Quantum gravity and the mainstream misunderstanding of electroweak gauge theory


Above: the incorporation of mass (gravitational charge) and quantum gravity (spin-1 gravitons) into the empirical, heuristically developed Standard Model of particle physics. SU(3) colour charge theory for strong interactions and quark triplets (baryons) is totally unaltered. The electroweak U(1) x SU(2) symmetry is radically altered in interpretation but not in mathematical structure! Conventionally U(1) represents weak hypercharge and SU(2) the weak interaction, with the unobserved B gauge boson of U(1) ‘mixing’ (according to the Glashow/Weinberg mixing angle) with the W0 unobserved gauge boson of SU(2) to produce the observed electromagnetic photon, and the observed weak neutral current gauge boson, the Z0. (It’s not specified in the Standard Model whether this mixing is supposed to occur before or after the weak gauge bosons have actually acquired mass from the speculative Higgs field. The Higgs field is a misnomer since there isn’t one specific theory but various speculations, including contradictory theories with differing numbers of ‘Higgs bosons’, none of which have been observed. Woit mentions in Not Even Wrong that since Weinberg put a Higgs’s mechanism into the electroweak theory in 1967, the Higgs theory is called ‘Weinberg’s toilet’ by Glashow – Woit’s undergraduate adviser – because, although a mass-giving field is needed to give mass to weak bosons and thus break electroweak symmetry into separate electromagnetic and weak forces at low energy, Higgs’ theories stink.)

In the empirical model we will describe in this post, U(1) is still weak hypercharge but SU(2) without mass is electromagnetism (with charged massless gauge bosons, positive for positive electric fields and negative for negative electric fields) and left-handed isospin charge (forming quark doublets, mesons). The Glashow/Weinberg mixing remains, but the massless electrically neutral product is the graviton, an unobservably high-energy photon whose wavelength is so small that it only interacts with the tiny black hole-sized cores of the gravitational charges (masses) of fundamental particles. This has the advantage of making U(1) x SU(2) x SU(3) a theory of all interactions, without changing the experimentally-confirmed mathematical structure significantly (we will show below how the Yang-Mills equation reduces to the Maxwell equations for charged massless gauge bosons). The addition of mass to the half of the electromagnetic gauge bosons gives them their left-handed weak isospin charge so they interact only with left-handed spinors. The other features of the weak interaction (apart from just acting on left-handed spinors) such as the weak interaction strength and the short range, are also due to the massiveness of the weak gauge bosons. has particular advantages to electromagnetism and leads to quantitative predictions of the masses of particles, and predicting the force coupling strengths for the various interactions. E.g., as shown in previous posts, a random walk of charged electromagnetic gauge bosons between similar charges randomly scattered around the universe gives a path integral with a total force coupling that is 1040 times that from quantum gravity, and so it predicts quantitatively how electromagnetism is stronger than gravity:

final-theory21Above: some benefits of the new theory for physically understanding electromagnetic interactions (without invoking the magical ‘4-polarization photon’), understanding fields, resolving anomalies in electromagnetism, and predicting masses of fundamental particles and the strength of electromagnetism relative to gravity (electromagnetism is theoretically stronger by the square root of the number of fermions, 1080/2 = 1040). If a discrete number of fixed-mass gravitational charges clump around each fermion core, ‘miring it’ like treacle, you can predict all lepton and hadron inertial and gravitational masses. The gravitational charges have inertia because they are exchanging gravitons with all other masses around the universe, which physically holds them where they are (if they move, they encounter extra pressure from graviton exchange in the direction of their motion, which causes contraction, requiring energy; hence resistance to acceleration, which is just Newton’s 1st law, inertia). The illustration of a miring particle mass model shows a discrete number of 91 GeV mass particles surrounding the IR cutoff outer edge of the polarized vacuum around a fundamental particle core, giving mass. A PDF table comparing crude model mass estimates to observed masses of particles is linked here. There is evidence for the quantization of mass from the way the mathematics work for spin-1 quantum gravity. If you treat two masses being pushed together by spin-1 graviton exchanges with the isotropically distributed mass of the universe accelerating radially away from them (viewed in their reference frame), you get the expected correct a prediction of gravity as illustrated here. But if you do the same spin-1 quantum gravity analysis but only consider one mass and try to work out the acceleration field around it, as illustrated here, you get (using the empirically defensible black hole event horizon radius to calculate the graviton scatter cross-section) a prediction that gravitational force is proportional to mass2, which suggests all particles masses are built up from a single fixed size building block of mass. The identification of the number of mass particles to each fermion (fundamental particle) in the illustration and in the table here is by the analogy of nuclear magic numbers: in the shell model of the nucleus the exceptional stability of nuclei containing 2, 8, 20, 50 or 82 protons or 2, 8, 20, 50, 82 or 126 neutrons (or both), which are called ‘magic numbers’, is explained by the fact that these numbers represent successive completed (closed) shells of nucleons, by analogy to the shell structure of electrons in the atom. (Each nucleon has a set of four quantum numbers and obeys the exclusion principle in the nuclear structure, like electrons in the atom; the difference being that for orbital electrons there is generally no interaction of the orbital angular momentum and the spin angular momentum, whereas such an interaction does occur for nucleons in the nucleus.) Geometric factors like twice Pi appear to be obtained from spin considerations, as discussed in earlier blog posts, and they are common in quantum field theory. E.g., Schwinger’s correction factor for Dirac’s magnetic moment of the electron is 1 + (alpha)/(2*Pi).

Beta radioactivity, controlled by the weak force, is the process whereby neutrons decay into protons, electrons and antineutrinos by a downquark decaying into an upquark by emitting a W weak boson which they decays into an electron and an antineutrino.

This weak interaction is asymmetric due to the massive gauge bosons: free protons can’t ever decay by an upquark transforming into a downquark through emitting a W+ weak boson which then decays into a neutrino and a positron. The reason? Violation of mass-energy conservation! The decay of free protons into neutrons is banned because neutrons are heavier than protons, and mass-energy is conserved. (Protons bound in nuclei get extra effective mass from the binding energy of the strong force field in the nucleus, so in some cases – such as radioactive carbon-11 which is used in PET scanners – protons decay into neutrons by emitting a positive weak gauge boson which decays into a positron and a neutrino.) The left-handedness of the weak interaction is produced by the coupling of the gauge bosons to massive vacuum charges. The short-range, strength and the left-handedness of weak interactions are all due to the effect of mass on electromagnetic gauge bosons and charges. Mass limits the range and strength of the weak interaction and it prevents right-handed spinors undergoing weak interactions. The whole point about electroweak theory is that the electromagnetic and weak interactions are identical in strength and nature apart from the effect that the weak gauge bosons are massive. Whereas the electromagnetic force charge for beta decay is {alpha} ~ 1/137.036…, the corresponding weak force charge for low energies (proton-sized distances) is {alpha}*(Mproton/MW)2, so that it depends on the square of the ratio of the mass of the proton (the decay product in beta decay) to the mass of the weak gauge boson involved, MW. Since Mproton ~ 1 GeV and MW ~ 80 GeV, the low-energy weak force charge is on the order of 1/802 of the electromagnetic charge, alpha. It is the fact that the weak interaction involves massive virtual photons, with over 80 times the mass of the decay products (!), which cause it to be so much weaker than electromagnetism at low energies (nuclear-sized distances). Neglecting the effects of mass on the interaction strength and range of the weak force, it is the same thing as electromagnetism. At very high energies exceeding 100 GeV (short distances, less than 10-18 metre), the massive weak gauge bosons can be exchanged without the distance being an issue, and the weak force is then similar in strength to the electromagnetic force! The weak and strong forces can only act over a maximum distance of about 1 Fermi (10-15 metre) due to the limited range of the gauge bosons (massive W’s for the weak interaction, and pions for the longest-range residual component of the strong colour force).

Electromagnetic and strong forces conserve the number of interacting fermions, so that the number of fermion reactants is the same as the number of fermion products, but the weak force allows the number of fermion products to differ from the number of fermion reactants. The weak force involves neutrinos which have weak charges, little mass and no electromagnetic or strong charge, so they are weakly interacting (very penetrating).

beta-decayAbove: beta decay is controlled by the weak force which is similar to the electromagnetic interaction (on a Feynman diagram, an ingoing neutrino is equivalent to having an antineutrino as an interaction product). In place of electromagnetic photons mediating particle interaction, there are three weak gauge bosons. If these weak gauge bosons were massless, the strength of the weak interaction would be the same as the electromagnetic interaction. However, the weak gauge bosons are massive, and that makes the weak interaction much weaker than electromagnetism at low energies (i.e. relatively big, nucleon-sized distances). This is because the massive virtual weak gauge bosons are short-ranged dut to their massiveness (they suffer rapid attenuation with distance in the quantum field vacuum), so the weak boson interaction rate drops sharply with increasing distance. Hence, by analogy to Yukawa’s famous 1935 theoretical prediction of the pion mass using the experimentally known radius of pion-mediated nuclear interactions, it was possible to predict that the mass of the weak gauge bosons using Glashow’s theory of weak interactions and the experimentally known weak interaction strength, giving was 82 (W and W+) and 92 GeV (Z0), predictions which were closely confirmed by the 27-km diameter LEP (large electron-positron) collider experiments announced at CERN on 21 January 1983. (The masses are now established to be 80.4 and 91.2 GeV respectively.) Neutral currents due to exchange of electrically neutral massive W0 or Z0 (as it is known after it has undergone Weinberg-Glashow mixing with the photon in electroweak theory) gauge bosons had already been confirmed experimentally in 1973, leading to the award of the 1979 Nobel Prize to Glashow, Salam and Weinberg for the SU(2) weak gauge boson theory (Glashow’s work of 1961 had been extended by Weinberg and Salam in 1967). (No Nobel Prize has been awarded for the entire electroweak theory because nobody has detected the speculative Higgs field boson(s) postulated to give mass and thus electroweak symmetry breaking in the mainstream electroweak theory.) One neutral current interaction is illustrated above. However, other Z0 neutral currents exist and are very similar to electromagnetic interactions, e.g. the Z0 can mediate electron scattering, although at low energies this process will be trivial in comparison to electromagnetic (Coulomb) scattering on account of the mass of the Z0 which makes the massive neutral current interaction weak and trivial compared to electromagnetism at low energies (i.e. large distances).

How this gravity mechanism updates the Standard Model of particle physics

‘The electron and antineutrino [both emitted in beta decay of neutron to proton as argued by Pauli in 1930 from energy conservation using the experimental data on beta energy spectra; the mean beta energy is only 30% of the energy lost in beta decay so 70% on average must be in antineutrinos] each have a spin 1/2 and so their combination can have spin total 0 or 1. The photon, by contrast, has spin 1. By analogy with electromagnetism, Fermi had (correctly) supposed that only the spin 1 combination emerged in the weak decay. To further the analogy, in 1938, Oscar Klein suggested that a spin 1 particle (‘W boson’) mediated the decay, this boson playing a role in weak interactions like that of the photon in the electromagnetic case [electron-proton scattering is mediated by virtual photons, and is analogous to the W-mediated ‘scattering’ interaction between a neutron and a neutrino (not antineutrino) that results in a proton and an electron/beta particle; since an incoming (reactant) neutrino has the same effect on a reaction as a released (resultant) antineutrino, this process W-mediated scattering is equivalent to the beta decay of a neutron].

‘In 1957, Julian Schwinger extended these ideas and attempted to build a unified model of weak and electromagnetic forces by taking Klein’s model and exploiting an analogy between it and Yukawa’s model of nuclear forces [where pion exchange between nucleons causes the attractive component of the strong interaction, binding the nucleons into the nucleus against the repulsive electric force between protons]. As the pion+, pion, and pion0 are exchanged between interacting particles in Yukawa’s model of the nuclear force, so might the W+, W, and [W0] photon be in the weak and electromagnetic forces.

‘However, the analogy is not perfect … the weak and electromagnetic forces are very sensitive to electrical charge: the forces mediated by W+ and W appear to be more feeble than the electromagnetic force.’ – Professor Frank Close, The New Cosmic Onion, Taylor and Francis, New York, 2007, pp. 108-9.

The Yang-Mills SU(2) gauge theory of 1954 was first (incorrectly but interestingly) applied to weak interactions by Schwinger and Glashow in 1956, as Glashow explains in his Nobel prize award lecture:

‘Schwinger, as early as 1956, believed that the weak and electromagnetic interactions should be combined into a gauge theory. The charged massive vector intermediary and the massless photon were to be the gauge mesons. As his student, I accepted his faith. … We used the original SU(2) gauge interaction of Yang and Mills. Things had to be arranged so that the charged current, but not the neutral (electromagnetic) current, would violate parity and strangeness. Such a theory is technically possible to construct, but it is both ugly and experimentally false [H. Georgi and S. L. Glashow, Physical Review Letters, 28, 1494 (1972)]. We know now that neutral currents do exist and that the electroweak gauge group must be larger than SU(2).

‘Another electroweak synthesis without neutral currents was put forward by Salam and Ward in 1959. Again, they failed to see how to incorporate the experimental fact of parity violation. Incidentally, in a continuation of their work in 1961, they suggested a gauge theory of strong, weak and electromagnetic interactions based on the local symmetry group SU(2) x SU(2) [A. Salam and J. Ward, Nuovo Cimento, 19, 165 (1961)]. This was a remarkable portent of the SU(3) x SU(2) x U(1) model which is accepted today.

‘We come to my own work done in Copenhagen in 1960, and done independently by Salam and Ward. We finally saw that a gauge group larger than SU(2) was necessary to describe the electroweak interactions. Salam and Ward were motivated by the compelling beauty of gauge theory. I thought I saw a way to a renormalizable scheme. I was led to SU(2) x U(1) by analogy with the appropriate isospin-hypercharge group which characterizes strong interactions. In this model there were two electrically neutral intermediaries: the massless photon and a massive neutral vector meson which I called B but which is now known as Z. The weak mixing angle determined to what linear combination of SU(2) x U(1) generators B would correspond. The precise form of the predicted neutral-current interaction has been verified by recent experimental data. …’

Glashow in 1961 published an SU(2) model which had three weak gauge bosons, the neutral one of which could mix with the photon of electromagnetism to produce the observed neutral gauge bosons of electroweak interactions. (For some reason, Glashow’s weak mixing angle is now called Weinberg’s mixing angle.) Glashow’s theory predicted massless weak gauge bosons, not massive ones.

For this reason, a mass-giving field suggested by Peter Higgs in 1964 was incorporated into Glashow’s model by Weinberg as a mass-giving and symmetry-breaking mechanism (Woit points out in his book Not Even Wrong that this Higgs field is known as ‘Weinberg’s toilet’ because it was a vauge theory which could exist in several forms with varying numbers of speculative ‘Higgs bosons’, and it couldn’t predict the exact mass of a Higgs boson).

I’ve explained in a previous post, here, where I depart from Glashow’s argument: Glashow and Schwinger in 1956 investigated SU(2) using for the 3 gauge bosons 2 massive weak gauge bosons and 1 uncharged electromagnetic massless gauge boson. This theory failed to include the massive uncharged Z gauge boson which produces neutral currents when exchanged. Because this specific SU(2) electro-weak theory is wrong, Glashow claims that SU(2) is not big enough to include both weak and electromagnetic interactions.

However, this is an arm-waving dismissal and ignores a vital and obvious fact: SU(2) has 3 vector bosons but you need to supply mass to them by an external field (the Standard Model does this with some kind of speculative Higgs field, so far unverified by experiment). Without that (speculative) field, they are massless. So in effect SU(2) produces not 3 but 6 possible different gauge bosons: 3 massless gauge bosons with long range, and 3 massive ones with short range which describe the left-handed weak interaction.

It is purely the assumed nature of the unobserved, speculative Higgs field which tries to get rid of the 3 massless versions of the weak field quanta! If you replace the unobserved Higgs mass mechanism with another mass mechanism which makes checkable predictions about particle masses, you then arrive at an SU(2) symmetry with in effect 2 versions (massive and massless) of the 3 gauge bosons of SU(2), and the massless versions of those will give rise to long-ranged gravitational and electromagnetic interactions. This reduces the Standard Model from U(1) x SU(2) x SU(3) to just SU(2) x SU(3), while incorporating gravity as the massless uncharged gauge boson of SU(2). I found the idea that that chiral symmetry features of the weak interaction connects with electroweak symmetry breaking in Dr Peter Woit’s 21 March 2004 ‘Not Even Wrong’ blog posting The Holy Grail of Physics:

‘An idea I’ve always found appealing is that this spontaneous gauge symmetry breaking is somehow related to the other mysterious aspect of electroweak gauge symmetry: its chiral nature. SU(2) gauge fields couple only to left-handed spinors, not right-handed ones. In the standard view of the symmetries of nature, this is very weird. The SU(2) gauge symmetry is supposed to be a purely internal symmetry, having nothing to do with space-time symmetries, but left and right-handed spinors are distinguished purely by their behavior under a space-time symmetry, Lorentz symmetry. So SU(2) gauge symmetry is not only spontaneously broken, but also somehow knows about the subtle spin geometry of space-time. Surely there’s a connection here… So, this is my candidate for the Holy Grail of Physics, together with a guess as to which direction to go looking for it.’

As discussed in previous blog posts, e.g. this, the fact that the weak force is left-handed (affects only particles with left-handed spin) arises from the coupling of massive bosons in the vacuum to the weak gauge bosons: this coupling of massive bosons to the weak gauge bosons prevents them from interacting with particles with right-handed spin. The massless versions of the 3 SU(2) gauge bosons don’t get this spinor discrimination because they don’t couple with massive vacuum bosons, so the massless 3 SU(2) gauge bosons (which give us electromagnetism and gravity) are not limited to interacting with just one handedness of particles in the universe, but equally affect left- and right-handed particles. Further research on this topic is a underway. The ‘photon’ of U(1) is mixed via the Weinberg mixing angle in the standard model with the electrically neutral gauge boson of SU(2), and in any case it doesn’t describe electromagnetism without postulating unphysically that positrons are electrons ‘going backwards in time’; however this kind of objection is an issue you will get with new theories due to problems in the bedrock assumptions of the subject and so such issues should not be used as an excuse to censor the new idea out; in this case the problem is resolved either by Feynman’s speculative time argument – speculative because there is no evidence that positive charges are negative charges going back in time! – or as suggested on this blog, by dumping U(1) symmetry for electrodynamics and adopting instead SU(2) for electrodynamics without the Higgs field, which then allows two charges – positive and negative without one going backwards in time, and three massless gauge bosons and can therefore incorporate gravitation with electrodynamics. Evidence from electromagnetism:

‘I am a physicist and throughout my career have been involved with issues in the reliability of digital hardware and software. In the late 1970s I was working with CAM Consultants on the reliability of fast computer hardware. At that time we realised that interference problems – generally known as electromagnetic compatibility (emc) – were very poorly understood.’

– Dr David S. Walton, co-discoverer in 1976 (with Catt and Malcolm Davidson) that the charging and discharging of capacitors can be treated as the charging and discharging of open ended power transmission lines. This is a discovery with a major but neglected implication for the interpretation of Maxwell’s classical electromagnetism equations in quantum field theory; because energy flows into a capacitor or transmission line at light velocity and is then trapped in it with no way to slow down – the magnetic fields cancel out when energy is trapped – charged fields propagating at the velocity of light constitute the observable nature of apparently ‘static’ charge and therefore electromagnetic gauge bosons of electric force fields are not neutral but carry net positive and negative electric charges. Electronics World, July 1995, page 594.

Above: the Catt-Davidson-Walton theory showed that the transmission line section as capacitor could be modelled by the Heaviside theory of a light-velocity logic pulse. The capacitor charges up in a lot of small steps as voltage flows in, bounces off the open circuit at the far end of the capacitor, and then reflects and adds to further incoming energy current. The steps are approximated by the classical theory of Maxwell, which gives the exponential curve. Unfortunately, Heaviside’s mathematical theory is an over-simplification (wrong physically, although for most purposes it gives approximately valid results numerically) because it assumes that at the front of a logic step (Heaviside signalled using Morse code in 1875 in the undersea cable between Newcastle and Denmark) the rise is a discontinuous or abrupt step, instead of a gradual rise! We know this is wrong because at the front of a logic step the gradual rise in electric field strength with distance is what causes conduction electrons to accelerate to drift velocity from the normal randomly directed thermal motion they have.

Above: some of the errors in Heaviside’s theory are inherited by Catt in his theoetical work and in his so-called “Catt Anomaly” or “Catt Question”. If you look logically at Catt’s original anomaly diagram (based on Heaviside’s theory), you can see that no electric current can occur: electric current is caused by the drift of electrons which is due to the change of voltage with distance along a conductor. E.g. if I have a conductor uniformly charged to 5 volts with respect to another conductor, no electric current flows because there is simply no voltage gradient to cause a current. If you want an electric current, connect one end of a conductor to say 5 volts and the other end to some different potential, say 0 volts. Then there is a gradient of 5 volts along the length of the conductor, which accelerates electrons up to drift velocity for the resistance. if you connect both ends of a conductor to the same 5 volts potential, there is no gradient in the voltage along the conductor so there is no net electromotive force on the electrons. The vertical front on Catt’s original Heaviside diagram depiction of the “Catt Anomaly” doesn’t accelerate electrons in the way that we need because it shows an instantaneous rise in volts, not a gradient with distance.

Once you correct some of the Heaviside-Catt errors by including a real (ramping) rise time at the front of the electric current, the physics at once becomes clear and you can see what is actually occurring. The acceleration of electrons in the ramps of each conductors generates a radiated electromagnetic (radio) signal which propagates transversely to the other conductor. Since each conductor radiates an exactly inverted image of the radio signal from the other conductor, both superimposed radio signals exactly cancel when measured from a large distance compared to the distance between the two conductors. This is perfect interference, and prevents any escape of radiowave energy in this mechanism. The radiowave energy is simply exchanged between the ramps of the logic signals in each of the two conductors of the transmission line. This is the mechanism for electric current flow at light velocity via power transmission lines: what Maxwell attributed to “displacement current” of virtual charges in a mechanical vacuum is actually just exchange of radiation!

There are therefore three related radiations flowing in electricity: surrounding one conductor there are positively-charged massless electromagnetic gauge bosons flowing parallel to the conductor at light velocity (to produce the positive electric field around that conductor), around the other there are negatively-charged massless gauge bosons going in the same direction again parallel to the conductor, and between the two conductors the accelerating electrons exchange normal radiowaves which flow in a direction perpendicular to the conductors and have the role which is mathematically represented by Maxwell’s ‘displacement current’ term (enabling continuity of electric current in open circuits, i.e. circuits containing capacitors with a vacuum dielectric that prevents stops real electric current flowing, or long open-ended transmission lines which allow electric current to flow while charging up, despite not being a completed circuit).

Commenting on the mainstream focus upon string theory, Dr Woit states (http://arxiv.org/abs/hep-th/0206135 page 52):

‘It is a striking fact that there is absolutely no evidence whatsoever for this complex and unattractive conjectural theory. There is not even a serious proposal for what the dynamics of the fundamental “M-theory” is supposed to be or any reason at all to believe that its dynamics would produce a vacuum state with the desired properties. The sole argument generally given to justify this picture of the world is that perturbative string theories have a massless spin two mode and thus could provide an explanation of gravity, if one ever managed to find an underlying theory for which perturbative string theory is the perturbation expansion. This whole situation is reminiscent of what happened in particle theory during the 1960’s, when quantum field theory was largely abandoned in favor of what was a precursor of string theory. The discovery of asymptotic freedom in 1973 brought an end to that version of the string enterprise and it seems likely that history will repeat itself when sooner or later some way will be found to understand the gravitational degrees of freedom within quantum field theory. While the difficulties one runs into in trying to quantize gravity in the standard way are well-known, there is certainly nothing like a no-go theorem indicating that it is impossible to find a quantum field theory that has a sensible short distance limit and whose effective action for the metric degrees of freedom is dominated by the Einstein action in the low energy limit. Since the advent of string theory, there has been relatively little work on this problem, partly because it is unclear what the use would be of a consistent quantum field theory of gravity that treats the gravitational degrees of freedom in a completely independent way from the standard model degrees of freedom. One motivation for the ideas discussed here is that they may show how to think of the standard model gauge symmetries and the geometry of space-time within one geometrical framework.’

That last sentence is the key idea that gravity should be part of the gauge symmetries of the universe, not left out as it is in the mainstream ‘standard model’, U(1) x SU(2) x SU(3).

Electromagnetism is described by SU(2) isospin with massless charged positive and negative gauge bosons

The usual argument against massless charged radiation propagating is infinite self-inductance, but as discussed in the blog page here this doesn’t apply to virtual (gauge boson) exchange radiations, because the curls of magnetic fields around the portion of the radiation going from charge A to charge B is exactly cancelled out by the magnetic field curls from the radiation going the other way, from charge B to charge A. Hence, massless charged gauge bosons can propagate in space, provided they are being exchanged simultaneously in both directions between electric charges, and not just from one charge to another without a return current.

You really need electrically charged gauge bosons to describe electromagnetism, because the electric field between two electrons is different in nature to that between two positrons: so you can’t describe this difference by postulating that both fields are mediated by the same neutral virtual photons, unless you grant the 2 additional polarizations of the virtual photon (the ordinary photon has only 2 polarizations, while the virtual photon must have 4) to be electric charge!

The virtual photon mediated between two electrons is negatively charged and that mediated between two positrons (or two protons) is positively charged. Only like charges can exchange virtual photons with one another, so two similar charges exchange virtual photons and are pushed apart, while opposite electric charges shield one another and are pushed together by a random-walk of charged virtual photons between the randomly distributed similar charges around the universe as explained in a previous post.

What is particularly neat about this is having electrically charged electromagnetic virtual photons is that it automatically requires a SU(2) Yang-Mills theory! The mainstream U(1) Maxwellian electromagnetic gauge theory makes a change in the electromagnetic field induce a phase shift in the wave function of a charged particle, not in the electric charge of the particle! But with charged gauge bosons instead of neutral gauge bosons, the bosonic field is able to change the charge of a fermion just as the SU(2) charged weak bosons are able to change the isospin charges of fermions.

We don’t see electromagnetic fields changing the electric charge of fermions normally because fermions radiate as much electric charge per second as they receive, from other charges, thereby maintaining an equilibrium. However, the electric field of a fermion is affected by its state of motion relative to an observer, when the electric field line distribution appears to make the electron “flatten” in the direction of motion due to Lorentz contraction at relativistic velocities. To summarize:

U(1) electromagnetism: is described by Maxwellian equations. The field is uncharged and so cannot carry charge to or from fermions. Changes in the field can only produce phase shifts in the wavefunction of a charged particle, such as acceleration of charges, and can never change the charge of a charged particle.

SU(2) electromagnetism (two charged massless gauge bosons): is described by the Yang-Mills equation because the field is electrically charged and can change not just the phase of the wavefunction of a charged particle to accelerate a charge, but can also in principle (although not in practice) change the electric charge of a fermion. This simplifies the Standard Model because SU(2) with two massive charged gauge bosons is already needed, and it naturally predicts (in the absence of a Higgs field without a chiral discrimination for left-handed spinors) the existence of massless uncharged versions of the these massive charged gauge bosons which were observed at CERN in 1983.

The Yang-Mills equation is used for any bosonic field which carries a charge and can therefore (in principle) change the charge of a fermion. The weak force SU(2) charge is isospin and the electrically charged massive weak charge gauge bosons carry an isospin charge which is IDENTICAL to the electric charge, while the massive neutral weak boson has zero electric charge and zero isospin charge. The Yang-Mills equation is:

dFmn/dxn + 2e(An x Fmn) + Jm = 0

which is similar to Maxwell’s equations (Fmn is the field strength and Jm is the current), apart from the second term, 2e(An x Fmn), which describes the effect of the charged field upon itself (e is charge and An is the field potential). The term 2e(An x Fmn) doesn’t appear in Maxwell’s equations for two reasons:

(1) an exact symmetry between the rate of emission and reception of charged massless electromagnetic gauge bosons is forced by the fact that charged massless gauge bosons can only propagate in the vacuum where there is an equal return current coming from the other direction (otherwise they can’t propagate, because charged massless radiation has infinite self-inductance due to the magnetic field produced, which is only cancelled out if there is an identical return current of charged gauge bosons, i.e. a perfect equilibrium or symmetry between the rates of emission and reception of charged massless gauge bosons by fermionic charges). This prevents fermionic charges from increasing or decreasing, because the rate of gain and rate of loss of charge per second is always the same.

(2) the symmetry between the number of positive and negative charges in the universe keeps electromagnetic field strengths low normally, so the self-interaction of the charge of the field with itself is minimal.

These two symmetries act together to prevents the Yang-Mills 2e(An x Fmn) term from having any observable effect in laboratory electromagnetism, which is why the mainstream empirical Maxwellian model works as a good approximation, despite being incorrect at a more fundamental physical level of understanding.

Quantum gravity is supposed to be similar to a Yang-Mills theory in regards to the fact that the energy of the gravitational field is supposed (in general relativity, which ignores vital quantum effects the mass-giving “Higgs field” or whatever and its interaction with gravitons) to be a source for gravity itself. In other words, like a Yang-Mills field, the gravitational field is supposed to generate a gravitational field simply by virtue of its energy, and therefore should interact with itself. If this simplistic idea from general relativity is true, then according to the theory presented on this blog page, the massless electrically neutral gauge boson of SU(2) is the spin-1 graviton. However, the structure of the Standard Model implies that some field is needed to provide mass even if the mainstream Higgs mechanism for electroweak symmetry breaking is wrong.

Therefore, the massless electrically neutral (photon-like) gauge boson of SU(2) may not be the graviton, but is instead an intermediary gauge boson which interacts in a simple way with massive (gravitational charge) particles in the vacuum: these massive (gravitational charge) particles may be described by the simple Abelian symmetry U(1). So U(1) then describes quantum gravity: it has one charge (mass) and one gauge boson (spin-1 graviton).

‘Yet there are new things to discover, if we have the courage and dedication (and money!) to press onwards. Our dream is nothing else than the disproof of the standard model and its replacement by a new and better theory. We continue, as we have always done, to search for a deeper understanding of nature’s mystery: to learn what matter is, how it behaves at the most fundamental level, and how the laws we discover can explain the birth of the universe in the primordial big bang.’ – Sheldon L. Glashow, The Charm of Physics, American Institute of Physics, New York, 1991. (Quoted by E. Harrison, Cosmology, Cambridge University press, London, 2nd ed., 2000, p. 428.)

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