# Is asymmetric time dilation in twin paradox possible in SR?

1. Oct 24, 2012

### arindamsinha

I am trying to understand if SR can explain a real, measurable velocity time dilation as seen in experiments/observations like GPS satellite or Bailey et. al.

Let us say we have twins sitting in their identical, individual spaceships in space, close to each other, and far away from any large masses. One of them fires his engine and goes some distance at high velocity, reverses, and comes back to the original location. Would he really have aged less than the stationary twin, and if so why?

I have seen the explanations based on the traveling twin not being in an inertial frame at all times, but do not find them conclusive. I mean, from SR perspective, when the traveling twin is accelerating, he may consider from his point of view that the stationary twin is in a non-inertial frame, while he is in an inertial one. Since there is no third party observer involved, each twin should be entitled to expect that the other has aged less by a specific amount (as per SR formula).

I am thinking that the traveling twin feeling acceleration should not differentiate between the twins from an SR perspective, since we cannot consider the acceleration asymmetrically (i.e. both twins are identically accelerating or in uniform motion w.r.t. each other at all times, from SR perspective).

So, how would SR predict correctly whose clock will turn out to have recorded a longer passage of time if this is a real experiment?

2. Oct 24, 2012

### ghwellsjr

3. Oct 24, 2012

### arindamsinha

Wrong guess, but good point. I am unable to convince myself with the reasonings given.

What I am trying to state here is that when we are talking about 'traveling', 'reversing', or 'returning', it is happening symmetrically to each twin in the other's frame of reference, and there is no third party frame of reference which can arbitrate to break this symmetry. There is no absolute 'velocity' or 'acceleration' in SR, only relative.

If you look at the original postulates of SR, there is nothing that states that a so-called unilateral acceleration breaks this symmetry, as an acceleration cannot be unilateral in SR without breaking the basic tenets of the theory itself. If an acceleration provides a certain instantaneous velocity at every point in the path of one twin, it provides the same symmetrically to that of the other twin - since we have no reason to see things 'preferentially' from the point of view of either of them.

4. Oct 24, 2012

### ghwellsjr

You said in your first post that the traveling twin feels the acceleration. The one that fires his rockets is the one that accelerates.

But beyond that, if you look at my posts in the linked thread, you will see that the Doppler analysis answers your question without regard to any frames at all. While they are departing, they each symmetrically see the other ones clock ticking more slowly than their own by the same amount. This continues for as long as they both remain at a constant speed and without regard to which one originally fired his rockets. But as soon as one of them fires his rockets after they are separated by some distance, he is the only one that immediately sees a change in the tick rate of the other twin's clock. The other twin will not see that change until some time later. Is that so hard to grasp?

5. Oct 24, 2012

### arindamsinha

'Feeling' acceleration is not a differentiator based on SR postulates. It matters only in GR.

As for the second part, there are two issues:
- The first firing of the rocket doesn't make a difference, but the second one does? Apparently this is because there is some spatial distance between them in the second case. I do not see anything in SR that says that such a spatial distance matters from a symmetry perspective
- This is important - the traveling twin sees the other's tick rate change immediately while the stationary one sees such a change later by Doppler effect and speed of light delay - granted. But note that since time is slowed down for the traveling twin, he also sees the other's clock tick 'faster' for a 'shorter' period of time by his clock - effectively cancelling out any difference! (Before you ask, I have not seen this in any reference, just my own logic, so certainly open to criticism, but think about it)

6. Oct 24, 2012

### ghwellsjr

Why do you think that? What ever time it took according to his own clock for the traveling to get to his turn around point is exactly the same amount of time that it takes for him to get back, assuming that he is traveling at the same speed in both directions.

7. Oct 24, 2012

### ghwellsjr

You've just granted that the situation is not symmetrical for both twins--something that you did not recognize until now. Why do we need to consider this any more?

8. Oct 24, 2012

### arindamsinha

- stationary twin: faster clock, so more elapsed time by his clock, before the traveling twin come back
- traveling twin: slower clock, so less time elapsed by his clock, before he gets back

This is as per SR only. We cannot say that the clock of one slows down (the traveling twin's), and then interpret the results based on one preferred clock (the stationary twin's). I feel the two effects cancel out, so when they meet again, their clocks will be in synch.

Interested to hear your views on this.

9. Oct 24, 2012

### arindamsinha

See the logic after that statement. It is not a simple asymmetry, but reciprocal.

10. Oct 24, 2012

### ghwellsjr

Ok, what's the problem? They both agree the traveling twin's clock accumulated less time.
If you want to analyze this according to SR, then you can pick any Inertial Reference Frame (IRF) because, as you pointed out, none is preferred. In the first quote, you were using the IRF of the stationary twin. There's nothing wrong with that and you got the right answer. I don't know why you then "feel the two effects cancel out". Once you analyze the situation from one IRF, there is no need to use any other IRF, they will all produce the same result.
These are not my views, they are Einstein's.

11. Oct 24, 2012

### arindamsinha

How? As I see it: (faster clock)/(longer time by fast clock) = (slower clock)/(shorter time by slow clock) = same clock tick-rate. No? Perhaps I am explaining this badly :-(

Oops! I meant on my logic, not on SR! :-)

12. Oct 24, 2012

### ghwellsjr

Let's say the speed of the traveling twin is 0.6c. That means the time dilation factor is 0.8. And let's say the traveling twin is gone for ten years according to the stationary twin. That means the traveling twin's clock will advance by eight years. Is this how you see it:

faster clock = 1
longer time by fast clock = 10
slower clock = 0.8
slower time by slow clock = 8

So 1/10 = 0.8/8 = 0.1

What's the problem?

13. Oct 24, 2012

### Staff: Mentor

This is false, and is the key error that leads to your further incorrect conclusions.

The common definition of an inertial frame is a frame where accelerometers at rest everywhere read 0. Clearly by this definition the accelerating twins frame is non inertial, since accelerometers at rest in the cockpit read non-0 values.

A closely related definition is that an inertial frame is one where objects not subject to external forces travel in straight lines at constant speed. The accelerating twins frame is non inertial by this definition since if he drops something in his cockpit it accelerates to the floor.

An approximate definition of an inertial frame is one where the distant fixed stars are not accelerating (note, I don't like this definition since it is only an approximation). The accelerating twins frame is non inertial by this approximate definition since the distant fixed stars are accelerating on average in his frame.

AFAIK, there is no definition of an inertial frame which would entitle the accelerating twin to consider his frame to be inertial. If you disagree then please explicitly post the definition and clearly show how it applies. Otherwise, stop repeating this demonstrably false assertion.

Last edited: Oct 24, 2012
14. Oct 24, 2012

### harrylin

Even post #104
and post #159 ??

Did you read any of the references?
As you are talking about SR, that is wrong as I explained in those posts; you mix up SR with GR. :grumpy:
In that thread I explained in posts #188 and #190 (my explanation) as well as #264 (Einstein's explanation) what frames SR uses for the physics.

Oh and one more, essential thing:
I guess that your "feeling" is not based on calculation.... did you actually try? If you didn't, then we can talk endlessly without getting anywhere. :grumpy:
But in case you did try, please show us your calculation and we can show you where you made a mistake.

Last edited: Oct 24, 2012
15. Oct 24, 2012

### Mentz114

Acceleration is not relative. It is possible to distinguish a state of accelerated motion from a state of uniform motion. This means that if one twin accelerates it is possible to distinguish them.

But it is not acceleration per se that causes the differential ageing - it is the different proper lengths of the paths.

16. Oct 24, 2012

### stevendaryl

Staff Emeritus
I don't understand why you think that. It's just wrong. In SR, there is a privileged collection of trajectories, the inertial trajectories. If a twin is not following an inertial trajectory, then he is accelerated. There is no ambiguity about whether a trajectory is accelerated or not.

17. Oct 26, 2012

### arindamsinha

Thanks for all the responses, guys. They are definitely helpful in furthering the thoughts.

As I mentioned earlier, I may not have been able to explain very well the points I am trying to make. My responses below are an attempt to explain my thoughts better. It is not meant to oppose any of the opinions provided, and does not mean I am ignoring the opinions in the threads I am not specifically responding to.

Request you to please read this post completely to understand my reasoning, before responding to any specific points.

Sorry, my original thoughts had got derailed just around here.

What I meant was this - on the outward trip, there is no difference between the observations of the two twins based on Doppler effect. This is fine. Only when the traveling twin reverses course does he see the other twins clock rate suddently getting faster based on Doppler effect. However, this is an effect that will be seen even without considering relativity, as long as we consider only one twin to be traveling.

My objection to this is:
• In the postulates of SR, relative velocity is common to both observers. Acceleration in no more than a set of different values of instantaneous relative velocities between them. Why should we then attribute the acceleration to one and not the other? I do not see anything in the postulates of SR or derivation of the equations that allows a 'physical feeling of acceleration' or looking at it from 'one preferentially "at rest" observers point of view' to justify this. From what I have gathered, these explanations were added later on to resolve paradoxes within SR framework, and justify asymmetrical time dilation observed in experiments, but do not follow from the postulates and derivation of SR theory.
• The additional fact is that the traveling twin's clock will jump back by a certain amount at the point of reversal, i.e. he will travel into the past instantaneously. This is another part I am finding hard to digest.

Nowhere in the derivation of SR is the above 'common defintion' of inertial frames, or even the concept of acceleration used. The only definition of inertial frames used in the derivation is 'two systems of coordinates in uniform translatory motion'.

Other definitions of inertial frames (like the above) were introduced much later to resolve SR paradoxes and explain asymmetrical time dilation observed in experiments.

Going by the postulates of SR, each twin will be entitled to equally consider the other twin to be in a non-inertial frame, or in other words, to have different but reciprocal/symmetric instantaneous relative velocities over time.

This is what I really am trying to get at in this topic. Acceleration is not relative, but velocity is? Again going back to the postulates of SR, the only way we can consider acceleration is different instantaneous 'relative velocities' over a period of time, and that applies symmetrically to both observers. If we can assign acceleration to one but not the other observers in question, we can extend the same logic down to velocity, and say that velocity is also not relative. I strongly believe these are not part of original SR theory, but 'borrowed and retrofitted' into it from GR and experimental observations, to keep SR consistent and to explain paradoxes.

In fact, when GR is applied to situations like GPS satellite time dilation, note that velocity is not taken as the 'relative velocity' between Earth surface and satellites, but from the CG of the system (or ECIF actually), which is absolutely in agreement with observations and experiments.

---------------------

Why do we need to force such absurd logic into SR to somehow or the other explain 'within the framework' some solution for paradoxes and experimental observations, when clearly GR has encompassed all of SR and given a clearer picture of how physics works in the Universe?

In summary, let me quote Einstein' thoughts that inspired me to start this thread in the first place:
"... according to the general theory of relativity, the law of the constancy of the velocity of light ... cannot claim any unlimited validity. A curvature of rays of light can only take place when the velocity of propagation of light varies with position ... the special theory of relativity cannot claim an unlimlited domain of validity... No fairer destiny could be allotted to any physical theory, than that it should of itself point out the way to the introduction of a more comprehensive theory, in which it lives on as a limiting case."

So, are we trying too hard to resolve within SR inconsistencies and paradoxes that are outside the domain of validity of the theory itself, instead of looking at the more general theory for the proper explanations?

I will rephrase my original question as:
"Is asymmetric time dilation in twin paradox possible in SR, or should we really look to GR for such an explanation?" (Asymmetrical time dilation = actual experimental clock time dilation)

Last edited: Oct 26, 2012
18. Oct 26, 2012

### ghwellsjr

Yes, even with sound when the traveler reverses direction, he observes an increase in the pitch of the sound coming from a remote stationary source. However, the Doppler factors for going and coming are not reciprocals like they are for light and that is what makes the difference. You really should read up on your subject matter before you present these false notions.
The Twin Paradox was introduced by Einstein in his first paper on Special Relativity in 1905 at the end of section 4. It involved a continuously accelerating clock traveling in a circle and reuniting with a stationary clock and running slower than the stationary clock. Einstein didn't call this a paradox (because it isn't) but he did show the asymmetrical time dilation right from the very beginning of his theory. It wasn't something added later.
You should find that hard to digest because it isn't true. Where'd you get such a strange notion from?

This was answered previously in my reference to Einstein's paper. Yes, of course we can understand the twin paradox with SR (that's where it was introduced) but you can also get an explanation from GR if you want.

19. Oct 26, 2012

### ImaLooser

Physicist Max Born, a colleague and good friend of Albert Einstein, wrote that “the clock paradox is due to a false application of the special theory of relativity.” Wolfgang Pauli says of the paradox in his brilliant (according to Albert E.) 1921 treatise on relativity, “Of course, a complete explanation of the problem can only be given within the framework of the general theory of relativity.”

The issue is discussed in detail here http://mathpages.com/rr/s4-07/4-07.htm

20. Oct 26, 2012

### ghwellsjr

But if you read to the end of the relevant paragraph, you will see:
As I said, you can use GR to explain the twin paradox but if we assume the absence of gravity, you can do it just with SR as Einstein did in his 1905 paper.

21. Oct 26, 2012

### harrylin

Good - but it should (or at least could!) have been sufficient to bring this to an end. Everything that followed in your post was already answered several times by several people including myself, and with references again in this thread.
Yes indeed! I now unsubscribe from both these twin paradox spin-off threads.

22. Oct 26, 2012

### arindamsinha

Oh, let me acknowledge that the responses have been very helpful, guys. It has clarified a number of things on how the SR theory is interpreted and applied. Perhaps at the cost of repetition and disagreements, I have been able to get some very good insights.

23. Oct 26, 2012

### ghwellsjr

Good, now do you see that the answer to your question is "yes" and no more questions need to be asked on this thread?

24. Oct 26, 2012

### arindamsinha

Yes, I think all the responses were very helpful.

25. Oct 26, 2012

### Staff: Mentor

This is not correct. Those words are simply an English translation of some of Einstein's early writings. They do not limit the modern definition of the two postulates. In physics the early pioneers are respected, but not worshipped, and their words are not considered some sort of final gospel, never to be modified in any way.

The modern definition of SR, the two postulates, is very much focused on the concept of an inertial frame, despite the fact that it was not explicitly mentioned by Einstein. See any college lecture notes or textbook on SR, e.g. http://www.phys.ufl.edu/~acosta/phy2061/lectures/Relativity2.pdf

OK. This seems to destroy your own argument since you appear to realize that, now that the modern definitions of inertial frames have been introduced, they have resolved any SR paradoxes and explained the observations.

No. This is not correct. Please update your definitions, they are 107 years old now.