# Testing the twins problem with an accelerator

Re the twins paradox in relativity: has anyone performed an analysis of a pair of identical particles, inside a storage ring? Specifically, we posit that one is stationary - the 'home twin' - while the other circumnavigates the perimeter.

• Voting to reopen. A perfectly clear question with a straightforward "yes" answer - see answer below. Commented Jul 7 at 8:34
• Hi Rich D. Welcome to Phys.SE. Do you mean identical particles in the sense that they are quantum mechanically indistinguishable? Commented Jul 7 at 15:16

Yes. This was studied by Bailey et al. in "Measurements of relativistic time dilation for positive and negative muons in a circular orbit," Nature 268 (July 28, 1977) pg 301.

They used muons and measured the time dilation of highly relativistic muons in a storage ring compared to muons in the lab frame. This is an experimental test of both the twins paradox and the clock hypothesis.

• It has been studied by more than just a 1977 paper. Precision measurements of the properties of muons in accelerators may lead to new physics. It is the subject of large active research programs. Why the Muon g-2 Results Are So Exciting! Commented Jul 7 at 2:23
• Muons were a nice choice because they actually do confirm SR directly when in a storage ring at all. They decay in microseconds; if you can keep them around longer than a blink, then time dilation is confirmed. Commented Jul 8 at 20:43
• From the reference frame if the moving muons, did the stationary muons live longer? Commented Jul 9 at 20:36
• @foolishmuse if you can write down the coordinate transform from an inertial frame to the one you have in mind then I could evaluate that.
– Dale
Commented Jul 9 at 21:26
• Thanks. However, it occurs to me, in this case, the 'traveler' continually accelerates around the ring. Therefore, it must be analyzed using general relativity, via the spacetime metric. What about the common textbook case, where the traveler flies straight away, at constant speed, turns suddenly, then back? He's inertial 99% of the voyage. How to analyze that? Commented Jul 9 at 22:54

It has been performed even by/on humans. Check Hafele-Keating experiment from 1971 (https://en.wikipedia.org/wiki/Hafele%E2%80%93Keating_experiment), where they took a pair of atomic clocks: one on board of an airplane, the other left of ground. After some time spent flying, the two clocks developed a mutual lag, in full accordance with relativity.

• The Hafele Keating is pertinent. However, I don't see the asymmetry. One clock is 'stationary', while the 'moving' clock flew east. Reverse the references: designate the latter clock is stationary, while the former flies west. Relativity 101: all motion is relative. What distinguishes them? The 'moving clock' continually accelerates as it circles the earth, is that the answer? Commented Jul 9 at 22:46
• @RichD you've come across the main problem with SR; the thought that all motion is relative. As far as I can find, there is not one single example where the moving clock sees the stationary clock as running slower. And I can give you a ton of examples where this does not hold. And yet for some reason people continue to insist that all motion is relative and they do (as I say) mathematical backflips to make it work on paper. I've been asking about this on the stack exchange for some time and have yet to find a satisfactory answer. Commented Jul 10 at 16:47