# Could Einstein have been wrong about the train experiment?

Einstein introduced the train-hit-by-lightening thought experiment to illustrate "the relativity of simultaneity". For the three reasons below, I think he was wrong when he held that the onboard observer sees the forward flash before seeing the rear flash. I realize I'm challenging the Great Man himself as well as every author who's described this scenario. I'm looking to resolve my dilemma, not to pick arguments with authorities.

No experiment within an inertial reference frame can distinguish between "movement" and "rest".

1. If Einstein's train were at rest relative to the tracks the onboard observer would see the two lightening strikes as simultaneous.

2. According to the conventional (Einsteinian) explanation, with the train in motion relative to the tracks, the onboard observer sees a temporal gap between strikes, the forward strike appearing to have taken place before the rear strike.

3. Therefore, by noting whether the strikes appear simultaneous or sequential, the onboard observer can discern the difference between the absolute rest and the absolute motion of the train.

4. Point 3 violates SR in that no experiment performed in an inertial frame of reference can determine the frame's absolute rest or motion.

5. Further, the length of the gap could be used to calculate the train's absolute speed. In his 1948 book, The Universe and Dr. Einstein — with an introduction by Einstein himself — author Lincoln Barnett says:

"Imagine temporarily that the train is moving at the impossible rate of 186,242 miles per second, the velocity of light. In that event, flash B [the rear flash] will never be reflected in the mirrors at all because it will never be able to overtake the train."

The author's obvious implication is that the gap between the two flashes is an indication of the train's speed.

There is no preferred reference frame.

One of the tenets of SR is that the laws of physics are the same in all inertial reference frames. In Einstein's thought experiment both the train and the embankment are inertial reference frames. Neither is accelerating. This means that the train and the embankment are interchangeable: We can assign "movement" to either one and "rest" to the other without altering the conditions of the scenario in any way as long as the relative motion between the two conforms to the original specification.

So, let's assign "rest" to the train and "movement" to the embankment. Now, surely the onboard observer will see the two lightening flashes as simultaneous. (We're not concerned here with the trackside observer.) If the onboard observer sees the flashes as simultaneous under one scenario he cannot see them differently in the other, equivalent scenario. Our arbitrary choice of which inertial frame to consider "moving" cannot alter the physical result of the experiment.

Einstein's train experiment incompatible with Greene's.

In his book, The Elegant Universe, author Brian Greene presents an alternative thought experiment to Einstein's. In Greene's version two kings, sitting at opposite ends of a long table on a moving train, attempt to simultaneously sign copies of a peace accord. Neither wants to go first. So they agree to begin signing when an electric lamp at the table's midpoint is illuminated.

The onlookers on the train all agree that the two kings signed simultaneously. But those on the embankment complain that the forward-facing king signed first because, while the light from the lamp propagated toward the kings, the train's forward motion brought the forward-facing king closer to the source of the light, while the backward-facing king receded from it. Thus, the light had less distance to cover to reach the forward-facing king than to reach the backward-facing king.

If, in the Einstein experiment the onboard observer saw the forward lightening flash first because the train carried him closer to its source, why, in the Greene experiment didn't the onboard observers see the forward-facing king sign first for the same reason? They didn't; they saw the two kings sign simultaneously.

• Your (2) and (3) miss a precondition of the argument which is that the strikes are simultaneous in the platform frame. You can re-build the argument with the strikes simultaneous in the train frame as well. The argument is fully symmetric and does not disclose absolute motion. Feb 4 '17 at 18:07
• Your point 3 should say "Therefore, by noting whether the strikes appear simultaneous or sequential, the onboard observer can discern the difference between the rest and the motion of the train relative to the light source", not "between the absolute rest and the absolute motion of the train". Mar 9 at 14:25

Look more closely at your point 3). What can the onboard obserer discern? Consider scenarios in which the train has and does not have windows. If the windows have to be open your measurement relies on the other frame. The theory is that you cannot tell if the train is going past the platform or the other away around. This is where you thoughts are going off the rails (joke, see?)

in Greene's and Einstein's experiment the observers that are unhappy or see non simultaineous flashes are not the ones onboard.

Did you know the equivalence principle is highly local, so actually by measuring tidal force distributions accurately you can in fact tell if you are in a rotating, linearly accelerating or gravitational frame. It's not an argument with Einstein so much as what they tell you about his theories.

Therefore, by noting whether the strikes appear simultaneous or sequential, the onboard observer can discern the difference between the absolute rest and the absolute motion of the train.

You're not determining the absolute motion of the train. You're just determining the motion of the train relative to the platform. It's true that in this scenario, the platform plays a special role, but that's just because it's the frame where we happened to synchronize the flashes.

We could make a similar argument in Newtonian mechanics. We could set an object at rest on the platform, and observe that in any other frame we see the object as moving. Thus, by looking at the object, we're able to tell what reference frame we're in. Does this imply that we're somehow able to determine absolute motion? Of course not! We're just determining our motion relative to the platform frame of reference. There's nothing special about the platform's frame of reference, except that it's where we decided to stick our object. Similarly, there's nothing special about the platform frame in special relativity, except it's where we decided to make our flashes. Once we've picked one frame of reference to measure against, it shouldn't be surprising that we can determine our motion relative to that original frame.

So, let's assign "rest" to the train and "movement" to the embankment. Now, surely the onboard observer will see the two lightening flashes as simultaneous.

In order to make this assignment, you need to change when the flashes happen (remember, we're not assuming things that are simultaneous in one frame are simultaneous in another). You're free to do this experiment. You'll find that when the people on the train see simultaneous flashes, the people on the platform do not, and when the people on the platform see simultaneous flashes, the people on the train do not. This isn't a contradiction, since to switch between the two scenarios you need to change when the flashes are occurring. You're not just changing reference frames, you're actually changing the timing of the flashes.

I do not know whether the example is a fudge or not (I suspect it actually is).

But I am certain that his explanation is awful. After a long introduction, he just asserts, in one short sentence, that they are not simultaneous for M' on the train.

Meaningless to anyone that does not already understand what he is saying.

Yes, I believe he could have been wrong regarding the above-mentioned thought experiment. In fact, serious people have written papers on this. One example can be found on the arXiv pre-print server. J.H. Field has worked at CERN. You can find his assessment of the problem here: https://arxiv.org/abs/physics/0606135v2.

• Note that the paper cited above was submitted to arxiv in 2006 and is still not published in a peer reviewed journal. This is not a very credible source.
– Dale
Mar 9 at 16:20