 

Ardeshir <http://homepage.mac.com/ardeshir/education.html>

************************************************************