# Permeability/permittivity constants and one way speed of c

## Main Question or Discussion Point

I have heard people argue about an anti-symmetric synchronizing convention allows for a different or even an infinite one-way speed of light. I thought about it and I wanted to know what you thought about the notion that the permeability and permittivity constants completely preclude this notion of a one-way speed of light equal to anything other than c.

Basically, it seems to me that since the permeability and permittivity constants are measured using your basic electromagnetic objects like magnets and capacitors, that measuring their values has nothing to do with any synchronizing convention. And since c = 1/sqrt(permeability*permittivity), the only possible way for c to ever be infinite is if one or both can be measured to be zero, and only possible way for it to be anything other than c is if both of them change.

Thus the whole notion seems to be complete nonsense. There is no way either can be found to be zero (or anything other than their normal value) since, unless I'm mistaken here, any measurement in a suitable reference frame will give the same value. The laws of physics are the same in all reference frames, therefore the constants of the universe have to be the same, correct? There isn't a preferred reference frame so there is no reason for either or these constants to ever be zero (or anything other than what they are defined to be).

So, it seems to be that unless you conveniently forget that light is an electromagnetic wave, there is no possible way for the speed of light to be anything but c no matter what direction it is going.

Is this a reasonable conclusion? Why or why not?

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Nugatory
Mentor
Thus the whole notion seems to be complete nonsense. There is no way either can be found to be zero (or anything other than their normal value) since, unless I'm mistaken here, any measurement in a suitable reference frame will give the same value. The laws of physics are the same in all reference frames, therefore the constants of the universe have to be the same, correct? There isn't a preferred reference frame so there is no reason for either or these constants to ever be zero (or anything other than what they are defined to be).

So, it seems to be that unless you conveniently forget that light is an electromagnetic wave, there is no possible way for the speed of light to be anything but c no matter what direction it is going.

Is this a reasonable conclusion? Why or why not?
If it were really that simple it wouldn't have taken almost a half-century (1861 to 1905) to figure it out... You have the benefit of more than a century (1905 to now) of hindsight and unimpeachable experimental results to support your conviction that Einstein's second postulate is the only reasonable way to reconcile the first postulate and Maxwell's electrodynamics.

That experience is leading you to make the leap from "the laws of physics are the same in all inertial frames" to "there is no preferred frame" without even noticing that it's a leap. Why shouldn't the measured value of the permeability and permittivity constants and hence the speed of light differ slightly according to your velocity relative to some hypothetical ether? (Consider that the laws of hydrodynamics are the same in all inertial frames, but any sailor knows that the frame in which you are at rest relative to the water is special). In denying that possibility you're making an assumption subject to validation through experiments equivalent to Michelson-Morley.

Of course in hindsight we know that it's a really good assumption and it's hard to imagine how it could be otherwise - but that's hindsight.

With that said, I have to admit that I often use your argument that electrodynamics working in all frames implies a constant speed of light. With tongue in cheek I paraphrase the second postulate as "And I'm serious about the first postulate, especially when it comes to Maxwell's equations". It's a very powerful hand-waving argument, with the pedagogical advantage that we don't have to introduce the luminiferous ether just to reject it... But I'm cutting a corner, leaving a crucial assumption unstated on the grounds that it's so natural an assumption that I don't need to distract my audience by mentioning it point it out. It wasn't always that natural.

• Battlemage!
If it were really that simple it wouldn't have taken almost a half-century (1861 to 1905) to figure it out... You have the benefit of more than a century (1905 to now) of hindsight and unimpeachable experimental results to support your conviction that Einstein's second postulate is the only reasonable way to reconcile the first postulate and Maxwell's electrodynamics.

That experience is leading you to make the leap from "the laws of physics are the same in all inertial frames" to "there is no preferred frame" without even noticing that it's a leap. Why shouldn't the measured value of the permeability and permittivity constants and hence the speed of light differ slightly according to your velocity relative to some hypothetical ether? (Consider that the laws of hydrodynamics are the same in all inertial frames, but any sailor knows that the frame in which you are at rest relative to the water is special). In denying that possibility you're making an assumption subject to validation through experiments equivalent to Michelson-Morley.

Of course in hindsight we know that it's a really good assumption and it's hard to imagine how it could be otherwise - but that's hindsight.

With that said, I have to admit that I often use your argument that electrodynamics working in all frames implies a constant speed of light. With tongue in cheek I paraphrase the second postulate as "And I'm serious about the first postulate, especially when it comes to Maxwell's equations". It's a very powerful hand-waving argument, with the pedagogical advantage that we don't have to introduce the luminiferous ether just to reject it... But I'm cutting a corner, leaving a crucial assumption unstated on the grounds that it's so natural an assumption that I don't need to distract my audience by mentioning it point it out. It wasn't always that natural.
Oh yeah I can appreciate how difficult it was come to these conclusions, especially considering how obviously common sense the Galilean transformation is (you have now also made me notice the jump in reason from all inertial reference frames being equally valid to their being no preferred reference frame). Even now as I understand it there isn't an observable difference between the Lorentz aether type relativity and special relativity (not that this topic is about that. It's only about permeability/permittivity and the one-way speed of light). But are you saying that the permeability and permittivity constants could CONCEIVABLY have different values in different reference frames if we assume the principle of relativity is valid? If so how would that occur or what kind of situation would allow that?

Dale
Mentor
I thought about it and I wanted to know what you thought about the notion that the permeability and permittivity constants completely preclude this notion of a one-way speed of light equal to anything other than c.

Basically, it seems to me that since the permeability and permittivity constants are measured using your basic electromagnetic objects like magnets and capacitors, that measuring their values has nothing to do with any synchronizing convention.
The vacuum permeability and permittivity don't really have anything to do with physics anyway. They are purely artifacts of your choice of units. They are even more arbitrary than the choice of synchronization convention.

• Battlemage!
The vacuum permeability and permittivity don't really have anything to do with physics anyway. They are purely artifacts of your choice of units. They are even more arbitrary than the choice of synchronization convention.
Huh. But so is the speed of light, right? If it can be written as a function of those two?

But what about this. What if we agreed upon certain units to use in every frame of reference. Could the argument make sense then? (that since c is always 1/sqrt(u*e) c cannot be infinite unless one or both are zero, which can't happen).

Dale
Mentor
Huh. But so is the speed of light, right?
Yes. This is why the speed of light can be arbitrarily set to an exact value by a vote of the BIPM.

What if we agreed upon certain units to use in every frame of reference. Could the argument make sense then?
The argument makes perfect sense, but it doesn't mean anything about physics. Yes, you can make one arbitrary choice which is then logically incompatible with another arbitrary choice. But you can't use one arbitrary choice to "disprove" another.

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Nugatory
Mentor
But are you saying that the permeability and permittivity constants could CONCEIVABLY have different values in different reference frames if we assume the principle of relativity is valid? If so how would that occur or what kind of situation would allow that?
The vacuum permeability and permittivity don't really have anything to do with physics anyway. They are purely artifacts of your choice of units. They are even more arbitrary than the choice of synchronization convention.
This is true (and more important than OP probably realizes) but I think that he's asking a different question. If two observers make the same arbitrary choice of units so that they can assign comparable numerical values to these quantities, is it possible that they will find different numerical values if they are in relative motion?

The answer is certainly not if the second postulate is accepted, the speed of light is the same for all observers, and there is no preferred frame.
However, if there were a luminiferous ether and the behavior of electromagnetic phenomena depended on the motion of the source relative to that ether, then such differences would be observed and these differences could be used to identify the preferred frame that is at rest relative to that hypothetical ether. One such difference would be a slight variation of the speed of light in various directions as measured by any experimenter not at rest in the preferred frame; that's essentially what the MMX experiment looked for and didn't find.

• Battlemage!
jtbell
Mentor
The vacuum permeability and permittivity don't really have anything to do with physics anyway. They are purely artifacts of your choice of units. They are even more arbitrary than the choice of synchronization convention.
Huh.
I guess you've never done electromagnetism in Gaussian units, in which $\varepsilon_0$ and $\mu_0$ don't appear at all, but c does. This is common in advanced electromagnetism textbooks and in research work.

In a medium, one still has the (relative) permittivity $\varepsilon$ and permeability $\mu$.

• Battlemage!
Dale
Mentor
The answer is certainly not if the second postulate is accepted,
I agree with this, but since the OP is asking about non standard synchronization conventions I don't think that we can assume the second postulate is accepted.

I agree with this, but since the OP is asking about non standard synchronization conventions I don't think that we can assume the second postulate is accepted.
How about this (note obviously this is ridiculous but it is one of the ideas I have seen regarding this topic from quacks): the round trip speed of light is c, but the outward speed is infinity and the return speed is 0.5c. The net result is the beam will take the same time if it went c in both directions. If the object is one light year away, if c is constant both up and back, the time is given by: (cy)/c + (cy/c) = two years. Likewise if c is infinite on the way to the object and 0.5c on the way back, the time is: (cy/infinity) + (cy/.5c) = 0 + 2 years = two years.

So lets assume the second postulate applies to round trips of light but not the one way speed of light. Would this then be incompatible with the two free space constants assuming everyone involved chooses the same units?

Nugatory
Mentor
So lets assume the second postulate applies to round trips of light but not the one way speed of light. Would this then be incompatible with the two free space constants assuming everyone involved chooses the same units?
That's not the second postulate. The second postulate is that speed of light is the same for all observers, not that the round-trip speed of light (literally, distance out and back divided by time elapsed between emission and reception) is the same for all observers. The latter claim can be tested experimentally, but the former has to be assumed.

You can and have made a strong case that the alternatives to that assumption are all implausible, but that doesn't make them wrong - the universe doesn't care what we think is plausible. The assumption is attractive (almost irresistibly so) so I have no qualms about accepting it, but it's still an assumption.

• Battlemage!
That's not the second postulate. The second postulate is that speed of light is the same for all observers, not that the round-trip speed of light (literally, distance out and back divided by time elapsed between emission and reception) is the same for all observers. The latter claim can be tested experimentally, but the former has to be assumed.

You can and have made a strong case that the alternatives to that assumption are all implausible, but that doesn't make them wrong - the universe doesn't care what we think is plausible. The assumption is attractive (almost irresistibly so) so I have no qualms about accepting it, but it's still an assumption.
It just doesn't make much sense to me for it not to be completely symmetrical. I keep thinking there's got to be something that would theoretically prevent something being so seemingly arbitrary.

Dale
Mentor
So lets assume the second postulate applies to round trips of light but not the one way speed of light. Would this then be incompatible with the two free space constants assuming everyone involved chooses the same units?
I don't think so, but I rarely work with SI units in EM problems if I can avoid them. I would have to work through the math.

Dale
Mentor
It just doesn't make much sense to me for it not to be completely symmetrical. I keep thinking there's got to be something that would theoretically prevent something being so seemingly arbitrary.
It doesn't make sense, which is why nobody actually assumes it in practice. But there is nothing that theoretically prevents it.

Mister T
It's very possible that the equation $c^2=\frac{1}{\epsilon_o \mu_o}$ is valid only in a frame of reference in which the observer is at rest. It takes experimental verification to show that it's true in all frame of reference and hence that the Principle of Relativity (equivalence of all inertial reference frames) applies not just to mechanical phenomena, but also to electromagnetic phenomena. At least that's the current state of our understanding.
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