# Einstein's Train Thought Experiment

• ecoo
In summary: 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.So who is correct? The lady inside the train or the guy outside on the platform?
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?

ecoo said:
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?
There is no such absolute timing, because

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?

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.

Nugatory said:
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.

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.

ecoo said:
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?

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.

Nugatory said:
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.

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.

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ecoo said:
So who is correct? The lady inside the train or the guy outside on the platform?

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.

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

ecoo said:
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.

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".

ecoo said:
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?

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.

Nugatory said:
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".

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?).

ecoo said:
But is there any way to find out what the sequence of events "really was".
That has no meaning. There is no "one true" sequence of events that are not causally connected.

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?).
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.

Nugatory said:
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".

thank you thank you thank you :D

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

ecoo said:
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?).

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.

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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.

Nugatory said:
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.

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/teaching/HPS_0410/chapters_2013_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.)

Nugatory said:
This quantity ##S## has several remarkable properties.

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.
.

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

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

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.

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

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.

duri said:
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.
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.

Velocity invariance with inertial frame is not required to explain this. If velocity is invariant with train frame then observer in train should receive the signal simultaneously. Since distance traveled by light is same from front of the train to the middle, time = distance/velocity this implies both time or velocity is dependent on frame of reference. If I believe velocity is constant with any inertial frame then time taken by light to travel half the train distance should be same. But in this case velocity is taken as c+v and c-v from front and rear of train. This implies velocity is changing with frame.

duri said:
Velocity invariance with inertial frame is not required to explain this. If velocity is invariant with train frame then observer in train should receive the signal simultaneously. Since distance traveled by light is same from front of the train to the middle, time = distance/velocity this implies both time or velocity is dependent on frame of reference. If I believe velocity is constant with any inertial frame then time taken by light to travel half the train distance should be same. But in this case velocity is taken as c+v and c-v from front and rear of train. This implies velocity is changing with frame.
No, the speed of light is the same, c, in each frame. Those quantities c+v and c-v are the rates at which the light flashes approach the ends of the train according to the track frame. They are not the velocities of anything, certainly not the velocity of light.

duri said:
Since distance traveled by light is same from front of the train to the middle
The distance traveled by light is only the same in both directions in the rest frame of the train. In all other frames the distance traveled is different, specifically the distance is shorter for the end of the train that is moving towards the light source and longer for the end of the train that is moving away from the light source.

Since the speed of light is c the time that it reaches the end of the train is equal to c/d. For sound and other signals, not only is the d different for the forward and backwards ends, but also the velocity is different, so the time is unknown. That is why the invariance of c is the essential characteristic.

Doc Al said:
No, the speed of light is the same, c, in each frame. Those quantities c+v and c-v are the rates at which the light flashes approach the ends of the train according to the track frame. They are not the velocities of anything, certainly not the velocity of light.

I agree velocity of light cannot change within the inertial frame of reference. My point is, this holds even for other waves or simply if you throw a ball at velocity c from front and rear end. Special relativity is not required to explain this. Note that I am not talking about difference between two frames of reference.

duri said:
I agree velocity of light cannot change within the inertial frame of reference. My point is, this holds even for other waves or simply if you throw a ball at velocity c from front and rear end. Special relativity is not required to explain this. Note that I am not talking about difference between two frames of reference.
Sure. If you have any isotropic v then you can say t=v/d.

So what? If you limit yourself to a single frame then there is not much else you can say. Certainly, if you are limiting yourself to a single frame then you are not doing anything related to Einstein's train thought experiment.

DaleSpam said:
The distance traveled by light is only the same in both directions in the rest frame of the train. In all other frames the distance traveled is different, specifically the distance is shorter for the end of the train that is moving towards the light source and longer for the end of the train that is moving away from the light source.

Since the speed of light is c the time that it reaches the end of the train is equal to c/d. For sound and other signals, not only is the d different for the forward and backwards ends, but also the velocity is different, so the time is unknown. That is why the invariance of c is the essential characteristic.

This boils down to the notion that how the source of signal relative to the frame. Same argument hold if source of the signal is relatively stationary to the observer frame then he will get the signal simultaneously. This is true whether he is in the train or outside the train. If source is moving with respect to observers frame then he will receive the first signal from source where relative velocity is high between source and observer.
Simply, for observer in train he is stationary but the source of light is moving with velocity v. At some point of time the source emits the signal with velocity c. The net velocity of the signal at the point of emission is c+-v. If c and v are in same direction then it adds simple vector addition. Since the location when signal is emitted is fixed and observer location is fixed with respect to his frame then signal travels at c+v would reach him first followed by c-v signal.
When the signal velocity is invariant with velocity of source (this is same as invariance with inertial frame) then he should receive both signal at same time.

duri said:
Same argument hold if source of the signal is relatively stationary to the observer frame then he will get the signal simultaneously.
No, it doesn't. It only holds if the speed of the signal is frame invariant.

Or are you focused on the source of the signal? That is indeed irrelevant. The key point is the speed of the signal, not the speed of the source.

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DaleSpam said:
No, it doesn't. It only holds if the speed of the signal is frame invariant.

If I consider only the observer in the train frame (what ever be the observer's frame, observer will feel himself to be stationary). The source of the signal moves relative to him with velocity v. But the signal velocity is c. When source of the signal is moving towards him at the front of the observer and away from him at rear of the observer. Then relative velocity of the signal measured by observer from front and rear are c+v and c-v respectively. If this is wrong then the observer in the train should receive the signal simultaneously. So, in this case he will receive the front signal first.
Here, only one frame is involved. So, the question of frame invariant is really unnecessary. Then why it should happen only to the light signal.

duri said:
If I consider only the observer in the train frame (what ever be the observer's frame, observer will feel himself to be stationary). The source of the signal moves relative to him with velocity v.
The velocity of the source is irrelevant. All that matters is the speed of the signal.

But the signal velocity is c. When source of the signal is moving towards him at the front of the observer and away from him at rear of the observer. Then relative velocity of the signal measured by observer from front and rear are c+v and c-v respectively.
No, the speed of the signal with respect to that observer is c. That's all that matters.

If this is wrong then the observer in the train should receive the signal simultaneously.
Only if the flashes struck the ends of the train at the same time according to the train frame. But that is not given (and is the point of the exercise).

So, in this case he will receive the front signal first.
The only reason you know this is because you have viewed the experiment from the track frame, which is the frame in which the flashes strike the ends of the train simultaneously. This allows you to deduce that the flashes were not simultaneous in the train frame.

Here, only one frame is involved.
No. You cheated.

Let me put this way,
1. Observer moving with velocity v and source of signal from the front and rear are stationary from stationary reference. Observer is stationary with his own reference and source of signal is moving at velocity -v. These two are identical. This doesn't talks about speed of signal so invariance of c is not required.

2. Simultaneity of the observer in the train breaks because of c+v and c-v in his frame. Here v is the prime variable for break down of simultaneity and not c. If v goes to zero observer will receive the signals simultaneously. Here also c is irrelevant, only condition is c in c+v and c in c-v must be same. Since c+v and c-v is on the same frame. Frame invariant condition is not required for this.

3. Due to symmetry in 1 and dependence of v in 2, source of velocity v which is really causing the break down of simultaneity and not c.

Can someone explain which one of these three points are wrong in classical sense. And why frame invariance of speed of light affects required.

duri said:
Let me put this way,
1. Observer moving with velocity v and source of signal from the front and rear are stationary from stationary reference. Observer is stationary with his own reference and source of signal is moving at velocity -v. These two are identical. This doesn't talks about speed of signal so invariance of c is not required.
Why do you think the speed of the source is relevant?

Make it simple. Set it up like this: There are giant flash bulbs at each end of the train. Now the source of each flash moves with the train, so the speed of the source is zero with respect to the train observer.

The setup is the same: The bulbs flash at the same time according to the track observer.

Now what?

duri said:
2. Simultaneity of the observer in the train breaks because of c+v and c-v in his frame. Here v is the prime variable for break down of simultaneity and not c. If v goes to zero observer will receive the signals simultaneously. Here also c is irrelevant, only condition is c in c+v and c in c-v must be same. Since c+v and c-v is on the same frame. Frame invariant condition is not required for this.
...
Can someone explain which one of these three points are wrong in classical sense. And why frame invariance of speed of light affects required.

#2 is predicted by Newtonian mechanics, but is demonstrably false (google for "Michelson-Morley experiment") and also is not predicted (but not precluded) by the laws of electricity and magnetism (google for "Maxwell's equations", look at the derivation of ##c## there).

You are right about what happens when ##v## goes to zero... But that's going to be true of all theories.

Nugatory said:
#2 is predicted by Newtonian mechanics, but is demonstrably false (google for "Michelson-Morley experiment")

If I interpret Michelson-Morley experiment in other way. There is no relative motion between source and observer in observer's frame. So, I can't expect changes in fringe pattern what ever angle the table is rotated. Assumption of ether flowing with velocity v is what demonstrated as incorrect.

Take for example ripple in the water. It doesn't matter observer moves or water container moves, as long as water doesn't flows waves would reflect back at same time. Only in case of water flows, wave reflects at different time. Its all about relation between medium and energy moving through the medium. In case of light since there is no medium, relative velocity is not possible to define between wave and medium. Light has to travel at same speed in vacuum. This also given by electromagnetic properties of vacuum.

I got some understanding while replying this. But I got new confusion too, If medium velocity is the key factor (which is not the case for light in vacuum). How inertial frame comes into picture.

## 1. What is Einstein's Train Thought Experiment?

Einstein's Train Thought Experiment, also known as the "Relativity Train", is a hypothetical scenario created by Albert Einstein to illustrate the concepts of special relativity. It involves a train moving at a constant velocity and a person standing on the train observing the behavior of a light beam.

## 2. How does the train thought experiment work?

In the thought experiment, there are two observers: one on the train and one on the platform. The observer on the train shines a light beam from the middle of the train towards the front and back of the train. The observer on the platform sees the light beam travel at the same speed in both directions. However, the observer on the train sees the light beam travel at the same speed in both directions. However, the observer on the train sees the light beam travel at different speeds due to the train's motion.

## 3. What does Einstein's Train Thought Experiment prove?

This thought experiment demonstrates the principles of special relativity, specifically the concept of relative motion and the constancy of the speed of light. It shows that the laws of physics are the same for all observers in uniform motion, regardless of their frame of reference.

## 4. Why is Einstein's Train Thought Experiment important?

Einstein's Train Thought Experiment is important because it helped to revolutionize our understanding of space and time. It led to the development of the theory of special relativity, which has had a significant impact on modern physics and has been confirmed by numerous experiments.

## 5. What are the real-world applications of Einstein's Train Thought Experiment?

The principles demonstrated in Einstein's Train Thought Experiment have practical applications in fields such as GPS technology and particle accelerators. They also play a crucial role in our understanding of the universe and how it works, including phenomena such as black holes and the expanding universe.

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