I’m gently pointing out that everything is a matter of travelling though spacetime. There in no difference between travelling in space and travelling in time. The entire time dilation you start with in the original question is a result of this fact.
You travel through spacetime at a constant rate. The time you perceive is your proper time. But what is happening is a result of your travel through spacetime at a constant rate. If you move in space relative to another object your observed travel in time slows to keep the overall rate the same. Move enough and you can get an appreciable change in the rate time appears to pass. Distance travelled and time passing are the same thing, you just exchange between them to keep the rate constant.
So, overall, the manner in which you accumulated a history in which time was ever so slightly slower for you was nothing but exchanging some of your time for some of that distance. So the same arguments for time apply for distance, as they are interchangeable. It is, again, how you got your experienced time difference.
Asking for a method to determine the differences in experienced time is identical to asking for a method to determine which of you had travelled the longer route.
Mr A and Mrs B both start on the origin (0,0) and each carry a meter stick. Let’s say they agree to meet at the point (x,y). At no point during his journey does Mr A take a measurement with his meter stick. When they meet how can they use their meter sticks to see who took the longest path?
The kid and I perceive events 2 microseconds out of phase. She has a clock but, as has been pointed out amply above, I do not, because of my negligence. But if we could both work with events in the fraction of microseconds domain, it seems we might be able to detect the difference.
Since this knowledge has been around for a while and a solution has not occurred to some very smart folks, I doubt I’m going to solve it in an afternoon.
Again. No you don’t. You are co-located in the same reference frame. You both perceive events at exactly the same time. You do not carry any time displacement relative to current events.
Except that it has not. There is no such time displacement.
Also, of course sci-fi fudges science for the sake of the story. It’s fiction and while some authors try to be true to current science most take liberties.
If I understand it correctly, the reason they “spring back” is that the effect is reversed / opposite when they turn around and return to Earth, so in the end things balance out.
Again, there isn’t. You keep asserting that there is, but there is no such effect.
Your pasts are slightly different. But once you are co-located in the same reference frame your futures are identical. This means you both experience events at exactly the same time. You do not carry any sort of residual offset, there is no such thing.
Note - phase is not the same thing as time. Phase is an angle. It makes sense when talking about periodic events, but not otherwise. Being out of phase means being out of step. Not being out of time.
That would make sense but then the clocks would have experienced a phase difference in orbit which would have vanished upon return. Perhaps that is the case.
No again. The pasts of the clocks are different. But their futures are identical once they come together. The recorded time difference persists because it records the different history.
You seem stuck in a Galliean model of time. But trying to apply relatavisitc effects in it. This isn’t ever going to work, as you are clashing together two incompatible models of space and time. We don’t live in a Galliean universe, and trying to shoe horn things into it isn’t working.
OK, but you said that you could exchange distance for time. That implies an exchange of units of measure. So, the phase difference represents a displacement in some exchangeable units of measure. I am referring to that as position.
Also, is the time dilation of returning space ships just a fiction?