Simultaneity in Special Relativity - 3

by

Ottawa, Canada

*Monday, November 12, 2001*

Relativity claims that if two events are simultaneous in an
inertial frame of reference, then they cannot be simultaneous
in *another* inertial frame of reference which is moving
uniformly and rectilinearly at a velocity **v** relative
to the first inertial frame of reference. But a simple
thought-experiment, as outlined below, is sufficient to refute
Relativity's claims in this regard.

Suppose Klingons and Vulcans do exist, and on their home
worlds -- which we shall assume are in high-speed relative
motion to each other, and to the Earth as well -- there are
clocks for measuring time, even though their units of time are
different from ours. So at the exact moment when our Master
Clock **C** at Greenwich, England, indicates a time
instant **t** for us today, the Klingon Master Clock,
which we shall call **K**, must surely indicate *some *unique
time in Klingon units. This time instant we shall call **k**.
And likewise, when it's time instant **t** for us by our
Master Clock at Greenwich, the Vulcan Master Clock, which we
shall call **V**, must indicate *some *unique time
in Vulcan units: and we shall call that time instant **v**.
So to us, the instant **t** indicated by our clock **C**
is simultaneous to the reading **k** by the Klingon clock
**K** ... which means that to the Klingons too, their
reading **k** on their clock **K** is simultaneous
with *our *reading of **t**. (Simultaneity, after
all, works in *both *directions -- *i.e.,* if for
us humans, an event **E-1** in our world is simultaneous
with an event **E-2** in the Klingon world, the two events
must also be simultaneous for the Klingons: which is to say,
basically, that the time interval between **E-1** and **E-2**
must be zero for both us and the Klingons, at least up to the
limits of the accuracy of the available measuring instruments
on each side ... for even if there *is *such a thing as
time dilation, zero dilated by any amount is still zero!)

And for the same reason, since to us, our reading of **t**
on our clock **C** is simultaneous with the reading **v**
on the Vulcan clock **V**, this means that to the Vulcans
too, *their *reading **v** on their clock **V**
must be simultaneous with *our *reading of **t** on
our clock **C**.

But then **v** and **k** must be simultaneous for the
Vulcans and the Klingons too; for if not, at least one of
these two readings would *not *be simultaneous with our
human reading **t**! That is, if for the Vulcans, say, the
interval between **v** and **k** were a non-zero
duration of time **T'**, then this **T'** would
correspond to a non-zero duration **T** by our clock **C**:
which contradicts the earlier statement we made that for us
Earthlings, the time interval between **v** and **t**
is zero, and so is the time interval between **k** and **t**
-- which means that the time interval **T**, for *us,*
between **k** and **v** must be zero. (Again, zero
dilated by any amount can only be *zero,* and can never
be non-zero.)

This proves that what's simultaneous for one must be simultaneous for all.

Any comments? e-mail me.