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If simultaneity is not a universal characteristic (eg. events are not simultaneous in all reference frames), then why do some events seem to be simultaneous in all reference frames as in the following narrative:

Consider two good ol' boys, each in his pickup, driving down a lonely dirt highway at night. Each, having downed many beers, is heading for an intersection at reckless speed, swerving periodically as he dozes off. As fate would have it--they are headed for the same intersection though their speeds are such that they will just miss colliding. Or will they? On this particular night, there are a great many other travelers also in the vicinity of this intersection, not all of whom are of terrestrial origin. To avoid detection, they fly their spaceships around in random directions at unfathomable (relativistic) speeds. When our good ol' boys arrive at the intersection, what do the visitors see?

Given the scenario (multiple observers, multiple directions, varying relativistic speeds) it seems like it would be possible to have an observer that sees them collide and another that does not. I am told that such a combination of observers is not possible which seems to imply that the collision/event is simultaneous/not simultaneous in all reference frames. If that's true, then why are some events simultaneous in all reference frames?

Allen
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3 Answers3

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Since you mentioned that they don't collide, they will not do so in any frame of reference. So no, no one will see them collide.

However, the way the pass each other will be percieved in different ways. E.g. due to length contraction, one of the alien observers might see a very short car passing behind a normal one.

The point here is, that different observers see different things, but the physics, i.e. the outcome of an experiment, is the same for all of them.

Clever
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So ... A and B collide at the intersection. You want to say that the collision is "simultaneous in all reference frames". But...simultaneous with what? The collision is a single event. It makes no sense to ask whether that event is "simultaneous". Simultaneity is a property of a pair of events. And if A and B are inertial observers, moving relative to each other, then there are always events that A considers simultaneous with the collision and B does not, and vice versa. This is obvious if you draw the spacetime diagram.

WillO
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Let me point out first that the key technical term to ask and address your question sensibly is: "coincidence".

Coincidence can be judged (in principle) by any one participant; e.g.

  • one particular observer judging whether she observed two particular signal flashes by two particular separated signal sources "at the same time", or not; or

  • one driver judging whether he experienced a collision with (at least) one other driver, or not.

In contrast, determination of simultaneity (or non-simultaneity) is usually understood to involve two (or more) participants who are separate from each other (for instance the two signal sources mentioned above).

(Einstein used the term "coincidence" in some of his writings, for instance when discussing the so-called "point-coincidence argument". But it seems he didn't quite know this word before 1915, and he used the word "simultaneity" indicriminately in his earlier writings.)

Now:

Consider two good ol' boys, each in his pickup, [...] they will just miss colliding. Or will they?

Well, foremost, they themselves would judge definitively (or, recalling the above: either one of them would be able to judge, consistently) whether they satisfied your setup prescription and did not collide, but just missed each other. Any additional observers, whether actual or imagined (in a thought-experiment) better agree to that, or they might "suffer" from different resolution (or plainly be wrong). Therefore:

it seems like it would be possible to have an observer that sees them collide and another that does not.

Not in principle; but conceivably only due to collecting observations at different resolutions.

the collision/event is simultaneous/not simultaneous in all reference frames.

Apart from resolution considerations, the judgement of the drivers is definitive, unambiguous, and binding for anyone else (regardless of any "frame" membership).

  • Either they did collide; they were "in coincidence", both together taking part in one-and-the-same coincidence event.

  • Or both left the intersection without having collided; so there was no one event ("so far") in which both had been taking part together/coincidently. (But each of them separately took part in many events.)

(So the last question of the OP (present version), which happens to be the title question, too, is not really pertinent here. However, of course, determination of simultaneity or non-simultaneity can be and are being discussed separately.)

Note:
All of this is so basic and should be so self-evident that it can and must be comprehended without referring to any "diagrams", but rather it's a precondition for drawing and interpreting relevant "diagrams" at all.

p.s.

Could there be 2 observers with velocities such that one sees truck A pass the intersection first and then truck B, while the other sees truck B pass first?

So, here (with this setup prescription): A and B agree that they did not collide.
The definitive judgement of the order ("sequence") in which A and B both passed the intersection is obviously left to ... (drum-roll) ...: the intersection itself, at least as far as there are some identifiable "material points" (pavement, traffic light, ...) associated with it.

However, there's a subtlety or loop-hole left (due to the wording of the question, when considering actual road intersections):

Any actual road intersection has "some size", it consists of several distinct and separate parts, such as several stop lines;
and any car (pickup trucks! :) would be judged having passed the (entire) intersetion only if and when it has passed by the stop line on the lane of the oncoming traffic (or in other words: as it "passed the finish line").

Also, in practice, an actual road intersection may be so much bigger than the extensions of actual pickups so that both, A and B may already be separating from each other (after having escaped their almost-collision unscathed) before either had completely passed the intersection.

Therefore, in this practical case, depending on some more specifics of geometry and speeds, it may indeed be that

  • the event of A passing its "finish line" ("P"), and

  • the event of B passing its "finish line" ("Q")

have no particular "sequence".
So it might be (depending on specifics) that the two finish lines P and Q (who are at rest to each other) find that P's indication of having been passed by A and Q's indication of having been passed by B were simultaneous to each other;

while A and some suitable participant J who "trails A" (such that A and J remained at rest to each other) and who also happened to take part in the coincidence event of B and Q passing each other (i.e. such that B and Q and J passing each other was just one event) find that A's indication of having been passed by P was before J's indication of having been passed by B and Q.

(Perhaps this description may actually benefit from being illustrated; I hope I get around to add a "diagram" next week.)

user12262
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