Is the perception of backwards time possible in relativity during deceleration?

[Ookke]

Hi. A short question regarding relativity of simultaneity, its interpretation and maybe some terminology.

Suppose A and B are distant space stations, at rest with each other, clocks synchronized. A rocket R travels with high speed passing A at time t=0, heading towards B. Not going into details, from R's perspective the clock reading at B could be couple of years ahead.

If the rocket suddenly stops at A, it enters the frame of A and B, where the clocks are synchronized. After stop R will agree with A that the time at B is t=0.

Should we say that from R's perspective time went backwards at B during the deceleration? Of course R could not really watch the event because of distance and finite light speed, but nevertheless R "observed" it (in the sense commonly used in relativity, involving calculations). Or should we think this only a coordinate system change, not an observation at all?

 

[Ibix]

If the rocket suddenly stops at A, it enters the frame of A and B, where the clocks are synchronized. After stop R will agree with A that the time at B is t=0.

Setting of clocks is a convention. If, when the rocket stops, it wants its clocks to match those of B, it will need to set them manually. It's like clocks changing in winter (in countries where that happens!) - you simply change your clock to match the "official" time.

The point is that the rocket does not "enter the frame of A and B". It can always be described in any frame - just like anything else. It's motion change means that its clocks now tick at the same rate as A's and B's clocks, but it doesn't mean that they must show the same time.

Should we say that from R's perspective time went backwards at B during the deceleration?

No. If you want a single coherent perspective for R, it cannot be two inertial frames naively stitched together, precisely because doing that would cause some events to have two coordinates assigned to them and some none. My favourite way of constructing non-inertial coordinates is Dolby and Gull's radar time - see https://arxiv.org/abs/gr-qc/0104077.