Relationship between charge of quarks and leptons is very simple (based on previous post):
the electron has a higher electric charge than a quark because some of the gauge boson (charge) energy of electromagnetism is used as color force (strong nuclear) binding energy in hadrons like mesons (pairs of quarks) and baryons (triads of quarks), and as weak force (for example, the weak force controls the decay of neutrons into protons, and free neutrons are thus radioactive)
which in the case of a single core particle (electron) is entirely used for long-range electric fields.
This immediately predicts that the nuclear binding energy in strong and weak forces is exactly equal to two-thirds of the electromagnetic charge (exchange photon) energy in a proton, and is equal to 100% in the case of a neutron. Presumably the extra energy used in a neutron is due to the weak force which controls beta radioactivity.
The prediction for the proton can be checked by doing a detailed analysis of force unification dynamics by energy conservation for the different gauge bosons as a function of distance/interaction energy (rather than by supersymmetry).
List of key issues in previous posts:
1. Lee Smolin's loop quantum gravity work.
2. Heisenberg's uncertainty relationship tells you the lifetime and radius of the loops of virtual charges in the vacuum: Et ~ h. Hence for electron energy scale (0.511 MeV), the lifetime for electron-positron pairs is on the order of 10^-21 second before annihilation, and a maximum separation distance on the order of 10^-12 metre. So the vacuum is after all radioactive, but only with very short-ranged ionising radioactivity which is can't disrupt atoms or molecules but is just able to upset electron orbits in atoms (like Brownian motion whereby air molecules affect pollen grains; David Bohm showed around 1952-4 that this sort of model can give rise to the Schroedinger equation for the statistical electron distributions in atoms).
3. Despite the short lifetime and range of the electron-positron pairs, they do have a structure according to quantum field theory, since they are definitely polarized around long-lived charges such as electrons. This is proved by the experimental success of renormalization in calculating Lamb shift and electron magnet moment to many significant figures, which physically implies a shielding of charges due to vacuum polarization. So although the vacuum is not stable, it is statistically simple in the overall effect. (Similarly, air pressure is predictable as the averaged impact effect from individual air molecules striking at random.)
4. The vacuum will also contain heavier pairs of charges (muons, quarks, etc) presumably in very much smaller abundances (due to the fact that the Heisenberg uncertainty principle, which implies that the duration of such charges is inversely proportional to their energy), except near matter where the strong electric field adds to the background vacuum energy density (which is due to gauge boson exchange radiation involves in the gravity and contraction of general relativity).
5. There are some severe problems in quantum field theory pertaining to the discontinuity introduced by the cutoff needed to prevent the electric charge of a single electron from setting off an infinitely extensive polarization of the vacuum of the universe which entirely cancels the electron's electric charge. This renormalization problem is mentioned in the Dirac and Feynman quotes on http://www.cgoakley.demon.co.uk/qft/. Ultimately these problems stem to the use of statistical equations (the wavefunction in the Schroedinger equation and Dirac equation doesn't tell you detailed facts, just averaged statistics) to obtain detailed facts which they are incapable of doing. Quantum mechanics for example is compatible with the exponential decay law of radioactivity. In reality, radioactivity decays in steps due to individual decay events, and it is only the averaged overall decay rate which approximates the exponential decay curve.
Reflecting on the log(E/A) type term mentioned in the previous two posts, on the one hand it could be that the log(E/A) type term may be right after all, if some mechanism can be found for the lower cutoff discontinuity. This low energy cutoff implies - if correct - that vacuum polarization only begins at a certain distance from the middle of the electron, where the electromagnetic field has just enough energy, to create electron-positron pairs in the vacuum which get polarized by the field and shield the electron charge. If this is the case, then the vacuum presumably does not contain any electron-positron pairs beyond that distance from an electron.
However, the log(E/A) type term is definitely wrong for another reason: the upper energy limit E allows the term to increase toward infinity as distance from the middle of the electron decreases towards zero. Because the vacuum polarization over a finite distance cannot have infinite shielding, this is clearly false. The bare core charge of an electron is not infinite, but ~137e- as demonstrated in previous posts (example here).
If we take the standard QFT electron charge formula to be e(x)/e(x = infinity) ~ 1 + [0.005 ln(A/E)], with E = 0.511 MeV and A the upper cutoff energy which is roughly inversely proportional to distance, we can roughly approximate the way the electron charge is supposed to vary as a function of distance from the middle of the electron.
For a 0.511 MeV electron-electron head on collision, the distance of closest approach is given by equating the entire kinetic energy of the moving electron to the potential energy of the electric field, (e-)2/(4.Pi.permittivity.distance of closest approach).
Obviously as energy increases beyond 0.511 MeV, the effective value of the electric charge (e-) decreases because there's less polarized vacuum causing electric field shielding between the two charges, and of course there can be energy losses due to elastic scatter effects (such as gamma ray emissions).
However, I'll do some calculations. In the meanwhile, just take the standard formula of the type e(x)/e(x = infinity) ~ 1 + [0.005 ln(A/E)]. If as a rough approximation you put 1/(scaled distance) for A, you might expect to get a feel for how the charge is supposed to vary with distance. It is very unnatural. Normally you get a natural logarithm in rearranging an exponential equation (finding the inverse function), so you would not mathematically expect that an exponential equation would usefully approximate a logarithmic one. However, you would expect that physically a vacuum polarization shielding should have some type of exponential term.
It is possible that the detailed dynamics of scattering effects like , in determining the relationship between collision energy and distance from middle of particle, make the correct relationship substantially different (from the simplistic low energy result that energy is proportional to 1/distance of closest approach).
Copy of a comment to http://evolutionarydesign.blogspot.com/2006/06/not-even-wrong.html
in case it is deleted for being too long:
"I wonder if ST or anything can really explain this: the *physical mechanism* of renormalization. Sure, they just deduct it with a rather ad-hoc math trick, but what in nature makes it happen? I don't see any good attempts to address this." - neil
Yes, renormalization is adjusting the electric charge and mass to make the theory work. The electric charge of an electron is only given by the normal databook value (in Coulomb's law, and Gauss'/Maxwell's equation for electric field divergence) at large distances.
The charged particle loops in the vacuum get polarised. Virtual electron-positron pairs exist for a period of about 10^-21 second before annihilating, and in this time they can separate by up to 10^-12 metre.
This is enough to allow them to get polarised around real (long-lived) electrons, with the virtual positrons being attracted and therefore on average closer to the real electron core than the virtual electrons which are repelled and on average are further for the electron core.
The shell of polarized vacuum charge therefore has a net radial electric field vector which points in the opposite direction to the electric field vector from the real electron in the middle, and nearly cancels it out. What we see as the electric charge on an electron is the small residue which is not cancelled by charge polarization.
Penrose in "Road to Reality" speculates that the central bare electron has an electric charge equal to the observed charge multiplied by the reciprocal of the square root of alpha, i.e., 11.7e. However, when you took at the natural charge suggested by Heisenberg's uncertainty principle, it is 137 times the Coulomb law for electrons, hence indicating the bare electron core has a charge of 137e.
Close to the electron, the charge increases because there is less intervening polarized vacuum shielding, and so there should be a variation of some sort from an asymptotic minimum charge of e at long distances to a maximum value of either 11.7e (Penrose) or 137e near the middle when you get past the polarized vacuum veil effect.
Renormalization is the failure of the mathematical solution to have the right asymptotic limits. The abstract QFT (including not just electron-positron polarization, but all the loops of other charges up to 92 GeV) suggests the electron charge is approximately
e + e[0.005 ln(A/E)],
where A and E are respectively upper and lower cutoffs, which for a 92 GeV electron-electron collision are A = 92,000 MeV, and E = 0.511 MeV. (Reference: http://electrogravity.blogspot.com/2006/06/relationship-between-charge-of-quarks.html)
The problem is the limits in this formula: the formula falsely predicts that the charge endlessly increases with collision energy (i.e., proximity to the electron core), which physically can't happen because you are going to have less and less polarization and eventually there won't be room for any pairs of charges to be polarized between you and the core.
It is also false because of the lower cutoff! Without the lower cutoff, the answer is infinity.
In theory, this is described as the problem that the entire vacuum of the universe should be polarized by a single electron.
Clearly you don't expect the lower limit of the cutoff to be zero in a logarithmic formula of this kind or you get infinity. So instead the electron rest-mass energy of 0.511 MeV is usually used as the lower cutoff.
But this is unnatural, because there is no reason. Again there is a large dose of engineering logic (common sense) missing from QTF.
It seems that there are two sources for the virtual charge creation-annihilation loops in the vacuum: the background energy density of the vacuum (gravitational gauge bosons for the spacetime fabric in general relativity, in a quantum gravity context), and the energy of the force field around a charge.
If the polarized vacuum around the electron core is mostly due to the the background energy of the vacuum, you'd expect it to have an exponential shielding so charge at distance x from an electron core would be modelled by something like
e + (137 - 1)e.exp(-ax)
which has the correct limits of charge e at large distances and charge 137e at short distances.
However, this semi-empirical Dirac sea model lacks a concrete mechanism for why the vacuum polarization doesn't shield 100% of the electron charge, leaving the electron neutral.
The alternative is that the charge pairs, which contribute to the polarised vacuum shielding of the electron core, are those produced by the field itself.
This would suggest a more complex relationship than the simple exponent, and the logarithmic result from abstract QFT is more acceptable.
You could then argue that the lower cutoff limit exists because there is a mechanism: beyond a certain distance, the electric field of the electron is too weak to poroduce and polarize pairs of charges in the vacuum.
I'm interested in the exact physical dynamics of this effect because I think it will explain force unification at high energy without SUSY speculation. It should also make checkable predictions, unlike SUSY.
For instance, since the quarks in a hadron are close together, they should share a mutual polarized vacuum. This should produce a greater shielding effect from the polarized vacuum (due to the higher energy density) than occurs around an electron if d, u quarks have electric charges of integer units, with the increased vacuum polarization shielding these down to effectively the fractional contributions in the Standard Model (-1/3, +2/3).
In this case, the fractional charge values of quarks has a natural physical explanation, and the charge reduction seen at large distances may be balanced by the energy of the nuclear binding forces (color and weak) at short distances.
If you think about force unification in terms of distance instead of interaction energy, you start to get into real, practical physics models. For instance, what happens to gauge boson energy when the charge varies with distance? It's pretty likely that the cause of unification at extremely high collision energies (near the middle of a particle) is due to conservation of energy for the different force gauge bosons. The Yang-Mills interaction picture seems to completely neglect physical dynamics of how the energy of exchange bosons is conserved. When a force strength (alpha) varies as a function of distance, the exchange energy passing through the surface must remain the same . Think about Green's theorem or hydrodynamics when contemplating exchange radiation. If you physically shield the charge (gauge bosons exchange dynamics), by vacuum polarization or whatever, the energy has to go either into heating the shield up or it gets converted into another force.
This is just what is observed in high energy physics: weak and electromagnetic charges increase with interaction energy, and the strong force coupling strength falls. Therefore, you'd expect unification without SUSY from conservation of charge energy.
If the strong force falls because the electroweak force is rising, then eventually you get perfect unification, unlike the picture in the Standard Model (minus SUSY) where the forces cross-over and go on increasing or falling indefinitely.
There is too much prejudice in favor of an abstract solution to the final theory. I think the guys responsible [for SUSY] must be the real geeks who can integrate any function in their heads, but don't have the time to think about whether extra dimensional speculation is really relevant to the problem of modelling effects in a cloud of charges around a particle.