Relativity, speed of light and stuff...

granpa

my bad. you meant 'anything moving at that speed which is constant for all observers'.

still not sure what you mean about photon mass. are you talking about air molecules that would have to move at least as fast as the sound wave. I'm not sure that holds for a solid medium though (waves can move pretty fast through a spring). but even if it did it is a fact that space itself seems to be able to move faster than light.

rbj

i've been in this argument before. in some other thread, i was saying (and i still maintain) that the 2^nd postulate of SR is unnecessary or superfluous when you have the first. the second postulate (the constancy of c) is a consequence of the first (that the laws of physics remain invariant for every inertial frame of reference). by "laws of physics", i mean not only the functional form of the laws, but also that the parameters (like c, G, [itex]\hbar[/itex], and [itex]\epsilon_0[/itex]) in those laws remain invariant. 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.

time dilation and length contraction are a consequence of the fact that every inertial observer observe identical laws of nature in observed phenomena which means they observe identical speeds of propagation of the E&M interaction as well as all other "instantaneous" interactions (gravitation and nuclear).

Fredrik

I don't think that's exactly right. You can't derive the second from the first. What I've been saying in other threads (and still maintain) is that Einstein's "postulates" are ill-defined because they use the term "inertial frame" without a definition, and that any definition of "inertial frame" that's appropriate for SR must include both of Einstein's "postulates" in some form.

Einstein's "postulates" shouldn't be treated as axioms. They are just a list of properties that he wanted the theory he was trying to find to have.

atyy

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 v_i that is invariant in all the frames, from those 2 assumptions you can derive the Lorentz transformations, with v_i replacing the usual speed of light c. With some additional assumptions, which JesseM and I have both forgotten, we can derive E=mv_i², where m is the relativistic mass. From which we see that a thing moving at the v_i must be massless. So if sound were to be a thing that travelled at v_i, and it also had mass, then presumably at least one of the assumptions in getting to E=mv_i² must be wrong.

Edit:
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

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

"Six of one, half-dozen of the other"

granpa

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

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

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

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

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

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

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

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

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

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

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.