Einstein's train-lightning scenario doesn't demonstrate relativity

[Peter Martin]

TL;DR Summary

The train-lightening thought experiment merely reinforces the popular but incorrect attribution of absolute velocity by stating that the embankment observer remains stationary relative to the strike locations while the train passenger moves forward.

The popular account of Einstein's train-and-lightening thought experiment doesn't demonstrate "the relativity of simultaneity" as it is always claimed. In fact, it does the opposite: By describing the embankment observer as "at rest" relative to the strike locations and the train passenger as "moving" toward the front strike location, the scenario merely reinforces the common but incorrect belief in absolute motion, which is contrary to the whole essence of Special Relativity (SR).

I suggest that the usual scenario be coupled with another slightly different example in order to bring relativity into the picture. In this example the lightning hits the train -- fore and aft -- and not the tracks. Thus, the action takes place in the train's reference frame, not the landscape's. Thus, it is the train passenger who remains at the midpoint of the two strikes and thus sees them as occurring simultaneously, while the embankment observer, rushing toward the train's rear, sees the rear strike followed by the front strike.

This second experiment, coupled with the first, makes the point that neither the train nor the landscape can have the attribution of either "moving" or "resting'. All that can be said is that they are moving relative to each other at the speed normally attributed to the train.

 

[PeroK]

In truth, I've never liked that thought experiment for a number of reasons. Modern textbooks, benefiting from one hundred years of experience in teaching SR, generally use better scenarios. See, for example, section 1.3. of Morin's book:

https://scholar.harvard.edu/files/david-morin/files/relativity_chap_1.pdf

 

[Ibix]

This National Geographic article, the Wikipedia article on the relativity of simultaneity, and this thread here are the top three hits for me if I search for "train lightning thought experiment". All three have the lightning striking the train. I'm not sure "the popular account" is quite as you say.

Indeed, it doesn't matter what the lightning actually strikes. I've seen the experiment argued with fire crackers, lamps and lasers on the platforms and on the train. If you want to use the thought experiment, lamps on the platform and on the train, or a lightning strike that leaves burn marks on both the train and the platform is easiest. Then the experiment is symmetric except for the choice of definition of "simultaneous".

 

[Dale]

The popular account of Einstein's train-and-lightening thought experiment ...

The complaint you seem to have is regarding the wording of a specific source. Please cite this specific source with the problematic wording.

Other versions are carefully worded to be correct.

In this example the lightning hits the train -- fore and aft -- and not the tracks.

Why not have the lightning leave scorch marks on both the tracks and the train?

 

[Dale]

See, for example, section 1.3. of Morin's book:

I like that one much better too. It is “cleaner”.

 

[Sagittarius A-Star]

By describing the embankment observer as "at rest" relative to the strike locations and the train passenger as "moving" toward the front strike location

In Einstein's popular book, the strikes are idealized as events. Events cannot be "at rest" relative to an observer. Also, they cannot be "moving" relative to an observer. Reason: Events are points in 4D-spacetime.

Are two events (e.g. the two strokes of lightning A and B) which are simultaneous with reference to the railway embankment also simultaneous relatively to the train? We shall show directly that the answer must be in the negative.

Source:
https://en.wikisource.org/wiki/Rela..._I#Section_9_-_The_Relativity_of_Simultaneity

 

[vanhees71]

Which version of the train example are we discussing? There are at least two in the literature (maybe many more), I've discussed here

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

and here

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

 

[FactChecker]

I suggest that the usual scenario be coupled with another slightly different example in order to bring relativity into the picture. In this example the lightning hits the train -- fore and aft -- and not the tracks. Thus, the action takes place in the train's reference frame, not the landscape's.

Isn't this a distinction without a difference? If lightning strikes at a location on the tracks that is also the location of the train end, what difference does that make? How can you say that it strikes one and not the other? The lightning strikes in both reference frames. And the scenario must be considered in both reference frames to even discuss relativity.

 

[italicus]

I have made a Minkowski diagram of the scenario given by Einstein. The red lines are light signals coming from the two strokes in A and B . I hope it’s sufficiently clear, even if written in italian. The point M’ at the middle of the train meets in Q and P the signals , so they are simultaneous for M on the embankment (because they meet on the universe line of M at point R) but aren’t simultaneous for M’ , which is moving to the right w.r.t. the embankment.

 

[PeterDonis]

By describing the embankment observer as "at rest" relative to the strike locations and the train passenger as "moving" toward the front strike location, the scenario merely reinforces the common but incorrect belief in absolute motion

Please give a specific reference in which the specific wording you are describing occurs. So far, everyone else has given references in which that specific wording does not occur.

 

[pervect]

Some references that I think are noteworthy:

Einstein's original description in chapter 9 of "Relativity, the special and general theory", https://www.bartleby.com/173/9.html

Scherr (et al) paper, "The challenge of changing deeply held student beliefs about the relativity of simultaneity", http://www.physics.umd.edu/perg/papers/scherr/ScherrAJP2.pdf

Einstein's paper is important for it's obvious historical significance. Scherr, Stafer, and Vokov's paper is interesting because they did some research into what works to teach the theory to students, based on how well the students were able to answer standardize test questions on the topic. Scherr et al found that many students did not understand Einstein's original presentation, performing poorly on standardized tests. Note that this is not a criticism of Einstein's presentation as far as accuracy goes, it just shows that students struggled with it. Their conclusion was that there were more effective presentations to teach the theory.

I'm sure there are many other references, of course, those are just my two favorite.

 

[FactChecker]

By describing the embankment observer as "at rest" relative to the strike locations and the train passenger as "moving" toward the front strike location, the scenario merely reinforces the common but incorrect belief in absolute motion, which is contrary to the whole essence of Special Relativity (SR).

I actually prefer that terminology. I don't read any significance into it other than that they are convenient labels. I quickly get confused by other labels like A, B, C, D, Joe, Jane, Smith, Jane's uncle Fred, etc. I lose track of who is who. But I am not the sharpest knife in the drawer. ;-)

 

[vanhees71]

I would always say an observer (be he or she at rest relative to an inertial frame or not) is always at rest in his or her own (local) reference frame, and you can ask what he or she observes for a given physical situation (which is of course independent of any choice of reference frame). Then it's clear.

In Einstein's original example of the light signals sent at $t=t'=0$ towards the observer at rest wrt. the embarkment (located at $t=0$ in the middle of the train), this observer will see the light signals arrive at the same time at his place, while the observer in the middle of the train and at rest wrt. the train will see them to arrive at different times. It's nicely shown by the Minkowski diagram by @italicus in #9.

 

[italicus]

@Peter Martin
Let me add some simple words to what already said, with great rigour, by other experts.
Special Relativity is concerned with relative motion of two inertial reference frames. It is only a convention to say that the platform is at rest and the train is moving; if you are sitting in the train, you will see the landscape coming towards you; so you have all the right to say you are at rest, because nobody moves with respect to himself; but the so called common sense makes people say :”What are you talking about! The train in which I am seated is moving, the Earth is at rest!” . So one has to spend some time to explain simple galileian relativity, and maybe not everyone understands...It’s really a pity that Galileo wasn’t able to explain the relativity of (uniform and not accelerated) motion to those people that accused him to be heretical, may be for his age and health conditions, which weren’t so good at that time! Do you remember his dialogue, and thought experiment ?

Shut yourself up with some friend in the main cabin below decks on some large ship...

you can continue reading “the proposal” here : https://en.wikipedia.org/wiki/Galileo's_ship

it’s a masterpiece of physics!

But let’s go back to Einstein and his light signals. You want to consider the r.f. of the train as being at rest, and the platform moving w.r.t. the sitting passenger, with velocity $-\vec v$. Ok, but now I ask to modify just a little the experiment proposed by Einstein ( which is a little confusing, I agree with others that prefer the experiment set forth by D.Morin in his book). Suppose there are two lamps in the train, one in A (aft) and the other in B (fore) , which are turned on simultaneously in the train time. This means that the passenger M’ in the middle of the train receives the two light signals at the same time, his proper time . But an observer standing on the platform in M receives the signal from A before that from B, because he is approaching A with speed v, and moving away from B with the same absolute value of speed. All this can be put in mathematics, but it would be more interesting to make a drawing like that of post #9 .

 

[Peter Martin]

This National Geographic article, the Wikipedia article on the relativity of simultaneity, and this thread here are the top three hits for me if I search for "train lightning thought experiment". All three have the lightning striking the train. I'm not sure "the popular account" is quite as you say.

Indeed, it doesn't matter what the lightning actually strikes. I've seen the experiment argued with fire crackers, lamps and lasers on the platforms and on the train. If you want to use the thought experiment, lamps on the platform and on the train, or a lightning strike that leaves burn marks on both the train and the platform is easiest. Then the experiment is symmetric except for the choice of definition of "simultaneous".

IBIX, Thanks for the feedback. Obviously, you've had more exposure to various versions of this experiment than I have. But isn't it critical whether the lightning strikes occur in the train's reference frame or the embankment observer's? It seems to me that in whichever case the observer in that frame will remain at the midpoint of the strike locations and therefore see the strikes as simultaneous.

Meanwhile, I'll check out the two accounts you cite in your response. Thanks again for your interest.

Peter

 

[PeroK]

But isn't it critical whether the lightning strikes occur in the train's reference frame or the embankment observer's?

Events occur full stop. They do not occur in one reference frame any more than another.

 

[PeterDonis]

isn't it critical whether the lightning strikes occur in the train's reference frame or the embankment observer's?

As @PeroK says, events just occur. They are "in" all reference frames; they don't occur "in" one frame but not another.

However, it does make a difference as far as which scenario you are talking about, whether you specify the scenario as having the lightning strikes being simultaneous in the train frame or the embankment frame. Or, if you don't like using the word "simultaneous" in the specification of the problem, it makes a difference whether you specify that the observer standing on the embankment sees the lightning strikes at the same instant, or whether the observer on the train does. That is the key specification you have to make that determines which scenario you are discussing: the one in which the lightning strikes are simultaneous relative to the embankment, or relative to the train.

I strongly suggest drawing spacetime diagrams of both cases; I find that it makes it a lot easier to see what is going on and to see the difference between the two scenarios.

 

[Sagittarius A-Star]

It seems to me that in whichever case the observer in that frame will remain at the midpoint of the strike locations and therefore see the strikes as simultaneous.

No. In Einstein's scenario, the two light-strokes happen (in the rest frame of the train) at different times.

 

[Ibix]

But isn't it critical whether the lightning strikes occur in the train's reference frame or the embankment observer's?

The lightning strikes happen in all frames. The only choice is in which frame they are simultaneous. Einstein set them up as simultaneous in the embankment frame, but he could have set them up as simultaneous in the train frame.

 

[Ibix]

No. In Einstein's scenario, the two light-strokes happen in the rest frame of the train not at the same time.

I think this is unclear. I think what you mean to say is that, viewed from the train's frame, the strikes are not simultaneous in Einstein's version of the experiment (ref section 8 of the Wikisource page you linked in #6). If so, I agree. But your wording is ambiguous.

 

[Sagittarius A-Star]

I think this is unclear. I think what you mean to say is that, viewed from the train's frame, the strikes are not simultaneous in Einstein's version of the experiment (ref section 8 of the Wikisource page you linked in #6). If so, I agree. But your wording is ambiguous.

Yes, I mean this. I don't know, what exactly is ambiguous. With "happen ... not at the same time" I mean "are not simultaneous".

 

[Ibix]

Yes, I mean this. I don't know, what exactly is ambiguous. With "happen ... not at the same time" I mean "are not simultaneous".

You can parse "the two light-strokes happen in the rest frame of the train not at the same time" in two ways. On a first reading I read it as "the two light-strokes happen in the rest frame of the train (and not in any other frame), and not at the same time in any frame". That's a valid reading of what you wrote, but is physically nonsense (as I know you are aware). Only on my second reading did I realize that I could also parse it as "the two light-strokes happen (in the rest frame of the train) at different times" (which is correct).

It may be just me reading things in a funny way, but I thought it worth confirming that you didn't mean what I originally thought you meant.

 

[FactChecker]

It seems to me that in whichever case the observer in that frame will remain at the midpoint of the strike locations and therefore see the strikes as simultaneous.

Whether the observer thinks the strikes are simultaneous depends on how the clocks in that reference frame have been synchronized to indicate time in that reference frame. You might look hard at how that can be done on the train, considering that the speed of light will still be measured as c on the train, and how that process on the train would look to observers on the platform. In fact, the train time synchronization can not agree with the bank time synchronization if they are both measuring the speed of light as c. Then you must conclude that both observers can not think that the front and rear lightning strikes are simultaneous. Of course, if an observer does not think that the front and rear strikes are simultaneous, he will not see the flashes simultaneously in the middle.

 

[italicus]

For example, here is another situation. O’(t’,x’) is the reference frame of the train, O(t,x) is the r.f. of the embankment. The pale blue strip is the world strip of the train,which is the blue segment of length 2L and moves to the right w.r.t. the platform. So in the r.f. of the train the platform appears to move to the left. At a certain instant, a passenger in the middle point M of the train sends two simultaneous signals towards A (aft) and B ( fore) of the train. So there are two events :
1) light reaches A
2) light reaches B
they are simultaneous for M ; but the observer on platform sees (*) the event A before than event B, because he goes towards A and moves away from B. I have translated the origin in P just for having a clearer drawing.

(*) One has to be careful with the verb “to see” in relativity. Simultaneity of two events doesn’t mean that they are “seen" by an observer at the same moment. In general, people are not at ease with this concept. Two events are simultaneous w.r.t. an observer when they are on his axis of simultaneity, orthogonal with his time axis ( in the sense of the hyperbolic geometry of Minkowski space-time , not orthogonal in the drawing!) .

 

[Dale]

One has to be careful with the verb “to see” in relativity.

Yes, unfortunately authors and teachers use sloppy terminology frequently so it is often difficult for students.

 

[vanhees71]

No. In Einstein's scenario, the two light-strokes happen (in the rest frame of the train) at different times.

I think, it's important to clearly define which of the many train scenarios we are discussing. There are many in the literature!

There are at least three that come to my mind:

(a) two light signals are sent from the front and the rear of the train simultaneously to the observer at restin within the train located in the middle of the compartment.

(b) two light signals are sent from the front and the rear of the train simultaneously to the observer at rest on the platform.

(c) a (spherical) light wave is sent from the observer in the middle of the compartment. Then you can discuss when the signal reaches the front and rear end of the train from the point of view of the observer in the train the one at the platform.

 

[Sagittarius A-Star]

I think, it's important to clearly define which of the many train scenarios we are discussing. There are many in the literature!

I spoke about Einstein's scenario. To my knowledge, he published only one train/lightstrokes-scenario. I provided the link already in my above posting #6.

https://en.wikisource.org/wiki/Rela..._I#Section_9_-_The_Relativity_of_Simultaneity

 

[vanhees71]

Ok, but then it's clear that the observer $M'$ (moving with the train) observes the signal from B before the signal from A, while the signals reach $M$ (at rest on the embarkment) simultaneously. That's also very clearly written by Einstein.

 

[Sagittarius A-Star]

That's also very clearly written by Einstein.

A little bit problematic for understanding may be, that he used the same letters $A$ and $B$ for events and positions:

But the events $A$ and $B$ also correspond to positions $A$ and $B$ on the train.

Source:
https://en.wikisource.org/wiki/Rela..._I#Section_9_-_The_Relativity_of_Simultaneity

Proposal for naming: For event $A$, position in frame $S$ is called $a$ and position in frame $S'$ is called $a'$ ...

Ok, but then it's clear that the observer $M'$ (moving with the train) observes the signal from B before the signal from A, ...

Yes. Einstein concluded correctly from this:

Observers who take the railway train as their reference-body must therefore come to the conclusion that the lightning flash $B$ took place earlier than the lightning flash $A$.

 

[vanhees71]

Events are independent of the coordinate system. So event A and event B has a frame-independent meaning. Only the their space-time coordinates change under a Lorentz transformation.

 

[RW137]

Einstein published this thought experiment about simultaneity in a popular book with the challenge to explain it in an easy way. However, in my opinion he tried to oversimplify and his explanations turned out to be rather confuse.

I did some thinking about it and here is how I understand the experiment.

Let’s consider two light sources A and B, the midpoint M of the line segment AB and the following events: AM = <<A emits a light signal to M>>, BM = <<B emits a light signal to M>>, MA = <<M receives the signal from A>> and MB = <<M receives the signal from B>>. If you observe that MA and MB happened simultaneously, than you can conclude that the two spatially separated events AM and BM happened simultaneously too (Einstein’s definition). You may imagine two detectors with synchronized clocks at M. Each clock is stopped by the correspondent signal. The clocks show the same time.

Now these devices are mounted on a train and the train moves in the AB direction along an embankment. Whereas the uniform motion does not change the outcome of the experiment for travelers in the train (first postulate), the situation is different for observers on the embankment. In the reference frame of the embankment, M is approaching the signal from B and is fleeing the signal from A. As the velocity of the light does not add to the velocity of the source (second postulate), people on the embankment, who observe the events MA and MB, measure with their synchronized clocks different times at different places. It is according to their clocks that BM happens before AM. It is worth noting that nothing happens to the detector clocks on the train. They still show the same time for everyone, for the observers on the embankment too.

Now some remarks about Einstein’s reasoning.

Einstein draws a figure with A and B on the embankment and on the train. This procedure makes his reasoning difficult to understand. Then he asks a question:

Are two events (e.g. the strokes of lightning A and B) which are simultaneous with reference to the railway embankment also simultaneous relatively to the train?

After defining simultaneity, Einstein should ask a more precise question: do the light signals arrive simultaneously at M for the travelers in the train?

Besides, it is not enough to say that the observer M’ in the train is hastening towards the beam of light coming from B, whilst he is riding on ahead of the beam of light coming from A. The light sources must be moving in order to get relativity in. The difficulty with Einstein’s reasoning is that he does not explain where he makes use of the second postulate.

 

[Ibix]

This is mostly correct. However, there are a couple of important points.

people on the embankment, who observe the events MA and MB, measure with their synchronized clocks different times at different places.

This isn't correct, or is confusingly worded. If MA and MB, the reception events in the middle of the train, are at the same time and place for one frame then they are at the same time and place for all frames (edit: frames may assign different coordinates to MA/MB compared to other frames, but each frame will always assign the same coordinates to MA as it does to MB). If you are trying to say that spatially separated clocks synchronised in one frame are not synchronised in other frames, I agree. But I don't think that's what your sentence actually says.

The light sources must be moving in order to get relativity in.

This is not correct. The point about lightning strikes is that they are (or are modeled as) instantaneous flashes of zero duration. As such, the sources are neither moving nor not moving. Trying to establish the speed of an event is like asking for the angle of slope of a point. In fact, the speed of the sources is irrelevant. This whole experiment is about analysing the flight times of light pulses - the sources are irrelevant.

 

[Sagittarius A-Star]

Then he asks a question:

Are two events (e.g. the strokes of lightning A and B) which are simultaneous with reference to the railway embankment also simultaneous relatively to the train?

Einstein's question is completely precise, because of his definition of simultaneity (in the frame of the train, this definition is valid related to M'):

"... That light requires the same time to traverse the path $A -> M$ as for the path $B -> M$ is in reality neither a supposition nor a hypothesis about the physical nature of light,
[ 28 ]
but a stipulation which I can make of my own freewill in order to arrive at a definition of simultaneity."

Source:
https://en.wikisource.org/wiki/Rela..._I#Section_8_-_On_the_Idea_of_Time_in_Physics

and:

[ 32 ]
Observers who take the railway train as their reference-body must therefore come to the conclusion that the lightning flash $B$ took place earlier than the lightning flash $A$.

Source:
https://en.wikisource.org/wiki/Rela..._I#Section_9_-_The_Relativity_of_Simultaneity

After defining simultaneity, Einstein should ask a more precise question: do the light signals arrive simultaneously at M for the travelers in the train?

No. The light signals arrive simultaneously at M (frame-independent) and not simultaneously at M' (frame-independent). In the frame, in which the train is regarded to be at rest, the events AM and BM happen at different times.

 

[PeterDonis]

The light signals arrive simultaneously at M (frame-independent) and not simultaneously at M' (frame-independent).

Using the term "simultaneously" here is a very bad idea, since here it does not mean "two spacelike separated events that are assigned the same coordinate time", which is of course not frame independent, but "two light signal worldlines cross the observer's worldline at the same event", which is. Also, since the whole point of the thought experiment is to explain relativity of simultaneity, it makes no sense to use the term "simultaneous" for something that is not relative.

 

[Janus]

Einstein published this thought experiment about simultaneity in a popular book with the challenge to explain it in an easy way. However, in my opinion he tried to oversimplify and his explanations turned out to be rather confuse.

I did some thinking about it and here is how I understand the experiment.

Let’s consider two light sources A and B, the midpoint M of the line segment AB and the following events: AM = <<A emits a light signal to M>>, BM = <<B emits a light signal to M>>, MA = <<M receives the signal from A>> and MB = <<M receives the signal from B>>. If you observe that MA and MB happened simultaneously, than you can conclude that the two spatially separated events AM and BM happened simultaneously too (Einstein’s definition). You may imagine two detectors with synchronized clocks at M. Each clock is stopped by the correspondent signal. The clocks show the same time.

Now these devices are mounted on a train and the train moves in the AB direction along an embankment. Whereas the uniform motion does not change the outcome of the experiment for travelers in the train (first postulate), the situation is different for observers on the embankment. In the reference frame of the embankment, M is approaching the signal from B and is fleeing the signal from A. As the velocity of the light does not add to the velocity of the source (second postulate), people on the embankment, who observe the events MA and MB, measure with their synchronized clocks different times at different places. It is according to their clocks that BM happens before AM. It is worth noting that nothing happens to the detector clocks on the train. They still show the same time for everyone, for the observers on the embankment too.

Now some remarks about Einstein’s reasoning.

Einstein draws a figure with A and B on the embankment and on the train. This procedure makes his reasoning difficult to understand. Then he asks a question:

Are two events (e.g. the strokes of lightning A and B) which are simultaneous with reference to the railway embankment also simultaneous relatively to the train?

After defining simultaneity, Einstein should ask a more precise question: do the light signals arrive simultaneously at M for the travelers in the train?

Besides, it is not enough to say that the observer M’ in the train is hastening towards the beam of light coming from B, whilst he is riding on ahead of the beam of light coming from A. The light sources must be moving in order to get relativity in. The difficulty with Einstein’s reasoning is that he does not explain where he makes use of the second postulate.

If you want to examine this scenario by comparing clocks on the train to those at rest with respect to the embankment, you have to consider time dilation along with length contraction,
Here is the scenario according to the embankment frame:

The light flashes from the strikes being represented by the expanding domes.
What needs to be noted here is that in the embankment frame, the moving train is length contracted.
When we switch over to the rest frame of the train, it is the embankment that is moving, So the train measures its length as being not length contracted, but does measure the embankment and tracks to be so.

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 are next to each respective dot along the tracks.
The light flashes expand outward at c from the strikes. (While the track observer would see the dots remaining at the center of the expanding flash, the train observer would see the ends of the train remaining at the center of the flashes.)
Note that in the top animation, the train observer meets up with the right light flash when he is ~ 3 ties to the right of the embankment observer, and the left flash catches up to him just about the time he is even with the right dot.
This is also what happens in the bottom animation. If our train observer were carrying a clock, everyone would also agree as to what time was on that clock when each light flash reached him. If you strung clocks along the length both the train and track, Everyone would agree what time was on any pair of clocks as they passed. (though embankment observers would say that the train clocks ran slow and were not synchronized to each other, while train observers would say the same about the embankment clocks.)