### Varying Alpha

I have been enjoying some of the talks at this week's PI conference on the variation of fundamental parameters. M. Kozlov gives a clear outline of current results, such as a single source analysis for the three basic parameters, yielding the result consistent with zero variation. In a new analysis of varying $\alpha$ using absorption lines from many quasar sources, M. Murphy et al (MNRAS 2008) conclude that there is a variation of

$\frac{\Delta \alpha}{\alpha} = -0.44 \pm 0.16 \times 10^{-5}$

in disagreement with other results that are consistent with zero change. In the plot below, the black points are binned data. He gave convincing arguments that their analysis of cloud dynamics etc was careful, which is also the impression I got from reading the papers a few years ago, but the analysis is very complex, requires model fitting and the theoretical implications are always glossed over. The question I have is, since one can only assume that a theoretical explanation of varying $\alpha$ would have wide implications across all of physics, how reliable is the molecular theory input? Murphy also briefly discussed recent varying $\mu$ (proton electron mass ratio) results, which are consistent with zero variation for a $z = 0.685$ source.

$\frac{\Delta \alpha}{\alpha} = -0.44 \pm 0.16 \times 10^{-5}$

in disagreement with other results that are consistent with zero change. In the plot below, the black points are binned data. He gave convincing arguments that their analysis of cloud dynamics etc was careful, which is also the impression I got from reading the papers a few years ago, but the analysis is very complex, requires model fitting and the theoretical implications are always glossed over. The question I have is, since one can only assume that a theoretical explanation of varying $\alpha$ would have wide implications across all of physics, how reliable is the molecular theory input? Murphy also briefly discussed recent varying $\mu$ (proton electron mass ratio) results, which are consistent with zero variation for a $z = 0.685$ source.

## 4 Comments:

It is good that "varying constants" is now a subject of discussion. Flambaum and Murphy's work has led to a lot of controversy. Even Nelson Nunes' talk does not consider that you can reproduce an "accelerating universe" by changing the speed of light.

I must admit, I have not yet watched the Nunes' talk because, quite frankly, I find the idea that one needs to account for a classical fudge factor with unproven radical quantum gravitational ideas, well, ridiculous. If varying alpha is observable, what on Earth would we need the Dark Force for? It would have already lost it's explanatory power. But maybe it's an interesting talk.

The amount of variation that even Murphy is claiming for alpha is only 4.4 parts per million.

The time period over which this variation is supposed to occur is a large fraction of the age of the universe. Bohr's original theory of atomic quantum mechanics made alpha the ratio of the orbital speed of an electron v in the ground state of hydrogen to the velocity of light c (Sommerfeld first defined alpha in 1916):

v/c = 1/137.036... = alpha.

So a change in alpha would need to be accompanied by a reason why the ratio of electron speed in atoms to the velocity of light should be varying.

Maybe an interesting observation is that it seems to be the ratio between Coulomb's law for the force between two electrons and the fundamental force predicted by Heisenberg's uncertainty principle for virtual particles.

Heisenbergâ€™s uncertainty principle (momentum-distance form):

ps = h-bar (minimum possible uncertainty, there can be other sources of uncertainty in momentum p and distance s)

For relativistic particles the momentum p ~ mc, and distance s ~ ct.

h-bar = ps

= (mc)*(ct)

= (t)*(mcc)

= (t)*(mc^2) = tE = h-bar

This is the well-known energy-time form of Heisenbergâ€™s law. Now for the fun stuff.

E = h-bar/t

= h-bar*c/s

= Fs (work energy equals force multiplied by distance moved in direction of force)

F = h-bar*c/s^2

This force due to virtual particles is an inverse square law force (the 1/s^2 term). It is also different from the Coulomb force law by a factor of alpha!

(Penrose's book

Road to Realitygives a misleading suggestion that the observed charge in low energy physics for an electron is not alpha times the unobserved high energy bare core charge, but the square root of alpha, i.e. Penrose suggests there that the core charge of an electron is only 11.7 times the low energy observed charge. This comes from a naive argument that alpha is proportional not to charge but to the square of charge, so that charge is proportional to the square-root of alpha. The idea that alpha is proportional to the square of charge comes from the relation: alpha = (e^2)/[4*Pi*c*(h-bar)*Permittivity]. Although this includes e^2 in the numerator, there are several othyer factors in the denominator which together can be a function of e, so Penrose can't claim a direct proportionality between alpha and e^2 just by picking e^2 out in the numerator. E.g., by analogy Newton's law for force between masses m and M is F = mMG/r^2. This suggests that F is directly proportional to m and also directly proportional to M. But if we deal with gravity between two equal (e.g. fundamental particle) masses m = M, we then get something like F = (m^2)G/r^2, and using Penrose's argument we could falsely conclude that F is directly proportional to thesquareof mass, instead of concluding as we did previously that F was proportional to mass. So Penrose's argument that the ratio of observed electron charge to bare core charge is the square root of alpha is deeply flawed.)So alpha is the ratio of observed electron charge to bare-core charge. The observed electric charge of the electron is 137.036 times smaller than it's bare core charge, which is only observable at very high energy (the black hole event horizon radius from an electron, which is smaller than the Planck scale and thus requires energy beyond the Planck scale).

However this isn't untested speculation: a 7% increase in the electron's electric charge has been experimentally observed in 90 GeV collisions (I. Levine, D. Koltick, et al., Physical Review Letters, v.78, 1997, no.3, p.424), confirming the coupling or alpha value runs or increases at high energy, due to seeing less core charge shielding from the polarized vacuum which is partially penetrated when particles approach very closely in high-energy collisions.

So alpha in QFT seems physically to be the electron core charge to long ranges charge ratio, the dimensionless shielding factor by vacuum polarization. There is no strong physical mechanism apparent for this ratio to vary.

So maybe the best places to look for variations are not dimensionless numbers like alpha (or other ratios without any dimensionful units, e.g. the ratio of electron mass to proton mass) but alleged constants which do have units such as the velocity of light c, and the absolute strength of gravity and electromagnetism (or dimensionful measures of each).

It annoyed a while back to read in New Scientist the careless claim by some people investigating alpha, that, because alpha can be written to include light velocity c, it follows that the observational limits on alpha variation impose similar limits on c variation. That's totally incorrect, because c alone does not determine alpha

alpha = 1/137.036...

= (e^2)/[4*Pi*c*(h-bar)*Permittivity]

So if c was falling while the vacuum permittivity increased, alpha would remain constant. Altermatively, other kinds of changes to electron charge e and h-bar could occur without alpha changing.

However, the fact that alpha appears to show very little if any change over a large fraction of the age of the universe is still interesting for Louise's suggestion that c may fall with time.

Louise's equation GM = tc^3 suggests a couple of possibilities, including:

c = (GM/t)^{1/3}.

This is a large variation in c (a variation inversely proportional to the cube-root of the age of the universe), compared to Murphy's argument for a 4.4 parts per million variation in alpha.

E.g., for a time variation of half the age of the universe, Louise's suggestion c = (GM/t)^{1/3} leads to a factor of 2^{1/3} = 1.26, or 260,000 parts per million.

Taking Sommerfeld's v/c = alpha, the relatively little (or no) change in alpha compared to a massive change in c would suggest that v is changing in almost (or exactly) the same way as c is changing, in other words the speed of electrons in orbit may fall inversely in proportion to the cube root of the age of the universe for consistency between the alpha studies and Louise's c variation suggestion. I hope it gets more investigation.

I believe to remember that the original definition of alpha is not a velocity but an angular momentum. It is the maximum angular momentum for a closed relativistic orbit in a coulombian potential.

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