Why is the speed of light constant for all observers?

[Ivan Seeking]

I have no idea why anyone has objected to anything I have said here. I will read the link and pick this up later.

 

[Ambitwistor]

Originally posted by zoobyshoe
Well, Ambitwistor's is the best explanation of the twin paradox I have run into. It's the first time I even understood the importance of the "Spacetime Interval".

Here's a secret: I almost never perform Lorentz transformations. I just work with 4-vectors, and extract physical information from them by finding their spacetime lengths or projections onto other 4-vectors.

 

[Ambitwistor]

Originally posted by Ivan Seeking
I have no idea why anyone has objected to anything I have said here.

It hasn't been clear to me what your points have been, but it has seemed at times that you have been implying that acceleration is necessary for the twins to experience different elapsed proper times, and/or general relativity is required to resolve the twin paradox in the presence of acceleration, neither of which is true.

 

[zoobyshoe]

Originally posted by chroot If you think about it, it has to be that way... if it weren't, then some cosmic ray particle moving at 0.9c with respect to you somewhere in the depths of space would somehow affect YOUR clock!

This part, I don't get. I thought cosmic rays were photons, and as such, could never be observed going less than C.

In other words, I have been under the impression that even if I am traveling at 0.9c all photons whose speed I measure going in any direction relative to mine will be clocked going at C. Is this not the case?

 

[chroot]

Originally posted by zoobyshoe
This part, I don't get. I thought cosmic rays were photons

No, sorry for the confusion -- some cosmic rays are photons -- but many are massive particles like protons and electrons. The photons, of course, will always be observed traveling at c, while the massive particles will always be < c.

- Warren

 

[zoobyshoe]

Originally posted by chroot some cosmic rays are photons -- but many are massive particles like protons and electrons.

Interesting. How did they all get the same name, being such different things?

 

[Ambitwistor]

"Cosmic ray" is just a catch-all term for "particles that come from outer space".

 

[zoobyshoe]

In Six Easy Pieces he mentions cosmic rays as the highest energy photons we are aware of. Is there a term that can be used to differentiate these from the "riff raff" cosmic rays?

 

[Ambitwistor]

Originally posted by zoobyshoe
In Six Easy Pieces he mentions cosmic rays as the highest energy photons we are aware of. Is there a term that can be used to differentiate these from the "riff raff" cosmic rays?

Ultrasuperduper high energy cosmic rays.

Actually, we've detected cosmic rays with much higher energies than the highest-energy cosmic-ray photons we've detected. The most energetic photons we've seen are from gamma-ray bursts, maybe on the order of 10 TeV (possibly 100's of TeV's; I'm not sure what the state of the art is). But we've seen charged cosmic rays up beyond 100 million TeV.

 

[Ivan Seeking]

Originally posted by Ambitwistor
It hasn't been clear to me what your points have been, but it has seemed at times that you have been implying that acceleration is necessary for the twins to experience different elapsed proper times, and/or general relativity is required to resolve the twin paradox in the presence of acceleration, neither of which is true.

Well, somehow we got off track I think...perhaps you are expecting Ivan the Terrible?

First, I was explaining the mechanics of the paradox; that's all.

Next, I addressed the issue of preferred observers; and I still think correctly so. Perhaps this language is out of favor, but specifically I meant that no absolute state of rest or motion exists. This is a still significant concept of SR; no?

Finally, I keep addressing the issue that if we wish to describe one frame of reference as preferred, this in response to Zooby's question about whose clocks run slowly - meaning to prefer one system over the other - a frame of rest must be defined. I meant this all within the context of SR. In all cases we must still define a frame of rest by which we determine who will age less quickly; true? With our twins, we know who is in motion - the one who leaves earth...and this requires acceleration. The page linked makes this assumption immediately

 

[Ambitwistor]

Originally posted by Ivan Seeking
Next, I addressed the issue of preferred observers; and I still think correctly so. Perhaps this language is out of favor, but specifically I meant that no absolute state of rest or motion exists. This is a still significant concept of SR; no?

Yes, it's why people find the twin paradox puzzling: they think that since there are no preferred frames, each observer should observe the same thing.

(Actually, there are senses in which states of motion are absolute in SR: you can absolutely determine the magnitude of your proper acceleration.)

Finally, I keep addressing the issue that if we wish to describe one frame of reference as preferred, this in response to Zooby's question about whose clocks run slowly - meaning to prefer one system over the other - a frame of rest must be defined.

Well, you don't have to work in the rest frame of some observer --- if you wanted, you could choose some bizarre curvilinear coordinate system --- but it's easiest to do so when such a global inertial frame exists (as in Minkowski spacetime).

In all cases we must still define a frame of rest by which we determine who will age less quickly; true? With our twins, we know who is in motion - the one who leaves earth...and this requires acceleration. The page linked makes this assumption immediately

I wouldn't say that we know that the Earth twin is "at rest", if that's what you're implying by defining a rest frame, but it is true that we know that acceleration breaks the symmetry between the two twins in this variant of the twin paradox. (There are other variants in which this is not the case.)

 

[S = k log w]

Originally posted by Ivan Seeking
When the car is in motion, it is shorter in the frame of the garage. Likewise, from the frame of the garage, the car's clocks are running more slowly. When the car stops, that is, when the frame of the car coincides with the frame of the garage, the two lengths L and L₀ agree. Likewise, it we compare the ticks of the clocks, we find that again they agree – they occur at the same rate. However, and this was a key test of relativity, we find that while the frames of the car and garage did not coincide, ie, while the car is in motion as viewed from the garage, the clocks in the car really were running more slowly...just as observed and predicted.

This was finally verified I think in the early sixties using two atomic clocks; one on the ground, and one in a jet. After flying one of the clocks around for a while, and after accounting for the effects of gravity, the clock on the plane had indeed lost time as predicted to within the accepted margins of error. This has since be replicated in many other ways. Also, we see the lifespan of subatomic particles increase according to Relativity and their relative speed – since their clocks run more slowly, we see them live longer. This is seen in particle accelerators as well as in nature.

To the extent that isotopes have a 1/2t, does that in relativity,
an accelerating particle runs more slowly than than at rest, factor in when calculating the 1/2t of an isotope?

 

[jcsd]

Yes, a particle will appear to have a longer half-life when it is travelliong at relativistic speeds in some rest frame, indeed this is a famous example of a relativtic effect.

 

[Ivan Seeking]

Originally posted by Ambitwistor
I wouldn't say that we know that the Earth twin is "at rest", if that's what you're implying by defining a rest frame, but it is true that we know that acceleration breaks the symmetry between the two twins in this variant of the twin paradox. (There are other variants in which this is not the case.)

This was a poor choice of words on my part.

There are other variants in which acceleration does not break the symmetry between the two twins? I may not know what you mean. Could you give an example or two?

 

[Ambitwistor]

There are other variants in which acceleration does not break the symmetry between the two twins? I may not know what you mean. Could you give an example or two?

I already gave two examples in my first post to this thread. (Note that, as I clarified later, I am speaking of proper acceleration.)

 

[Ivan Seeking]

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.

 

[Ambitwistor]

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 traveling 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.

 

[S = k log w]

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 traveling 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?

 

[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

 

[Ambitwistor]

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]

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.

 

[Ambitwistor]

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 traveling 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]

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 traveling 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 traveling 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.

 

[Ambitwistor]

If we never break symmetry, then how does address the paradox?

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]

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.

 

[Ambitwistor]

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]

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 let's 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]

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?

 

[Ambitwistor]

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 traveling 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]

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 traveling 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..

 

[Ambitwistor]

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]

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.

 

[Ambitwistor]

I mean that we never break symmetry.

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

 

[Ivan Seeking]

Originally posted by Ambitwistor
Can you describe a physical scenario in which the traveling 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.

 

[Ambitwistor]

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.