# Was Einstein lucky when not considering twin paradox as paradox?

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1. Nov 5, 2014

### adoion

hi,

Einstein did not even consider the twin paradox as problematic at all, he argued that it is a simple consequence of his special relativity?

obviously he never gave a explanation of why the two twins don't age the same he instead left it to others to do so.

was Einstein just having a hunch witch turned out to be just a lucky guess?

2. Nov 5, 2014

### Staff: Mentor

The twin paradox was properly understood by Einstein and other physicists from the beginning; no one who understands relativity has ever thought that it is problematic. It only started being called a "paradox" later, when we realized that it could be used as a teaching tool like the other "paradoxes" of relativity, such as the classic pole-barn and bug-rivet problems (google will find both of these online).

There is an interesting and important problem associated with the twin paradox (and these other "paradoxes") but it's not a problem of understanding. It's how to explain them to someone who is still learning special relativity, and teachers have been working on that one for a century now.

Last edited: Nov 5, 2014
3. Nov 5, 2014

### adoion

All right so how did Einstein understand the twin paradox, did he consider the acceleration of the traveling twin witch goes out of the scope of special relativity or did he argue that the traveling twin uses 2 inertial frames of reference?

4. Nov 5, 2014

### ghwellsjr

Of course not. He described in his 1905 paper the result and calculated the difference in "aging" between two clocks starting out together but one remaining inertial while the other one takes a trip and circles back to the inertial clock. You can read about it here at the end of section 4:

http://www.fourmilab.ch/etexts/einstein/specrel/www/

5. Nov 5, 2014

### Staff: Mentor

There's a widespread misconception that you need general relativity in situations involving acceleration, but it's just not true; special relativity handles acceleration just fine. You can google for "Rindler coordinates" for one example, and you'll find another example (a clock experiencing uniform circular motion due to the earth's rotation) in Einstein's original 1905 paper to which ghwellsjr gave you a link above.

This misconception propagates because very few first-year courses and textbooks cover this material. The math is appreciably more complex and introduces no new physical insights, so the examples and problems in these courses and books generally don't include acceleration.

6. Nov 5, 2014

### adoion

as far as I can tell there is no explanation of the twin paradox just a similar statement in his paper, a statement without deeper inside in why this has to be or a consideration of what would happened if we assume the earth is moving and the rocket twin is still. as I said just a statement confusingly written for modern standards I guess.
and if he was so precise about this statement then why was there a need anyway to clarify this "PARADOX". if it was just stated for educational purposes and a couple of different explanations where given??

7. Nov 5, 2014

### Staff: Mentor

One of meanings of the English word "paradox" is "something that appears at first glance to be contradictory, but with deeper understanding is not". We're using this definition when we speak of the "paradoxes" of special relativity, and we use a student's ability to properly explain them as a measure of the student's understanding of SR.

8. Nov 5, 2014

### phinds

Einstein certainly understood, as would a physics 101 student, that relative to the Earth, the stay at home twin was not accelerating whereas the traveling twin was and thus they are not symmetrical. He probably didn't feel that that needed to be pointed out.

9. Nov 5, 2014

### stevendaryl

Staff Emeritus
Einstein starts off, in his derivation of the Lorentz transforms, with:

Let us take a system of co-ordinates in which the equations of Newtonian mechanics hold good...​

This line is not explained in any more detail, but the way I interpret it is that it means an inertial system of coordinates. In a noninertial coordinate system, the laws of Newtonian mechanics don't hold good--that is, objects can accelerate relative to a noninertial coordinate system without any physical force being applied.

So from the very beginning, Einstein was talking about a special set of coordinate systems. In the case of a rocket taking off from the Earth, turning around, and returning, there is no inertial coordinate system in which the rocket is at rest at all times.

10. Nov 5, 2014

### PeroK

Special Relativity is not, solely, the Twin Paradox! The point of the 1905 paper was not to explain this one aspect of SR, but (with beautiful insight and simplicity) to prove that (given the postulates which are clearly stated) time and distance are not universal for all observers, and to provide quantitative predictions for the experimentalists to verify.

If you are saying: "Einstein didn't explain the twin paradox very well". Well, maybe so, but that was not what he was trying to do.

By limiting your interest to this one "paradox", you are missing the whole essence of SR. Why not read the paper and try to understand what it is saying?

11. Nov 8, 2014

### ghwellsjr

It's not an issue of one clock moving and the other clock not moving, it's that one clock is inertial and the other clock is not inertial.

In his 1905 paper, Einstein only considered Inertial Reference Frames (IRF's) and he described the "twin paradox" using the IRF in which the inertial clock was stationary. You only ever need one IRF to define a scenario. It doesn't matter whether the clocks are stationary, moving inertially at a constant velocity in any direction, or changing speeds and/or directions (accelerating), one IRF is all you need. But if you want, you can transform the coordinates of all the significant events according to the defining IRF to another IRF that is moving with respect to the defining IRF and this will make the stationary clock move at some constant speed but it is still inertial and it will make the other clock move at different speeds, even being stationary during some part of the scenario, but it is still non-inertial.

So when you define a scenario according to one IRF where the first twin remains inertial on the earth and the other twin travels away from the earth at a constant speed and direction and then turns around and travels back at that same constant speed but in the opposite direction, there are two more different IRF's in which the traveling twin is at rest during each half of the trip and the earth twin is moving inertially but you must consider the entire scenario from each of these two IRF's. The Time Dilations of the twins will be different in each of these three IRF's but they will all explain the difference in aging between the twins identically.

Perhaps a concrete example will help. Let's consider a typical Twin Paradox. I'm going to depict the earth twin in blue and the traveling twin in red. The traveling twin departs earth at a speed of 0.6c and after 8 years according to his clock, he turns around and spends another 8 years coming back at the same speed. When he reunites with the earth twin, they find that the earth twin has aged 25 years while the traveling twin has aged 16 years. The dots on this diagram mark off one-year increments of time for both twins:

Please note that in this IRF, it is only the traveling twin whose clock is Time Dilated by a factor of 1.25 during the entire scenario. This is because his speed is 0.6c during the entire scenario according to this IRF. Also note that the earth twin is inertial during the entire scenario while the traveling twin is not inertial during the entire trip.

For the next two IRF's and their diagrams, I'm going to refer to the earth twin as the inertial blue twin and the traveling twin as the non-inertial red twin.

First we're going to transform to the IRF in which the non-inertial red twin is at rest during the first part of the scenario. The diagram looks like this:

Note how the inertial blue twin is moving at -0.6c during the entire scenario and so his clock is Time Dilated by 1.25 the entire time. During the first part of the scenario, the non-inertial red twin's clock is not Time Dilated because he is not moving. But at his time of 8 years, he starts moving at -0.882c where his Time Dilation is now 2.125 and after 8 more years he catches up to the inertial blue twin who has aged 25 years by the time they reunite.

Finally we're going to transform to the IRF in which the non-inertial red twin is at rest during the last part of the scenario:

This is similar to the previous IRF so we can use the same numbers but in different orders but the net result is that the twins age by the same amounts.

I hope this is clear and removes all your confusion. If not, ask.

12. Nov 8, 2014

### Fantasist

It seems to me that the OP read and understood Einstein's paper very well. What he is asking is, whether there is any information why Einstein did not check the consistency of his time dilation calculation by changing the rest frame to the other observer/clock. Was it deliberate or an oversight?

13. Nov 8, 2014

### stevendaryl

Staff Emeritus
Checking your work isn't usually part of the final paper.

14. Nov 8, 2014

### adoion

the thing is that you can use all 3 of those diagrams interchangeably on both the earth twin and the traveling twin.

1. inertial frame is fixed at the earth twin and it is determined what time he calculates has passed .
in this case the traveling twins time goes slower as he goes away from the earth twin, but also as he returns to the earth , at the same amount.
the traveling twin uses 2 IRF, in this case.

2. IRF is fixed to the traveling twin. the earth is moving away from the traveling twin who is at rest. the traveling twin will measure that the earth twins time goes slower by the same factor as the earth twin measured before for the traveling twin.
in this case the earth twin uses 2 IRF, if he would believe that the earth is moving, one on the trip away and one for the trip back.

3. the last possibility is that both agree to use a IRF in witch the earth twin moves at a speed $v_1$ and the traveling twin with a speed $v_2$ and in this case just like in the first case the traveling twin changes speed and the traveling twin is the one who would use 2 IRF.

so the first 2 cases are absolutely symmetric and they would both measure that the other twin is younger at the end so both would have to be older and younger at the same time when they meet.
only with the presence of a third observer (case 3.) is the asymmetry obvious and that is only if the third observer doesn't travel at the same speed (direction and velocity) as the traveling twin.

even if we take acceleration into account, the acceleration can be attributed to the earth as well as to the traveling twin, so symmetry again.

so again if somebody thinks he can correct me please do so id really like to know?

15. Nov 8, 2014

### Staff: Mentor

This frame is not inertial. The I in IRF stands for Inertial, so this is not a valid IRF.

In any IRF (remember I stands for Inertial), if you do the calculation you will get that the "travelling" twin is younger on reunion. That is the point of ghwellsjr's exercise above.

No, only the first case is even self consistent. The second case is not self consistent since it uses the time dilation formula for an IRF for a reference frame which is not inertial. This is a self-contradiction which invalidates the second case, regardless of any other case.

Last edited: Nov 8, 2014
16. Nov 8, 2014

### adoion

if you have only 2 point particles an nothing else, how do you determent witch one is accelerating?
so what is your opinion, what would be the IRF ( I stands for inertial) in this case??

17. Nov 8, 2014

### Staff: Mentor

Two point particles with nothing else is inconsistent with the twins paradox scenario.

18. Nov 8, 2014

### adoion

hows that?

19. Nov 8, 2014

### stevendaryl

Staff Emeritus
An object travels inertially if it is not acted on by any external force. We have a pretty good idea of what forces are relevant in space: Collision forces (which are ultimately electromagnetic in nature, for ordinary macroscopic objects), electromagnetic forces, gravity. That's basically it. If those forces are approximately zero, then the object is moving approximately inertially.

20. Nov 8, 2014

### Staff: Mentor

As stevendaryl mentioned if you have two point particles and nothing else then they will travel inertially only. If one were to turn around without anything else then the conservation of momentum would be violated.

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