the twin paradox

[surdrawrod]

There is something that has always bothered me about Einstein's famous twin paradox. One of a set of twins gets in a rocket and leaves Earth at a relativistic speed, and then returns. While only a short time has elapsed for the rocket-bound twin, his brother is an old man because time dilation slowed the passage of time for the twin in the rocket. But in relativity there are supposed to be no preferred frames of reference. It should be possible to view the rocket ship as stationary and the Earth as having moved away from the rocket ship at relativistic speeds. How does time know that it is the rocket that is accelerated and not the Earth? Before someone tells me it is an effect of the rocket motor's acceleration, consider a third person, a triplet of the original twins. He sets out at the same time as the first twin. They both are in rockets that accelerate to near the speed of light in a brief fraction of their travel time, and then coast until they turn around and reaccelerate back to the Earth. This time however, the third triplet stays coasting near the speed of light for twice as long as the other travelling twin, and arrives back on Earth to find his first brother long dead, and his second brother (who had been in the other rocket ship) very old, while he--the third triplet--is still young. Yet both travelling triplets were accelerated and decelerated for exactly the same amount of time--only the time spent coasting differed! It seems to me that the twin paradox cannot be real unless there is a preferred frame of reference, that of the Earth which stays behind.

[hhEb09'1]

It seems to me that the twin paradox cannot be real unless there is a preferred frame of reference, that of the Earth which stays behind.

This is a hard question to answer.

There is no paradox of course, but I'm sure that's not what you meant by it cannot be real.

A "preferred frame of reference" means a frame of reference where the physics works, but it doesn't work in others. For intance, in the rotating earth frame, in Newton's mechanics, we must take into account so-called fictitious forces to account for coriolis effects, for instance. Newton's laws do not work in that rotating frame, without adding additional terms.

Not so, with relativity. It just gets more complicated

Twin Paradox, SR
Twin Paradox, GR
Twin Pardox, etc

Welcome to BAUT!

[Steve Limpus]

I think the answer you're looking for is that the twin in the rocket turns around to come back home. This is the acceleration that makes the difference. It's usually depicted in Minkowski diagrams (and is usually simplified with 'instant' acceleration etc.) where you can see how the worldline of the twin in the rocket 'sweeps across' the world line of the other.

EDIT: the other way to look at it is that there are already three frames of reference in the twin paradox:
1.earthbound twin
2.outbound twin
3.inbound twin

The wiki arcticle descibes it quite well.

[surdrawrod]

If it were the turning around that did it, why does the third traveller, who spends as much time turning around as the second traveller, age more slowly than the second traveller?

[Steve Limpus]

Yes, sorry, my first answer was really just referring to twin one and twin two.

I hope someone more knowledgeable will confirm this (and I hope I'm picturing you question correctly), but if you look at the diagram in the wiki article and imagine the third twins outbound and inbound legs are twice as long, there will be a simple geometric relationship with the portion of the first twins world line that is 'swept' when twin three turns around (the part of the first twins worldline between the red and blue simultaneity lines. The third twin will have 'aged' more than the second, and 'much more' than the first.

Don't take that as gospel, though, unless someone better qualified gives it the thumbs up!

Grant Hutchison is a wizz at these diagrams. This thread descibes them quite well.

[grant hutchison]

I hope someone more knowledgeable will confirm this (and I hope I'm picturing you question correctly), but if you look at the diagram in the wiki article and imagine the third twins outbound and inbound legs are twice as long, there will be a simple geometric relationship with the portion of the first twins world line that is 'swept' when twin three turns around (the part of the first twins worldline between the red and blue simultaneity lines. The third twin will have 'aged' more than the second, and 'much more' than the first.

Don't take that as gospel, though, unless someone better qualified gives it the thumbs up!

Yes, that's how it works. The simultaneity shift the accelerated twin experiences is greater the farther she is from "home" when she makes here turnaround. The effect is visible in the geometry of the spacetime diagram of the twins' relative motion.

Grant Hutchison

[Delvo]

The "no preferred frame" thing refers to inertial reference frames, reference frames that are not accelerating (or relative to which the rest of the universe isn't accelerating). As soon as a reference frame is accelerating, inertial ones are immediately different and preferred.

[grant hutchison]

The "no preferred frame" thing refers to inertial reference frames, reference frames that are not accelerating (or relative to which the rest of the universe isn't accelerating). As soon as a reference frame is accelerating, inertial ones are immediately different and preferred.

Well, the accelerating twin is moving though a succession of instantaneous inertial reference frames, none of which is "preferred" any more or any less than the Earth frame.
What makes the difference is that the accelerated twin does shift from one inertial reference frame to another, whereas the Earth twin does not. That's how "time knows" (to quote the OP) which twin accelerates and which doesn't: because one twin changes the tilt of her simulaneity lines by changing inertial frames, and the other does not.

Grant Hutchison

[hhEb09'1]

The "no preferred frame" thing refers to inertial reference frames, reference frames that are not accelerating (or relative to which the rest of the universe isn't accelerating). As soon as a reference frame is accelerating, inertial ones are immediately different and preferred.

No, "no preferred frame" does not just refer to inertial reference frames, except in special relativity.