Einstein's Train and a simple consequence

[robert Ihnot]

This should be a simple question for this Forum: Einstein tells us that when the train is moving and the lightning flashes on both ends of the train,if it meets at the center of the tracks, it will not meet at the center of the train for the obvious reason that the train has moved off from that position.

The webmaster for Relativity for Cranks can not see the difference between the lightning bolts at rest on the tracks and light beams flashed by the conductor and the engineer on the train at equal distance from the center, instead of the exterior lightning bolts, to the middle of the train. In this second case, I say that the light flashes must meet in the center of the train otherwise we could detect absolute motion. Look at it this way: We can always consider the train at rest and the tracks as moving.

I would like someone to assure me that I have this correct, if I do. Thanks, Bob

 

[Integral]

If I read your question correctly, it sounds like the Webmaster of Relativity for cranks knows something about Relativity. If you would not listen to him I doubt you will listen to anyone here.

It does not matter if the light beams are emitted from the stationary ground or the moving train they will meet in the same place. The speed of light is independent of the speed of the emitting body.

 

[HallsofIvy]

What do you mean by "meet in the center of the tracks"? Since we are talking about the length of the track, where exactly is the center?

 

[franznietzsche]

The webmaster is right. Add to the situation an observer on the ground, and then have the engineer and the conductor, and the stationary bulbs all emit flashes simultaneoulsy as the engineer and conductor line up with the stationary bulbs. Because of the constancy of the speed of light the paired light beams (the engineer/one bulb and the conductor/the other bulb) must remain paired as they were emitted from the same point (along the one-dimensional motion of the track) and so must meet their counterparts at the same time and at the same point (again speaking one-dimensionally along the direction of motion). There is no difference between beams emitted by tghe stationary bulbs or the moving people.

 

[robert Ihnot]

What do you mean by "meet in the center of the tracks"? Since we are talking about the length of the track, where exactly is the center?

I am looking at this directly from what Einstein wrote: When we say that the lightning strokes A and B are simultaneous with respect to the embankment, we mean: the rays of light emitted at the places A and B, where the lightning occurs, meet each other at the mid-point M of the length A —> B of the embankment. But the events A and B also correspond to positions A and B on the train. Let M' be the mid-point of the distance A —> B on the traveling train. Just when the flashes 1 of lightning occur, this point M' naturally coincides with the point M, but it moves towards the right in the diagram with the velocity v of the train. If an observer sitting in the position M’ in the train did not possesses this velocity, then he would remain permanently at M, and the light rays emitted by the flashes of lightning A and B would reach him simultaneously

 

[robert Ihnot]

Well, what if we consider the train at rest and the tracks as moving?

 

[franznietzsche]

Well, what if we consider the train at rest and the tracks as moving?

You'll get the same result, that is the principle of relativity.

 

[robert Ihnot]

the train at rest

WEll, if the train is at rest and the engineer and the conductor both send off beams half way from the center of the train, why would they not arrive at the center at the same time, while with regards to the track this would not happen?

 

[franznietzsche]

WEll, if the train is at rest and the engineer and the conductor both send off beams half way from the center of the train, why would they not arrive at the center at the same time, while with regards to the track this would not happen?

Your mistake is not specifying the frame of reference you are using. In my post i used the frame of reference of the stationary observer at all times. He saw the two sets of light pulses converging simultaneously at the midpoint between the two stationary bulbs.

In your statement you have switched reference frames to the train. An observer on the train sees the beams meet at the mid point between the engineer and the conductor, and not at the mid point between the bulbs on the embankment, for both pairs of beams, again because of the constancy of the speed of light.

 

[robert Ihnot]

Train at rest...

I thought that was what I had in mind. With the train system "at rest," we have no way to determine absolute motion. So maybe I was not entirely wrong, just sounded wrong. With the train at rest, the lightning bolts at rest, they meet in the center of the train. However with the train at rest, the tracks moving and the lightning bolts moving the same way, then the bolts meet in the middle of the tracks. Yes?

 

[franznietzsche]

I thought that was what I had in mind. With the train system "at rest," we have no way to determine absolute motion. So maybe I was not entirely wrong, just sounded wrong. With the train at rest, the lightning bolts at rest, they meet in the center of the train. However with the train at rest, the tracks moving and the lightning bolts moving the same way, then the bolts meet in the middle of the tracks. Yes?

Yes, but you can take that further. In both cases you are talking about the frame taken to be at rest. An observer taken to be in the moving frame will see the same thing as if his frame were taken to be at rest. So there is no absolute motion. And furthermore, motion being described in terms of space and time, if there is no absolute motion, there is neither absolute space nor absolute time, all 3 must be relative to the frame of reference of the observer. All of this proceeds directly from the combination of the constancy of the speed of light for all observers and the relativity principle (and of course other assumptions too fundamental for us to consciouly take note of, despite their obvious epistemological significance)