New Version of the Twin Paradox: Accelerated Twin Older

[PraedSt]

I don't understand any of this, but I thought some of our GR specialists would enjoy a bust-up.

Physorg article; ArXiv paper

From the physorg article:

Physicist Marek Abramowicz of Goteborg University in Sweden and astronomer Stanislaw Bajtlik of the Nicolaus Copernicus Astronomical Center in Warszawa, Poland, have proposed the surprising new version of the twin paradox, which at first seems to run contrary to the traditional version. However, the scientists show that the traditional version is actually a specific case of a more general concept.

I've tried to quote some relevant bits of their argument, but seeing as I don't know much about this, I've probably picked exactly the wrong paragraphs. Apologies in advance.

In the new scenario, both twins are in circular orbit at different velocities around a large body, with the velocities measured by observers rotating with zero angular momentum with respect to the sky. Abramowicz and Bajtlik considered what happens when twin A stops moving, and so has a velocity of zero, and therefore a non-zero acceleration. Twin B continues to orbit at a set velocity corresponding to Keplerian free orbit and therefore has zero acceleration. Twin A is the accelerated twin, and twin B is not accelerated. As the scientists calculate, contrary to the classical version of the paradox, twin B is younger.

The scientists then considered a situation where the large body that the twins orbit decreases in mass, while the twins’ orbiting radius stays the same. Under these circumstances, twin B’s orbiting velocity no longer follows Kepler’s laws, and so he experiences an acceleration like twin A. However, the ratio of the twins’ proper times still depends only on their velocities, not on their acceleration. Since the twins’ velocities stay the same, with twin B orbiting at a larger velocity than twin A (who is not moving at all), twin B is still younger.

In the examples so far, the faster twin is younger, regardless of any acceleration. However, if the mass of the large body decreased to zero, the situation becomes the original twin paradox: twin A is not accelerated, and twin B is accelerated. In this special case, twin B is still younger - but not because he is moving faster. As the scientists explain, when the mass of the large body is zero, the explanation for the paradox changes: time dilation here is due to twin B’s acceleration, not his velocity.

“The mass causes a non-zero curvature of the spacetime, and curvature gives the spacetime a structure that defines the absolute standard of rest,” the scientists explained. “In Minkowski spacetime there are no such structures, and there is no way to tell who of the twins in moving faster in an absolute way.”

More there. Enjoy.

[Ken G]

I'll give it a read, but I find something to object to even from the quote above-- asserting that the spacetime defines an absolute frame of rest is a bit misleading. The "absolute" frame of rest is simply relative to the source of the gravity, so is still a relative frame of rest. The "spacetime" is merely being used as a proxy for the presence of the object that is the source of the gravity.

[PraedSt]

What does "with respect to the sky" mean?

[Ken G]

I think they mean with respect to the prevailing state of the matter out in space. It sounds like a Machian perspective.

[publius]

I am somewhat surprised by that paper. There's nothing there that should surprise anyone. Schwarzschild, which the authors use, is a simple example. The clock rate of a clock orbiting in a circular orbit at some r is always slower than an observer stationary at that r. The orbiting clock is inertial while the stationary clock is accelerated against it's geodesic. And we can add a third clock, one that we throw up with just enough velocity so it goes up, stops, and falls back down at the same point the orbiting clock returns. That third clock is inertial itself, and will tick faster than the stationary clock.

So there we have one inertial clock ages the most, followed by the stationary clock, followed by the orbiting clock. Inertial1 > accelerated > inertial2.

There is nothing there other the differing path lengths in a curved space-time. The problem is getting hung up on some very specific explanation of the twin paradox such as "acceleration causes the difference". Now, in flat space-time, one twin must always accelerate to get back to the other. In curved space-times, that does not hold. Inertial twins can follow different paths between events as well as accelerated ones.

What matters is the path length, the integral of ds^2.

And second I do not like that "standard of absolute rest" business. There is no such thing in Relativity. He mentions something about the Killing fields in Schwarzschild. All I can figure is yes, that can define a certain family stationary relative to the source mass, which is sort of trivial anyway. There's nothing special about it.

-Richard

[PraedSt]

I am somewhat surprised by that paper. There's nothing there that should surprise anyone.

You mean that this is essentially a straw man paper?

[Ken G]

Perhaps "tempest in a teacup" is a better descriptor than "straw man". A cynic might conclude it was done because of how easily it can be blown out of proportion by pop sci media. But I'll give them the benefit of the doubt that they think it really does inform us about the twin paradox in SR, unifying it with some larger class of phenomena in GR. It just sounds like publius is saying that this unification follows in a more or less obvious way from how SR gets extended to GR.

[PraedSt]

Perhaps "tempest in a teacup" is a better descriptor than "straw man". A cynic might conclude it was done because of how easily it can be blown out of proportion by pop sci media. But I'll give them the benefit of the doubt that they think it really does inform us about the twin paradox in SR, unifying it with some larger class of phenomena in GR. It just sounds like publius is saying that this unification follows in a more or less obvious way from how SR gets extended to GR.

Gaah. Sorry about that guys. Looks like I got pop-scied a bit. I'll be more careful next time. And maybe use a PM rather than a thread...

[Ken G]

Please don't conclude that, if publius is right, it still benefits us all to see why he is right. And there might also be some who feel the article does offer some useful insights. publius is just giving us his take on the subject, he is not saying the article offers no value to hold up and look at.

[PraedSt]

Ok, that's good to hear. Thanks. It does help me I have to say, starting out as I am.

[publius]

Yes, tempest in a teacup, not "straw man". I just get the sense they're making a big deal out of something that's not really a big deal.


-Richard