Time Shift Reference Point: Earth or Other?

[akmtnrunner]

I have been thinking about the classic example of two twins traveling at different speeds and the effect of time passage. One twin that goes off to travel near the speed of light while the other twin is left on earth. We theorize that the traveling twin will pass through less time and be younger than the earth-bound twin when they are back together. The issue that I am having trouble with, is why the stationary reference point is necessarily assigned to the twin on the earth. To the traveling twin, everything else could be traveling near the speed of light so why isn't the time effect opposite? It's not like the Earth or any other point has a special right to be the stationary reference point, yet the effect of time says so?

 

[PeroK]

There are several ways to explain the twin paradox, which is what you are asking about. And, indeed, there are dozens of such posts on this site.

The simple answer is that the twin who remains on the Earth, moves inertially (or approximately inertially) throughout the experiment. Whereas, the traveling twin must move non-inertially at some stage. It's not motion that is the issue but not moving inertially.

 

[Ibix]

One twin accelerates to turn around and come back. That's the younger one (and this isn't theoretical - the experiment has been done - google Hafele-Keating experiment).

In fact it turns out that elapsed time is a measure of something called interval, which is the 4d analog of distance. Because the two twins followed different paths with different intervals ("lengths") through spacetime they end up with different ages. Because interval and distance aren't perfectly analogous, the one who followed the straight line path experiences more time than the one who followed the non-straight path.

 

[PeterDonis]

the experiment has been done - google Hafele-Keating experiment

This is not a good experiment for illustrating the SR twin paradox by itself, because GR effects due to the Earth's gravitational potential were significant. Also, all three of the "twins" in this experiment (the ground clock and the two clocks that were flown around the world in opposite directions) had nonzero proper acceleration.

One could try to disentangle the "SR" part of the effects from all this, but I'm not sure it's worth it.

 

[PeterDonis]

why the stationary reference point is necessarily assigned to the twin on the earth.

In the usual scenario, as has been pointed out, the "Earth" twin (actually better thought of as floating in space in the Earth's vicinity, with Earth idealized as a non-gravitating body so gravity is not included in the scenario), moves inertially--in free fall--for the entire experiment. The other twin does not; at the very least, they have to fire rockets to turn around and are not in free fall during that portion of their trip. So the situation between the twins is not symmetric, and since in SR inertial frames have a preferred status, the twin who is at rest in a single inertial frame the whole time--the Earth twin--is the one who serves as the stationary reference point.

One can try to analyze the experiment in the "frame" of the traveling twin, but this frame will not be inertial, which complicates the analysis. You will still end up getting the same answer, but it's more difficult to get it (and raises issues that are not raised if you do the analysis in the inertial frame in which the Earth twin is always at rest).

The Usenet Physics FAQ article on the twin paradox is worth reading:

https://math.ucr.edu/home/baez/physics/Relativity/SR/TwinParadox/twin_paradox.html

 

[Vanadium 50]

One could try to disentangle the "SR" part of the effects from all this, but I'm not sure it's worth it.

One did. Well, two did. Hafele and Keating. The SR and GR effects are comparable: (W vs. E is 2x up vs. down) It's in the paper.

 

[PeterDonis]

One did. Well, two did. Hafele and Keating. The SR and GR effects are comparable: (W vs. E is 2x up vs. down) It's in the paper.

That's assuming that one can call the effect of speed relative to Earth, of objects all of which have nonzero proper acceleration, an "SR" effect. I'm not saying it's impossible to do an analysis of this kind, where "speed relative to Earth" (more precisely, relative to the center of the Earth) is a useful parameter; as you point out, Hafele and Keating make such an analysis in their paper. My point is just that, since none of the "rest frames" involved are inertial, one does not even have the option of the simple analysis in the stay at home twin's rest frame that can be used for the standard twin paradox in flat spacetime. So it doesn't seem to me to be a good starting point for learning.

 

[Vanadium 50]

I don't see this as fundamentally different than frictionless planes and stretchless ropes. Pulling the signal you want out of the myriad other effects. Heck, the classic "pure" test of GR, the precession of mercury's perihelion, is only an 8% effect.