SU(2) x SU(2) = SO(4) and the Standard Model

The Yang-Mills SU(N) equation for field strength is Maxwell’s U(1) Abelian field strength law plus a quadratic term which represents net charge transfer and contains the matrix constants for the Lie algebra generators of the group.  It is interesting that the spin orthogonal group in three dimensions of space and one of time, SO(4), corresponds to two linked SU(2) groups, i.e.

SO(4) = SU(2) x SU(2),

rather than just one SU(2) as the Standard Model would suggest, which is U(1) X SU(2) X SU(3).  This is one piece of “evidence” for the model proposed in, where U(1) is simply dark energy (the cosmological repulsion between mass, proved in that paper to accurately predict observed quantum gravity coupling by a Casimir force analogy!), and SU(2) occurs in two versions, one with massless bosons which automatically reduces the SU(2) Yang-Mills equation to Maxwell’s by giving a physical mechanism for the Lie algebra SU(2) charge transfer term to be constrained to a value of zero (any other value makes massless charged gauge bosons acquire infinite magnetic self inductance if they are exchanged in an asymmetric rate that fails to cancel the magnetic field curls).  The other SU(2) is the regular one we observe which has massive gauge bosons, giving the weak force.

Maybe we should say, therefore, that our revision of the Standard Model is

U(1) x SU(2) x SU(2) x SU(3)


U(1) x SO(4) x SU(3).

As explained in, the spin structure of standard quantum mechanics is given by the SU(2) Pauli matrices of quantum mechanics.  Any SU(N) group is simply a subgroup of the unitary matrix U(N), containing specifically those matrices of U(N) with a positive determinant of 1.  This means that SU(2) has 3 Pauli spin matrices.  Similarly, SU(3) is the 8 matrices of U(3) having a determinant of +1.  Now what is interesting is that this SU(2) spinor representation on quantum mechanics also arises with the Weyl spinor, which Pauli dismissed originally in 1929 as being chiral, i.e. permitting violation of parity conservation (left and right spinors having different charge or other properties).  Much to Pauli’s surprise in 1956 it was discovered experimentally from the spin of beta particles emitted by cobalt-60 that parity is not a true universal law (a universal law would be like the 3rd law of thermodynamics, where no exceptions exist).  Rather, parity conservation is at least violated in weak interactions, where only left handed spinors undergo weak interactions.  Parity conservation had to be replaced by the CPT theorem, which states that to get a universally applicable conservation law involving charge, parity and time, which applies to weak interactions, you must simultaneously reverse charge, parity and time for a particle together.  Only this combination of three properties is conserved universally, you can’t merely reverse parity alone and expect the particle to behave the same way!  If you reverse all three values, charge, parity and time, you end up, in effect, with a left handed spinor again (if you started with one, or a right handed spinor if you started with that), but the result is an antiparticle which is moving the opposite way in time as plotted on a Feynman diagram.  In other words, the reversals of charge and time cancel the parity reversal.

But why did Pauli not know that Maxwell in deriving the equations of the electromagnetic force in 1861, modelled magnetic fields as mediated by gauge bosons, implying that charges and field quanta are parity conservation breaking (Weyl type chiral handed) spinors?  We discuss this Maxwell 1861 spinor in, which basically amounts to the fact Maxwell thought that the handed curl of the magnetic field around an electric charge moving in space is a result of the spin of vacuum quanta which mediate the magnetic force.  Charge spin, contrary to naive 1st quantization notions of wavefunction indeterminancy, is not indeterminate but takes a preferred handedness relative to the motion of charge, thus being responsible for preferred handedness of the magnetic field at right angles to the direction of motion of charge (magnetic fields, according to Maxwell, are the conservation of angular momentum when spinning field quanta are exchanged by spinning charges).  Other reasons for SU(2) electromagnetism are provided in, such as the prediction of the electromagnetic field strength coupling.  Instead of the 1956 violation of parity conservation in weak interactions provoking a complete return to Maxwell’s SU(2) theory from 1861, what happened instead was a crude epicycle type “fix” for the theory, in which U(1) continued to be used for electrodynamics despite the fact that the fermion charges of electrodynamics are spin half particles which obey SU(2) spinor matrices, and in which the U(1) pseudo-electrodynamics (hypercharge theory) was eventually (by 1967, due to Glashow, Weinberg and Salam) joined to the SU(2) weak interaction theory by a linkage with an ad hoc mixing scheme in which electric charge is given arbitrarily by the empirical Weinberg-Gell Mann-Nishijima relation

electric charge = SU(2) weak isospin charge + half of U(1) hypercharge

Figure 30 on page 36 of gives an alternative interpretation of the facts, better consistent with reality.

Although as stated above, SO(4) = SU(2) x SU(2), the individual SU(2) symmetries here are related to simple spin orthogonal groups

SO(2) ~ U(1)

SO(3) ~ SU(2)

SO(4) ~ SU(3)

It’s pretty tempting therefore to suggest as we did, that the U(1), SU(2) and SU(3) groups are all spinor relations derived from the basic geometry of spacetime.  In other words, for U(1) Abelian symmetry, particles can spin alone; and for SU(2) they can be paired up with parallel spin axes and each particle in this pair can then either have symmetric or antisymmetric spin.  In other words, both spinning in the same direction (0 degrees difference in spin axis directions) so that their spins add together, doubling the net angular momentum and magnetic dipole moment and creating a bose-einstein condensate or effective boson from two fermions; or alternatively spinning in opposite directions (180 degrees difference in spin axis directions) as in Pauli’s exclusion principle, which cancels out the net magnetic dipole moment.  (Although wishy-washy anti-understanding 1st quantization QM dogma insists that only one indeterminate wavefunction exists for spin direction until measured, in fact the absence of strong magnetic fields from most matter in the universe is continuously “collapsing” that “indeterminate” wavefunction into a determinate state, by telling us that Pauli is right and that spins do generally pair up to cancel intrinsic magnetic moments for most matter!)  Finally, for SU(3), three particles can form a triplet in which the spin axes are all orthogonal to one another (i.e. the spin axis directions for the 3 particles are 90 degrees relative from each other, one lying on each x, y, and z direction, relative of course to one another not any absolute frame).  This is color force.

Technically speaking, of course, there are other possibilities.  Woit’s 2002 arXiv paper 0206135, Quantum field theory and representation theory, conjectures on page 4 that the Standard Model can be understood in the representation theory of “some geometric structure” and on page 51 he gives a specific suggestion that you pick U(2) out of SO(4) expressed as a Spin(2n) Clifford spin algebra where n = 2, and this U(2) subgroup of SO(4) then has a spin representation that has the correct chiral electroweak charges.  In other words, Woit suggests replacing the U(1) x SU(2) arbitrary charge structure with a properly unifying U(2) symmetry picked out from SO(4) space time special orthogonal group.  Woit represents SO(4) by a Spin(4) Clifford algebra element (1/2)(e_i)(e_j) which corresponds to the Lie algebra generator L_(ij)

(1/2)(e_i)(e_j) = L_(ij).

The Woit idea, of getting the chiral electroweak charges by picking out U(2) charges from SO(4), can potentially be combined with the previously mentioned suggestion of SO(4) = SU(2) x SU(2), where one effective SU(2) symmetry is electromagnetism and the other is the weak interaction.

My feeling is that there is no mystery, one day people will accept that the various spin axis combinations needed to avoid or overcome intrinsic magnetic dipole anomalies in nature are the source of the fact that fundamental particles exist in groupings of 1, 2 or 3 particles (leptons, mesons, baryons), and that is also the source of the U(1), SU(2) and SU(3) symmetry groups of interactions, once you look at the problems of magnetic inductance associated with the exchange of field quanta to cause fundamental forces.

Quack money making pseudophysics hype by John Gribbin, according to Peter Woit’s “Past the End of Science” article

Mathematician Peter Woit, on Not Even Wrong, points out that John Gribbin is “author of the 2009 multiverse-promotional effort In Search of the Multiverse. I don’t know how Gleiser treats this, but Gribbin emphasizes the multiverse as new progress in science… Gribbin and his multiverse mania for untestable theories provides strong ammunition for Horgan, since it’s the sort of thing he was warning about.”

In an email to me about a decade ago, author John Gribbin asked me if a theory had any confirmed falsifiable predictions. When these were supplied, he didn’t reply and showed no further interest. Catering to prejudice, or entering popular (media aware) controversy, is more profitable and rewarding for the “free media” than getting into backwaters.  The rise of popular quack physics like the multiverse is an infiltration tactic in the physics lobby, a tactic first employed successfully by communist infiltrators of socialist parties.  The reason for infiltration tactics is that an an honest call to turn physics into a religion or quackery is unpopular, just as an honest call for Communism leads to defeat in the elections.  So proponents are “forced” into duplicity and sailing under false flags:

“In 1950 all the Communist Party’s 100 candidates were defeated, including the two Communist MPs who had sat in the 1945 Parliament.  This heightened the determination of the Communists to control the Labour Party by indirect means since they could not establish themselves in Parliament under their own name.”

– Woodrow Wyatt, What’s left of the Labour Party?, Sidgwick and Jackson, London, 1977, p43.

Wyatt, himself one of the authors of the 1947 Keep Left book, goes on to document how religious style bigotry by the hard-left control of the Labour Party (and eventually of the British Government) was indirectly established when in 1956 the Kremlin’s Khrushchev-fan, Mr Frank Cousins, became the general secretary of the Transport and General Workers Union, which held the vote swing in the Labour Party Conference; in 1969 Cousins was succeeded by the even more militant, eye-to-eye with Brezhnev, Jack Jones, leading to Britain’s strife, strikes, IMF bailout (due to national bankrupcy), winter of discontent, etc. in the 1970s.  Our point is, indirect infiltration and subversion tactics are used by fanatics to overcome direct barriers.

It’s like the Maginot Line, the French fortifications supposedly guaranteeing peace for all time by physically preventing German tanks from entering France.  The problem was, the tanks went around it.  Similarly, Nagasaki actually had bomb shelters for 70,000 which survived the nuclear explosion intact with 100% survival rate for the 400 people in them, but because it was a surprise attack, nobody took notice of the single B-29 in the sky and most people were not in the shelters.  The point we’re driving at is that if you pass a law or build a barrier, you must expect that opponents will try to seek a way around it.  In other words, you must deliberately focus on seeking out the weakest link in your defense, and strengthening it, or else the enemy will exploit it.  It’s not good enough to try to close down this argument by using propaganda which promotes the strongest links in your defense to try to stifle criticisms, or to label critics of mainstream defense propaganda as paranoid.  What usually gets dismissed as paranoid is actually often valid criticism.  To assume that the enemy will not exploit weaknesses in your defense is not anti-paranoia, but rather is insanity.

If in science you have a law saying “Law 1: Falsifiable predictions only”, and if opponents of the law can’t directly overturn it to make science a religion by “honest” (i.e. open, fairly stated) democracy means, they simply agitate to add an exception that effectively reverses the law: “Law 1, exception 1: theories that are incomplete need not make falsifiable predictions”.

Similarly, the Soviet Union dismissed critics who claimed that it was an unequal, unjust, non-communist dictatorship of hatred by claiming that once it had disposed of all its enemies like capitalists, it would then be able to become the promised utopia.  Because it was never able to achieve its aims, it had the perfect excuse to remain a fascist-type dictatorship of censorship and enforced poverty.

The propaganda level of science, driven by ruthless fanatics of quackery, makes it far exceed the threat to liberal equality that the USSR presented. The USSR was a failed version of capitalism pretending to on the road to utopia and maintained by force; quack science today is far better at media and taxpayer funding manipulation than the USSR ever was.


Inflation theory debunked by Paul Steinhardt in Nature

“The … truth about inflationary theory. The common view is that it is a highly predictive theory. … the inflationary paradigm is so flexible that it is immune to experimental and observational tests. First, inflation is driven by a hypothetical scalar field, the inflaton, which has properties that can be adjusted to produce effectively any outcome. Second, inflation does not end with a universe with uniform properties, but almost inevitably leads to a multiverse with an infinite number of bubbles, in which the cosmic and physical properties vary from bubble to bubble. The part of the multiverse that we observe corresponds to a piece of just one such bubble. … No experiment can rule out a theory that allows for all possible outcomes. Hence, the paradigm of inflation is unfalsifiable… Taking this into account, it is clear that the inflationary paradigm is fundamentally untestable, and hence scientifically meaningless.”

– Paul Steinhardt, Big Bang blunder bursts the multiverse bubble, Nature, 3 June 2014.

QG fundamentals 1

The quantum gravity theory which quantitatively predicted dark energy in 1996 ( and predicts the low curvature of the early universe that’s normally attributed to “inflation” speculation, also predicts the electromagnetic coupling for the for same verified cross-section used in quantum gravity:

QG fundamentals

Testable alternative to inflation theory: quantum gravity theory provably flattens early spacetime curvature as observed, without introducing any epicycles, please see and other papers at vixra, e.g.

Quantum Gravity is a Result of U(1) Repulsive Dark Energy,

Rival for inflation theory to explain cosmology

  1. A commenter at Not Even Wrong asks the following question:
    1. Monty says:

      I watched the video from the World Science Festival. Could I ask Peter, or the commenters, what would be wrong with the following response to Steinhardt’s complaint that whatever the BICEP2 results had been, they could be made to fit with some variant of inflationary theory: yes, the observation of B-mode polarisation (let’s assume it’s not an artifact of foreground dust–this will be shown one way or the other soon in any case) cannot by itself prove inflation. But it lets us choose appropriate candidate theories from within the previous set of inflationary theories, and, more importantly for inflation-backers, it adds another item to the list of things requiring explanation for any competing theory. So now we have not only isotropy, flatness, absence of relics, and large-scale structure to explain, but we also have otherwise unexplained B-mode polarisation of the CMB. An appropriately narrowed inflation model can account for all of those things at once; that makes it correspondingly harder for an alternative theory to be equally successful. Doesn’t that make it a stronger theory than it was this time last year?

    2. My response: No if it’s an epicycle theory which “explains” stuff by using censorship of alternatives: “that makes it correspondingly harder for an alternative theory to be equally successful.”  The success of epicycles was that it gave vacuous ammunition to those who wanted for subjective reasons to ignore Aristarchus’s unpopular, unfashionable, apparently more complex system of earth rotating and orbiting the sun. There were various spurious (false law-based, rather than direct evidence-based) no-go theorems against Aristarchus’s solar system, but the alleged simplicity and elegance of epicycles won over in the minds of charlatans (“let’s simply have every thing orbit earth, adding epicycles to make it work! How beautiful! The landscape of possible models is big enough to be non-falsifiable, yipee! Great science!”).  Of course, inflation is different since it’s seeking to close down the scientific search for better alternatives before they’re even emerged into public view…

    3. I will add a paper specifically concerning the quantum gravity alternative to “inflation theory” to vixra when time permits.

B-mode quantum gravity evidence from 300,000 years after the big bang and its abuse by inflationists

  • “Have you detected B-modes from inflation
    We have detected B-mode polarization at precisely the angular scales where the inflationary signal is expected to peak with very high significance (> 5 sigma). We have extensively studied possible contamination from instrumental effects and feel confident we can limit them to much smaller than the observed signal. Inflationary gravitational waves appear to be by far the most likely explanation for the signal we see.” – BICEP2 propaganda error,
  • The problem with assuming that because inflation theory is the most fashion-hyped mechanism to suppress gravitational curvature in the early universe, it is the most likely mechanism.  (E.g., in 250 BC, Aristarchus of Samos suggested the earth rotates daily and orbits the sun annually, as an “alternative theory” to the theory that the sun orbits the earth daily; but Aristarchus was later dismissed falsely as contrived, complex and improbable by Ptolemy in 150 AD.  Science is about objectivity, which means not subjectively dismissing alternative theories because they look more complex or less fashionable or popular!  If you have more than one theory which models the data, you should be honest and admit it, not lying!)
  • The “New Scientist” and other mainstream media are ignoring the alternative quantum gravity theory which predicts the correct weak curvature at 300,000 years given by the cosmological background radiation temperature fluctuations, and falsely assuming that inflation is the only theory!  As a “strawman criticism” against BICEP2 data, New Scientist is now reporting MHD-EMP (compression of magnetic field lines by expanding supernovae explosion debris) as a contaminant to the data.  However, this just deflects attention from the key argument, which is over the mechanism for small scale of the temperature fluctuations:

cosmological background radiation polarization

Lee Smolin astutely pointed out on Woit’s Not Even Wrong blog that the B-mode polarization of the CBR is more important for quantum gravity than for anything else: “we may have confirmation of quantum gravity effects before we have direct detection of classical gravitational waves”.

Left handed circularly polarized light animation

B mode polarization diagram

There’s a kids-level description of the very simple polarization of the cosmic background radiation (which is just a normal Planck radiation spectrum at 2.7 K temperature) in section 6.5 (Polarization of the Cosmic Microwave Background Radiation) on pages 121-5 of Luis Álvarez-Gaumé and Miguel Á. Vázquez-Mozo, “An Invitation to Quantum Field Theory (Springer-Verlag Berlin Heidelberg, 2012):

“The differential cross section of Thomson scattering we have derived is relevant in many areas of physics, but its importance is paramount in the study of the cosmological microwave background radiation (CMB). Here we are going to review briefly how polarization emerges in the cosmic background radiation and discuss why its detection could serve as a window to the physics of the very early universe. … Just before recombination [3000 K or ~0.3 kev temperature at 300,000 years after the big bang] the universe is filled with a plasma of electrons interacting with photons via [non-relativistic] Compton scattering [hence the low energy Thomson cross-section applies to the Compton effect, not the Klein-Nishina formula that is needed for higher energy, relativistic effects from 1 keV to 1 MeV when pair-production starts]. … so the approximations leading to Thomson differential cross section apply. … Since Thomson scattering suppresses all polarizations in the direction of the incoming photons we find that the two polarizations in the scattered radiation come from the ‘horizontal’ polarizations of the incoming photons …

“The previous heuristic arguments show that the presence of a net polarization in the CMB is the smoking gun of quadrupole anisotropies in the photon distribution at the last scattering surface. … Gravitational waves propagating through the plasma induce changes in its density with precisely the quadrupole component necessary to produce the polarization in the CMB radiation. [Lengthy calculation follows …] In other words, what we have concluded is that the measurement of the polarization of the CMB gives direct information about the quadrupole component of the distribution function of photons at decoupling!”

B mode polarization calculation

Dr Igor Khavkine, who you will remember is one of those who censored out my quantitative, fully predictive and proof checked evidence for quantum gravity (1996 prediction of the correct quantity of dark energy, first seen two years later), now writes at Not Even Wrong on 29 March 2014 somewhat ironically about the new B-mode gravity wave evidence and the big bang inflation hypers who seize it as proof of their particular non-existent “theory”:

“I’m not an expert in the various physical effects surrounding inflation. However, based on information provided in some of the presentations of the BICEP2 results, it seems to me that the status of the B-mode signal detection as evidence of quantum gravitational effects + inflation can be put on the same footing as the status of CMB temperature fluctuations as evidence primordial quantum fluctuations of the inflaton field. Indeed, the latter seems to be fairly well accepted and the two observations are indirect in similar ways. I’ve based the following on information from various talks I’ve attended and discussions with cosmologists. It would be rather hard for me, unfortunately, to dig up specific references. …

“In my understanding, the temperature anisotropies that we see (provided all foreground effects can be assumed to have been eliminated) tell us directly only about the photon times of flight (accounting for different amounts of red shift) from the surface of last scattering to us. These varying times of flight are then considered evidence for (classical) density fluctuations present at the time of recombination. The distribution of mode amplitudes of these fluctuations appears to be gaussian …

“Similarly, the observed B-modes tell us directly only the presence of (classical) gravitational waves at the time of recombination. Actually, already this point could be disputed, because the degree of directness depends on the ability to exclude other sources of B-modes. Perhaps magnetic fields could be another source, but the BICEP2 analysis team didn’t seem to think that it was likely. I’m not sure about all the reasons, but lets take that for granted now. Lets also presume that the distribution of mode amplitudes of these gravitational waves was also gaussian, with covariance matrix estimated from the B-mode 2-point function. At the very least, I have not yet seen anyone bring up any evidence of non-gaussianity in the detected B-modes. … If inflation did happen, then it would leave behind this kind of signature, as amplified quantum vacuum fluctuations: (a) gaussian distribution of fluctuations connected to the gaussian shape of the quantum vacuum, (b) “large” amplitude (large enough for the fluctuations to have become classical) set by the amount of expansion during inflation, (c) a fixed relationship between gravitational and scalar amplitudes as a function of frequency …

“So, in the absence of other pre-recombination physics that would generate signals with specific signatures (a), (b) and (c), the observations of temperature anisotropies and B-modes do point toward inflation, an inflaton-driven period of rapid expansion in the early universe. And, if inflation did happen, then the detected B-modes do in fact descend from amplified graviton quantum vacuum fluctuations. A similar thing was said, and widely accepted, of temperature anisotropies long before the B-mode detection. Of course, alternatives where a signal with signatures (a), (b) and (c) is not of quantum origin might be possible, but they’d have to be subject to investigation and testing like any other hypothesis. At the moment, the inflation hypothesis seems to be doing rather well compared to its rivals.”

You have a theory, let’s say inflation. At 10^{-32} second or so, fundamental forces decouple from an unproved grand unification (by which most of these political guys mean a communist “equality” of running coupling parameters), and the universe “inflates” faster than the velocity of light, thereby distributing the matter over a large volume and drastically reducing the gravitational field curvature.  That’s Guth’s “theory”.  Now there are many problems with calling it a “theory”.  First, there’s no proved grand unified theory for inflation.  Second, there’s no hard quantitative predictions, merely equations with unknown and therefore adjustable parameters, which permit (but don’t prove) epicycle-like fits to data.  But the worst thing is that the “theory” isn’t unique.  It has to be hyped with giant neon lights in order to deflect attention from rival theory that do better, predicting quantum gravity, dark energy and weak gravitational curvature at 300,000 years after the big bang in a quantitative way (including predictions of constants and parameters, which don’t need to be “deduced” from the data they are claiming to “explain”), unlike the adjustable (ad hoc or qualitative) equations of inflation “theory”.  In the rival theories, you get politics.  The biggest hyped rival theory is equally non-predictive nonsense, as is the third.  Only a totally ignored theory way down the list, which is censored out by all lying hype and neon adverts for the “top” theories, has actual evidence that replaces inflation!  But if you point this out quietly, you’re ignored, and whatever you say you’re ignored.

(In fact, if you merely point out that you’re ignored, you get angry ad hominem attacks claiming that you’re a publicity seeker or whatever, which totally ignore what you’re saying, and the “editors” refuse to edit or even make constructive criticisms.  They’re paranoid and bitter with anyone truly innovative, but like the censors in George Orwell’s fairy tale, they redefine works to try to convey those qualities on to the people whose ideas they refuse to check.  Innovators are then labelled paranoid and bitter.  All this simply wastes time and effort.  Trying to get through biased peer-review is a waste of everybody’s time, just like “peaceful diplomacy” with Nazis.)


84.5% of mass (dark matter) is massive right-handed neutrinos

Right handed neutrinos: dark matter

See links herehere, here, here and here.  The hard fact is: massive right handed neutrinos don’t contribute much to weak interactions because of their immense mass, but do interact with gravity unlike massless left handed neutrinos.  I can’t understand why dark matter in the form of massive right handed neutrinos isn’t already considered a confirmed fact, based on experimental evidence of neutrino flavor mixing!  (See my discussion of massive right handed neutrino lifespan evidence below.)

Right handed neutrinos are implied by neutrino flavor mixing data and the see-saw mechanism for neutrino mass: left handed neutrinos are massless, right handed neutrinos are massive, so the small apparent (“observed”) masses of neutrinos are an average over time for oscillations between the briefly-existing massive right-handed neutrinos (which, due to their large mass, have a short mean-free-path before transforming back into massless left-handed neutrinos in the vacuum) and the longer-existing (massless) left handed neutrinos, which can only undergo weak interactions!

The (large) mass of right-handed neutrinos makes them couple to the gravity field, not only the weak interaction; but the lack of mass of left-handed neutrinos ensures that those merely couple to the weak force, not gravity.  This asymmetry in couplings for the two kinds of neutrinos is responsible for the small observable apparent mass of neutrinos, which is simply a time-average superposition between both of the states.  I don’t understand how anyone can accept the model for neutrino oscillation between between left and right handed states, if they don’t accept that both states have at least one interaction (i.e. Standard Model weak charge) in common, so I disagree strongly with Peter Woit’s statement that right-handed massive neutrinos don’t undergo weak (or any other S.M.) interactions:

Right-handed neutrino fields fit naturally into the SM pattern of fundamental fields, but with zero SU(3)xSU(2)xU(1) charges. That such fields have something to do with dark matter looks more promising than the SUSY or axion proposals of introducing a new and different sector of fields. – Woit

I disagree that right-handed neutrinos need to have a lack of weak charge: their short life (due to their mass) reduces the effective weak charge of right-handed neutrinos, simply because they aren’t there for long, as compared to left-handed neutrinos!  So I very much prefer Professor Matt Strassler’s far more cautiously-worded comment about right handed neutrinos:

… the dark matter particles are kind of like neutrinos — they’re fermions, like neutrinos, and they are connected to neutrinos in some way, though they aren’t as directly affected by the weak nuclear force.  [Emphasis added to key words.]

The fact that the right-handed neutrinos “aren’t as directly affected by the weak nuclear force” as left-handed neutrinos is simply down to their short-lifetime due to their immense mass.

The lifetime for spontaneously produced particles of mass in vacuum is only h-bar/(mc^2) seconds, whereas left handed neutrinos are massless and therefore have an effectively infinite lifetime, and so they remain unchanged until they undergo a weak interaction with either a flavour-changing, massive, short-lived right-handed neutrino in the vacuum, or else a Standard Model weak charge.

Since the massive Standard Model charges that form ordinary matter are long lived (not spontaneous pair-production short-life particles in the vacuum), their weak charge cross-sections are more apparent, simply because they last far than those of massive right-handed neutrinos, a simple fact that apparently appears so “facile” to some highly technical dudes, that no effect is made to grasp it at all!

Milner-Zuckerberg Prizes for Mathematics

Peter Woit states: “At the Hollywood-style awards ceremony last night for $3 million string theory and biomedical research prizes, it was announced that Yuri Milner and Mark Zuckerberg will now start funding something similar in mathematics, called the Breakthrough Prize in Mathematics. … I’ve written extensively about the “Fundamental Physics Prize” and what I see as the worst problem with it (heavily rewarding and propping up a failed research program).  … The physics prize has turned out to be extremely narrowly targeted at one particular subfield of physics … the main argument for the prizes is that the money (and Academy Awards-style ceremonies) will help make them celebrities … I still think the whole concept is problematic. The US today is increasingly dominated by a grotesque winner-take-all culture that values wealth and celebrity above all else.”

I strongly disagree with everything Peter Woit states here (see footnote at end of this post for my take on his classic anti-capitalism politics), but especially his hypocrisy in speaking out against celebrity while also claiming to take a stand against the dictatorship of physics by one failed unification idea which has become a religious dogma among leading physicists, with objections being deemed heretical, resulting in excommunication. The dangers here need spelling out clearly:

(1) that if he acquires celebrity status as the “debunker of string theory” and gets his argument wrong, he’ll only make the problem worse for others (in other words, if he leads the anti-string lobby and fails to overturn string, he’ll be used as a straw man opponent by the string theorists);

(2) the only way to overturn a failed dogma theory historically has been to replace it with something better.  This is not Woit’s approach, which is to make criticisms without suggesting a better theory.  So, on this basis, Woit is making the problem worse and providing a straw man target;

(3) Woit reproduces the electroweak sector charges of the standard model (including chiral features, since right-handed spinors in his model have zero weak charge) by picking out a U(2) symmetry as a subset of SO(4) spacetime (on page 51 of, based on his 1988 paper “Supersymmetric quantum mechanics, spinors and the standard model”, Nuclear Physics, vol. B303, pp. 329-42), yet he does not try to strongly market this theory as an alternative by making it the focus of a book or popular article, instead writing weakly/humbly on page 51 of a long technical paper: “The above comments are exceedingly speculative and very far from what one needs to construct a consistent theory. They are just meant to indicate how the most basic geometry of spinors and Clifford algebras in low dimensions is rich enough to encompass the standard model and seems to be naturally reflected in the electro-weak symmetry properties of Standard Model particles.”

Woit weak leadership

However it is clear that this fact – that progress in low dimensions is possible – leads Woit to his criticisms of string dogma.  In other words, Woit appears to me to be putting forward arguments against string which are weaker than they need to be, for a psychological reason (modesty).  Let’s make this fact crystal clear: Woit in 1988 discovered an alternative approach to developing a better understanding of electroweak symmetry, based on the mathematical representation of the U(2) symmetry in simple 4 dimensional Euclidean space.  This caused Woit to feel uneasy with Witten’s 1995 10/11 dimensional M-theory hype, despite the fact that Woit’s graduate work in computational (Wilson formulation) lattice QCD nuclear physics utilized Edward Witten’s earlier conjecture on the large N expansion (Witten’s 1979 paper: “Baryons in the 1/N expansion”, Nuclear Physics, vol. B160, pp. 57-115, a mathematical conjecture which seems to be based on thinking of the strong force using a hadronic string model).

Witten’s problem for physics today is his 1995 M-theory (conjecture) that 10 dimensional superstring is a brane surface on an 11 dimensional supergravity bulk. This speculation reinforces and hardens dogmas like SUSY, increasing the parameters of the Standard Model from 19 to at least 125 parameters in the minimally supersymmetric standard model.

The bottom line is, instead of presenting his strongest (objective) evidence against M-theory (his own research as a replacement direction for physics to go in), Woit instead raises a lot of relatively subjective arguments about the lack of “progress” in M-theory.  This is unsatisfactory, because “progress” is ill-defined in science: to someone digging in a hole, the deeper the hole gets, the more “progress” is being made.  To critics, it’s the opposite, and people in holes should stop digging.  Such arguments go nowhere, because if you are digging for gold and don’t know how deep the gold is (if it is there at all), it’s an arbitrary decision to quit.  Moreover, the more time and effort you “invest” (to critics: “waste”) in digging your hole, the less inclined you are to admit failure, lose face, etc.  Only when you get hungry and run out of supplies, are you likely to relent, and then you won’t admit failure. You’ll go to your grave dreaming of digging deeper in your hole.  The only way to defeat this, is for someone else to find the gold.  What drives some of us, is not the dream of seeing gold, but the desire to find the gold simply to discredit smug mathematical elitism.


Peter Woit attacks prizes for promoting capitalism with smug words: “The US today is increasingly dominated by a grotesque winner-take-all culture that values wealth and celebrity above all else.”

The problem is that this attitude ends up making prizes even more warped, because it introduces a political-type crusading aspect, rewarding high-profile scientists with failed grand unification theories but who are “worthy” in some other way. For instance, people either famous for making lots of money out of best-selling non-mathematical hype-style kids books “about mathematics”, or else famous for some kind of politically correct anti-capitalism or pro-environmentalism crusade (based on subjective or controversial interpretations of ambiguous data).

Apart from this purely “Matthew effect” corruption in prize ceremonies, there is also the egotism of those giving the prizes, which sometimes corrupts the selection of recipient: money is used to “buy” free publicity in the media, so you must give a prize to an already interesting or famous celebrity, to host an awards ceremony with media attendance. This is contrived “news” but it works.

Staged ad-style philanthropy is more praiseworthy than high-profile mega-rich celebrities begging those poorer to donate to good causes, while pretending to do this “free” (their payback is the relatively positive free “positioning” publicity they receive in the process of doing it, usually aided by public service awards). This is what Woit is missing in his analysis.

It’s not a choice of good versus bad options, but of bad versus very bad. It’s far better to take the lesser of two evils. Capitalism has its problems, but it works better than the USSR type socialist idealism, with its monolithic centralized control and its demotivating, restricting bureaucracy. Similarly, arbitrary prizes are vulnerable to corruption like capitalism, but probably work better than regimented consensus, which has its own set of groupthink problems.

Woit reproduces the electroweak sector charges of the standard model (including chiral features, since right-handed spinors in his model have zero weak charge) by picking out a U(2) symmetry as a subset of SO(4) 4-dimensional spacetime (on page 51 of which is based on his 1988 paper “Supersymmetric quantum mechanics, spinors and the standard model”, Nuclear Physics, vol. B303, pp. 329-42), yet he does not try to strongly market this theory as an alternative by making it the focus of a book or popular article.

Although Woit “only” reproduced the electroweak charges and chiral features of the electroweak sector correctly in 1988, there has been some technical work since then dealing with the non-symmetry details of U(2) theory which Woit left untouched.  See, for example, the paper by Aranda, Carone and Lebed, U(2) Flavor Physics without U(2) Symmetry, which models the weak mixing angles (CKM matrix) and fermion mass relations.  So U(2) is not just a threadbare model of the electroweak sector charges and handedness.

Whether this specific example is totally correct or not, Woit’s conjecture that “The quantum field theory of the standard model may be understood purely in terms of the representation theory of the automorphism group of some geometric structure” (quoted from, page 4) remains a promising avenue of investigation and should be rigorously pursued as an alternative to superstring.

Relevant technical trivia

Sophus Lie invented Lie symmetry group theory in 1874 and William Clifford invented Clifford algebras in 1876.  For the purposes of particle physics (but not necessarily math de la rigor mortis),  since Spin(n) is a double-cover of SO(n), they fit together and are therefore isomorphisms geometrically.  From the perspective of the number patterns involved, as utilized in particle physics, the following useful isomorphisms or equivalences hold:

Spin(2) = U(1) = SO(2)

Spin(3) = Sp(1) = SU(2) = SO(3)

Spin(4) = SU(2) × SU(2) = Sp(1) × Sp(1) = SO(4)

(It’s not always mathematically rigorous to treat an isomorphism as a strict equality, however useful it is in physics.  For example, E = mc if literally true would imply that 9 × 1016  Joules of energy has exactly the same price as 1 kilogram of manure.  If Einstein was literally asserting a simple equivalence, we could substitute or sell one for the other in that exact ratio.  Since nobody will buy 1 kilogram of manure for the same price as 9 × 1016  Joules  of energy, it’s obvious that the conversion equivalence is not always as simple as that.  Similarly, the equation 1 + 1 = 2 taken naively would suggest that two halves of a wedding cake are the same value as a whole  wedding cake.  It’s obviously not true.  If you chop 10 feet of rope into 10 separate 1 foot sections, you still have literally “10 feet of rope”, but may be of far less value to a sailor.  The point is, any equivalence in general may only have a limited range of exact validity, like an analogy between the similarities of different systems. Two halves of a car are less useful than one whole car.  This is so obvious that it is omitted from arithmetic, but this logical “reductionist problem” can cause problems in more abstract areas of science where things are not so obvious, and so you need to be far more careful.)

With the above isomorphism

SU(2) × SU(2) = SO(4)

where SO(4) is used to produce Woit’s U(2) electroweak particle charges, we can represent weak interactions by one SU(2) with massive bosons, and the other SU(2) as a hidden electrodynamics symmetry with massless bosons that reduces the Yang-Mills via a technical mutual magnetic self-inductance mechanism (which prevents the one-way motion of charged massless bosons, but not massive charged bosons; thus eliminating the charge transfer quadratic term in the Yang Mills equations and reducing them to Maxwell’s equations), to appear like the familiar Abelian U(1) Maxwell electrodynamics theory.

Backing this up SU(2) electrodynamics up further, the three Pauli matrices of SU(2) isospin are extremely similar in basic structure to the two gamma matrices of Dirac, with the third Pauli matrix being equivalent to Weyl’s chiral spinor:

SU (2) electrodynamics spinor. The sigma components in the second Dirac gamma matrix are themselves given by the SU(2) Pauli matrix, a fact which has helped to confuse the simplicity of this SU(2) electrodynamics symmetry.  Dirac's omission of chiral handedness from QED was later corrected by the addition of a chiral spinor by Weyl, yet the hype of Dirac's work and the initial obscurity of Weyl's (Pauli dismissed Weyl's prediction of chiral effects until 1957 when the left handed nature of weak interactions was discovered experimentally) turned half-baked initial ideas into a dogma, which resists correction to this day.  Electrodynamics is an SU(2) theory; the fact you need 4 polarizations  (not two as for onshell photons) for electromagnetic gauge bosons (offshell photons) to mediate attractive and repulsive forces in QED should make this clear, but is currently camouflaged by "proud statements" of the sort: "nobody understands quantum mechanics", which are today used as an excuse to censor out progress.

SU (2) electrodynamics spinor. The sigma components in the second Dirac gamma matrix are themselves given by the SU(2) Pauli matrix, a fact which has helped to confuse the simplicity of this SU(2) electrodynamics symmetry. Dirac’s omission of chiral handedness from QED was later corrected by the addition of a chiral spinor by Weyl, yet the hype of Dirac’s work and the initial obscurity of Weyl’s (Pauli dismissed Weyl’s prediction of chiral effects until 1957 when the left handed nature of weak interactions was discovered experimentally) turned half-baked initial ideas into a dogma, which resists correction to this day.  The standard textbook approach to the standard model is that Dirac’s equation gives the lagrangian for massive fermions, and Weyl’s spinor only comes into play for “massless fermions” (formerly believed to be neutrinos).  But this is falsified by the empirical observation that neutrinos change flavor as they propagate and therefore have mass, despite engaging in weak left-handed interactions.  So it does appear that massive fermions can contradict Pauli’s ad hoc parity conservation law, thus Weyl’s handedness spinor applies to massive particles.   Electrodynamics is an SU(2) theory because of the fact you need 4 polarizations (not two as for onshell photons) for electromagnetic gauge bosons (offshell photons) to mediate attractive and repulsive forces in QED should make this clear, but is currently camouflaged by “proud statements” of the sort: “nobody understands quantum mechanics”, which are today used as an excuse to censor out progress.

The rationale for including Weyl’s chiral spinor in QED (not just in weak theory) goes back to Maxwell himself, who argued that the fixed direction of curl of the magnetic field circling around moving electrons (or a wire carrying a current) is evidence for a chiral handedness of spin: Maxwell had a spin angular momentum transfer  (spinning vortex or “gear box”) model for the mediation of magnetic forces through space.  Abstract gauge theory today needs to properly replace Faraday’s old field line theory, or Einstein’s curved space time theory, with a mechanism for force production by gauge boson exchange.  The Casimir force is an example: two conducting metal plates exclude pressure effects from the space between them by virtual photons of wavelengths that are longer than the distance between the plates.  Therefore, there is a deficit in the cut-off spectrum of wavelengths exerting pressure between the Casimir plates, compared with the full spectrum that is pushing them together from the surrounding space.  So the net effect is that they get pushed together.  Extending this, it’s easy to see that if electrodynamics is SU(2), the magnetic curl (self- inductance problem) for massless charged bosons only allows the exchange of charged-bosons to similar charged particles (thus causing them to repel); opposite charges can’t exchange charged-bosons because the geometry of the magnetic vectors of the exchanged bosons is such that they don’t cancel out but add together instead (so this exchange is impossible due to the uncancelled, infinite magnetic self-inductance of the charged bosons).  In summary, opposite charges repel, but similar charges don’t repel and are hence pushed together by a Casimir-type “attraction” mechanism.

Professor Edsger Wybe Dijkstra (1930-2002), The strengths of the academic enterprise, EWD 1175, University of Texas, 9 February 1994:

“In the wake of the Cultural Revolution and now of the recession I observe a mounting pressure to co-operate and to promote ‘teamwork’.  For its anti-individualistic streak, such a drive is of course highly suspect; some people may not be so sensitive to it, but having seen the Hitlerjugend in action suffices for the rest of your life to be very wary of ‘team spirit’.  Very.  I have even read one text that argued that university scientists should co-operate more in order to become more competitive….. Bureaucracies are in favour of teamwork because a few groups are easier to control than a large number of rugged individuals.  Granting agencies are in favour of supporting large established organizations rather than individual researchers, because the support of the latter, though much cheaper, is felt to be more risky; it also requires more thinking per dollar funding.  Teamwork is also promoted because it is supposed to be more efficient, though in general this hope is not justified. … the co-operation seems more to force the researchers to broaden their outlook than to increase the efficiency of the research. … everybody complains about the amount of red tape … Why should a vigorous, flourishing department seek co-operation when it is doing just fine all by itself? It is the weak departments that are more tempted to seek each other’s support and to believe that there is might in numbers.  But such co-operation is of course based on the theory that, when you tie two stones together, the combination will float.”

Update (17 December 2013):

As predictable, Woit is now deemed, by Business Insider, a “famous math professor” for his pretty much worthless criticism of Zuckerberg.  All Woit is doing in the”criticism” is a disfavor to physics, by effectively preventing himself from being considered a possible recipient of such prizes, and thereby preventing his own theory from being funded with the sort of money required for its media hype to the extent needed for it replace string theory as a major research direction!

Update (3 Jan 2014): To his credit, Peter Woit has made a stance against the cringeworthy self-imposed money-making-aimed-self-censorship by fashion-dominated journals: “The policy of Physics Today to charge $30 to look at an article seems to have no point other than to ensure that no one does it.”

Real “freedom” of the press (internet) for everyone, or  “intellectual communism” – as contrasted to the anti-“intellectual communism” of pro-Marxist “financial communism” of anti-capitalist people in the BBC/Guardian/left wing who are paid subsidies or USSR style taxation funding for issuing biased “information” or propaganda (analogous to opinions of the Witten M-theory variety, dressed up as facts) – is the number one “problem” for “journalism” in the internet age.  How do journals and journalists retain their elitism when anybody is now free to circumvent their groupthink censorship?  The whole idea of “freedom of the press” is a complete lie: see the 3 January 2014 released secret UK National Archives file PREM 19/1394 which 22 May 1984 report by Sir James Goldsmith for the Defense Strategy Forum of the National Strategy Information Center, Soviet Active Measures versus the Free Press: A European Perspective, stating:

“Then comes the outer layer consisting of those who follow fashion and seek easy praise. Responsible journalists can also be disinformed by these campaigns. When a journalist works on an article, he refers to the press cuttings file which covers the subject about which he is writing. Information … will be used over and over again. So, once the press cuttings files have been polluted by propaganda, the false information will be repeated quite innocently and as it is repeated will gather further credibility and momentum. … Here are some thoughts … We need … better journalism. The better informed the public, the better equipped it is … The trouble with today’s intellectual environment is that few dare discuss the problem. … It is taboo. … It is a genuine problem which needs free and open discussion. … in a free country the best remedy is wide publication of the true facts. … journalists should investigate and publish. But they face a problem. There is a tradition of forbidden areas. Dog must not eat dog. Not only is it unpopular to expose a colleague or a journal, bit it is also difficult to find papers who would publish your material. Investigation should not be concentrated on the unpopular. It takes no courage to be fashionable, to express conventional wisdom and comfortably to join the pack in attacking the same wounded stag. Courage resides in saying the truth that does not please and which can make you a pariah in the eyes of your peers. This precisely is the duty of the press and one of the great justifications for the freedom of the press.”

The usual defense of a “free press” is totally wrong: it was mass press in Britain in the 1930s which rubbished, ridiculed and censored Churchill’s warnings about Hitler and the Nazis, instead playing the song of appeasement and “collaboration” for pacifist utopia and Nobel Peace Prizes all round for pacifists like Sir Norman Angell.  The mass media is professional, which means it’s profession (money-making) relies on being fashionable: money corrupts the professional journal or journalist (who won’t sell papers or TV time to be paid if unpopular) just as it corrupts the professional politician (who won’t get elected and paid unless he is popular enough to get votes), or the professional scientist (who won’t get paid unless he gets sponsorship).  Real freedom of equality for speech on facts or a “communism of thought”, is opposed by precisely the bigots who are professional liars, the “Marxist communists” who want not a communism or freedom and equality of ideas but a communism of money.  They want to censor people on any reason other than fact (because they have no fact to defend themselves with).  “Marxist communists” want to dictate opinions but never to listen to facts.  They are professional (money making) quacks.  God knows how long they will continue to be lauded.  What’s wrong is allowing a freedom of speech on unsubstantiated opinion, but permitting fashionable bigots to censor facts that contradict their popular opinions.  There are many ways to sort this problem out.  Bullets.  Vitriol.  A censorship of opinion to clear a breathing space for an airing of facts.  A discrimination between opinion and facts based on objective evidence.  These methods traditionally “don’t work” because they don’t maintain hegemony, in other words they’re like the Ancient Greek style method of democracy (daily referendums on issues, not a choice between two near-clone parties once every four years) which was considered too “volatile” or “insecure” by the founders of dictatorship or “modern democracy”.  (Daily referendums are perfectly possible logistically and technologically, with the same systems as the secure databases that allow millions of people to safely access online bank accounts daily.)  If you look at how modern “democracy” works, with people forced to start campaigns and effectively fight propaganda wars for years against status quo for every tiny revision to nonsensical groupthink-error laws, it’s very similar to dictatorship.  Its’ whole aim is to hinder change as much as possible, not to aid or objectively facilitate it!  No wonder why people get tired of political propaganda.  Politics, like string theory, attracts the Stalinist mind-set.

Sir Basil Henry Liddell Hart, Why Don’t We Learn from History?, PEN Books, 1944; revised edition, Allen and Unwin, 1972:

“If a man reads or hears a criticism of anything in which he has an interest, watch whether his first question is as to its fairness and truth. If he reacts to any such criticism with strong emotion; if he bases his complaint on the ground that it is not in ‘good taste,’ or that it will have a bad effect – in short, if he shows concern with any question except ‘is it true?’ he thereby reveals that his own attitude is unscientific. Likewise if in his turn he judges an idea not on its merits but with reference to the author of it; if he criticizes it as ‘heresy’; if he argues that authority must be right because it is authority; if he takes a particular criticism as a general depreciation; if he confuses opinion with facts; if he claims that any expression of opinion is ‘unquestionable’; if he declares that something will ‘never’ come about, or it is ‘certain’ that any view is right. The path of truth is paved with critical doubt, and lighted by the spirit of objective enquiry… We learn from history that in every age and every clime the majority of people have resented what seems in retrospect to have been purely matter of fact … We learn too that nothing has aided the persistence of falsehood, and the evils resulting from it, more than the unwillingness of good people to admit the truth … Always the tendency continues to be shocked by natural comment, and to hold certain things too ‘sacred’ to think about. I can conceive no finer ideal of a man’s life than to face life with clear eyes instead of stumbling through it like a blind man, an imbecile, or a drunkard – which, in a thinking sense, is the common preference. How rarely does one meet anyone whose first reaction to anything is to ask: ‘is it true?’ Yet, unless that is a man’s natural reaction, it shows that truth is not uppermost in his mind, and unless it is, true progress is unlikely.”  (Emphasis added.)

BBC and Guardian newspaper and others who read their copy unfailingly manage to swallow the liars propaganda (hook, line and sinker), thus taking the wrong side because  journalists and their readers always find fiction more appealing and saleable (££££$$$$££££$$$$, money) than facts!  Thus, they prefer utopian hopeful fantasies to tough reality. They are ideologues who want to believe in contrived propaganda that reinforces their ideals:

“… fashionable trends of thought and ideas are carefully separated from those which are not fashionable … what is not fashionable will hardly ever find its way into periodicals or books or be heard in colleges.  Legally your researchers are free, but they are conditioned by the fashion of the day.  There is no open violence such as in the East; however, a selection dictated by fashion and the need to match mass standards frequently prevent independent-minded people from giving their contribution to public life. There is a dangerous tendency to form a herd, shutting off successful development. I have received letters in America from highly intelligent persons, maybe a teacher in a faraway small college who could do much for the renewal and salvation of his country, but his country cannot hear him because the media are not interested in him. This gives birth to strong mass prejudices, blindness, which is most dangerous in our dynamic era.

– Aleksandr Solzhenitsyn’s 1978 Harvard address (section discussing the dictatorship by fashion in the Western media).