Length Contraction & Simultaneity: Train-and-Platform Experiment

[mrsmitten]

I was reading about (The train-and-platform thought experiment) from https://en.wikipedia.org/wiki/Relativity_of_simultaneity
and was wondering a couple of things.
1.) Would the observer on the train agree with the stationary observer that event A and B happen at the same place in the stationary observer's frame?

2.) Would they both agree that the distance between event A and B is the same?

3.) Would the distance between A and B be just the length of the train?

 

[Nugatory]

1.) Would the observer on the train agree with the stationary observer that event A and B happen at the same place in the stationary observer's frame

In the train/platform experiment, we have two lightning strike events and (in the simplest form of the experiment) one "light from both flashes reaches both observers' eyes at the moment that they're even with one another" event. None of the three happen at the same place according to any observer, nor could they as none of them are time-like separated. So which of these are the ones that you are calling "event A" and "event B", and did you mean "at the same time" above?

 

[mrsmitten]

did you mean "at the same time" above?

Nope

In the train/platform experiment, we have two lightning strike events and (in the simplest form of the experiment) one "light from both flashes reaches both observers' eyes at the moment that they're even with one another" event. None of the three happen at the same place according to any observer, nor could they as none of them are time-like separated. So which of these are the ones that you are calling "event A" and "event B"

(In the simplest form of the experiment) I think both observers would agree that one lightning strike hit the front of the train and the other hit the back.
let's say that "event A" is the moment that the moving observer sees the lightning strike the front of the train and "event B" is the moment when the moving observer sees the lightning hit the back of the train. If the moving observer marks the points in the stationary observer's frame at which he sees "event A", let's call it X1 and at "event B" X2.

Would the stationary observer agree that events A and B happened at X1 and X2?

 

[Nugatory]

let's say that "event A" is the moment that the moving observer sees the lightning strike the front of the train and "event B" is the moment when the moving observer sees the lightning hit the back of the train. If the moving observer marks the points in the stationary observer's frame at which he sees "event A", let's call it X1 and at "event B" X2.

You need to be careful with that word "sees" - an observer sees something when light emitted from it reaches his eyes, and he calculates when it happened by subtracting the light travel time from the time the light hits his eyes (he can read this time from his wristwatch). In the train experiment as it is usually set up there is a point in spacetime where the platform and train observer are colocated as the one passes by the other. That's one point in spacetime so it is a single event; we can call it event O if we want to name it.

The light from both lightning flashes hits both observers' eyes at this point in spacetime, so we say that both observers see both flashes at event O. Of course event O is different than the other two events in the thought experiment, namely the two lightning flashes striking the rails at two different places.

 

[mrsmitten]

You need to be careful with that word "sees" - an observer sees something when light emitted from it reaches his eyes

Agreed, I think the wording in my last statement was bad. I will try and think of a better way to word it.

But the principle is I want to know if both observers agree on the position X1 (in the stationary observer's frame) of the front of the train when it's struck, and the position of the back of the train X2 when it's struck.

 

[jbriggs444]

Agreed, I think the wording in my last statement was bad. I will try and think of a better way to word it.

But the principle is I want to know if both observers agree on the position X1 (in the stationary observer's frame) of the front of the train when it's struck, and the position of the back of the train X2 when it's struck.

If you are ask about "position X1 (in the stationary observer's frame)" then it does not matter what observer you question. You've chosen a frame and that's the end of the story. From the way you pose the question, the observer you query is obliged to transform into the stationary observer's frame before providing his answer.

All observers agree that the lightning bolt blasted the front of the train and a charred a spot on the tracks at the same place and time that the front of the train passed that spot on the tracks.

 

[Mister T]

1.) Would the observer on the train agree with the stationary observer that event A and B happen at the same place in the stationary observer's frame?

Event A is the lightning striking the front of the train. Yes, both observers agree that lightning struck the front of the train, at the front of the train.
Likewise Event B is lightning striking the rear of the train, so both observers agree that lightning struck the rear of the train, at the rear of the train.

Of course, Events A and B don't occur at the same place as each other!

2.) Would they both agree that the distance between event A and B is the same?

No.

3.) Would the distance between A and B be just the length of the train?

Yes.

 

[Chestermiller]

Both observers would agree on the coordinates of the two strikes both in their own frame and in the other's frame. They just would not agree on the distance between the two strikes, (i.e., the differences in the coordinates, even though they are using identical rulers in their own frames). If the guy on the train receives the flashes at the same time, the guy on the ground would not. He would conclude that one strike happened first, and the other strike happened afterwards. And, in his frame of reference, he would be correct.