Relativity, speed of light and stuff

[granpa]

the electric field follows an inverse square law because space is 3 dimensional. aether theory explains this very well.

 

[Fredrik]

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".

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.

 

[rbj]

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 $4 \pi G$ and $\epsilon_0$ rather than normalizing $G$ and $4 \pi \epsilon_0$ 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.

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.

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 $4 \pi r^2$ 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]

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 possesses 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]

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).

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]

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 http://www.billionquotes.com/index.php/Albert_Einstein#Misattributed claims that he said it to his assistant, Ernst Straus, but doesn't give a reference.

 

[granpa]

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.

 

[Dale]

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]

your second paragraph is unclear.

it might be an enormous coincidence or it might indicate the existence of an underlying symmetry that we haven't 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 doesn't entirely eliminate the aether. it just renames it 'space'. according to relativity even empty space has properties.

 

[Dale]

If a wave does not propagate in a medium then what other speed could it possibly propagate at besides the invariant speed?

 

[granpa]

zero

 

[Dale]

Then it wouldn't be a wave

 

[granpa]

exactly

 

[atyy]

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]

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)

 

[Dale]

granpa, you are not making any sense

 

[granpa]

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 wouldn't be a wave.

 

[Dale]

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]

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.

 

[Dale]

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.

$$\nabla \cdot \mathbf{E} = 0$$

$$\nabla \cdot \mathbf{B} = 0$$

$$\nabla \times \mathbf{E} = - \frac{\partial\mathbf{B}} {\partial t}$$

$$\nabla \times \mathbf{B} = \mu_0\varepsilon_0 \ \ \frac{\partial \mathbf{E}} {\partial t}$$

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?

 

[granpa]

you're using light as an example of a wave without a medium to support your belief that light can move without a medium?

no I don't know that they all share the same medium (it would obviously be simpler if they did not). and you don't know that they all propagate at the same speed.

 

[JesseM]

you're using light as an example of a wave without a medium to support your belief that light can move without a medium?

Do you think there is something inherently impossible about the idea of an electromagnetic field which fills all of space, and which assigns electrical and magnetic force vectors to each point in space? If not, then you should have no additional problem with the idea that this field obeys Maxwell's equations, which means that waves in the magnitude of the force vectors will propogate at c.

 

[granpa]

whats the difference between the electric field in a light wave and the electric field from a charge? if aether explains one then it explains the other. I can't imagine why you would think otherwise.

 

[Dale]

you're using light as an example of a wave without a medium to support your belief that light can move without a medium?

No, I am using Maxwell's equations as a justification of why I believe that electromagnetic waves can propagate without a medium. According to the equations all that is needed are the fields themselves, no medium is required.

You still have yet to offer any evidence supporting your position.

 

[granpa]

maxwells equations describe light, they don't explain it.

 

[Dale]

Of course not. But they describe it as a wave that does not require a medium in which to propagate.

Still waiting on any evidence of the aether ...

 

[granpa]

you're just being argumentative now. go argue with someone else.

since, moreover, my own points are being ignored I see no reason to continue.

 

[JesseM]

whats the difference between the electric field in a light wave and the electric field from a charge? if aether explains one then it explains the other. I can't imagine why you would think otherwise.

What are you talking about? Of course there is no difference, the point is that there is nothing inherently contradictory about the idea that there is only the electromagnetic field operating in both cases, no additional aether needed to explain either one. Do you think there is something contradictory about this idea of space being filled by an electromagnetic field which obeys Maxwell's equations?

 

[atyy]

Do you think there is something inherently impossible about the idea of an electromagnetic field which fills all of space, and which assigns electrical and magnetic force vectors to each point in space? If not, then you should have no additional problem with the idea that this field obeys Maxwell's equations, which means that waves in the magnitude of the force vectors will propogate at c.

If the electric field fills all space, that is coming very close to the aether isn't it? I kinda of do away with the aether in classical field theory by thinking that light can move into a region where it previously wasn't.

The idea of an electric field filling all space comes very close to quantum field theory, in which light and electrons are excitations of the photon and electron fields which pervade all space, and are very much like the aether in that sense. The fields are more primary than the excitations, because there are (physically meaningful) excitations of the fields which don't really correspond to photons or electrons.

 

[Dale]

you're just being argumentative now. go argue with someone else.

Calling me names doesn't help your position. A scientific theory must be backed up with evidence, and after more than 100 years of looking there is still no direct evidence of the luminiferous aether.

 

[JesseM]

If the electric field fills all space, that is coming very close to the aether isn't it?

Not really, because it doesn't have a rest frame of its own--I would say that's the defining difference between aether theories and field theories.

 

[granpa]

when a changed particle moves at relativistic speed its field becomes compressed. how does the field far from the particle know how much to compress itself if it doesn't have a velocity of its own?

the wave nature of light is the evidence for an aether. a medium is intrinsic to the definition of a wave. no wave has ever been empirically observed to not have a medium.

 

[JesseM]

when a changed particle moves at relativistic speed its field becomes compressed. how does the field far from the particle know how much to compress itself if it doesn't have a velocity of its own?

I couldn't tell you about the details, but presumably it follows from Maxwell's equations. And Maxwell's equations are local ones (stated in differential form), so the vector at each point only has to "know" how vectors infinitesimally close to it are behaving...I assume you could approximate the field's behavior to arbitrary accuracy using a cellular automaton style computer simulation where the electromagnetic field vectors for each cell update themselves every time-increment based only on the field vectors of neighboring cells.

the wave nature of light is the evidence for an aether.

Field theories predict waves too, so no, it isn't "evidence".

a medium is intrinsic to the definition of a wave.

No it isn't. If you think it is, please give your "definition of a wave".

no wave has ever been empirically observed to not have a medium.

You're just begging the question here, as we have empirically observed electromagnetic waves, and there is no evidence whatsoever that they have a medium...what else would it mean to "observe" a wave "to not have a medium", if not just a failure to observe any evidence that it does have a medium, and a theory that adequately explains the wave without the need to invoke a medium?

 

[Dale]

the wave nature of light is the evidence for an aether.

When asked to offer evidence that light propagates through a medium the best that you have been able to come up with is to point to a few other kinds of waves and essentially say "sound waves and ocean waves are waves in mediums therefore all waves must have mediums". This is certainly not direct evidence for the aether. At best it is an assumption that was reasonable a century ago.

Your logic is "hamburgers and patty melts are sandwiches with beef therefore all sandwiches must have beef". Then, when confronted with a BLT, you simply assert the existence of some beef that miraculously has no taste, no calories, no texture, no weight etc. When challenged to produce evidence of the beef you simply assert that a BLT is a sandwich and therefore there must be beef even if we cannot otherwise detect it.

Do you not see how embarassingly ridiculous your logic is? As JesseM mentioned, you are assuming your conclusion, and going to absurd lengths to do so.

 

[granpa]

you can hardly use the idea that light has no medium as evidence that light has no medium.

it is you who are using circular logic.