Relativity, speed of light and stuff

[JesseM]

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

You can use the fact that we have a self-consistent theory of electromagnetism which gives correct predictions about all empirical observations related to light, and which does not involve a medium, as evidence that there is no physical motivation for postulating that there should be a medium, although of course we can never "prove" there isn't. Similarly, the fact that we have a self-consistent theory of evolution which adequately explains observations and which does not require an intelligent designer is evidence that there is no scientific need to postulate such a designer.

it is you who are using circular logic.

You're the one who made the assertion "no wave has ever been empirically observed to not have a medium." Please answer my question about what you think it would mean for a wave to have been "empirically observed not to have a medium"; if you can't think of any (hypothetical) observations that would qualify, then your argument is nonsensical.

 

[Dale]

I have used Maxwell's equations and a century of failed experiments designed to detect it as evidence that it doesn't exist.

Where's the beef, granpa?

 

[granpa]

You can use the fact that we have a self-consistent theory of electromagnetism which gives correct predictions about all empirical observations related to light, and which does not involve a medium, as evidence that there is no physical motivation for postulating that there should be a medium, although of course we can never "prove" there isn't. Similarly, the fact that we have a self-consistent theory of evolution which adequately explains observations and which does not require an intelligent designer is evidence that there is no scientific need to postulate such a designer.

You're the one who made the assertion "no wave has ever been empirically observed to not have a medium." Please answer my question about what you think it would mean for a wave to have been "empirically observed not to have a medium"; if you can't think of any (hypothetical) observations that would qualify, then your argument is nonsensical.

theory is consistent with aether as well.

it wouldn't mean anything because its meaningless. a wave by definition requires a medium. I stand behind what I said. you can't use the idea that light has no medium as evidence that light has no medium. its that simple.

 

[JesseM]

theory is consistent with aether as well.

Unlike electromagnetic theory, aether theory postulates that there are facts about the physical world which are impossible to determine experimentally, in this case the rest frame of the aether. I suppose you could take any successful theory and add to it the idea of invisible ghostly dragons which are impossible to detect with any physical instrument, and then say the evidence is "consistent with a theory involving invisible ghostly dragons", but the dragons would obviously be superfluous to the theory, and the same is true of the aether.

it wouldn't mean anything because its meaningless. a wave by definition requires a medium. I stand behind what I said.

I specifically asked you for a definition of a wave--if you can't provide one your statement is meaningless. I would say that in physics a wave is a spatial/temporal variation in any physical quantity (whether density in a medium or electromagnetic field strength in the electromagnetic field) which obeys a wave equation. If you think a wave "by definition" must be a variation in the density of a medium, can you point to any reputable mainstream sources which use such a definition, or is it one you just made up yourself?

you can't use the idea that light has no medium as evidence that light has no medium.

Not the mere idea, no, but you can use the fact that all observational evidence agrees with a theory which does not involve a medium as evidence that there is no physical need for a medium. Just like you can use the fact that all the evidence is consistent with Darwin's theory of evolution as evidence that there is no scientific need for an intelligent designer. Your argument is analogous to a creationist saying "you can't use the idea that evolution happened with no intelligent designer as evidence that there is no intelligent designer". Of course he'd be right that you can't use the mere idea as evidence, but you can use the fact that this theory has enjoyed great success in the empirical realm of making predictions and explaining observations as evidence that there is no need to postulate such a designer. If you disagree with this analogy, please explain how you think your argument is different from that of my hypothetical creationist above.

 

[granpa]

well it sounds like you're not really eliminating the aether. your just depriving it of its material nature. that I could not and would not argue against (though I don't think we really know).

 

[George Jones]

well it sounds like you're not really eliminating the aether. your just depriving it of its material nature. that I could not and would not argue against (though I don't think we really know).

The concept of aether is well outside of mainstream physics as it is now practiced, and, as such, its discussion violates the Physics Forums posting guildelines

https://www.physicsforums.com/showthread.php?t=5374

Overly Speculative Posts: One of the main goals of PF is to help students learn the current status of physics as practiced by the scientific community; accordingly, Physicsforums.com strives to maintain high standards of academic integrity. There are many open questions in physics, and we welcome discussion on those subjects provided the discussion remains intellectually sound. It is against our Posting Guidelines to discuss, in most of the PF forums, new or non-mainstream theories or ideas that have not been published in professional peer-reviewed journals or are not part of current professional mainstream scientific discussion. Posts deleted under this rule will be accompanied by a private message from a Staff member, and, if appropriate, an invitation to resubmit the post in accordance with our Independent Research Guidelines. Poorly formulated personal theories, unfounded challenges of mainstream science, and overt crackpottery will not be tolerated anywhere on the site.

 

[Dale]

a wave by definition requires a medium. I stand behind what I said.

Then your proper course of argument is to claim that light is not a wave, by definition, since it does not have a medium. You cannot define something into existence.

Definition: Christmas is the day that Santa Claus delivers presents to children all around the world
Observation: December 25 is Christmas
Conclusion: Santa Claus exists

Aren't you a little old for such logic, granpa?

It is fine for you to use a medium as part of the definition of a wave, but then, in order to call something a wave, you must independently demonstrate that it has a medium. Otherwise you could define anything into existence simply by judicious choice of definition, as shown above.

 

[Vanadium 50]

how does the field far from the particle know how much to compress itself if it doesn't have a velocity of its own?

How does a thermos know to keep something hot hot and something cold cold?

 

[Vanadium 50]

theory is consistent with aether as well.

If so it's a rather bizarre aether. It's absolutely undetectable, and has properties such that they are consistent with no aether.

 

[rbj]

theory is consistent with aether as well.

no theory with any observational support.

all sorts of people, past and present, have theories that are consisntant with magic.

a wave by definition requires a medium.

no, waves do not, by definition, require a medium. some waves are a displacement quantity regarding some medium (like sound or waves on a string). but disturbances in interaction from the motion of charge (E&M) or sub-atomic particles (nuclear) or mass (gravity) do not propagate in a medium. the reach of those interactions are across a vacuum, nothing but space. and the speed of propagation of such waves are all the same c which is a consequence of the nature of space and time and not a property of which of these interactions are causing it. all of those interaction are virtually instantaneous, until distances get large enough that those interactions with sufficient effect at those distances (E&M and gravity) gets large enough that some 3^rd party can see that the time elapsed between cause and effect of the interaction is not zero.

I stand behind what I said. you can't use the idea that light has no medium as evidence that light has no medium. its that simple.

you can stand behind what you said, but you'll be shot anyway. no one (except maybe you) are using circular logic. we're saying that light (the E&M interaction) has no medium because no properties of such a hypothetical medium have ever been measured, and they should have been measured with the Earth passing through this medium at a speed exceeding 10⁵ km/hr at least some time of the year.

it's simple. and you're simply mistaken.

 

[rbj]

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

pot calling the kettle black?

since, moreover, my own points are being ignored

no, they're being examined (the opposite of ignored) and rejected.

I see no reason to continue.

that would be welcome.

 

[Primordial]

How does a thermos know to keep something hot hot and something cold cold?

Entropy.

 

[DrGreg]

2nd postulate

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).

I almost agree, but the 2nd postulate does contain within it two assumptions that don't automatically follow from the 1st postulate.

1. The speed of light is finite, not infinite.
2. The speed of light is independent of the object that emitted it (which is another way of saying that one photon cannot overtake another following the same spatial path).

Once you have those properties, the fact the speed has to have the same value in every inertial frame follows from the first postulate (otherwise you could identify one frame from another).

For a published paper expressing this view and giving some historical context, see "Two myths about special relativity", Ralph Baierlein, http://link.aip.org/link/?AJPIAS/74/193/1 , section III.

 

[Dale]

the 2nd postulate does contain within it two assumptions that don't automatically follow from the 1st postulate.

1. The speed of light is finite, not infinite.
2. The speed of light is independent of the object that emitted it (which is another way of saying that one photon cannot overtake another following the same spatial path).

Don't both of those follow directly from applying Maxwell's equations in each frame?

 

[rbj]

Don't both of those follow directly from applying Maxwell's equations in each frame?

and applying the same Maxwell's equations (same $\epsilon_0$ and same $\mu_0$) to each frame.

(thanks Dale.)

 

[atyy]

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.

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.

Ah, I finally understood what you meant about "no rest frame of its own" from your reply on another thread! I didn't reply there, because I thought we should confine pointless discussions to one thread.

Yes, I agree with you, that's why I said "very close". So the aether doesn't come about when an electromagnetic wave permeates all space (in which case, space itself is the aether), but rather when a partially static electromagnetic field permeates all space. The non-zero rest state of an electromagnetic field only really begins to make sense within quantum field theory. But within classical SR, we can think of some parts of space having a static electric field - which is an electromagnetic field at rest - and other parts having a traveling electromagnetic wave.

 

[JesseM]

Ah, I finally understood what you meant about "no rest frame of its own" from your reply on another thread! I didn't reply there, because I thought we should confine pointless discussions to one thread.

Actually what I was talking about on the other thread was a different issue, namely the fact that light waves don't have their own rest frame. In aether theory the rest frame of the aether is not the same as the rest frame of light waves, in fact the aether was thought to be a material substance that would be at rest with respect to some sublight observers (as an analogy, the rest frame of the air is not the same as the rest frame of a sound wave).

So the aether doesn't come about when an electromagnetic wave permeates all space (in which case, space itself is the aether), but rather when a partially static electromagnetic field permeates all space.

What is a "partially static electromagnetic field"? Just one where the electromagnetic field vectors at each point in space are unchanging in some frame? This is not the same as the field having a rest frame, though.

The non-zero rest state of an electromagnetic field only really begins to make sense within quantum field theory.

Huh? There is no rest frame of the electromagnetic field in classical electromagnetism either.

But within classical SR, we can think of some parts of space having a static electric field - which is an electromagnetic field at rest

There's no reason to think that because the field is static in that frame, that's an "electromagnetic field at rest". After all, if you believe in aether, the frame where the field vectors are static could be completely different from the rest frame of the aether! (for example, look at the electromagnetic field around a charge moving inertially relative to the aether, in the charge's own rest frame)

 

[atyy]

The non-zero rest state of an electromagnetic field only really begins to make sense within quantum field theory.

Huh? There is no rest frame of the electromagnetic field in classical electromagnetism either

I meant the opposite of what you understood. I agree that in classical SR, it is more helpful to identify the aether with spacetime itself. So the aether is not really useful as a concept distinct from spacetime in classical SR. However, it is useful in quantum field theory - as the vacuum state of the electromagnetic field - it is an entity distinct from spacetime because it is obligatorily non zero. I understand this is quite uncontroversial. Apart from Xiao-Gang Wen's analogy that the vacuum is like an ocean (quoted in an earlier post), there is also Wilczek's analogy (http://query.nytimes.com/gst/fullpa...1A35751C0A96F958260&sec=&spon=&pagewanted=all). There's an amusing claim by deWitt that Einsten made an appeal in 1920 that the aether should not be abandoned (Google books: p178 of "Conceptual Foundations of Quantum Field Theory" edited by Tian Yu Cao, CUP 1999).

 

[JesseM]

I meant the opposite of what you understood. I agree that in classical SR, it is more helpful to identify the aether with spacetime itself. So the aether is not really useful as a concept distinct from spacetime in classical SR.

Again, my point is that one of the defining features of the aether is that it has a rest frame of its own. Spacetime does not have a rest frame, so most authors do not identify the aether with it, they simply consider relativity to have discarded the aether (there are some exceptions, as the Einstein quote below shows, but in this case the authors make clear that they are defining 'aether' in a new way which differs from the classical notion)

However, it is useful in quantum field theory - as the vacuum state of the electromagnetic field - it is an entity distinct from spacetime because it is obligatorily non zero.

The ground state of the vacuum doesn't have a rest frame either, so it would normally not be identified with the aether either.

I understand this is quite uncontroversial. Apart from Xiao-Gang Wen's analogy that the vacuum is like an ocean (quoted in an earlier post), there is also Wilczek's analogy (http://query.nytimes.com/gst/fullpa...1A35751C0A96F958260&sec=&spon=&pagewanted=all).

Wilczek says the quantum vacuum should be seen as "descended from" the aether, but that's not the same as saying the quantum vacuum is a type of aether, since again it lacks a particular rest frame.

There's an amusing claim by deWitt that Einsten made an appeal in 1920 that the aether should not be abandoned (Google books: p178 of "Conceptual Foundations of Quantum Field Theory" edited by Tian Yu Cao, CUP 1999).

DeWitt is presumably referring to this, but Einstein does emphasize that relativity altered aether theory by getting rid of the idea of aether as a motionless substance, and was instead using a new definition of "aether" which only was meant to denote the idea that empty space has properties of its own, like spacetime curvature and electromagnetic fields:

It may be added that the whole change in the conception of the ether which the special theory of relativity brought about, consisted in taking away from the ether its last mechanical quality, namely, its immobility.

...More careful reflection teaches us, however, that the special theory of relativity does not compel us to deny ether. We may assume the existence of an ether; only we must give up ascribing a definite state of motion to it, i.e. we must by abstraction take from it the last mechanical characteristic which Lorentz had still left it.

...Recapitulating, we may say that according to the general theory of relativity space is endowed with physical qualities; in this sense, therefore, there exists an ether. According to the general theory of relativity space without ether is unthinkable; for in such space there not only wonld be no propagation of light, but also no possibility of existence for standards of space and time (measuring-rods and clocks), nor therefore any space-time intervals in the physical sense. But this ether may not be thought of as endowed with the quality characteristic of ponderable inedia, as consisting of parts which may be tracked through time. The idea of motion may not be applied to it.

 

[jtbell]

A crude analogy might be this: A horse and a hippopotamus share some features (e.g. both have four legs), but that does not mean you can call a hippopotamus a horse.

 

[atyy]

The ground state of the vacuum doesn't have a rest frame either, so it would normally not be identified with the aether either.

Wilczek says the quantum vacuum should be seen as "descended from" the aether, but that's not the same as saying the quantum vacuum is a type of aether, since again it lacks a particular rest frame.

On the basis of your definition - I agree!

 

[russ_watters]

This has already been pointed out, but it really is the critical issue here, so...

a wave by definition requires a medium.

Granpa, quite simply, you are not "doing" science correctly. Scientific theories are not logical frameworks for connecting/explaining definitions, they are logical frameworks for connecting/explaining facts. You are getting hung up on a definition and ignoring facts. Given:

-The classical definition of a wave requires a medium.
-Light has not been found to have a medium and indeed has been found to disobey classical understanding of waves.

Only one conclusion is possible to a scientifically minded person: light is not a wave in the classical sense. Whether it is a new type of wave or is just wavelike isn't really important. It doesn't change the facts or how the theory works.

Now, you were given a gentle warning about forum rules. Consider this the final one: we want to help people learn and quite a few people have spent quite a bit of effort in that endevour, but you simply refuse to learn. Dogmatically clinging to this idea of yours -- and claiming it's validity in the face of irrefutable evidence/logic to the contrary -- is crackpottery and we don't allow it here. If you can't abide by these rules, the thread will not be allowed to continue.

 

[DrGreg]

but the 2nd postulate does contain within it two assumptions that don't automatically follow from the 1st postulate.

1. The speed of light is finite, not infinite.
2. The speed of light is independent of the object that emitted it (which is another way of saying that one photon cannot overtake another following the same spatial path).

Don't both of those follow directly from applying Maxwell's equations in each frame?

Yes, they do. But who said Maxwell's equations were one of the postulates of relativity?

Let me guess you might answer this by saying that Maxwell's equations are one of the "laws of physics" covered by the 1st postulate. To my way of thinking, that doesn't really cover it. The 1st postulate doesn't actually explicitly identify which laws of physics it applies to. Just "all of them", whatever they turn out to be. But the 2nd postulate is explicitly necessary for relativity to work, an intrinsic part of the theory itself, and therefore ought to be explicitly identified, albeit in the watered-down version I suggested.

I've never thought about this much, but I imagine it might be possible to invent some fictitious laws of physics for a hypothetical universe that are incompatible with Maxwell's equations but still fully compatible with the postulates of relativity, and with each other.

By the way, there was a heated exchange on this very subject on the talk page of Wikipedia's article on special relativity. See here.

 

[rbj]

Yes, they do. But who said Maxwell's equations were one of the postulates of relativity?

Let me guess you might answer this by saying that Maxwell's equations are one of the "laws of physics" covered by the 1st postulate. To my way of thinking, that doesn't really cover it. The 1st postulate doesn't actually explicitly identify which laws of physics it applies to. Just "all of them", whatever they turn out to be.

no, just the valid ones. what relativity does is orthogonal to the other physical law. it just says that the expressions of that other physical law must apply identically to every inertial frame of reference. no qualitative or quantitative difference. since one of these "other physics" is EM, then two different observers observing the identical beam of light, will both observe the very same changing E field causing this other changing B field which itself is causing this other changing E field, etc. both observers of the same phenomena using the same Maxwell's equations to describe it, will both see the same wave advance at the same speed, having identical $\epsilon_0$ and $\mu_0$ in those Maxwell's equations.

But the 2nd postulate is explicitly necessary for relativity to work, an intrinsic part of the theory itself, and therefore ought to be explicitly identified, albeit in the watered-down version I suggested.

it's follows from the first and the other laws of physics. there is nothing about relativity that isn't conformed to the Correspondence principle. Newton's 2^nd law works both ways if it's expressed as dp/dt.

it turns out that the magnetic action, expressed as a fundamental law in classical physics, can be expressed as a consequence of the sole electrostatic action, but with the effects of special relativity accounted for. the inverse-square law of gravitation (in fact an entire set of corresponding Maxwell-like GEM equations) can be derived from the GR equation. SR can do away with the necessity of the equations of magnetism (essentially leaving just one action) and GR gets rid of Newton's law of gravitation.

relativity doesn't eliminate all other laws of physics. but it does help us understand that some of the old Laws are approximations to the new Laws for speeds much less that c and for reasonably flat space-time (i don't know how to quantitatively express it).

I've never thought about this much, but I imagine it might be possible to invent some fictitious laws of physics for a hypothetical universe that are incompatible with Maxwell's equations but still fully compatible with the postulates of relativity, and with each other.

it doesn't matter. if some other expression of what happens to charged particles ends up obsoleting Maxwell's equations, it would be those laws of physics that would be subject to the postulates of physics.

By the way, there was a heated exchange on this very subject on the talk page of Wikipedia's article on special relativity. See here.

no one is saying that Maxwell's equations are the specific physics that fall under the postulates of relativity but that Maxwell's equations are in the set of what is covered under the postulates of relativity. i guess some of them become unnecessary. but if they didn't become unnecessary, they're still physical law that is expressed within the context of relativity.

 

[rbj]

too late to edit the previous post. where i said

if some other expression of what happens to charged particles ends up obsoleting Maxwell's equations, it would be those laws of physics that would be subject to the postulates of physics.

i meant to say

if some other expression of what happens to charged particles ends up obsoleting Maxwell's equations, it would be those laws of physics that would be subject to the postulates of relativity.

 

[JesseM]

no one is saying that Maxwell's equations are the specific physics that fall under the postulates of relativity but that Maxwell's equations are in the set of what is covered under the postulates of relativity.

Well, not anymore--nowadays they are just seen as an approximation to quantum electrodynamics, and quantum electrodynamics may someday be seen as an approximation to a "theory of everything" which unites electromagnetism with the other three forces. In any case, if you want to define relativity via a set of axioms then you shouldn't include major implicit assumptions that aren't spelled out--the whole point of axioms is to spell out precisely what assumptions you want to make!

 

[rbj]

Well, not anymore--nowadays they are just seen as an approximation to quantum electrodynamics, and quantum electrodynamics may someday be seen as an approximation to a "theory of everything" which unites electromagnetism with the other three forces.

a worthy holy grail. but even if QED replaces Maxwell's equations, do not the expressions of physical interaction in QED (i don't know what they are) apply identically to any inertial frame of reference?

In any case, if you want to define relativity via a set of axioms then you shouldn't include major implicit assumptions that aren't spelled out--the whole point of axioms is to spell out precisely what assumptions you want to make!

no, i think it's the other way. you do not want to itemize: "these are the specific laws of physics that the first postulate of SR applies to". if the postulate is fundamental (as i believe it is), then whatever system of physics that you show are valid (to whatever degree of experimental precision) in your inertial reference frame, that system of physics is just as valid in my inertial frame of reference, even if it is moving (at a constant velocity) with respect to yours. the postulate is that fundamental. and i think it's pretty damn reasonable.

 

[JesseM]

a worthy holy grail. but even if QED replaces Maxwell's equations, do not the expressions of physical interaction in QED (i don't know what they are) apply identically to any inertial frame of reference?

Sure, but my point is that you don't want your axioms to depend on implicit assumptions about the correct theory of electromagnetism, you want a broad definition of "relativity" that would allow you to see that a universe where Maxwell's laws are correct in every frame respects relativity, and that a universe where QED is correct in every frame respects relativity, not to mention every other possible universe in which the laws of physics are the same in each frame and that things that move at c in one frame move at c in all frames.

In any case, if you want to define relativity via a set of axioms then you shouldn't include major implicit assumptions that aren't spelled out--the whole point of axioms is to spell out precisely what assumptions you want to make!

no, i think it's the other way. you do not want to itemize: "these are the specific laws of physics that the first postulate of SR applies to". if the postulate is fundamental (as i believe it is), then whatever system of physics that you show are valid

Huh? I didn't say anything about itemizing laws of physics, I'm the one arguing for general axioms that don't depend on any implicit assumptions about the specific form of the laws of electromagnetism, while you're the one arguing that we should implicitly take for granted that "all laws of physics" includes some specific theory like classical electromagnetism or QED where light has a constant speed. You need to do this because you've dropped the axiom that things that move at c in one frame move at c in all frames, and clearly the axiom "the laws of physics are the same in every inertial frame" alone is not enough to specify a relativistic universe without additional implicit assumptions about the exact form of the laws of physics, since this axiom would hold true in a universe obeying Newtonian laws as well.

(to whatever degree of experimental precision) in your inertial reference frame, that system of physics is just as valid in my inertial frame of reference, even if it is moving (at a constant velocity) with respect to yours. the postulate is that fundamental. and i think it's pretty damn reasonable.

And again, this axiom would hold true in a Newtonian universe (Galilean relativity), but we all know that a Newtonian universe is nonrelativistic because there is no invariant speed. That's why you need to include the notion of an invariant speed as a separate axiom, unless you want the first axiom to include implicit assumptions about the correct theory of electromagnetism.

 

[Al68]

a wave by definition requires a medium.

I'm surprised that no one has pointed out that EM (light) "waves" are not considered waves in the classical sense. So the classical definition of a wave (progressive disturbance of a medium) would not be relevant to modern theory which no longer uses that definition. It's only semantics, but you can't bait and switch definitions to make a point, it's just faulty logic.

Al

 

[Al68]

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?'

I see what you mean here. But I wouldn't consider length contraction, time dilation, or gravitational force to be fundamental laws. Maybe the inverse square law, but that's not a law of physics or gravity, it's just a property of (Euclidean) geometry, it doesn't explain how gravity works.

Of course it's silly to think of a "theoretical explanation" of the inverse square law, because it's just true by mathematical convention in geometry.

Al

 

[DrGreg]

no one is saying that Maxwell's equations are the specific physics that fall under the postulates of relativity but that Maxwell's equations are in the set of what is covered under the postulates of relativity. i guess some of them become unnecessary. but if they didn't become unnecessary, they're still physical law that is expressed within the context of relativity.

I would agree with that, but DaleSpam's message...

Don't both of those follow directly from applying Maxwell's equations in each frame?

...seemed to imply he couldn't see the difference between "falling under the postulates" and "being in the set of what is covered under the postulates" as you put it.

Bear in mind that all "laws" of physics boil down to being mathematical models that approximate to how our universe really behaves, and as our knowledge improves we may generate new models that are better approximations than our old models. The postulates of relativity reflect our current understanding of the constraints that we believe apply to all models. (And as our understanding evolves we may need to reinterpret the wording of the postulates.) The second postulate (however we word it) does seem to represent an additional constraint beyond the first postulate that we need to apply to all our models (of which Maxwell's equations are just one).

(By the way, I agree entirely with JesseM's posts #131 and #133.)

On a final note, when you get down to the mathematics of it all, the two postulates aren't really used directly; it all boils down to symmetries. Any relativity-compatible model is required to be locally "Lorentz covariant", which means, roughly speaking, its symmetry group must include the group of Lorentz transforms.

 

[Dale]

Yes, they do. But who said Maxwell's equations were one of the postulates of relativity?

Let me guess you might answer this by saying that Maxwell's equations are one of the "laws of physics" covered by the 1st postulate. To my way of thinking, that doesn't really cover it. The 1st postulate doesn't actually explicitly identify which laws of physics it applies to. Just "all of them", whatever they turn out to be. But the 2nd postulate is explicitly necessary for relativity to work, an intrinsic part of the theory itself, and therefore ought to be explicitly identified, albeit in the watered-down version I suggested.

I've never thought about this much, but I imagine it might be possible to invent some fictitious laws of physics for a hypothetical universe that are incompatible with Maxwell's equations but still fully compatible with the postulates of relativity, and with each other.

By the way, there was a heated exchange on this very subject on the talk page of Wikipedia's article on special relativity. See here.

OK, I can see the basic idea. First you throw out all physical laws. Then assume that whatever unknown set of physical laws are all frame invariant. Then you have to further specify that one of those unknown physical laws results in light going at c in all frames. I can see the approach, but I don't like it.

If you are going to throw out all physical laws and start from scratch, then just postulate the Minkowski geometry of spacetime (or symmetry groups as you mentioned). That seems better than throwing out all physical laws except one. Especially since if a photon is ever determined to have mass then light will not move at the invariant speed, but the invariant speed will still exist as part of the geometry of the universe.

Also, if I recall correctly the first postulate is often expressed as something along the lines "the same laws of electrodynamics and optics will be valid for all frames of reference for which the equations of mechanics hold good" which seems to include Newton and Maxwell both.

 

[rbj]

Sure, but my point is that you don't want your axioms to depend on implicit assumptions about the correct theory of electromagnetism, you want a broad definition of "relativity" that would allow you to see that a universe where Maxwell's laws are correct in every frame respects relativity, and that a universe where QED is correct in every frame respects relativity, not to mention every other possible universe in which the laws of physics are the same in each frame and that things that move at c in one frame move at c in all frames.

i wonder if "other possible universe" is nonsequitur.

anyway yeah, that's what i mean but the later part still follows from the first.

And again, this axiom would hold true in a Newtonian universe (Galilean relativity), but we all know that a Newtonian universe is nonrelativistic because there is no invariant speed. That's why you need to include the notion of an invariant speed as a separate axiom, unless you want the first axiom to include implicit assumptions about the correct theory of electromagnetism.

i don't see at all that it follows. i still think that an invariant c follows, semantically, from the first postulate of SR.

OK, I can see the basic idea. First you throw out all physical laws. Then assume that whatever unknown set of physical laws are all frame invariant. Then you have to further specify that one of those unknown physical laws results in light going at c in all frames. I can see the approach, but I don't like it.

If you are going to throw out all physical laws and start from scratch, then just postulate the Minkowski geometry of spacetime (or symmetry groups as you mentioned). That seems better than throwing out all physical laws except one. Especially since if a photon is ever determined to have mass then light will not move at the invariant speed, but the invariant speed will still exist as part of the geometry of the universe.

i think that is the more fundamental way to think about it. this essentially obviates the question we see here occasionally: "Why light?" questions, where my immediate answer is that it's not just light or EM, but this geometry of space and time that has this invariant c (which can be any real, positive, and finite value; call it "1", it doesn't matter), it's all fundamental interactions. this is, in my opinion, one level more fundamental than hearing that "information cannot be propagated at faster than c" postulate. i think this also follows from the fact that this geometry of space and time applies to any otherwise "instantaneos" interaction. you can't physically transmit information to anywhere else without the use of some physical interaction, all of which propagate at through space and time with at this unit speed.

Also, if I recall correctly the first postulate is often expressed as something along the lines "the same laws of electrodynamics and optics will be valid for all frames of reference for which the equations of mechanics hold good" which seems to include Newton and Maxwell both.

that's what i think. and i think that, semantically, that includes c (obviating the need for the 2^nd postulate), since Maxwell's equations can be easily rewritten with $\mu_0^{-1} c^{-2}$ replacing $\epsilon_0$. since $\mu_0$ is defined by the unit current (or, equivalently, the unit charge, if the unit time is independently defined) and c is just this other parameter in Maxwell's equations that remains invariant, simply because of the semantics of the 1^st postulate.

i continue to see no compelling need for the 2^nd postulate of SR. i think the 1^st postulate is necessary, and from what little i understand about GR, i think the equivalence principle is fundamentally a postulate (that seems reasonable, even though it would also seem reasonable, but less pleasing, if there were experimentally determined differences between inertial mass and gravitational mass).

 

[JesseM]

Sure, but my point is that you don't want your axioms to depend on implicit assumptions about the correct theory of electromagnetism, you want a broad definition of "relativity" that would allow you to see that a universe where Maxwell's laws are correct in every frame respects relativity, and that a universe where QED is correct in every frame respects relativity, not to mention every other possible universe in which the laws of physics are the same in each frame and that things that move at c in one frame move at c in all frames.

i wonder if "other possible universe" is nonsequitur.

Well, feel free to substitute "any possible new laws of physics we might discover in our own universe". For instance, suppose we find a TOE and find that its laws are actually Galilei-symmetric, not Lorentz-symmetric. If we construct our inertial coordinate systems so that they're related by the Galilei transform (and in a universe with Galilei-symmetric laws it should be possible to build types of rulers which don't shrink and types of clocks which don't slow down), isn't it still going to be true that the laws of physics are the same in every inertial frame? And yet clearly this would be a disproof of Einstein's notion of relativity.

i don't see at all that it follows. i still think that an invariant c follows, semantically, from the first postulate of SR.

Would not the first postulate still be true if it turned out the most fundamental laws were Galilei-symmetric rather than Lorentz-symmetric? But if you construct your inertial coordinate systems such that they're related by the Galilei transform rather than the Lorentz transform, then clearly an object moving at c in one frame can't be moving at c in all other frames, just by the way velocity addition works under the Galilei transform.

 

[atyy]

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.

Hi JesseM, another question to make sure I understand this definition correctly:

I enclose air in a rigid box, and declare the box the entire universe. I am an observer in the box who only has low energy tools, so air is a continuum to me, and all excitations of the air are sound waves. Let's assume Galilean relativity. This means I can travel at a speed that makes a sound wave stationary relative to me. But I guess from our earlier conversations that this only means the wave has a rest frame of its own, and isn't equivalent to the medium having no rest frame of its own. My previous understanding of air having a rest frame of its own was that air without sound waves could itself move relative to space. But that doesn't seem to work here, since the box is the entire universe. How is the rest frame of the air determined in this case? (I have a rigid ruler and protractor)