# B Einstein's train and simultaneity

#### TheQuestionGuy14

There's just one thing I don't understand about all this, Einstein's train thought experiment.

It basically states that an observer in a train moving sees two lightning flash at the front and the back of the train car. To them, the front happens first, whereas the back happens next. To a stationary observer, they are simultaneous.

But, wouldn't they be simultaneous to the person in the train too? As light always travels at c in all frames, so the light would have to reach them from the front and the back at the same time, right?

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#### Ibix

But, wouldn't they be simultaneous to the person in the train too? As light always travels at c in all frames, so the light would have to reach them from the front and the back at the same time, right?
No. Because, as you note, the strikes weren't simultaneous in the train frame.

#### Dale

Mentor
Ok, I understand.

There's just one thing I don't understand about all this, Einstein's train thought experiment.

It basically states that an observer in a train moving sees two lightning flash at the front and the back of the train car. To them, the front happens first, whereas the back happens next. To a stationary observer, they are simultaneous.

But, wouldn't they be simultaneous to the person in the train too? As light always travels at c in all frames, so the light would have to reach them from the front and the back at the same time, right?
Again, I recommend working out the math on this.

#### Mister T

Gold Member
But, wouldn't they be simultaneous to the person in the train too? As light always travels at c in all frames, so the light would have to reach them from the front and the back at the same time, right?
But the point being made does not concern the simultaneity of the arrival of the light flashes, it concerns the simultaneity of the emission of those light flashes.

If it were true that the observed speed of light differed from $c$ in such a way that we add to (when moving away from source) or subtract from (when moving toward source) the train's speed to get the light speed then the two light beams would have been emitted simultaneously in all inertial frames. The fact that the speed is always $c$ regardless of the train's speed means that the two light beams had not been emitted simultaneously in some inertial reference frames.

#### TheQuestionGuy14

But the point being made does not concern the simultaneity of the arrival of the light flashes, it concerns the simultaneity of the emission of those light flashes.

If it were true that the observed speed of light differed from $c$ in such a way that we add to (when moving away from source) or subtract from (when moving toward source) the train's speed to get the light speed then the two light beams would have been emitted simultaneously in all inertial frames. The fact that the speed is always $c$ regardless of the train's speed means that the two light beams had not been emitted simultaneously in some inertial reference frames.
So, would a better example be this:

Two supernova occur, one 1 lightyear to my right, the other 1 lightyear to my left. When they both arrive 1 year later, I assume they are simultaneous. However, if I travelled toward the supernova on the right, the light from the two would still arrive simultaneously, so, I assume since I headed right, that the left supernova must've occurred first, due to the light having to travel more distance. Is this the same as the train example?

#### PeterDonis

Mentor
Two supernova occur, one 1 lightyear to my right, the other 1 lightyear to my left. When they both arrive 1 year later, I assume they are simultaneous.
No, you don't "assume" they are simultaneous. This sequence of events is what defines "simultaneous": both supernovas are the same distance from you (because you said so), and the light from both of them arrives at you at the same event (it's better not to use the term "simultaneous" here since now we're talking about a single observer receiving two signals at the same place--where the observer is--at the same instant, so we're talking about only one event in spacetime, not two).

if I travelled toward the supernova on the right, the light from the two would still arrive simultaneously
No, it wouldn't. You would receive the light from the supernova on the right before you received the light from the supernova on the left. Just as in the train example, the train observer receives the light from the flash at the front of the train before he receives the light from the flash at the back. In both cases, the reason for this is very simple: the moving observer is moving towards the flash on the right and away from the flash on the left.

#### TheQuestionGuy14

No, you don't "assume" they are simultaneous. This sequence of events is what defines "simultaneous": both supernovas are the same distance from you (because you said so), and the light from both of them arrives at you at the same event (it's better not to use the term "simultaneous" here since now we're talking about a single observer receiving two signals at the same place--where the observer is--at the same instant, so we're talking about only one event in spacetime, not two).

No, it wouldn't. You would receive the light from the supernova on the right before you received the light from the supernova on the left. Just as in the train example, the train observer receives the light from the flash at the front of the train before he receives the light from the flash at the back. In both cases, the reason for this is very simple: the moving observer is moving towards the flash on the right and away from the flash on the left.
So, the event you move towards always happens first, basically? But doesn't that mean the events are still simultaneous, and it just took the light longer to reach you from the other?

#### PeroK

Homework Helper
Gold Member
2018 Award
So, the event you move towards always happens first, basically? But doesn't that mean the events are still simultaneous, and it just took the light longer to reach you from the other?
How could that be? When an event happens is not dependent on the time it takes a light signal to reach you. When you learn about that event may be dependent on the time light takes.

That Einstein train-lightning example is possibly the worst way to think about simultaneity, IMHO, because it does seem to infer that something happens when the light reaches you. Although that is definitely not what was intended.

PS while I'm on the subject: what's the worst possible way to learn about Special Relativity?

Study the paradoxes, which are designed deliberately to confuse you!

[\spoiler]

#### Ibix

So, would a better example be this:

Two supernova occur, one 1 lightyear to my right, the other 1 lightyear to my left. When they both arrive 1 year later, I assume they are simultaneous. However, if I travelled toward the supernova on the right, the light from the two would still arrive simultaneously, so, I assume since I headed right, that the left supernova must've occurred first, due to the light having to travel more distance. Is this the same as the train example?
You've stated this problem ambiguously. In the "travelling" version, did you pass the stationary observer at the same time as the light arrives from the supernovae? Or did you start off at the same place as the stationary observer and move towards one of the stars before the supernova flashes arrived? Peter is reading you as meaning the latter, but I have a suspicion you meant the former.

It doesn't change the conclusion about simultaneity, but it does change the route you take to get there.

#### Mister T

Gold Member
So, the event you move towards always happens first, basically?
If it were that simple that's the explanation you'd see stated. Do you think that if it were that simple people would give more complicated explanations? Why would anybody want to do that?

#### PeterDonis

Mentor
So, the event you move towards always happens first, basically?
Not "always". Under the particular conditions specified in this problem, yes.

But doesn't that mean the events are still simultaneous, and it just took the light longer to reach you from the other?
No. "Simultaneous" according to a given observer is defined as light signals from events at the same distance from the observer, arriving at the observer at the same event (same instant). The two flashes are equidistant from the moving observer (train, or ship moving towards the right), so the fact that they arrive at the moving observer at different events (different instants) means they are not simultaneous according to that observer.

Staff Emeritus
PS while I'm on the subject: what's the worst possible way to learn about Special Relativity?
Post a parade of wrong statements, hoping someone will correct you?

"Simultaneous" according to a given observer is defined as light signals from events at the same distance from the observer, arriving at the observer at the same event (same instant).
I would not define simultaneous this way. Two events are simultaneous to a given observer if they have the same time coordinate. You have provided one example of establishing that the events are simultaneous, but I wouldn't use this example as a definition.

#### PeterDonis

Mentor
I would not define simultaneous this way
I gave Einstein's operational definition of simultaneity, which is the one he used when he presented his train thought experiment. I agree that this is not the most general definition, but it seems like the most relevant one for this particular discussion (since the OP doesn't appear to be considering non-inertial coordinates or curved spacetimes).

#### OCR

Post a parade of wrong statements, hoping someone will correct you?
I'm happy to do that... .

That Einstein train-lightning example is possibly the worst way to think about simultaneity, IMHO, because it does seem to infer imply that something happens when the light reaches you.

Imply or Infer?

Also...
How did you screw up the spoiler tag ?

.

.

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#### Janus

Staff Emeritus
Gold Member

There's just one thing I don't understand about all this, Einstein's train thought experiment.

It basically states that an observer in a train moving sees two lightning flash at the front and the back of the train car. To them, the front happens first, whereas the back happens next. To a stationary observer, they are simultaneous.

But, wouldn't they be simultaneous to the person in the train too? As light always travels at c in all frames, so the light would have to reach them from the front and the back at the same time, right?
According the track observer, the lightning strikes both ends of the train and the tracks at at points that are an equal distance from him, he sees the flashes from those strikes at the same time and thus knows that the strikes occured simultaneously. He also notes that the flash from one strike reaches the train observer before the other one does, like this:

Note that the right flash meets up with the train observer when he has traveled ~1/3 of the distance to the right dot ( where the lightning struck the tracks), But left flash doesn't catch up to him until he is about even with the right dot.
The other thing to keep in mind is the the length of the moving train is length contracted according to the track observer.

when we switch to the train observer, we need to note a few things:
The train is its proper length while it is the tracks that are length contracted, thus the train does not fit exactly between the red dots.
As a result the front of the train reaches the right dot before the rear reaches the left dot.
The lightning strikes still hit the ends of the train when they next to their respective dots.
The right flash and train observer still meet up when the train observer is ~1/3 of the way between the track observer and right dot.
The left flash still meets up with the train observer when he is about even with the right dot.
both flashes still meet up at the track observer at the same moment.
In order for all the above to remain true while still maintaining a constant speed for the flashes as measured by the train, events must unfold like this:

With the right right lightning strike occurring first and then the left lightning strike.

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#### stevendaryl

Staff Emeritus
Post a parade of wrong statements, hoping someone will correct you?
I think that's the approach some people take. Or others are inspired by the elegant thought experiments of Einstein, but instead of trying to understand his, they make up their own and come to completely...shall we say "non-mainstream"?...conclusions. Then rather than asking for help in understanding the standard theory, they demand that you understand their arguments.

I suppose that if you have an Einstein-caliber mind, you can get away with it. Unfortunately, people are not great judges of their own brilliance.

#### Peter Martin

It seems to me that Einstein is inadvertently claiming absolute motion and absolute rest when he states that the train observer sees the strikes sequentially while the ground observer sees them as simultaneous. Since there's no acceleration, we are free to reverse the roles and consider the train "at rest" and the landscape "in motion". In which case the train observer would see the strikes as simultaneous and the ground observer would see the rear strike first. No??

#### Ibix

No. He's simply declaring that the lightning strikes happen to be simultaneous in the ground frame this time. Next time we run the experiment the strikes might be simultaneous in the train frame, but this time they aren't.

#### Janus

Staff Emeritus
Gold Member
It seems to me that Einstein is inadvertently claiming absolute motion and absolute rest when he states that the train observer sees the strikes sequentially while the ground observer sees them as simultaneous. Since there's no acceleration, we are free to reverse the roles and consider the train "at rest" and the landscape "in motion". In which case the train observer would see the strikes as simultaneous and the ground observer would see the rear strike first. No??
No. While there are events that the train observer would deem as being simultaneous and the ground observer does not, they would have to be different pair of of events.
The point is that we start with the fact that the events in question( the lightning strikes) are deemed simultaneous in the ground frame, and then go on to determine whether or not these same events are deemed simultaneous in the train frame.
There are going to be events that both frames must agree on. For example, both frames will agree that the light flashes from the lightning strikes will reach the ground observer at the same moment, and both frames will agree as to where the train observer is located relative to the tracks, when each the light flashes reaches him( different points of the tracks according to both frames).

#### pervect

Staff Emeritus
So, would a better example be this:

Two supernova occur, one 1 lightyear to my right, the other 1 lightyear to my left. When they both arrive 1 year later, I assume they are simultaneous. However, if I travelled toward the supernova on the right, the light from the two would still arrive simultaneously, so, I assume since I headed right, that the left supernova must've occurred first, due to the light having to travel more distance. Is this the same as the train example?
You appear to be describing a different experiment than Einstein's. It's not entirely clear what you mean by "If I travelled toward the supernova on the right", I am assuming that you are imagining another observer, moving towards the right, an obsever I will call youprime. You and youprime happen to be at the same point when the light flashes arrive, and you and youprime agree that the light flashes arrive simultaneously.

Let's compare this to Einstein's experiment, though.

From Einstein's original description of his thought experiment <<link>>

Einstein works out that an observer in the middle of the train would not see both light flashes simultaneously.

f an observer sitting in the position M’ in the train did not possess this velocity, then he would remain permanently at M, and the light rays emitted by the flashes of lightning A and B would reach him simultaneously, i.e. they would meet just where he is situated. Now in reality (considered with reference to the railway embankment) he is hastening towards the beam of light coming from B, whilst he is riding on ahead of the beam of light coming from A. Hence the observer will see the beam of light emitted from B earlier than he will see that emitted from A.
You have worked out that you and youprime do see the light flashes simultaneously. But by comparing your version of the thought experiment to Einstein's , we can see that the

By comparison to Einstein's thought experiment, though, we can conclude that youprime cannot be in the "center of the train". Another way of saying this is that youprime has a frame of reference in which he is at rest, and the supernova are moving. In youprime's frame of reference, because he is not "in the center of the train", the supernova are not equally distant at the instant in time, as defined in his frame of reference, when the light flahses arrive.

#### Mister T

Gold Member
It seems to me that Einstein is inadvertently claiming absolute motion and absolute rest when he states that the train observer sees the strikes sequentially while the ground observer sees them as simultaneous.
He's assuming that the speed $c$ is absolute.

#### FactChecker

Gold Member
2018 Award
It seems to me that Einstein is inadvertently claiming absolute motion and absolute rest when he states that the train observer sees the strikes sequentially while the ground observer sees them as simultaneous.
No assumption about the claim. The best experiments imaginable kept showing that if two lights were flashed simultaneously according to carefully synchronized clocks of an observer then they will reach the midpoint at the same time. The light flashes are simultaneous as defined by the synchronized clocks of the observer on the embankment. They are not simultaneous as defined by the synchronized clocks on the train. That is what "relativity of simultaneous" means.
Since there's no acceleration, we are free to reverse the roles and consider the train "at rest" and the landscape "in motion". In which case the train observer would see the strikes as simultaneous and the ground observer would see the rear strike first. No??
Not for those lightning strikes. The train observer does not think that those strikes were simultaneous. You can reverse the situation using other lightning strikes that the train observer does think are simultaneous. In that case, you are correct -- the observer on the embankment will think that they were not simultaneous and that the rear strike happened first. From this, you can start to see how both observers can think that the other observer's clocks are running slow.

#### Erland

PS while I'm on the subject: what's the worst possible way to learn about Special Relativity?

"Einstein's train and simultaneity"

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