# Theory of Simultaneity & Wikipedia article

1. Jul 12, 2010

### werunom

Hello all.
This question is not specifically about the theory itself; but the way of explaining or interpreting it. I have found few explanations about theory of simultaneity which explain in the below mentioned fashion.

My doubt is that -
1.1 Light speed is same in all the reference frames.
1.2 If that is the case, irrespective of the observer's place, the light would travel with the same speed.
1.3 Go to this http://en.wikipedia.org/wiki/Relativity_of_simultaneity#The_train-and-platform_thought_experiment". Now, consider the first figure - inside the train.
Here, the light would travel with the same speed irrespective of the speed of the train with respect to the platform.
If that is the case, and if the train is traveling at relativistic speed from left to right, then obviously the light would take longer time to touch the right end than the left end.

[Below I have paraphrased the same experiment in the link in my own words ... ]
If the speed of light is frame invariant, then the light has to be frame independent.
And if it is so, I can consider the following two scenarios. I am on one end of a sufficiently long railway coach and there is a mirror at the other end. Since I am in the frame under consideration, i can measure its true length "L".
1. Now, if the coach is stationary [I know that I cannot say an object to be stationary on its own, but only with reference to some outside frame of reference - just assume this for the time being], and if I fire a light ray, the light ray would reach the mirror in expected time period [L/c].
2. Now, if the coach is moving at relativistic speed [again the same disclaimer], the light beam would have to take more time to reach the mirror than the usual one [explained in 1].

Is my pt.2 wrong or correct? The pt.2 is contrary to the first case of the example mentioned in the link.

It would be great if anyone of you guys clarify my point.

Last edited by a moderator: Apr 25, 2017
2. Jul 12, 2010

### djy

Yes, in the reference frame of the train, the two light rays reach the ends of the train simultaneously regardless of how fast the train is going, while in the frame of the platform, the left-moving ray hits the left end before the right-moving ray hits the right end.

Not sure what you mean by "light has to be frame independent"...

Yes.

No. It always takes L/c time in the coach's frame, regardless of how fast it's moving with respect to the platform.

Last edited by a moderator: Apr 25, 2017
3. Jul 12, 2010

### werunom

My whole point of saying light is frame independent follows from this explanation.
1. The main postulate of relativity is that light would have the same speed in any frame.
2. Using this postulate, we can demonstrate that from two frames the observers would measure different lengths and times.
2.1 While discussing this, light speed is considered as the datum.
3. So that is why light is frame independent. Irrespective of which frame I consider, the speed would be the same.

Now, you have mentioned the same thing what the article says. But my question is - why is that the light should be specific to the coach frame and would reach both the sides simultaneously? And why is that in the platform frame the light would be reaching the right side late than the left side? Why this bias for the light?
As far as the light is considered, its position and time it takes to reach something should be same - frame independent.

Can you guys please correct, if I am wrong, where exactly I am going wrong in the above thought flow?

In his book, Einstein, uses a similar example, but NOT the same. There, there is train and the platform and the lightning happens somewhere outside - not INSIDE the train. That example wouldnt have the above mentioned discrepancy.

4. Jul 12, 2010

### djy

Yes, the speed of light is frame-independent, but the speed of the train is, obviously, not frame-independent: it is zero in its own frame and non-zero in the platform frame. In fact, in the platform frame, the speed of light relative to the train is less than c for the right-moving ray and greater than c for the left-moving ray. This is what allows the left-moving ray to strike the end of the train first, in the platform frame.

5. Jul 12, 2010

### werunom

You are saying that -
On the platform, an observer would find the speed of light to be c and the train to be moving at v and that is why he would observe that the left hand ray strikes first.
And in the train, there is just light traveling; so the observer in the train would observe the light ray to touch both the sides at the same time.
Right?

Let me think over your point. Give me sometime.

6. Jul 12, 2010

### djy

Yes, exactly.

7. Jul 13, 2010

### Austin0

The time it takes to reach from point A to point B is dependant on the clocks at both points and the assumption that they are synchronous.

But the clocks on the train are not synchronous relative to the track clocks colocated at either point.

Reciprocally; at two points that are simultaneous acclording to the trains clocks the colocated tracks clocks are not synchronous by the same temporal interval.

I think regarding measured speed it is irrlevant whether the origen of the light is inside or outside the train. In the scenario with the light flashes striking the interface between the frames both frames will regard that point of origen relative to their own frame.
IMO