Relativity is not an easy concept. Special relativity is hard enough, and General relativity really ups the ante; I am not well-versed in anything beyond the basics of the latter, but one of the notions of GR is that freefall in a uniform gravitational field is actually an inertial frame, i.e. non-accelerating, which is not a concept present in Special Relativity.
Which appears to be the linchpin behind the argument presented here: In Twin Paradox Twist, the Accelerated Twin is Older
In 1905, Einstein described the ideas behind the twin paradox to demonstrate the effects of time dilation according to special relativity. In 1911, physicist Paul Langevin turned the concept into a concrete story involving two hypothetical twins. Ever since then, scientists have offered various explanations for exactly why this aging paradox occurs, and whether it is even a true paradox at all.
As Abramowicz and Bajtlik note in their study, it is often claimed that the twin paradox can be explained by the acceleration of the traveling twin that occurs when he turns around to go back to Earth. Abramowicz and Bajtlik show, however, that it is not the acceleration that causes the age difference in most cases. By presenting a scenario in which the accelerated twin is older at the reunion, the scientists show that the final time difference between the twins often depends only on their velocities as measured with respect to an absolute standard of rest, and not on acceleration.
First of all, a note that “absolute standard of rest” is not something that is part of the original twins paradox. Which is because in 1905, there was only Special Relativity. The scenario presented is of the twins near a large mass, and one of them in a Keplerian obit, and thus not accelerating according to General Relativity. The notion of absolute rest is in contrast to accelerations and rotations, which can be distinguished, while motion in special relativity cannot. The mixing of the two frameworks isn’t even an instance of the reporter mucking things up — it’s presented in the ArXiv paper that way.
It is often claim that the resolution of the classical
twin paradox should be the acceleration of the “travel-
ing” twin: he must accelerate in order to turn around and
meet his never accelerating brother. The twin who accel-
erates is younger at the reunion. Here we challenge this
notion. We start with describing a situation in which,
like in the classical version of the paradox, one of the
twins accelerates, and the other one does not accelerate.
Quite contrary to what happens in the classical version,
the accelerated twin is older at the reunion.
That’s because you have changed the parameters, and are no longer describing the classical twin paradox.
I have no complaint about the physics. I just don’t think the authors should feign surprise at the result, as if it were somehow unforeseen that changing conditions could yield a different answer. The answer should not be surprising at all, because what they describe is one twin being at rest, and the other in an orbit. Which is exactly what would be described by an observer on a non-rotating planet, and another on a satellite. Maybe a satellite which is part of a navigation platform, able to communicate with a receiver and quadrangulate position and local time, with the modification that the satellite isn’t orbiting at a different distance from the planet.
All of this is pointed out in “Relativity in the Global Positioning System” by Neil Ashby. In section 5 there’s a graph of the results of differing orbital distances, and below some threshold we see that the satellite will age more slowly than someone on the planet surface. I’m not sure how old it is, but the update posted in June 2007 says
I have updated the text in quite a few places, such as eliminating the word “recently” which is no longer really recently.
So the notion is definitely not new, nor should have been surprising.
Acceleration is irrelevant. The clock that travelled through the most space logs the least tme elapsed when reunited with the other clock.
[In the Newtonian approximation to GR, the line element for “Newtonian coordinates” is to excellent approximation:
ds^2 = -(1 – 2phi) dt^2 + dx^2 + dy^2 + dz^2
where phi is the Newtonian gravitational potential, c=1
The only deviation from Minkowski spacetime is in the time coordinate – using these coordinates the 3-space corresponding to a given value of t is Euclidean flat.]
Twin Paradox: One twin travels relativistically, one twin stays home. They reunite. The traveling twin aged much less. The twin who travels through more space accumulates less time; also true for an orbit. Interval sqrt(t^2 – x^2 – y^2 – z^2) between the two events, expressed in inertial coordinate system (t,x,y,z), is conserved. Given the invariant interval, the larger sqrt(x^2 + y^2 + z^2)is the smaller sqrt(t^2) must be.
The ratio by which the two aged when they are again local is identical in all reference frames: ratio = sqrt(t^2 – x^2 – y^2 – z^2)/t (units of c=1).
Demonstrated by Triplets: Three identical clocks as kits are not constructed until the experiment is running. Each clock has a short toggle switch. Individual spaceships carry a kit each. Set up the experiment.
CLOCK 1: Our clock sits stationary in our inertial reference frame with its toggle sticking out. Touch the toggle and “off” state goes “on” or “on” state goes “off.” Build it from parts just before needed, in the “off” state, zeroed.
CLOCK 2: In a spaceship traveling at 0.999c relative to our inertial frame and positioned far to our left. Clock 2 was built after all acceleration ceased during setup, set to zero, “off” state. It skims past Clock 1 (our clock) in vacuum free fall, toggles touch, both Clocks 1 and 2 are “on” and locally synchronized by touching. Elapsed time accumulates in each clock.
CLOCK 3: In a spaceship traveling at 0.999c relative to our inertial frame of reference, but 180 degrees counter in direction to Clock 2, far far to our right. It was built after all acceleration ceased during setup, set to zero, “off” state.
An arbitrary time after Clocks 1 and 2 synchronize and turn “on” by touching, Clocks 2 and 3 brush past each other, both in vacuum free fall, touching toggles. Clock 2 is now “off,” Clock 3 is now “on.” Write down the elapsed time in “off” Clock 2. The spaceship with Clock 3 returns over the path taken by the spaceship with Clock 2.
CLOCK 1: Our clock. It sits stationary in our inertial reference frame with a little toggle sticking out. Clock 3 vacuum free falls past, toggles touch. Clocks 3 and 1 are off. Write down elapsed times. No clock accelerated while “on” or while existing.
BOTTOM LINE: Send results by radio. Numbers on paper don’t change. Throughout the entire run three clocks were passive observers in vacuum free fall with zero acceleration.
Compare elapsed times. Elapsed times #2+#3 does not equal #1, the local stationary reference frame summation. The sum of #2+#3 elapsed time is about 4.5% that than of #1’s accumulated elapsed time. The Twin (Triplets) Paradox obtains without any clock having been accelerated.
You can do it with counter-orbits, too.
I’m fascinated by the phrase “…it is often claimed that the twin paradox can be explained by the acceleration of the traveling twin that occurs when he turns around to go back to Earth.”
Does this preclude the idea that under certain curved space-time you could travel in one direction and, without changing course, return to the place where you once started?
Curved spacetime is not part of the original twins paradox, but I think Einstein addresses this in one of his papers that led up to his formulation of GR.
“Abramowicz and Bajtlik show, however, that it is not the acceleration that causes the age difference in most cases. ”
It almost seems like they’re presenting a straw-man argument here. I’ve personally never said that acceleration causes the age difference, or even worse said that the acceleration causes the traveling twin to be older. I’ve always noted that acceleration breaks the symmetry of the problem — that illusory ‘symmetry’ in the twin’s circumstances is the origin of the original paradox, and it is broken because one twin accelerates, and not the other. I wouldn’t have necessarily expected to be able to concoct a situation in which the accelerating twin is older, but it isn’t necessarily shocking, either.