# Einstein Thought Experiment

## Main Question or Discussion Point

I do not understand Einstein's thought experiment explaining special relativity. If I understand it correctly, you have two people. One is on the center of a moving train, and the other is on the ground next to the tracks. As the one on the train and the observer pass eachother, lightning strikes the two ends of the train. This, first of all, is illogical to me. It has just been stated that two bolts of lightning strike just as the two people pass eachother. Is that not simultaneous? But continuing, the person off the train sees the lightning bolts at the same exact time, because light travels constantly. This also seems to prove to me that the lightning struck at the same time. Finally, the person on the train does not see the bolts at the same time, because he has moved while the light was traveling towards him. Instead of concluding that they didn't strike at the same time, that observer would know that he is moving, and therefore know that his perceptions of the lightning strikes are slightly inaccurate. Right?

## Answers and Replies

Related Special and General Relativity News on Phys.org
Hootenanny
Staff Emeritus
Gold Member
As the one on the train and the observer pass eachother, lightning strikes the two ends of the train. This, first of all, is illogical to me. It has just been stated that two bolts of lightning strike just as the two people pass eachother. Is that not simultaneous?
The two strikes are simultaneous as seen by the observer on the platform. Simultinatiety is a relative concept. If two observers are in realtive motion and one finds two events to be simultaneous, in general the other will not.
But continuing, the person off the train sees the lightning bolts at the same exact time, because light travels constantly. This also seems to prove to me that the lightning struck at the same time. Finally, the person on the train does not see the bolts at the same time, because he has moved while the light was traveling towards him. Instead of concluding that they didn't strike at the same time, that observer would know that he is moving, and therefore know that his perceptions of the lightning strikes are slightly inaccurate. Right?
That is of course assuming that the observer on the train accepts SR.

"The two strikes are simultaneous as seen by the observer on the platform. Simultinatiety is a relative concept. If two observers are in realtive motion and one finds two events to be simultaneous, in general the other will not."

That is my misunderstanding. If the lightning strikes hadn't been simultaneous, than the train observer would not have received them at the times he did.

HallsofIvy
Homework Helper
I do not understand Einstein's thought experiment explaining special relativity. If I understand it correctly, you have two people. One is on the center of a moving train, and the other is on the ground next to the tracks. As the one on the train and the observer pass eachother, lightning strikes the two ends of the train. This, first of all, is illogical to me. It has just been stated that two bolts of lightning strike just as the two people pass eachother. Is that not simultaneous?
As Hootenanny said, that is misquoting Einstein. The observer on the platform sees the two bolts of lightning strike at the same time as the passenger on the train passes him. The passenger on the train does not see it that way.

But continuing, the person off the train sees the lightning bolts at the same exact time, because light travels constantly. This also seems to prove to me that the lightning struck at the same time.
Why does it? It proves that the lightning struck at the same time in the reference frame of the person on the platform.

Finally, the person on the train does not see the bolts at the same time, because he has moved while the light was traveling towards him. Instead of concluding that they didn't strike at the same time, that observer would know that he is moving, and therefore know that his perceptions of the lightning strikes are slightly inaccurate. Right?
How would he know that he is moving? By watching the ground move by? All motion is relative to something else. Suppose he could not see the ground or any buildings outside the train, only the unchanging tracks stretching out behind and before him- would that tell him he could was moving? Even if he were watching the ground and "knew he was moving" (relative to the ground), he would only conclude that his perceptions were "distorted" compared to the person on the platform. Why should he accept that person perceptions as be "the" correct ones.
Try this to get rid of any extraneous "landmarks" that might make one person think he is the one moving, instead of making this a person on a train and a person on a platform, make it two people passing each other in outer space with no "landmarks"- one of them, for some reason, carrying a very long pole on which he sees two flashes of light just as he is passing the other person. Again one sees the two flashes as simultaneous, the other doesn't. Which one is to conclude that he is moving and his perceptions are distorted? Yes, the one who sees the flashes as not simultaneous might conclude that the flashes really were simultaneous but because he is moving toward one its light go to him first and it appeared to occur earlier. But the other person could just as well conclude that the flashes were NOT really simultaneous- he just saw them as simultaneous because he is moving toward the one that "really" occured later.

"As Hootenanny said, that is misquoting Einstein. The observer on the platform sees the two bolts of lightning strike at the same time as the passenger on the train passes him. The passenger on the train does not see it that way."
That is not what I read. What I read said that two bolts of lightning strike just as the two people pass eachother:

Lightning flashes strike two ends of the train just when the two observers pass each other. According to the observer on the platform, the flashes occurred simultaneously because he receives the flashes at the same time. This is based on the assumption (or, as Einstein emphasized, the stipulation) that light speed is the same in all directions. On the other hand, the observer in the train is moving toward the point at which the front flash was given off, and moving away from the rear flash. This means that the light flash coming from the front will have less distance to cover toward the train observer compared to the distance the flash needs to cover that is coming from the back of the train. Consequently, the flashes do not reach the train observer simultaneously. Assuming that the speed of light is a constant relative to the train, the train observer must conclude that the lightning flashes did not strike the ends of the train simultaneously. from http://http://en.wikipedia.org/wiki/Talk:Relativity_of_simultaneity" [Broken]
Is this not what Einstein said?

Last edited by a moderator:
This thread and its variants come up so many times that it seems the way the thought experiment is explained in many text books does not clearly explain to everyone this basic illustration of non simultaneity in moving in frames moving relative to each other.

Assume simultaneity in the platform frame. The light fronts meet halfway between the strikes on the PLATFORM at the platform observer. Because all observers must agree that this event happened, the train based observer must also see this happen at this point.

However, and this is the important point, the train based observer will reason ( CORRECTLY ) that if the strikes were simultaneous in his frame then the light fronts would meet at the centre of the TRAIN and the ground based observer would not have simultaneity in his platform based frame.

Because there is no absolute frame the reasoning is equally valid with the observers interchanged.

So what they both see and agree on, and they must agree on what they SEE, depends on which frame you, the thought experimenter, decide simultaneity to be in.

Matheinste.

"How would he know that he is moving? By watching the ground move by? All motion is relative to something else. Suppose he could not see the ground or any buildings outside the train, only the unchanging tracks stretching out behind and before him- would that tell him he could was moving? Even if he were watching the ground and "knew he was moving" (relative to the ground), he would only conclude that his perceptions were "distorted" compared to the person on the platform. Why should he accept that person perceptions as be "the" correct ones.
Try this to get rid of any extraneous "landmarks" that might make one person think he is the one moving, instead of making this a person on a train and a person on a platform, make it two people passing each other in outer space with no "landmarks"- one of them, for some reason, carrying a very long pole on which he sees two flashes of light just as he is passing the other person. Again one sees the two flashes as simultaneous, the other doesn't. Which one is to conclude that he is moving and his perceptions are distorted? Yes, the one who sees the flashes as not simultaneous might conclude that the flashes really were simultaneous but because he is moving toward one its light go to him first and it appeared to occur earlier. But the other person could just as well conclude that the flashes were NOT really simultaneous- he just saw them as simultaneous because he is moving toward the one that "really" occured later."

All that is necessary is movement. If neither person knows who moved, all that does is make it so that you don't know who is right. One of them is still right. But what if they both start a stopwatch at the moment they pass eachother. We will say the train is 10 units long and that light moves at one unit per second. If the person on the train is moving, he will see the bolt that he is moving towards strike five feet away in less than five seconds. He will therefore conclude that he is moving. If the other person is moving, and not the one on the train, he will see both bolts strike after times agreeable to the speed of light and to the distance he was away from where they struck.

Last edited:
Hootenanny
Staff Emeritus
Gold Member
All that is necessary is movement. If neither person knows who moved, all that does is make it so that you don't know who is right. One of them is still right.
This raises a fundamental point regarding special relativity. Einstein's first postulate of special relativity states that the laws of physics are the same for all inertial reference frames. In other words, there are no preferred frames of reference, an observation made in one inertial frame of reference is equally valid as another observation made in any other frame. So in your train experiment, both observers are correct.
However, let's say that light moves at one unit per second, and that the train is 10 units long. One of the two people is moving at one unit per 5 seconds.
Planck units, I like
When the two people pass eachother (at five feet from both ends of the train), they both start a stopwatch. One of them will end up seeing lightning strike five feet away after 4 and 6 seconds, or 4 and 6 feet away after 5 seconds. The only explanation for this is that that person was the moving one. Also, if both were moving, than both scenarios would happen, and both would know that they are moving.
I don't quite follow your reasoning here. Tell me, have you met the Lorentz transformations yet? If you have we could clear this up in two seconds.

"This raises a fundamental point regarding special relativity. Einstein's first postulate of special relativity states that the laws of physics are the same for all inertial reference frames. In other words, there are no preferred frames of reference, an observation made in one inertial frame of reference is equally valid as another observation made in any other frame. So in your train experiment, both observers are correct."

I guess I didn't really mean "right". I meant that I think simultaneity is still possible even if nobody knows who is moving.

"I don't quite follow your reasoning here. Tell me, have you met the Lorentz transformations yet? If you have we could clear this up in two seconds."

Sorry, my reasoning was very faulty there. I edited it. Unfortunately, I have not met the Lorentz transformations. I am unacquainted with nearly all of physics, unfortunately

JesseM
All that is necessary is movement. If neither person knows who moved, all that does is make it so that you don't know who is right.
In relativity there is no absolute notion of "movement", only movement relative to something else. In the Earth's frame, the train is moving, but in the train's frame, the Earth is moving, and both perspectives are equally valid.
go9ers14 said:
But what if they both start a stopwatch at the moment they pass eachother. We will say the train is 10 units long and that light moves at one unit per second.
The distance that light travels in a second is known as a "light-second" (ls). So the train is 10 ls long...but is that in the train's frame, or in the Earth's frame? Keep in mind that each observer measures the length of objects in motion relative to themselves to shrink.
go9ers14 said:
If the person on the train is moving, he will see the bolt that he is moving towards strike five feet away in less than five seconds.
Did you mean "five units away" rather than "five feet away? One thing that's important to note is that the two observers disagree about the distance between the lightning strike and the train-observer at the moment the strike happens. If the Earth-observer measures the lightning strike to happen five light-seconds from the train-observer, the Earth-observer also measures the train-observer's ruler to be shrunk relative to his own, so that the lightning strike happens at a greater distance as measured by the train-observer. For example, if the train is moving at 0.6c (0.6 times the speed of light) relative to the Earth, an increment of 1-ls on the train-observer's ruler will appear to be shrunk to a length of 0.8-ls in the Earth-observer's frame*, so if the Earth-observer measures the lightning strike to happen at a distance of 5 ls according to his own ruler, that means the train-observer measured the lightning strike to happen at a distance of 5/0.8 = 6.25 ls using a ruler on the train (the train-observer also measures the length of the train to be 12.5 ls rather than 10 ls).

There is a further complication in that clocks which are synchronized in one frame are out-of-sync in another--this is known as "the relativity of simultaneity". Suppose the train-observer has one clock sitting next to him in the middle of the train, and another clock sitting on the end of the train where the lightning hits, and these two clocks are synchronized in his own frame. In the Earth observer's frame, these two clocks actually appear out-of-sync, with the clock at the center of the train ahead of the clock at the end by 3.75 seconds**. So if the lightning hits the spot near the far end when the train's clock there reads t=2 seconds, from the Earth's perspective the clock at the center of the train reads t=5.75 seconds at that moment. After 3.125 seconds in the Earth's frame, the light from the lightning has moved 3.125 light-seconds in the direction of the center, and the center itself has moved (3.125 ls)*(0.6c) = 1.875 ls in the direction of the strike...since the center of the train was originally 5 ls from the position of the strike in the Earth's frame, it is now 5 - 1.875 = 3.125 ls from the position of the strike, so this is how long it takes the light from the strike to meet up with the center of the train, in the Earth's frame. However, because of time dilation the clock at the center only appears to be ticking at 0.8 the normal rate in the Earth's frame***, so since it started off reading t=5.75 seconds at the moment of the strike in the Earth's frame, it reads t = 5.75 + (3.125)*(0.8) = 5.75 + 2.5 = 8.25 seconds at the moment the light from the strike reaches it.

From the perspective of the train's frame, the clocks at the end and center were synchronized, so if the lightning struck the end when the clock there read t=2 seconds, then the clock at the center of the train must also have read t=2 seconds "at the same moment" that the lightning struck (the relativity of simultaneity means that different frames disagree on whether events at different locations happened simultaneously, i.e. 'at the same moment'). Since the light reached the center of the train when the clock at the center read t = 8.25 seconds, that means the light must have taken 8.25 - 2 = 6.25 seconds to travel from the end of the train to the center, in the train's frame. And remember, in the train's frame the distance between the center and the end is 6.25 light-seconds! So there is no sense in which the train observer must consider himself to be "moving"--he measures light to travel at one light-second per second relative to the train, just as the Earth observer measures light to travel at one light-second per second relative to the Earth.

*the length contraction formula says that if an object is moving at speed v in your frame, and its length is L in its own rest frame, its length in your frame will be $$L*\sqrt{1 - v^2/c^2}$$. So if the train is moving at v=0.6c in the Earth's frame, and there is a ruler on the train which is 1 light-second long in the train's frame, then its length will only be (1 ls)*squareroot(1 - 0.6^2) = (1 ls)*0.8 = 0.8 ls.

**If two clocks are a distance of x apart in their own frame, and synchronized in their own frame, and they're moving at speed v relative to you, then in your frame the back clock will be ahead of the front clock by a factor of vx/c^2. In this case the clock at the center and the clock at the end are a distance of 6.25 ls apart in their own frame, and moving at 0.6c in the Earth's frame, so in the Earth's frame the center clock is ahead by (0.6c)(6.25 ls)/c^2 = 3.75 seconds.

***The time dilation formula says that clocks in motion relative to you will be slowed down by a factor of $$\sqrt{1 - v^2/c^2}$$ in your frame.

Last edited:
Hootenanny
Staff Emeritus
Gold Member
Nice post Jesse, not much else to say after that...:uhh:

Hi Go9ers14.

We must first clear up the idea of absolute motion before we can move on to non simultaneity.

You are assuming that there is a fixed background frame relative to which light travels and which observers move or are at rest relative to. Being at rest or moving in this frame has no meaning as there is no such frame.

Imagine there is a fixed frame such as a pool of water. You are moving relative to this and someone else is not. As you pass each other the still observer drops a stone. The ripples radiate outwards from him. He remains at the centre of the disturbance away from which the ripples move. You do not.
This is how you think things are in the case of light.

In the case of light this is not thre case. If the so called still observer starts a ripple of light waves ( a flash of light ) he remains at the centre of the ripple as far as he is concerned and you do not. BUT as far as you are concerned it is you who remain at the centre of the ripples and he does not. Strange but this is a consequence of the speed of light being the same for ALL observers.

This point is fundamental to the whole idea of relativity.

Bye Matheinste.

In the case of light this is not thre case. If the so called still observer starts a ripple of light waves ( a flash of light ) he remains at the centre of the ripple as far as he is concerned and you do not. BUT as far as you are concerned it is you who remain at the centre of the ripples and he does not. Strange but this is a consequence of the speed of light being the same for ALL observers.
That is exactly right.

Another way of looking at this is to take a space-time view of this.

The two observers are semi-rotated with respect to each other which causes them to measure distance and time differently. However, with respect to the photons their semi-rotation is identical, so their views on the photons are identical.