# Acceleration

In Discussions of the Twin Paradox, some experts say it’s all about acceleration and others say the opposite. How can I trust any of them?

Despite the strong words used in some discussions of this, there is no real difference of opinion between real experts about the physics of the matter. The difference is rather a matter of paedagogy and semantics – as I will now attempt to explain.

The so-called Twin Paradox arises as a result of confusion about how each of two observers can think that the other one has clocks which are running more slowly. How can this be? Well, we have to admit that IF there was any absolute concept of things happening at the same time then there would indeed be a paradox. For if there is a universally agreed instant when one observer’s clock shows 1 hour this must be before the other one (with the slower clock) gets to that point. But the other observer sees it the other way around – and if they both have the same idea of simultaneity that is a contradiction. But Special Relativity explicitly denies the need for a universal clock which applies everywhere to all observers. If I synchronize a set of clocks at different points in the universe by sending signals between them (and taking account of the travel time for those signals) then my clocks will not agree with those synchronized by someone else who is moving relative to me. This means that in order to display a paradox we have to bring the two clocks together again. And this is where the twins come in.

Imagine two twins floating together in space in an inertial (unaccelerated) frame of reference (I would say standing on the Earth, but the Earth is constantly spinning and accelerating in its orbit around the Sun, so that’s not such a good idea). Now let one of the twins rocket up to a high speed  and then coast to a distant point (maybe a star, but since there’s no gravity in Special Relativity let’s consider it a massless one). On reaching her destination the traveller turns around and rockets back up to the same speed for the return trip. During all of the travel time out and back, each twin thinks the other’s clock (and body) is running more slowly. But when they get back together it would be a paradox for them not to agree about which of them is older (and has a bigger time showing on their clock).

The question then is “Why is this not a paradox? (and if there’s an age difference, which one do they both agree is older?)”

The answer, as all the experts will agree, is that the one who stayed behind is older. And the explanation, which they also all agree on, is as follows:

Just before the turn-around, the traveller thinks that the stay-at-home has only aged a little bit, but just after the turn-around she is in a different frame of reference in which her understanding of the current time-at-home is suddenly much later than it was before.

To see this difference in perceptions of the stay-at-home time, it can be helpful to imagine a third traveller who is coming in from far away and meets the outbound traveller at the turn-around point (and whose system of synchronized clocks she adopts for the return trip).

Some people say that the traveller’s change in understanding about the time-at-home is a result of accelerating from one inertial frame to another. Others say that it’s just because the returning traveller is in a different frame and so “acceleration has nothing to do with it”. You be the judge!

(But remember that in the end it’s just a matter of chest puffing and posturing over a meaningless semantic quibble.)