It shouldn’t. Moving from B to A slower than light is possible*, moving from A to B faster than light isn’t, and you can’t change whether something is possible by changing reference frames.
What I’m trying to get at is, What does a physicist mean when she says she saw X move from A to B faster than light? The measurement is made from a single point; say A. So the physicist is at A, sees X leave at time tX, sends a photon to B at time t0, and gets a photon back from B at time t1, which shows X at B at some time tB. I’m tempted to set tB = (t0+t1)/2, but I don’t think relativity lets me do that, except within a particular reference frame.
“X travelled faster than light” only means that tX < t1. The FTL interpretation is t0 < tX < tB < t1: The photon left at t0, then X left at tX, and both met at B at time tB, X travelling faster than light.
Is there a mundane interpretation under which tB < tX < t1? The photon left A at t0, met X at B at tB, causing X to travel back to A and arrive there at tX.
The answer appears to be No, because X would need to travel faster than light on the return trip. And this also explains that Owen’s original answer was correct: You can say that X travelled from A to B faster than light, or from B to A faster than light.
moving from A to B faster than the speed of light in one reference frame is equivalent to moving from B to A faster than the speed of light in another reference frame
or
moving from A to B faster than the speed of light in one reference frame is equivalent to moving from B to A slower than the speed of light in another reference frame
I meant the first one: faster than light in both directions.
You can think of it this way: if any reference frame perceived travel from B to A slower than light, then so would every reference frame. The only way for two observers to disagree about whether the object is at A or B first, is for both to observe the motion as being faster than light.
It shouldn’t. Moving from B to A slower than light is possible*, moving from A to B faster than light isn’t, and you can’t change whether something is possible by changing reference frames.
*(Under special relativity without tachyons)
What I’m trying to get at is, What does a physicist mean when she says she saw X move from A to B faster than light? The measurement is made from a single point; say A. So the physicist is at A, sees X leave at time tX, sends a photon to B at time t0, and gets a photon back from B at time t1, which shows X at B at some time tB. I’m tempted to set tB = (t0+t1)/2, but I don’t think relativity lets me do that, except within a particular reference frame.
“X travelled faster than light” only means that tX < t1. The FTL interpretation is t0 < tX < tB < t1: The photon left at t0, then X left at tX, and both met at B at time tB, X travelling faster than light.
Is there a mundane interpretation under which tB < tX < t1? The photon left A at t0, met X at B at tB, causing X to travel back to A and arrive there at tX.
The answer appears to be No, because X would need to travel faster than light on the return trip. And this also explains that Owen’s original answer was correct: You can say that X travelled from A to B faster than light, or from B to A faster than light.
An interpretation putting t1<tX seems to have the photon moving faster than light backwards in time to get from B back to A
My question is whether he meant to say
moving from A to B faster than the speed of light in one reference frame is equivalent to moving from B to A faster than the speed of light in another reference frame
or
moving from A to B faster than the speed of light in one reference frame is equivalent to moving from B to A slower than the speed of light in another reference frame
both of which involve moving faster than light.
I meant the first one: faster than light in both directions.
You can think of it this way: if any reference frame perceived travel from B to A slower than light, then so would every reference frame. The only way for two observers to disagree about whether the object is at A or B first, is for both to observe the motion as being faster than light.
I know Owen was not talking about impossibility, I brought up impossibility to show that what you thought Owen meant could not be true.
Moving from B to A slower than the speed of light does not involve moving faster than light.