6 ms·

The twin paradox cannot be handled by SR. The difference in aging comes about due to time dialation caused by the differential acceleration that the twins exper

The twin paradox cannot be handled by SR. The difference in aging comes about due to time dialation caused by the differential acceleration that the twins experience (the twin in the spaceship is accelerated and the other is not). SR can be used to judge the middl period after the acceleration but it will not give any useful information because you can always switch viewpoints. If you have two bodies moving at some relative velocities, both can claim that the other is moving slowly in time. The mathematics of communication and speed of light work out so that this system is consistent. The difference in measured time comes from the acceleration that one of the bodies must undergo to enter the same time frame as the other. Secondly, electric fields have intrinsic effects as in EM radiation (colloquially known as light) and need not apply any force to have effects. The movement of emitters of electrical fields through space and acceleration thereof actually give rise to magnetic fields. Read Berkley Phys. Vol. 2 ch. 5 which shows how this happens in the framework of SR. It later hints how tensors can be used to generalize this result to GR. So... in response to your question, if force is applied, either it must be approximated in a Newtonian or SR context, or GR must be used in its full generality. Usually, the forces and particles involved are sufficiently small that approximations work (see success of Newtonian mechanics), but that is not the general case. Also, very common is the tendency to derive general results and then use them is special cases. Maxwell's equations are an excellent example. They refer only to EM fields and are exact (uptil QM of course).

cool-RR 18y ago
Okay Newt, now we have something we can compare! Because I claim that SR can handle such a case. I propose that I will give the answer as I calculate it from my version of SR, and you can give it from GR or whatever you think is necessary. Does that seem like a worthwhile comparison to you? Let's say that our travelling twin takes a trip of one second (not one year, to make the calculation easier). Let's say he goes in the following trajectory: x(t)=0.9 c sin (k t) /k Where k equals (pi/second). How older will the twin be after the journey? I got the result of 0.7459255 seconds. What is yours?
- cool-RR 18y ago
  Are you working on it?
- newt0311 18y ago
  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

Okay Newt, now we have something we can compare! Because I claim that SR can handle such a case. I propose that I will give the answer as I calculate it from my version of SR, and you can give it from GR or whatever you think is necessary. Does that seem like a worthwhile comparison to you? Let's say that our travelling twin takes a trip of one second (not one year, to make the calculation easier). Let's say he goes in the following trajectory: x(t)=0.9 c sin (k t) /k Where k equals (pi/second). How older will the twin be after the journey? I got the result of 0.7459255 seconds. What is yours?

cool-RR 18y ago
Are you working on it?
newt0311 18y ago
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.