I have my hypothesis.

When examining early universe inflations and fundamental math structure I found that if energetic expansion tuned definitions for spatial dimensions one by one, then the charge structure could be based on separated shells of dimension grades just like that:

1 / (1^0+2^1+3^2+5^3+1^0/2^1*3^2/5^3) = 1 / 137,036

So the fine-structure constant α could be constant in uniform spacetime at euclidean quiet gravity field (vacuum). So permeability and permittivity follow gravitational and motional state of objects and so do α. It has larger value when object and oserver are in different reference frames. It's observed at LHC. The value of α have been measured shifting up to value 1/130 and over.

I wonder how you came to the conclusion that the fine structure constant and the electron charge could vary as a function of energy.

Both are known constants just like c.

Actually, both are defined as a combinations of other known constants:

$

\alpha = \frac{e^2}{2 \epsilon_0 h c}

$

just like c is defined as the product of 2 constants, one of which is epsilon_0, which also is included in the set defining alpha

$

\epsilon_0 \mu_0 c^2=1

$

The electron charge is possibly the most easily and best verified constant of the lot.

If even one of these constants had a varying value, at least one of the other constants that are needed to define it would also need to vary in opposition, which never could be experimentally even hinted at for any of the other constants.

Besides, Energy is expressed in joules, which requires the presence of 3 of these constants (the constant unit charge, epsilon_0 and alpha) and also a length in meters (a wavelength) for the units defining the joule to correctly pan out:

$

E = \frac{e^2}{2 \epsilon_0 \alpha \lambda}

$

In this equation, that involves both the charge of the electron and the fine structure constants, only the wavelength can be a variable to allow obtaining the actual energy for any wavelength in joules.

If you were to vary either the value of the charge or alpha, then the joules values obtained cease coherently matching the verifiable energy values related to the wavelength.

The definition of joules is

$

Joules = \frac{Coulomb^2 meter}{second^2}

$

if you omit the wavelength, you end up with Coulomb squared multiplied by the square of the speed of light, which does not define energy.

I hope this helps.

One important property of quantum mechanics in the QED theory is that the fine structure constant could be shown to vary with energy; it increases with increasing energy. At today's accelerators, for example the CERN LEP accelerator, the value has been measured as 1/128 rather than 1/137 at energies corresponding to approximately 100 billion electronvolts. If the energy dependence for the fine structure constant is depicted in relation to the energy, the curve slopes slightly upwards. Theoretical physicists say that the derivate, or the beta function, is positive.

http://www.nobelprize.org/nobel_prizes/physics/laureates/2004/popular.html

I hope this helps or have we better newer conclusions?

Thanks for the link Esa

This seems worth exploring.

But this brings the following questions to me because I see no mathematical relation being made with the other constants defining alpha in the article:

What other constant or constants in the set that defines alpha would also vary then in relation with alpha. Are there any experiments confirming such variation of at least 2 constants in the set (alpha plus one other)?

By structure, two constants in the set need to vary if even one becomes variable.

Electromagnetism is quite unforgiving you know. Nothing pans out according to verifiable reality if even one of these constants becomes variable.

It just crossed my mind also that epsilon_0 is defined with only one dimentioned constant, which is c, the speed of light. The only other component being pi, which is dimentionless and whose constancy has never been disputed, and for good reason.

$

\epsilon_0 = \frac{1}{4 \pi c^2 10^{-7}}

$

 This means that if epsilon_0 were to vary, then even the speed of light would also have to be variable in opposition.

For models integrity the Planck constants could better be real constants. So the local 4-dimensional speed of light can vary, 3-dimensional still being exact c.

So there is the need for extra (cyclic?) dimension...

ε0 = 1 / (μ0*c*c)

α = 1/(2*ε0)*e^2/(h*c0)

Where c0 is local value for speed of light and c is c. The local c0 is 4-dimensional quantity always smaller than c, ε0 doesn't vary but only the relation to Planck's constant in α.

So we are back to (c) and $(\epsilon_0)$ being constants (in vacuum).

On the other hand, it is a known fact that lignt travels slower than (c) in any material denser than vacuum or air. The same for the value of $(\epsilon)$ by the way.

Since this seems to relate to experiments carried out in a very high energy environment, it is quite possible that the alpha values obtained be related to this special environment.

If this is the case, this would mean nothing with respect to the fundamental constants, which have been established with respect to vacuum and it seems to me that someone on the research team would have been well advise to clarify the issue.

Yes, it would be nice to get some deeper information about what was actually explored, measured and gauged when got the raised value of alpha...

Total agreement

See Webb et al for measurement of alpha up to 10 billion years ago. They first reported a time variation but on using a second telescope they got the opposite sign for the variation so then changed their analysis, the best fit became no time variation but possibly a spatial variation. However, that may be an artefact of a slight difference in calibration between the two telescopes.

http://arxiv.org/abs/1008.3907

@George, although the paper mainly describes the spatial variations and threatens the equivalence principle i'm interested in the z-dependence of alpha. what would a smaller alpha -- α may have been smaller at high redshift, at the 5σ level -- imply?

Asher, Webb et al initially found α to be about 5.7ppm lower at high z using the Keck which is at 19.8 degrees north latitude.

Chand found the variation to be around -0.6ppm but with a comparable uncertainty.

However, Webb subsequently found it was higher in the past using the VLT which is at 24.6 degrees south. Overall, they then decided there was really no evidence for a time variation but instead suggested a spatial variation of the order of 1ppm.

The question is still open and the suggested variation remains disputed, an improvement in the measurements of an order of magnitude is really necessary to determine if it is real or not, and preferably from a single telescope which would need to be space based to cover the whole sky.

@George, I think I understand the spatial dispute, but what would have a smaller alpha imply had it been established ?