# Physical explanation of velocity time dilation

1. Dec 22, 2012

### arindamsinha

In SR, pure relative velocity between two observers causes a time dilation between them.

It seems that if the two observers were at rest w.r.t. each other at some point in time, then the one who accelerates to achieve the relative velocity is the one who gets time dilation (i.e. comparatively slower clock rate).

The acceleration itself though is not the cause for the time dilation. The acceleration can be very brief anyway.
- The velocity achieved by the accelerating observer is what causes the time dilation.
- The longer he travels at that velocity, greater the total time dilation
- When he decides to decelerate and stop (to breathe perhaps) w.r.t. the stationary observer, the time dilation between the two also stops
- When the traveling observer decides to accelerate back to the other observer, his clock again starts ticking slower
- So when the two get together again, the traveling observer's clock shows less time elapsed than the observer who never moved.

If the above is correct, my questions is:
- Is there a physical difference between the traveling observer and the stationary one, after the traveling observer has accelerated for a short period and then reached a steady inertial velocity w.r.t. the stationary observer?

In other words, why is the asymmetric time dilation continuing for the traveling observer? Is this because his acceleration has made some fundamental change to his physical properties, which continues to exist even after the acceleration has stopped?

2. Dec 22, 2012

### ghwellsjr

It's always risky to explain a phenomenon with a single simple scenario because it can always be contradicted by another simple scenario and completely unnecessary when a proper explanation will work for any scenario, no matter how complicated.

Suppose your two observers both accelerate identically in opposite directions so that there is a pure relative velocity between them. Will there be a time dilation between them?
Can you see that you just contradicted yourself? You just said that a "pure relative velocity between two observers causes a time dilation between them" and now you're saying that only one gets time dilated.
Rather than thinking about time dilation as something that happens between two observers, you should think of time dilation as something that happens to each observer individually with respect to a chosen Inertial Reference Frame (IRF) and not with regard to any other observers. This works in all cases, whether simple or complex and will remove any confusion you might have.

It's no different than thinking about speed. If you're always trying to think about speed as happening between two observers, you will only succeed in the simplest of cases, such as when one observer never accelerates and is always inertial. But then you could have merely considered the "traveling" observer to have a speed with respect to the IRF in which the "stationary" observer remains at rest.

If you do this, then there is never any ambiguity over what is meant by the speed of any and all observers or objects in your scenario and therefore there is never any ambiguity over what is meant by the time dilation of any and all observers or objects--you just calculate gamma as a function of the speed in the IRF. This always works, never has any problem, never has any confusion, never has any ambiguity and is always very simple, even in the most complex scenarios.
If there is a physical difference between a "traveling" observer and "stationary" one, then nature won't disclose it to us any more than it discloses which observer is physically traveling and which is stationary. You're asking the same question as those who sought the rest state of the ether. If you can find the answer, you will have found the ether and Special Relativity will no longer be valid.

3. Dec 22, 2012

### arindamsinha

I was simply stating that relative velocity is the cause of time dilation in SR. Are you saying that is wrong?

Till now, I said (A) relative velocity is the cause of time dilation in SR, and (B) the observer who accelerates has the velocity and therefore the time dilation. In what way am I contradicting myself? Are you nitpicking on the way I frame my sentences?

If time dilation is something that happens between each observer and a chosen inertial frame, then ultimately we can relate it to be between the two observers as well. This is very basic logic. My question is about one observer who is at rest w.r.t. the inertial frame and another who is traveling w.r.t it. I though that was quite obvious from my question.

I know all this, and this has nothing to do with the question I am asking.

Wrong. In experiments at least, Nature does disclose to us which observer is physically traveling and which is stationary. Considering the Earth and GPS satellites, it is clear which one is traveling and therefore has its clock slowed down (ignoring the gravitational time dilation part). Similarly, in the Bailey experiment, it is the muon that is traveling in the muon ring, not the laboratory. Had this not been the case, we would never have been able to observe any measurable and asymmetric time dilation.

Funnily enough, I think even if a suitable ether is found, SR can still remain valid. I don't see a contradiction.

On the whole, George, you have addressed everything in this post, except my question.

Last edited: Dec 22, 2012
4. Dec 22, 2012

### ghwellsjr

You said it was the "pure relative velocity between two observers" meaning that and nothing else. I said that even if you can make that definition work in some simple scenarios, it doesn't work in all. What works in all is if you make the velocity of each observer relative to an IRF.
You said, "In SR, pure relative velocity between two observers causes a time dilation between them." Just like the pure relative velocity is between two observers, so is the time dilation, meaning that it isn't assigned to either one of them but shared between the two of them. Then you said that time dilation is assigned to just one of them and not both. It can't be both between two observers and be assigned to just one. I'm not nitpicking, I'm trying to help you with an understanding so that you will not start threads like this but rather be able to help other people who are struggling in the same way that you are right now.
Only if one of them is inertial and remains inertial. But now you have deviated from your first statement.
Even if it is, why do you want to limit yourself in your understanding of time dilation? With SR, you can explain the traveling twin's aging without regard to a twin, you can analyze what happens to a single observer taking at trip and how his clock ticks during the entire trip. His clock doesn't tick more slowly because he has at twin, it ticks more slowly because he has a speed in an IRF.
Well good. Let's see how you would apply it to the situation of a muon that never accelerated, it began its existence at a high speed with respect to the earth and the earth never accelerated to that high speed. So how does your idea that accelerations determines physically which observer is the one that is time dilated? See this thread for an ongoing discussion about time dilation in a muon:

Nature is not disclosing which observer is traveling in a circle, as if that was some secret that takes time dilation to figure out. Yes, we know when objects are inertial and not inertial but this has nothing to do with your concept that there is some sense in which one particular inertial observer/object is physically stationary as opposed to some other inertial observer/object. How can you tell which of two inertial object is physically stationary?
Then you have a lot to learn about SR. SR does not deny the possibility of the existence of an absolute ether, but it does deny that it could ever be identified.
I did answer your question--you just don't like the answer. Maybe you need to hear the answer from a whole bunch of other people.

5. Dec 22, 2012

### Mentz114

I think you are confusing the term 'time dilation' with 'differential aging'. Please note the distinction between them. Differential aging is something that happens between two events, and is not 'continuing' as you suggest.

Symmetry or asymmetry is not a cause in differential aging. The time on each worldlines clock depends only on the proper interval of the segment.

No. When the frame stops accerating it is inertial, and so equivalent to any IRF.

6. Dec 22, 2012

### arindamsinha

OK. I thought time dilation = differential aging, but there may be a terminology issue.

My question can then be restated as:
"Is there a difference in physical condition between two objects/observers when they are undergoing differential aging?"

7. Dec 22, 2012

### Staff: Mentor

Time dilation and differential aging are different things. Time dilation refers to way that a clock moving relative to an observer advances at a different rate than a clock at rest relative to that observer. It is observer-dependent, in the sense that A sees B's clock running slow, but B also sees A's clock running slow.

Differential aging refers to the way that a different amount of proper time can pass on different paths through space-time between the same two events (twins separate and twins rejoin, for example). It is not observer-dependent.

The two phenomena are related, of course. If two vehicles travel different routes of different length between two points in ordinary space yet end up arriving at the destination at the same time, you would know that at some point the the odometer of the one that traveled the longer distance must have been advancing more rapidly. And it's the same with the twins moving through space-time; stay-at-home travelled further through space-time, so his clock must have been advancing more rapidly at some point.

But there's no physical difference between the two. They just traveled different paths of different length through space-time, and their different ages show it.

8. Dec 22, 2012

### arindamsinha

This part really bugs me. The 'seeing' another observers clock running slow would happen even in classical mechanics without any relativity required. This is not an actual clock time difference, but just observational difference (given limited speed of light and Doppler effect).

However, time dilation is not this - it is actual difference of the clock rates, over and above the observed rates. That is why I think 'time dilation' and 'differential aging' are the same thing, independent of appearances.

Which I believe is also the 'relative time dilation' and it is the same as 'differential aging', that actually results in a clock difference when the two twins come together again.

I understand the analogy, but believe that while widely used it is not an identity with SR. In this particular case, their clocks will still show the same time when they meet at the destination, and that is reasonable given one travelled faster along a longer route, and one slower along a shorter route.

Thanks for confirming this understanding in terms of the physical difference. I realize this is what SR essentially says (or at least implies that physical difference is not important in the framework for the conclusions).

My point is a bit more fundamental. While SR explains this in a certain way, there seems to be always a clear understanding in experiments that have been done, on who is traveling and with what velocity, between two 'observers'.

This is however, post facto given the experiment results. Let me take following examples to illustrate what I mean:

When the first GPS satellite were sent into space, no one could clearly predict whether their clocks would slow down, or speed up, or remain in synch with Earth clocks. It turned out they showed a combination of speeding up because of the gravitational time dilation and slowing down because of velocity time dilation, leading to a net speeding up. As fas as I know, before the satellites were sent, people could predict how the gravitational time dilation will work, but no one could predict which direction the velocity time dilation will take. The Hafele-Keating experiment was the same in terms of the velocity time dilation - it was just found out after the experiment who actually shows a velocity time dilation.

If in our wanderings in deep space, we were to come upon a situation where we found two objects traveling w.r.t. each other at high speed, we would not have any a priori means of predicting if there is a differential aging going on between the two. All 3 outcomes - one's clock going slower, the other's clock growing slower, or the clocks remaining in synch - are possible.

Would there be any physical means of differentiating the situation between the two observed objects that would help us identify whether there is some differential aging going on between them?

9. Dec 23, 2012

### universal_101

I think Time Dilation and Differential ageing are two names for one phenomenon, Consider two relatively moving frames(inertial) A and B, and a third inertial frame X(moving as it pleases, inertially). Then the Time Dilation of A's clock w.r.t B's clock is differential ageing, No matter which frame X we choose, i.e Time Dilation of A w.r.t B or B w.r.t A, (whichever case you are considering) is observer independent just as Differential ageing.

Well, arindham, this is the essence of Twin Paradox, there is No way to give preference one over other, But it is the asymmetry of the relative motion i.e. acceleration, which is utilized in order to give preference one over other(atleast for the case of Twin Paradox), but there are also examples where there is No asymmetry, in those cases it is assumed that both frames have Time Dilated w.r.t each other.

That is, In muons frame of reference Earth's clocks are Time dilated(Differential ageing), where as, in the reference frame of Earth it is the Muon's clocks that is Time Dilated(Differential Ageing). And It is this Obvious contradiction, why Differential ageing is suggested to have different meaning or physicality, compared to Time Dilation.

Essentially, Time Dilation can be used both ways, where as, Differential ageing cannot, because using Differential ageing to explain symmetrical Time Dilation will immediately produce contradictions in more profound way. Or as Nugatory said, Differential ageing is observer independent and Time Dilation is observer dependent.

10. Dec 23, 2012

### arindamsinha

That is my thinking too...
You've got the point I am bringing up. Asymmetrical time dilation (i.e. differential aging) cannot be explained by 'history', e.g. observed acceleration, in many cases like cosmic muon time dilation. So is there a way to find physically different conditions that cause velocity time dilation or differential aging between two objects, so that it can be applied to cases where we don't know the history - e.g. the case I mentioned?
That's the point. I see time dilation as a real phenomenon which is not observer dependent, and can be established by experiment (e.g. GPS clocks vs. Earth clocks). Differential aging is the same thing.

11. Dec 23, 2012

### universal_101

No, you cannot see Time Dilation as a real phenomenon according to present understanding of relativity(i.e. SR). This is the point everyone would make, who would attempt to reply to your post. i.e. What is real, is a matter of perspective, and measurement is reality (Even though I myself think Time Dilation of Muons is real). So, if you want to understand SR, you must not think Time Dilation is real, i.e. it is equally applicable for the frame of reference of Muons which says otherwise(i.e. it is Earth's clocks which are Time Dilated)

As I said, and I know it is very confusing, but thinking Time Dilation as real and one way is not going to help you with SR.

Last edited: Dec 23, 2012
12. Dec 23, 2012

### ghwellsjr

You have given an excellent definition of 'differential aging'. It's when two clocks are together, separate and come back together and they have accumulated different amounts of time on the two clocks.

In order to make sense out of this in all situations, you need to follow the discipline of Special Relativity which says to first assign the clocks to an Inertial Reference Frame. Their instantaneous speed determines their Time Dilation in that selected IRF. If you want, transform all the events into a second IRF moving with respect to the first IRF and now you have clocks moving at different speeds than before and therefore different Time Dilations. But in order to have differential aging, you need to start with the two clocks at the same location at the same time (it doesn't matter where or when or even if they are at rest in the IRF or even at rest with respect to each other). While together, they either note the times on their clocks or they set them to the same time. Then they need to separate in any manner so desired. While they are separated, you need to keep track of each of their speeds and for how long they stay at that speed so that you can calculate their respective time dilations and from that, how much time their clocks accumulate during that segment. You need to repeat this last process for each segment of the trips. Finally, they need to rejoin (not necessarily at the same location as before nor even at rest in the IRF nor even at rest with respect to each other) and now they are able to compare how much time they each accumulated on their clocks. The difference is differential aging, although I described how Time Dilation is used to calculate what that differential aging will be.

Now obviously, since the two clocks physically ended up with different accumulated times, this must have happened during their trips, however, we can never know how it happens, that is, we can never know which IRF is the one that corresponds to the absolute ether rest frame.

13. Dec 23, 2012

### arindamsinha

Thanks for the clarification on this.

In the light of that, would you say it would be impossible for us, without performing some experiments, to tell the differential aging situation between two bodies we suddenly meet in space? {Refering last para but one in my post #8}

I seem to think that would be the case if there is nothing else that can be considered different about the two (ignoring any gravitational effects).

14. Dec 24, 2012

### ghwellsjr

Remember, as you pointed out, differential aging is "a clock difference when the two twins come together again". If those two bodies that we suddenly meet (and I presume you mean they also suddenly meet each other) had not previously met before, then the definition of differential aging does not apply. It's not an issue of our lack of experimentation--it's nothing more than their lack of meeting twice.

It's also not an issue of any difference between the two. For example, one of them could have been inertial forever and the other one could have accelerated a lot--if they had not previously been together to establish a clock relationship, then differential aging cannot be established if and when they ever meet for the first time.

And if they had met once before and recorded the times on their clocks, then when we mutually meet them during their second meeting, we just ask them what the outcome of their differential aging is. Or, if we had been monitoring their history, we could have recorded the times we saw on their clocks during their first and second meetings and with a little subtraction determined their differential aging.

Even if we could not see their clocks but if we could determine their travel history, that is, how long, based on our IRF, they spent at each speed, then using the formula for Time Dilation, we could calculate their differential aging.

But someone else stationary in a different IRF could do the same thing and in spite of the fact that they would apply different speeds for different periods of time and different Time Dilations, they would calculate the same differential aging that we did. So in one IRF, one clock could be running slower during a portion of the history while in another IRF, the other clock could be running slower. I made a series of diagrams to illustrate this effect for the Twin Paradox. See posts #69 & #70 in this thread.

15. Dec 25, 2012

### stevendaryl

Staff Emeritus
Not exactly, although time dilation can be used to computer differential aging.

Differential aging is the fact that two different paths through spacetime that start at the same point and end at the same point may nevertheless have different proper times. This fact is independent of any choice of coordinates.

Time dilation is the fact that the rate of one clock, as measured in an inertial cartesian coordinate system, is slowed by the velocity-dependent factor $\gamma$.

Differential aging is objective and coordinate independent---all observers, regardless of what coordinate system they use, agree about which path has the greatest proper time.

Time dilation is a coordinate-dependent effect---which clock is running faster depends on what coordinate system you are using.