Measurement-observation vs causality in a special relativity scenario

Question

This scenario is adapted from Brian Greene's book The Elegant Universe:

Two people are sitting towards each other at opposite ends of a long table on a train traveling at a constant velocity. Person One is sitting in the direction of motion of the train, and Person Two is sitting opposite. In the exact center of the table is a light that sends a single pulse of light, at the same instant, towards the two people. In their reference frame, the light reaches both at the same time. They both agree about this as they are sitting equidistant from the center of the table where the light originates.

Now a stationary obsever watches the same train as it goes by. From this perspective, Person One is heading toward the emitted light while Person Two is retreating from it. This means that, to the oberver, the light beam does not have to travel as far to reach the Person One, who moves toward the approaching light, as it does to reach Person Two, who moves in the same direction as it. Since the distance is less for Person One, the light will be observed reaching Person One first. Special Relativity.

Now my question: does this mean that even if both have equal claims on the truth of what they experienced and saw, that if the observer and the two people on the train met later, the train people would say the light reached them at the same time? Meaning, that even though what the observer on the platform saw was a correct measurement-observation, it didn't actually have any consequence (for the lack of a better word)?

Answer 1

Yes, it is perfectly fine in special relativity for two observers to disagree on the temporal order of two events. In your case, the train observers say that the events were simultaneous, while the platform observer says that Event 1 happened before Event 2. There is nothing inherently problematic about this, other than that it disagrees with pre-Einstein concepts of how time behaves.

What would be problematic is if Event 1 and Event 2 were connected by a causal influence, so that in one frame the effect happened before the cause and in another frame the effect happened after the cause. But it can be shown that if a particle traveling at $c$ or less can be present at Event 1 and Event 2, then all observers will agree on their order in time. This is the root of the idea that causal influences can't travel faster than the speed of light.

Answer 2

The experience of person 1 and 2 about the simultaneity is not falsified by the observer on the station. What they say is that the events were simultaneous in the train's frame where they were.

The observer in the station agrees with that. What he says is: the events were not simultaneous in the platform frame, were he was.

The key is: there is not an universal simultaneity.

Answer 3

Everybody agrees that the two events occurred simultaneously in the train frame and non-simultaneously in the station frame. These are objective facts.

Answer 4

Perhaps a useful analogy might be this. Suppose you are standing in an apartment the floor of which is 50m above the ground. There is a light above you. When asked how high the light is, you take a tape measure and report that the light is 2.3m off the ground, by which you mean the floor of your apartment. To somebody standing on the ground outside the apartment, the light is 52.3m from the ground. The light has a fixed vertical position, which you label with one coordinate and someone outside labels with another coordinate. The two of you are simply using different reference frames to label the same reality.

Now imagine there are two lights, one at either end of your apartment, and each 2.3m above the floor. You would say the lights are at the same height. Now imagine someone outside the building standing on the ground, and let's suppose the ground is slightly sloped, so it is .1m higher below one end of your apartment than it is at the other. To the person on the sloping ground, one of your lights might be 52.3m above the ground, while the other might only be 52.2m, because the ground slopes upwards. To you, the two lights are level vertically, while to the person outside the lights are at two different levels vertically. Again you don't disagree where the lights are, but you label their positions with different coordinates.

An exactly similar set of circumstances accounts for the varying descriptions of the events on the train. To the people on the train, both events might happen at 12:00 say. However, when it is 12:00 at the trailing end of the carriage, the time outside on the platform frame will be just before 12:00, and when it is 12:00 at front of the carriage the time outside on the platform frame is just after 12:00. It is not that the people on the train and the people on the platform disagree about when the events happen, but just that they label the events with different time coordinates.