Sheldon Glashow on SU(2) as a gauge group for unifying electromagnetism and weak interactions

The Standard Model uses SU(2) x U(1)  as the electroweak gauge group, SU(2) contributes 3 short ranged weak force gauge bosons, while U(1) contributes the electromagnetic gauge boson. However, there’s evidence, see here, here (below the illustration) and here, that the correct electroweak gauge group is somewhat different: SU(2) with massive gauge bosons represents weak interactions, while SU(2) with massless gauge bosons represents gravity and electromagnetism, where the massless uncharged particle mediates gravity,while the massless positive charge and massless negative charges mediate electromagnetic interactions.

So there are two effects of SU(2) operating: a version in which the three gauge bosons are massless and have infinite range (decreasing with distance as the inverse square law due to geometry) with two of them giving rise to electromagnetism and the third to gravity, and a version in which the three gauge bosons are massive and short ranged, giving rise to weak interactions at high energy. This scheme physically models why you get attractions between unlike charges, repulsions between similar charges, and a very weak attraction between masses (see the illustration in this post).

Now I’ve found that the Nobel Laureate Sheldon Glashow has already investigated SU(2) as an electromagnetism and weak force unification scheme, and has actually discussed it in his Nobel acceptance lecture of 8 December 1979, Towards a Unified Theory – Threads in a Tapestry:

‘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. …’

It’s clear that the problem they had was in believing that a special photon could mediate electromagnetic interactions. This is wrong, because if you could remove the charges from a capacitor, the electromagnetic field (positive electric field near where the positive charge had been, and negative where the negative charge had been) would persist, since it is being mediated at light speed (not instantly) by gauge boson exchange radiation. The nature of such exchange radiation must be that it conveys the effects of the particular type of charge involved: positive or negative.

The most lucid presentation of the mainstream QED model is probably that in chapter I.5, Coulomb and Newton: Repulsion and Attraction, in Professor Zee’s book Quantum Field Theory in a Nutshell (Princeton University Press, 2003), pages 30-6.  Zee uses an approximation due to Sidney Coleman, where you have to work through the theory assuming that the photon has a real mass m, to make the theory work, but at the end you set m = 0. (If you assume from the beginning that m = 0, the simple calculations don’t work, so you then need to work with gauge invariance.)

Zee starts with a Langrangian for Maxwell’s equations, adds terms for the assumed mass of the photon, then writes down the Feynman path integral, which is  ò DAeiS(A) where S(A) is the action, S(A) = ò d4xL, where L is the Lagrangian based on Maxwell’s equations for the spin-1 photon (plus, as mentioned, terms for the photon having mass, to keep it relatively simple and avoid including gauge invariance). Evaluating the effective action shows that the potential energy between two similar charge densities is always positive, hence it is proved that the spin-1 gauge boson-mediated electromagnetic force between similar charges is always repulsive. So it works.

A massless spin-1 boson has only two degrees of freedom for spinning, because in one dimension it is propagating at velocity c and is thus ‘frozen’ in that direction of propagation. Hence, a massless spin-1 boson has two polarizations (electric field and magnetic field). A massive spin-1 boson, however, can spin in three dimensions and so has three polarizations.

Moving to quantum gravity, a spin-2 graviton will have 22 + 1 = 5 polarizations. Writing down a 5 component tensor to represent the gravitational Lagrangian, the same treatment for a spin-2 graviton then yields the result that the potential energy between two lumps of positive energy density (mass is always positive) is always negative, hence masses always attract each other.

This is very nice maths, but it doesn’t deal with the physical dynamics. When you want to deal with the physical dynamics, the whole model changes.  The proper represention of all fundamental interactions is either SU(3) x SU(2) with the three SU(2) gauge bosons existing in both massive (weak force) and massless (electromagnetism and gravity) forms, or SU(3) x SU(2) x SU(2) where one SU(2) represents weak interactions with three massive gauge bosons, and the other SU(2) represents the electromagnetism and gravity interactions:

SU(3) is OK, but SU(2)xU(1) and the Higgs mechanism are too complicated and SU(2) is rich enough, with a very simple mass mechanism, to encompass the full electroweak phenomena, allowing the prediction of the strength of the electromagnetic force and weaker gravity correctly

Illustration of physical mechanisms for exchange radiation in quantum field theory and the modification to the standard model implied therewith: SU(3) is OK, but SU(2)xU(1) and the Higgs mechanism are too complicated and SU(2) is rich enough (with a very simple mass-giving mechanism) to encompass the full electroweak phenomena, allowing the prediction of the strength of the electromagnetic force and weaker gravity correctly. So the standard model should be modified to SU(3)xSU(2) where the SU(2) has a mechanism for chiral symmetry and mass at certain energies, or perhaps SU(3)xSU(2)xSU(2), with one of the SU(2) groups describing massive weak force gauge bosons, and the other SU(2) is electromagnetism and gravity (mass-less versions of the W+ and W- mediate electric fields and the mass-less Z is just the photon, and it mediates gravity in the network of particles which give rise to mass). It is simply untrue that electromagnetic gauge boson radiation must be uncharged: this condition only holds for isolated photons, not for exchange radiation, where there is continual exchange of gauge bosons between charges (gauge bosons going in both directions between charges, an equilibrium). If the mass-less gauge bosons are uncharged, the magnetic field curls cancel in each individual gauge boson (seen from a large distance), preventing infinite self-inductance, so they will propagate. This is why normal electromagnetic radiation like light photons are uncharged (the varying electromagnetic field of the photon contains as much positive electric field as negative electric field).

If the gauge bosons are charged and massless, then you would not normally expect them to propagate, because their magnetic fields cause infinite self-inductance, which would prevent propagation. However, if you have two similar, charged massless radiations flowing in opposite directions, their interaction will be cancel out the magnetic fields, leaving only the electric field component as observed in electric fields.

This has been well investigated in the transmission line context of TEM (travsverse electromagnetic) waves (such as logic steps in high speed digital computers, where cross-talk, i.e., mutual inductance, is a limiting factor on the integrated circuit design) propagated by a pair of parallel conductors, with charges flowing in one direction on one conductor, and the opposite direction in the other. When a simple capacitor, composed of metal plates separated by a small distance of vacuum (the vacuum acts as a dielectric, i.e., the permittivity of free space is not zero), is charged up by light-velocity electromagnetic energy, that energy has no mechanism to slow down when it enters the capacitor, which behaves as a transmission line. Hence, you get the ‘energy current’ bouncing in all directions concurrently in a ‘steady, charged’ capacitor. The magnetic field components of the TEM waves cancel, leaving just electric field (electric charge) as observed. See the illustration in the previous post here.

There is some discussion of spin-2 graviton ideas failure here:

“On the speculative nature of conjectures concerning spin-2 gravitons, Richard P. Feynman points out in The Feynman Lectures on Gravitation, page 30, that gravitons do not have to be spin-2, which has not been observed. Renormalization works in the standard model (for electromagnetic, weak nuclear and strong nuclear charges) because the gauge bosons which mediate force do not interact with themselves to create massive problems. This is not the case with the spin-2 gravitons in general. Spin-2 gravitons, because they have energy, should according to general relativity, themselves be sources for gravity on account of their energy, and should therefore themselves emit gravitons, which usually makes the renormalization technique ineffective for quantum gravity. String theory is supposed to dispense with renormalization problems because strings are not point particles but of Planck-length. The mainstream 11-dimensional supergravity theory includes a superpartner to the unobserved spin-2 graviton, called the spin-3/2 gravitino, which is just as unobserved and non-falsifiable as the spin-2 graviton. The reason is that this supersymmetric scheme gets rid of problems which the spin-2 graviton idea would lead to at unobservably high energy where gravity is speculated to unify with other forces into a single superforce.

“So a supersymmetric partner for the spin-2 attractive graviton is postulated in mainstream supergravity to make the spin-2 graviton theory work by cancelling out the unwanted effects of the grand unified theory speculations. Hence, you have to add extra speculations to spin-2 gravitons just to cancel out the inconsistencies in the original speculation that all forces should have equal coupling constants (relative charges) at unobservably high energy. The inventing of new uncheckable speculations to cover up inconsistencies in old uncheckable speculations is not new. (It is reminiscent of the proud Emperor who used invisible cloaks to try to cover up his gullibility and shame, at the end of an 1837 Hans Christian Andersen fairytale.) There is no experimental justification for the speculative mainstream spin-2 graviton scheme, nor any way to check it.”

‘Worst of all, superstring theory does not follow as a logical consequence of some appealing set of hypotheses about nature. Why, you may ask, do the string theorists insist that space is nine dimensional? Simply because string theory doesn’t make sense in any other kind of space.’ – Nobel Laureate Sheldon Glashow (quoted by Dr Peter Woit in Not Even Wrong: The Failure of String Theory and the Continuing Challenge to Unify the Laws of Physics, Jonathan Cape, London, 2006, p181).

‘Actually, I would not even be prepared to call string theory a ‘theory’ … Imagine that I give you a chair, while explaining that the legs are still missing, and that the seat, back and armrest will perhaps be delivered soon; whatever I did give you, can I still call it a chair?’ – Nobel Laureate Gerard ‘t Hooft (quoted by Dr Peter Woit in Not Even Wrong: The Failure of String Theory and the Continuing Challenge to Unify the Laws of Physics, Jonathan Cape, London, 2006, p181).

‘… I do feel strongly that this is nonsense! … I think all this superstring stuff is crazy and is in the wrong direction. … I don’t like it that they’re not calculating anything. I don’t like that they don’t check their ideas. I don’t like that for anything that disagrees with an experiment, they cook up an explanation … All these numbers [particle masses, etc.] … have no explanations in these string theories – absolutely none!’ – Richard P. Feynman, in Davies & Brown, ‘Superstrings’ 1988, at pages 194-195.


21 thoughts on “Sheldon Glashow on SU(2) as a gauge group for unifying electromagnetism and weak interactions

  1. copy of a comment:

    It’s an interesting post about the Planck units. Actually, the Planck units are very useful to befuddled lecturers who confuse fact with orthodoxy.

    The Planck scale is purely the result of dimensional analysis, and Planck’s claim that the Planck length was the smallest length of physical significance is vacuous because the black hole event horizon radius for the electron mass, R = 2GM/c^2 = 1.35*10^{-57} m, which is over 22 orders of magnitude smaller than the Planck length, R = square root (h bar * G/c^3) = 1.6*10^{-35} m.

    Why, physically, should this Planck scale formula hold, other than the fact that it has the correct units (length)? Far more natural to use R = 2GM/c^2 for the ultimate small distance unit, where M is electron mass. If there is a natural ultimate ‘grain size’ to the vacuum to explain, as Wilson did in his studies of renormalization, in a simple way why there are no infinite momenta problems with pair-production/annihilation loops beyond the UV cutoff (i.e. smaller distances than the grain size of the ‘Dirac sea’), it might make more physical sense to use the event horizon radius of a black hole of fundamental particle mass, than to use the Planck length.

    All the Planck scale has to defend it is a century of obfuscating orthodoxy.

  2. Non-submitted comment (saved here as it is a useful brief summary of some important points of evidence; I didn’t submit the comment to the following site in the end because it covers a lot of ground and doesn’t include vital mathematical and other backup evidence):

    This is interesting. A connection I know between a toroidal shape and a black hole is that, if the core of an electron is gravitationally trapped Heaviside-Poynting electromagnetic energy current, it is a black hole and it has a magnetic field which is a torus.

    Experimental evidence for why an electromagnetic field can produce gravity effects involves the fact that electromagnetic energy is a source of gravity (think of the stress-energy tensor on the right hand side of Einstein’s field equation). There is also the capacitor charging experiment. When you charge a capacitor, practically the entire electrical energy entering it is electromagnetic field energy (Heaviside-Poynting energy current). The amount of energy carried by electron drift is negligible, since the electrons have a kinetic energy of half the product of their mass and the square of their velocity (typically 1 mm/s for a 1 A current).

    So the energy current flows into the capacitor at light speed. Take the capacitor to be simple, just two parallel conductors separated by a dielectric composed of just a vacuum (free space has a permittivity, so this works). Once the energy goes along the conductors to the far end, it reflects back. The electric field adds to that from further inflowing energy, but most of the magnetic field is cancelled out since the reflected energy has a magnetic field vector curling the opposite way to the inflowing energy. (If you have a fully charged, ‘static’ conductor, it contains an equilibrium with similar energy currents flowing in all possible directions, so the magnetic field curls all cancel out, leaving only an electric field as observed.)

    The important thing is that the energy keeps going at light velocity in a charged conductor: it can’t ever slow down. This is important because it proves experimentally that static electric charge is identical to trapped electromagnetic field energy. If this can be taken to the case of an electron, it tells you what the core of an electron is (obviously, there will be additional complexity from the polarization of loops of virtual fermions created in the strong field surrounding the core, which will attenuate the radial electric field from the core as well as the transverse magnetic field lines, but not the polar radial magnetic field lines).

    You can prove this if you discharge any conductor x metres long which is charged to v volts with respect to ground, through a sampling oscilloscope. You get a square wave pulse which has a height of v/2 volts and a duration of 2x/c seconds. The apparently ‘static’ energy of v volts in the capacitor plate is not static at all; at any instant, half of it, at v/2 volts, is going eastward at velocity c and half is going westward at velocity c. When you discharge it from any point, the energy already by chance headed towards that point immediately begins to exit at v/2 volts, while the remainder is going the wrong way and must proceed and reflect from one end before it exits. Thus, you always get a pulse of v/2 volts which is 2x metres long or 2x/c seconds in duration, instead of a pulse at v volts and x metres long or x/c seconds in duration, which you would expect if the electromagnetic energy in the capacitor was static and drained out at light velocity by all flowing towards the exit.

    This was investigated by Catt, who used it to design the first crosstalk (glitch) free wafer scale integrated memory for computers, winning several prizes for it. Catt welcomed me when I wrote an article on him for the journal Electronics World, but then bizarrely refused to discuss physics with me, while he complained that he was a victim of censorship. However, Catt published his research in IEEE and IEE peer-reviewed journals. The problem was not censorship, but his refusal to get into mathematical physics far enough to sort out the electron.

    It’s really interesting to investigate why classical (not quantum) electrodynamics is totally false in many ways. I think quantum electrodynamics and particle-wave duality have blocked progress.

    Some calculations of quantum gravity based on a simple, empirically-based model (no ad hoc hypotheses), which yields evidence (which needs to be independently checked) that the proper size of the electron is the black hole event horizon radius.

    There is also the issue of a chicken-and-egg situation in QED where electric forces are mediated by exchange radiation. Here you have the gauge bosons being exchanged between charges to cause forces. The electric field lines between the charges have to therefore arise from the electric field lines of the virtual photons being continually exchanged.

    How do you get an electric field to arise from neutral gauge bosons? It’s simply not possible. The error in the conventional thinking is that people incorrectly rule out the possibility that electromagnetism is mediated by charged gauge bosons. You can’t transmit charged photons one way because the magnetic self-inductance of a moving charge is infinite. However, charged gauge bosons will propagate in an exchange radiation situation, because they are travelling through one another in opposite directions, so the magnetic fields are cancelled out. It’s like a transmission line, where the infinite magnetic self-inductance of each conductor cancels out that of the other conductor, because each conductor is carrying equal currents in opposite directions.

    Hence you end up with the conclusion that the electroweak sector of the SM is in error: Maxwellian U(1) doesn’t describe electromagnetism properly. It seems that the correct gauge symmetry is SU(2) with three massless gauge bosons: positive and negatively charged massless bosons mediate electromagnetism and a neutral gauge boson (a photon) mediates gravitation. This predicts the right strength of gravity, because the charged gauge bosons will cause the effective potential of those fields in radiation exchanges between similar charges throughout the universe (drunkard’s walk statistics) to multiply up the average potential between two charges by a factor equal to the square root of the number of charges in the universe. Since there are around 10^80 charges, electromagnetism is 10^40 times gravity. On average, gauge bosons spend as much time moving away from us as towards us while being exchanged between the charges of the universe, so the average effect of divergence is exactly cancelled by the average convergence, simplifying the calculation. This model also explains why electromagnetism is attractive between dissimilar charges and repulsive between similar charges.

  3. Non-submitted comment originally intended for

    Thanks for those new particle names! I’ll use the anyon (beginning with the same letter as anode, positive charged) for a massless positive gauge boson, equivalent to a massless W+, and a moron (beginning with the same letter as the surname of a famous Harvard assistant string professor) will be the massless W-.

    These anyons and morons mediate electromagnetic interactions in an SU(2) gauge symmetry. The massless neutral current from the photon like gauge boson mediates gravitation. This replaces the U(1) symmetry in the standard model.

    I think the corrected standard model is SU(3) x SU(2) instead of SU(3) x SU(2) x U(1).

    The error in the standard model is the assumption that electromagnetic forces can be mediated by uncharged photons with some extra polarizations.

    Since net electric fields must be produced by “neutral” photons, U(1) is wrong. SU(2) works to replace SU(2) x U(1) because it dispenses with electroweak symmetry breaking.

    Instead, SU(2) exists in two versions, one having three massless gauge bosons (two charged, one neutral) and the other having the same particles but with mass. More details here.

  4. Obviously the major question in determining whether the correct gauge group of the universe is SU(3) x SU(2) x SU(2) or not is how mass is acquired; i.e. the Higgs sector.

    There are also questions as to how chiral symmetry will work when replacing SU(2) x U(1) with SU(2) x SU(2) or SU(2) + {replacement for Higgs sector which will enable some of the electromagnetic gauge bosons to acquire mass at high energy, thus creating massive weak gauge bosons}.

    The problem centres on looking at the details of the weak charges (which depend on the spin direction, i.e. chiral symmetry).

  5. copy of a comment:

    …Curiously enough there isn’t a single book which succeeds in popularizing LQG or its relatives. But I think this is not necessarily a bad thing, and can even be justified by the fact that it is harder to get a first intuitive physical picture of LQG than it is of string theory. – Thomas D

    This is the key to the problem: should mainstream hype be attacked or should rival theories be hyped like string theory? Professor Smolin has previously tried to popularise alternatives in books like Three Roads to Quantum Gravity, but such books fail (like academic books on loop quantum gravity, such as Rovelli’s), to really combat string theory.

    In his lecture series (available at Perimeter Institute website), Introduction to Quantum Gravity, Prof. Smolin does make the point very clearly that loop quantum gravity is an effective model for interactions between gauge bosons that carry energy and thus are a source of gravitation (i.e. gravitons carry a quantum gravity charge) as well as mediating gravitational interactions. Normally, the fact that gravitons should carry a gravitational charge makes their interactions crazy at high energy.

    The key fact is that you can get background independent (metric-less) general relativity from quantum field theory by summing interaction graphs in a Penrose spin network. That alone is impressive thing about LQG. What is interesting is that this result of LQG should apply to other things too; any field with gauge bosons which carry a charge. In the standard model, electromagnetism is mediated by uncharged photons, and this is supposed to be reason why electromagnetism is renormalizable. However, it might be the case that electromagnetism and gravity are related in a different way. For example, the U(1) part of the standard model might not be correct. It’s inelegant to explain with extra polarizations how an electric field can be either positive or negative if the gauge boson responsible is neutral. A simpler way would be to replace the standard model’s U(1) by a second SU(2), but this time with entirely massless gauge bosons: one positively charged (giving rise to positive electric fields), one negative (giving negative electric fields) and one which is neutral (giving rise to gravity). This scheme incorporates gravity into the standard model and makes predictions. Another option might be to modify the Higgs mechanism so that just a single SU(2) group produces both short range massive W+/- and W gauge bosons for weak interactions, and mass-less versions of those which mediate electromagnetism and gravity, respectively.

  6. copy of a comment:

    “Theoretically if an accelerator fired enough mass into a tiny space a singularity would be created. The Black Hole would almost instantly evaporate, but could be detected via Hawking radiation. Unfortunately quantum mechanics says that a particle’s location can not be precisely measured. This quantum uncertainty would prevent us from putting enough mass into a singularity.”

    I disagree with Lisa Randall here. It depends on whether the black hole is charged or not, which changes the mechanism for the emission of Hawking radiation.

    The basic idea is that in a strong electric field, pairs of virtual positive fermions and virtual negative fermions appear spontaneously. If this occurs at the event horizon of a black hole, one of the pair can at random fall into the black hole, while the other one escapes.

    However, there is a factor Hawking and Lisa Randall ignore: the requirement of the black hole having electric charge in the first place, because pair production has only been demonstrated to occur in strong fields, the standard model fields of the strong and electromagnetic force fields (nobody has ever seen pair production occur in the extremely weak gravitational fields).

    Hawking ignores the fact that pair production in quantum field theory (according to Schwinger’s calculations, which very accurately predict other things like the magnetic moments of leptons and the Lamb shift in the hydrogen spectra) requires a net electric field to exist at the event horizon at the black hole.

    This in turn means that the black hole must carry a net electric charge and cannot be neutral if there is to be any Hawking radiation.

    In turn, this implies that Hawking radiation in general is not gamma rays as Hawking claims it is.

    Gamma rays in Hawking’s theory are produced just beyond the event horizon of the black hole by as many virtual positive fermions as virtual negative fermions escaping and then annihilating into gamma rays.

    This mechanism can’t occur if the black hole is charged, because the net electric charge [which is required to give the electric field which is required for pair-production in the vacuum in the first place] of the black hole interferes with the selection of which virtual fermions escape from the event horizon!

    If the black hole has a net positive charge, it will skew the distribution of escaping radiation so that more virtual positive charges escape than virtual negative charges.

    This, in turn, means that the escaped charges beyond the event horizon won’t be equally positive and negative; so they won’t be able to annihilate into gamma rays.

    It’s strange that Hawking has never investigated this.

    You only get Hawking radiation if the black hole has an electric charge of Q > 16*Pi*Permittivity*[(mMG)^2]/(c*e*h-bar).

    (This condition is derived below.)

    The type of Hawking radiation you get emitted is generally going to be charged, not neutral.

    My understanding is that the fermion and boson are both results of fundamental prions. As Carl Brannen and Tony Smith have suggested, fermions may be a triplet of prions to explain the three generations of the standard model, and the colour charge in SU(3) QCD.

    Bosons of the classical photon variety would generally have two prions: because their electric field oscillates from positive to negative (the positive electric field half cycle constitutes an effective source of positive electric charge and can be considered to be one preon, while the negative electric field half cycle in a photon can be considered another preon).

    Hence, there are definite reasons to suspect that all fermions are composed of three preons, while bosons consist of pairs of preons.

    Considering this, Hawking radiation is more likely to be charged gauge boson radiation. This does explain electromagnetism if you replace the U(1)xSU(2) electroweak unification with an SU(2) electroweak unification, where you have 3 gauge bosons which exist in both massive forms (at high energy, mediating weak interactions) and also massless forms (at all energies), due to the handedness of the way these three gauge bosons acquire mass from a mass-providing field. Since the standard model’s electroweak symmetry breaking (Higgs) field fails to make really convincing falsifiable predictions (there are lots of versions of Higgs field ideas making different “predictions”, so you can’t falsify the idea easily), it is very poor physics.

    Sheldon Glashow and Julian Schwinger investigated the use of SU(2) to unify electromagnetism and weak interactions in 1956, as Glashow explains in his Nobel lecture of 1979:

    ‘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).’

    This is plain wrong: Glashow and Schwinger believed that electromagnetism would have to be explained by a massless uncharged photon acting as the vector boson which communicates the force field.

    If they had considered the mechanism for how electromagnetic interactions can occur, they would have seen that it’s entirely possible to have massless charged vector bosons as well as massive ones for short range weak force interactions. Then SU(2) gives you six vector bosons:

    Massless W_+ = +ve electric fields
    Massless W_- = -ve electric fields
    Massless Z_o = graviton (neutral)

    Massive W_+ = mediates weak force
    Massive W_- = mediates weak force
    Massive Z_o = neutral currents

    Going back to the charged radiation from black holes, massless charged radiation mediates electromagnetic interactions.

    This idea that black holes must evaporate if they are real simply because they are radiating, is flawed: air molecules in my room are all radiating energy, but they aren’t getting cooler: they are merely exchanging energy. There’s an equilibrium.


    To derive the condition for Hawking’s heuristic mechanism of radiation emission, he writes that pair production near the event horizon sometimes leads to one particle of the pair falling into the black hole, while the other one escapes and becomes a real particle. If on average as many fermions as antifermions escape in this manner, they annihilate into gamma rays outside the black hole.

    Schwinger’s threshold electric field for pair production is: E_c = (m^2)*(c^3)/(e*h-bar) = 1.3*10^18 volts/metre. Source: equation 359 in or equation 8.20 in

    So at least that electric field strength must exist at the event horizon, before black holes emit any Hawking radiation! (This is the electric field strength at 33 fm from an electron.) Hence, in order to radiate by Hawking’s suggested mechanism, black holes must carry enough electric charge so make the eelectric field at the event horizon radius, R = 2GM/c^2, exceed 1.3*10^18 v/m.

    Now the electric field strength from an electron is given by Coulomb’s law with F = E*q = qQ/(4*Pi*Permittivity*R^2), so

    E = Q/(4*Pi*Permittivity*R^2) v/m.

    Setting this equal to Schwinger’s threshold for pair-production, (m^2)*(c^3)/(e*h-bar) = Q/(4*Pi*Permittivity*R^2). Hence, the maximum radius out to which fermion-antifermion pair production and annihilation can occur is

    R = [(Qe*h-bar)/{4*Pi*Permittivity*(m^2)*(c^3)}]^{1/2}.

    Where Q is black hole’s electric charge, and e is electronic charge, and m is electron’s mass. Set this R equal to the event horizon radius 2GM/c^2, and you find the condition that must be satisfied for Hawking radiation to be emitted from any black hole:

    Q > 16*Pi*Permittivity*[(mMG)^2]/(c*e*h-bar)

    where M is black hole mass.

    So the amount of electric charge a black hole must possess before it can radiate (according to Hawking’s mechanism) is proportional to the square of the mass of the black hole.

    On the other hand, it’s interesting to look at fundamental particles in terms of black holes (Yang-Mills force-mediating exchange radiation may be Hawking radiation in an equilibrium).

    When you calculate the force of gauge bosons emerging from an electron as a black hole (the radiating power is given by the Stefan-Boltzmann radiation law, dependent on the black hole radiating temperature which is given by Hawking’s formula), you find it correlates to the electromagnetic force, allowing quantitative predictions to be made. See for example.

    To summarize: Hawking, considering uncharged black holes, says that either of the fermion-antifermion pair is equally likey to fall into the black hole. However, if the black hole is charged (as it must be in the case of an electron), the black hole charge influences which particular charge in the pair of virtual particles is likely to fall into the black hole, and which is likely to escape. Consequently, you find that virtual positrons fall into the electron black hole, so an electron (as a black hole) behaves as a source of negatively charged exchange radiation. Any positive charged black hole similarly behaves as a source of positive charged exchange radiation.

    These charged gauge boson radiations of electromagnetism are predicted by an SU(2) electromagnetic mechanism, see Figures 2, 3 and 4 of

    It’s amazing how ignorant mainstream people are about this. They don’t understand that charged massless radiation can only propagate if there is an exchange (vector boson radiation going in both directions between charges) so that the magnetic field vectors cancel, preventing infinite self inductance.

    Hence the whole reason why we can only send out uncharged photons from a light source is that we are only sending them one way. Feynman points out clearly that there are additional polarizations but observable long-range photons only have two polarizations.

    It’s fairly obvious that between two positive charges you have a positive electric field because the exchanged vector bosons which create that field are positive in nature. They can propagate despite being massless because there is a high flux of charged radiation being exchanged in both directions (from charge 1 to charge 2, and from charge 2 to charge 1) simultaneously, which cancels out the magnetic fields due to moving charged radiation and prevents infinite self-inductance from stopping the radiation. The magnetic field created by any moving charge has a directional curl, so radiation of similar charge going in opposite directions will cancel out the magnetic fields (since they oppose) for the duration of the overlap.

    All this is well known experimentally from sending logic signals along transmission lines, which behave as photons. E.g. you need two parallel conductors at different potential to cause a logic signal to propagate, each conductor containing a field waveform which is an exact inverted image of that in the other (the magnetic fields around each of the conductors cancels the magnetic field of the other conductor, preventing infinite self-inductance).

    Moreover, the full mechanism for this version of SU(2) makes lots of predictions. So fermions are blac[k] holes and the charged Hawking radiation they emit is the gauge bosons of electromagnetism and weak interactions.

    Presumably the neutral radiation is emitted by electrically neutral field quanta which give rise to the mass (gravitational charge). The reason why gravity is so weak is because it is mediated by electrically neutral vector bosons.

  7. Двадцатилетняя Алиса – подруга моей сестры Маши, гостившая у нас на даче уже неделю – была наделена фигурой, которую иногда называют «песочные часы». Длинные стройные ноги, большая упругая грудь и очень тонкая талия, плавно переходящая в меру широкие бедра – ее формы явно были близки к идеальным 90-60-90. Свои блестящие каштановые волосы, абсолютно прямые, девушка всегда носила распущенными, даже в такую сильную жару, какая выдалась этим летом – длиной они доходили до талии. Обычно Алиса надевала шортики «в облипку», а также короткие маечки, которые плотно обтягивали ее груди – сквозь тонкую ткань мне отлично были видны ее торчащие соски, так как лифчик она никогда не надевала. Ну, а когда она расхаживала по нашему двору в одном только миниатюрном купальнике, виляя своим аппетитным задом, член мой готов был выпрыгнуть из штанов.

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