As soon as you accelerate there will be a Lorentz/FitzGerald contraction. All uniform motions should present us with it too. Otherwise you would have to infer that the only time a 'real' contraction exist is in the acceleration. As all uniform motion are without 'expending energy' locally, but we on the other hand assume a length contraction from eh, Bobs point of view, right

as he is the one moving, assumingily uniformly at the time of the question? How does relative motion 'know' its 'speed', as expressed relative that 'inertial observer' I assume Alice to be

Bob does not expend any energy, neither will his and the ships inertia be any bigger as I understands it. What is the gold standard of the universe here?

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The universe should contract from his frame of reference, although I'm unsure how you think here "Alice will measure that the distance from her to Andromeda is 2.5 millions ly, i.e. Alice will not see any length contraction from a proper frame.

However, Alice will measure that Bob only needs to travel 0.01*2.5 ly to get to Andromeda."

Alice will notice his ship being contracted, ( as well as it should present itself slightly 'rotated' from her frame of reference if I'm thinking right here

, as well as Bob 'slowing down' in all manners definable, including red shifting all light signals from him. Her perception of the rest of the universe, as her measured distance to Andromeda, assuming her to have a inertial frame of reference here, shouldn't differ though? Assuming she knows relativity she can calculate it though, what Bob will find from his frame of reference I mean? If that was what you meant?