Does Relativity Affect How We See Simultaneous Events on a Moving Train?

[stevmg]

Outstanding!

Now, the key element for dumb me here is this: It was never made clear until I entered this blog that an event that occurs in one time frame occurs in all time frames. JesseM pointed that out. Einstein never made that clear in his explanation in section IX of "Relativity." In the case presented, the event is the reaching of the flash to the observer on the train, not the ground. So, in the inertial time frame, the flashes meet at different times (B-flash before A-flash) so in all time frames, the same must be true. The ground observer is irrelevant in this case, just a point of reference but he has no play in the relativity of simultaneity that Einstein wants to present. Your animation is quite "spot on" I wish that this had made clearer to me initially but that's what these blogs are for.

Steve G
The light reaching

 

[Doc Al]

I have made an animated gif of the train thought experiment showing both the point of view of the observer on the train and that of the observer on the track in a split screen, that I hope is more accurate than the youtube video mentioned in the OP.

Nice job, kev!

 

[DrGreg]

Kev's great animation presents a good opportunity to learn about space-time diagrams. I've attached some to this post, depicting just what kev's animation shows and with the same colour scheme. You might like to compare the two side-by-side to see how space-time diagrams work. Time goes vertically up and distance goes horizontally.

Note my diagrams are not to scale and doesn't show exactly the same velocities as kev, so don't get out a ruler to measure distances from them!

 

[stevmg]

To JesseM or anyone who can help... Using Einstein's Train Example

If the train is 1-light-sec long, and is moving at 0.5c to the right, and the observer on the train is clearly at 0.5lightsec at the midpoint

1) What is the time difference between observation of the flash from B and A using the Earth as the reference frame (clearly B is seen before the flash from A)

2) What is the time difference between observation of the flash from B and A using the train as the reference frame.

I'd like to see how the calculations are carried out.

 

[Saw]

In case it helps, I made the attached ST diagram for a case that considers v=0.5c, as you asked, although the train is 2 l-s long (it's each half what is 1 l-s long). It depicts a thought experiment proposed by Brian Greene where a referee on the train fires light signals to duellers on the back and on the front of the train and, when warned by their respective signals, the duellers fire lasers to their opponents.

In the train frame, Back and Front receive their signals simultaneously (at t=1 s) and are fired by the other's laser also simultaneously (at t=3s). The difference is 2 s.

In the ground frame, Back receives his signal earlier (at t=0.577 s) and Front later (at t = 1.732 s). Back is fired at t=2.886 s and Front at t = 4.041 s. The difference is 2.309 s.

There are many ways to get the numbers. One is calculating first in the rest frame of the train, where obviously light takes 1 s to traverse each 1 l-s distance. Then you apply the Lorentz Transformations to get the coordinates in the ground frame.

Edit: it appears that the system does not attach the drawing because it's already in https://www.physicsforums.com/showpost.php?p=2123480&postcount=22"

 

[Doc Al]

To JesseM or anyone who can help... Using Einstein's Train Example

If the train is 1-light-sec long, and is moving at 0.5c to the right, and the observer on the train is clearly at 0.5lightsec at the midpoint

1) What is the time difference between observation of the flash from B and A using the Earth as the reference frame (clearly B is seen before the flash from A)

2) What is the time difference between observation of the flash from B and A using the train as the reference frame.

I'd like to see how the calculations are carried out.

You asked a related question https://www.physicsforums.com/showpost.php?p=2599684&postcount=33", to which I responded. But you never followed up.

 

[TcheQ]

Question 1) relies on question as 2). As other's have stated, it a simple coordinate transfer once 2) is derived. Also you didn't state how long the train is when at rest, but I'm going to assume it's 1ls long in it's own frame (it really doesn't matter since I'm going to use train length =L, however it does matter for question 1), which i am not going to answer)

If the train is 1-light-sec long, and is moving at 0.5c to the right, and the observer on the train is clearly at 0.5lightsec at the midpoint

2) What is the time difference between observation of the flash from B and A using the train as the reference frame.

I'd like to see how the calculations are carried out.

train length L
train velocity v
unknown time t1, t2
I am going to place the observer at 0,
the back of the train at -L/2
the front of the train L/2
observer O travels at v
light travels at c to the right, -c to the left
light1 from the back of the train reaching the observer -L/2 +ct1=vt1
light2 from front of the train reaching the observer L/2-ct2=vt2
solve for t1, t2

-L/2=vt1-ct1, L/2-ct2=vt2
-L/2=t1(v-c), L/2=t2(v+c)
t1=L/2*1/(c-v), t2=L/2*1/(c+v)
subsitute your values
L=1ls, v=.5c, c=c
t1=ls/c, t2=ls/3c
t2-t1=2/3*ls/c=.667s