I do recall at one point in the time I spent on Usenet decades ago, somebody presenting a proof that given certain reasonable-looking assumptions you could derive what the transformation between observers with different velocities has to look like, and there were 3 possibilities:
Gallileo's (Newton's) version (where the time axis shears sideways, time and spatial measurements are the same for everybody, and the set of events that are 1 hour in your future for all possible velocities forms a line parallel to your current space axis)
Lorentz's (Einstein's) version (where the time and space axes both shear towards the diagonal [light ray trajectory] and stretch out, time slows down in the boosted frame, and the set of events that are 1 hour in your future for all possible velocities forms a hyperbola whose asymptotes are the light ray trajectories)
This weird 3rd possibility where the time and space axes rotate rigidly, time speeds up in the boosted frame, and the set of events that are 1 hour in your future for all possible velocities forms a circle…
and then the question was what the hell is #3? Answer: best name for it is the Euclidean transformation; it really is just a rigid rotation of everything. If you go fast enough you're going sideways in time with respect to the original observer (travelling along his/her simultaneity axis). Speed up further and you're going backwards…
… which means time travel is trivially easy in this world. That is, if you have enough fuel for your spaceship, you can rotate your frame 180 degrees and coast as far back into the past as you want (well okay, it'll take you 50 years to go 50 years into the past, so you're still limited by your lifetime, but that's still enough to do damage).
And I really hope that Greg Egan considered this because if he didn't, then his story most likely runs afoul of JWZ's rule
Re: Clockwork Rocket
I do recall at one point in the time I spent on Usenet decades ago, somebody presenting a proof that given certain reasonable-looking assumptions you could derive what the transformation between observers with different velocities has to look like, and there were 3 possibilities:
- Gallileo's (Newton's) version (where the time axis shears sideways, time and spatial measurements are the same for everybody, and the set of events that are 1 hour in your future for all possible velocities forms a line parallel to your current space axis)
- Lorentz's (Einstein's) version (where the time and space axes both shear towards the diagonal [light ray trajectory] and stretch out, time slows down in the boosted frame, and the set of events that are 1 hour in your future for all possible velocities forms a hyperbola whose asymptotes are the light ray trajectories)
- This weird 3rd possibility where the time and space axes rotate rigidly, time speeds up in the boosted frame, and the set of events that are 1 hour in your future for all possible velocities forms a circle…
and then the question was what the hell is #3? Answer: best name for it is the Euclidean transformation; it really is just a rigid rotation of everything. If you go fast enough you're going sideways in time with respect to the original observer (travelling along his/her simultaneity axis). Speed up further and you're going backwards…… which means time travel is trivially easy in this world. That is, if you have enough fuel for your spaceship, you can rotate your frame 180 degrees and coast as far back into the past as you want (well okay, it'll take you 50 years to go 50 years into the past, so you're still limited by your lifetime, but that's still enough to do damage).
And I really hope that Greg Egan considered this because if he didn't, then his story most likely runs afoul of JWZ's rule