That it reduces with gravitational potential.
What exactly do you mean “reduces with gravitational potential”? How exactly would such a reduction be a “test” of if “a gravitational field was the result of a gradient in the relative strength of the strong force and electromagnetic force” as you asserted?
Not directly. What you quoted says "Given two hypothetical point particles each of Planck mass and elementary charge, separated by any length, α is the ratio of their electrostatic repulsive force to their gravitational attractive force".
You’ll note the part where it directly says “α is the ratio of their electrostatic repulsive force to their gravitational attractive force.” So yes directly.
But Planck mass is 2.389 x 10²² times the electron mass, and you've got two of them.
How observant of you to note that the plank mass is larger than the mass of an electron and similarly very observant of you to note that there are two charged masses in this consideration. Any other obvious observations you’d care to, well, observer.
I’ll note that you didn’t make note of the fact the mass of the sun is 1.99 x 10
38 times the planks mass and you’ve only got one of them in your “test”.
The fine structure constant is usually described as being 1/137, but it's a running constant, see
NIST. It isn't constant.
An aspect one could observe as being noted on page one of this thread, as well as your claim that…
...I can tell you why the fine structure constant takes the value it does, and why it's a running constant.
A demonstration that has yet to be observed. Two years have past now, are you any closer to actually fulfilling that claim?
Let's write that as α = e²αg/4πε0m²G and compare it with α = e²/4πε0ħc. The e is said to be "effective charge", but the electron unit charge doesn't actually vary, only the effect of it when it's in a different environment.
“different environment”? What’s different about the “environment”?
Oh and if you compare “α = e²α
g/4πε
0m²G” with “α = e²/4πε
0ħc” as you assert to do then you will find α
g/ m²G = 1/ħc
Since the 4π doesn't vary, what's actually varying is ε0 and/or ħ and/or c. Since permittivity is intimately related to permeability, and since c = √(1/ε0μ0) let's say that ε0 and c are both varying.
Why? As “e is said to be "effective charge", and "effective charge" can vary (see your own citation
NIST)? Just to give you a hint that’s why it’s called the “effective charge". Also “Since permittivity is intimately related to permeability” that means μ
0must remain constant or change in such a way that c does not remain constant. Oh I know why, because all you want to actually say is just that c is varying.
This is borne out by the way the coordinate speed of light varies in a non-inertial reference frame - optical clocks run slower at lower gravitational potential. I'll leave Planck's constant alone for now, but note that nothing in sacrosanct.
“nothing in sacrosanct”? You mean except for your desire to have c vary as opposed to just the "effective charge" varying (as your own citation claims) or even both ε
0 and μ
0. Heck you could have even went for ħ but choose to leave it alone for now to preserve the sanctity of your varying c.
Anyway, your expression employs αg and m² and G instead of ħ and c. I prefer to work with the latter myself, but nevermind. If c is varying one at least one of your terms is varying too. The m is varying for sure. If you lift a brick you do work on it, and you give it gravitational potential energy. This is real energy, and it's now in the in brick. So the mass of the brick has increased. The energy isn't in the gravitational field, because if you lift the brick so much that it escapes the earth's gravitational field, the energy you supplied has gone.
Wait, what? “the energy you supplied has gone”? Has gone where in you notion exactly? Under the consideration of binding energy and bound states “the energy you supplied has gone” into increasing the gravitational potential energy of the brick in relation to the Earth. Unless of course your claim is that as the brick get higher its gravitational potential energy increases and then suddenly at some mysterious point “it escapes the earth's gravitational field” and no longer has any gravitational potential energy in relation to the earth.
And if m varies with gravitational potential, the gravitational coupling constant is looking a bit shaky. Sorry, the wife is calling me, I have to go, but note that constants aren't always constant, and see
mass in general relativity.
You mean “constants aren't always constant” unless you just want them to be, so the constant c will vary. If the "effective charge" varies then so does the fine structure constant without any change in the other, well, constants.