# Special Relativity-Simultaneity

1. If two events are simultaneous in one reference frame, are they simultaneous in all reference frames? Please provide thorough qualitative explanation

2. 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.
– user4552
Feb 27, 2018 at 2:07
• 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, 2018 at 2:18
• 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. Feb 27, 2018 at 2:51
• Subquestion 2 is a duplicate of physics.stackexchange.com/q/11398/2451 and links therein. Feb 27, 2018 at 8:32

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.

2. No. Special relativity doesn't allow frames of reference moving at the speed of light.

• 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.) Feb 27, 2018 at 2:11
• 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. Feb 27, 2018 at 2:27
• Might be worth clarifying that the the spacial line between the events is perpendicular to the direction of boost simultaneity remains. Feb 27, 2018 at 3:02

(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.

1. 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.

2. 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.

• 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, 2018 at 2:00
• This answer is completely wrong. The answers to both questions are no, not yes.
– user4552
Feb 27, 2018 at 2:03
• 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. Feb 27, 2018 at 2:16
• If I am concerned only in one direction, that of motion, why is Steve's answer to 2 incorrect?
– Ryan
Feb 27, 2018 at 2:19
• 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. Feb 27, 2018 at 2:54