[tr0ll] so possibly... there's a region in the universe where the "Difficulty in learning OpenGL/GLSL" constant is non-infinite?? [/tr0ll]
Anyway... I'm a complete noob when it comes to scientific matters compared to Battman or Herra, but why would variance in physical constants imply variance in physical laws? Is there a concrete reason why this "alpha" (which I've never heard of btw, so this is all wild mass guessing) should be constant everywhere when, say, the speed of light isn't (in a non-vacuum)?
The speed of light in a non-vacuum is constant and equal to the speed of light in a vacuum. The speed of light never changes.
When you hear people talking about the speed of light changing in various materials, what they actually mean is that the photons run into various atoms and get absorbed, then re-emitted a while later. The actual speed of the photons is still C; they simply spend some of the overall travel time not existing.
Yeah, all photons while traveling move at c... non-vacuum medium however affects the group velocity of EM wave motion (even though individual quanta always travel at c through the intermediary vacuum!)
The group velocity of electromagnetic wave motion depends on the permittivity and the permeability of the medium. Vacuum has certain discrete values for these (electric constant aka. permittivity of vacuum and magnetic constant aka. permeability of vacuum). In vacuum, the velocity of EM-radiation is defined from Maxwellian equations as
c = 1 / (ε0 μ0)½where ε
0 is the permittivity of vacuum and μ
0 is the permeability of vacuum.
Basically, as far as electromagnetic wave motion is concerned, vacuum is not
nothing, as in, it impedes electric and magnetic fields at certain level - otherwise, if these values were zero, you can see that the speed of light in vacuum would be infinite and world would be, eh, quite a different place.
Now, the reason why this has any relevance to the topic is that the fine structure constant is tied to many different so-perceived constants of the nature - vacuum's permeability and permittivity being two of them (almost all the rest appear as well). To be specific, fine structure constant can be defined in following ways:
α = e2 / (4 π ε0) ħ cor
α = e2 c μ0 / 2 hor
α = ke e2 / ħ c...and the sharp-eyed of you might notice that the two notations are somewhat circular as they use both speed of light and/or electric/magnetic constant, making the definition a tad bit circular since speed of light depends on electric and magnetic constants. The third one is less so. The symbols used in these equations are:
e = elementary charge
ħ = "h-bar", reduced Planck constant (defined as h / 2π ) - h is obviously the Planck constant
c = speed of light in vacuum
ε
0 = electric constant (permittivity of vacuum)
μ
0 = magnetic constant (permeability of vacuum)
k
e = Coulomb constant
This is a bit of a mouthful to use in equations, of course, so most of the time electrostatic cgs units are used, where the Coulomb constant is 1 and dimensionless, and then the electroc constant can be abbreviated as
α = e2 / ħ c...and by now if you have any working knowledge of physics you should see that since the fine structure constant is basically a glue that ties pretty much all the natural constants
(save gravitational constant, though it's more of a part of Newtonian mechanics - general relativity uses metric tensors to resolve the curvature of space and resulting gravitational interactions, so its' a bit different than Newton's point source gravity fields interacting with each other...) together, and change in the fine structure constant could result (or cause) a change in any or all constants related to it.
This includes such basic stuff as charge of an electron and proton, the resulting attracting or separating forces, speed of light, the frequency of photons with certain energy (E = hf) and pretty much all equations of particle physics and cosmology as a result.
TL;DR - fine structure constant pretty much defines the, well, fine structure
of the vacuum.
If vacuum's properties change, everything in it changes as well. Including speed of light and almost all of quantum physics in general.