# Einstein's relativity of simultaneity train/embankment thought experiment

Einstein's thought experiment I'm referring to is this one: http://www.bartleby.com/173/9.html

briefly: train/embankment experiment is where lightning strikes at either ends of the running train (points A and B) and there's an observer inside the train (call him INSD), and outside the train (call him OTSD). if the observer OTSD sees the lightning strikes to be simultaneous, the observer INSD will see that one happens after the other. detailed explanation can be found in the link above.

anyways, so i get the reasoning. the speed of light is always constant, and from the observer INSD's frame of reference, the lightning strikes happened equi-distance from him, and since lightning on the front (B) reached him before the lightning on the back (A), then the one on the front (B) must have happened first... so what's simultaneous to OTSD is not simultaneous to INSD; i get it.

now, what i'm actually confused is;

assuming lightning stroked not the train, but the embankment outside, also at the same points A and B; and left a mark where it hit.

the observer INSD will still see the lightning strike from B first before A; but this time, observer sees where B actually hit the embankment; so can see the distance it actually traveled; which should be shorter..

that's the part i'm confused about; if the lightning striked on the embankment and left a mark there, can you still make the argument that both traveled equi-distance in INSD's frame of reference?

i know i'm missing something, but i struggled alone on this problem for a full day; and i don't have anyone personally to ask this question (not in school anymore); so please be nice and teach it to me like a little kid :)

• It is generally assumed that (a) the train passes very close to the platform (meticulous German engineering, 'ya see) so that (b) the lightning can mark both cars and platform over time scales shorter than anything else happening in the problem. That way both participants can check afterward that they were, in fact, halfway between the two strikes. Feb 25, 2016 at 3:23
• the observer on the train will see the platform contracted in the direction of motion and will see a delay in strike B. Strike A will occur first then strike B will occur at a later time, just when the two point Bs are meeting each other. Feb 25, 2016 at 17:23

If we assume that the lightning strikes leave marks on both the train car, and the platform, then both observers can measure the distance independently. And yes, the OTSD observe will judge the marks to be closer together than the INSD observer.

But the key to the lightning-and-train experiment is not whether those distances are the same, but whether the distance from the front to the middle point is the same as the distance from the rear to the middle point. And note that each observer has their own middle point. The OTSD observer judges that the light does arrive at his middle point at the same time. The INSD observer judges that the light does not arrive at her middle point at the same time. That is, the INSD observer, sitting at the middle point of the train car, clearly sees the lightning strike the front of the train car before it strikes the back. The only conclusion that she can draw is that the lightning strikes were not simultaneous.

You are mixing up observations from the two frames of reference.

Let's say Bolt A hits the rear of the train and leaves Mark A on the adjacent platform, while Bolt B hits the front of the train and leaves Mark B on the adjacent platform.

As far as the INSD observer at the centre of the train is concerned, the bolts hit the front and rear of the train. According to INSD, the train is stationary, and it is the platform that is moving away. INSD measures distances and times relative to the train. INSD says 'I and the train have been at rest. I have been at the centre of the train. I saw Bolt B before I saw Bolt A, and each has travelled the same distance to meet me, so Bolt B happened first'.

If you ask INSD to start considering what has happened by analysing the marks on the platform, you are effectively asking INSD to put herself in the shoes of OTSD, in other words to view what has happened from the platform frame of reference, in which case she will readily appreciate that if the two bolts were seen at the same instant by OTSD, then they were simultaneous in OTSD's frame. There's no mystery to it- she can see that in her frame the two bolts travelled the same distance and were not simultaneous, while in OTSD's frame they also travelled the same distance and were simultaneous.

The point you have missed is that the two perspectives are equally valid. You cannot say that the platform perspective is 'what really happened' and that INSD needs to come round to that way of thinking

This paper discusses the train and embankment though experiment (TETE) in detail and answers your question:

https://arxiv.org/abs/physics/0606135

the correct relativistic analysis of Einstein’s original TETE shows that the ‘lightning strokes’ will be judged to be simultaneous by both the train and the embankment observers, in contradiction to Einstein’s conclusion.

• The study you refer to is trivially incorrect, because it ignores the main reason why the lightning strikes are judged to be not simultaneous from the train: the proper synchronisation of clocks. It also makes an incorrect assumption without justification that the sound from the front and back lightning strikes arrives simultaneous at the middle of the train. Apr 15, 2021 at 21:08