Is Gravi-GUT a candidate theory of everything?

[PeterDonis]

If c alone fully characterizes vacuum electromagnetism

The term "vacuum" might be causing a problem here.

$c$ alone fully characterizes source-free electromagnetism, at least classically. That's obvious just from looking at Maxwell's Equations. Even in SI units, if the source terms all vanish, $\mu_0$ and $\epsilon_0$ only appear in the product $\mu_0 \epsilon_0$ in the displacement current term, which of course is just $1 / c^2$. Just one parameter. And of course you can then derive wave equations for both the electric and magnetic fields that have them propagating at speed $c$.

It's when you have to deal with sources that you need a second parameter to describe the strength of the interaction with the sources--which in the modern view is best expressed by $\alpha$ since that's the dimensionless coupling constant for the electromagnetic interaction.

 

[renormalize]

If c alone fully characterizes vacuum electromagnetism, then Z₀ must be derivable from c without invoking ε₀ or μ₀ individually. Can you show that derivation, or cite a reference that does?
c gives you their product. Z₀ gives you their ratio. You need both to recover either one. Redistributing ε₀ into charge dimensions in CGS doesn't eliminate it — it moves it.

Not according to Wikipedia. The first 3 entries in the first column involve only $c\,$:

(https://en.wikipedia.org/wiki/Gaussian_units)
How do you explain that?

 

[ChrisF]

Not according to Wikipedia. The first 3 entries in the first column involve only $c\,$:
View attachment 371033
(https://en.wikipedia.org/wiki/Gaussian_units)
How do you explain that?

Your table actually illustrates the point I was making.

Rows 2 and 3 show that Gaussian units set epsilon_0 and mu_0 to dimensionless 1 by convention. Row 1 then gives Z_0 = 4*pi/c. But that 4*pi didn't come from c — it came from the convention in rows 2 and 3 that absorbed epsilon_0 into the unit definitions.

Row 4 confirms this. The fine structure constant in Gaussian units is alpha = (e^G)^2/(hbar*c). In SI it's alpha = (e^SI)^2/(4*pi*epsilon_0*hbar*c). These give the same dimensionless number only because e_Gaussian = e_SI /sqrt(4*pi*epsilon_0). The epsilon_0 that vanished from Z_0 is inside the Gaussian charge.

This is exactly what "redistributed, not eliminated" means. Gaussian units move epsilon_0 from the field equations into the charge definition. The physics — that electromagnetic coupling has a strength alpha independent of propagation speed c — is the same in both columns.

PeterDonis made this point well in his previous post: source-free EM needs only c, but coupling requires a second independent parameter alpha. Your own table shows two different notations for the same two-parameter physics.

And respectfully — I was asked for peer-reviewed references. Wikipedia is a useful summary, but shouldn't the same standard apply in both directions?

 

[PeterDonis]

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