*Notes about some new advances to go on my home page*

It is possible that some deep things in nature can be explained by simple maths, just as Bohr’s atomic equation for energy levels matches spectroscopic line positions, and Restricted Relativity equations are good. But deep down, the maths is more complex, so Bohr’s vulgar atomic model is replaced by quantum mechanics, while Einstein replaced his own simplistic Restricted (‘Special’) Relativity with general relativity which is mathematically complex but describes absolute motions called accelerations!

At some level, the masses of fundamental particles will be explained. What we have to see is whether the equation will a Bohr-type inverse-square type law with a very simple heuristic energy level explanation, or whether it will come first as the solution to a massive abstruse theory with an infinite series of coupling terms that get harder to interpret heuristically. Another option is that the maths will be derivable in a totally new way: by guessing equations that summarise the empirical data compactly, then cooking up theories that predict the empirical equations plus other things. Nobody has ever done this before, have they? (Certainly not Einstein in 1905, Bohr in 1913, or Schroedinger in 1926.)

**Baryon, Meson, and Lepton mass predictions**

Taking things simply, the virtual vacuum surrounding each charge core is polarised, which screens the core charge. This is geometrical. The virtual positron-electron pairs in the vacuum are polarised: the virtual positive charges are attracted closer to the negative core than the virtual electrons, which are repelled to greater distances. Hence the real negative core has a positive virtual shell just around it, with a negative virtual shell beyond it, which falls off to neutral at great distances. This virtual particle or heuristic (trial and error) explanation is used in the Feynman approach to quantum field theory, and was validated experimentally in 1997, by firing leptons together at high energy to penetrate the virtual shield and observe the greater charge nearer the bare core of an electron.

Some 99.27 % of the inward-directed electric field from the electron core is cancelled by the outward-directed electric field due to the shells of virtual charges polarised in the vacuum by the electron core. Traditionally, the normal mathematics of quantum field theory has had the issue of having to be ‘renormalised’ to stop the electron core from interacting with an infinite number of virtual charges. The renormalisation process force-fits limits the size of the integral for each coupling correction, which would otherwise be infinity. Heuristically, renormalisation is limiting each coupling correction (Feynman diagram) to one virtual charge at one time. Hence, for the first coupling correction (which predicts the electron’s magnetism right to 5 decimals or 6 significant figures), the electron core charge is weakened by the polarised charge (positron shell) and is 137 times weaker when associating with 1 virtual electron in the space around the positive shell. The paired magnetic field is 1 + 1/(2.Pi.137) = 1.00116 Bohr magnetons, first term is the unshielded magnetism of the real electron core, and the second is the contribution from the paired virtual electron in the surrounding space, allowing for the transverse direction of the core magnetic field lines around the electron loop equator (the magnetic field lines are radial at the poles). My understanding now is that the transverse magnetic field surrounding the core of the electron is shielded by the 137 factor, and it is this shielded transverse field which couples with a virtual electron. The radial magnetic field lines emerging from the electron core poles are of course not attenuated, since they don’t cross electric field lines in the polarised vacuum, but merely run parallel to electric field lines. (This is a large step forward in heuristic physics from that a couple of weeks back.)

The pairing is the Pauli-exclusion process. Because an electron has a spin, it is a magnet. Every two adjacent electrons in the atom have opposite spin directions (up or down). There are two natural ways tou can put two magnets together, end to end or side to side. The side to side arrangement, with one North pole facing up and the other down, is most stable, so it occurs in the atom where the electrons are in chaotic orbits. The only way you can measure the spin of an electron is by using a magnetic field, which automatically aligns the electron, so the spin can only take two possible values (up or down), so the magnetism is either adding to or subtracting from the background field. You can flip the electron over by adding the energy needed for it to add to the magnetic field. None of this is mystical, any more than playing with magnets and finding they naturally align in certain (polar) ways only. The Pauli exclusion principle states that the four quantum numbers (including spin) are unique for every electron in the atom. Spin was the last quantum number to be accepted.

Now we so far have only been building a heuristic model for the abstract maths of QFT. Let’s now make a test of the model, a new test. If the electron core were to overcome the 137 vacuum shielding factor, its effective charge would be 137 times greater. It would then pull towards it 137 times as much virtual charge as a normal electron. Since inertial and gravitational mass arises from the miring resistance to acceleration by space (Higgs field or whatever), its core mass would be 137 times bigger, and spenting on average half its time paired to a similar virtual charge, the mass would be 137 + 0.5x137 = 205.5 times the electron mass. Is there such a particle, similar to the electron but 205.5 times as massive? This is the second charged lepton, the muon, with 206.8 times the electron mass!

A. O. Barut (Physical Review Letters, v. 42, 1979, p. 1251) decades ago came up with an empirical formula for the three charged lepton masses (electron mass 1, muon mass 206.8, and tauon with a mass of 3,492 electron mass units). Both of the heavier charged leptons under beta decay, which is interesting since they are fundamental particles. The muon has a 2.2 microsecond half-life, decaying into an electron and neutrino plus antineutrino.

**Dr Roger Penrose and the spacetime fabric**

On my home page and on Dr Peter Woit’s blog, I’ve referred vaguely to some good ideas from Penrose. I’ve just checked the references again, and find them better than I remembered. The first is the article by Penrose in the book compilation ‘It Must Be Beautiful’ about equations. First, Penrose explains the tensors of general relativity physically:

‘… when there is matter present in the vicinity of the deviating geodesics, the volume reduction is proportional to the total mass that is surrounded by the geodesics. This volume reduction is an average of the geodesic deviation in all directions … Thus, we need an appropriate entity that measures such curvature averages. Indeed, there is such an entity, referred to as the Ricci tensor, constructed from [the big Riemann tensor] Rabcd. Its collection of components is usually written Rab. There is also an overall average single quantity R, referred to as the scalar curvature.’

Einstein’s field equation states that the Ricci tensor, minus half the product of the metric tensor and the scalar curvature, is equal to 8.Pi.GT(ab)/c^2, where T(ab) is the mass-energy tensor which is basically the energy per unit volume (this is not so simple when you include relativistic effects and pressures). The key physical insight is the volume reduction, which can only be mechanistically explained as a result of the pressure of the spacetime fabric. On the same subject, spacetime fabric, Penrose has a nice heuristic illustration on page 677 of his tome, The Road to Reality. The illustration shows the electron core with the polarised sea of virtual charges, so that the virtual positrons are attracted close to the real electron core, while the virtual electrons are repelled further from the real core:

‘Fig. 26.10. Vacuum polarisation: the physical basis of charge renormalisation. The electron [core] E induces a slight charge separation in virtual electron-positron pairs momentarily created out of the vacuum. This somewhat reduces E’s effective charge [seen at a long distance] from its bare value – unfortunately by an infinite factor, according to direct calculation.’

Penrose gets it a bit wrong on page 678 where he says ‘the electron’s measured dressed charge is about 0.0854 [i.e., 1/square root of 137], and it is tempting to imagine that the bare value should be 1, say.’

In fact, the bare value in these units is 11.7, not 1, because the ratio of bare to veiled charge is 137, as the bare core electric force is hc/(2.Pi.x^2), proved on my home page, which is 137 times Coulomb. It the bare core charge is not completely ‘unobservable’ since in high energy collisions a substantial reduction of the 137 factor has been experimentally observed (Koltick, Physical Review Letters, 1997), showing a partial penetration of the polarised vacuum veil. The bare core of the electron, with a charge 137 times the vacuum-shielded one, is a reality. At early times in the big bang, collisions were energetic enough to penetrate through the vacuum to bare cores. (You can’t dismiss the electron core model as being not directly observable unless you want to do the same for atomic nuclei!)

**Background to mass ratios of elementary particles**

On my home page, I’ve applied the gravity mechanism to electromagnetism that has both attractive and repulsive forces, and nuclear attractive forces. These are all powered by the gravity mechanism in a simple way. Spinning charges in heuristic quantum field theory all radiate and exchange energy as virtual photons, which gets red-shifted when travelling large distances in the universe, due to the big bang. As a result, the exchange of energy between nearby similar charges, where the expansion of the universe does not occur between the charges, is strong and they recoil apart (repulsion), like two people accelerating in opposite directions due to exchanging streams of lead bullets from machine-guns! (Thank God for machine guns and big bangs, or physics would seem daft.) As a virtual photon leaves any electron, the electron must recoil, like a rifle firing a bullet. According to the uncertainty principle, the range of the virtual photon is half its wavelength. Since the inverse-square law is simple geometric divergence (of photons over increasing areas) with no range limit (infinite range), the wavelength of the virtual photons in electromagnetism is infinite. Hence, they are continuous energy flow, not oscillating. This is why you can’t hear steady electromagnetic forces on a radio: there is no oscillation to jiggle the electrons and introduce a resonate current. (Planck’s formula E = hf implies that zero net energy is carried when f = 0, which is due to the Prevost exchange mechanism of 1792 that also applies to quantum energy exchange at constant temperatures, where cooling objects are in equilibrium, receiving as much as they radiate each second.) When we accelerate a charge, we then get a detectable photon with a definite frequency. The spin of a loop electron is continuous not a periodic phenomena so it radiates energy with no frequency, just like a trapped electric TEM wave in a capacitor plate.

Electric attraction occurs between opposite charges, which stop virtual photons from each other’s direction, and so are pushed together like gravity, but the force is multiplied up from gravity by a factor of about 10^40, due to the drunkard’s walk (statistical zig-zag path) of energy between similar charges in the universe. This ‘displacement current’ of electromagnetic energy can’t travel in a straight line or it will statistically encounter similar numbers of equal and opposite charges, cancelling out the net electric field. Thus mathematical physics only permits a drunkard’s walk, in which the sum is gravity times the square root of the number of similar charges in the universe. A diagram in my April 2003 Electronics World article, and linked to on my home page, proves that the electric repulsion force is equal to the attraction force for equal charges, but has opposite directions depending on whether the two charges are similar in sign or different.

The result of this ‘electrogravity’ is that people dismiss the facts with experimental evidence – the prediction of the strength of gravity, strength of electromagnetism, and the mass ratio of electron to proton which results – as being ‘only a theory’ while applauding official ‘string theory’ which does nothing except create a mess with many dimensions that can’t be observed, and ‘parallel universes’.

In order to heuristically explain the abstruse 1 + 1/(2.Pi.137) = 1.00116 first coupling correction for the electron’s magnetism in QED, we suggested on Motl’s blog that the electron core magnetism is not attenuated by the polarised vacuum of space, while the electric field is attenuated by a factor of 137. The 2.Pi factor comes from the way a virtual electron in the vacuum couples with the real core electron, both of which are spinning. (Magnetism is communicated via the spin of virtual particles in the vacuum, according to Maxwell’s electromagnetism.) The coupling is related to the mechanism of the Pauli exclusion principle. The coupling is weakened by the 137 factor because the polarisation of virtual charges creates an inner virtual positron shell around the real electron core, with an outer virtual electrons shell. The polarised vacuum shields the core charge by a factor of 137.

The extra mass-energy of a muon means that interacts not only with virtual electrons and positrons, but also more energetic virtual particles in the vacuum. This very slightly affects the measured magnetic moment of the muon, since it introduces extra coupling corrections that don’t occur for an electron.

Could it be that the effect on the electron’s mass is greater for the same reason, but that the effect for mass is greater than magnetic field, because it doesn’t involve the 137-attenuation factor? Somehow you get the feeling that we are going towards a ‘bootstrap’ physics approach; the muon is more 207 times more massive than the electron, because the greater mass causes it to interact more with the spacetime fabric, which adds mass! (‘I pulled myself upward by my own bootstraps.’)

I don’t normally like this kind of physics! But this strange idea is not so weird when you look at the maths of contemporary modern physics. What you want is a prediction method that gives you not just the 207 ratio of muon to electron mass, but also some other ratios that can be checked against experiment. In other words, you want a general predictive mechanism and not one numerological fit.

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