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.