# Einstein's resolution of the clock paradox

1. Jul 20, 2008

### Al68

Einstein's resolution of the "clock paradox"

I have read that most physicists believe that Einstein's resolution of the "clock paradox" or "twins paradox" is flawed and just plain wrong. I'm curious about what everyone here thinks about it.

And I believe Einstein generally was interested in the more profound aspect of the "paradox", ie why inertial frames must be treated "special", from his writings, not the trivial exercise found here and elsewhere just showing how to do the math in SR from the inertial frame's point of view.

Another example of a related idea might be the spinning globes. For those unfamiliar, Einstein referred to two adjacent liquid globes in deep space each one spinning relative to the other about a common axis, and only one of them had a bulging equator, so we conclude that it's the one "really" spinning while the other is stationary. But, he asks, it's spinning relative to what? He finally concluded that since each globe was spinning relative to the other, the cause of the one's bulging equator must lie outside the system containing the globes, since nothing locally could explain why one equator bulged but not the other.

Any thoughts?

Thanks,
Al

2. Jul 20, 2008

### Staff: Mentor

Re: Einstein's resolution of the "clock paradox"

Which method of resolving the clock paradox is "Einstein's"? I don't remember.

3. Jul 20, 2008

### George Jones

Staff Emeritus
Re: Einstein's resolution of the "clock paradox"

From the Physics Forum Posting Guidelines:

You might feel that that these questions were not discussed adequately in that thread, so, for now, I will allow this thread to continue, but
you need to give specific references. You need to back up the claim
with more than anecdotal evidence. If you cannot do so, the thread will be locked.

Discussing endlessly the twin parardox and Mach's principle is not the purpose of the relativity forum.

Last edited: Jul 20, 2008
4. Jul 20, 2008

### Al68

Re: Einstein's resolution of the "clock paradox"

The one using GR to analyze the scenario from the point of view of the ship's observer.

5. Jul 20, 2008

### Mentz114

Re: Einstein's resolution of the "clock paradox"

Al68,
I don't believe Einstein thought anything of the kind. References please.

Acceleration and rotation are absolute in the sense that they can always be detected and measured in the local frame. There is no mysyery/paradox or puzzle involved.
You do not need to define rotation 'relative' to something.

Also, note that rotation cannot be defined except for an extended object, in which case there's no problem in defining mass-centred frames.

6. Jul 20, 2008

### Al68

Re: Einstein's resolution of the "clock paradox"

Einstein, A. (1918) "Dialog über Einwände gegen die Relativitätstheorie", Die Naturwissenschaften 48, pp697-702, 29 November 1918 (English translation: dialog about objections against the theory of relativity). I thought that a new thread was appropriate, and would maybe help prevent "endlessly discussing" the same aspects of the twins paradox that are discussed endlessly all over the net.
Well, I'm only claiming that I've read this, on an older version of the Wikipedia entry http://en.wikipedia.org/w/index.php...5960#Einstein.27s_general_relativity_solution, among other places. I'm not claiming anything else. I was asking what others thought of this resolution.
It's not endless. We all die eventually.

Thanks,
Al

7. Jul 20, 2008

### Al68

Re: Einstein's resolution of the "clock paradox"

Einstein, A. (1916) "The Foundation of the General Theory of Relativity".

Referring to the globes S1 and S2: The only satisfactory answer must be that the physical system consisting of S1 and S2 reveals within itself no imaginable cause to which the differing behaviour of S1 and S2 can be referred. The cause must therefore lie outside this system. We have to take it that the general laws of motion, which in particular determine the shapes of S1 and S2 , must be such that the mechanical behaviour of S1 and S2 is partly conditioned in quite essential respects, by distant masses which we have not included in the system under consideration. These distant masses and their motions relative to S1 and S2 must then be regarded as the seat of the causes (which must be susceptible to observation) of the different behaviour of our two bodies S1 and S2.

Well, I won't argue with that. Please see above.

Thanks,
Al

8. Jul 20, 2008

### matheinste

Re: Einstein's resolution of the "clock paradox"

Hello Al68

The following is an extract from your, partial, paraphrased extract of the quoted source:-

""But, he asks, it's spinning relative to what? He finally concluded that since each globe was spinning relative to the other, the cause of the one's bulging equator must lie outside the system containing the globes, since nothing locally could explain why one equator bulged but not the other."""

Just to clear up some ambiguity do you think he is saying that one will bulge and not the other. Or is he is presenting a scenario in which one bulges and not the other and then asking with regards to this scenario, to what can we attribute this bulge.

Matheinste.

9. Jul 20, 2008

### Al68

Re: Einstein's resolution of the "clock paradox"

Is it safe to assume that Einstein's published writings are fair game, even if some of them are not part of "current professional mainstream scientific discussion"?

Some of Einstein's writings are not currently discussed much, some even discounted or ignored, which is why I ask about them. I thought this was the appropriate forum for that purpose.

I now realize that I need to include references for my sources instead of just assuming familiarity with them. I apologize for omitting them earlier.

Thanks
Al

10. Jul 20, 2008

### Al68

Re: Einstein's resolution of the "clock paradox"

The latter. Sorry if that wasn't clear.

Thanks, Al

11. Jul 20, 2008

### matheinste

Re: Einstein's resolution of the "clock paradox"

Hello Al68.

Thanks, it is the wording in the original ( translation ) that was not clear to me although it should have been obvious what was meant.

Matheinste.

12. Jul 20, 2008

### Mentz114

Re: Einstein's resolution of the "clock paradox"

Al,
thanks for the reference etc. I think the great man was just plain wrong, or I don't understand the scenario.

The reason one body has a bulging equator is that it has sufficient intrinsic spin ( rotation about an axis through the body) to deform itself. Intrinsic spin can be defined without relation to outside influences, so I don't follow why E says "... the cause of the one's bulging equator must lie outside the system containing the globes, since nothing locally could explain why one equator bulged but not the other."

M

13. Jul 20, 2008

### Fredrik

Staff Emeritus
Re: Einstein's resolution of the "clock paradox"

These things seem obvious to us because we've already made up our minds about what sort of mathematical structure to use as a model of space and time, and what identifications we have to make between things in the mathematical model and things in the real world in order to turn the mathematical model into a testable theory of physics. (An example of the latter is that the quantity that's measured by a clock in the real world is the integral of $\sqrt{-g_{\mu\nu}dx^\mu dx^\nu}$ along the curve in the spacetime manifold that represents the clock's path through real-world space and real-world time). What you're saying is true in the mathematical model you have in mind, but Einstein was probably still trying to figure out what sort of theory he should be looking for. So maybe his statements make a lot more sense than they seem to, but it's hard to tell without knowing more about the context.

14. Jul 20, 2008

### Mentz114

Re: Einstein's resolution of the "clock paradox"

Hi Frederik,
well, acceleration in rotating frames is a fact of life and not model dependent.
I think Einstein was talking about the origin of inertia at some point. The rotating body would not bulge if its parts did not have inertia. Anyhow, as you say, without reading the work in question one cannot be sure.

The OP says he wants to find out why Einstein thought inertial frames are a special class - I can tell him that the reason is that they are connected by the Lorentz transformations, and proper intervals are preserved by the LT. This is what the word 'special' in special relativity means.

M

15. Jul 22, 2008

### Al68

Re: Einstein's resolution of the "clock paradox"

I seems obvious to me that E was pointing out that no local measurement could explain the cause of the bulging equator(along with other results of rotation) of one globe but not the other. Of course we can use the equatorial bulge(along with other results of rotation) to say which globe is rotating, but that would just be circular logic.

Thanks,
Al

16. Jul 22, 2008

### Al68

Re: Einstein's resolution of the "clock paradox"

You can read more here: http://hem.bredband.net/b153434/Works/Einstein.htm.

Warning, Einstein obviously had no problem defining and using accelerated reference frames. Of course he had to consider them differently in SR, which he considered a shortcoming of SR.

Thanks,
Al

17. Jul 22, 2008

### Al68

Re: Einstein's resolution of the "clock paradox"

You must have misunderstood me, I don't see this in any of my posts. I did mention that Einstein questioned why they should be considered privileged in his writings, and concluded that they are not (in GR). [References provided in earlier post].

Thanks,
Al

18. Jul 23, 2008

### Al68

Re: Einstein's resolution of the "clock paradox"

Well, we frequently refer to a ball thrown up in the air as "accelerating" toward earth and turning around to return to earth, but that acceleration of the ball is only coordinate acceleration relative to the "stationary" observer at earth's surface. A tiny observer attached to the ball would justifiably consider the ball at rest wrt an inertial frame, this tiny observer would feel no acceleration, could say that the earth's surface "really" accelerated to turn around wrt his frame, and also point out that the large observer at earth's surface "felt" the (proper) acceleration. And the tiny observer would be right, and the cause of the "turnaround" of the ball relative to earth is the same as the cause of the proper acceleration felt by the large observer on earth.

My point here is that an observer can be considered stationary although he "feels" the acceleration, and an object can be said to accelerate relative to this accelerated obserever, although that object was in inertial freefall and felt no acceleration.

Einstein's clock paradox resolution [http://en.wikisource.org/wiki/Dialog_about_objections_against_the_theory_of_relativity] basically considers the ship's twin "stationary", and the earth to "turnaround" (in the same sense that a ball thrown up in the air will turnaround relative to an "accelerated" observer at earth's surface), and uses the equivalence principle to claim that the ship's acceleration causes its clock to run slow compared to the earth clock, in the same way that (proper) acceleration due to gravity effects clocks.

Right or wrong, it actually attempts to resolve what Einstein considered to be an issue with the clock paradox. (Unlike the SR resolutions which only "resolve" a problem that never existed to begin with).

But my initial question was, what do others think of Einstein's resolution?

Thanks,
Al

19. Jul 23, 2008

### Fredrik

Staff Emeritus
Re: Einstein's resolution of the "clock paradox"

I'm too lazy to read all that, but it's definitely possible to define an accelerating point of view in this case, and there's nothing wrong with using it to prove that there's no paradox. It's kind of pointless though, since you can do it without considering accelerating frames.

20. Jul 24, 2008

### Al68

Re: Einstein's resolution of the "clock paradox"

Sure, if you only want to prove that there's no internal paradox in SR. Einstein apparently wanted a solution that resolved the problem he saw with it, which was that if we analyze the situation from the ship's twin's point of view (frame in which he is considered stationary), we should be able to get a consistent answer. And I believe that was the whole point of the "clock paradox" to begin with.

Obviously, the SR "resolutions" resolve that issue by saying it's not an issue in SR. I would agree it's not a problem or paradox in SR, but it's the whole point of the clock paradox.

Does nobody have an opinion on E's resolution? It almost seems like I'm the only person around who's even read it, which I know can't be true.