Thread split from https://www.physicsforums.com/threads/can-an-observer-perceive-he-is-traveling-faster-than-light.955469/
There is no unique standard definition for the frame of reference for a non inertial spaceship. Please see the paper I posted earlier for an example of how to rigorously define such a concept.What happens if he decelerates? Does it appear to recede?
Again, this is simply not B-level material
You cannot ignore it and answer the question. Depending on the arbitrary choices you make in the mathematical definition of the non-inertial frame you can get any answer you want.
Do you really need to absorb an advanced paper to answer the question? Let's view the problem this way:
- The ship is traveling at a constant .999c relative to Earth just prior to reaching Earth
- The ship puts on the brakes moments before reaching Earth, so that it is now at rest relative to Earth
It is interesting that you say that arbitrary choices in the math can lead to arbitrary answers. For instance, if a machine on the ship during deceleration records Alpha Centauri's light, it doesn't seem like the question of whether the light is red-shifted or blue-shifted (and by how much) would be arbitrary nor should it depend on whatever choices you made in defining the non-inertial frame. If you have a real ship making a real breaking maneuver, it seems like the answer should be deterministic.
I'm sure I'm missing something, but it's not obvious (as usual).