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

[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.