# I If permeability and permittivity of the vacuum could be lowered, would this allow FtL communication?

#### TerranIV

Let's start with permeability. Do you think the 4π is a) an artifact of the definition of units or b) a physical constant that just accidentally happens to be 4π?
Do you think that something having a larger or smaller value than something else is dependent on units?
Do you think permeability of a volume is only determined by e_0?
Do you think that e_water = e_0?

#### TerranIV

You may want to try some of our many many threads about what would happen if $c$ had some other value.

The speed of light is determined by the permittivity and permeability values in the sense that given any two you can calculate the third, but that doesn’t mean what you think it does. I could just as reasonably argue that the permittivity is determined from the speed of light and the permeability, for example.

In fact, the value of all three depends only on our choice of units and the value of the fine structure constant, which being dimensionless has the same value (about 1/137) no matter what units we choose. Any physically meaningful change in the propagation of electromagnetic waves in a vacuum must imply a change in the fine structure constant; if that constant does not change the physics doesn’t change.
$c$ DOES have many values. $c0$ has a specific value. It doesn't matter what units you use to describe it. The units used determine the number of them when indicating the value.

The change of propagation of the electromagnetic waves in THE vacuum don't change, however if you make a change to the volume of space (fill it with water, fill it with glass, etc) this DOES change the speed EM waves propagate. If we changed the value of permittivity and permeability in the vacuum it would obviously no longer be THE vacuum.

I realize I am postulating a non-real volume to discuss how EM waves would propagate but I assumed most people in a physics forum would be familiar with the concept of a thought experiment. I guess I wasn't clear enough in my question.

Staff Emeritus
I notice you didn't answer my question. I think you're not here to learn, you're here to pitch your own iconoclastic beliefs.

#### Nugatory

Mentor
$c$ does have many values. $c0$ has a specific value
$c$ is the invariant speed in the special theory of relativity. It has multiple values only in the trivial sense that we can give it any value we please by appropriate choice of units (1 lightyear per year, 2999792458 meters/sec, 186000 miles per second, ....).

It so happens (as a consequence of the Lorentz invariance of Maxwell’s equations) that light propagates at that speed in a perfect vacuum. It also so happens (because of the historical accident that the speed of light was measured long before the discovery of Maxwell’s equations and then special relativity) that we casually refer to $c$ as “the speed of light” but that’s thinking about it backwards. It’s the invariant velocity, and light in a vacuum is one of the things that must propagate at that speed.

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#### Nugatory

Mentor
Do you think that something having a larger or smaller value than something else is dependent on units?
As long as we’re using the same units consistently (obviously the numerical value of the speed of light in water is greater than the numerical value of the speed of light in vacuum if we measure the first in miles per hour and the second in light years per years, but that’s just inconsistent units) then the answer is “of course not”. But now you’ve hit on why all the meaningful physics is in the dimensionless ratios. The ratio of the the speed of light in water to the speed of light in vacuum is the dimensionless quantity .75, and that’s a real comparison with real physical significance. Likewise, the ratio of the speed of light in vacuum to the invariant velocity of special relativity is 1.0.

Are you familiar with the modern definition of $\mu_0$ and $e_0$? Both have a fixed relationship to the fine-structure constant, so any “measurement” of either can serve only to refine our best known value for that quantity.

Staff Emeritus
Are you familiar with the modern definition of μ0\mu_0 and e0e_0? Both have a fixed relationship to the fine-structure constant
I don't think they do, since the fine structure constant is quantum mechanical, and c is purely classical:

μ0 is just the definition of the ampere. If one measures space and time in the same units (just as one measures northness and eastness in the same units), then ε0 = 1/μ0.

#### Dale

Mentor
c0 has a specific value. It doesn't matter what units you use to describe it.
Actually, if you dig down into this concept you will find that what you actually mean is not related to the speed of light but to the fine structure constant. Think, what do you mean by the specific value of the speed of light if you don’t use units to describe it.

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#### ohwilleke

Gold Member
I don't think they do, since the fine structure constant is quantum mechanical, and c is purely classical
The fine structure constant is quantum mechanical. c is just as much a part of quantum physics as it is a part of classical physics. Special relativity is observed in both Maxwell's equations and in QED.

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#### Nugatory

Mentor
Are you familiar with the modern definition of $\mu_0$ and $\epsilon_0$? Both have a fixed relationship to the fine-structure constant, so any “measurement” of either can serve only to refine our best known value for that quantity.
I don't think they do, since the fine structure constant is quantum mechanical, and c is purely classical:
I'm using (or misunderstanding?) the 2019 definitions. We have $\alpha=\frac{\mu_0}{2}\frac{e^2c}{h}$ with $e$, $c$, and $h$ all fixed, and we have $\epsilon_0=\frac{1}{\mu_0c^2}$. That leaves $\mu_0$ and $\alpha$ proportional to one another with a fixed constant of proportionality, and $\epsilon_0$ in a fixed relationship with $\mu_0$. Thus there is no freedom to vary them independently.

Staff Emeritus
Sorry this took so long. By the time I thought it through, I couldn't find the message any more.

I think we can agree that the equation alone is a necessary but not sufficient condition for a physical relationship in it. In the case of alpha, we don't want to imply that there is a relationship between c and the number 2 for instance. So we need to understand where each term comes from.

The h comes in because there is no classical way to measure alpha: it is purely quantum-mechanical.

The first complication is that one can "hide" the h. In units where h is 1, one can replace the h with a plain old one. In other units, you can absorb it in the definition of μ0. So one can write down what looks like a purely classical α, even though it is really quantum mechanical.

Are there any parts that can't be hidden? Yes, the e2. Not only is it present no matter what units you are using, every measurement of α on objects of charge q1 and q2 has a q1 and q2 in it. So that's real. And, to jump to A-level for one line, if you are discussing different fundamental forces, they have different coupling constants (α is the coupling constant for electromagnetism) because they have different elementary charges. So α is essentially the electric charge of the electron (squared).

Let me slightly rewrite what you wrote: $\alpha \sim \frac{e^2}{\epsilon_0}$. This is a force times a distance squared. You can sort of see where this is going to cause you trouble relativistically, because distance is not an invariant, and α, being just a number, must be. So the reason the c is there comes into the fact that by convention we measure space and time in different units. (To jump to an I.5 level for one line, this is actually wrapped up in the definition of ε0; it comes from Coloumb's Law, where you have a Force (which has a time derivative) on one side of the equation and something purely spatial on the other)

Had we worked in conventional units for airplane flight, where horizontal distances are measured in nautical miles and vertical distances in 100's of feet, we'd see the constant 60.76 appearing in these definitions as well.

So that's why I don't consider α a measure of c.

#### Dale

Mentor
So that's why I don't consider α a measure of c.
I agree that $\alpha$ is not a measure of c, but when people actually express what they mean by statements like “c has a specific value regardless of the units used to describe it” what they are looking at is in fact the fine structure constant.

Staff Emeritus
when people actually express what they mean by statements like “c has a specific value regardless of the units used to describe it” what they are looking at is in fact the fine structure constant.
I think that when people write that, they either don't believe in relativity, or they are completely confused.

Historically we measured time in seconds and length in meters. Also, for airplanes, we measure horizontal distances in nautical miles and vertical distances in 100-feet increments. In one case, you need c's and in the other you need 60.76's. They serve exactly the same function.

"If permeability and permittivity of the vacuum could be lowered, would this allow FtL communication?"

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