- #36
Ibix
Science Advisor
- 12,269
- 14,173
I don't disagree with this. I am just trying to argue that it is the whole route that matters, not just the corners. Darwin123 seems to me to be arguing the converse.PeterDonis said:If there are no rockets firing, then whatever it is that is following the "different route", it can't be the traveling twin, or indeed any single object. The only word I can come up with for whatever it is that does follow the different route is "information". Perhaps that's not the best word, but we have to have some word for whatever it is that picks out the "route in spacetime" whose length is to be evaluated, in cases where no single object follows that route.
Perhaps I need a different example. Consider twins at rest at a space station. They leave together in identical rockets at velocity +v. At time t1, one twin fires his motors and turns round, returning to the space station at velocity -v before braking to a relative stop. The other twin carries on until time t2, when he also turns around and returns at -v before stopping at the space station. Both twins do identical accelerations, but it's easy to show that the difference in ages when they meet up is [itex]\Delta t=2(t_2-t_1)(1-1/\gamma)[/itex], which is zero only if they turn around at the same time or they don't travel at all. So acceleration isn't the only thing that matters. Both the amount of time between accelerations and the accelerations matter.
In the limited context of the classic twin paradox, you only need to know which twin accelerated to determine everything. So in this narrow circumstance, I agree one could argue that acceleration is the key. However, this isn't a useful view in general. In general, you need the complete history of both twins - i.e., their routes through spacetime.
Acceleration (or at least a frame change) is necessary for the worldlines to cross again. But it doesn't cause the age difference, any more than corners cause the triangle inequality. Different paths through a spacetime with a Minkowski geometry causes that.