Special Relativity-Simultaneity

Question

If two events are simultaneous in one reference frame, are they simultaneous in all reference frames? Please provide thorough qualitative explanation
If blue light is going at speed $c$, with red light emitted in opposite direction, at speed $-c$, would't the speed of red light in the frame of someone moving along the blue light, be $2c$? Is this a violation of SR? Any help is appreciated.

It's a bad idea to immediately accept an answer as you did. The answer you accepted is wrong. — , Feb 27 '18 at 02:07
I am new here. Just majored in Physics, and hoping to understand Special Relativity! Unfortunately most online ressources get deep into mathematical Lorentz transforms while my instructor prefers theory (theoretical physicist). — Ryan, Feb 27 '18 at 02:18
Ryan, if you are under the impression that doing theory and getting deep into the mathematics are in opposition you are in for a rude surprise one of these days. Most theorists are thoroughly accomplished in the mathematical minutia. Your instructor may be giving you the high-altitude view for the moment, but dealing with the nitty-gritty in some way is coming. — dmckee --- ex-moderator kitten, Feb 27 '18 at 02:51
Subquestion 2 is a duplicate of https://physics.stackexchange.com/q/11398/2451 and links therein. — Qmechanic, Feb 27 '18 at 08:32

score 1 · Answer 1 · answered Feb 27 '18 at 02:07

1

No. The Lorentz transformation gives $t'=\gamma t -(\gamma/c^2) vx$. If the events are distinct but simultaneous, and $v\ne0$, then the second term will never vanish.
No. Special relativity doesn't allow frames of reference moving at the speed of light.

answered Feb 27 '18 at 02:07

1
This answer assumes one-dimensional space. In fact, if I rotate my frame from, say, $(t,x,y,z)$ to $(t,x-y,x+y,z)$, then events that were originally simultaneous remain simultaneous. 2. Correct as stated, though I think the OP would probably still want to ask what happens if $c$ is replaced by $.9c$, so while this answers the question that was asked, I'm not convinced it answers the question that was intended. (I hope this doesn't come off crankier than I intend it to; obviously this is all correct in spirit, but I thought a bit more care was worthwhile.)

WillO

Feb 27 '18 at 02:11

Re 2, I interpreted his question as meaning what is the relative speed between two light waves going in opposite directions, hence how I cast my answer. It is true nothing (of a massive nature) can travel with the light. – Steve Feb 27 '18 at 02:27

Might be worth clarifying that the the spacial line between the events is perpendicular to the direction of boost simultaneity remains. – dmckee --- ex-moderator kitten Feb 27 '18 at 03:02

score 0 · Answer 2 · answered Feb 27 '18 at 06:08

(1) If 2 events have a space-like separation, then there is a reference frames where they are simultaneous (and also frames where A is before B and B is before A).

(2) If we work just on the collinear line of the photon's motion (or light pulses if you prefer)--then any observer confined to this line with any boost sees them moving away from each other at $2c$. Now if you boost orthogonal to that with $\gamma=10^9$--those photons are going to be nearly collinear, with a very low relative velocity.

BTW: this answer had no math in it--but @dmckee is right: you're going to need it.

Steve · Answer 3 · 2018-03-02T02:41:42.977

-4

Two events can be simultaneous in other frames. It depends the position of the events and the orientation of the movement between the frames. But no two events would be simultaneous in all possible frames.
Taken literally the answer to the question is no, simply because no massive object can travel alongside the blue light.

However, the wavefronts of light emitted in two diametrically opposite directions can be said to be moving at 2c relative to one another. It's not a violation of SR, because relativity deals with the speed of the interaction between two objects, not between two wavefronts of light.

In your example, any object which received any light from your source (whether it be the red or the blue light), will still have received it at c from the source.

edited Mar 02 '18 at 02:41

answered Feb 27 '18 at 01:44

Steve

2,689

Thank you! for question 1, if two events are simultaneous for me, at rest, would they also be simultaneous to an alien at rest on Mars? – Ryan Feb 27 '18 at 02:00
1

This answer is completely wrong. The answers to both questions are no, not yes. – Feb 27 '18 at 02:03
Contra @BenCrowell, the first part of this answer is certainly correct (see my comment on Ben's answer). But I agree that the second part is way off base. – WillO Feb 27 '18 at 02:16
If I am concerned only in one direction, that of motion, why is Steve's answer to 2 incorrect? – Ryan Feb 27 '18 at 02:19
@BenCrowell, they are not wrong. – Steve Feb 27 '18 at 02:21
@Ryan, have a look at my comment on Ben's answer regarding what I thought you meant by 2, and what I was therefore answering. – Steve Feb 27 '18 at 02:43
1

You first answer isn't wrong as physics (there are some cases where they are still simultaneous), but that's because you have only answered for special cases. Your second one is wrong. Oh, from the POV of any material observer the closing speed of the two rays is $2c$, but that is not the relative speed which is mathematically undefined. – dmckee --- ex-moderator kitten Feb 27 '18 at 02:54
@dmckee, my answer on 1 was clearly made contingent, so I don't think you can fault me on that. I once had to really haggle with an academic who insisted as a flat matter of principle that no two events could be simultaneous in two frames in relativity - until he admitted that they could - and he said the same as you "oh that's a special case", which totally undermined the absurd principle he was pushing. Re 2, I'll accept your clarification on the terminology - although I would point out that the OP seemed to be describing a contra-closing (or "opening") situation. – Steve Feb 27 '18 at 03:05
@Steve I would change your answer on 1 to "No, although two events can...," because the original question is a yes-or-no question to which the answer is "no." Besides that, the content of the first answer is fine. For the second part, OP asks about "the speed of red light in the frame of someone moving along the blue light," which is the relative velocity as described by dmckee (and is undefined, as that frame is invalid). – Chris Mar 02 '18 at 02:20
@Chris, I'm reluctant to change 1 because it is true. It is no more a special case than someone who asks "can a triangle have two angles equal?", the answer to which is most certainly "yes" and not "no", even though the scalene triangle is the more general case and the isosceles, equilateral, and right-angle triangles are all "special cases". – Steve Mar 02 '18 at 02:25
You're right about 2, but I answered the question I thought the OP was meaning to ask - as commented. – Steve Mar 02 '18 at 02:26
@Steve Everything past "Yes" is true, yes. But the question was "are they simultaneous in all [emphasis mine] reference frames," so starting your answer with "Yes" is confusing. (To use your example, it's more like you answered the question "Do all triangles have two angles equal?" with "Yes, some triangles have two angles equal.") And there's no shame in fixing your answer- indeed if you fix the problems in part 2 some people will probably take back their downvotes. – Chris Mar 02 '18 at 02:32
@Chris, fair point. – Steve Mar 02 '18 at 02:35

Special Relativity-Simultaneity

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