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by TeMPOraL
3451 days ago
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IANAP, but doesn't speed of light actually define "at the same time"? I.e. for all intents and purposes, it's happening "now" for us, because there's no meaningful way of getting there faster than light. In a way what I'm imagining is speed of light being a kind of "clock signal" of digital electronics, except continuous, not discrete. |
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If you wanted to say that when a light signal goes from A to B its emission and reception should be considered simultaneous, then you'd have to say the same about a signal sent back from B to A when the first one is received. ... And then, if you also wanted to believe that "x is simultaneous with y and y is simultaneous with z ==> x is simultaneous with z", you'd get the absurd conclusion that two events in the same place but separated in time are simultaneous.
So here's the actual situation (at least in special relativity):
Once you define a frame of reference, which is basically the same thing as a velocity of motion, you then have a notion of simultaneity in that frame. If you fix your frame of reference, simultaneity has the nice properties you might want it to have (like transitivity, which I appealed to above). But you can have "x simultaneous with y in frame F" and "y simultaneous with z in frame G" without x and z being simultaneous in any frame.
If a signal can get from x to y (here x and y are locations in spacetime, not just in space) then there is no frame in which x and y are simultaneous. If it's possible only for a signal propagating at the speed of light, then it is (just barely) impossible to find a frame in which they are simultaneous. If it's not possible even at the speed of light, then there is a frame in which they are simultaneous.
So, in particular, consider the collision between these stars and the arrival of the light from the collision here on earth. In an (impossible) reference frame moving at the speed of light in the direction from there to here, the events would be simultaneous. Actually, they can't quite be -- but by considering a frame that moves fast enough, you can make the time difference as short as you like.
In an (equally impossible) frame moving at the speed of light the other way, they would be 3600 years apart. With actually-admissible reference frames, the time can be anywhere strictly between zero and 3600 years.
So far as I know, we and these stars are not moving very rapidly (in comparison with the speed of light) relative to one another. It seems reasonable to use a frame corresponding roughly to their motion and ours. That gives you a time difference of about 1800 years, and any plausible adjustment for our actual relative motion will make no difference to speak of because we're moving so much slower than light relative to one another.
But: There is another related notion that you may have in mind. You can compute a numerical measure of separation between any two points in spacetime, called the "interval", which is positive when the separation is "space-like" and negative when it's "time-like". If light could go from one to the other, this separation is zero.
(How does this escape the scenario I described in the first paragraph above? Because knowing the interval, as it's called, between x and y, and the interval between y and z, isn't enough to determine the interval between x and z any more than knowing the distances x-y and y-z is enough to determine the distance x-z. In fact the situation is worse for intervals than for distances because there isn't anything corresponding to the triangle inequality. And the "interval=0" relation isn't transitive. So knowing that the intervals x-y and y-z are zero tells you nothing at all about the interval x-z.)