# Einstein's train once more

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1. Aug 24, 2015

### GhostLoveScore

We all know the experiment - here

It says that for the observer on a train the lightning strike that we are traveling to happened first, but I have some questions.

1) We are moving towards right, so we must see the right lightning first. And we are moving away from left lightning so that light reaches us later than right lightning light. So that means that if the train speed is 0.5c, than we are moving towards right lightning at 1.5c and moving away from left lightning at 0.5c?

2) So for c to remain constant we say that for the reference frame on the moving train, the right lightning happened first?

That leads me to other question

3) If we were moving with 0.99c towards some galaxy. When we would look at it we would see it accelerated because we were moving towards its light and its time would seem to flow faster?

2. Aug 24, 2015

### Orodruin

Staff Emeritus
First, There is nothing accelerated in the train thought experiment.

Second, you have to distinguish seing something at a certain time and the two things happening at the same time. In the train, these are equivalent because the lightnings are equidistant from the observer.

3. Aug 24, 2015

### GhostLoveScore

That is what I am asking - how do we know that the two lightnings didn't really strike at the same time but we are seeing it in different times because we are at different distances from it? Watching from the moving train reference point.

4. Aug 24, 2015

### Orodruin

Staff Emeritus
Since you know the speed of light and how far away the lightnings are, you can compute when they struck.

5. Aug 24, 2015

### GhostLoveScore

But to me the problem is in understanding this - it seems that for the observer on the train, that we are moving towards right lightning with 1.5c and moving away from left lightning with 0.5c.

6. Aug 24, 2015

### Orodruin

Staff Emeritus
No it does not. You cannot just add velocities in relativity. Light always moves with the speed of light. This is one of the relativity postulates.

7. Aug 24, 2015

### GhostLoveScore

I know. So than the observer on the train would see both lightning flashes at the same time? But it doesn't see both flashes at the same time. See what confuses me?

8. Aug 24, 2015

### Orodruin

Staff Emeritus
No, I dont know how you could interpret my responses like that. The observer in the train will observe the flashes at different times because in his frame they occur at different times.

9. Aug 24, 2015

### GhostLoveScore

They occur at different times because the light needs time to reach the observer? Is that similar to this - the sun explodes and we see it on Earth. It has happened, but on Mars it is not happened yet since the light didn't react Mars yet?

10. Aug 24, 2015

### Orodruin

Staff Emeritus
No. They occur at different times because they occur at different times. It has nothing to do with the actual observation.

11. Aug 24, 2015

### GhostLoveScore

Can you than explain why they occur at different times? And please don't say "because the train is moving".

12. Aug 24, 2015

### Orodruin

Staff Emeritus
Because this follows directly from the postulates of special relativity. In relativity, there is no such thing as an absolute time defining events to be simultaneous, it all depends on the reference frame.

13. Aug 24, 2015

### GhostLoveScore

I think I understand now. An event has happened only when its light reaches us. As I said, any event on the Sun does not happen at the same time for Earth and for Mars, or any other planet?

14. Aug 24, 2015

### Orodruin

Staff Emeritus
No, this makes it obvious that you do not understand.

Whether two events are simultaneous or not in a given frame depends only on how the frame is moving, it has nothing to do with when light is observed.

15. Aug 24, 2015

### GhostLoveScore

OK, more general question - why does the right lightning strike happens first?

16. Aug 24, 2015

### A.T.

This might help:

17. Aug 24, 2015

### GhostLoveScore

But that video also shows that from the ground frame of reference, the photons were fired at the same time, the photon on the right took more time to arrive at the detector because it had to travel longer distance. That doesn't mean that the right photon fired first.

18. Aug 24, 2015

### Orodruin

Staff Emeritus
It seems to me that you are trying to understand relativity simply from reading about the effects and not by looking into how the theory actually predicts these effects. In order to really understand relativity, you need to sit down and read the derivations of the Lorentz transformations, understand how the speed of light being the same in all directions in all frames lead to length contraction and time dilation, and to the relativity of simultaneity.

19. Aug 24, 2015

### GhostLoveScore

Do you have any recommendation on what book to read about that?

20. Aug 24, 2015

### Orodruin

Staff Emeritus
Any textbook on basic special relativity should do. Which one really depends on your level.