

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer


share|cite|improve this question
Just today I was looking for a Twin paradox explanation and here it is. Wikipedia article has some nice pictures that help to understand how clocks are ticking on Earth and on the space ship. ( – gigacyan Jan 6 '11 at 19:05
I concede defeat :). It is clear from the context. – Joshua May 28 '14 at 16:36
up vote 29 down vote accepted




Let's see how this works on this simple doodle I put together

alt text







share|cite|improve this answer





share|cite|improve this answer
Found a free copy of the paper here: – vonjd Jan 7 '11 at 17:34



share|cite|improve this answer


share|cite|improve this answer
Special relativity can indeed describe accelerated movement.… – Mark Eichenlaub Jan 6 '11 at 13:54
@Marek Well, almost everything I have every read says you can do acceleration in SR, and also I have done calculation with acceleration in SR. See a blog post I wrote on it, for example, or look at the many explanations from google that I linked.… – Mark Eichenlaub Jan 6 '11 at 19:16
@Marek: Path lengths are perfectly well defined in SR, all you need is vector calculus and the minkowski signature. You don't need any of the machinery of General Relativity to do that. It's true that special relativists don't often do any of this, but you can certainly treat the problem. The whole second half of Jackson is basically a treatment of the acceleration of objects in special relativity. – Jerry Schirmer Mar 5 '11 at 0:29
For the sort of acceleration needed to reverse the direction of a twin (i.e. small value constant), it's easy to do the calculation in pure SR. I did it as a homework assignment years ago, I recall. In fact, I'd be willing to bet that the twin paradox predates the invention of GR. I'd +1 the answer except for the statement that this requires GR. No, the effect is entirely present for twins moving in flat Minkowski space and that is entirely governed by SR. – Carl Brannen Mar 5 '11 at 0:50

The question is: what do you mean by "classical"? To me the Classical Twin Paradox is what Einstein called the Clock Paradox, i.e. the version without any accelerations. And this paradox has never been resolved.

If there are no accelerations involved in the situation, than the whole paradox results only from the simple equation for time dilatation:


As we can see, there is just constant $v$ there, and yet one of the clocks must be time-dilated.

If someone says that space-travel requires acceleration of a spaceship, they are absolutely right. The thing is that any time-dilatation due to acceleration is only on top of dilatation due to constant $v$.

We can imagine simply that both twins go on a space trip in different spaceships and travel in opposite directions. In such case we can easily assume that they both undergo exactly the same accelerations which effectively "cancel" each other out. And yet we still have the paradox resulting from time dilatation between inertial frames. The above equation still holds. Therefore, we need to answer the question: Which of the twins is younger and why?

As you can see, introducing accelerations only masks the real paradox, and not solves it. And perhaps that's why nobody solves the paradox with real numbers. Because if you make actual calculations, you will immediately see that you need to add time-dilatation due to acceleration to time-dilatation due to constant $v$. Which leaves the other one still unresolved.

In order to illustrate the classical paradox best, we can formulate it in two ways:

1) If one of the twins actually becomes older due to difference in constant $v$, than the axiom of Special Relativity that there are no preferred (inertial) reference frames is falsified. Because this means the reference frame with slower clock is moving with respect to the other in absolute terms. Therefore movement is absolute.

Someone can reply to this that I don't understand SR which allows us to revert the whole situation, i.e. switch the moving and the stationary frames. Sure, but then we have paradox 2):

2) If we claim that clock A is slower than clock B, and also that clock B is slower than clock A, than Special Relativity cannot be proved to be true. For in such case both clocks are late with respect to each other, which boils down to no real time-dilatation at all. If there is a difference measured, however, then we are back to paradox 1), i.e. one of the frames is clearly preferred, and therefore we proved absolute movement exists.

To sum up. There is no solution to the classical (strictly inertial) Twin Paradox. And also, any accelerations do not solve the paradox either - they only mask it.

EDIT: Professor Chad Orzel in his answer gave this paper as a source claiming that dilatation in SR (without accelerations) can be proved. That's simply astonishing, as anybody can see that this paper is based on a trick whereby the parents of the traveling twins stay on Earth and see there is some distance between them equal $γx_0$. However: 1) length calculations in SR are made from the two reference frames, and not from a 3rd one, 2) if twins travel in opposite directions (as in my thought experiment above) you can always claim the other twin is younger, and - most importantly - 3) this paper shows dilatation based on velocity $v$, and yet there is no velocity difference between the twins - they travel in two rockets in the same direction, having been accelerated in exactly the same way. The velocity $v$ is measured from their parents frame, i.e. Earth, and the author even admits that saying that effective velocity between the twins is null. Now how come a paper claiming SR time dilatation between reference frames stationary wrt. each other (and not accelerated) has been accepted for publication?!?! And how come it has been presented here as source by a professor?!

(And if vonjd didn't find this free paper, we might think that some smart guy proved the unprovable. And if I paid for it, I would be simply coned.)

NOTiCE: Any comments concerning this line of reasoning are more than welcome.

share|cite|improve this answer

protected by Qmechanic Apr 20 '13 at 16:21


Would you like to answer one of these unanswered questions instead?
