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Relativity, speed of light and stuff...

by ricmat
Tags: light, relativity, speed
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rbj
#73
Aug31-08, 02:11 PM
P: 2,251
Quote Quote by granpa View Post
the electric field follows an inverse square law because space is 3 dimensional.
if you bring into this an additional concept of flux, which is conserved and makes Gauss's Law possible. the concept of conserved flux seems natural and satisfying, but it wouldn't have to necessarily be the case. the inverse-square law of gravitation would require the same hypothesis; a gravitational flux emitted by quantities of mass, unless, like we're discussing here, the Newtonian inverse-square law is derived from some other more fundamental principle (like GR).

now, inverse-square laws regarding radiant intensity (E&M or acoustic) do necessarily follow from a combination hypotheses of conservation of energy and 3-dim space (both reasonable). the radiant energy (or power) comprises a natural form of "flux", which is conserved.

BTW, it is because of this concept of flux in inverse-square laws that make me wish that Planck units had originally normalized [itex]4 \pi G[/itex] and [itex]\epsilon_0[/itex] rather than normalizing [itex]G[/itex] and [itex]4 \pi \epsilon_0[/itex] as was done. i believe these rationalized Planck units are a little more natural (yielding simpler field equations) than the existing definitions. with any extraneous constants removed from the field equations, i think that might lead to insight to what might be behind such. we know that Nature isn't really performing a multiplication in her head to convert a particle wave frequency to its energy. that multiplication is necessary only because of the anthropocentric units we arbitrarily chose to use. and Nature doesn't give a rat's as$ what units humans (or some alien race) chose to use.

aether theory explains this very well.
i don't see a hypothetical aether having anything to do with the inverse-square relationship.

Quote Quote by kev View Post
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.
it's not surprising because of the correspondence principle. any newer, more advanced, theory must degenerate to the old theory in the context where the old theory was known to be valid. even though Einstein knew that his new GR theory would need to do that, i don't think that Newtonian gravity was where he started and extrapolated from. i think it was those classic elevator and spaceship thought experiments.

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.

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--
but, because of a concept of flux (which can be cooked up from pure thought) and knowledge of the mathematical fact that a sphere in 3-dimensional space has a surface area of [itex]4 \pi r^2[/itex] can lead one to predict or hypothesize an inverse-square law for some quantity. doesn't mean, of course, that the hypothesis need not be tested in reality.

i think that Einstein first, from pure thought experiments with just a few really reasonable postulates (like the laws of physics are invariant for every inertial observer and that a free-falling observer cannot differentiate his or her state from being inertial - the equivalence principle), came up with SR, and with a little mathematical help from folks like Mercel Grossman, the GR. there is no evidence that Einstein ever drew on or referred to the Michaelson-Morley experiment and the null result, and i am convinced that it made little difference to him ("as if God had any choice in the matter"). assuming he knew of the experiment and result, Einstein was likely utterly not surprized. it's amazing what you can cook up from a very few extremely reasonable postulates, thought experiments, and math (all from pure thought). that is, if your brain is the size of a small planet and you have truly historical levels of insight. such persons are rare in history.
JesseM
#74
Aug31-08, 02:43 PM
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P: 8,470
Quote Quote by rbj View Post
there is no evidence that Einstein ever drew on or referred to the Michaelson-Morley experiment and the null result, and i am convinced that it made little difference to him ("as if God had any choice in the matter").
Well, in his original 1905 paper, in his first paragraph he discussed some theoretical reasons to suspect that electromagnetism doesn't have a preferred frame, but then in his second paragraph he said:
Examples of this sort, together with the unsuccessful attempts to discover any motion of the earth relatively to the "light medium,'' suggest that the phenomena of electrodynamics as well as of mechanics possess no properties corresponding to the idea of absolute rest.
And the Einstein quote you're referring to is "What really interests me is whether God had any choice in the creation of the world"--this was not a positive assertion that he was confident God had no choice about special relativity as you made it sound, it seems like more of a general philosophical question about the laws of physics as a whole (if it's an accurate quote at all, there are a lot of fake Einstein quotes that have circulated around, you can really only trust the ones attributed to some published source).
rbj
#75
Aug31-08, 03:24 PM
P: 2,251
thanks for the reference to the original 1905 paper. i stand corrected about that. he clearly indicates he knew of the MM experiment and result (but he should have cited it).

Quote Quote by JesseM View Post
And the Einstein quote you're referring to is "What really interests me is whether God had any choice in the creation of the world"--this was not a positive assertion that he was confident God had no choice about special relativity as you made it sound, it seems like more of a general philosophical question about the laws of physics as a whole.
i disagree with you about his position about this (and i assume the quote is for real). i really think that Einstein is questioning whether the form of reality could possibly be different. of the fundamental (dimensionless) constants that go into the description of reality, that's different, but the functional form, i think that Einstein was wondering, even challenging, if they could possibly be different.
JesseM
#76
Aug31-08, 03:48 PM
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Quote Quote by rbj View Post
disagree with you about his position about this (and i assume the quote is for real). i really think that Einstein is questioning whether the form of reality could possibly be different. of the fundamental (dimensionless) constants that go into the description of reality, that's different, but the functional form, i think that Einstein was wondering, even challenging, if they could possibly be different.
How is that disagreeing with me, though? That's just what I said, it was a philosophical question about the laws of physics as a whole.

edit: also, note that the quote is listed in the "misattributed" section of this page. On the other hand, this page claims that he said it to his assistant, Ernst Straus, but doesn't give a reference.
granpa
#77
Aug31-08, 04:47 PM
P: 2,258
if light is thought of as a KIND OF sound wave in the aether then I believe it follows naturally that electric fields must follow an inverse square law. there is no difference between the electric field in a light wave and the electric field from an electron.
DaleSpam
#78
Aug31-08, 06:24 PM
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A wave which propagates through a medium has a propagation velocity that depends on the medium and is relative to that medium. If, by some coincidence, the propagation velocity of a wave in some medium were equal to the invariant speed then all observers would measure the propagation velocity to be the invariant speed regardless of what they measure the velocity of the medium to be.

However, a wave that does require a medium must propagate at the invariant speed. Since light does not require a medium it propagates at the invariant speed, which is how we originally discovered the invariant speed and its implications for the geometry of spacetime.

Since the aether is otherwise undetectable, and since it would be an enormous coincidence if the propagation of light through the aether were equal to the invariant speed, and since the speed of light is more simply explained by assuming it does not require a medium, what is the value of the concept of aether?
granpa
#79
Aug31-08, 06:28 PM
P: 2,258
your second paragraph is unclear.

it might be an enormous coincidence or it might indicate the existence of an underlying symmetry that we havent been smart enough to figure out yet.

why should light alone of all known waves not require a medium? it is much simpler to just take its wave nature as evidence of the existence of such a medium. in any event, relativity doesnt entirely eliminate the aether. it just renames it 'space'. according to relativity even empty space has properties.
DaleSpam
#80
Aug31-08, 06:33 PM
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If a wave does not propagate in a medium then what other speed could it possibly propagate at besides the invariant speed?
granpa
#81
Aug31-08, 06:37 PM
P: 2,258
zero
DaleSpam
#82
Aug31-08, 06:40 PM
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P: 16,963
Then it wouldn't be a wave
granpa
#83
Aug31-08, 06:44 PM
P: 2,258
exactly
atyy
#84
Aug31-08, 06:45 PM
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Quote Quote by DaleSpam View Post
Since the aether is otherwise undetectable, and since it would be an enormous coincidence if the propagation of light through the aether were equal to the invariant speed, and since the speed of light is more simply explained by assuming it does not require a medium, what is the value of the concept of aether?
Not much within SR (only pedagogically for explaining the significance of the Michelson-Morley null result). But apparently it's useful within condensed matter physics (artificial "light" and "electrons"), and the interplay between condensed matter theories, quantum field theories and the search for a quantum theory of gravity. In these theories, the "aether" is typically not so much embedded in space, but spacetime and matter emerge from the "aether".
atyy
#85
Aug31-08, 06:55 PM
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Quote Quote by Fredrik View Post
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.
Would it help to say that the inverse square law cannot be derived from GR, only an approximate inverse square law. So GR explains why we were deceived that it is an inverse square law? (If the inverse square law were exactly derivable, we wouldn't have perihelion precession)
DaleSpam
#86
Aug31-08, 06:57 PM
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granpa, you are not making any sense
granpa
#87
Aug31-08, 07:10 PM
P: 2,258
it does not follow that a wave without a medium would travel at c. it follows that a wave without a medium would not travel at all and if it did it wouldnt be a wave.
DaleSpam
#88
Aug31-08, 07:29 PM
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P: 16,963
granpa, first, even a propagation velocity of 0 wouldn't work, because 0 in one frame is non-zero in another frame. Second, what you are really saying is that it is not possible for any wave to propagate without a medium, do you have any logical reason to think that?

None of the four fundamental forces have a medium in which they propagate.
granpa
#89
Aug31-08, 07:34 PM
P: 2,258
none of the forces have a medium? what do you think the aether is?

do you have any reason to think that a wave can propagate without a medium? I've never seen one do so.
DaleSpam
#90
Aug31-08, 07:48 PM
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P: 16,963
Yes, I have a reason to think that a wave can propagate without a medium, and if you have never seen one do so then you must be blind.

[tex]\nabla \cdot \mathbf{E} = 0[/tex]

[tex]\nabla \cdot \mathbf{B} = 0[/tex]

[tex]\nabla \times \mathbf{E} = - \frac{\partial\mathbf{B}} {\partial t}[/tex]

[tex]\nabla \times \mathbf{B} = \mu_0\varepsilon_0 \ \ \frac{\partial \mathbf{E}} {\partial t}[/tex]

So according to you, all four fundamental forces require a medium in which to propagate, they all share the same medium, it is completely undetectable, it just happens that all four forces have the same propagation speed in this medium, and that propagation speed also happens to be the invariant speed.

Have you even one piece of evidence to support this rather long list of coincidences?


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