Are the transforms instantaneous?

[Leo.Ki]

Hello Board,

When you accelerate, the world changes its spacetime "slant" with respect to your own frame. Is this change instantaneous throughout the whole universe? I'm aware that "instantaneous" is a dangerous word here, since we are changing frame when accelerating, but I hope you see what I mean. What are the consequences if the change is instantaneous, and what are they if it is not?

 

[JesseM]

Hello Board,

When you accelerate, the world changes its spacetime "slant" with respect to your own frame. Is this change instantaneous throughout the whole universe? I'm aware that "instantaneous" is a dangerous word here, since we are changing frame when accelerating, but I hope you see what I mean. What are the consequences if the change is instantaneous, and what are they if it is not?

Frames are just coordinate systems for describing different events in spacetime, it is just a matter of convention that each inertial observer should call "their" frame the one in which they are currently at rest, they could just as easily analyze things from the perspective of some other frame. So, it would likewise be just a subjective decision whether an accelerating observer should define simultaneity at every instant in terms of his instantaneous inertial rest frame, or whether he should calculate everything from the perspective of his original rest frame before he began accelerating, or what. There isn't a physical answer to your question any more than their would be to the question of whether the origin of an observer's spatial coordinate axes travels along with him when he accelerates, or stays put, or what.

 

[Leo.Ki]

Thanks, Jesse. It makes sense to me. I now see that I was adding a second temporal dimension along which spacetime would change, which is insane.