The Twin Paradox

I recently read a book, or much of a book, called The Philosophy of Physics, by Tim Maudlin.



I say "much of it" because, quite frankly, I couldn't follow it and gave up on it well before the end.

But there were parts that I believe I did understand, and on the basis thereof I can say that this was a good book to read so soon  after reading Ratcliffe. Ratcliffe, as you may remember, had a quite idiosyncratic take on Euclidean and non-Euclidean geometries. It was an eccentricity that for me rather vitiated his efforts to contribute to cosmology.

Anyway: back to Maudlin. In one portion of the book he considers at some length the "twins paradox," a puzzle arising from, and often commented upon in the context of, the theory of relativity. 

Here it is in my understanding, not his. An astronaut takes off for a distant spaceport, travels at near the speed of light, so time slows. Comes back. He is now only, say, 1 year older than he was when he left. His stay-on-earth twin is (again, making up numbers) forty years older.

One is brought to see the plausibility of that through various inferences. But then one is supposed to say, "hey! isn't the premise of the underlying theory that motion is relative?" From the point of view of Paul, Peter was doing a lot of travelling over 40 years. From the point of view of Peter, presumably Paul and the rest of the earth population did a lot of travelling. Why isn't their situation symmetrical? And if it is, why should either be the older one now?

The usual answer to the questions raised by this paradox involves the acts of accelerating and decelerating. The twin in the spaceship accelerated on his way outbound, decelerated when he arrived at the spaceport, accelerated again when he started to trip home, decelerated again as he approached the earth. The situation is not symmetrical because the earth-bound twin didn't do any of this.

But Maudlin disagrees with that analysis of the paradox. It is true, he says, that acceleration is an asymmetry in the situation as described, but it isn't the critical one.

He sees the answer as one involving world-lines through space time. The "inertial" world line, the stay-at-home line, is straight. The travellers' world-line moves away from, then comes back to, intersection with the inertial line. In Euclidean space, we see the travellers' line inevitably as two lines, thus making up with the inertial line a triangle in which the sum of the length of the two non-inertial lines in necessarily greater than the length of the inertial line.

Now, this is the tricky part. Take any clock on the spaceship (or take the "clock" consisting of the rate at which a human being's cells age) as measuring the length of the line. We would expect (still thinking like Euclideans) that the traveler is the one who has aged more. But the key to the non-Euclidean geometry of relativity theory is that this is exactly reversed. The inertial line in the longer one. The traveller has taken a short-cut through space-time in coming back to earth. Thus his comparative youth, which is not at all a relative matter, forty years or one year later.

The conclusion? Relativity is not a relativism.