# Variable speed of light

Ivan Seeking
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No, acceleration isn't the critical point. You can construct variants of the twin paradox in which nobody accelerates, but the twins come back with different ages.

How exactly does this apply to the twins paradox? I thought a key assumption is that they start and end in the same frame of reference. By this it would seem that the twin set into motion must experience a force in order to start, and to end his trip.

How exactly does this apply to the twins paradox? I thought a key assumption is that they start and end in the same frame of reference.

Not really; they just need to start and end at the same place. If you stick in an arbitrarily large acceleration, it changes the elapsed proper time by an arbitrarily small amount. In my example, if the travelling twin goes out and comes back, it still takes him only 6 subjective years to do that, regardless of whether he stops at the end or keeps going.

Originally posted by Ambitwistor
Not really; they just need to start and end at the same place. If you stick in an arbitrarily large acceleration, it changes the elapsed proper time by an arbitrarily small amount. In my example, if the travelling twin goes out and comes back, it still takes him only 6 subjective years to do that, regardless of whether he stops at the end or keeps going.

This poses an interesting question. IF, as you had said, there is both a theoretical model in which one of the twins does not accelerate, but non-the-less 'comes back' at a different time (or age, as the case may be), and also if it is so that an acceleration need not be 'large' (you have not defined a range for 'large'), but
an arbitrary 'small' (whatever 'small' may mean), the would, if string theory were true, the 'vibration' of the string be (by each string an element in a large dynamic consisting of the sum of all of the strings), would all matter exist in two or more times?

If neither twin accelerates or decelerates then how do you determine which twin is younger since they can both argue the other is moving? Sorry if you already covered this.

Kaw

If neither twin accelerates or decelerates then how do you determine which twin is younger since they can both argue the other is moving? Sorry if you already covered this.

That's what much of this thread has been about. The short version: the younger twin is the one who travels along a shorter path in spacetime. For the long version, read the thread.

russ_watters
Mentor
Originally posted by kawikdx225
If neither twin accelerates or decelerates then how do you determine which twin is younger since they can both argue the other is moving? Sorry if you already covered this.

Kaw
That's what much of this thread has been about. The short version: the younger twin is the one who travels along a shorter path in spacetime. For the long version, read the thread.
Actually, if neither twin accelerates, then they are both sitting next to each other not moving with respect to each other for their entire lives. They stay the same age relative to each other.

The whole point of them being "twins" is that at the starting point in their lives they are sitting next to each other in the same frame. To get an age difference, one MUST accelerate.

I think the problem got so complicated, the initial intent of a "twins paradox" may have been lost.

The whole point of them being "twins" is that at the starting point in their lives they are sitting next to each other in the same frame. To get an age difference, one MUST accelerate.

That's how you get them to follow different spacetime paths, if you assume they were originally following the same spacetime path. (There are versions of the twin paradox in which you don't assume that.) But the main point concerning acceleration in this thread was that some people say that acceleration is what causes the travelling twin to be younger, and that's not really accurate. The elapsed proper time experienced by an observer is not tied up in what happens at the beginning, end, or middle of the trip; it has to do with the geometry of the entire worldline.

Ivan Seeking
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Originally posted by Ambitwistor
Not really; they just need to start and end at the same place. If you stick in an arbitrarily large acceleration, it changes the elapsed proper time by an arbitrarily small amount. In my example, if the travelling twin goes out and comes back, it still takes him only 6 subjective years to do that, regardless of whether he stops at the end or keeps going.

If we never break symmetry, then how does address the paradox? For example, suppose someone happens by planet earth while travelling near the SOL. I look through my telescope at this person and see someone who appears to be twenty years old. Assume the traveller follows the proper path - only proper acceleration - and then passes by earth in another eighty years or so and I look again. Through my ancient eyes I see a barely aged, 26 year old in the ship. He has also looked at me on first pass, and again on the return path. From his point of view, I was the one in motion. I am the younger. It seems that we have the original paradox. In other words, I don't see how we resolve the twins paradox without breaking symmetry.

If there's no symmetry breaking, then there's no age difference. All I'm trying to say here is that acceleration is not the key to the twin paradox; you can have twin paradoxes in which acceleration breaks the symmetry, and paradoxes in which something else breaks the symmetry. All that matters is something break the symmetry.

(I was also pointing out that whether you break the symmetry by accelerating/decelerating at turnaround, you don't have to involve any inital or final acceleration or deceleration either; the end result depends on the entire history of the worldline, not just the endpoints.)

Ivan Seeking
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Originally posted by Ambitwistor
If there's no symmetry breaking, then there's no age difference....the end result depends on the entire history of the worldline, not just the endpoints.)

OK, this is the crux of the paradox to me. Under SR, we have no absolute frame of reference; and the relative motion between our two observers dates back ultimately to the big bang. So, it seems that we can never find a common or preferred frame no matter how far back we look. So it would seem that the answer is not that there is no age difference, the answer is that unless we break symmetry, there is no unique answer to the question: Who ages less quickly? To me, this also implies that the age of the universe depends on the observer. I have never been clear on this point.

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OK, this is the crux of the paradox to me. Under SR, we have no absolute frame of reference; and the relative motion between our two observers dates back ultimately to the big bang.

Okay. (Although if you're talking about Big Bangs, you're not doing SR anymore.)

So, it seems that we can never find a common or preferred frame no matter how far back we look.

There doesn't have to be a common or preferred frame to compare ages. However, the two twins' worldlines have to be able to intersect in two places in order to compare clocks.

So it would seem that the answer is not that there is no age difference, the answer is that unless we break symmetry, there is no unique answer to the question: Who ages less quickly?

If the situation is truly symmetric, you can uniquely answer the question: they both age at the same rate.

To me, this also implies that the age of the universe depends on the observer.

You're right, the age of the universe does depend on the observer. There is a preferred class of observers in cosmology that everyone uses when talking about the age of the universe: the ones who see the universe as maximally isotropic. The Earth is close to, but not quite, one of those preferred observers.

chroot
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Originally posted by Ambitwistor
the ones who see the universe as maximally isotropic. The Earth is close to, but not quite, one of those preferred observers.
Just to add to what Ambi said: these preferred frames are just those frames in which the cosmic microwave background radiation is uniform in all directions. If you have some relative motion with respect to the CMBR, you see it as blueshifted along the direction you're moving, and redshifted in the opposite direction. A "comoving" observer is one who is just sort of going along with the flow of the expansion of the universe.

An analogy are two people floating in a river. One guy just floats and lets the water carry him -- he's a comoving observer, and sees the water moving the same speed all around him: zero.

Another guy swims hard in some arbitrary direction. He sees the water moving faster in some directions than in others.

There's nothing that violates relativity theory: this CMBR rest frame is not an absolute rest frame or anything like that. There's nothing special about it relativistically. There is, however, something special about it cosmologically.

Cosmologists measure the age of the universe as the proper time experienced by such comoving observers.

- Warren

Ivan Seeking
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Originally posted by Ambitwistor
If the situation is truly symmetric, you can uniquely answer the question: they both age at the same rate.

Truly symmetric? I'm not sure what exceptions you refer too here.

So you are saying that in my example, when we use our telescopes during each of our two passes near each other, we see each other aging at the same rate? That is, on his second pass by earth, I don't see a 26 year old in my scope, I see a 100 year old person in the ship?

So you are saying that in my example, when we use our telescopes during each of our two passes near each other, we see each other aging at the same rate? That is, on his second pass by earth, I don't see a 26 year old in my scope, I see a 100 year old person in the ship?

I can't say for sure, since I asked and you didn't clarify the details of how the other twin is returning. But I would guess that the situation is not symmetric and nor will be their ages. If the travelling twin returns by accelerating/decelerating, or by gravitational slingshot, or by circumnavigating a closed universe, then his worldline is very different from the Earth twin's, so there is no symmetry (regardless of whether he starts or ends at rest with respect to the Earth twin).

Ivan Seeking
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Gold Member
Originally posted by Ambitwistor
I can't say for sure, since I asked and you didn't clarify the details of how the other twin is returning. But I would guess that the situation is not symmetric and nor will be their ages. If the travelling twin returns by accelerating/decelerating, or by gravitational slingshot, or by circumnavigating a closed universe, then his worldline is very different from the Earth twin's, so there is no symmetry (regardless of whether he starts or ends at rest with respect to the Earth twin).

I mean the situation is which our world lines have never crossed since the big Band, and where our traveler follows a course having only proper accelerations - allowing a second pass by earth and a second comparison of our clocks, by telescope..

Originally posted by Ivan Seeking I mean the situation is which our world lines have never crossed since the big Band, and where our traveler follows a course having only proper accelerations

What does "having only proper accelerations" mean? That the traveller has a nonzero proper acceleration at all times? Does he accelerate and decelerate? Or what?

Ivan Seeking
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Originally posted by Ambitwistor
What does "having only proper accelerations" mean? That the traveller has a nonzero proper acceleration at all times? Does he accelerate and decelerate? Or what?

I mean that we never break symmetry.

I mean that we never break symmetry.

Can you describe a physical scenario in which the travelling twin is able to pass the Earth twice, without breaking symmetry?

Ivan Seeking
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Gold Member
Originally posted by Ambitwistor
Can you describe a physical scenario in which the travelling twin is able to pass the Earth twice, without breaking symmetry?

From some of your earlier comments, I thought that you knew of such a trick. If this is not possible, then all is well.

From some of your earlier comments, I thought that you knew of such a trick. If this is not possible, then all is well.

I can invent such a scenario (but not in pure special relativity); I just didn't know what scenario you were considering. For instance, both twins could circumnavigate a closed universe, with opposite velocities relative to a cosmological observer. In that case, their aging would be symmetric.

Ivan Seeking
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Originally posted by Ambitwistor
I can invent such a scenario (but not in pure special relativity); I just didn't know what scenario you were considering. For instance, both twins could circumnavigate a closed universe, with opposite velocities relative to a cosmological observer. In that case, their aging would be symmetric.

So in this case, if on some near pass one twin accelerates and joins the other, we find that the twins are [almost exactly] the same age?

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Ivan Seeking
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Gold Member
Originally posted by chroot
Cosmologists measure the age of the universe as the proper time experienced by such comoving observers.

- Warren

Is there a maximum age for the universe as viewed by some class of observers; where all other observers will measure a lesser age?

So in this case, if on some near pass one twin accelerates and joins the other, we find that the twins are [almost exactly] the same age?

Yes, assuming that they were the same age during one of the passes, they will remain the same age on successive passes. Accelerating into the same frame doesn't change this (much).

Is there a maximum age for the universe as viewed by some class of observers; where all other observers will measure a lesser age?

Yes. The preferred comoving cosmological observers experience maximal proper time.

Originally posted by russ_watters
Actually, if neither twin accelerates, then they are both sitting next to each other not moving with respect to each other for their entire lives. They stay the same age relative to each other.

The whole point of them being "twins" is that at the starting point in their lives they are sitting next to each other in the same frame. To get an age difference, one MUST accelerate.

I think the problem got so complicated, the initial intent of a "twins paradox" may have been lost.

If neither twin accelerates, than can their either be no twin, or perhaps can both twins exist at the same time in the same place?