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Relativity, speed of light and stuff...

by ricmat
Tags: light, relativity, speed
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atyy
#55
Aug30-08, 02:43 AM
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Quote Quote by granpa View Post
still not sure what you mean about photon mass.
Quote Quote by JesseM View Post
I've forgotten precisely what additional assumptions beyond Lorentz-invariance are used to derive the relation E^2 = m^2*c^4 + p^2*c^2 (which naturally implies that if a particle is moving at the speed of light, the only way it can avoid having infinite energy is if it has 0 rest mass m
Hi granpa, JesseM's quote is what I'm talking about. I believe if you have the Principle of Relativity (existence of a class of reference frames moving with constant velocity relative to each other in which the laws of physics all look the same), and you also have an velocity vi that is invariant in all the frames, from those 2 assumptions you can derive the Lorentz transformations, with vi replacing the usual speed of light c. With some additional assumptions, which JesseM and I have both forgotten, we can derive E=mvi2, where m is the relativistic mass. From which we see that a thing moving at the vi must be massless. So if sound were to be a thing that travelled at vi, and it also had mass, then presumably at least one of the assumptions in getting to E=mvi2 must be wrong.

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Quote Quote by ricmat View Post
it seem that there is no consensus among today scientist that there is no "something" like ether as opposite to vacuum....
I'm having second thoughts that a massive medium for the thing that travels at the invariant velocity causes difficulties. I'm not really sure, so I'm just going to state a bunch of stuff and let someone correct it. The dispersion relation for a phonon is like a photon. So maybe even though phonons are made from a medium, they can be considered massless. And maybe photons, by analogy to phonons, can be considered to be made from a medium. I wonder if ricmat is thinking about a model like this: http://arxiv.org/abs/cond-mat/0210040
atyy
#56
Aug30-08, 02:49 AM
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Quote Quote by rbj View Post
two different sets of Maxwell's equations, identical in every respect except for the permittivity parameter, are not identical laws of physics. "identical", in the strong sense of the word, means not only qualitatively the same, but also quantitatively the same.

the "plus" is semantically not necessary.
I agree, but I think you are counting Maxwell's equations as a zeroth postulate, whereas JesseM doesn't have this zeroth postulate and puts the constancy of the speed of light as a second postulate. So the number of postulates is still the same, ie.

Maxwell's equations + Principle of Relativity = Principle of Relativity + constancy of speed of light
DaleSpam
#57
Aug30-08, 08:15 AM
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Quote Quote by granpa View Post
NO. the point isnt that the speed of sound would be constant when the medium was moving. the point is that the speed of sound would be constant even when the observer was moving.
"Six of one, half-dozen of the other"
granpa
#58
Aug30-08, 10:05 AM
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Quote Quote by atyy View Post
So if sound were to be a thing that travelled at vi, and it also had mass, then presumably at least one of the assumptions in getting to E=mvi2 must be wrong.
it isnt clear to me that the particles in a solid which is transmitting a sound would necessarily be moving at the speed of sound. one can increase the speed of sound simply by increasing the stiffness of the material and decrease the motion of the particles by simply decreasing the amplitude of the sound. or at least, I guess you can. I'm not an expert on sound. or anything else for that matter.
Al68
#59
Aug30-08, 07:01 PM
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Quote Quote by JesseM View Post
I don't think it's a good idea to approach questions in philosophy of science by appealing to dictionary definitions. The definition is good enough to cover most situations in science, where you're explaining some high-level laws governing a system by appealing to more fundamental laws which govern the basic parts of that system (reductionism); but when you reach the level of the most fundamental laws, what exactly would it mean to have a "theoretical explanation" of these laws?

Here is Feynman writing about this topic in The Character of Physical Law, using gravitation as an example:
Well, if we did have a good "theoretical explanation", it would belong in a physics textbook, not a literature textbook. So I would consider it physics. The fact that we don't have such a theory doesn't mean that such a theory is not within the scope of physics.

Al
JesseM
#60
Aug30-08, 07:25 PM
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Quote Quote by Al68 View Post
Well, if we did have a good "theoretical explanation", it would belong in a physics textbook, not a literature textbook. So I would consider it physics. The fact that we don't have such a theory doesn't mean that such a theory is not within the scope of physics.
I repeat my question: but when you reach the level of the most fundamental laws, what exactly would it mean to have a "theoretical explanation" of these laws? I can't imagine what a theoretical explanation of fundamental laws would even look like (aside from boiling them down to some minimal set of axioms), so it's not clear what you're imagining here, but it sounds like you're talking about something totally unprecedented in the history of science.
atyy
#61
Aug30-08, 07:37 PM
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Quote Quote by granpa View Post
it isnt clear to me that the particles in a solid which is transmitting a sound would necessarily be moving at the speed of sound. one can increase the speed of sound simply by increasing the stiffness of the material and decrease the motion of the particles by simply decreasing the amplitude of the sound. or at least, I guess you can. I'm not an expert on sound. or anything else for that matter.
Yes, hence the second thoughts in my above post. So I guess the question can be split in 2:
1) What transformations are consistent with 2 invariant speeds (speed of light and something else). I suppose this us related to doubly special relativity.
2) Can light (and gravity) be usefully modelled as a medium? For light, it appears the answer is yes. For gravity, the answer is unknown, but there are several intriguing leads (http://arxiv.org/abs/0712.0427)
granpa
#62
Aug30-08, 07:50 PM
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2 invariant speeds?

it gets confusing since we are talking about sound but what we are really talking about is light. I never meant to say anything implying 2 invariant speeds.
atyy
#63
Aug30-08, 07:52 PM
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Quote Quote by Al68 View Post
Well, if we did have a good "theoretical explanation", it would belong in a physics textbook, not a literature textbook. So I would consider it physics. The fact that we don't have such a theory doesn't mean that such a theory is not within the scope of physics.

Al
Quote Quote by JesseM View Post
I repeat my question: but when you reach the level of the most fundamental laws, what exactly would it mean to have a "theoretical explanation" of these laws? I can't imagine what a theoretical explanation of fundamental laws would even look like (aside from boiling them down to some minimal set of axioms), so it's not clear what you're imagining here, but it sounds like you're talking about something totally unprecedented in the history of science.
There's an interesting discussion by Wen in his Quantum Field Theory book (OUP 2004, p 12):
Chinese philosophers theorized that the division could be continued indefinitely, and hence that there were no elementary particles. Greek philosophers assumed that the division could not be continued indefinitely ... Those ultimate particles were called "atomos".

He quotes the Dao De Jing (p11): The Dao that can be stated cannot be eternal Dao. The Name that can be named cannot be eternal Name. The Nameless is the origin of the universe. The Named is the mother of all matter.

Which he mischievously translates as (footnote, p11): The physical theory that can be formulated cannot be the final ultimate theory. The classification that can be implemented cannot classify everything. The unformulable ultimate theory does exist and governs the creation of the universe. The formulated theories describe the matter we see everyday.

Preface (pviii): we still know so little about the richness of nature. However, instead of being disappointed, I hope the readers are excited by our incomplete understanding. ... The human imagination is also boundless. ..... I wonder which will come out as a 'winner', the richness of nature or the boundlessness of the human imagination.
atyy
#64
Aug30-08, 07:57 PM
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Quote Quote by granpa View Post
2 invariant speeds?

it gets confusing since we are talking about sound but what we are really talking about is light. I never meant to say anything implying 2 invariant speeds.
Ah, I see, the discussion was just on the second point then. Another interesting quote from Wen's QFT book, this particular one is quite uncontroversial, but he has nice imagery:
Our vacuum is more like an ocean which is not empty. Light and fermions are collective excitations that correspond to certain patterns of 'water' motion.
Fredrik
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Aug30-08, 09:14 PM
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Quote Quote by JesseM View Post
I repeat my question: but when you reach the level of the most fundamental laws, what exactly would it mean to have a "theoretical explanation" of these laws? I can't imagine what a theoretical explanation of fundamental laws would even look like (aside from boiling them down to some minimal set of axioms), so it's not clear what you're imagining here, but it sounds like you're talking about something totally unprecedented in the history of science.
I don't know what his answer is, but my answer would be that a deeper, more fundamental theory, can be considered a theoretical explanation of the fundamental laws in your theory. For example, general relativity is a theoretical explanation of Newton's law of gravity (the inverse square law). Newton's theory of gravity can't explain the inverse square law because it's a fundamental law of the theory, but GR can explain it because it's just one of many results that can be derived from the fundamental laws of that theory.
JesseM
#66
Aug30-08, 09:45 PM
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Quote Quote by Fredrik View Post
I don't know what his answer is, but my answer would be that a deeper, more fundamental theory, can be considered a theoretical explanation of the fundamental laws in your theory. For example, general relativity is a theoretical explanation of Newton's law of gravity (the inverse square law). Newton's theory of gravity can't explain the inverse square law because it's a fundamental law of the theory, but GR can explain it because it's just one of many results that can be derived from the fundamental laws of that theory.
My question was, 'but when you reach the level of the most fundamental laws, what exactly would it mean to have a "theoretical explanation" of these laws?' If a given theory turns out to be an approximation of some more fundamental theory, like Newtonian gravity is understood as an approximation of GR, that shows that the first theory (Newtonian gravity) wasn't really one of the "most fundamental laws". Of course I'm assuming here that there are some final, most fundamental laws out there waiting to be discovered; as atyy brought up, it's conceivable that it's just wheels within wheels forever, that every particle is really a composite entity made up of even smaller particles, etc.
MeJennifer
#67
Aug30-08, 10:49 PM
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Quote Quote by Fredrik View Post
INewton's theory of gravity can't explain the inverse square law because it's a fundamental law of the theory, but GR can explain it because it's just one of many results that can be derived from the fundamental laws of that theory.
I think you are mistaken. In fact if you look how Einstein derived GR you will see he simply included the Newtonian limit as a given. Technically GR is simply Newtonian gravity plus relativistic effects. GR does not explain anything, it is simply a more accurate theory.

If you think I am mistaken, please demonstrate how it explains the inverse square law. Or an even simpler question: How does GR get to the Newtonian limit.
rbj
#68
Aug30-08, 11:32 PM
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Quote Quote by MeJennifer View Post
I think you are mistaken. In fact if you look how Einstein derived GR you will see he simply included the Newtonian limit as a given. Technically GR is simply Newtonian gravity plus relativistic effects. GR does not explain anything, it is simply a more accurate theory.

If you think I am mistaken, please demonstrate how it explains the inverse square law. Or an even simpler question: How does GR get to the Newtonian limit.
does John Baez do that here?

or maybe Sean Carroll does that here or here?

i think they can derive the inverse-square relationship (or maybe it's a 1/r relationship for potential energy) for the flat space-time limit. the constant of proportionality in the Einstein equation ([itex]8 \pi G[/itex]) does come about to be compatible with Newtonian gravitation.

i can't actually do the math myself (i am ashamed to confess i never figured out tensors), but it appears that this is what they do.
yuiop
#69
Aug31-08, 12:02 AM
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I tend to agree with Jennifer here. I can not see how a physicist isolated in a small spacestation that had never experienced gravity or even heard of it, would conclude from a knowledge of Special Relativity alone, that two particles would have to move towards each other, let alone that they accelerate towards each other with an acceleration inversely proportional to the distance separating them.

As far as I can tell General Relativity started with a knowledge that we experience "Newtonian gravity" and extrapolated or reverse engineered that knowledge to more extreme conditions than we normally experience. It is hardly surprising that Newtonian gravity is recovered from GR in the weak field limit because GR started with that assumption. lease do not get me wrong here. I am not saying there is anything wrong with GR, I am just saying that it does not fundementally explain or predict gravity and just provides a pretty good mathematical description of what we observe.

Put it another way. In multiverse theories where there are any number of possible universes each with their own laws of nature, would a universe that obeys the laws of Special Relativity have to have an inverse square law of gravity in the weak field limit or come to that, any gravity at all?
JesseM
#70
Aug31-08, 12:21 AM
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Quote Quote by kev View Post
I tend to agree with Jennifer here. I can not see how a physicist isolated in a small spacestation that had never experienced gravity or even heard of it, would conclude from a knowledge of Special Relativity alone, that two particles would have to move towards each other, let alone that they accelerate towards each other with an acceleration inversely proportional to the distance separating them.
When did Fredrik say anything like that? He didn't say you could discover the inverse-square law from pure thought, he just said that if you already know the equations of GR you can get the inverse-square law as a derived consequence. Of course you could say the same thing about the equations of Newtonian gravity in some sense, so I'm not sure this is a totally clear distinction, but at least in Newtonian gravity it's obvious from the fundamental equations whereas in GR it's not.
Quote Quote by kev
As far as I can tell General Relativity started with a knowledge that we experience "Newtonian gravity" and extrapolated or reverse engineered that knowledge to more extreme conditions than we normally experience.
I don't know whether or not that's true of Einstein's original derivation as a historical matter, but it is at least true that GR can be derived from assumptions that have nothing to do with Newtonian gravity--on this page Steve Carlip writes:
If you want to derive the Einstein field equations from scratch, you can do so without making very many assumptions. You must assume that

1. the geometry of spacetime is dynamical;
2. there are no extra fixed, nondynamical "background structures" that influence the geometry;
3. special relativity becomes a good approximation when gravitational fields are weak;
4. the field equations can be derived from a Lagrangian, or an action principle; and
5. the field equations involve no more than second derivatives; that is, they determine "accelerations" rather than requiring accelerations as initial data.

These assumptions lead almost uniquely to a set of field equations with two undetermined constants. One of these is Newton's constant, which determines the strength of the gravitatonal interaction. The other is the cosmological constant, Lambda.
I think it is also true that you can come up with theories that are identical to Newtonian gravity in every respect except for the fact that the strength of the force is inversely proportional to some other real power like r^2.05, whereas in GR you don't have this sort of wiggle room, trying to make it no longer obey an inverse-square law would give a very different theory (presumably it would require violating one of Carlip's basic assumptions above).
granpa
#71
Aug31-08, 09:06 AM
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the electric field follows an inverse square law because space is 3 dimensional. aether theory explains this very well.
Fredrik
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Aug31-08, 10:15 AM
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Quote Quote by JesseM View Post
My question was, 'but when you reach the level of the most fundamental laws, what exactly would it mean to have a "theoretical explanation" of these laws?'
To me, the idea of a law being fundamental or not only makes sense within the framework of a specific theory. What you call "fundamental laws" seems to be what I would describe as "a final theory". If such a theory is found, it won't be possible to explain its postulates. This isn't a very deep statement. It's just the definition of what I mean by "final".

Quote Quote by JesseM View Post
When did Fredrik say anything like that? He didn't say you could discover the inverse-square law from pure thought, he just said that if you already know the equations of GR you can get the inverse-square law as a derived consequence.
Thanks. If I hadn't been asleep I would have said something very similar.

To Kev and MeJennifer, I would like to add a couple of things:

I don't consider the way Einstein discovered SR and GR to be "derivations" of those theories. In both cases he wrote down a somewhat ill-defined list of properties that he wanted the theory to have, and then searched for a theory that had those properties. The reason why I can't consider this method a "derivation" is that the "list of properties" was ill-defined to begin with, and later made well-defined by the theory that was found. (E.g. we need Minkowski space to properly define the inertial frames in which the speed of light is supposed to be a constant).

I understand that your opinion is that the fact that GR was found by looking only for theories that could reproduce the Newtonian limit means that GR can't be said to explain the inverse square law. That is a valid opinion (about the meaning of the word "explain") but I don't agree with it. There is no deeper form of understanding than having a theory that agrees with experiment, so if derivation from a theory that agrees with experiment can't be considered an explanation, nothing can. It makes no difference to me (at all) how the theory was found. All that matters to me is what range of phenomena it's capable of describing and how well it agrees with experiment.


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