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,