For the traveller it’s not the same distance; due to length contraction it’s a smaller distance, and so takes less time. For the observer who sees the distance as a full light year it appears to take more than a year, but the traveller’s clocks appear slowed down and so will advance by less than that. (The time experienced by the traveller will still be more than a year unless the travel speed exceeds , ie just over 70% of the speed of light.)
Month: February 2025
Timelike vs Spacelike
If two distinct events are such that there is any inertial frame in which they have zero spatial distance between them, then there is no frame in which they are simultaneous and so they are said to be “timelike separated”. This is because the frame in which they have zero spatial separation corresponds to an observer who sees them both happening at the same place one after the other; and for any other inertial observer, the time between them is also nonzero (since for any v<c the Lorentz contraction factor is never zero).
On the other hand, any two events which are seen as simultaneous by some inertial observer (which is different from being seen simultaneously by that observer!) are said to be “spacelike separated”. But the appearance of simultaneity is relative to the observer and only happens in one particular frame. Other inertial observers won’t see the events as simultaneous but all will agree that it would take faster than light travel to see them both at the same place – eg to actually be present at both of them.
GR and Twin Paradox
General relativity theory does not “solve the twin paradox of special relativity”.
Despite being “paradoxical” in the sense of contradicting our intuition that the time ordering of separated events should be absolute, there is no “paradox” in the sense of internal contradiction in special relativity. Nor is it impossible to analyse the experience of an accelerated observer in special relativity; and in the case where one twin is turned back (eg by a rocket) this leads to the conclusion that both agree on the difference between their ages when reunited.
The only case in which general relativity is needed is when the acceleration is due to gravity (eg by slingshotting about a massive star) – and so does not lead to the feeling of applied force by the freely falling traveller. But as soon as gravity comes into the picture we are no longer talking about special relativity.