3 ms·

There is a problem with your analysis. Switch viewpoints to the reference frame of the traveling twin. In that case, that twin stays in a constant position and

There is a problem with your analysis. Switch viewpoints to the reference frame of the traveling twin. In that case, that twin stays in a constant position and the other twin travels with a trajectory of x(t) = -0.9 c sin(kt) / k. The negative sign is irrelevant as we are only interested in absolute velocity and the negative sign implies that the movement is in the opposite directions. Then by your calculations, the other twin should now experience 0.74... seconds. Ie. Without accounting for the acceleration that one of the twins experiences, you can always switch frames and therefore cannot draw any conclusive results for both twins simultaneously unless you fix the reference frame (but in that case, differential aging really makes very little sense). As to calculation the actual difference in age, I don't know GR sufficiently well to be able to calculate the aging of the twins but I know some people who do. I have contacted them and will get back to you once they send me an answer.

cool-RR 18y ago
Hello Newt, Thanks for answering and for forwarding this to people who know GR, this might really help me. Regarding your first paragraph: I didn't give you my analysis, I only gave you a final answer, so how can you say there's a problem with my analysis? It's more like, there's a problem with your guess of what my analysis was. I phrased the original question accurately and gave a final answer. The contradiction you're talking about does happen if you try to switch reference frames without taking note of the acceleration. I didn't try to switch reference frames.
- newt0311 18y ago
  That is the problem. One of the central tenants of relativity is that what reference frames we choose is irrelevant as long as we account for all the relativistic effects. In you analysis, whatever that may be, you have two twins which separate, move around, and then return to the same reference frame and your result is apparently dependent on which twin's reference frame you are using. That is a contradiction. Thus the need to account for the acceleration that one of the twins experiences w.r.t. the rest of the universe.
  - cool-RR 18y ago
    We are having quite a funny argument, because it seems we both see the problem. "One of the central tenants of relativity is that what reference frames we choose is irrelevant as long as we account for all the relativistic effects." I think that applies only to inertial frames. At least in my version of SR that is so. "your result is apparently dependent on which twin's reference frame you are using. That is a contradiction." I know it is dependent. I don't see what's the contradiction. The earth twin has a special status - he is non-accelerating. His reference frame is therefore inertial. The other twin is accelerating. His reference frame is non-inertial. Where is the problem here?

cool-RR 18y ago

Hello Newt, Thanks for answering and for forwarding this to people who know GR, this might really help me. Regarding your first paragraph: I didn't give you my analysis, I only gave you a final answer, so how can you say there's a problem with my analysis? It's more like, there's a problem with your guess of what my analysis was. I phrased the original question accurately and gave a final answer. The contradiction you're talking about does happen if you try to switch reference frames without taking note of the acceleration. I didn't try to switch reference frames.

newt0311 18y ago
That is the problem. One of the central tenants of relativity is that what reference frames we choose is irrelevant as long as we account for all the relativistic effects. In you analysis, whatever that may be, you have two twins which separate, move around, and then return to the same reference frame and your result is apparently dependent on which twin's reference frame you are using. That is a contradiction. Thus the need to account for the acceleration that one of the twins experiences w.r.t. the rest of the universe.
- cool-RR 18y ago
  We are having quite a funny argument, because it seems we both see the problem. "One of the central tenants of relativity is that what reference frames we choose is irrelevant as long as we account for all the relativistic effects." I think that applies only to inertial frames. At least in my version of SR that is so. "your result is apparently dependent on which twin's reference frame you are using. That is a contradiction." I know it is dependent. I don't see what's the contradiction. The earth twin has a special status - he is non-accelerating. His reference frame is therefore inertial. The other twin is accelerating. His reference frame is non-inertial. Where is the problem here?