The idea that the experience of an accelerated observer might be approximated by considering its worldline as comprising many small inertial pieces is a good one. And during each inertial step the speed of light seems to be constant everywhere. But at the velocity boosts or “frame jumps” between the steps, the apparent coordinates of all events (including those on the world line of a light signal) get shifted, so the light seems to jump ahead or back. Taking the limit of these approximations leads to the conclusion that the light signal does not seem to have constant velocity from the point of view of the accelerated observer. (Since the “frame jumps” lead to coordinate changes that are proportional to the distance of the event from the observer, this does not change the fact that every light signal seems to have the same speed when it reaches the observer, so there is no local change and it is just when the signal is far away from the observer that its velocity appears to vary.)
Tag: acceleration
More TwinStuff from Quora
In the twin paradox where does the missing time go? If the twin turns back to Earth then turns away again their notion of now switches back to the past. What does this mean for the experience of the observer on Earth relative to the moving twin?
“In the twin paradox where does the missing time go?” I am not aware of any “missing” time. One twin experiences less time than the other but there is no gap where any time goes missing. (There is however an apparent speed-up of the Earth clock from the point of view of the traveller while turning around, and in the physically impossible case of an instantaneous turn-around that would look like a gap in the traveller’s understanding of what was happening “at the same time” on Earth; but in any possible actual scenario it would just be an apparent speed-up rather than a jump.)
“If the twin turns back to Earth then turns away again their notion of now switches back to the past. What does this mean…” Indeed! Does that sentence actually have any meaning at all?
Perhaps what that second sentence is referring to is the traveller’s idea of the time that is “now” back on Earth. It is true that when we accelerate away from something we infer a slowing down of its clock at a rate proportional to the distance. If the distance is great enough this effect can make the clock “behind” us appear to stop, but beyond that distance (called the “Rindler horizon”), rather than see it run backwards we actually just don’t see it at all. (And, yes, the Rindler horizon perceived by an accelerated observer is indeed related to the Event horizon surrounding a gravitational singularity.)