Logical Invalidity of Einstein's
"Train" Thought-Experiment

by

Ardeshir Mehta, N.D.

ardeshir@mac.com

First written in June 2001

Amended March 2002




Einstein's Train: A Thought-Experiment

Imagine an extremely high speed train moving in a straight line at an enormous speed with respect to the ground. Inside the train a lady stands in the centre of the train. Outside the train a lone man stands on a station platform, watching the train speed by. 

As the train passes the man, two lightning bolts strike either end of the train, leaving burn marks on the track and on the train's caboose and engine, and sending flashes of light into the train and along the platform. 

Let's assume that the man sees the lightning bolts strike the two ends of the train, and the tracks under them, simultaneously. Let's also assume that later the man measures the distance from where he was standing to each of the two burn marks on the track, and finds that the distances of each of two marks from where he was standing are exactly the same. 

The man, therefore, must conclude that the two flashes of lightning struck the track simultaneously. Since according to the Theory of Relativity we are postulating that the speed of light in all directions is a constant for all observers, and independent of the source or observer, the two flashes must take the exact same amount of time to travel the identical distances from each of the burn marks to where the man happened to be standing.

The passenger, however, must see things differently — or so argues Einstein. She is standing in the middle of the moving train. (Let's assume that afterwards she, too, measures the distance from where she was standing to the burn marks on the engine and caboose, and also finds them to be exactly equidistant from where she was standing.) The train however was moving towards the front flash of lighting and away from the rear flash. So after the lightning strikes, she first sees a flash of light from the front of the train then a bit later a flash of light from the back of the train. 

She must thereupon conclude that the engine was stuck by lightning before the caboose. 

This, in a nutshell, is Einstein's brilliant argument.
 
 

Einstein's Mistake: Think About It!

Hel-lo! Mr Genius! Aren't we forgetting something? If the speed of light has got to be a constant for all observers, as is postulated by the Theory of Relativity, then it must be the same for the lady as well as for the man ... and if that's the case, she has got to see the flashes simultaneously as well!

Note that if the speed of light has got to be the same for all observers – that is, for the lady as well for the man – light should take just as long to go from the rear of the train to the front of the train, as it does to go from the front of the train to the rear of the train.

And that means that it should take exactly the same mount of time to travel halfway along the train as well, regardless of whether it is coming from the front or the rear!

Now the passenger is standing smack bang dead-centre in the middle of the train, right? The burn mark on the caboose is just as far away from her as the one on the engine, right? In her frame of reference they are both the exact same distance away from her, right? She measures speed just like everyone else, namely by dividing distance by time ... right?

If she were to see the flashes at different times, she would have to conclude that it took one of the flashes a longer time to travel to her inside the train, than it took for the other! But in her frame of reference — namely the train — both flashes travelled the same distance, right? 

And if that's the case, the flash that took the longer time to travel the exact same distance must have been travelling slower!

Note that it doesn't matter how much the train "shrank" due to so-called "length contraction" or how much her watch slowed down due to so-called "time dilation". In fact it doesn't matter whether the so-called "Relativistic Lorentz transformations" occurred or did not! No matter what the length of the train, the caboose will still be as far from the lady as the engine; and no matter how much slower her watch ticked, it still would tick the same for the purposes of measuring the duration of light travel from the caboose to her, as for measuring the duration of light travel from the engine to her!

Note also that she and the man can always meet later, and compare notes. He will, if he is honest, tell her that he saw the flashes simultaneously — and (hopefully) she will believe him. If she saw the flashes at different times, then she would have to conclude that the speed of light in the train's frame of reference was not constant: that light moved faster in one direction than in the opposite direction!

Either she has to give up the notion of the constancy of the speed of light for all reference frames, or she has to give up the notion that there can be no simultaneity between frames of reference that are in movement compared to one another — because the two notions are mutually incompatible.

Of course if she gives up the notion of the constancy of the speed of light, she would have to give up Relativity too — because that is one of the basic postulates from which all of Einsteinian Relativity is derived.

But even if she gives up the notion of "no simultaneity between frames of reference that are in rectilinear motion compared to one another" she would have to give up Relativity — because if there can be such simultaneity, it would be possible to synchronise clocks all over the universe, regardless of the speed of movement of the clocks! Which means that a concept of "universal time" or "absolute time" would have meaning.

One way or another, she would have to give up Relativity — and that is but natural, because Relativity contradicts itself!
 
 

A Logical Analysis in Support of the Above Conclusion

We take as a hypothesis the following:

  • a train of "proper" length l, moving rectilinearly along the tracks at a relative velocity v,

  •  
  • a passenger on the train,

  •  
  • a flash of light occurring at the front end of the train and another at the rear end. (See diagram below).




Now:
  1. If the first postulate of relativity — the postulate of the constancy of the speed of light for all inertial observers — is correct, according to the passenger's calculations, the light from the flash at the front end of the train ought to take the same amount of time to reach the rear end of the train, as the light from the flash at the rear end of the train takes to reach the front end of the train.

  2.  
  3. By the argument given by Einstein in his "Train" thought-experiment, if the train is moving at a velocity v along the tracks, according to the passenger's calculations, the light from the flash at the rear end of the train should take more time to travel to the front of the train, than the light from the flash at the front end of the train takes to travel to the rear end of the train.

  4.  
  5. Statements (1) and (2) above contradict one another, so both cannot be correct.

  6.  
  7. If statement (1) above is not correct, the postulate of the constancy of the speed of light cannot be correct. And if this postulate is not correct the Theory of Relativity cannot be correct.

  8.  
  9. If statement (2) above is not correct, the logical incompatibility between the first postulate of Relativity and the "Principle of Relativity" cannot be removed (see Einstein's own words at <http://www.bartleby.com/173/7>, paragraphs 4 and 5.) Thus if statement (2) above not correct, the Theory of Relativity must be based on a logical incompatibility, and thus cannot be correct either.
Q.E.D.

 
 
 
 
 
 

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