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

[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.)

 

[etotheipi]

@Janus did you make those animations yourself (with blender)? They're very nice

 

[FactChecker]

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.

What would be the correct way to rephrase his statement?
I see your point, but I am struggling to phrase the statement. Can you say that the light flashes arrive at M as a single event but they arrive at M' as separate events?

 

[Janus]

@Janus did you make those animations yourself (with blender)? They're very nice

Thanks.
I did make them myself, though not with Blender. They are from a few year ago, and at that time I was working with Moray and POV-Ray

 

[Nugatory]

What would be the correct way to rephrase his statement?
I see your point, but I am struggling to phrase the statement. Can you say that the light flashes arrive at M as a single event but they arrive at M' as separate events?

Natural language is not well-suited to accurate descriptions of events as points in a four-dimensional Euclidean spacetime. I don't think we can improve much on @PeterDonis's wording: "two light signal worldlines cross the observer's worldline at the same event".

 

[Sagittarius A-Star]

Natural language is not well-suited to accurate descriptions of events as points in a four-dimensional Euclidean spacetime. I don't think we can improve much on @PeterDonis's wording: "two light signal worldlines cross the observer's worldline at the same event".

An alternative formulation would be that of Einstein:

When we say that the lightning strokes $A$ and $B$ are simultaneous with respect to the embankment, we mean: the rays of light emitted at the places $A$ and $B$, where the lightning occurs, meet each other at the mid-point $M$ of the length $A -> B$ of the embankment.

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

 

[Dale]

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",

I think it is OK. If two things happen at the same time they are simultaneous, including if they happen at the same time and the same place. Usually the fact that one event is simultaneous with itself is of little interest, but I wouldn't say that pointing it out is a very bad idea.

 

[robphy]

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",

I think it is OK. If two things happen at the same time they are simultaneous, including if they happen at the same time and the same place. Usually the fact that one event is simultaneous with itself is of little interest, but I wouldn't say that pointing it out is a very bad idea.

While not incorrect, I think it's
not too hard to avoid ambiguities
and
be more precise now
in order to avoid having to clarify it later with more words.

Borrowing a term from geometry,
we could say that the two reception events coincide [on the worldline of the observer].

 

[PeterDonis]

Can you say that the light flashes arrive at M as a single event but they arrive at M' as separate events?

That's how I would state it, yes.

 

[PeterDonis]

If two things happen at the same time they are simultaneous, including if they happen at the same time and the same place.

But this conflates something that is frame-dependent (whether two things that happen at different places happen at the same time) with something that is invariant (whether two things happen at the same point in spacetime). I think that is a bad idea. To me the optimum would be to never talk about frame-dependent things at all--express everything entirely in terms of invariants. But if we can't do that (and I can see how for convenience it can make sense to talk about things that depend on your choice of frame), at least we should make sure our terminology makes clear which kind of thing we are talking about.

 

[PeterDonis]

Borrowing a term from geometry,
we could say that the two reception events coincide [on the worldline of the observer].

This seems like a good suggestion to me.

 

[vanhees71]

But this conflates something that is frame-dependent (whether two things that happen at different places happen at the same time) with something that is invariant (whether two things happen at the same point in spacetime). I think that is a bad idea. To me the optimum would be to never talk about frame-dependent things at all--express everything entirely in terms of invariants. But if we can't do that (and I can see how for convenience it can make sense to talk about things that depend on your choice of frame), at least we should make sure our terminology makes clear which kind of thing we are talking about.

True, it's always good to express finally all theoretical results in a manifestly covariant way. If you want to compare to experiment, of course, you have to refer to the quantities measured in the "lab frame".

 

[Dennis Rohatyn]

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.

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

Wouldn't that require GRT (general relativity), to account for the transfer of (kinetic) energy from the
lightning bolt to the tracks and the train? Or is that irrelevant to the scenario?

 

[PeterDonis]

Wouldn't that require GRT (general relativity), to account for the transfer of (kinetic) energy from the
lightning bolt to the tracks and the train?

No. Energy transfer works just fine in special relativity. General relativity would only be required if you are dealing with enough energy to curve spacetime measurably. That's not going to be the case for a couple of lightning bolts (or for them plus the train plus the tracks, for that matter).

Or is that irrelevant to the scenario?

If we have lightning bolts making marks on the tracks and train, we are assuming that that process does not affect the motion of the tracks and train, so both remain inertial. For actual lightning bolts and actual tracks and train, that would be a very good approximation.

 

[Dennis Rohatyn]

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

That is true. However, too much rigor is often as bad as too little, at least from a beginner's standpoint.
Einstein himself made many tacit assumptions which weren't exactly kosher. Yet they enabled him to
get his point across, and thus to "sell" his theories, not to students but to his seniors, long before they
were validated by observation and experiment. Newton did the same--that's one reason why he relied on
geometry for most of his proofs, rather than the calculus which he (co-)invented. To us the latter is much
simpler, but to his contemporaries, it was novel, unfamiliar, and therefore suspect. Whereas, no one dared
to challenge Euclid, which was tried and true. Hence his proofs were convincing--so much so, that they
decided the fate of heliocentrism, once and for all. The logic of a theory is one thing; its rhetoric is quite
another. We think of the two as being mutually exclusive, but they complement each other, as Davis and
Hersh showed in exemplary detail (The Mathematical Experience, 1998). As for Galileo, he convinced
everyone except the Pope--but that had nothing to do with either a lack of literary skill on his part or a
stubborn streak of dogma that kept the Church in arrears for centuries. Yet if he came to life (sic) now,
he would have no more luck than he did then, not because the Dialogues aren't masterful, but because
no one knows how to read a text--or is at all interested, unless it's shorter than the Gettysburg Address.

 

[PeroK]

That is true. However, too much rigor is often as bad as too little, at least from a beginner's standpoint.
Einstein himself made many tacit assumptions which weren't exactly kosher. Yet they enabled him to
get his point across, and thus to "sell" his theories, not to students but to his seniors, long before they
were validated by observation and experiment. Newton did the same--that's one reason why he relied on
geometry for most of his proofs, rather than the calculus which he (co-)invented. To us the latter is much
simpler, but to his contemporaries, it was novel, unfamiliar, and therefore suspect. Whereas, no one dared
to challenge Euclid, which was tried and true. Hence his proofs were convincing--so much so, that they
decided the fate of heliocentrism, once and for all. The logic of a theory is one thing; its rhetoric is quite
another. We think of the two as being mutually exclusive, but they complement each other, as Davis and
Hersh showed in exemplary detail (The Mathematical Experience, 1998). As for Galileo, he convinced
everyone except the Pope--but that had nothing to do with either a lack of literary skill on his part or a
stubborn streak of dogma that kept the Church in arrears for centuries. Yet if he came to life (sic) now,
he would have no more luck than he did then, not because the Dialogues aren't masterful, but because
no one knows how to read a text--or is at all interested, unless it's shorter than the Gettysburg Address.

Five score and sixteen years ago, Albert Einstein brought forth a new theory conceived in relativity and decicated to the proposition that all light waves are created equal. Now we are now engaged in a great thread testing whether that theory can long endure ... and that this theory shall not perish from the Earth.

 

[Dale]

That is true. However, too much rigor is often as bad as too little, at least from a beginner's standpoint.

You are missing the point. We have now over a century of experience teaching this material to beginners. We know exactly which concepts are difficult (relativity of simultaneity), we know the specific sloppy terminology that leads to confusion (observer, see), we know which examples are ineffective (Einstein’s train). And yet we continue using ineffective examples and sloppy terminology; so students continue failing to learn the difficult concepts.

I am not advocating unnecessary rigor, I am advocating necessary rigor. Instead of “Bob sees” we should use “in frame B”. The sloppy wording “Bob sees” is intended to be understood as shorthand for “in frame B”, but it is not much shorter and not worth the mental confusion that results. Students hear “Bob sees” and think that biological observers are necessary and that optical illusions are being discussed.

 

[PeroK]

And yet we continue using ineffective examples and sloppy terminology; so students continue failing to learn the difficult concepts.

A prime example being:

https://www.physicsforums.com/threads/relativity-of-simultaneity.1009698/

 

[vanhees71]

Indeed, the "relativity of simultaneity" is the key for an understanding of all the apparent paradoxes, people (including students!) seem to like. I also thought for some time, it's better not to start relativity with a treatment of all these "paradoxes" (including the twin paradox, the train example, ...). So I started with the usual "two postulates" (the special principle of relativity which is identical with Newton's Lex Prima, i.e., the existence of inertial refference frames, and the independence of the speed of light from the velocity of the source wrt. an inertial frame), introducing Minkowski space with its pseudo-metric and derived the Lorentz- (Poincare) transformation between inertial frames and then of course depicted everything with Minkowski diagrams (with the hyperbolae for construction of the unit lengths in different frames, emphasizing to forget about our "Euclidean Intuition" when reading these diagrams). Then you can do physics, including point-particle mechanics and classical electrodynamics in covariant form and avoid the discussion of all these kinematical paradoxes.

However, the students (and they are students aiming to become high-school teachers) pretty soon asked about all these paradoxes, because the wanted to understand them, because in the usual German high-school texts, of course, these paradoxes all occur and they have to teach them. So I included some of the paradoxes in the problem sets accompanying the lectures and make them draw the corresponding Minkowski diagrams. My impression is that this works pretty well, and the Einstein's train example (in different forms) is not at all bad or confusing but it emphasizes that the explanation for all the apparent paradoxes is that one tends to forget about the relativity of simultaneity. The most loved paradox is the "garage paradox" with a car "fitting" or "not fitting" into a garage, depending on the view of either the driver or an observer at rest relative to the garage.

I think the key is to first explain Minkowski space, including the pseudo-metric and then discuss the kinematical paradoxes as an application which can be depicted nicely in Minkowski diagrams. It's also helpful to stress that we don't "see" the length contraction, because length contraction occurs when measuring lengths, while what we see is determined how the light from the seen objects reaches our eyes.