Exploring the Variability of Big G & Dark Energy

[PeterDonis]

Are you saying that alpha changes iff e2 changes ?

No. I am saying that $\alpha$ doesn't change at all. You can "change" the value of $e$ or $h$ or $c$ by choosing different units. However, you can only pick two of those values by choosing units; once you've picked two, the third value is forced by the fact that $\alpha$ has to stay the same.

 

[hutchphd]

I thought the discussion here was changes to fundamental constants like G over time. I took this to mean changes instituted by the "hand of God". To my poor brain all you are saying is "by our definition of units if alpha changes then so must e²". I see that .
But if we entertain a "god" change in G over time why not then equally a change in e in the same spirit?

 

[PeterDonis]

I thought the discussion here was changes to fundamental constants like G over time.

As has been brought out in the discussion, calling $G$ a "fundamental constant" is problematic. What we call $G$ is a mixture of an inherent coupling constant of gravity, considered as an interaction (but we don't have a good underlying quantum theory of this interaction, so this is all speculative at this point) and a choice of units.

Also, even if we remove the choice of units and treat $G$ as a "fundamental constant" like $\alpha$, there is a key difference between them. Electromagnetism, as an interaction, is renormalizable; gravity is not. That is why $\alpha$ is a dimensionless constant but $G$ has units. (This was also discussed earlier in the thread.)

As far as actual evidence for $\alpha$ or the "fundamental constant" part of $G$ changing over time, we have none.

if we entertain a "god" change in G over time why not then equally a change in e in the same spirit?

Because the proper way to ask this question is not to ask if $e$ can change. It's to ask if $\alpha$ can change. (And, as I said just now, we have no evidence that it actually has. That is how to interpret my previous statement that $\alpha$ doesn't change at all.)

 

[Haelfix]

But the rest of my point stands. Variation of the gravitational coupling constant at least measures change in fundamental physics without dependence on any unit definitions.

You're guess about putting in the Planck Mass wasn't crazy, b/c that would be the naive yet natural scale to attempt to plug in for a reference system. And indeed the problem becomes manifest. Which is that
1) It is an intrinsically quantum regime, and so you have to make sense of that mess in order to really talk about the problem.
2) The value of 1 when you plug in the Planck mass^2 makes perturbation theory completely hopeless.. Which small parameter do you expand around?
3) Plugging in some arbitary reference value at scales that are order of magnitudes removed to get the dimensions to come out (like the mass of the electron and the mass of the proton) is very much a subjective choice that seems to have nothing to do with fundamental physics.

So then trying to get a hold on the problem using known methods of effective field theory it can be shown that the quantum mechanics of this putative dimensionless coupling constant is a great deal more involved than the analogous story with the QED version and the screening and running of the fine structure constant. So much so that there is doubt it even makes sense as a universal concept.