I have an observer on Earth with an atomic clock, let's call this the unprimed frame with space coordinate x=0 and t. Universe is one dimensional.

I have a rocket ship sitting stationary in empty space to the far "left" of the earth on the x-axis. Because it is stationary wrt the Earth, rocket ship and earth have the identical spacetime coordinates (up to a shift in space). It begins to accelerate to the right at t=0 with immense force such that relativistic effects can be felt quickly. Special relativity would say that the travelling space ship plane of simultaneity begins to rotate counter-clockwise in a standard Minkowski diagram. To me, this seems to mean that "things" to the left of the spaceship would advance in time more quickly (the further left, the further the time advances), while things to the right of the spaceship must go backwards in time. Since the rocket ship is to the left of the earth, won't it mean that the rocketship crew sees events on Earth going backwards in time?

I have an observer on Earth with an atomic clock, let's call this the unprimed frame with space coordinate x=0 and t. Universe is one dimensional.

I have a rocket ship sitting stationary in empty space to the far "left" of the earth on the x-axis. Because it is stationary wrt the Earth, rocket ship and earth have identical spacetime basis (up to a shift in space). The ship begins to accelerate to the right at t=0 with immense force such that relativistic effects can be felt quickly. Special relativity would say that the travelling space ship plane of simultaneity begins to rotate counter-clockwise in a standard Minkowski diagram. To me, this seems to mean that "things" to the left of the spaceship would advance in time more quickly (the further left, the further the time advances), while things to the right of the spaceship must go backwards in time. Since the rocket ship is to the left of the earth, won't it mean that the rocketship crew sees events on Earth going backwards in time?