Reconciling different reference frames in Einstein's train-lightening thought experiment

Question

In all accounts of Einstein’s train-lightening thought experiment the ground observer sees the two flashes simultaneously because he remains “at rest” with respect to the landscape, while the train passenger sees the forward flash first because she is “moving” toward the location where it occurred. However the only motion here is the relative motion between the train and the landscape as they slide past one another.

Our Earthly experience leads us to consider the ground to be “at rest”, while trains “move”. But relativity says this isn’t so. We are just as free to consider the train “at rest” while the landscape rushes by.

In this scenario the train passenger remains “at rest” midway between the two strike locations and therefore sees the strikes as simultaneous. The ground observer, rushing toward the train’s rear, sees the rear strike as occurring first for the same reason the original scenario has the passenger see the forward strike first.

Thus, both observers see the strikes as simultaneous. Their mistake is in assuming that the other observer sees them as sequential. But this is non-relativistic thinking.

I have relied on the exact same reasoning as does the original explanation. The “resting” observer sees the flashes simultaneously while the “moving” observer sees the closer flash first.

I submit that my description is the only one which employs true relativity while the others employ absolute motion and rest.

Answer 1

One of the pitfalls of understanding relativity is getting fixated on "seeing". Seeing implies visual observations of delayed light, which you do not need to consider in a gedanken experiment, since resources are unlimited.

So: consider the women in the train has a team of grad students lined up front-to-back with perfectly synchronized atomic clocks, and like wise for the man on the platform.

Also, why use lightning? It fixes the mind in ground frames. Since resources are unlimited, we can use the worlds shortest laser pulse (53 atto-seconds). Four of them: 2 on the train and 2 on the platform, synched to their co-moving clocks. Preprogrammed to fire at time(s) and place(s).

When the ground lasers pulse in synch as the train passes, the train clock next to it leads the train clock in the center while the train clock in the rear of the car lags: The train measures the front event as before the rear event (because it is before it, in the train-frame), while the platform team just sees unsynchronized clocks on the train.

And likewise (or a little vice versa) if the lasers in the train car fire at the same time.

Answer 2

Your post doesn't contain a question, but I will address it anyway.

In this scenario the train passenger remains “at rest” midway between the two strike locations and therefore sees the strikes as simultaneous.

This is where your error is. The lightning strikes are assumed to be simultaneous in the ground's rest frame. It does not follow that they are simultaneous in the train's rest frame.

There would be a perfect symmetry between the ground and the train, were it not broken by the choice that the lightning strikes are simultaneous with respect to the ground. They could equally well be chosen to be simultaneous with respect to the train, but that would be a different situation. The underlying theory is symmetric, but this particular situation is not.

I gather from your post history that you have had this specific confusion for several years. I can only recommend to write it out in actual mathematics. Write down the coordinates of the two simultaneous lightning strikes in the rest frame, do the Lorentz transformation and you will find that they are not simultaneous. Then try to interpret your results in words and you will find where you are going wrong.

I also agree with JEB's answer. Relativity of simultaneity is not because light takes a different amount of time to reach the observers. It rather says that even after the observers correct for the travel time of the light, the two events are simultaneous in one frame and not simultaneous in the other.