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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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  • I thought this presentation would be more fun than "Given two particles, A and B,..." Apparently, I was incorrect. – Allen Jan 20 '15 at 05:53
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    It isn't clear what you're asking. Are you asking if the order in which A and B arrive at the intersection will be different for different observers? – John Rennie Jan 20 '15 at 06:54
  • It seems that in such a scenario (multiple observers, multiple directions, varying relativistic speeds), it would be possible to have an observer that sees them collide, and another that does not. (I agree that may not be clear from the narrative. I'll try to think of an addendum to make it clear what the problem is.) – Allen Jan 20 '15 at 07:09
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    No, if they collide in one frame they collide in every possible frame. – John Rennie Jan 20 '15 at 07:21
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    Welcome to the site Allen. The style of this question is rather different than the established, which most people are used to (hence the negative votes). I recommend reading a few questions to familiarize yourself with it and then maybe edit yours accordingly. I would recommend changing the title to something more informative and removing the completely irrelevant photo. – Heterotic Jan 20 '15 at 08:32
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    I initially downvoted this, but I think it has the potential to be an interesting question. At its heart, I think what this question is really asking is, "If events are not necessarily simultaneous in all reference frames, why are particular types of events (ie collisions) simultaneous in all reference frames). – Sean Jan 20 '15 at 14:53
  • I don't find the question unclear, it's just about whether predictions about localized events like collisions can differ between frames (I discussed this issue a bit in this answer, but the short answer is no, they can't). – Hypnosifl Jan 23 '15 at 05:20

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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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  • 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? – Allen Jan 28 '15 at 03:20
  • @Allen: No, there is not. If you are familiar with Minkowski diagrams, you can easily illustrate this. Otherwise you can imagine, that something happens at the intersection which has to be happening in all reference frames. E.g. there is a mine that will detonate as soon as the first truck hits it $\Rightarrow$ it cannot be that in one frame truck A explodes, while in another truck B is destroyed. – Clever Jan 28 '15 at 07:59
  • I am familiar with them, but only in passing. I lack the ability to do such analysis on my own. You say that there could not be two such observers and that this can be easily illustrated. I would really appreciate it if you (or someone) could sketch such a diagram showing this impossibility and add it to your answer. – Allen Jan 29 '15 at 05:08
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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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  • "The collision is a single event" is a different approach to this that I haven't considered before. I'll have to spend some time letting that sink in. To aid that, let me ask this: can different observers measure truck A's distance to the intersection and get different results? If not, why not? – Allen Jan 29 '15 at 06:25
  • No, there are two events: For a given reference frame, Truck A arrives at intersection ($x_0$) at time ($t_A$). Truck B arrives at intersection ($x_0$) at time ($t_B$). If they arrive simultaneously then $t_A=t_B$ and they collide. If you Lorentz transform each of these events and $t_A=t_B$, then the transformed times (and locations) will be identical and the collision still occurs. The time and location will be different in other IRFs, but the collision always occurs. Simultaneous events at different locations will not generally be simultaneous in other IRFs. – Bill N Jan 29 '15 at 06:34
  • If you want to consider the collision as a single event then the spacetime coordinates will be $(c\Delta t,\Delta x)$ = (0,0) which will transform to other IRFs as (0,0). – Bill N Jan 29 '15 at 06:37
  • @BillN: The collision occurs at a single point of spacetime and is most certainly just one event. And it most certainly makes no sense to ask whether Observers A and B consider that event "simultaneous". You can ask whether observer A considers the collision simultaneous with the chiming of Big Ben, and you can ask whether observer B considers the collision simultaneous with the chiming of Big Ben, but to talk about simultaneity at all, you need to compare two events, not just one. – WillO Jan 29 '15 at 07:00
  • @Allen: Yes, given any two events, there will always be observers who consider the (spatial) difference between those events to be different. If one event is $A$ yelling "Eek! I'm about to crash" and the other event is the crash, observers will differ about the distance between where $A$ was when he screamed and where $A$ was when he crashed. – WillO Jan 29 '15 at 07:03
  • @WillO To avoid confusion, I want to try to make your answer definite: are you saying, "yes, different observers can measure truck A's distance to the intersection and get different results"? If so (stress on the "if"), then I'm back to the start: it seems like we can arbitrarily set truck A's distance to the intersection by appropriately setting "an observer's" velocity. – Allen Jan 29 '15 at 07:53
  • @Allen: If I understand your question, then yes, obviously different observers will measure this distance and get different results, and you don't need relativity to see this. If driver $A$ sneezes when he crosses Main street and crashes when he crosses Elm street, he'll say that the distance between the sneeze and the crash was zero. If you're standing on the corner of Elm street, you'll say the distance was (say) one mile. If you didn't know relativity, you'd say that other observers can measure any distance at all. – WillO Jan 29 '15 at 16:36
  • WillO: "The collision is a single event. It makes no sense to ask whether that event is "simultaneous"." -- That's correct and an important insight; +1. Other aspects of your answer I find less agreeable, cmp. my own answer here. – user12262 Jan 29 '15 at 20:38
  • You're right @WillO. I mis-interpreted what you were saying about A and B. A collision is an event, and if it happens in one frame, it happens in all frames. I was thinking about the definitions of "collision," one of which would be when the world lines of two different object cross, therefore having identical spacetime points. That's what had me considering two events since a specific space-time point along a world line can be considered event, too. (See Thomas Moore's A Traveler's Guide to Spacetime.) – Bill N Jan 31 '15 at 18:56
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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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