Turning Einstein’s train thought experiment on its head

[vstbagdad]

Let us first review Einstein’s train and platform thought experiment which consists of one observer midway inside a speeding train car and another observer standing on a platform as the train moves past.

A flash of light is given off at the center of the train car just as the two observers pass each other. The observer on board the train sees the front and back of the train car at fixed distances from the source of light and as such, according to this observer, the light will reach the front and back of the train car at the same time.

The observer standing on the platform, on the other hand, sees the rear of the train car moving (catching up) toward the point at which the flash was given off and the front of the train car moving away from it. As the speed of light is finite and the same in all directions for all observers, the light headed for the back of the train will have less distance to cover than the light headed for the front. Thus, the flashes of light will strike the ends of the train car at different times.

But let’s not just stop there. Why don’t we up the ante a little bit ? What if the light in the center of the train is actually a light pulse generator (LPG) consisting of a lens pointed toward the front of the train and a second light/lens pointing toward the back of the train. Let us further say that after the first pulse is provoked manually by a switch, all subsequent pulses are generated by the returning beams of light. The front pulse being produced by the beam being reflected from the front of the train and the rear pulse by the reflected light returning from the rear of the train.

So, to the observer on the train, the LPG goes off in both directions at exactly the same time based on what we established earlier. If our device is sufficiently sophisticated, it could come with 2 timing devices for each side of the LPG which would record the exact time a pulse was generated on each side. The 2 listings will be identical. BUT to the outside observer, the pulse located on the front will not flash until after the pulse on the rear, since it has to wait for the return of the light beam from the front of the train, which takes longer based on relativity. Does this really make sense though since in actuality, the LPG went off on both sides at the same time inside the train ? Can we really have it both ways – i.e. both pulses flashing simultaneously and also have the rear pulse flash before the front one does to the outside observer ?

What is the difference between the above scenario and one in which both pulses are provoked by either beam returning to the LPG ? In this case, we cannot say that the front lens “waits” for the return of the front beam. Instead because of the initiation of the rear beam, we see a pulse being released at the rear as well as at the front of the LPG before the front beam has even returned to the LPG. On the train, the timing is exactly the same as in the former scenario in which each side had to wait for the return of its associated light beam. So now to the outside observer we have a pulse moving toward the front of the train while the prior frontward pulse is still returning to the LPG. The same returning frontward pulse that in the prior scenario would have given rise to the second pulse that is now speeding toward it. Is it really possible to have a future event colliding with the past event that gave it birth in the former scenario ? To state it a different way, can the parent embrace the child before the child has even been conceived ?

Here is another unsettling implication of this scenario. Since we established that the LPG can now be provoked by a returning beam of light from either side and since the returning rear beam has set off a fresh pulse moving in both directions, will the returning front beam also set off a second pulse in both directions (to the outside observer) ? How can this be since on board the train the observer sees both beams return simultaneously and only one new pulse generated ? In this case we now we have a second event being observed by the outside observer which doesn’t even exist in the onboard observer’s reality. Has the “universe” of the train then generated an alternate event/reality/universe that isn’t even visible to the one that generated it but is to an outside observer ? This seems absurd. I have a couple of more scenarios along these lines, but I don’t want to overwhelm my readers. Can anyone out there offer any insight/resolutions to these conundrums ? Thanks, VST Bagdad, KY

 

[Ibix]

You have built a light clock. You may wish to Google the term. It is entirely self consistent in both frames when described correctly.

 

[Samy_A]

So many words, so few numbers.

Why don't you translate the story into formulas, using the Lorentz transformation between the two relevant frames of reference?

 

[vstbagdad]

Fair enough - I will look into Dr. Lorentz's transforms and see if they can offer some insight to this case - if I can figure them out (I am a software engineer by trade, but its been years since I've actually had to solve calculus or diffeq's). I guess I was wondering if this specific scenario had already been covered and could be elucidated in plain English. thanks, vst

 

[Ibix]

It has - see the light clock.

 

[Vitro]

... BUT to the outside observer, the pulse located on the front will not flash until after the pulse on the rear, since it has to wait for the return of the light beam from the front of the train, which takes longer based on relativity. ...

The last statement in there is a guess, and it's wrong. It's where some numbers would help, no calculus needed just arithmetic. It's even better if you also draw it on paper once you have the numbers, it helps you visualize what's going on.

 

[Mister T]

Can we really have it both ways – i.e. both pulses flashing simultaneously and also have the rear pulse flash before the front one does to the outside observer?

Yes. One thing that you may be failing to account for in your thinking is that, in the train's rest frame, the arrival of each pulse occurs not only at the same time, but also in the same place. However, in the platform's rest frame those pulses arrive not only at different times, but also at different places.

The type of logical inconsistency that you are getting at, I think, is the following. Let's say that in Frame A two events occur at the same place and at the same time. In Frame B if those same two events occur at different times they must necessarily occur at different places, too. If they were to occur, in Frame B, at different times but in the same place that would indeed be a logical inconsistency.

 

[Janus]

Let us first review Einstein’s train and platform thought experiment which consists of one observer midway inside a speeding train car and another observer standing on a platform as the train moves past.

A flash of light is given off at the center of the train car just as the two observers pass each other. The observer on board the train sees the front and back of the train car at fixed distances from the source of light and as such, according to this observer, the light will reach the front and back of the train car at the same time.

The observer standing on the platform, on the other hand, sees the rear of the train car moving (catching up) toward the point at which the flash was given off and the front of the train car moving away from it. As the speed of light is finite and the same in all directions for all observers, the light headed for the back of the train will have less distance to cover than the light headed for the front. Thus, the flashes of light will strike the ends of the train car at different times.

But let’s not just stop there. Why don’t we up the ante a little bit ? What if the light in the center of the train is actually a light pulse generator (LPG) consisting of a lens pointed toward the front of the train and a second light/lens pointing toward the back of the train. Let us further say that after the first pulse is provoked manually by a switch, all subsequent pulses are generated by the returning beams of light. The front pulse being produced by the beam being reflected from the front of the train and the rear pulse by the reflected light returning from the rear of the train.

So, to the observer on the train, the LPG goes off in both directions at exactly the same time based on what we established earlier. If our device is sufficiently sophisticated, it could come with 2 timing devices for each side of the LPG which would record the exact time a pulse was generated on each side. The 2 listings will be identical. BUT to the outside observer, the pulse located on the front will not flash until after the pulse on the rear, since it has to wait for the return of the light beam from the front of the train, which takes longer based on relativity. Does this really make sense though since in actuality, the LPG went off on both sides at the same time inside the train ? Can we really have it both ways – i.e. both pulses flashing simultaneously and also have the rear pulse flash before the front one does to the outside observer ?

This last bit is incorrect. Both observers, train and outside, agree that the both pulses( to the rear and front) take the same amount of time to return to the pulse generator. To put it simply, while the forward pulse takes more time to reach the front of the train than the rearward pulse takes to reach the the rear of the train as seen by the outside observer, the reverse it true for the reflected pulse, the pulse reflected back from the front of the train takes less time to return to the pulse generator than the reflected pulse from the rear of the train does. When you add together the outbound and return leg times for each pulse, you find that the round trip times are equal for both pulses according to the outside observer. ( just like they are for the train observer),

 

[vstbagdad]

@Janus - of course ! I failed to take into account that on the return of the two beams, the pulse generator is racing toward the beam reflected from the front while it is racing away from the beam reflected from the rear. The net effect of which would be that the two would indeed return to the middle of the train at the same time from the point of view of both observers. Thanks !