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In Einstein's thought experimental description illustrating the definition of (how to measure) "simultaneity" (1917), we're given to consider two "places, A and B, of the rails of our railway embankment, far distant from each other". (Surely, these two are supposed to be and to remain at rest wrt. each other; at least "to reasonable approximation"; and the rails may be tought as "reasonably straight".)

A is supposed to give off a (distinctive, very brief) flash (due to having been hit by a strike of lightning); and B is supposed to give off a (distinctive, very brief) flash. Having raised the question whether A's flashing and B's flashing had occured "simultaneously", or not, Einstein stipulates to determine "the middle between" A and B. (Under the prescribed conditions, there exists a rail constituent which can be identified accordingly; which is conventionally denoted as "M". Moreover, it is guaranteed that M, being the middle between A and B, is and remains at rest wrt. A as well as wrt. B.)

A's flashing and B's flashing are then said to have "occured simultaneously" if M received these two flashes together (in coincidence).
(The converse conclusion is apparently implied: A's flashing and B's flashing are said to have "occured not simultaneously" if M received these two flashes not together (but only one first, and the other significantly afterwards).

Supposedly, A (or a conscientious observer associated with A) and B (or a conscientious observer associated with B) themselves, as well as any (conscientious observer associated with any) constituent of the rails or the embankment (and found reasonably at rest wrt. A, B, and M) is expected to respect and to adopt this judgement of M (or a conscientious observer associated with M); and they are thereby all guaranteed to agree on their result.

But there are of course also other participants thinkable, and perhaps even identifiable, who are not at rest wrt, A, B, M, but who are nevertheless interested in answering the question whether A's flashing and B's flashing had occured "simultaneously", or not.

If they, too, refer to M's judgement, then they are guaranteed to agree with the answer given by M and A and B themselves.
(A question on the side: Would this (very general) method of of determining simultaneity (or non-simultaneity) be (therefore) considered "proper" ?)

If anyone (with exception of M itself) reaches an answer (on whether A's flashing and B's flashing had occured "simultaneously", or not) contrary to M's judgement, and therefore necessarily by using a different method than the one prescribed by Einstein, as referred above, including "adopting M's judgement".
(Another question on the side: Would that different method be (therefore) considered "improper" ?)

My question:

Does Einstein's description mean that the judgement of M, the middle between A and B (as far as it has been obtained and reported "correctly, to the best of M's knowledge and conscience"), on whether A's flashing and B's flashing had occured "simultaneously", or not, should be respected and equally adopted by everybody ?

Or if not:
What exactly is the complete description of the method intended by Einstein instead, for determining whether A's flashing and B's flashing had occured "simultaneously", or not; especially in regard to its application by participants who are not "the middle between A and B", and who are not even at rest wrt. A, B, and M ?

user12262
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    What does "adopt M's judgment" mean? Does it mean acknowledging that two events are simultaneous in M's frame? Of course everyone does that. Does it mean pretending that those events are simultaneous in some other frame? Of course nobody does that, nor should they. – WillO Nov 02 '23 at 02:16
  • @WillO: "What does "adopt M's judgment" mean?" -- "Adopting M's judgment" means (for anyone except M): If M pronounces the judgement "A's flashing and B's flashing occured simultaneously (because ...)" then to conclude and to affirm "I agree that A's flashing and B's flashing occured simultaneously; because that's M's judgement, and my method of determining whether A's flashing and B's flashing occured simultaneously, or not, is: to adopt M's judgement.", and vice versa, If M pronounces the judgement "A's flashing and B's flashing occured simultaneously (because I, M, received ...)" then ... – user12262 Nov 02 '23 at 02:30
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    The unqualified statement "X and Y occurred simultaneously" is not a statement at all because it is meaningless. The statement "X and Y occurred simultaneously in frame F" is meaningful, and all well-informed observers will agree on its truth value. – WillO Nov 02 '23 at 02:35
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    Suppose John makes the statement "Pigs are larger". In what circumstances should all observers accept that judgment? Answer: In no circumstances at all, because the statement is meaningless. The relation "larger" applies to an ordered pair of things, not to a single thing. Likewise the relation "simultaneous" applies to a pair of events and a frame, not just to a pair of events. The statement "X and Y are simultaneous" is missing a frame and therefore meaningless, just like "Pigs are larger" is missing a second animal and therefore meaningless. – WillO Nov 02 '23 at 02:37
  • @WillO: "[...] acknowledging that two events are simultaneous in M's frame?" -- Events ?? No: The Q raised by Einstein, quoted in the OP, is asking (merely) about "A's flashing" (only A's indication, as part of a general event involving additional participants) and "B's flashing" having occured simultaneously (or not). Simultaneity (nor non-sim.ty) isn't attributable to pairs of whole events, e.g. to the event of "A's flashing together w train end P passing A together w P receiving A's flash together w P being char-marked together w A noticing ....", and some event involving B + train end Q, – user12262 Nov 02 '23 at 02:44
  • @WillO: "The unqualified statement "X and Y occurred simultaneously"" -- The technical term (J. D. Norton's vocabulary, FWIW) is apparently: "simultaneous simpliciter". "The statement "X and Y occurred simultaneously in frame F" is meaningful," -- Apparently there's no mentioning at all of "frame" in the whole chapter (1917, §8) which introduces Einstein's definition of "simultaneity". (This might be another, very distinct reason for suspecting "incompleteness", though ...) – user12262 Nov 02 '23 at 02:55
  • This is intimately related to the Einstein synchronisation convention and Reichenbach's epsilon. See https://physics.stackexchange.com/a/591436/123208 & https://sites.pitt.edu/~jdnorton/teaching/HPS_0410/chapters/significance_conv_sim/index.html#epsilon – PM 2Ring Nov 02 '23 at 03:22
  • In relativity, the term "event" doesn't have its conventional meaning. An event in relativity is merely a point in spacetime, specified by its (t, x, y, z) coordinates in some frame. The Lorentz transformations transform the coordinates of an event from one inertial frame to another inertial frame. – PM 2Ring Nov 02 '23 at 03:28
  • @PM 2Ring: "[...] intimately related to E synchr. conv., Reichenbach's epsilon" -- Hardly. OP doesn't mention "speed", "clock readings", nor "coord.s". Also $$ ~ $$ "I maintain my def. nevertheless; {...} it assumes absolutely nothing about light." $$ ~ $$ "An event in RT is merely a point in spacetime" -- They're so represented, yes. Still, each is generally identified as coincidence of several "mat" participants. – user12262 Nov 02 '23 at 07:07
  • The point you are missing is that the spatial location of an event is frame dependent. If an event happens at a point x in one frame, which has the coordinate x' in another moving relative to it, then over time those points drift further apart. Given that, the mid-point of two spatial locations is frame dependent too. If light from two spatially separate flashes meets at their mid-point in a given inertial frame, the flashes were simultaneous in that frame. – Marco Ocram Nov 02 '23 at 13:16
  • In another frame, the spatial midpoint between the flashes is somewhere else at a later time- the light, therefore, does not meet there, so the flashes were not simultaneous in that other frame. – Marco Ocram Nov 02 '23 at 13:17
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    You say there is no mentioning of 'frame' in Einstein's description- but Einstein explicitly mentions the train and the platform, which represent two separate frames. The midpoint of the flashes in the frame of the train is the middle of the train. The mid-point of the flashes in the frame of the platform is the middle of the platform. The two midpoints are moving relative to each other. – Marco Ocram Nov 02 '23 at 13:20
  • Suppose a fire-cracker goes off in the midpoint of the platform just as the mid point of the training is passing by, the flash being a meter to one side of the train. In the frame of the platform, the event occurred at the midpoint of the platform. In the frame of the train, the event occurred a metre to one side of the centre of the train. After ten minutes, say, those two locations could be miles apart. – Marco Ocram Nov 02 '23 at 14:35
  • @Marco Ocram: "E. explicitly mentions train and platform" -- No, not the train at all in §8 (to which the OP refers); but explicitly only: the railway embankment incl. track; incl. constituents A,B,M. "two spatially separate flashes" -- §8 and OP don't consider abstract/general flashes with all sorts of participants; but strictly only A's flashing, and B's flashing. However: I'll appreciate your commenting/answering my upcoming Qs on Taylor-&-Wheeler, where Train and Track are explicitly featured. "The point you are missing" -- This presumption is likely wrong; and thus offensive. – user12262 Nov 02 '23 at 17:49
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    'The point you are missing' agreed, apologies. – Marco Ocram Nov 02 '23 at 18:45

1 Answers1

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Promoted from a comment:

Suppose that John, a world-expert on pigs, declares that "Pigs are larger". In light of John's expertise, ought we all accept that judgment?

Answer: Surely not, because John's expertise cannot outweigh the fact that "Pigs are larger" is a meaningless statement. The word "larger" applies to a pair of entities, not to just one.

Suppose that Jill declares that "Those flashes are simultaneous". When ought we accept that judgment?

Answer: Never, because no observation of Jill's can outweigh the fact that "Those flashes are simultaneous" is a meaningless statement. The word "simultaneous" applies to a pair of events and a frame, not just to a pair of events.

John can fix his statement by saying "Pigs are larger than ants" or "Pigs are larger than elephants", and then we can all agree on the truth value. Jill can fix her statement by saying "Those flashes are simultaneous in frame F", and then we can all agree on its truth value.

Depending on which frame she's referring to, Jill is either unambiguously right or unambigously wrong. We should believe things that are true and disbelieve things that are false. "Accepting Jill's judgment" has nothing to do with it. All we need to do is to calculate.

WillO
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  • WillO: "The word "simultaneous" applies to a pair of events and a frame, not just to a pair of events." -- Apparently a false dilemma. In the first paragraph of (1917, §8), where Einstein raises the Q of interest, neither A's flashing nor B's flashing are characterized as entire events, involving train ends (e.g. being char-marked), planes and automobiles, etc. – user12262 Nov 02 '23 at 03:12
  • WillO: ""Those flashes are simultaneous" is a meaningless statement." -- The statement under consideration (as "M's judgement") is rather: "I, M, having been identified as middle between A and B throughout the entire trial, have received the distinctive flash of A and the distinctive flash of B together, in coincidence. I therefore, in application of Einstein's definition, pronounce A's flashing and B's flashing as simultaneous." – user12262 Nov 02 '23 at 03:12
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    @user12262 In other words, M is saying that A and B are simultaneous in M's rest frame. That is meaningful and if it is true we should believe it. More generally, we should believe a lot of things that are true. Nobody disputes that. So what is your question? – WillO Nov 02 '23 at 03:19
  • WillO: "IOW, M says that A and B are simultaneous in M's rest frame." -- Well, A (simpliciter) as well as B are by themselves supposed to be specific, widely separated constituents/pieces of railroad track. To characterize any two of those as "simultaneous", or (likewise) as "not simultaneous" is: meaningless. But (it goes without mentioning): A and B and M are together members of the same inertial frame. So M says: "A's flashing and B's flashing were simultaneous-simpliciter". (Period.) My OP question is: By which explicit method of determination could anyone disagree, if at all ?!? – user12262 Nov 02 '23 at 03:41
  • If "simpliciter" means "in the rest frame of the track" then you and I are saying exactly the same thing, and you seem to want to argue only about whether we should say it in Latin. If it means "in some other frame", then you need to tell us what frame you have in mind. If it means anything else at all, then your statement is meaningless because the relationship "simultaneity" takes a frame as one of its arguments. – WillO Nov 02 '23 at 15:25
  • And two minor points: Yes, I wrote A and B for the flashes, not the corresponding track sections. But either way, A and B are not "members" of any frame at all. Only a tangent vector can be a member of a frame --- unless you are choosing to use the word "member" in some non-standard way (i.e. to mean something other than set membership), in which case you need to define it. Preferably in English, not in Latin. – WillO Nov 02 '23 at 15:27
  • WillO: "If "simpliciter" means "in the rest frame of the track" [...]" -- Einstein's def. §8 doesn't contain any explicit hedge of this sort at all. By (Norton's) "simpliciter" I meant: judgements exactly like that. "anything else at all is meaningless" -- That's your indictment of Einstein's §8. "A and B are not "members" of any frame at all" -- ??? Refer to W. Rindler's dictum that "An inertial frame is simply an infinite set of point particles sitting still in space relative to each other". – user12262 Nov 02 '23 at 18:10