Simultaneity: Train and Lightning Thought Experiment

[taenyfan]

I am puzzled over einstein's thought experiment on simultaneity.

In this experiment, a man is standing on a train platform. A woman is sitted in the middle of a moving train traveling towards the man. When the train is half past the man, lightning strikes at the same instant at both ends of the train. The man sees the lightning at the same time. This makes sense since the distance traveled by light from both ends is the same.

However, the thought experiment propose that the woman sees the light from the front of the train first. This is because she 'runs' into light from the front since she is moving forward with the train.She then conclude that lightning struck the front first since she is equidistant from the front and back of the train.

I am confused. Since the train is not accelerating, it can be treated as an inertial frame of reference. Speed of light c should be constant in the woman's frame of reference. Thus when only regarding the woman's frame, shdn't she see both lightning at the same time? Since both light travels at c and have to cover half of the train's length.

The fact that the woman runs into the front lightning is the observation from the man's frame of reference. So when we are talking about the woman's observations, why are we trying to use the man's frame of reference to predict the results? Shdn't we be isolating the woman's frame of reference and analysing that independently?

I hope my words are clear! Thanks for reading and help me out if you can[emoji1]

 

[Orodruin]

Thus when only regarding the woman's frame, shdn't she see both lightning at the same time? Since both light travels at c and have to cover half of the train's length.

No, this is the entire point. The strikes are simultaneous in the man's frame by definition. If you postulate that the strikes are simultaneous in the woman's frame it is a different setup and so in this setup you cannot get rid of the man's frame because it is part of the definition of when the lighting strike. The entire point is to compare what happen in the two frames and the conclusion is that if the strikes are simultaneous in the man's frame, they are not in the woman's.

Seen from the man's frame:

• He observes the strikes at the same time because they are equidistant from him and occur at the same time.
• The woman observes the strikes at different times because they are equidistant but the woman is moving towards one of the signals.

We can conclude the following about the woman's frame (she has to observe the same things as the man, i.e., that the man sees the strikes at the same time and she does not):

• The flashes are occur at the same distance from her because they occur at the ends of the train and she is in the middle.
• She sees one flash before the other, since the speed of light is the same in all directions, the one she sees first must have occurred first. Hence the strikes were not simultaneous. One occurred before she passed the man and the other after.
• Even if the strikes did not occur at the same time, the man is moving away from the one that occurred first and it will therefore take the light from that strike longer to catch up with him - resulting in that he sees both strikes at the same time.

I am confused. Since the train is not accelerating, it can be treated as an inertial frame of reference. Speed of light c should be constant in the woman's frame of reference.

Exactly, but your conclusion is not the logical one. The logical conclusion is that the strikes are not simultaneous in her frame. Otherwise the descriptions from the different inertial frames would not follow the same rules.

Thus when only regarding the woman's frame, shdn't she see both lightning at the same time? Since both light travels at c and have to cover half of the train's length.

This would be true only if the strikes were simultaneous in her frame. Your conclusion from this should be that, since whether she sees one first or both at the same time cannot depend on the inertial frame, you have to drop the assumption that the strikes were simultaneous in her frame.

The fact that the woman runs into the front lightning is the observation from the man's frame of reference. So when we are talking about the woman's observations, why are we trying to use the man's frame of reference to predict the results? Shdn't we be isolating the woman's frame of reference and analysing that independently?

Which signal arrives to the woman first cannot be frame dependent since any frame has to describe the same physical reality. You can do the computation in whatever frame you would like and you should get the same result.

 

[pixel]

Which signal arrives to the woman first cannot be frame dependent since any frame has to describe the same physical reality.

What qualifies as physical reality? Couldn't one say that to the man it's physical reality that flashes of light hit the front and back of the train at the same time? The distinction maybe needs to be made between spatially separated events and events that occur at the same location.

 

[pixel]

taneyfan: Suppose there is a device sitting next to the woman, with forward and backward looking sensors, that emits a beep when light strikes both sensors at the same time (in its frame of reference). If we analyze the situation in the man's frame of reference, he concludes that there should be no beep. Now it would be a strange world if the man didn't hear a beep but the woman did because she was moving relative to him. So she concludes that the light flashes reach her at different times. Since the lengths of the train in front and behind her are the same and the speed of light is c in both directions, the time taken for the flashes to reach her has to be the same, and she concludes that one occurred earlier than the other. Note that we're considering the simultaneity of two events at a given location in the woman's frame, that of the device.

 

[Orodruin]

What qualifies as physical reality?

By this I mean any measurable frame independent statement, which simultaneity is not (unless you in the statement specify the frame in which the events are simultaneous).

 

[Janus]

I am puzzled over einstein's thought experiment on simultaneity.

In this experiment, a man is standing on a train platform. A woman is sitted in the middle of a moving train traveling towards the man. When the train is half past the man, lightning strikes at the same instant at both ends of the train. The man sees the lightning at the same time. This makes sense since the distance traveled by light from both ends is the same.

However, the thought experiment propose that the woman sees the light from the front of the train first. This is because she 'runs' into light from the front since she is moving forward with the train.She then conclude that lightning struck the front first since she is equidistant from the front and back of the train.

I am confused. Since the train is not accelerating, it can be treated as an inertial frame of reference. Speed of light c should be constant in the woman's frame of reference. Thus when only regarding the woman's frame, shdn't she see both lightning at the same time? Since both light travels at c and have to cover half of the train's length.

Consider this: What is the woman's position with respect to the tracks when she sees each strike? If you are watching this from the tracks, it is clear that she is at a different point along the tracks when the light from each strike reaches her. Now consider this from the view of the woman. If, as you suggest, she sees the strikes simultaneously then she will be at a single point along the tracks when she sees both strikes. This would set up a physical contradiction between what she's says happens and what the person standing along the tracks says happened. For example, give her a camera and have her take a picture of the tracks when she's sees the strikes. Give a camera to each of a string of observers placed along the tracks with the instructions to take a picture of her is she is next to them when the light reaches her. After the experiment is over, we bring the photos together and compare them. You can't have her showing up with just one photo while the track cameras recorded two photos of her taking a picture, each at a different point of the tracks.
Once you agree that both observers must agree that the woman sees the strikes at different times and at different times, then you apply the constant speed of light and her equal distance from the ends of the train to determine that the strikes did not happen simultaneously according to her.

The fact that the woman runs into the front lightning is the observation from the man's frame of reference. So when we are talking about the woman's observations, why are we trying to use the man's frame of reference to predict the results? Shdn't we be isolating the woman's frame of reference and analysing that independently?

The point is that if she meets the light from the strikes at different times and different points of the tracks in one frame (the man's) she has to meet them at different times and different points of the tracks in her frame. We start in the man's frame simply because we set hings up so that it would be the frame in which the strikes occurred simultaneously. We then use this frame to worked out the events that both frames must agree on (for instance, both frames must agree that the light from the flashes reach the man simultaneously), to work out the sequence of events in the Woman's frame. You can't completely isolate the woman's frame from the man's frames because there are common events that they both must agree on.

 

[Ibix]

What qualifies as physical reality?

The physical reality is four dimensional. The emissions happen at different events. There is more than one way to slice spacetime into sets of "all of space, now". Different ways of doing that lead to different ideas about what's simultaneous. That's the thing that isn't physical - it's just a matter of which slicing ("foliation") is convenient for you.

 

[pixel]

By this I mean any measurable frame independent statement, which simultaneity is not (unless you in the statement specify the frame in which the events are simultaneous).

I guess the issue for me is that Einstein's train thought experiment is used to derive the fact that simultaneity is relative (presumably before knowing the Lorentz transformation, from which all of this simultaneity stuff can be easily derived). So can we make any statements about simultaneity being frame independent or not during the analysis of the experiment?

 

[Orodruin]

I guess the issue for me is that Einstein's train thought experiment is used to derive the fact that simultaneity is relative (presumably before knowing the Lorentz transformation, from which all of this simultaneity stuff can be easily derived). So can we make any statements about simultaneity being frame independent or not during the analysis of the experiment?

The statement is about events along the world lines of the observers. This is well defined.

 

[Mister T]

What qualifies as physical reality?

For the man the two flashes arrive at the same time. This is an example of a physical reality. It's a single event because it occurs at a single location at a single time. You might imagine, for example, that the man's head will explode if the two flashes arrive at the same time. The woman will agree that the two flashes arrived at the same time and that therefore the man's head explodes. It's a physical reality. It can't be that the head explodes in one frame and not in the other.

Likewise they'll both agree that the woman's head doesn't explode because the flashes don't hit her at the same time.

But the thought experiment is designed to show that a pair of spatially separated events can be simultaneous in one frame and not in another.

I guess the issue for me is that Einstein's train thought experiment is used to derive the fact that simultaneity is relative (presumably before knowing the Lorentz transformation, from which all of this simultaneity stuff can be easily derived).

It all follows from the two postulates. You can use the two postulates to derive the Lorentz transformation equations, which can then in turn be used to illustrate that simultaneity is relative. Or you can use the two postulates to illustrate it directly (by using, for example, the train thought experiment).

 

[pervect]

To borrow an example from the literature, suppose you have a small tape player that starts when a light signal hits the front side and stops when it hits the back side. The tape player is small enough that the internal propagation delays are negligible - an important point. If simultaneity were frame dependent, the tape player could play in some frames, and not play in others. But this doesn't make sense - everyone agrees on whether the tape player plays, or does not play, regardless of their frame of reference.

Sometimes the tape player is replaced more dramatically with a bomb.

It's important that the tape player be small enough to be regarded as point-like, but this shouldn't be a huge issue in practice. For instance, you could imagine the train cars being 100km long, and the tape player being a 1 cm.

 

[pixel]

To borrow an example from the literature, suppose you have a small tape player that starts when a light signal hits the front side and stops when it hits the back side. The tape player is small enough that the internal propagation delays are negligible - an important point.

How is this different from the example in post #4?

If simultaneity were frame dependent, the tape player could play in some frames, and not play in others.

But the frame dependence of simultaneity is the whole point of the train experiment. Again, I think the key point is distinguishing between spatially separated events and events at the same location such as your tape player example.

 

[pixel]

You might imagine, for example, that the man's head will explode if the two flashes arrive at the same time. The woman will agree that the two flashes arrived at the same time and that therefore the man's head explodes. It's a physical reality. It can't be that the head explodes in one frame and not in the other.

Isn't this again the same example as in post #4?

 

[Mister T]

Isn't this again the same example as in post #4?

Yes, but it's a response to a question that you asked after Post #4 was made.

But the frame dependence of simultaneity is the whole point of the train experiment. Again, I think the key point is distinguishing between spatially separated events and events at the same location such as your tape player example.

Not just events at the same location, but events at the same location and at the same time! We then call it a single event. If it happens according to one observer, it happens according all observers.

The relativity of simultaneity does indeed to refer to spatially separated events. But there's more to the story. For the two spatially separated events to occur simultaneously in one frame of reference, they have to be spatially separated in all frames of reference. No observer can be present at both events because it would require him to travel at a speed that's faster than light. Thus the order in which the events occur depends on the observer's velocity. The events are said to be causally disconnected, or in other words, they have a spacelike (as opposed to timelike) separation.

 

[harrylin]

I am puzzled over einstein's thought experiment on simultaneity.

In this experiment, a man is standing on a train platform. A woman is sitted in the middle of a moving train traveling towards the man. When the train is half past the man, lightning strikes at the same instant at both ends of the train. The man sees the lightning at the same time. This makes sense since the distance traveled by light from both ends is the same.

However, the thought experiment propose that the woman sees the light from the front of the train first. This is because she 'runs' into light from the front since she is moving forward with the train.She then conclude that lightning struck the front first since she is equidistant from the front and back of the train.

I am confused. Since the train is not accelerating, it can be treated as an inertial frame of reference. Speed of light c should be constant in the woman's frame of reference. Thus when only regarding the woman's frame, shdn't she see both lightning at the same time? [..]]

There is a variant of that experiment which may be easier to follow: https://en.wikipedia.org/wiki/Relativity_of_simultaneity#The_train-and-platform_thought_experiment
Here you start with a single source in the middle of the train, and analyse what will happen with the detection, as nicely depicted in the figure. If you can follow that, then Einstein's version may next be easy to understand too, as it's the return path of signals sent back to the center.

 

[Collin237]

What qualifies as physical reality?

Physical reality doesn't need to "qualify". It exists by itself and wends its way through things in an order which -- as physics is currently understood -- is unknowable. If event A is capable of causing event B, then it's impossible to see event B before event A. Otherwise it's a toss-up, and causality ensures that it doesn't make any difference.

On a classical scale, there are three kinds of direction:
Time-like, with both orientation and magnitude.
Light-like, with orientation but not magnitude.
Space-like, with magnitude but not orientation.
Event A can cause event B if and only if there is a path of time-like or light-like segments oriented from A to B.

 

[PeterDonis]

On a classical scale, there are three kinds of direction:
Time-like, with both orientation and magnitude.
Light-like, with orientation but not magnitude.
Space-like, with magnitude but not orientation.

This is not correct. Where are you getting this from?

The correct statement is that all three types of tangent vectors (the proper way of saying "direction") have an orientation; timelike vectors have negative squared magnitude (using the -+++ metric signature convention), lightlike vectors have zero squared magnitude, and spacelike vectors have positive squared magnitude.

 

[Collin237]

I was referring to line segments, not vectors. Yes of course you can orient a line segment through space by putting an arrow at one end. But if the line segment is time-like or light-like it has an orientation even without an arrow, because one end is later than the other.

 

[PeterDonis]

I was referring to line segments, not vectors.

I see. This works OK in flat spacetime, but in curved spacetime (i.e., in the presence of gravity), it has limitations. The tangent vector approach avoids these limitations.

However, there is also an alternative, which is to focus, not on the line segment itself, but on the two endpoints, i.e., on a pair of events. The separation of these events, timelike, lightlike, or spacelike, is an invariant even in curved spacetime and doesn't bring in any of the limitations of the "line segment" view.

if the line segment is time-like or light-like it has an orientation even without an arrow, because one end is later than the other.

Ah, I see, by "orientation" you mean "time ordering". Yes, this is true, two events which are timelike or lightlike separated have an invariant time ordering, whereas two spacelike separated events do not. However, "orientation" is not a good term for this, because it has other meanings: the one I had assumed before, which is more or less the "direction in spacetime" that a vector points (and as noted, all three types of vectors have orientations in this sense), and also the parity or "handedness" of a set of basis vectors.

 

[Stephanus]

You might want to check this out

Consider Einstein's Train example.
You have a train with an observer at the midpoint between the ends. you also have an observer standing along the tracks. Lightning strikes the end of the trains when, according to the track-side observer the train observer is passing him. Thus he sees the light from the strikes at the same time and determines that the strikes occurred simultaneously. Thus, according to the frame of the tracks, events look like this:..

There is still more. See his full explanation in the post.

These are the simulations that helped my SR learning.
With courtesy of @Janus

 

[Peter Martin]

After reading many of the replies to the lightening-train example, I think the confusion -- at least for me -- is that the description of the problem says that the two lightning strikes occur "simultaneously". This ignores that the whole purpose of the problem is to demonstrate that there is no such thing as objective simultaneity! So the very definition of the problem contradicts its conclusion: that objective simultaneity is a figment of the mind.

 

[vanhees71]

You have to keep very clear in which reference frame something is simultaneous. That's indeed the whole point of the train example. See

https://www.physicsforums.com/threa...trains-speed-relative-to.828679/#post-5211160
https://www.physicsforums.com/threa...trains-speed-relative-to.828679/#post-5211919

 

[Collin237]

It should be something like "the two lightning strikes come from the same discharge in the same cloud".

(Technically, even this doesn't exactly work, because lightning is crooked. A better example would be two searchlights mounted on an airplane.)

 

[Ibix]

It should be something like "the two lightning strikes come from the same discharge in the same cloud".

(Technically, even this doesn't exactly work, because lightning is crooked. A better example would be two searchlights mounted on an airplane.)

No - neither of those define "simultaneous" in this context. The definition of simultaneity is that an observer half way between sees (literally, receives light from) the two strikes touch the train at the same time. The source of the strikes doesn't matter. You could use firecrackers that just happen to go off in such a way that they satisfy this criterion.

 

[PeterDonis]

The definition of simultaneity is that an observer half way between sees (literally, receives light from) the two strikes touch the train at the same time.

To really be precise, the phrase "at the same time" should not be used here, since it could be taken as a synonym for "simultaneous" and make it seem like the definition is circular. It should be "at the same event (point in spacetime)", which makes it clear what is being stated.

 

[Ibix]

To really be precise, the phrase "at the same time" should not be used here, since it could be taken as a synonym for "simultaneous" and make it seem like the definition is circular. It should be "at the same event (point in spacetime)", which makes it clear what is being stated.

Indeed. Not my best phrasing - must proof read more carefully on a Friday night.

 

[Mister T]

After reading many of the replies to the lightening-train example, I think the confusion -- at least for me -- is that the description of the problem says that the two lightning strikes occur "simultaneously". This ignores that the whole purpose of the problem is to demonstrate that there is no such thing as objective simultaneity! So the very definition of the problem contradicts its conclusion: that objective simultaneity is a figment of the mind.

I agree. This part ...

When the train is half past the man, lightning strikes at the same instant at both ends of the train. The man sees the lightning at the same time. This makes sense since the distance traveled by light from both ends is the same.

would have been better stated as ...

Lightning strikes each end of the train. The man sees the strikes at the same time. It makes sense for him to conclude they struck at the same time since the distance traveled by light from both ends is the same.

 

[Josh_Seedman]

I'm obviously a bit late to this conversation but I was wondering: Suppose that two synchronized clocks were mounted on either end of the train, which are configured in such a way that each clock records the exact time instant (to within an adequate level of accuracy/precision) at which the lightning strikes the respective ends of the train. Since these clocks are both on the train (same reference frame), they should experience the same time dilation effects. Regardless of what the observer on the train "sees", it would seem that after the incident(s), the woman could take a very leisurely walk to both ends of the train, and make a note of the instant in time that each clock recorded. If the time instants are identical (to within an acceptable margin of error), I would think she could justifiably conclude that the lightning strikes were 'simultaneous'.

Now it would seem that the 'moving' train would suffer length contraction, with respect to the 'stationary' train. So perhaps we should stipulate that the moving train has a "rest-length" which just so happens to cause the front and back of the train to perfectly match up with the two points at which the two lightning strikes occur, when the train is traveling at the given constant velocity.

 

[Ibix]

two synchronized clocks

Synchronised in which frame? The two frames don't agree on what "synchronised" means. That's the fundamental point.

All of the stuff with the flashes of light turns out to be a procedure for synchronising two clocks. But the same procedure produces a different result in the two different frames.

 

[Josh_Seedman]

Well I guess I was thinking something like well before the lightning event, in fact how about well before the train started to move at all, the woman on the train synchronizes the two clocks with each other. That is, she verifies that the clocks are counting time at the same rate (again, within an acceptably small magnitude of error). She then carries one clock to the front of the train, mounts it, and then walks the other clock to the back of the train and mounts it. (And she walks at the exact same speed while she is carrying these clocks.) Now the train starts moving down the track. Can't we claim that these two clocks are in fact synchronized with each other, regardless of whichever inertial reference frame they both reside in?

I don't know, perhaps I am missing the point. I guess I would not be so concerned with what various observers might themselves observe. Instead, I would suggest that if the two clocks recorded the same time instant, that information would indicate that the lightning strikes were simultaneous, even if they did not appear to be simultaneous to the observer on the moving train.

 

[Arkalius]

Can't we claim that these two clocks are in fact synchronized with each other, regardless of whichever inertial reference frame they both reside in?

No. Assuming the train has Born rigidity (it maintains its proper length in each momentary rest frame during its acceleration), then the clock at the front of the train will run faster than the clock at the back during the acceleration, and when acceleration ends, both clocks will again run at the same speed but will be out of sync in the train's rest frame. In the platform rest frame, both clocks would slow down as the train accelerates at the same rate and remain synchronized. This is due to the fact that the plane of simultaneity at each point on the train is shifting during acceleration, causing "now" for any point on the train ahead of the point of interest (in the direction of acceleration) to shift into the "future" from where it was, and causing "now" for any point behind the point of interest to shift into what was the past of where it was.

The most important fact to remember about the relativity of simultaneity is that if you have two clocks separated by some nonzero distance in space, then they can be synchronized in at most one valid inertial frame of reference. In all others they will not be.

 

[Ibix]

Well I guess I was thinking something like well before the lightning event, in fact how about well before the train started to move at all, the woman on the train synchronizes the two clocks with each other. That is, she verifies that the clocks are counting time at the same rate (again, within an acceptably small magnitude of error).

Two clocks at rest with respect to one another will tick at the same rate. That isn't a problem. The question is, how do you determine that they're showing the same time? That they've been zeroed correctly? It's easy enough to come up with some procedure for checking this (for example, seeing if the clocks appear to show the same time when you are half way between them), but when you follow through the details of any procedure you'll find that the answer to that question depends on the velocity of the person making the measurement.

 

[Mister T]

She then carries one clock to the front of the train, mounts it, and then walks the other clock to the back of the train and mounts it.

That's a valid way to synchronize the clocks. Now consider another train moving along a parallel track. A man on that train does the same thing with his clocks so they are also synchronized. When the two trains pass each other the woman can check to see if the man's clocks are synchronized, to her they won't be but to him they will. Likewise, the man can check to see if the woman's clocks are synchronized. To him they won't be, but to her they will.

I don't know, perhaps I am missing the point. I guess I would not be so concerned with what various observers might themselves observe.

Well, the woman observed that her clocks were synchronized, so being concerned about her observations is what got your thought experiment started.

The bit about the lightning strikes is just a teaching tool, used to demonstrate one of many different ways that you can synchronize clocks.

 

[Nugatory]

I guess I would not be so concerned with what various observers might themselves observe. Instead, I would suggest that if the two clocks recorded the same time instant, that information would indicate that the lightning strikes were simultaneous, even if they did not appear to be simultaneous to the observer on the moving train.

It's not just a matter of what they observe; if it were we could write the whole thing off as an optical illusion and not worry about it. But the problem is deeper than that.

Suppose a star five light years away explodes. Eventually the light from the explosion reaches your eyes and you observe it. When did the star explode? The only sensible answer is "five years before the light reached your eyes" because it took five years for the light to travel from the explosion to your eyes.

We can push this idea a bit further: Suppose that there are two stars, one five light-years away and one eight light-years away. They both explode, and you observe the light from the nearer explosion at noon on 1 January 2012. Three years later, at noon on 1 January 2015, you observe the light from the more distant explosion. It is clear that both explosions happened at the same time, namely noon on 1 January 2007. It doesn't matter that you observed them at different times. Knowing when the light reached your eyes and how long it took to reach them let's you calculate when the explosions really happened, and in this case you correctly calculate that they happened at the same time. It also doesn't matter whether the stars were moving or not; all that matters is where they were at the moment that they blew up.

But the point of Einstein's train experiment is that someone who is moving relative to you will do the exact same analysis (take the time the light reached them; subtract out the time it took the light to get there; and they have the time that the light started out) and correctly calculate that the two explosions did not happen at the same time. Thus, we have to accept that "at the same time" is inherently frame-dependent.

 

[Peter Martin]

Here’s my attempt at answering taenyfan’s very fine question on Einstein’s train experiment:

The problem defines two frames of reference moving with respect to one another. In the platform observer’s frame the two strikes are simultaneous. In this scenario the woman must be considered to be moving relative to the lightning strikes, specifically, toward the forward strike and away from the rear strike.

We could just as well consider the train to be “at rest” and the landscape, including the platform observer moving from the train’s front to its rear. In this case the woman will see the two strikes as simultaneous but the man — who is “moving” toward the back of the train and away from the front — will see the rear strike first.

Since the two frames are moving relatively you must pick one or the other when describing the two strikes as “simultaneous”. You can’t have it both ways.