Yes, I do read Rivero’s papers and the model above is based in the major “coincidence” on one of them!

The paper http://arxiv.org/abs/hep-ph/0503104 by Hans de Vries and Alejandro Rivero, “Evidence for radiative generation of lepton masses”, 11 Mar 2005, inspired the model in my last comment.

They write that in November 2004 de Vries noticed numerical coincidences between the the anomalous magnetic moment of electron, and muon (mainly the Schwinger first coupling correction of alpha/(2*Pi)) appeared numerically close to the ratio of muon mass to Z boson mass, and to the ratio of electron mass to Z boson mass, respectively.

I was already interested in the relationship between alpha and particle masses, because I had some evidence that the core charge of the electron is e/(alpha) ~ 137e, and that the vacuum polarization between UV and IR cutoffs shielded it down to e. Therefore, the 137 factor 1/alpha is a general shielding factor where it crops up in quantum field theory. Most of the differences in masses between particles are artifacts of the way vacuum polarization shielding weakens the association between the standard model charge core and the mass-giving particle, which is well separated from the charge core and separated by two vacuum polarizations in the case of an electron (hence low mass) but is less shielded (one vacuum polarization shield only) in the case of the muon, tauon, and hadrons (differences in mass being due there to the number of particles present in the core, eg the number of quarks, and differences in the discrete number of mass-giving particles around the core), and is unshielded in the case of Z bosons, which have a 1:1 correspondence with mass giving particles, a bit like the idea of supersymmetry.

If this idea is right, obviously it has a way to go and is just a crude model at present. Ideally, you would want to get a way of calculating masses with all the necessary corrections and fine tuning so that the theory could be checked against data to high precision, not just with an accuracy of a couple of percent either way. That is likely to take time. However, it might not be that difficult. http://arxiv.org/abs/hep-ph/0503104 does show some relationships between vacuum polarization corrections and the “coincidences” in detail. I’d like to examine this carefully and see if it is possible to come up with a complete mechanism-based approach to calculating quantum field theory expansions for different loop corrections to mass.

The “fine tuning” of the mass model is obviously due to the loops of charges spontaneously appearing in the vacuum for a brief period, acquiring mass, and then disappearing.

So the accurate prediction of masses is likely to involve precisely the same kinds of calculations as are involved in calculating, say, the precise magnetic moment of the electron to 10 significant figures.

If this can be done to theoretically predict precise, empirically checkable values of masses for a range of particles, then the practical benefits of the model will be improved.

]]>For the neutral electroweak boson mass, the Z, 91 GeV:

91 GeV/ (2*Pi*137) ~ 105 MeV

similar to Muon mass.

91 GeV/ (3*Pi*137^2) ~ 0.51 MeV

similar to electron mass.

Hence the masses of at least two leptons may correlate with the Z boson mass, depending on whether the idea of empirical data leading theory is deemed numerological crackpotism or not. (Here, for convenience I’m using 137 to represent 1/alpha or 137.036…, which is close enough for present purposes.)

If you want to have all particles arising from a single particle, it would seem natural to have a Higgs mass of 91 GeV, similar to the Z mass. I think the Higgs particle is supposed to have spin-0, whereas the Z has spin-1.

But if the Higgs is giving mass to the Z directly, then you could expect them to have similar masses.

Taking the coincidence above for Z mass and muon mass,

91 GeV/ (2*Pi*137) ~ 105 MeV,

the 2*Pi*137 attenuation factor would contain 2*Pi for geometric reasons relating to spin and the 137 for vacuum polarization (muon charge core shielding) reasons.

For the electron mass,

91 GeV/ (3*Pi*137^2) ~ 0.51 MeV.

the mechanism would be similar to the mion except that there is a 50% bigger geometrical reduction factor and an additional 137 polarized vacuum shielding factor.

Taking accepted facts from QFT, the vacuum polarization exists in the range from the UV cutoff to the IR cutoff (e.g. from the Planck scale out to about 1 fm).

Hence, if the mass-giving particle is glued to a fermion or massive boson by a polarizable field, there are two possibilities for the mass.

If the mass-giving particle is so close that it is inside the polarized zone (say at a distance equal to the Planck scale), then polarization won’t shield and attenuate the mass.

But if the mass-giving particle is outside the IR cutoff distance, then the effective mass will be shielded by a factor of 137 with some geometric correction.

An analogy is the magnetic moment of leptons. Whereas Dirac calculated the magnetic moment of the electron as 1 Bohr magneton, Schwinger obtained a closer approximation to allow for the effect of the field on the magnetic moment, which is 1 + 1/(2*Pi*137) = 1.00116 Bohr magnetons.

Obviously there are lots of further corrections for vacuum interactions. However, this is by far the biggest and most important vacuum correction.

The vacuum field is increasing the core magnetic moment, not by 1 Bohr magneton, but by that amount reduced with a combination of shielding factors of 2*Pi*137.

If both the electron core and the particle which gives mass to the electron have a polarized vacuum, and these don’t overlap, then the total polarizing shielding of the field associating them will be by the 137^2 factor because each polarization will shield by 137 fold.

The 2*Pi multiplier for one vacuum polarization may increase to 3*Pi for the case of two vacuum polarizations, because they take up more space.

For hadrons, the mass is correlated closely to a similar formula:

91*n(N+1)/(6*Pi*137) = hadron mass (GeV)

= 35n(N+1) MeV,

where n is the number of quarks in the hadron core (n=2 for mesons, n=3 for baryons), and N is an integer (N = the number of Higgs bosons associated with the hadron?).

This formula does post-dict or correlate all meson and baryon masses +/- 2%.

The explanation for the structure of nuclei can involk nuclear shell theory “magic numbers” for N which denote nuclei of high stability, so N = 2, 8 and 50 predict relatively stable systems.

For n = 3 (baryons) and N = 8 (stable), 35n(N+1) = 945 Mev which is approximately the mass of neutrons and protons (938, 940 Mev).

For n = 1 (lepton) and N = 2, 35n(N+1) = 105 Mev (muon mass)

For n = 1 (lepton) and N = 50 (magic number), 35n(N+1) = 1785 Mev

which is similar to the tauon mass.

For n = 2 (mesons) and N = 1, we get 35n(N+1) = 140 Mev (pions have masses 139.57 and 134.96 Mev).

All the measured meson masses seem close to 70(N+1) MeV where N is an integer, while baryon masses are close to 105(N+1) MeV.

If this general model is correct, then the electron is the most complex particle there is, not the simplest.

The electron would have two polarization factors shielding it from the mass-giving particle by 137 squared, in addition to a geometrical factor.

The muon is simpler, with the mass-giving particle outside a simple polarized vacuum, and all hadrons are similar to the muon except for differing number of core particles at the centre.

The fact a quark has a fractional electric charge can be grasped from the crude (and physically impossible) idea of bringing together three electrons. The polarized vacuum shielding is driven by the electric field strength of the core.

If you make the core charge 3 times stronger, the polarized vacuum is 3 times stronger at shielding the core charge. Hence, if you could (impossibly) bring 3 electrons together so that the vacuum polarization of each exactly coincided, the increased charge would be cancelled out by the stronger vacuum polarization.

Thus the core charge would be 3*137*e but the observable charge beyond the polarized vacuum would be 3*137*e/(3*137) = e. Each electron in the core would therefore appear to have an apparent electric charge of 1/3 of the electron’s charge. This corresponds to what probably is the cause for the downquark charge of -1/3.

It is just a polarization effect. This is not obvious because it is severely cloaked in the standard model by complex effects of chiral symmetry and weak charge, the exclusion principle, and colour charge/strong force.

A quick calculation which claims to justify the idea that the vacuum polarization shielding factor for electric charge is 137 is as follows.

Using uncertainty principle, uncertainty in momentum p and distance x is:

h/(2*Pi) = px = (~mc)(~ct) ~ (mc^2)t = Et = Ex/c

hence x = hc/(2*Pi*E)

although x and E are just uncertainties in distance and energy, this result is a good prediction, for instance it correctly shows that the range of a 91 GeV boson is about 10^{-17} m.

Rearranging x = hc/(2*Pi*E) gives

E = hc/(2*Pi*x)

Hence we are justified in treating x and E as real distance and real energy, and using E = Fx to estimate force:

F = E/x = hc/(2*Pi*x^2)

This result for force between electrons is directly comparable to Coulomb’s law because both are inverse-square law forces.

It turns out that the quantum field force above is 137.036… times the Coulomb law for electrons. Hence, there is some evidence that the core charge of an electron is 137.036e, and that the polarized vacuum shielding reduces this to the observed electron charge value of e beyond a distance of 1 fm from the core.

I realise that this is very sketchy in places, but it does seem to me to tackle some diverse issues with a general framework.

The human question is, what this is trying to achieve. It certainly is quite a different idea to say string theory, where experimental data is treated as crackpot, and theories are developed in complete isolation from reality (ie, extra dimensions, unobserved superpartners and gravitons, branes, etc.).

I don’t think that string theorists would take kindly to data driven theorising in particle theory. So anything like this will just annoy them, and cause them to freak out and try to censor it. I’m wondering how much time and effort I can afford to put in to writing up proper-looking papers. The problem is, you have to do a good deal of exploration to get ideas roughly right, before writing any papers.

There are enormous gaps in the above ideas, such as how to rigorously predict quark charges other than the crude argument for the downquark having -1/3 because the electric field driven polarization of the vacuum around a triad of electrons would be three times stronger than that around a single electron, so the long range observable charge per electron in the triad would reduced by a factor of 3 from its normal value.

How to predict the upquark charge of +2/3 from this sort of polarization model? Presumably, that will involve going deeply into representation theory for the standard model. I’ve a sneaking idea that even if I did have a complete paper which did everything, it would still be censored out by those who are sure that only string theories are real physics.

]]>The full hilarity of the “*bra measurement search problem*” cannot be appreciated until you actually click on the google search.

This is a sort of revenge. Back when the internet was young, (and I was middle aged) us engineers used it to find information about ICs. Sometimes it seemed like you had to wade through fathoms of porn or other crap to find a part like a “hex inverter” or an “open collector buffer”.

]]>Is it merely coincidence that the W gauge boson mass is 80.403 ± 0.029 GeV?

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