Tag: twins

The traveller’s clock can indeed be unambiguously compared with each space station clock at the event where they pass by one another, but that is still only comparing clocks when they are at the same location. And the problem with saying that comparing one’s time with that on a space station is equivalent to comparing it with the one on Earth is that it depends on agreeing that the space station clocks are properly synchronized. But if the space station clocks appear synchronized with the Earth clock in its own frame, then they will not appear synchronized to the traveller who is passing by them. So the time on the space station clock does not match the traveller’s idea of what is the current time back on Earth.
One can indeed go through the process of keeping track of the space-station clock times compared to the traveller’s clock, and will find that those recorded times are all greater on the space-station clocks by the same Lorentz gamma factor. But so long as the velocity remains constant, the traveller could be part of a lined up fleet of ships all moving at the same velocity past the Earth (and so stationary with respect to one another with the Earth and space stations moving past them), and if they all synchronize their clocks with the traveller then the Earth and space station clocks will record the intervals between successive ships of the fleet as greater than the time differences between the clocks on those ships. In other words the Earth (and space station) observers see the ship times as more closely spaced than their own and the traveller (and fleet ship) observers see the times on space station clocks as more closely spaced than the times (on their own ship-based clocks) at which they pass by them. At first sight perhaps this looks like a paradox, but we need to note that each observer of either kind is comparing times on different clocks of the other kind with successive times on the same clock of their own and each can attribute the effect to an assumption that the other set of clocks is not properly synchronized. So this isn’t really a paradox, but there is still no way of deciding which team is actually synchronized and which is not – and without being sure of that the traveller can’t rely on the space stations as true representatives of the time back on Earth.
Making the traveller turn around and return to Earth is just one way of getting some particular pair of clocks back together for an unambiguous comparison of time intervals. (Another would be to have the Earth chase after the traveller and compare notes when she catches up, and yet another would be to do things symmetrically.) But they all involve having someone change their inertial frame (ie accelerate) and the result depends on the acceleration pattern but is always basically that the one who experienced the most acceleration towards the other when they were far apart is the one who will end up younger.

[In the symmetrical twins story both end up the same age, and are not surprised because each has seen the other age first more slowly and then more rapidly but ending up with exactly the same total amount of ageing as they themselves have experienced. If they use the light travel time to infer when each tick of the other’s clock actually occurred (as opposed to when they see it), then each will infer that the other’s clock was running more slowly during both constant speed parts of the trip, but more rapidly during the period when they felt the force of acceleration during the turn-around process – with the same final result.]

Source: (1000) Alan Cooper’s answer to In the twin paradox it is often stated that the clocks can only be compared at the same location. Why can’t the clocks be compared at space stations synchronized with the earth clock on the travelling twin’s journey? – Quora