Dr Peter Woit’s representation theory for electroweak symmetry

Understanding spin is crucial to QFT. As shown in our paper, page 23, Figure 17, fermion spin results in angular momentum transfer in gauge boson exchange, producing magnetic fields, as Maxwell found in articles 822-3 of his final 1873 third edition of the Treatise on Electricity and Magnetism: “The … action of magnetism on polarized light leads … to the conclusion that in a medium … is something belonging to the mathematical class as an angular velocity … We must therefore conceive the rotation to be that of very small portions of the medium, each rotating [spin angular momentum].” (See Fig. 15 on page 21 of my paper for the origin of Maxwell’s theory.)

Maxwell’s deterministic magnetic field model of what is now called “field quanta” spin as the basis of magnetic fields makes electromagnetism an SU(2) Yang-Mills theory, not essentially an U(1) theory as assumed by Feynman and Pauli for QED (see Figure 31 in my paper for how isospin and electric charge are then related under SU(2) in the standard model). Abelian U(1) hypercharge still exists but only as the basis for quantum gravity, giving mass to the weak bosons via Weinberg-Glashow mixing, which replaces the Higgs mass mechanism, although the left-handed symmetry breaking due to mixing can still produce spin-0 Nambu-Goldstone bosons with a mass/gravitational charge of half the sum of the gravitational charges of the three weak bosons, (80 + 80 + 91)/2 = 125.5 GeV, and this accords with the Dirac spinor, the SU(2) Pauli spin matrix, and Weyl’s 1929 argument that Dirac’s spinor is chiral.

Copy of a comment submitted to: http://snarxivblog.blogspot.com/2012/01/dharwadker-and-khachatryans-prediction.html concerning the 2009 prediction by Dharwadker and Khachatryans of (80 + 80 + 91)/2 = 125.5 GeV spin-0 massive Nambu-Goldstone boson:

Cooper pairs of spin-1/2 fermions produce a spin-1 boson (condensate) explaining superconductivity, so since the Higgs spin-0 boson is already a boson, your case is that you’re not going to have two Higgs fermions forming a Cooper pair.

However, they do point out on pages 2-3:

“Theoretically, it is known that the SM Higgs boson is one neutral quantum component of the Higgs field, along with another neutral and two charged components acting as Goldstone bosons.”

– http://arxiv.org/PS_cache/arxiv/pdf/0912/0912.5189v1.pdf

What they are really doing (so far as their prediction is valid, ignoring BS arm-waving) is replacing this SM Higgs mechanism with a ~126 GeV spin-0 Higgs boson formed from two half integer spin particles (fermions).

While “supersymmetry” (postulating an additional high mass boson for every fermion in order to try to achieve similar couplings for all interactions at the Planck scale) is arm-waving unfalsifiable speculation, there is a glimmer of relevant physics you can gain here, if you go for a simpler and more predictive “supersymmetry” in which all bosons are composites of either massless or massive fermions.

Hence, SU(2) can be thought of as having two different charges of spin-1/2 fermions and their antiparticles, which can combine in 2×2 = 4 ways producing three distinctive bosons, with electric charges +1, -1, and 0 (there are two ways you get zero electric charge, thus a total of only three kinds of bosons from two charges of fermions).

Please see page 51 of Woit’s 2002 paper “QFT and representation theory” (part 10, Speculative remarks about the standard model) at http://arxiv.org/PS_cache/hep-th/pdf/0206/0206135v1.pdf where he shows that taking U(2) as a subset of SO(4) gives the standard model electroweak fermions with chiral features, for both leptons and quarks if the hypercharge is selected to make the “overall average U(1) charge of a generation of leptons and quarks to be zero.”

This is the underlying physics of the so-called “Higgs boson” mass (mass is quantum gravitational charge, and the “Higgs mechanism” ignores this), because since 1996 we have been publishing and a predictive U(1) gauge gravity theory, and the charge of quantum gravity is mass: so Woit’s 2002 argument about averaging hypercharge should also apply to masses for the particles. If there are right and left handed weak gauge bosons, half of the mass (the right-handed spinors) is “dark matter” because of the short-range (due to the mass) and the fact that it doesn’t undergo weak interactions. So Woit’s 2002 argument of averaging charges, applied to gravitational charges (masses) of the weak bosons, with only half of them engaging in weak interactions, could substantiate the formula (80.4 + 80.4 + 90)/2 ~ 126 GeV.

Weyl’s chiral electromagnetism was rejected by Pauli, who believed in parity conservation and thus apparently didn’t understand Lenz’s law in electromagnetism: all electrons in motion produce similar chiral helicity of magnetic field curl around the current, where this chiral magnetic field in Maxwell’s theory is due to spin. Thus, the curl of the magnetic field around a current is indicative of the chiral SU(2) nature of electromagnetism, if Maxwell’s theory of electromagnetism is correct. The problem for Woit is that spin quantum numbers are essential in quantum mechanics for the Pauli exclusion principle, which is an electromagnetic effect, not a weak force SU(2) interaction. Thus, there is empirical evidence for SU(2) spinor phenomena in electrodynamics. This indicates that U(1) is not the QED symmetry. Dr Thomas S. Love also makes this point by quoting Hans C. Ohanian’s article “What is spin” from the American Journal of Physics, v54, 1986, pp. 500-5:

“… contrary to the common prejudice, the spin of the electron has a close classical analog: it is an angular momentum of exactly the same kind as carried by the fields of a circularly polarized electromagnetic wave.”

However, Gerard ‘t Hooft rejects the spin by using a false argument based on a solid electron (which doesn’t exist), stating on page 27 of his 1997 Cambridge University press book In Search of the Ultimate Building blocks: “the ‘surface of the electron’ would have to move 137 times as fast as the speed of light.” This is a false objection to spin, since there the classical solid model of an electron upon which this calculation is based is wrong: the electron doesn’t have a surface moving faster than light. The spin is conveyed by field quanta, not a classical electron solid revolving like a planet.


Nitpicker (January 3, 2012 at 11:02 am): “A tad puzzled why you say “Spin(2n) as a double cover of SO(2n)”. For example Spin(3) = SU(2) is the double cover of SO(3) is the classic example of spin angular momentum.”


Peter Woit (January 3, 2012 at 11:43 am): “In the course I’ll certainly discuss the relationship between SO(3) and Spin(3)=SU(2) and their reps, but for the general case of SO(n) and Spin(n), even and odd n behave somewhat differently. In the even case there’s a beautiful parallelism with the symplectic group which I want to discuss, so that’s the case I’ll work out in detail. If you take a look at the old lecture notes linked to, maybe you can see what I’m doing.”

Woit’s 2002 paper on QFT and representation theory offers at page 51 an interesting and relevant U(2) representation in 4-d spacetime SO(4), which yields the correct chiral electroweak particle charges. This is interesting because as far as Woit is concerned, U(2) produces U(1) x SU(2), which is fair enough mathematically, but from our point of view the U(1) quantum gravity still contributes effectively (akin to hypercharge in the standard model) to SU(2) by Weinberg-Glashow mixing, although the actual mechanism is that the fractional SU(2) electric charges simply share field energy with mass (gravitational charge) as our model predicts. U(1) not only gives mass to SU(2) left-handed weak bosons by Weinberg-Glashow mixing, replacing the Higgs mass mechanism (although you can still have spin-0 massive Nambu-Goldstone bosons from the resulting breaking of symmetry), it also checkably predicted dark energy accurately two years ahead of discovery, and gravitation. General relativity is just a classical approximation, in which the Weyl quantum gauge type backreaction on the gravitational field is modelled by the contraction of the metric due to mass-energy. (This has nothing to do with Weyl’s earlier 1918 quantum gravity theory, which incorrectly quantized the metric, as explained in my paper.)

In the Einstein field equation which relates the Ricci curvature tensor to the stress-energy field source tensor, the product of the Ricci scalar and the metric represent the equivalent to the minimal coupling procedure in QED: the gravitational field is contracted due to the gravitational energy employed on mass. In other words, the contraction term in general relativity is nearest gravitational equivalent to the running coupling behind charge renormalization in QED. The gravitational field comes with only one sign of charge, not two as in electromagnetism, so it is not renormalized due to pair production polarization like electromagnetism. But it is renormalized in the sense that mass-energy is conserved, and the use of gravitational field energy affects the mass-energy which is the source of the gravitational field. You can’t do work by gravity without taking energy out of the gravitational field. Similarly, in electromagnetism, an electric charge can’t polarize virtual charges without some of the electric charge energy being used (core field “screening”). If an apple falls off a tree and hits the ground with a thump, the energy of the sound waves has come from gravitons in the gravitational field which accelerated the apple, converting gravitational potential energy (offshell field energy) into the kinetic energy of the apple (onshell energy).

This is the gravitational field “backreaction”. In QED, when the electromagnetic field does work, for instance in polarizing the vacuum, the energy used to polarize the vacuum has a backreaction upon the charge, “screening it”. This is just conservation of mass-energy. You cannot do work ordering the vacuum without expending energy. Einstein’s field equation contraction (needed to make both sides divergentless, for energy conservation) is analogous to this backreaction in the electromagnetic field. The work done energy by the gravitational field on mass (holding a planet together, for example) is exhibited by the conversion of gravitational charge (mass) into this energy. This is equivalent to a contraction of spacetime in the vicinity of mass. In other words, general relativity is already equivalent to QED in terms of quantum field theory. The major flaw of general relativity is the stress-energy tensor source term, which cannot correctly model discontinuous particles, but has to use “perfect fluid continuum” classical (smooth) approximations for the actually discontinuous distribution of matter. But the basic structure of Einstein’s field equation with the relativistic effects of the contraction term correctly models energy conservation.

Multipath interference causes the indeterminism in quantum field theory

On 30 Nov 2011, we completed a 63-page, 7.5 MB draft revision of the standard model, including quantum gravity predictions and confirmations for particle masses, couplings, etc. This is based on quantum field theory, Feynman’s approach to it, not Woit’s. Woit’s article in the American Scientist, “Grappling with Quantum Weirdness” claims that “quantum mechanics” (he doesn’t distinguish between 1st and 2nd quantization, one wavefunction or a path integral over separate wavefunctions for every path) “postulates that the state of a physical system is completely characterized by a vector in an infinite-dimensional vector space (the familiar quantum-mechanical “wavefunction”)”. Actually, each wavefunction amplitude is given by exp(iS/h bar), and you sum an infinite number of these wavefunctions, one for each path. So, yes, on an argand diagram this is represented by an infinite number of vectors (an infinite dimensional Hilbert space), and the resultant (integral of an infinite number of wavefunctions) is then equivalent to a single wavefunction for 1st quantization, but this is a false and wolly way of thinking. 1st quantization (a single wavefunction) is not relativistic and is not real: it’s a mathematical artifact of non-relativistic quantum mechanics. It’s wrong physically: there are field quanta, and the multipath interferences caused by these field quanta produce indeterminancy. The uncertainty principle is not a physical limit to understanding: in QFT it is caused by multipath interference from field quanta, as Feynman proves in his book QED (1985). Woit ignores this, proceeding instead with:

“The general consensus of the physics community is that Bohr’s point of view triumphed, enshrined in what became known as the “Copenhagen interpretation” of quantum mechanics. According to Bohr, the state-vector of a physical system evolves in time according to the Schrödinger equation and does not typically have a well-defined value for classical observables like position and velocity. When the system interacts with an experimental apparatus, the state-vector “collapses” into a state with a well-defined value of the observable being measured. In general, Bohr’s interpretation works perfectly well operationally, but it is conceptually incoherent and leaves important questions unanswered. How exactly does this “collapse” take place? … Most physicists generally believe that quantum mechanics, in its relativistic version as a theory of quantum fields, is a complete, consistent and highly successful conceptual framework.”

Woit shows he has no grasp of how 2nd quantization physically differs from 1st quantization. There is no single wavefunction for any particle: every particle has a separate wavefunction amplitude (wavefunction) for every single potential and real interaction with an onshell or offshell particle. It’s own field consists of offshell particles, with which it interacts. There is no single wavefunction! You always have a path integral, summing an infinite number of possible interaction paths. The Schrödinger equation has only a single wavefunction and is thus wrong: the real wavefunctions don’t “evolve” or “collapse”:

“If you … use the ideas that I’m explaining in these lectures – adding arrows [wavefunctions] for all the ways an event can happen – there is no need for an uncertainty principle! … The phenomenon of interference becomes very important, and we have to sum the arrows to predict where an electron is likely to be.” – Richard P. Feynman, QED, 1990, pp. 55-56, and 84-85.

(Feynman’s position is a path-integral over off-shell scattering interaction’s of a particle with its own field, which is just Sir Karl Popper’s argument on page 303 of his 1979 Oxford University press book Objective Knowledge, “… the Heisenberg formulae can be most naturally interpreted as statistical scatter relations, as I proposed [Popper, The Logic of Scientific Discovery, German ed., 1934] … There is, therefore, no reason whatever to accept either Heisenberg’s or Bohr’s subjectivist interpretation of quantum mechanics.”)

As Dr Love explains, the eigenstates in quantum mechanics are artificial discontinuities which produce wavefunction “collapse” mathematically, not physically whenever a measurement is taken. There are no real eigenstates. The electron has a path integral of field quanta interference which determines (to the electron, not to a human, who can’t do the path integral accurately or non-perturbatively) where it is at any time, so there is no real wavefunction collapse (except in the 1st quantization non-relativistic Schrödinger equation) when a measurement is taken. The point is, as Feynman explains very clearly, there is a difference between reality and 1st quantization. It is a lie that a single wavefunction exists; this is proved by the fact that the Schrödinger equation is non-relativistic and hence is wrong. It is quantum mechanics double-talk to lie that 1st quantization is not replaced by 2nd quantization. This double-talk is equivalent to claiming that phlogiston theory is a duality to oxygen theory, that epicycles are a duality to Kepler’s elliptical orbits, or that Piltdown man was not really a fraud but was a very helpful evolutionary pedalogical tool for convincing/teaching students, until discredited.