Einstein's Train Thought Experiment

1. Feb 17, 2014

ecoo

I recently watched a video in Einstein's train though experiment.

From what I got from it, events can appear to be at different times when compared to each other depending on the observer. But isn't there an absolute event timing of when the events occurred without regards to who observed it?

In the video, can't you measure back the light to find that the lighting strikes happened at the same time by tracing back the light?

2. Feb 17, 2014

Staff: Mentor

There is no such absolute timing, because

By "tracing back the light" do you mean that if the light reaches my eyes at time $T$ from a distance $D$ away, I can correctly conclude that the event happened at time $T-(D/c)$?

If that's what you mean, that's a valid way of determining when something happened, and therefore of determining whether two events happened at the same time or not. But (and this is the point of the thought experiment) observers moving relative to one another don't necessarily get the same results when they do.

3. Feb 17, 2014

ecoo

Hmmm. After reading the description, it says that both observers are correct? So that means that there is no way we can tell when events occur?

I thought that there was a definite time events occurred, we just interpret the events differently.

4. Feb 17, 2014

Staff: Mentor

It would be better to say "there's no universal absolute time that everyone in the universe will agree about". There's no giant clock in the sky that you, me, someone on Mars, and someone in the Andromeda galaxy can all use to synchronize our wristwatches at once.

However, if you play around with the train experiment some, you'll find that things still make sense. If two events happen at the same place, all observers, regardless of their relative velocity, will agree about which happened first; as long as nothing travels faster than light, no observer will ever see an effect happening before its cause; if a bomb is triggered by two events happening at the same time, all observers will agree that either the bomb exploded or it didn't; and so forth.

5. Feb 17, 2014

ecoo

Couldn't the lady inside the train find out the order of events? After each lighting strike, she knows that she is moving away from the strike in the rear. By inputting the speed at which she is moving away from the rear lighting strike, she can calculate if the rear lighting strike occurred before or after or at the same time as the lightning strike in the front.

Since the man on the platform is equal distance from both events, isn't he correct? If event A occurred before event C, he can tell since he is in location B, which is equal distance from events A and C.

Last edited: Feb 17, 2014
6. Feb 17, 2014

Staff: Mentor

They're both right. If two events happen close enough to each other in time and far enough away from each other in space, then there is no way of saying that one of them "really" happened before or at the same as the other.

7. Feb 17, 2014

ecoo

Sorry, I edited the response. Apologies if I am feeling like a burden :(. Just really want to grasp the concept.

8. Feb 17, 2014

Staff: Mentor

Try doing the exact same analysis, except as if the train is at rest and the platform is moving backwards. What makes platform-guy more "correct" than train-lady?

Before you answer that train-lady is the one who is moving and platform-guy is the one who is not moving, consider that the platform is attached to the earth which is going around the sun which is orbiting the galaxy which is drifting through intergalactic space. Or imagine that you're on Mars (moving at several kilometers per second relative to train and platform) watching the thought experiment on earth through a telescope and deeply amused that either of them should claim to be "really not moving".

9. Feb 17, 2014

ghwellsjr

This is a terrible video. It was discussed at great length in this thread. I finally realized how bad it was at post #139 (page 8) and analyzed it thoroughly starting at post #170 (page 10) and continuing through a great many posts. I hoped it would never be referenced again.

I also found an excellent video made by yuiop and mentioned it at post #235 (page 14). It was analyzed by cepheid in post #337 (page 19) and shapshots taken by me starting at post #340. If you want a correct understanding of the train scenario, study yuiop's video with my commentary.

10. Feb 17, 2014

ecoo

I see what you mean, thanks for being patient with me.

But is there any way to find out what the sequence of events "really was". It seems to me that there can be different interpretations on the order of events, but I there must be an order of events that really happened (if i'm wrong then wouldn't this imply that 2 different order of events occurred AT THE SAME TIME, which I can't wrap my head around?).

11. Feb 17, 2014

Staff: Mentor

That has no meaning. There is no "one true" sequence of events that are not causally connected.

Note that the time order of events that are not causally connected has no particular physical meaning or significance.

But the time order of events that are causally connected--for example a person throwing a rock and the rock breaking a window--does have significance. And all observers will agree on the order of those events.

12. Feb 17, 2014

ecoo

thank you thank you thank you :D

I think I may have finally grasped the basics of the concept.

13. Feb 17, 2014

Staff: Mentor

That phrase "At the same time" gets right to the heart of the problem. Something happens ten light-seconds to your left, something else happens ten light-seconds to your right. You know that the light from both events took ten seconds to get to to your eyes, so if the light from both reaches your eyes at the same time you know that both events happened at the same time, ten seconds ago. But - and this is what the train thought experiment is all about! - someone moving at a different speed than you will come to a different conclusion that's just as correct. Therefore, the term "at the same time" is inherently observer dependent. Saying that two things happened "at the same time" without specifying an observer is like saying that something is "bigger" without saying what it's bigger than - it's an incomplete statement, not a universal truth.

However, you need not despair about the relative order of events - effects will never happen before causes for any observer, and there will never be any disagreement about the order of two events that happen at the same place. And if you think about it, that's all that we should expect.

Mathematically:
Say you're somewhere along the tracks. You may or may not be moving relative to the tracks, that doesn't matter. If any event happens anywhere on the tracks you can assign it a position (the distance from you, negative if it's behind you and positive if it's in front of you) and a time (negative if it happened before noon according to your wristwatch, positive if it happened after that noon according to your wristwatch). We'll call these numbers the $x$ and $t$ coordinates of the event, and we don't care that observers moving at different speeds than us, or starting at different locations on the track, or using different clocks will use different values - their numbers are their problem.

Say we have two events named "one" and "two", with coordinates $(x_1, t_1)$ and $(x_2, t_2)$, and $t_2\gt{t_1}$ (which is to say that for us event one happened before event two). We can calculate the quantity $$S=(x_2-x_1)^2-(t_2-t_1)^2$$

This quantity $S$ has several remarkable properties.
1) It is the same for all observers, even though they have very different notions of what $x$ and $t$ are. (you'll have to google for the "Lorentz transforms" to verify this). This is essential for avoiding paradoxes, because....
2) If $S$ is negative then all observers, regardless of their speed, will agree that event one happened before event two. They may have very different values for $t_1$ and $t_2$, but they will all agree that their $t_2$ value is greater than their $t_1$ value. An observer who happens to be moving at speed $(x_2-x_1)/(t_2-t_1)$ relative to us (this speed will always be less than the speed of light) will report that the two events happened at the same place.
3) If $S$ is positive then some observers, depending on their speed, will report that event one happened before event two, others will report that they happened at the same time, and yet others will report that two happened before one. This is the case for the two lightning flashes in the thought experiment. No observer will report that the two events happened at the same $x$ position, and all observers will agree that a light signal from one event could not reach the other.

Last edited: Feb 17, 2014
14. Feb 17, 2014

Staff: Mentor

Hah - looks like my last post crossed your last post .

You can stop reading that post at the word "mathematically" if you don't want to dig into the math. But if you do, like I said, you'll have to learn the lorentz transforms.

15. Feb 17, 2014

ecoo

I just wanted to tell you that I got confused with Relativity of Simultaneity with what they label in the article as "Appearance Simultaneity" (they explain this in the section with the title "What the Relativity of Simultaneity is NOT").

http://www.pitt.edu/~jdnorton/teach...3_Jan_1/Special_relativity_rel_sim/index.html

I was using an example of Appearance Simultaneity in my own example in my head that I was thinking about. This caused me to think of that "different interpretations for the set sequence of events".

(Just wanted to tell you what made me confused so you can help future question askers more effectively.)

16. Feb 23, 2014

Yashbhatt

If the observer says that the events happened at the same place, then (x_2-x_1) is 0. So, is that observer stationary?

17. Feb 23, 2014

Staff: Mentor

When you use the words "stationary" or "moving", you must always say what it's relative to.

All observers are stationary relative to themselves.

The first event might be "I looked at my wristwatch" and the second might be "I looked at my wristwatch again". I will assign the same $x$ coordinate (but different $t$ coordinates) to the two events - as far as I'm concerned both events happened at the same place, and any observer who is at rest relative to me will agree with me. Observers who are moving relative to me will say that they're the ones who are at rest, that I'm the one that's moving, and therefore that the two events happened at different places because I moved in between glances at my wristwatch.

18. Feb 26, 2014

Yashbhatt

Got it. I mistook x_2 and x_1 as positions of the observer.

19. Sep 11, 2014

duri

There are lot of threads about this Einstein's experiment. I don't want to start a new one. My question is simple. What is so special about this experiment with respect to special relativity. This should hold in all sensory perception. For example, replace light with sound wave and observers were blind. Then person in stationary reference would hear sound from front and rear at same time. Person in train would hear sound from front at first and then from rear. So the conclusion would be same.
Another example is, imagine ball is thrown on these observed at same and constant velocity. Observes can detect them only when it touches him. There conclusions would also be same.

20. Sep 11, 2014

Staff: Mentor

I used to think this also, but it is not correct. The point is that the speed of light is invariant. The speed of sound is not frame invariant.