Catt and Walton’s lecture at Nottingham University on a key experiment

Electromagnetism SU 2 theory experiment

There are actually two different electric charges, hence SU(2) electromagnetism, not merely one charge which can travel backwards in time to reverse its sign (as Abelian U(1) QED dogma untruthfully asserts). On 9 October 2013, Ivor Catt (author of ‘Crosstalk (Noise) in Digital Systems,’ in IEEE Trans. on Elect. Comp., vol. EC-16, December 1967,  pp. 749–58), and David Walton (who after his PhD in atomic physics worked under Nobel laureate E. T. S. Walton at Trinity College) presented a new experiment to the ASL Electromagnetism Seminar at Nottingham University:

Before reviewing the physical mechanism of electromagnetism yet again, a brief comment on personal bad attitude problems in science. What’s curious about these guys is that like all academic hotshots, they’re bigoted “elitists” camouflaged as caring, brilliant socialists, just like quantum field theorist, the sometimes abusive, reliably patronising Dr Peter Woit of Columbia University maths department (string theory critic and author of an interesting new textbook, Quantum Theory, Groups and Representations, which will be published by Springer in 2015) or category theorist Dr Marni Dee Sheppeard: they’re all people who won’t spend a second listening or objectively responding to anybody, but just attack under a false charge, thus refusing to engage with the actual argument.  They do this by inventing a vacuous claim that anyone who has a technical argument must be ignorant of science or is anti-feminism, etc. and launching into a tirade about that, completely ignoring the point.  I’ve spend countless hours talking to Catt and publishing videos (also here and here) and journal articles about his work (Electronics World feature articles in August 2002, April 2003, January 2004, plus an op-ed), but that doesn’t lead to anything but abusive shouting as soon as I make an objective criticism.  It’s the same with all egotists, inside the mainstream or not!  Simplify the 10 commandments to 1, and you are crucified.

Feynman versus Dirac

“Already in the beginning I had said that I’ll deal with single electrons, and I was going to describe this idea about a positron being an electron going backward in time, and Dirac asked, ‘Is it unitary?’ I said, ‘Let me try to explain how it works, and you can tell me whether it is unitary or not!’ I didn’t even know then what ‘unitary’ meant. So I proceeded further a bit, and Dirac repeated his question: ‘Is it unitary?’ So I finally said: ‘Is what unitary?’ Dirac said: ‘The matrix which carries you from the present to the future position.’ I said, ‘I haven’t got any matrix which carries me from the present to the future position. I go forwards and backwards in time, so I do not know what the answer to your question is.”

– Feynman about his problem with Dirac at the 1948 Pocono Conference.  The argument was with Feynman’s U(1) as applied to pictorial Feynman diagrams, a theory where positrons (positively charged electrons) are represented as electrons travelling backwards in time, i.e. the simplistic U(1) single-charge QED theory.  Quotation source: J. Mehra and K. A. Milton, Climbing the Mountain: The Scientific Biography of Julian Schwinger, Oxford University Press, 2000, page 233.  See also the excellent discussion in that book on pages 231-234 of how badly Feynman was treated by Bohr, Teller, Dirac and others, who instead of being constructive and helping to build and improve Feynman’s theory of multipath interference via the path integral, just preferred to try to shoot it down.  Actually, the path integral works for any symmetry group for example SU(2) and SU(3) and not just for U(1) electrodynamics which has the “Dirac problem” that positrons are represented as electrons going backwards in time in the Feynman diagrams.

“Already in the beginning I had said that I’ll deal with single electrons, and I was going to describe this idea about a positron being an electron going backward in time, and Dirac asked, ‘Is it unitary?’ I said, ‘Let me try to explain how it works, and you can tell me whether it is unitary or not!’ I didn't even know then what ‘unitary’ meant. So I proceeded further a bit, and Dirac repeated his question: ‘Is it unitary?’ So I finally said: ‘Is what unitary?’ Dirac said: ‘The matrix which carries you from the present to the future position.’ I said, ‘I haven’t got any matrix which carries me from the present to the future position. I go forwards and backwards in time, so I do not know what the answer to your question is.” - Richard P. Feynman in J. Mehra and K. A. Milton, Climbing the Mountain: The Scientific Biography of Julian Schwinger, Oxford University Press, 2000, page 233
“Already in the beginning I had said that I’ll deal with single electrons, and I was going to describe this idea about a positron being an electron going backward in time, and Dirac asked, ‘Is it unitary?’ I said, ‘Let me try to explain how it works, and you can tell me whether it is unitary or not!’ I didn’t even know then what ‘unitary’ meant. So I proceeded further a bit, and Dirac repeated his question: ‘Is it unitary?’ So I finally said: ‘Is what unitary?’ Dirac said: ‘The matrix which carries you from the present to the future position.’ I said, ‘I haven’t got any matrix which carries me from the present to the future position. I go forwards and backwards in time, so I do not know what the answer to your question is.”
– Richard P. Feynman in J. Mehra and K. A. Milton, Climbing the Mountain: The Scientific Biography of Julian Schwinger, Oxford University Press, 2000, page 233

Perhaps this excessive and damaging egotism from Catt and also leading quantum field theorists is due to bad experiences with other people who have wasted their time with alternative ideas in the past, but that’s no excuse for people taking out your frustrations on other people who are offering constructive theories that are admittedly incomplete and in need for further development and wider circulation before funding.  Now, when I read a book, I try to see what the strongest arguments are, and focus on those.  That’s called objectivity.  “Critics” who ignore the substance of the argument and falsely make a show out of inventing spurious problems, are being subjective.  Emotional rants always leak into “peer” reviews, because if the “peer” reviewer abuses power when possible to reduce workload, they then tell lies about “rudeness” to escape the complaints.  So they’ll always end up, in the analysis of a radical innovation that does have evidence, claiming it is an “exceptional” case that doesn’t deserve their normal objective methods!

Anyway, the physics.  The new experimental data for the charged capacitor justifies the following interpretation of the Dirac equation’s spinor.

Electromagnetism SU 2 theory experiment
Electromagnetism SU(2) theory experiment, from chapter 1 of Electromagnetism 1, ISBN0906340101. See our analysis of why EM’s SU(2) Yang-Mills equations reduce to Abelian U(1) “observed Maxwell equations“.

As the diagram above proves, the classical electromagnetism which Dirac and Weyl assumed true when building U(1) Abelian quantum electrodynamics, contains an error due to a mathematical coincidence (or accident, as Catt put it in his 1995 book Electromagnetism 1), in that the false squaring of the superimposed electric fields for trapped Heaviside energy current cause a four-fold increase in energy density, which exactly compensates for the false assumption that magnetic field energy disappears.  The maths of electromagnetism work, but that is provably due to a fluke, a coincidence, an accident of mere numerology.  (Catt buries or hides the key evidence amid much clutter on his internet site.)  The physics of the EM mechanism is quite different to U(1).  However, Catt himself makes an error of inconsistency in his analysis, in not applying his own “separation of fields” (so vital for him when separating the TEM wave fronts flowing into the cable from the reflected TEM wave coming back from the open end of the cable to superimpose) to the individual fields from each conductor within the transmission line!  You then get the fact that the field quanta are charged, and you also get SU(2) QED.

The classical Maxwell (and apparently Abelian) electromagnetic equations are derived from a simple mechanism which cuts down the SU(2) Yang-Mills equations to the Maxwell ones, by eliminating the Yang-Mills charge transfer term. Since the charged EM bosons are massless, they cannot propagate because the magnetic field resulting from charge, prevents the motion of massless charge! The ONLY possible way massless charges can move, is by cancelling out their magnetic fields using a two-way equilibrium of exchange. Any two similar charges must always being exchange equal charge in opposite directions each second, to cancel out the magnetic fields, eliminating infinite self-inductance. Unless this happens, there is no electromagnetic field. So this mechanism means that massless SU(2) charged field quanta can never change the amount of charge present in an onshell particle: if it emits 1 coulomb per second, it also absorbs precisely the same amount. Hence, the Yang-Mills net charge transfer term is always zero for massless field quanta: effectively turning Yang-Mills equations into Maxwell’s in that case (massless charged field quanta). The Catt analysis of the Heaviside transmission line theory, when extended to include an examination of what’s happening to each conductor within the transmission line (accelerating free electrons radiate radio frequency energy to electrons in the other conductor, and this mutual exchange enables the propagation of electricity. The acceleration of electrons at the electrical wave front on the surface of each conductor in a transmission line is then in an opposite direction to that in the other conductor.

This is the cause of all the shouting from Catt when I tried to get a discussion of this point. His response to any objective criticism or improvement suggestion is to endlessly repeat himself more loudly, precisely what the mainstream does when string theory is criticised.  (A complete waste of time, since I had already read his books.)  This paranoid and delusional approach prevents any kind of critical collaborative progress, except homage.  I’m not interested in a dead science that either makes no progress, or is dictatorially constrained to stumble or crawl along worn paths in a very few research directions, with the most obvious and vital applications blocked by rude, silly censorship.

Weyl applied Abelian U(1) gauge theory to electromagnetism, despite the fact that it U(1) only one charge, whereas electromagnetism 2 charges (positive and negative).  There are also 2 charges in SU(2) isospin for weak forces, and 3 charges for SU(3).  Since electromagnetism has 2 charges, not one as U(1), why not therefore use SU(2) for electromagnetism?  This is just weak theory with massless neutral Z and massless charged W particles.  What is “charge”?  Has anyone ever seen or measured an “electron”.  What they have measured is trapped field with a quantized charge and mass, and named that an “electron”, much the way Pluto was once falsely classified as a planet!

(When interpretations of nature charge, like naming conventions, nature remains unaltered.  Pluto didn’t suddenly change when the consensus of expert opinion downgraded it from planet to planetoid.  You cannot therefore use today’s interpretation of any fact in science as a dogmatic “fact” with which to censor out advances, which may involve new theories which re-interpret the facts differently.  Put it another way, confusing facts with their interpretations is a censorship tool used by peer-consensus dogma-worshipping education, not objective science which tests new interpretations of facts.)

Planck scale electron cores are unobservable: nobody has seen them.  Only the fields and charge to mass ratio of “electrons” have been observed.  The sign of the charge (positive or negative) of the electron is therefore inferred from the field that is measured: the only thing observable about the “charge” of an electron is its field.  Therefore, the field quanta convey the information on whether the “charge” is positive or negative.  This can only happen if the 2 “extra polarizations” that field quanta have are charge indicators.

Field quanta have 4 polarizations, whereas uncharged photons (which don’t convey charge sign information) have only 2 observable polarizations.  The extra 2 polarizations of field quanta must therefore carry the information to the observer as to whether the electric field is one due to a “charge” which is positive, or negative.  Therefore, observations of field do indicate that massless charged electromagnetic field quanta exist, in the context of trapped light velocity field energy in Catt’s experiment, the charge of the field quanta being denoted by the quantum numbers for the 2 additional degrees of polarization.

Dirac’s equation predicted antimatter, suggesting that protons are the anti-electrons.  J. Robert Oppenheimer rejected Dirac’s interpretation in a paper in 1930, due to the mass difference between the electron and the proton (which we explain as conversion of screened QED charge into nuclear field energy, see discussion further below).  Dirac then accepted Oppenheimer’s arguments and revised this to predict what came to be called the positron, discovered by Carl Anderson in 1932.  This positron discovery has since been used by bigots tragically to “shut down the argument”, preventing a more careful analysis.

Sure, positrons arise as anti-electrons.  But that can’t be the full story, or there’d be equal amounts of positrons and electrons around, since Dirac’s equation predicts they they are created (by pair production) in equal quantities.  So although Oppenheimer’s objection to Dirac’s simplistic assignation of the proton as the anti-electron creates a problem of mass asymmetry, it did offer a solution to the question of “where is all the antimatter?”, a question which Oppenheimer doesn’t answer.  We argue that both Dirac and Oppenheimer were being far too simplistic, and in doing so laying down a shaky dogmatic interpretative foundation for U(1) electrodynamics which has messed up today’s electroweak theory.

SU(2) is now electroweak group, with U(1) being dark energy which causes gravitation by a Casimir type pseudo-attraction mechanism (plates being pushed together by spin-1 quanta on external sides, not by the simplistic idea of a mutual exchange of spin-2 superstring gravitons, which don’t need to exist in order for gravity to work).  Once you have an chiral SU(2) theory of electromagnetism where the handed curl of the magnetic field vector around the direction of propagation of a charge is analogous to the left-handed weak force SU(2).  Woit showed neatly in 2002 that you can get the handedness of SU(2) electroweak charges by picking out U(2) as a subset of SO(4).  (However, that doesn’t mean he is interested in really being objective.)

We can’t observe Planck size charges, only their fields, and we find two different kinds of fields: positive and negative.  Positive is not merely an absence of negative charge (hole theory): if there is no an absence of negative charge is zero charge.   Sure, in a sea of electrons, a “hole” behaves analogously to positive charge.  But an empty vacuum is not positively charged.  So absence of negative charge is not automatically positive charge.  Electromagnetism then is a 2 charge SU(2) gauge theory, a massless gauge boson version of SU(2).

If antimatter is produced in equal quantities by pair-production at energies above 1.022 MeV in the big bang, then where is it?  It is in upquarks.  They have 2/3rds the positron charge.  The missing 1/3 charge is due to the fact that electromagnetic pair production within femtometres of the core of a charge absorbs electromagnetic energy density in the polarization process, creating virtual particle which result – when you have pairs (mesons) or triplets (baryons) in close proximity (sharing an overlapping vacuum polarization veil of virtual particles) – converts EM field/charge energy into nuclear (weak and/or strong) fields.  The vacuum polarization effect occurs out to a radius where the field strength is about 1.3 x 10^18 volts/metre, Julian Schwinger’s IR cutoff radius for the running of the electric charge in QED.  Many textbooks wrongly follow Dirac’s sea analogy, which ignores the IR cutoff and claims that pair production occurs throughout the entire vacuum.  It doesn’t occur through the whole vacuum, because only gauge bosons – not virtual fermions – occur beyond a few femtometres: all observed couplings cease to run with energy when the energy is too low for onshell particles to be created (i.e. twice the 0.511 MeV electron rest mass energy equivalent or 1.022 MeV).

When EM fields are attenuated by vacuum polarization (causing the effective charges to run by some logarithmic function of distance and energy), electromagnetic energy density is converted into virtual mesons and virtual quarks and gluons that constitute nuclear fields, the SU(2) weak force and the SU(3) strong force. Thus, the reduction in the apparent electric charge of the upquark from the positron’s value of +1 to the value +2/3 needed to fit observations for protons (two upquarks and one downquark) and other hadrons, is explained and turned into a prediction since we can make detailed calculations with this simple approach. Where upquarks are electron antiparticles formed at very high energy, in addition to the simplistic Dirac/Oppenheimer antiparticle of the free positron which Anderson observed in 1932, where a >1.022 MeV gamma ray approaches a nucleus, you:

1. Explain the apparent paucity of antimatter in the universe, and

2. Have a new way to predict the weak and strong nuclear force running couplings, by making use of the fact of the principle of conservation of energy with the fact that one-third of the electric field energy of the electron exists in nuclear fields around upquarks in hadrons.  Coulomb field energy (half permittivity times the square of electric field strength, in Joules per cubic metre) that’s converted into virtual particle nuclear force gluon fields around upquarks in QED renormalization allows us to do simple QCD calculations of nuclear interaction running couplings from energy conservation! Genius or what?  Anyone can calculate the Coulomb field strength and energy density around an electron, and once you integrate over a shell of expanding radius that you get the total energy; incorporating the logarithmic running of the charge from QED now tells you how the QCD color force varies inversely, getting stronger as the QED running charge gets weaker: the sum of both is equal to that of an electron.

3. As Julian Schwinger explained in 1948, the running of couplings that causes charge renormalization in QED is accompanied by a renormalization of mass, in other words the virtual particles created by pair production in intense fields around a quark core contribute some mass to the quark core.  In fact, most of the mass of hadrons is generated in this way.  A simple model of this allows precise predictions to be made (see, linked here).  Nobel Laureate Dr Gerardus ‘t Hooft responded that the paper was unsuitable for his Foundations of Physics: “because it does notcite current peer-reviewed literature”.  (That’s a catch-22 because this is “new stuff”, with no literature and no “peers” in the field, as such. Duh!)

(In 2006, Harvard string theorist Dr Lubos Motl knocked the nail on the head when he wrote, on Woit’s blog: “Virtually all of string theorists are nice people who never argue with anyone else, they’re not chauvinists, and most of them are feminists. Most of them also think that string/M-theory are robust twin towers that are not threatened by any social effect or passionate proponents of alternative theories or proponents of no theories, and they almost always try to avoid interactions that could lead to tension which also gives them more time for serious work. Almost no string theorists drive SUV and they produce a minimum amount of carbon dioxide.”   Dr Motl was right that they usually “never argue with anyone else”, that’s the whole problem: they’re elitists who sit on their high horses in the clouds and refuse to engage in discussions with objective critics, to participate in constructive arguments, despite all their camouflaged journals of bigotry that paint their work as being precisely the opposite of that.  I made this point in my 2011 paper by quoting the famous string theorist Ed Witten who actually wrote to Nature instructing string theorists to deny critics the oxygen of publicity by refusing to engage in discussions.  Woit, Smolin, Catt, Her Majesty the Queen, and many others maintain prestige that way.)

Physics Review Letters and arxiv weird, egotistic, and frankly vile (not peer) “elitist” moderators proved not only lacking interest in non-standard alternative ideas beyond superstring theory that actually work (predicting cosmological constant accurately in 1996, long before dark energy was even discovered in 1998 from supernovae red-shift observations), but in demented mad bigotry against an attitude of no-bullshit progress:

Nigel says: July 7, 2005 at 7:15 pm Editor of Physical Review Letters says

Sent: 02/01/03 17:47

Subject: Your_manuscript LZ8276 Cook


Physical Review Letters does not, in general, publish papers on alternatives to currently accepted theories � Yours sincerely, Stanley G. Brown, Editor, Physical Review Letters

Now, why has this nice genuine guy still not published his personally endorsed proof of what is a �currently accepted� prediction for the strength of gravity? Will he ever do so? …

Peter Woit says: July 7, 2005 at 7:27 pm I’m tempted to delete the previous comment, but am leaving it since I think that, if accurate, it is interesting to see that the editor of PRL is resorting to an indefensible argument in dealing with nonsense submitted to him (although the “…” may hide a more defensible argument). Please discuss this with the author of this comment on his weblog, not here. I’ll be deleting any further comments about this.

[Note to Dr Woit: the email correspondence went on with PRL’s associate editor for months, with them repeatedly changing goalposts as I revised the paper to incorporate suggestions, until they simply refused to publish anything on this topic.  They thus wasted my time deliberately with lies.  The same for Physics Forums, on which it is heresy to engage in a serious objective campaign to make progress; trivial discussion of mainstream dogma is fine.  In the same way, serious politics campaigning is banned from the House of Commons coffee bars because it always ends in punch ups; small talk about football or cricket results is however encouraged.  Freedom of speech is something that makes our democracy different to Hitler’s and Stalin’s regimes.  Except that there is a rule in small print that it must not be heard if it is heretical.  Nobody points out that Hitler and Stalin had no real problems with people shouting their praise.  It’s therefore only in the treatment of heretics and outsiders that “freedom” or its absence can really be assessed.  Nobody seriously disputes that Hitler wanted everyone be was friends with to be free to praise the Nazis.  Freedom depends on progress is free and unopposed, or is blocked by bigots requiring tougher means.  Historian Edward Gibbon wrote controversially that education is only of use where practically superfluous; he would have been less controversial I suspect if he had written instead that: DIPLOMACY is only of use where it is practically superfluous.  Diplomacy only seems to “prevent wars” and fights where the people are honest, engaging with critics and thus non-dictatorial/civilized on boths sides; diplomacy fails where it is most needed, where one side is a bigoted dictator who refuses to engage in objective discussionOne possible way to proceed would be to publish a book quoting all the errors in fashionable textbooks, debunking each and thus ridiculing the aptitude, PhD credentials, educational background, Nobel prizes awarded, etc., to substandard behaviour and the confusion of facts with interpretations by qft textbooks.  Woit’s book contains many excellent cameos but is organized in such a way that the few key understandable mechanisms in QFT are totally ignored, e.g. Feynman’s 1985 QED book explanation that the uncertainty principle arises from multipath interference (the basis of the path integral) of QED field quanta jiggling the bound electron chaotically as it does its orbit.  The uncertainty principle is pre-second quantization, pre-Feynman’s path integral.  Woit simply ignores this and also the fact that vacuum polarization provides a testable, evolving calculation method and mechanism to understand and predict how couplings run and how masses of particles occur.  But to a great extent, this bigoted, anti-progress approach is used in many textbooks, which seek to misinform readers.  Woit also starts by recommending Eugene Wigner’s worst ever paper – which asserts the ignorance-based dogma bias, on false premises, that the universe is intrinsically non-understandable mathematics.  Of course, as the non-PhD quantum field theory professor Freeman Dyson keeps pointing out, the PhD system is a pseudoscientific: “abomination … a gross distortion of the educational process … the student is condemned to work on a single problem in order to write a thesis, for maybe 2-3 years … this straight-jacket which was imposed on the students … all the PhD students had these same constrains imposed on them which I basically disapprove of.  I just don’t like the system.  I think it is an evil system and it has ruined many lives.”  (See video of Dyson explaining this, linked here.],

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.