# How to differentiate permanent age difference in the twin paradox from reciprocal time dilation? [duplicate]

This question already has an answer here:

I'm hereby editing my previous question about the cause of permanent age difference in the twin paradox example as a result of the links I've been given as answers to my original question. I am trying to interpret the rules here correctly and don't know whether to leave my original question at the end.

In the 1st link, What is time dilation really? (I don't know how to HTML), there are figures 1 and 2 that represent time dilation yet they have a turnaround point and two spacetime paths that start and end co-located. Wouldn't that mean they are examples of permanent age difference and not time dilation? The difference between the two being that permanent age difference at the end co-location is the same from all perspectives and time dilation is different from different perspectives and only applies to inertial frame constant relative velocity.

Also, wouldn't the turnaround point in figure 1 also apply to the same person in figure 2 making figure 2 an incorrect representation of a switching of perspective? The vertical straight-line person in figure 1 should also be depicted as a diagonal straight line in figure 2. Maybe the examples are oversimplified because they seem to contradict the 3rd link in the series. The comments I've been getting also seem to reflect the confusion between permanent age difference, which is not a rate of time, and time dilation which is. I'm slowly making my way through the links provided and there are other questions like this that I have. Do I just keep adding them here?

ORIGINAL QUESTION (edited to reflect previous answers):

The best answer so far is the two parties must co-locate at the start and end of a journey at a relative velocity where one makes a change in that relative velocity to re-unite. If they do not re-unite there can be no universal agreement from all perspectives on the parties' permanent age difference while they are separated.

The problems I have with this answer are:

1. There is nothing stopping any of the perspectives to use relativity to calculate what the parties' age difference will be once they re-unite. (I'm working on understanding the answer given to this statement.) So at what point in the spacetime path can this call be made? One guy's expert opinion was the turnaround point invokes non-inertial acceleration or a gravity equivalent in GR and so the actual source of the age difference happens at the turnaround and you use GR formulae to come to the answer. (The answer given was explained in the difference between the Rindler and Minkowski metrics at the turnaround) They still need to re-unite anyway to turn the calculations into one common reality from all perspectives. The problems I have with this answer are:

a) A clock info handoff scenario has no acceleration involved but there is age difference at the end when the info gets back to the source. (Explained in link 3.)

b) If one of the parties relatively stops at a distance and doesn't re-unite, the result due to acceleration can never be validated by a re-unification of the two parties. There is no valid closure to the spacetime path despite there being an answer from the acceleration at the turnaround point and imposing a mathematical limit as v-> 0 to get an answer. The relative stop scenario also aligns the same lines of simultaneity between the two parties so at least there is no perspective conflict between the two and yet a conclusive answer is forbidden. (Not answered)

c) The GPS example involves using GR to calculate how gravity slows the earth clocks relative to the near non-gravity and free fall no force of acceleration on the satellites in orbit, and SR to calculate the age difference due to relative velocity with turnaround per orbit. Each orbit is a valid spacetime path with valid start and stop, a relative velocity and a turnaround. The problem is there is no force of acceleration or gravity at the turnaround and yet age difference still results. (Answered in link 3 but I intuitively feel there is something more behind the specifics of this example as no actual physical explanation of how a turnaround is handled where no force is felt on a single clock to signal a frame jump.)

d) If GR non-inertial acceleration is not the cause of age difference in SR, then what connection does SR have with GR? (Answered in link 3) Time dilation due to relative velocity is not equivalent to age difference caused by gravity. Length contraction in SR is not related to space contraction due to gravity in GR. I thought this GR explanation for age difference was a good connection between related theories but now I see none. (I see a connection now)

2. Abandoning GR's non-inertial acceleration as the cause of age difference, if one party relatively stops but drifts slowly back to re-unification, a universal call can be made on the final age difference. But if it's a perfect stop or the parties drift away from each other, no universal call can be made due to a violation of spacetime path rules. This means that if instead of a stop or turnaround, the change in relative velocity of a slow down or a speed up away from each other cannot result in age difference due to the fact they can't re-unite. The math can determine an universal answer from all perspectives in the same way a universal answer can be calculated for a stop but relativity also voids it due to spacetime path rules. Yet a testable answer does result from a slow down or speed up (instead of a turnaround). (Not answered)

3. (No longer relevant) If non-inertial acceleration is not the cause of age difference, I have seen too many other explanations of what is. The most popular one is you just count up the reciprocal time dilation for both legs of the journey and that gives you your age difference result at the end. The 2nd most popular is the swing of the line of simultaneity shows the one not causing the swing ageing while the other doesn't. Another is the one who changes the relative velocity becomes the preferred frame and establishes he was the one moving all along so his reciprocal time dilation becomes real. Another is age is what clocks measure but there is also an equivalent time value for the distance separation between the two that doesn't register on the clock. The distance becomes a hidden storage device for the time difference between the two. None are correct right?

Is there an answer from relativity addressing these apparent contradictions when trying to determine age difference? (Answered mostly)

P.S. I have found it impossible on other forums to convince people reciprocal time dilation, the doppler shift ratio and age difference are not all the same thing. So, please, no answers that confuse age difference with the other two. (Still true)

## marked as duplicate by Dale, Aaron Stevens, anna v, John Rennie special-relativity StackExchange.ready(function() { if (StackExchange.options.isMobile) return; $('.dupe-hammer-message-hover:not(.hover-bound)').each(function() { var$hover = $(this).addClass('hover-bound'),$msg = $hover.siblings('.dupe-hammer-message');$hover.hover( function() { $hover.showInfoMessage('', { messageElement:$msg.clone().show(), transient: false, position: { my: 'bottom left', at: 'top center', offsetTop: -7 }, dismissable: false, relativeToBody: true }); }, function() { StackExchange.helpers.removeMessages(); } ); }); }); Jan 26 at 6:00

This question has been asked before and already has an answer. If those answers do not fully address your question, please ask a new question.

• Comments are not for extended discussion; this conversation has been moved to chat. – David Z Jan 26 at 8:55
• @davidz I edited the question; I got no new answers and my reputation went down. I've read as many rules as I could find and I don't know what I'm doing wrong. – ralfcis Jan 29 at 14:08
• Well, your question is marked as a duplicate of another one so people can't add any more answers here. Besides, downvotes don't necessarily mean you're breaking the rules. That being said, one thing that sticks out about your question right now is that it's long, and it's hard for a reader to identify the main point of what you're asking. When you edit, you shouldn't leave the original question around in your post; we have a revision history for that. Edits should just get rid of anything that doesn't need to appear in the post anymore. – David Z Jan 31 at 8:44

## 3 Answers

GR is only needed if you want to talk about gravity - SR is perfectly capable of handling non-gravitational accelerations. I think this article answers your apparent contradictions.

I'm having trouble keeping up. I can now see my title will get my post listed as duplicate. I just started writing. I'm not sure how to avoid the problem now.

Don't be discouraged! There's lots of information regarding these ideas and lots of ways to think about it. If you're looking for a book to learn SR well, I heavily recommend Spacetime Physics. It's very deep, covers all kinds of apparent contradictions and paradoxes of SR, and reads almost like a comic book :)

It seems like you're really hung up on what is "causing" the age difference. In SR, clocks in relative motion will tick at different rates (the observer in the relatively faster frame has a wrist watch that ticks faster than the observer in the slower frame). To be clear, this difference in time is due to relative motion.

Now, in GR, observers that are at different gravitational potentials will also have a measureable difference in the rate at which their clocks tick. To be clear, this difference in time is due to gravitational-inertial motion.

These are two phenomena that in reality occur simultaneously (since everything is essentially in motion and gravitates), i.e. GPS satellites have to account for both phenomena to get the times correct.

• Books and wiki articles are fine for general knowledge but I'm asking a specific question that in 12 yrs of searching has never been answered the same way twice. Some expert out there must know the answer. – ralfcis Jan 26 at 3:43
• Reciprocal time dilation is not the same thing as age difference as I said in my original post. Your answer is not related to my question. There is reciprocal time dilation before and after the turnaround and none of it contributes to age difference. – ralfcis Jan 26 at 3:45
• Ageing is also not the same as age difference. Ageing is a rate, age difference is a permanent result from all perspectives so it is not dependent on reciprocal time dilation because that is dependent on perspective. – ralfcis Jan 26 at 3:48
• I'm not sure what you are even asking. Have you read this article? adsabs.harvard.edu/full/1992IrAJ...20..201K I agree that clock rates and clock readings are not the same thing - but that is the very point to the answer that you don't seem to like – N. Steinle Jan 26 at 3:50
• Science is really the art of forming well-posed questions. I don't see you asking a "specific question", rather there's LOTS of questions and its overwhelming. And reciprocal time dilation IS involved. Look at the very very last paragraph in the paper I just linked to – N. Steinle Jan 26 at 3:53

You can notice in the drawing below that the proper time, whose scale along both axis is the same, is smaller for the accelerating twin, the smaller the larger the acceleration, so that the entire path would fall on twin's 2 time axis if acceleration is infinite. $$\tau$$ is proper time (well, actually the greek letter that I used, which I dont rememmber in latex).The corve is the accelerated path for twin 2, which will be entirely along the t2 time axis if acceleration were infinite. So acceleration IS the explanation for the twin paradox, regardless of you denying it.

I am making this an answer, because there are too many comments which will be removed.

The basic answer is that there should not be a change in the inertial frame in order to keep the symmetry assigned to each twin, i.e. symmetries are broken when inertial frames change, as when introducing acceleration. Accelerating frames are non inertial frames. One has to delve into the mathematics of each particular case. It cannot be done with words.

In this link and the links therein , which I am suggesting for closure of your question due to duplication, you will find the mathematics. You cannot substitute words for mathematics as you are trying.