[… continued from part 1]

I’m simply pointing out that there is no evidence given for electroweak symmetry, by which I refer not to the weak bosons losing their mass at high energy. I don’t accept as evidence for electroweak symmetry a mere (alleged) similarity of the weak and electromagnetic cross-sections at very high energy (differing rates of running with energy in different couplings due to unknown vacuum polarization effects could cause apparent convergence simply by coincidence, without proving a Higgs field mechanism or the existence of electroweak symmetry). It’s hard to interpret the results of high energy collisions because you create hadronic jets which add epicycles into the calculations needed to deduce the relatively small electromagnetic and weak interactions. The energies needed to try to test for electroweak symmetry are so high they cause a lot of noise which fogs the accuracy of the data. If you wanted to use these HERA data to prove the existence of electroweak symmetry (massless weak bosons), you would need to do more than show convergence in the cross-sections.

“I am talking about very clean events of hard deep inelastic scattering, where the bosons are seen with great clarity due to their leptonic decays.”

You’re thinking possibly about weak SU(2) symmetry and electromagnetic symmetry, and you think these two separate symmetries together as “electroweak symmetry”. I’m 100% behind the extensive evidence gauge theory for weak interactions and 100% behind gauge theory for electromagnetic interactions. These separate symmetries, produced in the “electroweak theory” by mixing U(1) hypercharge boson with the SU(2) bosons, are not however “electroweak symmetry”, which only exists if massless weak bosons exist at very high energy. The Higgs field is supposed to give mass to those bosons at low energy, breaking the symmetry. At high energy, the weak bosons are supposed to lose mass, allowing symmetry of weak isospin and electromagnetic interactions by making the range of both fields the same.

I really need to find any alleged evidence for “electroweak symmetry” in my research for a paper, so if you ever recall the paper with the HERA data which you say contains evidence for electroweak symmetry, please let me know! So far I’ve read all the QFT books I can get (Weinberg, Ryder, Zee, etc.) and electroweak theory papers on arXiv, and I have not found any evidence for electroweak symmetry.

My understanding (correct me if I’m wrong here) is that if you collide protons and electrons at TeV energies, you knock free virtual quarks from the sheer energy of the collision? These virtual quarks gain the energy to become real (onshell) quarks, forming hadron jets. These jets are difficult to accurately predict because they are dominated by QCD/strong forces and the perturbative expansion for QCD is divergent, so you need lattice calculations which are inaccurate. So you can’t compare what you see with a solid prediction. You can measure what you see, but you can’t analyze the data very accurately. The color charge of the QCD jets can’t interact with the weak bosons, but the jets also have electromagnetic and weak charges which do interact with weak bosons. So you cannot do a precise theoretical analysis of the entire event. All you can really do is to produce particles and see what they are and how they interact. You can’t do a complete theoretical analysis that’s accurate enough to deduce electroweak symmetry.

Yes, definitely SU(2) weak symmetry is based on an enormous amount of good empirical evidence: what I’m questioning is “electroweak symmetry”. Evidence for the broken and mixed U(1) symmetry and SU(2) symmetry is not at issue. What should be regarded as an open question is whether electroweak symmetry exists. The simplest default alternative to the Higgs-electroweak theory is to have a mixed but broken “electroweak symmetry”, i.e. no electroweak symmetry. This is precisely what Feynman argued in the 1980s. Instead of having a Higgs field which makes weak field quanta massive at low energy but massless at high energy, you instead add a quantum gravity gauge theory to the standard model, which gives mass to the weak field quanta at all energies (as well as giving masses to other massive particles). The quantum gravity gauge theory has mass-energy as its charge and it has gravitons as its bosons. In other words, the Higgs/electroweak symmetry theory is a complete red-herring. If its advocates are allowed to continue their propaganda, then there will be no well-developed alternative to the Higgs/electroweak symmetry when the LHC rules out the Higgs. The result will be the usual last-minute panic with a consensus of ill-informed opinions promoting new epicycles to prop up nonsense (save face).

Feynman’s opposition to “electroweak symmetry” is in Gleick’s biography of Feynman:

When a historian of science pressed him on the question of unification in his Caltech office, he resisted. “Your career spans the period of the construction of the standard model,” the interviewer said.

” ‘The standard model,’ ” Feynman repeated dubiously. . . .

The interviewer was having trouble getting his question onto the table. “What do you call SU(3) X SU(2) X U(1)?”

“Three theories,” Feynman said. “Strong interactions, weak interactions, and the electromagnetic. . . . The theories are linked because they seem to have similar characteristics. . . . Where does it go together? Only if you add some stuff we don’t know. There isn’t any theory today that has SU(3) X SU(2) X U(1) — whatever the hell it is — that we know is right, that has any experimental check. . . . “

Virtual quarks form in pairs due to pair production around the proton. The pairs get knocked free in high energy collision. I do know that individual quarks can’t exist by themselves. I wrote that the quarks are produced in pair production, and get knocked free of the field of the proton in a high energy inelastic collision. I didn’t write that individual quarks exist alone.

The mass term in the lagrangian always exists, but it doesn’t have the same value. If m = 0, that is the same as getting rid of the mass term. Reference is for instance Zee’s QFT book. You can’t formulate a QFT very conveniently without the field having mass. Sidney Coleman is credited by Zee with the trick of adding a mass term for the massless QED virtual photon field, for example. You have to have a mass term in the field to get the gauge theory lagrangian, but at the end you can set the mass equal to zero. It’s a mathematical trick. It’s not physics, just math.

The precise reference is Zee, 1st ed., 2003, pp 30-31: “Calculate with a photon mass m and set m = 0 at the end … When I first took a field theory course as a Student of Sidney Coleman this was how he treated QED in order to avoid discussing gauge invariance.” He ends up with an electromagnetic potential of (e^{-mr})/(4 Pi r). The exponential part of this, e^{-mr}, is due to the mass term. Setting m = 0 gives e^{-mr} = 1, so the mass term has no effect, and you get the expected potential for a massless field. By exactly the same argument, mass terms in the weak field need to be eliminated for “electroweak symmetry” by making m = 0 where such symmetry exists. Otherwise, you end up with a weak field potential which has an exponential term (reducing the range and field strength) due to the mass of the weak field quanta. To get “electroweak symmetry”, the weak field potential must become similar to the electromagnetic field potential at unification energy. That’s the definition of this “symmetry”.

Pauli first applied Weyl’s gauge theory to electrodynamics and was well aware that that for electromagnetic interactions, it really doesn’t matter if you have a mass term in the propagator like 1/[(k^2)-(m^2)], because it just represents the momentum delivered by the field boson in the Feynman diagram. You can treat the relativistic field quanta (moving with velocity c) as non-relativistic, allow the rest mass momentum in the propagator to represent the relativistic momentum of photons, and then simply edit out the problem of field quanta mass in the field potential by letting m = 0 in the final stage. This math trick complements the physics of gauge invariance so there is no problem. Pauli however knew that the mass in the propagator is a real problem for non-Abelian fields that carry electric charge, so he objected to the Yang-Mills theory when Yang gave his lecture in 1954. Yang and Mills could not treat the mass of the field and Pauli made such a fuss Yang had to sit down. Electrically charged field quanta can’t propagate without rest mass (their magnetic self-inductance opposes their motion), so they must really have a mass in the propagator, as far as Pauli was concerned. This doesn’t apply to uncharged field quanta like photons, where you don’t need a massive propagator. Now the problem is: how do you get electroweak symmetry with electrically charged, massless SU(2) quanta at electroweak unification energy. As far as I can see, most of the authors of modern physics textbooks ignore or obfuscate the physics (which they mostly disrespect or frankly hate as being a trivial irrelevance in “mathematical physics”). But Noether makes all of the “mathematical symmetries” simple physical processes:

Noether’s theorem: every conservation law corresponds to an invariance or symmetry.

Gauge symmetry: conservation of charge (electric, weak, or color).

Electroweak symmetry: equality of couplings (strengths) of electromagnetic and weak interactions at electroweak unification energy.

Langrangian symmetry or local phase invariance: produced by a lagrangian that varies with changes in the wavefunction, so that emission of field quanta compensate for the energy used to change the wavefunction.

When you switch from describing massive to massless field quanta in electromagnetism, the equation for field potential loses its exponential factor and thus ceases to have short range and weak strength. However, the field quanta still carry momentum because they have energy, and energy has momentum. So there is no problem. Contrast this to the problems with getting rid of mass for SU(2) electrically charged W bosons!

“… concentrate on the hard subprocess, where the real (perturbative) physics is. There, the gamma and the W/Z have similar strengths once you reach virtualities of the order of the boson masses.”

You seem to be arguing is that “electroweak symmetry” is defined by similarity of the strengths of the weak and electromagnetic forces at energies equivalent to the weak boson masses (80 and 91 GeV). There is some confusion in QFT textbooks on exactly what the difference is between “electroweak symmetry” and “electroweak unification”.

At energies of 80 and 91 GeV (weak W and Z boson masses), the electromagnetic (gamma) and W/Z don’t seem to have very similar strengths: http://www.clab.edc.uoc.gr/materials/pc/proj/running_alphas.html

Yes, the electrically neutral Z weak boson has higher mass (91 GeV) than the electrically charged W weak bosons (80 GeV), but that’s just because the weak isospin charge coupling (g_W) has a value of only half the weak hypercharge coupling (g_B). The weak hypercharge for left-handed leptons (ie those which actually participate in weak interactions) is always Y = -1, while they have a weak isospin charge Y = +/-1/2. (Forget the right handed lepton hypercharge, because right handed leptons don’t participate in weak interactions.) So the weak isospin charge has just half the magnitude of the weak hypercharge! The Weinberg mixing angle Theta_W is defined by:

tan (Theta_W) = (g_W)/(g_B)

The masses of the weak bosons Z and W then have the ratio:

cos (Theta_W) = (M_W)/(M_Z)

Therefore, the theory actually predicts the difference in masses of the Z and W weak bosons from the fact that the isospin charge is half the hypercharge. This is all obfuscated in the usual QFT textbook treatment, and takes some digging to find. You would get exactly the same conclusion for the left-handed weak interaction if you replace weak hypercharge by electric charge for leptons (not quarks, obviously) above. Because isospin charge takes a value of +/-1/2 while electric charge for leptons takes the value +/-1, the ratio of isospin to electric charge magnitude is a half. Obviously for quarks you need an adjustment for the fractional electric charges, hence the invention of weak hypercharge. Physically, this “(electric charge) = (isospin charge) + (half of hypercharge)” formula models the compensation for the physical fact that quarks appear to have fractional electric charges. (Actually, the physics may go deeper than this neat but simplistic formula, if quarks and leptons are unified in a preon model.) I’m well aware of the need for some kind of mixing, and am well aware that the difference in W and Z boson masses was predicted ahead of discover at CERN in 1983.

I’m writing a paper clarifying all this, and it is good to be able to discuss and defend a criticism of electroweak symmetry here, to see what kind of arguments are used to defend it. It will help me to write the paper in a more concise, focussed way. Thank you Alejandro, thanks to Tommaso for tolerating a discussion, and other commentators.

For the record: the essential “tan (Theta_W) = (g_W)/(g_B)” is equation 10.21 in David McMahon’s 2008 “QFT Demystified” textbook.

The problem with the usual interpretation of the top quark mass for Higgs boson studies is that to counter this argument, I would have to discuss an alternative theory in detail, instead of just pointing out inconsistencies in the mainstream theory. Then critics will dismiss me as a crackpot and stip listening. But the top quark coupling seems to me to be evidence pointing exactly the other way, towards a quantum gravity gauge theory. The top quark mass fits in perfectly to a simple model for particle masses. The foundation is model for masses was a relationship between the Z boson mass and the electron mass (or similar) in a paper you wrote with Hans de Vries, so thank you for that. To summarize the essentials, we put a quantum gravity gauge group into the standard model in a very neat way (treating it like hypercharge), and remove the Higgs mass model. Mixing gives masses to the massive particles in a very novel way (not). A charged fundamental particle, eg a lepton, has a vacuum field around it with pair production producing pairs of fermions which are briefly polarized by the electric field of the fermion, and this shields the core charge (thus renormalization). The energy absorbed from the field by the act of polarization (reducing the electric field strength observed at long distances) moves the virtual fermions apart, and thus gives then a longer life on average before they annihilate. Ie, it causes a statistical violation of the uncertainty principle: the energy the off-shell (virtual) fermions absorb makes them move closer towards being on-shell. For the brief extra period of time (due to polarization) which they exist before annihilation, they therefore start to feel the Pauli exclusion principle and to behave more like on-shell fermions with a structured arrangement in space. One additional feature of this vacuum polarization effect in giving energy to virtual particles is that they briefly acquire a real mass. So the vacuum polarization has the effect of turning off-shell virtual fermions briefly into nearly on-shell fermions, simply by the energy they absorb from the electric field as they polarize! This vacuum mass and the Pauli exclusion principle have the effect of turning leptons into effectively the nuclei of little atoms, surrounded by virtual fermions which when being polarized add a Pauli exclusion principle structured real mass. It is this vacuum mass effect from the vacuum which is all-important for the tauon and also the top quark. The neutral Z acquires its mass by mixing of SU(2) with a quantum gravity gauge group. https://nige.wordpress.com/2010/05/07/category-morphisms-for-quantum-gravity-masses-and-draft-material-for-new-paper/

Theta_W or θ_W is empirically determined to be 29.3 degrees at 160 MeV energy using the 2005 data from parity violation in Møller scattering (sin^2 θ_W = 0.2397 ± 0.0013 was obtained at 160 MeV) and it was determined to 28.7 degrees at 91.2 GeV energy in 2004 data using the minimal subtraction renormalization scheme (sin^2 θ_W = 0.23120 ± 0.00015). This difference is usually cited as evidence of the running of the Weinberg angle with energy, due to the running coupling which is caused by vacuum polarization (shielding the core charges, which is a bigger effect at low energy than at high energy). See http://en.wikipedia.org/wiki/Weinberg_angle

What I stated was that, ignoring the running coupling effect (which is smaller for the weak isospin field than in QED, because of the weakness of the weak force field relative to QED), the Weinberg angle is indeed

tan θ_W =1/2.

This is gives θ_W = 26.57 degrees. Remember, empirically it is 29.3 degrees at 160 MeV and it is 28.7 degrees at 91.2 GeV. The higher the energy, the less vacuum polarization we see (we penetrate closer to the core of the particle, and there is therefore less intervening polarized vacuum to shield the field) Therefore, the figure for higher energy, 28.7 degrees is predicted to be closer to the theoretical bare core value (26.57 degrees) than the figure observed at low energy (29.3 degrees). The value of θ_W falls from 29.3 degrees at 160 MeV to 28.7 degrees at 91.2 GeV, and to an asymptotic value for the bare core of 26.57 degrees at much higher energy.

Yes, there must be a mixing of SU(2) and U(1). But no, I’ve never been against such a mixing. My incomplete draft paper from last October explains what I mean: https://nige.files.wordpress.com/2010/10/paper-draft-pages-1-5-2-oct-2010.pdf (ignore underlined Psi symbols; they should have an overbar). My argument is that the mathematics of the Standard Model are being misapplied physically. The electroweak unification is achieved by mixing SU(2) with U(1) but not anywhere near the way it is done in the Standard Model. SU(2) is electroweak symmetry: the three gauge bosons exist in massless and massive forms. Massless charged bosons can’t propagate unless the magnetic self inductance is cancelled, which can only happen in certain circumstances (e.g. a perfect equilibrium of exchange between two similar charge, so that the charged bosons going in each opposite direction have magnetic vectors than cancel one another, preventing infinite self-inductance, just electromagnetic energy in a light velocity logic step propagating along a two-conductor power transmission line). This effectively makes electric charge the extra polarizations that virtual photons need to account for attraction and repulsion in electromagnetism. The massive versions of those SU(2) bosons are the weak bosons, and arise not from a Higgs field but from a U(1) hypercharge/spin-1 quantum gravity theory.

There is a massive error of the Standard Model’s CKM parameter matrix in the “electroweak” theory, which has the contradiction that when a lepton like a muon or tauon decays, it decays via the intermediary step of a weak gauge boson to give a lepton, but when a quark decays it doesn’t delay into a lepton via the weak gauge boson, but instead into another quark: https://nige.files.wordpress.com/2010/08/diagram1.jpg. See

https://nige.wordpress.com/2010/05/07/category-morphisms-for-quantum-gravity-masses-and-draft-material-for-new-paper/ and

https://nige.wordpress.com/2010/06/29/professor-jacques-distler-disproves-the-alleged-anomaly-in-beta-decay-analysis/. When you correct this theoretical beta decay analysis error, all of the problems of the Standard Model evaporate and you get a deep understanding (this draft PDF paper is incomplete and underlined Psi symbols should have overbars, but most of the rest of the theory is on other blog posts).

“… it comes about that, step by step, and not realizing the full meaning of the process, mankind has been led to search for a mathematical description … mathematical ideas, because they are abstract, supply just what is wanted for a scientific description of the course of events. This point has usually been misunderstood, from being thought of in too narrow a way. Pythagoras had a glimpse of it when he proclaimed that number was the source of all things. In modern times the belief that the ultimate explanation of all things was to be found in Newtonian mechanics was an adumbration of the truth that all science as it grows towards perfection becomes mathematical in its ideas. … In the sixteenth and seventeenth centuries of our era great Italians, in particular Leonardo da Vinci, the artist (born 1452, died 1519), and Galileo (born 1564, died 1642), rediscovered the secret, known to Archimedes, of relating abstract mathematical ideas with the experimental investigation of natural phenomena. Meanwhile the slow advance of mathematics and the accumulation of accurate astronomical knowledge had placed natural philosophers in a much more advantageous position for research. Also the very egoistic self-assertion of that age, its greediness for personal experience, led its thinkers to want to see for themselves what happened; and the secret of the relation of mathematical theory and experiment in inductive reasoning was practically discovered. … It was an act eminently characteristic of the age that Galileo, a philosopher, should have dropped the weights from the leaning tower of Pisa. There are always men of thought and men of action; mathematical physics is the product of an age which combined in the same men impulses to thought with impulses to action.”

– Dr Alfred North Whitehead,

An Introduction to Mathematics,Williams and Norgate, London, revised edition, undated, pp. 13-14, 42-43.

Einstein’s tensors (second order differential equations) presuppose a classical distribution of matter and a classical, continuously acting acceleration. Einstein and others have problems with the fact that all mass and energy is particulate, in setting up the stress-energy tensor (gravity charge for causing spacetime curvature) in general relativity. How do we use a tensor formulation, that can only model a continuous distribution of matter, to represent discrete particles of mass and energy?

Simple: *we don’t*. They average out the density of discrete particle mass-energy in a volume of space by replacing it with the helpful approximation of an imaginary “perfect fluid” which is a continuum, not composed of particles. So all the successes of general relativity are based on lying, averaging out the discrete locations of quanta in a volume, to feed into the stress-energy tensor. If you don’t do this lie, general relativity fails completely: for discrete point-like particles in the stress-energy tensor, the curvature takes just two possible values, both of them unreal (zero and infinity!). So general relativity is just a classical approximation, based on lying about the nature of quantum fields and discrete particles!

“In many interesting situations… the source of the gravitational field can be taken to be a perfect fluid…. A fluid is a continuum that ‘flows’… A perfect fluid is defined as one in which all antislipping forces are zero, and the only force between neighbouring fluid elements is pressure.”

– B. Schutz,

A First Course in General Relativity,Cambridge University Press, 1986, pp. 89-90.

However, there is one thing that Einstein did do that was a step beyond Newton in general relativity, which is explained well at http://www.mathpages.com/home/kmath103/kmath103.htm:

It is this “trace” term that Einstein had to introduce to make the stress-energy tensor’s divergence zero (satisfying the conservation of mass-energy) that makes light deflect twice as much more due to gravity than Newton’s law predicts. But as Feynman showed in the final chapter to the second edition (not included in the first edition!) of the second volume of his “Lectures on Physics”, this special feature of curved spacetime is simple to understand as being a gravitational field version of the Lorentz-FitzGerald contraction. Earth’s radius is contracted by (1/3)MG/c^{2} = 1.5 millimetres to preserve mass-energy conservation in general relativity. Just as Maxwell predicted displacement current by looking physically at how capacitors with a vacuum for a dielectric allow current to flow through a circuit while they charge up, you don’t need a physically false tensor system to predict this. The fact that Maxwell used physical intuition and not mathematics to predict displacement current is contrary to the lying revisionist history at http://www.mathpages.com/home/kmath103/kmath103.htm, the author of which is apparently ignorant of the fact that Maxwell *never used vector calculus* (which was an innovation due to self-educated Oliver Heaviside, a quarter century later), messed up his theory of light, never unified electricity and magnetism consistently despite repeated efforts, and came up with an electrodynamics which (contrary to Einstein’s ignorant claims in 1905 and for fifty years thereafter) is only relativistic for a (non-existent) “zero action” approximation, and *by definition fails to be relativistic for all real-world situations* (that comprise of *small not non-zero actions which vary as a function of the coordinate system and thus motion, and so are not generally invariant*). You don’t need tensors to predict the modifications to Newtonian gravity that arise when conservation of mass-energy in fields is included; you don’t need general relativity to predict the excess radius that causes the apparent spacetime curvature, because a LeSage type quantum gravity predicts that spin-1 gravitons bombarding masses will compress them, explaining the contraction. And a light photon deflects twice as much due to a perpendicular gravity field than slow-moving bullets deflect, because of the Lorentz-FitzGerald contraction of the energy in the light photon: 100% of the energy is in the plane of the gravitational field, instead of just 50% for a bullet. So light photons interact twice as strongly with the gravity field. There is no magic!

**Prediction of gravitational time-dilation**

When light travels through a block of glass it slows down because the electromagnetic field of the light interacts with the electromagnetic fields in the glass. This is why light is refracted by glass. Light couples to gravitational fields as well as electromagnetic. The gravitational time dilation from the Einstein field equation is proved in an earlier blog post to be simply the same effect. The gravitons are exchanged between gravitational charges (mass/energy). Therefore, the concentration of gravitons per cubic metre is higher near mass/energy than far away. When a photon enters a stronger gravitational field, it interacts at a faster rate with that field, and is consequently slowed down. This is the mechanism for gravitational time dilation. It applies to electrons and nuclei, indeed anything with mass that is moving, just as it applies to light in a glass block. If you run through a clear path, you go faster than if you try to run through a dense crowd of people. There’s no advanced subtle mathematical “magic” at work. It’s not rocket science. It’s very simple and easy to understand physically. *You can’t define time without motion, and motion gets slowed down by dense fields just like someone trying to move through a crowd.*

Length contraction with velocity and mass increase by the reciprocal of the same factor are simply physical effects as FitzGerald and Lorentz explained. A moving ship has more inertial mass than its own mass, because of the flow of water set up around it (like “Aristotle’s arrow”, fluid moving out at the bows, flows around the sides and pushes in at the stern). As explained in previous posts, the “ideal fluid” aproximation for the effect of velocity on the drag coefficient of an aircraft in the 1920s was predicted theoretically to be the factor (1 – *v*^{2}/*c*^{2})^{-1/2}, where *c* is the velocity of sound: this is the “sound barrier” theory. It breaks down because although the shock wave formation at sound velocity carries energy off rapidly in the sonic boom, it isn’t 100% efficient at stopping objects from going faster. The effect is that you get an effective increase in inertial mass from the layer of compressed, dense air in the shock wave region at the front of the aircraft, and the nose-on force has a slight compressive effect on the aircraft (implying length contraction). Therefore, from an idealized understanding of the basic physics of moving through a fluid, you can grasp how quantum field theory causes “relativity effects”!

“… light … “smells” the neighboring paths around it, and uses a small core of nearby space.”

– Richard P. Feynman, *QED, *Penguin Books, London, 1990, Chapter 2, p. 54.

**Above:** classical light “wave” illustration from Wikipedia. Most people viewing such diagrams confuse the waving lines with axes labelled *field strengths* in a single physical dimension, for *field lines waving in three dimensional space!* Don’t confuse field strength varying along one axis for a field line waving in two dimensions. It’s interesting that field lines are just a mathematical convenience or abstract model invented by Faraday, and are no more real in the physical sense than isobars on weather maps or contour lines on maps. If you scatter iron filings on a piece of paper held over a magnet several times, the absolute positions of the apparent “lines” that the filings clump along occur in randomly distributed locations, although they are generally spaced apart by similar distances. The random “hotspot” locations in which high random concentrations of the first-deposited filings land, form “seeds”, which – under the presence of the magnetic field – have induced magnetism (called paramagnetism), which attract further filings in a pole-to-pole arrangement that creates the illusion of magnetic field lines.

This classical theory of light (the diagram is a colour one of the version in Maxwell’s original *Treatise on Electricity and Magnetism,* final 3rd ed., 1873) is wrong: it shows fields along a single, non-transverse, dimension: a longitudinal “pencil of light” which violates the experimental findings of the double slit experiment! (If you look, you will see *only one spatial direction* shown, the *z* axis! The apparent *y* and *z* axes are not actually spatial dimensions but just the electric *E* and magnetic *B* field *strengths*, respectively! You can draw a rather similar 3-dimensional diagram of the speed and acceleration of a car as a function of distance, with speed and acceleration plotted as if they are dimensions at right angles to the distance the car has gone. Obfuscating tomfoolery *doesn’t make the graph spatially real in three dimensions*.)

The real electromagnetic photon, needed to explain the double slit experiment using single photons (as Feynman shows clearly in his 1985 book *QED*), is entirely different to Maxwell’s classical photon guesswork of 1873: it is spatially extended in a transverse direction, due to the reinforcement of multiple paths (in the simultaneous sum of histories) where the action of the paths is small by comparison to about 15.9% of Planck’s constant (i.e., to *h*-bar or *h* divided by twice Pi). However, this quantum theory path integral theory of the light photon is today still being totally ignored in preference to Maxwell’s rubbish in the ignorant teaching of electromagnetism. The classical equations of electromagnetism are just approximations valid in an imaginary, unreal world, where there is simply one path with zero action! We don’t live in such a classical universe. In the *real world*, there are multiple paths, and we have to sum *all* paths. The classical laws are only “valid” for the physically false case of zero action, by which I mean an action which is not a function of the coordinates for motion of the light, and which therefore remains invariant of the motion (i.e. a “pencil” of light, following one path: this classical model of a photon *fails to agree with the results of the double slit diffraction experiment using photons fired one at a time*).

To put that another way, classical Maxwellian physics is only relativistic because its (false) classical action is invariant of the coordinates for motion. As soon as you make the action a variable of the path, so that light is not a least-action phenomenon but instead takes a spread of actions each with different motions (paths), special relativity ceases to apply to Maxwell’s equations! Nature isn’t relativistic as soon as you correct the false classical Maxwell equations for the real world multipath interference mechanism of quantum field theory on small scales, *precisely because action is a function of the path coordinates taken.* If it wasn’t a function of the motion, there would simply be no difference between classical and quantum mechanics. The invariance of path action as a false classical principle and its variance in quantum field theory is a fundamental fact of nature. Just learn to live with it and give up worshipping Dr Einstein’s special relativity fraud!

Thus, in quantum field theory we recover the classical laws by specifying no change in the action when the coordinates are varied, or as Dirac put it in his 1964 *Lectures on Quantum Mechanics* (Dover, New York, 2001, pp. 4-5):

“… when one varies the motion, and puts down the conditions for the action integral to be stationary, one gets the [classical, approximately correct on large-scales but generally incorrect on small scales] equations of motion. … In terms of the action integral, it is very easy to formulate the conditions for the theory to be relativistic [in the real contraction, FitzGerald-Lorentz-Poincare spacetime fabric, emergent relativity mechanism,

notEinstein’s damnable lies against a quantum field existing in the vacuum; remember Dirac’s public exposure of Einstein’s damned lies in his famousNaturev168, 1951, pp. 906-7 letter, “Is there an aether?”: ‘Physical knowledge has advanced much since 1905, notably by the arrival of quantum mechanics, and the situation has again changed. If one examines the question in the light of present-day knowledge, one finds that the aether is no longer ruled out by relativity, and good reasons can now be advanced for postulating an aether. . . . Thus, with the new theory of electrodynamics [vacuum filled with virtual particles] we are rather forced to have an aether.’!]: one simply has to require that the action integral shall be invariant. … [this] will automatically lead to equations of motion agreeing with [Dirac’s aether-based] relativity, and any developments from this action integral will therefore also be in agreement with [Dirac’s aether-based] relativity.”

Classical physics corresponds falsely to *just* the path of least action, or least time, whereas real (“sum over multiple path interference”) physics shows us that even in simple situations, light does not just follow the path of least action, but the energy delivered by a photon is actually spread over a range of paths with actions that are *small* compared to *h*-bar, but are *not zero!* There is a big difference between a path having zero action and a spread of paths having actions which are not zero but merely small compared to *h*-bar! This “subtle” difference (which most mathematical physicists fail to clearly grasp even today) is, as Feynman explained in his 1985 book *QED,* the basis of the *entirely different behaviour of quantum mechanics from the behaviour of classical physics!*

We have experimental evidence (backed up with a theory which correctly predicts observed force couplings) that the force-causing off-shell radiation of the vacuum isn’t a one-way inflow, but is falling in to the event horizon radius of a fundamental particle, then being re-emitted in the form of charged (off-shell) Hawking exchange radiation. The reflection process in some sense is analogous to the so-called normal reflection of on-shell light photons by mirrors, as Feynman explained in *QED* in 1985. Light isn’t literally reflected by a mirror, as Feynman showed by graphical illustration of path integral phase amplitude summation in *QED* (1985), light bounces off a mirror randomly in all directions and all paths of large action have random phase amplitudes which cancel one another out, leaving just paths with small path actions to add together coherently. The path integral for off-shell virtual photons (gauge bosons) is exactly the same. They go everywhere, but the net force occurs in the direction of least action, where their phases add together coherently, rather than cancelling out at random! The effective reflection of similarly charge polarized gauge bosons between similar charges is just the regular exchange process as depicted in basic (non-loopy) Feynman diagrams for fundamental interactions.

In 2002 and 2003 I wrote two papers in the *Electronics World* journal (thanks to the kind interest or patience of two successive editors) about a sketchy quantum field theory that replaces, and makes predictions way beyond, the Standard Model. Now in 2011, we can try an alternative presentation to clarify all of the technical details not by simply presenting the new idea, but by going through errors in the Standard Model and general relativity. This is because, after my articles had been published and attacked with purely sneering *ad hominem* “academic” non-scientific abuse, Leslie Green then wrote a paper in the August 2004 issue of the same journal, called “Engineering versus pseudo-science”, making the point that any advance that is worth a cent by definition must conflict with existing well established ideas. The whole idea that new ideas are supplementary additions to old ideas is disproved time and again. The problem is that the old false idea will be held up as some kind of crackpot evidence that the new idea must be wrong. Greene stated in his paper:

“The history of science and technology is littered with examples of those explorers of the natural world who merely reported their findings or theories, and were vehemently attacked for it. … just declaring a theory foolish because it violates known scientific principles [e.g. Aristotle’s laws of motion, Ptolemy’s idea that the sun orbits the earth, Kelvin’s stable vortex atoms of aether, Einstein’s well-hyped media bigotry – contrary to experimental evidence – that quantum field theory is wrong, Witten’s M-theory of a 10 dimensional superstring brane on an 11 dimensional supergravity theory, giving a landscape 10

^{500}parallel universes, etc.] is not necessarily good science. If one is only allowed to check for actions that agree with known scientific principles, then how can any new scientific principles be discovered? In this respect, Einstein’s popularisation of the Gedankenexperiment (thought-experiment) is potentially a backward step.”

**Fig. 1a:** the primary Feynman diagram describing a quantum field interaction with a charge is similar for mathematical modelling purposes for all of the different interactions in the Standard Model of particle physics. The biggest error in the Standard Model is the assumption that the physically simplest or correct model for electromagnetism is an Abelian gauge theory in which the field is mediated by uncharged photons, rather than a Yang-Mills theory in which the field carries charge. This blog post will explain in detail the very important advantages to physics to be obtained by abandoning the Abelian theory of electromagnetism, and replacing it by a physically (*but not mathematically*) simpler Yang-Mills SU(2) theory of electromagnetism, in which the massless field quanta can be not merely neutral, but can carry either positive or negative electric charge. (Source: Exchange Particles internet page. For clarity I’ve highlighted an error in the direction of an arrow in the weak interaction diagram; this is of course nothing to do with the error in electromagnetism which I’m describing in this post.)

Note also the very important point for high-energy physics where particles approach very closely into field strengths exceeding Schwinger’s 1.3 x 10^{18} volts/meter cutoff for vacuum fermion pair production, i.e. spacetime annihilation and creation “loops” as shown on a Feynman diagram, have been excluded for these simplified diagrams. In understanding the long range forces pertinent to the kind of low energy physics we see everyday, we can usually ignore spacetime loops in Feynman diagrams, because in QED the biggest effect for low energy physics is from the simplest Feynman diagram, which doesn’t contain any loops. The general effect of such spacetime loops due to pair-production at high energies is called “vacuum polarization”: the virtual fermions suck in energy from the field, depleting its strength, and as a result the average distance between the positive and negative virtual fermions is increased slightly owing to the energy they gain from their polarization by the field. This makes them less virtual, so they last slightly longer than predicted by Heisenberg’s uncertainty principle, before they approach and annihilate back into bosonic field quanta. During when gaining extra energy from the field, they modify the apparent strength of the charge as seen at lower energies or longer distances, hence the need to renormalize the effective value of the charge for QFT calculations, by allowing it to run as a function of energy. In QCD there is gluon antiscreening, which we explained in previous posts is due to the creation of gluons to accompany virtual hadrons created by pair production in very strong electric fields, so the QCD running coupling at the highest energies runs the opposite way to the QED running coupling. Field energy must be conserved, so the QED field loses energy, the QCD field gains energy, hence asymptotic freedom for quarks over a certain range of distances. This total field energy conservation mechanism is completely ignored by QFT textbooks! As the virtual fermions gain some real energy from the field via the vacuum polarization, they not only modify the apparent charge of the particle’s core, but they also get modified themselves. Onshell fermions obey the Pauli exclusion principle. Thus, the virtual fermions in strong fields can actually start to become structured like electron shells around the particle core. This mechanism for vacuum structuring, as shown in earlier blog posts, gives rise to the specific discrete spectrum of fundamental particle masses, a fact that has apparently led to the repeated immediate deletion of arXiv-submitted papers, due to ignorance, apathy, and hostility of mainstream physicists towards checkable, empirically based mechanisms in QFT. Elitist superstring theorists preach (off the record, on Dr Lubos Motl’s superstring theory blog, or in anonymous sneering comments) that all of this progress is merely “heuristically based” physics, that such experimentally guided theory makes them sick, is mathematically naive, inelegant or repulsive, and that it would “just” reduce physics to a simple mechanical understanding of nature that the person in the street could grasp and understand. (Amen to that last claim!)

**Fig. 1b:** Maxwell’s equations (Maxwell wrote them in long-hand first-order differential term summarizing the laws of Gauss, Ampere and Faraday with the addition of his own, now textbook-obfuscated, law of “displacement current” through the aether for the vital case of open circuits, e.g. the effects of net energy transfer through space from of accelerating and decelerating currents in the plates of a charging or discharging of a capacitor which has a vacuum as its “dielectric”; the advanced curl and div operator notation was introduced by self-taught mathematical physicist Oliver Heaviside) contradict reality experimentally in what is called the Aharonov–Bohm effect (or Ehrenberg–Siday–Aharonov–Bohm effect). The failure of Maxwell’s equations is their neglect of energy in fields in general, and neglect of the conservation of energy in supposedly “cancelled” fields in particular! E.g., inside a block of glass through which light travels, there is positive electric field energy density from atomic nuclei and negative electric field energy density from orbital electrons. The two fields superimpose and neatly “cancel”, leaving no effect according to Maxwell’s equations (which don’t predict the variation of relativity permittivity as a function of “cancelled” fields!). So why does light slow down and thus refract in glass? Answer: the energy density of the “cancelled” electric fields is still there, and “loads” the vacuum. The photon’s electromagnetic field interacts with the electromagnetic energy in the glass, and this slows it and can deflect its direction. All you can do with Maxwell’s equations to allow for this is to make an *ad hoc* modification to the permittivity of the vacuum, fiddling with the “constants” in the equation to make it agree with experiments! The same effect applies to magnetic fields, as the experimental confirmation of the Aharonov–Bohm effect proves. To correct Maxwell’s equations, we replace them with a similarly first-order but more comprehensive “field potential” vector which includes a term that allows for the energy of cancelled fields in the vacuum. Note, however, that this modification to Maxwell’s equations under some conditions leads to conflicts with “special relativity”. E.g., if the zero point vacuum itself is viewed as consisting of “cancelled” field energy by analogy to a block of glass, then the modified Maxwell equations no longer necessarily necessitate the principle of special relativity, but under some circumstances necessitate absolute motion instead. This fact is usually obfuscated either to defend mathematical mysticism in theoretical physics, or to “protect Einstein’s authority”, much as people used to reject Newton’s laws in deference to the more-ancient “authority” of Aristotle’s laws of motion.

The problem that the zero-point electromagnetic energy in the vacuum might constitute an absolute frame of reference due to gravitational effects is clearly stated by Richard P. Feynman and Albert R. Hibbs, *Quantum Mechanics and Path Integrals,* Dover, New York, corrected edition, 2010, page 245:

“… if we were to sum this ground-state energy over all of the infinite number of possible modes of ever-increasing frequency which exist even for a finite box, the answer would be infinity. This is the first symptom of the difficulties which beset quantum electrodynamics. … Suppose we choose to measure energy from a different zero point. … Unfortunately, it is really not true that the zero point of energy can be assigned completely arbitrarily. Energy is equivalent to mass, and mass has a gravitational effect. Even light has a gravitational effect, for light is deflected by the sun. So, if the law that action equals reaction has qualitative validity, then the sun must be attracted by the light. This means that a photon of energy {

h-bar}*{omega} has a gravity-producing effect, and the question is: Does the ground-state energy term {h-bar}*{omega}/2 [this assumes two modes per k] also have an effect? The question stated physically is: Does a vacuum act like a uniform density of mass in producing a gravitational field?”

On page 254, they point out that if the charged and neutral Pi mesons differ only in charge, then their observed differences in mass (the charged Pi meson has a greater mass than the neutral Pi meson) implies that this extra mass in the case of a charged particle comes from “the different way they couple to the electromagnetic field. So presumably the mass difference … represents energy in the electromagnetic field.” Using the same cutoff that works here for the electromagnetic field of an electron, on page 255 they find that the corresponding correction to the mass of the electron for electromagnetic field interactions “is only about 3 percent, but there is no way to test this, for we do not recognize a neutral counterpart to the electron.” As we pointed out since 1996, there are two separate long-range zero-point fields in the vacuum: gravitational (gravitons) and electromagnetic (off-shell photons), with very different energy densities due to the factor of 10^{40} difference in their long-distance couplings (the coupling at the low-energy IR cutoff limit, i.e. asymptotic limit of the running coupling that is valid for the low-energy physics domain, below ~1 MeV kinetic energy). The confusion in the value of the pseudo “cosmological constant” from the zero point vacuum comes from confusing the immense electromagnetic field energy density of the vacuum for the relatively tiny gravitational field energy density of the vacuum. It is the latter, manifested (as we proved effectively in 1996) by spin-1 gravitons, which causes the small observed cosmological acceleration of the universe, *a ~ Hc*. This is so because electric charge comes in two forms which balance, preventing long-range electromagnetic forces in the universe, whereas all observed gravitational charge has the same single sign and cannot cancel out. Gravitation thus pushes the matter apart (over long distances), causing cosmological acceleration. (On relatively small distance scales, the shielding of an observer by the presence of a relatively nearby mass, from the immense convergence of exchange gravitons with the surrounding isotropic universe, pushes the observer towards the nearby mass. The details of this have been carefully checked and confirmed to experimental accuracy!)

**Fig. 1c:** the SU(2) Yang-Mills field strength equation for electromagnetism utilizing massless charged field quanta reduces to the Maxwellian U(1) equation (equivalent to uncharged gauge bosons) under all necessary conditions, because of the motion-denying magnetic self-inductance of charged massless field quanta of SU(2). Note that the transfer of electric charge by Yang-Mills gauge bosons is not unaccompanied by a force. The charged gauge bosons carry both force-causing energy and charge. SU(2) includes one neutral boson as well as two charged bosons, so the neutral boson can deliver forces without carrying charge. SU(2) is thus a rich mathematical theory that can do a lot, and it is tempting with massless exchange radiation to attribute the neutral boson to graviton and the charged ones to electromagnetism (with left-handed interacting massive versions also existing to produce weak interactions). An addictive “drunkards walk” of charged massless gauge bosons between the ~10^{80} real fermion pairs in the universe the produces a path integral resultant that “conveniently” predicts the low-energy electromagnetism coupling IR limit to be (~10^{80})^{1/2} stronger than gravitation, because the neutral bosons (gravitons) don’t undergo such an addictive path integral! However, the theory is stronger than such superficial conveniences suggest, because it also predicted two years ahead of observation the correct observed cosmological acceleration of the universe, and vice-versa, it predicts the observed gravitational coupling (not using the 10^{40} factor just mentioned). It turns out that the simplest fully-consistent theory of nature has the graviton emerge from U(1) hypercharge which mixes with the neutral massless gauge boson of SU(2). Ignorant critics may claim that this correct limit proves that the SU(2) model is unnecessary under Occam’s Razor since for most cases it reduces to U(1) for practical calculations in electromagnetism, but this is a false criticism. The SU(2) electromagnetic theory is necessary to properly understand the relationship between electromagnetism and weak interactions (only left-handed interacting spin field quanta effectively acquire mass and partake in weak interactions)! The Abelian U(1) theory is a hypercharge which – when mixed with SU(2) – gives rise to the masses of the weak field quanta and also gives rise to a neutral field quantum, a spin-1 graviton. This is necessary. The spin-1 graviton pushes masses together, and this was falsely rejected by Pauli and Fierz in 1939 on the basis of a hidden implicit assumption which has been proved false. The currently fashionable claim that, because Maxwell’s equations are rank-1 tensors and general relativity’s Ricci tensor curvature is rank-2, electromagnetic field quanta are spin-1 and gravitons are spin-2, is a complete fraud; it is an expression of the most puerile physical and mathematical confusion between physical reality and the different mathematical models that can be used to represent that physical reality. We can, for instance, express electromagnetic forces in terms of rank-2 curvature equations. We don’t, not because this is the “wrong” thing to do, but because it is unnecessary, and it is far more convenient to use rank-1 equations (divs and curls of Faraday’s “field lines”).

Regarding mathematics being confused for reality, the great Eugene Wigner in 1960 published a paper called “The Unreasonable Effectiveness of Mathematics in the Natural Sciences”, *Communications in Pure and Applied Mathematics,* vol. 13, No. I. It’s mainly hand-waving groupthink fashion, that is a “not even wrong” confusion between reality and continuously-evolving mathematical models that are just approximations, e.g. differential equations for wavefunctions in quantum mechanics implicitly assume that wavefunctions are continuously variable – not discretely variable – functions, which disagrees with the physical premise of quantum field theory, namely that every change in the state of a particle is a discrete event! (This definition, of a change of “state” as being a discrete change, doesn’t include purely rotational phase amplitudes due to the spin of a particle which has a transverse polarization; the wavefunction for phase amplitude will be a classical-type continuous variable, but other properties such as accelerations involve forces which in quantum field theory are mediated by discrete particle interactions, not continuous variables in a spacetime continuum.)

The first false specific claim that Wigner makes in his paper is his allusion, very vaguely (the vagueness is key to his confusion), to the fact that the integral of the Gaussian distribution, exp(-*x*^{2}), over all values of *x* between minus infinity and plus infinity, is equal to the square root of Pi. He feels uneasy that the square root of Pi, the ratio of the circumference to diameter of a circle, is the result of a probability distribution. However, he ignores the fact that there is –*x*^{2} in the natural exponent, so this is a natural geometric factor. If *x* is a scaled distance, then *x*^{2} is an area, and you’re talking geometry. *It’s no longer simply a probability that is unconnected to geometry*. For example, the great RAND Corporation physicist Kahn in Appendix I to his 1960 thesis on deterrence, *On Thermonuclear War,* shows that the normal or Gaussian distribution applies to the effect of a missile aimed at a target; the variable *x* is the ratio of distance from intended ground zero, to the CEP standard error distance for the accuracy of the missile. We see in this beautiful natural example of falling objects hitting targets that the Gaussian distribution is implicitly geometric, and it is therefore no surprise that its integral should contain the geometric factor of Pi.

The circular area that objects fall into is the product Pi**r*^{2} where *r* is radius, which is directly proportional to the scaled radius, *x*. This is mathematically why the square root of Pi comes out of the integral of exp(-*x*^{2}) over *x* from minus to plus infinity (i.e., over an infinitely extensive flat plane, that the objects fall upon). Quite simply, the Gaussian distribution law fails to include the factor Pi in its exponent, so you get the square root of Pi coming out of the integral (thus the square root of Pi is the normalization factor for the Gaussian distribution in statistics). If only the great Gauss in 1809 had half a brain and knew what he was doing, he’d have included the Pi factor in the exponent, giving an integral output of 1, so we wouldn’t get the fictitious square root of Pi! The Gaussian or normal distribution is just the plain old negative exponential distribution of coin-tossing, with relative area as its variable! It’s therefore simply the insertion of area as the variable that introduces Pi (either directly in the exponent, or else as the square root of Pi in the integral result and related normalization factor). The error of Wigner was in not recognising that the square of dimensionless relative radius, *x*^{2}, *needs to be accompanied by the equally dimensionless geometric factor Pi, in the negative exponent*. It is a classic error of theoretical physicists to believe, on the basis of a mistaken understanding of dimensional analysis, that dimensionless geometric conversion factors like Pi only apply to dimensionful, absolute distances or areas, not to relative distances or areas. In fact, factors like Pi obviously *also* apply to dimensionless *relative* measures of distance or area, because it is self-evident that if the radius of a circle is one dimensionless unit, then its area is obviously Pi dimensionless units, and not one dimensionless unit, as confused people like Gauss and Wigner believed with their obfuscating formula for the normal distribution!

Statistician Stephen M. Stigler (best known for Stigler’s law of eponymy) first suggested replacing the Gaussian distribution exp(-*x*^{2}) with exp(-Pi**x*^{2}) in his 1982 paper, “A modest proposal: a new standard for the normal”, *The American Statistician* v36 (2). However, Stigler was too modest and therefore failed to make the point with sufficient physical force to get the world’s mathematics teachers and users to dump Laplace’s and Gauss’s obfuscating, fumbling nonsense and make statistics physically understandable to clear-thinking students. So even today, Wigner’s lie continues to be believed by the fashionable groupthink ideology of pseudo-mathematical physics prevailing in the world, as the following illustration indicates (note that the hoax began with Laplace, who infamously claimed that God was an unnecessary hypothesis in his crackpot mathematics!!!):

Wigner also ignores the fact that the mathematical concept of Pi is ambiguous in physics because of excess radius of mass in general relativity; general relativity and quantum gravity predict that around a spherical mass *M*, its *radius *shrinks by excess radius (1/3)MG/*c*^{2} metres, but the transverse direction (circumference) is unaffected, thus varying Pi unless there is curved spacetime. Since curved spacetime seems to be a classical large-scale approximation incompatible on the deeper level with quantum fields, where all actions consist of not of continuously variable differential equations but rather of a series of discrete impulsive particle interactions, it appears that the “excess radius” effect proves that the mathematical textbook value of Pi is wrong, and the real value of Pi is a variable quantity, which is the effect of the gravitational field warping spatial dimensions. Wigner simply ignores this mathematical failure of Pi, implicitly assuming that the textbook formula is correct. Actually, nobody verified the textbook formula precisely to more than a few significant figures, and since gravity is so small, the variation in Pi is small. So the point remains: mathematics has nothing to do with physics, beyond constituting a puerile tool or model for imperfect but often helpful calculations and is a danger in leading to arcane worship as an alternative to religion, a problem that goes back to the very roots of mathematics in the Egyptian priesthood and in the Greek Pythagorean cult.

The failure of mathematics to make deterministic predictions precisely even for classical systems like the collision of three balls in the “three body problem” which is beyond Newton’s laws, shows this mathematical failure so very clearly. Newton only came up with laws of motion that are deterministic when applied to an artificially simplistic situation which never really occurs precisely in our universe! Even if you tried to collide two balls in the vacuum of space, particles of radiation would affect the outcome! Nature isn’t mathematical! It’s physical. So Pi isn’t really the ratio of the circumference of a circle to its diameter; that’s only an approximation!

Wigner’s “mathematical reality” ideology nearly cost America the vital Nagasaki plutonium bomb that finally convinced Japan to agree to a conditional surrender without a horrific million plus casualties in an invasion of Japan, after Hiroshima and the Russian declaration of war against Japan failed. Wigner designed the plutonium production reactors but arrogantly tried to prevent the engineers from enlarging the core size to allow for unknowns. He raged that the engineers were ignorant of the accuracy of the cross-sections for fission and the accuracy of the mathematical physics of nuclear chain reactions, and were delaying plutonium production by insisting on bigger reactor cores than were needed. After the first reactor started up, it shut itself down a few hours later. Wigner’s data on the 200 fission products had been incomplete, and it turned out that some fission products like Xe-135 had large cross-sections to absorb neutrons, so after a few hours enough had been produced to “poison” the chain reaction. It was only because the engineers had made the cores bigger than Wigner specified, knowing that mathematical physics predictions are often wrong, that they were able to overcome the poisoning by adding extra uranium to the core to keep it critical!

Fig. 1d: he was unable to understand the immoral perils of relativism in blocking progress in physics, and was unable to understand the simplicity of physical mechanisms for fundamental forces, but at least Einstein was able to make the equations look pretty and attractive to the children who have only learned to count up to the number three, and who like patterns and very simple equations (a PDF version of above table is linked here, since I can’t easily put Greek symbols into html blog posts that will display correctly in all browsers; notice that the top-left to bottom-right diagonal of zero terms are the trace of the tensor, which is zero in this case). Actually, using the field tensor formulation to represent the various components of electric and magnetic fields, is quite a useful – albeit usually obfuscated – reformulation of Maxwell’s equations. However, mathematical models should *never* be used to *replace* physical understanding of physical processes, e.g. by deliberate attempts to obfuscate the simplicity of nature. If you’re not blinded by pro-tensor hype, you can see an “anthropic landscape” issue very clearly with Einstein’s tensor version of Maxwell’s equations in this figure: the field strength tensor and its partial derivative are indeed capable of modelling Maxwell’s equations. But only in certain ways, which are “picked out” specifically because they agree with nature. In other words, it’s just *ad hoc* mathematically modelling; it’s not a predictive theory. If you chisel a beautiful woman out of marble, all well and good; but you are a liar if you claim she was already in the marble waiting to be chiselled out. Your chisel work created the statue: it’s not natural. Similar arguments apply to mathematical modelling in Maxwell’s theory!

(On the subject of Einstein’s relativism worship as an alternative to religion, see the earlier post linked here. While many liars still try to “defend” relativism by claiming falsely that proponents of quantum field theory are racists out to gas Jews, the sad fact is the *precisely the opposite:* Einstein tried to get a handful of Jews out of Germany, including Leopold Infeld, but his popular relativism helped Professor Cyril Joad attack Winston Churchill’s call for an arms race with the Nazis in the early 1930s, making it politically unacceptable to the nation, and thus weakening the hand of the already weak-brained Prime Minister at the Munich watershed in September 1938. E.g., Joad was standing at the back of one of Churchill’s popular lectures. Churchill made the point that we could deter Hitler by having an arms race. Joad then stood up and “innocently” asked Churchill “whether this advice was what he would tell the enemy”, triggering cheers and applause and media criticism of Churchill. It is certainly true that if everything were relative with no absolute truth and no absolute distinction between good and evil, Churchill’s advice is rubbish. This relativism, however, is not the case in morality, any more than in light velocity under a real FitzGerald-Lorentz contraction. Joad’s popular deceit led to millions of unnecessary deaths, as Kahn proved in 1960. Joad’s successors simply attacked Kahn while ignoring the facts, and then tried the same error of relativism during the Cold War with the Soviet Union. “The people suffering in the Soviet Union had a *right* to be free to be forced by the KGB to live under Soviet communism, just as we are free to have “a different system of government”, you see! Relatively speaking, *neither* side was right, and it was just “playground politics” to have a Cold War instead of sensibly disarming to ensure peace and safety from the horrible risk of deterring invasions, you see!” After President Nixon’s Watergate scandal and failure in Vietnam, to deflect media attacks from Nixon, America began to press ahead with negotiations with the Soviet Union for SALT treaties just when the Soviet threat was reaching parity with the Western arms stockpile, and when Soviet civil defense was being transferred from civilian control to military control with vastly increased spending. If the arms race had been stopped, the Soviet Union might have survived instead of going effectively bankrupt when Reagan manipulated oil prices in the 1980s. In 1975, America signed the Helsinki Act, for the first time agreeing to the borders of the Soviet Union and its Warsaw Pact in Europe. This officially handed over those countries and people to Soviet control. After it was signed, the Chairman of the Soviet KGB (secret police), Yuri Andropov, stated in a letter to the Soviet Central Committee on 29 December 1975: “It is impossible at present to cease criminal prosecutions of those individuals who speak out against the Soviet system, since this would lead to an increase in especially dangerous state crimes and anti-social phenomena.” Einstein’s “peaceful co-existence” propaganda was a falsehood. How on earth can anyone surrender to such lying relativist evil?)

**Fig. 1e:** clever field strength tensor in SO(3,3): Lunsford using 3+3d obtains the Pauli-Lubanski vector for particle spin, hence obtaining a *quantum* phenomenon from *classical* electrodynamics! The quantum number of particle spin is crucial to classical physics because, as we shall see, it determines how the phase amplitudes of paths with different actions vary. The quantum path with least action in the path integral has the classical equations of motion. The other paths are excluded due to spin-related phase amplitude cancellation. It’s really that simple! Bosons with spin-1 are transformed by Dirac-Anderson pair-production into pairs of spin-1/2 fermions (the charged radiations in pair-production are trapped in loops by gravitation, thus giving the black hole event horizon cross-sectional area for quantum gravity interactions, which is confirmed by empirically-checked quantum gravity calculations, which allows the magnetic field of any portion of the loop to be cancelled by the magnetic field from the opposite side of the loop which has the opposite direction, allowing stable spin without self-inductance issues; this is shown in my 2003 *Electronics World* paper), so just as fermions combine at low temperatures into a Bose-Einstein condensate composed of Cooper pairs of electrons (or other fermions) that together behave *like* a frictionless, superconducting, low-viscosity boson, so too a spin-1 boson of radiation at any temperature is physically equivalent to a superposition of two spin-1/2 fermion-like components. (Higher temperatures cause random brownian motion with enough energy to break up the delicate Cooper pair spin-coupling, thus preventing superconductivity, etc.)

Fermion amplitudes during scatter *subtract*, while boson amplitudes add together with a *positive* sign, because of the superposition of the magnetic field self-induction vectors that are the consequence of spinning charges! (This rule applies to the scatter of similar particles in similar spin states with one another, not to unpolarized beams.) It is related to the Pauli exclusion principle, because Pauli stipulated that no two fermions with the same set of quantum numbers can exist in the same location; in a sense, therefore, the Pauli exclusion principle (only an empirically confirmed principle, not a mechanism or really deep explanation) causes fermions with originally similar sets of quantum numbers to change their states when they approach closely enough to interact. Bosons don’t obey Pauli’s exclusion principle, so they don’t need to change their states when they scatter! This problem is discussed – but it’s simple solution is ignored – by Feynman in the *Lectures on Physics*, v3, p.4-3:

“We apologise for the fact that we cannot give you an elementary explanation. An explanation has been worked out by Pauli from complicated arguments of quantum field theory and relativity. He has shown that the two [boson and fermion interaction amplitude sign rules] must necessarily go together, but we have not been able to find a simple way of reproducing his arguments on an elementary level. It appears to be one of the few places in physics where there is a rule which can be stated very simply [for particles with identical spin states: fermion scattering amplitudes subtract in scatter, but boson scattering amplitudes add with a positive sign], but for which no one has found a simple and easy explanation. The explanation is deep down in relativistic quantum mechanics [QFT]. This probably means that we do not have a complete understanding of the fundamental principle involved. For the moment, you will just have to take it as one of the rules of the world.”

(But don’t be fooled. Just because Feynman said that, doesn’t prove that peer-reviewers and journal editors are interested in the nurture and publication of deep-explanations to long-existing problems. Instead, the situation is the exact opposite. The longer an anomaly or “issue” has existed, the better the textbook authors learn to live with it, to camouflage it behind a wallpaper of obfuscating symbolism, and to reinterpret it as a badge of pride: “*nobody* understands quantum mechanics”. This is spoken with the “nobody” *snarled* as a threat accompanied by a motion of the hand towards the bulging holster, after you have just explained the answer! Progress comes from change, which is violently opposed by bigots. Niccolò Machiavelli, *The Prince* (1513), Chapter 6: “And let it be noted that there is no more delicate matter to take in hand, nor more dangerous to conduct, nor more doubtful in its success, than to set up as the leader in the introduction of changes. For he who innovates will have for his enemies all those who are well off under the existing order of things, and only lukewarm supporters in those who might be better off under the new.” The struggle for progress against the vested interests of the status quo is called politics, and the extension of politics against unreasonable opponents who won’t really listen or actually try to block progress is, as Clausewitz defined it, war: “War is not merely a political act, but also a real political instrument, a continuation of political commerce, a carrying out of the same by other means.”)

Danny Ross Lunsford’s magnificent paper *Gravitation and Electrodynamics over SO(3,3)* overcame the hurdles required to unify gravitation and electrodynamics dynamically, making confirmed predictions (unlike the reducible gravitation-electrodynamics unification ideas of 4+1d Kaluza-Klein, Pauli, Einstein-Mayer, and Weyl; Pauli showed that “any generally covariant theory may be cast in Kaluza’s form”, hence the mindless and fruitless addition of 6/7 extra spatial dimensions in “not even wrong” string theory), but despite acceptance and publication in a peer-reviewed journal (*International Journal of Theoretical Physics,* Volume 43, Number 1, 161-177), and despite supplying the required arXiv endorsement, his brilliant paper was mindlessly removed from the stringy unification theory dominated arXiv (U.S. Government part-funded) pre-print server, thus denying its circulation via the accepted mainstream electronic route to physicists around the world. To summarize Lunsford’s great idea is very easy. There is not one time dimension, but three, making a total of three spatial and three time dimensions. In other words, spacetime is symmetric, with one timelike dimension per spatial dimension.

One way to grasp this is to note that the age of the universe can be deduced (since the universe has been found to have a flat overall geometry, i.e. dark energy offsets the gravitational curvature on large scales), from looking at the redshift of the universe to obtain the Hubble parameter: the age of the universe is the reciprocal of that parameter. Since we build geometry on the basis of 90 degree angles between spatial dimensions, we have three orthagonal dimensions of space, SO(3). Measuring the Hubble constant in these 3 orthagonal dimensions by pointing a telescope in the three 90-degree different directions and measuring the redshift-distance Hubble parameter in each of them, would give 3 separate ages for the universe, i.e. 3 time dimensions! Obviously, if we happen to see isotropic redshift, all the 3 age measurements for the universe will be similar, and we will live under the delusion that there is only one time dimension, not three. But in reality, there may be a simple reason why the universe has an isotropic expansion rate in all directions, and thus why time appears to have only one discernable dimension: nature may be covering up two time dimensions by making all time dimensions appear similar to us observers. If this sounds esoteric, remember that unlike string theorists who compactify 6/7 unobservable extra spatial dimensions, creating a landscape of 10^{500} metastable vacua, Lunsford’s SO(3,3) is the simplest possible and thus the best dynamical electromagnetic-gravitational unification according to Occam’s razor. Lunsford proves that the the SO(3,3) unification of electrodynamics and gravitation eliminates the spurious “cosmological constant” from general relativity, so that the “dark energy” causing the acceleration must be spin-1 repulsive quantum gravity, just as we predicted in 1996 when predicting the small but later measured acceleration of the universe, *a ~ Hc.* (A prediction published via *Electronics World*, October 1996, p896, and also *Science World* ISSN 1367-6172, February 1997, after the paper had been rejected for “being inconsistent with superstring theory”, an (as yet) “unconfirmed speculation”, etc. (*after* confirmation, they just gave no reason for rejection when repeated submissions were made!) by the so-called “peer-reviewers” who censor predictive theories from publication for *CQG, Nature,* et al. Unfortunately, just like those mainstream bigots, IC – despite claiming to champion progress, and despite my efforts to write about his work which culminated in publications – has never in fifteen years agreed host a single discussion on his website of QFT, nor in his numerous scientific publications, but instead like the crank string theorists resorted to shouting the idea down and wasting time!)

Lunsford finishes his paper: “It thus appears that the indeterminate aspect of the Einstein equations represented by the ordinary cosmological constant, is an artifact [in general relativity, not in nature!] of the decoupling of gravity and electromagnetism. … the Einstein-Maxwell equations are to be regarded as a first-order approximation to the full calibration-invariant system. One striking feature of these equations that distinguishes them from Einstein’s equations is the absent gravitational constant – in fact the ratio of scalars in front of the energy tensor plays that role. This explains the odd role of *G* in general relativity and its scaling behaviour (see Weinberg, 1972 [S. Weinberg, *Gravitation and Cosmology*, Wiley, p. 7.1, p. 10.8, 1972]).”

**Fig. 1f:** Oleg D. Jefimenko and Richard P. Feynman (equation 28.3 in the *Feynman Lectures on Physics,* vol. 1) independently solved Maxwell’s equations in the early 1960s, which allows quantum field theory effects to be easily seen in the Maxwell correction to Coulomb’s force law for steady charges to an equation which allows for charge motion. The Jifimenko-Feynman equation for electric field strength is a three component equation in which the first component is from Coulomb’s law (Gauss’s field divergence equation in the Maxwell equations) where force **F** = *q***E** so that electric field **E** = *q*/(4*Pi*Permittivity**R*^{2}) . The Feynman-Jefimenko solution to Maxwell’s equations for field directions along the line of the motion and acceleration of a charge yields the simple summation of terms: **E**_{v/m} = [*q*/(4*Pi*Permittivity)] { *R*^{-2} + [**v**(cos *z*)/(*cR*^{2})] + [**a**(sin *z*)/(*Rc*^{2})] }

The sine and cosine factors in the two motion related terms are due to the fact that they depend on whether the motion of a charge is towards you or away from you (they come from vectors in the Feynman-Jefimenko solution; *z* is the angle between the direction of the motion of the charge and the direction of the observer). The first term in the curly brackets is the Coulomb law for static charges. The second term in the curly brackets with a linear dependence on **v**/*c* is simply the effect of the redshift (observer receding from the charge) or blue shift (observer approaching the charge) of the force field quanta, which depends on whether you are moving towards or away from the charge *q*; as the Casimir effect shows, field quanta or virtual photons do have physically-significant wavelengths. The third term in the curly brackets is the effect of accelerations of charge, i.e. the real (on-shell) photon radio wave emission: this radio emission field strength drops off inversely with distance rather than as the inverse square of distance. (The time-dependence of **E** at distance *R* in the equation is the retarded time *t* – *R/c*, which allows for the light speed delay due to the field being composed of electromagnetic field quanta and waves which must transverse that distance from charge to observer before the field can be observed.)

This solution to Maxwell’s equations is important for the analysis of quantum field theory effects due to gauge bosons.

**Physical mechanism of electric forces**

Fig. 1a shows the Feynman diagrams used for the *main* force-causing interactions (there are many others too; for example the pions aren’t the only mesons involved in the strong nuclear force that operates between nucleons).

**Fig. 2:** mathematical concepts like plots of electric and magnetic field strengths or even “field lines” inside photons are *not physically real* but they do constitute a useful *tool,* when mathematically shown on a graph, for establishing the physical distinctions and mechanisms for on-shell (real) and off-shell (virtual) radiations in quantum field theory, and it should be remembered that Maxwell’s equations are an incomplete description of electromagnetism (the field potential A_{{mu}} is needed to account for effects of the superimposed energy density in so-called “cancelled fields”, e.g. the Aharonov-Bohm effect, where the superimposed field energy loads the vacuum and thus affects quantum phenomena, just as the “cancelled” negative and positive fields from electrons and nuclei in a block of glass load the vacuum with energy density and thus slow down light).

**Fig. 3:** physical basis of path integrals for the simple case of light reflection by a mirror. Classically the reflection law is that the angle of incidence equals the angle of reflection, which is of course the path that light travels in the least time or least “action” (action is defined as the integral of the lagrangian over time; for classical systems the lagrangian is the difference between the kinetic and potential energy of a particle at any given time). Light follows all paths, but most of them have randomly orientated “phases” and thus cancel out in the vector summation. Only for small actions do the phases add together coherently. Thus, light effectively occupies not a one dimensional line as it propagates, but is spread out spatially in space due to the reinforcement of all those paths with actions small compared to Planck’s constant, *h = E/f* (which has units of action, and when divided by twice Pi, is equal to the proper unit of quantum action in quantum field theory). Hence Feynman’s great statement: “Light … uses a small core of nearby space. (In the same way, a mirror has to have enough size to reflect normally: if the mirror is too small for the core of nearby paths, the light scatters in many directions, no matter where you put the mirror.)” – R. P. Feynman, *QED* (Penguin, 1990, page 54).

**Fig. 4:** a minor mathematical modification of Feynman’s path integral theory involving replacing the imaginary (complex) phase amplitude with the real term in its expansion by Euler’s equation, which is needed to overcome Dr Chris Oakley’s mathematical problem with today’s sloppy (mathematically non-rigorous) textbook quantum field theory, namely Haag’s theorem, which proves that essential renormalization is impossible in a complex space like Foch space (an infinite-dimensional vector space) or Hilbert space (a complex inner product space, in which a complex number is associated to each pair of coordinate elements), *because the isomorphism that maps the free-field Hilbert space on to the renormalized-field Hilbert space is ambiguous!* (This theorem was proved by Hall and Wightman. The reason why the mainstream ignores Haag’s theorem is that Haag postulated that the whole interaction picture doesn’t exist, an interesting possibility which was investigated without great success by Dr Chris Oakley. Nobody seems to have grasped the obvious solution, namely that Hilbert space doesn’t exist and the phase factor is mathematically fictitious and in the real world must lose it’s complexity (this lack of sense is probably due to groupthink or mathematical respect to Euler, Hilbert, Schroedinger, Dirac, et al.; by analogy Newton should have resisted suggesting his laws of motion, purely out of respect for the dead genius Aristotle?). We must express the phase vectors as arrows in *real space* if we want quantum field theory to be renormalizable in a self-consistent, non-ambiguous manner. The path integral as shown above works just as well this way, it just eliminates the problem of Haag’s theorem. (Haag’s theorem is the argument behind Dr Oakley quotations from both Feynman and Dirac, who point out that because of renormalization, quantum field theory can’t be proved to be self-consistent. As Feynman wrote in his 1985 classic, *QED,* the lack of proof of self-consistency due to Haag’s theorem is embarrassing to any self-respecting mathematical physicist working in quantum field theory.) The diagram proves the equivalence of the resultant amplitudes when using *e*^{iS} and cos *S* for the phase factor in the path integral (sum over path histories). Basically, what we are suggesting is that we take Euler’s *e*^{iS} = cos *S* + *i* sin *S* then drop the complex term *i* sin *S*, which cuts out the use of the imaginary axis from the Argand diagram, giving only real space!

**Fig. 5:** how simply replacing the complex e^{iS} phasor with its real component cos (*iS*) replaces complex space with real space, averting the inability to prove self-consistency in quantum field theory due to Haag’s theorem. This allows the spatially distributed (truly transverse) on-shell and off-shell photons (unlike Maxwell’s idea of the photon) shown in Fig. 2 to have a *physically real* phase factor to be modelled, with the phase denoting a real physical property of the photons taking different paths, e.g. the phase factor can denote differing angles of spin polarization or differing charge combinations, unlike the imaginary, unphysical phase factor. The reasons why this isn’t done in textbooks is the fashionable groupthink argument that, historically, the origins of the textbook complex exponential phase factor are rooted in the solution to the time-dependent form of Schroedinger’s equation, and the time-dependent form of Schroedinger’s equation survives as Dirac’s equation because Dirac’s equation is only different from Schroedinger’s in its Hamiltonian (i.e., the spacetime-compatible Dirac “spinor”). However, as Feynman explained in his *Lectures on Physics,* Schroedinger’s equation was just a guess that “came out of the mind of Schroedinger”! It’s not a physical fact, and it’s actually contrary to physical facts because in quantum field theory it should take a discrete quantum interaction to cause a discrete wavefunction change, but Schroedinger’s equation intrinsically assumes a classical, continuously varying wavefunction! The error here is obvious. Why defend a guesswork derivation error which prevents renormalized quantum field theory from being rigorously, unambiguously formulated mathematically and proved self-consistent? Dr Thomas Love has explained that all of the problems of wavefunction collapse in quantum mechanics originate from this guess by Schroedinger: “‘The quantum collapse [in the mainstream interpretation of quantum mechanics, where a wavefunction collapse occurs whenever a measurement of a particle is made] occurs when we model the wave moving according to Schroedinger (time-dependent) and then, suddenly at the time of interaction we require it to be in an eigenstate and hence to also be a solution of Schroedinger (time-independent). The collapse of the wave function is due to a discontinuity in the equations used to model the physics, it is not inherent in the physics.”

Just as Bohr’s atom is taught in school physics, most mainstream general physicists with training in quantum mechanics are still trapped in the use of the “anything goes” false (non-relativistic) 1927-originating “first quantization” for quantum mechanics (where anything is possible because motion is described by an uncertainty principle instead of a quantized field mechanism for chaos on small scales). The physically correct replacement is called “second quantization” or “quantum field theory”, which was developed from 1929-48 by Dirac, Feynman and others.

The discoverer of the path integrals approach to quantum field theory, Nobel laureate Richard P. Feynman, has debunked the mainstream first-quantization uncertainty principle of quantum mechanics. Instead of anything being possible, the indeterminate electron motion in the atom is caused by second-quantization: the field quanta randomly interacting and deflecting the electron.

“… Bohr … said: ‘… one could not talk about the trajectory of an electron in the atom, because it was something not observable.’ … Bohr thought that I didn’t know the uncertainty principle … it didn’t make me angry, it just made me realize that … [ they ] … didn’t know what I was talking about, and it was hopeless to try to explain it further. I gave up, I simply gave up …”

– Richard P. Feynman, quoted in Jagdish Mehra’s biography of Feynman, *The Beat of a Different Drum,* Oxford University Press, 1994, pp. 245-248. (Fortunately, Dyson didn’t give up!)

‘I would like to put the uncertainty principle in its historical place: When the revolutionary ideas of quantum physics were first coming out, people still tried to understand them in terms of old-fashioned ideas … But at a certain point the old-fashioned ideas would begin to fail, so a warning was developed that said, in effect, “Your old-fashioned ideas are no damn good when …” If you get rid of all the old-fashioned ideas and instead use the ideas that I’m explaining in these lectures – adding *arrows* [path amplitudes] for all the ways an event can happen – there is no *need* for an uncertainty principle!’

– Richard P. Feynman, *QED, *Penguin Books, London, 1990, pp. 55-56.

‘When we look at photons on a large scale – much larger than the distance required for one stopwatch turn [i.e., wavelength] – the phenomena that we see are very well approximated by rules such as “light travels in straight lines [without overlapping two nearby slits in a screen]“, because there are enough paths around the path of minimum time to reinforce each other, and enough other paths to cancel each other out. But when the space through which a photon moves becomes too small (such as the tiny holes in the [double slit] screen), these rules fail – we discover that light doesn’t have to go in straight [narrow] lines, there are interferences created by the two holes, and so on. The same situation exists with electrons: when seen on a large scale, they travel like particles, on definite paths. But on a small scale, such as inside an atom, the space is so small that [individual random field quanta exchanges become important because there isn’t enough space involved for them to average out completely, so] there is no main path, no “orbit”; there are all sorts of ways the electron could go, each with an amplitude. The phenomenon of interference becomes very important, and we have to sum the arrows [in the path integral for individual field quanta interactions, instead of using the average which is the classical Coulomb field] to predict where an electron is likely to be.’

– Richard P. Feynman, *QED,* Penguin Books, London, 1990, Chapter 3, pp. 84-5.

His path integrals rebuild and reformulate quantum mechanics itself, getting rid of the Bohring ‘uncertainty principle’ and all the pseudoscientific baggage like ‘entanglement hype’ it brings with it:

‘This paper will describe what is essentially a third formulation of nonrelativistic quantum theory [Schroedinger’s wave equation and Heisenberg’s matrix mechanics being the first two attempts, which both generate nonsense ‘interpretations’]. This formulation was suggested by some of Dirac’s remarks concerning the relation of classical action to quantum mechanics. A probability amplitude is associated with an entire motion of a particle as a function of time, rather than simply with a position of the particle at a particular time.

‘The formulation is mathematically equivalent to the more usual formulations. … there are problems for which the new point of view offers a distinct advantage. …’

– Richard P. Feynman, ‘Space-Time Approach to Non-Relativistic Quantum Mechanics’, Reviews of Modern Physics, vol. 20 (1948), p. 367.

‘… I believe that path integrals would be a very worthwhile contribution to our understanding of quantum mechanics. Firstly, they provide a physically extremely appealing and intuitive way of viewing quantum mechanics: anyone who can understand Young’s double slit experiment in optics should be able to understand the underlying ideas behind path integrals. Secondly, the classical limit of quantum mechanics can be understood in a particularly clean way via path integrals. … for fixed h-bar, paths near the classical path will on average interfere constructively (small phase difference) whereas for random paths the interference will be on average destructive. … we conclude that if the problem is classical (action >> h-bar), the most important contribution to the path integral comes from the region around the path which extremizes the path integral. In other words, the article’s motion is governed by the principle that the action is stationary. This, of course, is none other than the Principle of Least Action from which the Euler-Lagrange equations of classical mechanics are derived.’

– Richard MacKenzie, Path Integral Methods and Applications, pp. 2-13.

‘… light doesn’t really travel only in a straight line; it “smells” the neighboring paths around it, and uses a small core of nearby space. (In the same way, a mirror has to have enough size to reflect normally: if the mirror is too small for the core of neighboring paths, the light scatters in many directions, no matter where you put the mirror.)’

– Richard P. Feynman, QED, Penguin Books, London, 1990, Chapter 2, p. 54.

There are other serious and well-known failures of first quantization aside from the nonrelativistic Hamiltonian time dependence:

“The quantum collapse [in the mainstream interpretation of first quantization quantum mechanics, where a wavefunction collapse occurs whenever a measurement of a particle is made] occurs when we model the wave moving according to Schroedinger (time-dependent) and then, suddenly at the time of interaction we require it to be in an eigenstate and hence to also be a solution of Schroedinger (time-independent). The collapse of the wave function is due to a discontinuity in the equations used to model the physics, it is not inherent in the physics.” – Thomas Love, California State University.

“In some key Bell experiments, including two of the well-known ones by Alain Aspect, 1981-2, it is only after the subtraction of ‘accidentals’ from the coincidence counts that we get violations of Bell tests. The data adjustment, producing increases of up to 60% in the test statistics, has never been adequately justified. Few published experiments give sufficient information for the reader to make a fair assessment.” – http://arxiv.org/PS_cache/quant-ph/pdf/9903/9903066v2.pdf

First quantization for QM (e.g. Schroedinger) quantizes the product of position and momentum of an electron, rather than the Coulomb field which is treated classically. This leads to a mathematically useful approximation for bound states like atoms, which is physically false and inaccurate in detail (a bit like Ptolemy’s epicycles, where all planets were assumed to orbit Earth in circles within circles). Feynman explains this in his 1985 book QED (he dismisses the uncertainty principle as complete model, in favour of path integrals) because *indeterminancy is physically caused by virtual particle interactions from the quantized Coulomb field becoming important on small, subatomic scales!* Second quantization (QFT) introduced by Dirac in 1929 and developed with Feynman’s path integrals in 1948, instead quantizes the field. Second quantization is physically the correct theory because all indeterminancy results from the random fluctuations in the interactions of discrete field quanta, and first quantization by Heisenberg and Schroedinger’s approaches is just a semi-classical, non-relativistic mathematical approximation useful for obtaining simple mathematical solutions for bound states like atoms:

‘You might wonder how such simple actions could produce such a complex world. It’s because phenomena we see in the world are the result of an enormous intertwining of tremendous numbers of photon exchanges and interferences.’

– Richard P. Feynman, QED, Penguin Books, London, 1990, p. 114.

‘Underneath so many of the phenomena we see every day are only three basic actions: one is described by the simple coupling number, j; the other two by functions P(A to B) and E(A to B) – both of which are closely related. That’s all there is to it, and from it all the rest of the laws of physics come.’

– Richard P. Feynman, QED, Penguin Books, London, 1990, p. 120.

‘It always bothers me that, according to the laws as we understand them today, it takes a computing machine an infinite number of logical operations to figure out what goes on in no matter how tiny a region of space, and no matter how tiny a region of time. How can all that be going on in that tiny space? Why should it take an infinite amount of logic to figure out what one tiny piece of spacetime is going to do? So I have often made the hypothesis that ultimately physics will not require a mathematical statement, that in the end the machinery will be revealed, and the laws will turn out to be simple, like the chequer board with all its apparent complexities.’

– R. P. Feynman, The Character of Physical Law, November 1964 Cornell Lectures, broadcast and published in 1965 by BBC, pp. 57-8.

Sound waves are composed of the group oscillations of large numbers of randomly colliding air molecules; despite the randomness of individual air molecule collisions, the average pressure variations from many molecules obey a simple wave equation and carry the wave energy. Likewise, although the actual motion of an atomic electron is random due to individual interactions with field quanta, the average location of the electron resulting from many random field quanta interactions is non-random and can be described by a simple wave equation such as Schroedinger’s.

This is fact, it isn’t my opinion or speculation: professor David Bohm in 1952 proved that “brownian motion” of an atomic electron will result in average positions described by a Schroedinger wave equation. Unfortunately, Bohm also introduced unnecessary “hidden variables” with an infinite field potential into his messy treatment, making it a needlessly complex, uncheckable representation, instead of simply accepting that the quantum field interations produce the “Brownian motion” of the electron as described by Feynman’s path integrals for simple random field quanta interactions with the electron.

Quantum tunnelling is possible because electromagnetic fields are not classical, but are mediated by field quanta randomly exchanged between charges. For large charges and/or long times, the number of field quanta exchanged is so large that the result is similar to a steady classical field. But for small charges and small times, such as the scattering of charges in high energy physics, there is some small probability that no or few field quanta will happen to be exchanged in the time available, so the charge will be able to penetrate through the classical “Coulomb barrier”. If you quantize the Coulomb field, the electron’s motion is indeterministic in the atom because it’s randomly exchanging Coulomb field quanta which cause chaotic motion. This is second quantization as explained by Feynman in *QED*. This is not what is done in quantum mechanics, which is based on first quantization, i.e. treating the Coulomb field *V* classically, and falsely representing the chaotic motion of the electron by a wave-type equation. This is a *physically false* mathematical model since it omits the physical cause of the indeterminancy (although it gives convenient predictions, somewhat like Ptolemy’s accurate epicycle based predictions of planetary positions):

**Fig. 6:** Schroedinger’s equation, based on quantizing the momentum p in the classical Hamiltonian (the sum of kinetic and potential energy for the particle), H. This is an example of ‘first quantization’, which is inaccurate and is also used in Heisenberg’s matrix mechanics. *Correct* quantization will instead quantize the *Coulomb field potential energy,* V, because the whole indeterminancy of the electron in the atom is *physically caused* by the chaos of the randomly timed individual interactions of the electron with the discrete Coulomb field quanta which bind the electron to orbit the nucleus, as Feynman proved (see quotations below). The triangular symbol is the divergence operator (simply the sum of the gradients in all applicable spatial dimensions, for whatever it operates on) which when squared becomes the laplacian operator (simply the sum of second-order derivatives in all applicable spatial dimensions, for whatever it operates on). We illustrate the Schroedinger equation in just one spatial dimension, x, above, since the terms for other spatial dimensions are identical.

Dirac’s quantum field theory is needed because textbook quantum mechanics is simply wrong: the Schroedinger equation has a *second-order* dependence on spatial distance but only a *first-order* dependence on time. In the real world, time and space are found to be on an *equal* footing, hence spacetime. There are deeper errors in textbook quantum mechanics: it *ignores* the quantization of the electromagnetic field and instead treats it classically, when the field quanta are the whole distinction between classical and quantum mechanics (the random motion of the electron orbiting the nucleus in the atom is *caused* by discrete field quanta interactions, as proved by Feynman).

Dirac was the first to achieve a relativistic field equation to replace the non-relativistic quantum mechanics approximations (the Schroedinger wave equation and the Heisenberg momentum-distance matrix mechanics). Dirac also laid the groundwork for Feynman’s path integrals in his 1933 paper “The Lagrangian in Quantum Mechanics” published in *Physikalische Zeitschrift der Sowjetunion* where he states:

“Quantum mechanics was built up on a foundation of analogy with the Hamiltonian theory of classical mechanics. This is because the classical notion of canonical coordinates and momenta was found to be one with a very simple quantum analogue …

“Now there is an alternative formulation for classical dynamics, provided by the Lagrangian. … The two formulations are, of course, closely related, but there are reasons for believing that the Lagrangian one is the more fundamental. … the Lagrangian method can easily be expressed relativistically, on account of the action function being a relativistic invariant; while the Hamiltonian method is essentially nonrelativistic in form …”

Schroedinger’s time-dependent equation is: Hy= iħ.dy /dt, which has the exponential solution:

y_{t} = y_{o} exp[-iH(t – t_{o})/ħ].

This equation is accurate, because the error in Schroedinger’s equation comes only from the expression used for the Hamiltonian, H. This exponential law represents the time-dependent value of the wavefunction for any Hamiltonian and time. Squaring this wavefunction gives the amplitude or relative probability for a given Hamiltonian and time. Dirac took this amplitude e^{-iHT/ħ} and derived the more fundamental lagrangian amplitude for action S, i.e. e^{iS/ħ}. Feynman showed that summing this amplitude factor over all possible paths or interaction histories gave a result proportional to the total probability for a given interaction. This is the path integral.

Schroedinger’s incorrect, non-relativistic hamiltonian before quantization (ignoring the inclusion of the Coulomb field potential energy, V, which is an added term) is: H = ½ **p**^{2}/m. Quantization is done using the substitution for momentum, p -> -iħ{divergence operator} as in **Fig. 6** above. The Coulomb field potential energy, V, remains classical in Schroedinger’s equation, instead of being quantized as it should.

The bogus ‘special relativity’ prediction to correct the expectation H = ½ **p**^{2}/m is simply: H = [(mc^{2})^{2} + **p**^{2}c^{2}]^{2}, but that was falsified by the fact that, although the total mass-energy is then conserved, the resulting Schroedinger equation permits an initially localised electron to travel faster than light! This defect was averted by the Klein-Gordon equation, which states:

ħ^{2}d^{2}y/dt^{2} = [(mc^{2})^{2} + **p**^{2}c^{2}]y.

While this is physically correct, it is non-linear in only dealing with second-order variations of the wavefunction. Dirac’s equation simply makes the time-dependent Schroedinger equation (Hy = iħ.dy/dt) relativistic, by inserting for the hamiltonian (H) a totally new relativistic expression which differs from special relativity:

H = a**p**c + b mc^{2},

where **p** is the momentum operator. The values of constants a and b can take are represented by a 4 x 4 = 16 component matrix, which is called the Dirac ‘spinor’. This is not to be confused for the Weyl spinors used in the gauge theories of the Standard Model; whereas the Dirac spinor represents massive spin-1/2 particles, the Dirac equation yields two Weyl equations for massless particles, each with a 2-component Weyl spinor (representing left- and right-handed spin or helicity eigenstates). The justification for Dirac’s equation is both theoretical and experimental. Firstly, it yields the Klein-Gordon equation for second-order variations of the wavefunction. Secondly, it predicts four solutions for the total energy of a particle having momentum p:

E = ±[(mc^{2})^{2} + p^{2}c^{2}]^{1/2}.

Two solutions to this equation arise from the fact that momentum is directional and so can be can be positive or negative. The spin of an electron is ± ½ ħ = ± h/(4p). This explains two of the four solutions! The electron is spin-1/2 so it has a spin of only half the amount of a spin-1 particle, which means that the electron must rotate 720 degrees (not 360 degrees!) to undergo one revolution, like a Mobius strip (a strip of paper with a twist before the ends are glued together, so that there is only one surface and you can draw a continuous line around that surface which is twice the length of the strip, i.e. you need 720 degrees turning to return it to the beginning!). Since the spin rate of the electron generates its intrinsic magnetic moment, it affects the magnetic moment of the electron. Zee gives a concise derivation of the fact that the Dirac equation implies that ‘a unit of spin angular momentum interacts with a magnetic field twice as much as a unit of orbital angular momentum’, a fact discovered by Dirac the day after he found his equation (see: A. Zee, *Quantum Field Theory in a Nutshell,* Princeton University press, 2003, pp. 177-8.) The other two solutions are evident obvious when considering the case of p = 0, for then E = ± mc^{2}. This equation proves the fundamental distinction between Dirac’s theory and Einstein’s special relativity. Einstein’s equation from special relativity is E = mc^{2}. The fact that in fact E = ± mc^{2}, proves the physical shallowness of special relativity which results from the lack of physical mechanism in special relativity. E = ± mc^{2 }allowed Dirac to predict antimatter, such as the anti-electron called the positron, which was later discovered by Anderson in 1932 (anti-matter is naturally produced all the time when suitably high-energy gamma radiation hits heavy nuclei, causing pair production, i.e., the creation of a particle and an anti-particle such as an electron and a positron).

(To be continued when time allows. In the meanwhile, as linked on an earlier post, the introductory pages from my draft PDF paper can be found at https://nige.files.wordpress.com/2010/10/paper-draft-pages-1-5-2-oct-2010.pdf, although please note that there are some trivial mathematical symbol typos that are outside my control, e.g. the QuarkXpress software I used doesn’t contain any apparent way of writing Psi with an overbar, so I’ve had to underline Psi instead. I also gave some comments about errors in “electroweak symmetry” on Tommaso’s blog which are of relevance, posts on this blog discuss particle masses and the quantum gravity mechanism.)

**Above:** a quantitative prediction of the cosmological acceleration of the universe in 1996, two years ahead of the discovery, was ignored! Pseudo-physicists at the so-called *Classical and Quantum Gravity* and also *Physics Review Letters* think anything fundamental that doesn’t agree with superstring liars must be wrong! Maybe the gravitons heat up or slow down planets? If so this should apply also to the well established off-shell Casimir radiation in the vacuum which would have dragged and slow the planets making them glow, slow down, and spiral into the sun millions of years ago. They didn’t. Contrary to string theorists who are ignorant of the basics of quantum field theory, field quanta are off-shell particles, which impart kinetic energy to accelerate charges thus causing forces, without causing direct heating or drag, merely the Lorentz mass increase and the real FitzGerald-Lorentz contraction effect. Maybe rank-2 tensors prove spin-2 gravitons? Nope, rank-1 tensors are first order field line gradients, and rank-2 tensors are second-order equations of motion. You can use either rank-1 or rank-2 equations for electromagnetism or gravity; it depends not on spin but purely on whether the theory is formulated as field lines (rank-1 equations) or accelerations in spacetime (rank-2).

**Update (20 January 2011):**

Sadly, superstring theorist Dr Lubos Motl, a Facebook friend who is 100% right about global warming hype, left-wing dangers and political correctness, has called for the famous superstring theorist Professor Greene at Columbia University to fire superstring critic Dr Peter Woit. Dr Woit, whose blog and paper on representation theory and quantum field theory since 2002 has led me to my current approach to the problem of fundamental interactions and unification, has replied robustly: “It seems that some unemployed guy in Pilsen who reads this blog thinks Brian Greene is my employer and is upset that Brian is not having me fired. For the record, my position as “Senior Lecturer” in the math department is not tenured, but I have a long-term contract and whether it gets renewed at some point in the distant future will have nothing to do with what Brian thinks about this blog, or with what I think about his books. Actually, my impression is that if most string theorists could choose one well-known blog dealing with string theory to shut down, it wouldn’t be this one …”

{NC note: the “Friend” who wrote this comment, which goes on to another paragraph of abject speculation, is not me, although I have contributed comments under anonymity where I can’t otherwise contribute comments. The probability that “Friend” is Dr Woit writing an anonymous comment on his own blog, or a friend of his doing so, is not 0. However I don’t really know what Dr Woit thinks about Feynman’s 1985 book QED. My wild guess from reading Dr Woit’s 2002 arXiv paper on “Quantum Field Theory and Representation Theory” is that he hasn’t really spent time on Feynman’s 1985 book, doesn’t physically put too much stress on the “heuristic” picture of 2nd quantization/QFT as virtual particles following every path and interfering to cause “wavefunction” chaos; he works in a mathematics department and is fixed into a belief that sophisticated maths is good, only objecting to misrepresentations of mathematics for hype and funding by superstring theorists and others. “Friend”, in a later comment time-stamped 9:29pm, writes about another pet interest of Dr Woit’s: “how about the financial market;-) Unsatisfied with economic progress, they’ve invented extravagant financial theories of prime-lending rates and complicated security instruments. Funny, I’ve heard that some physicists have found work in the financial industry. Perhaps their theories work in some other universe.” Dr Baez replied to Friend: ‘That’s a nice analogy because it seems to have been caused by a desperate search for “high rates of return”.’}

**Update (2 Feb 2011):** IC’s February 2011 *Electronics World* article has now been published, linked here. For the first part (in the same excellent on-line user friendly format), see the link here. I disagree with IC’s simplistic theoretical interpretation of his experimentally valid findings, for the reasons given in the blog post on QFT help for electromagnetic experiments, linked here. IC suffers from the same problem Einstein had with relativism, although IC is “sticking to his guns” (like Einstein did) despite having no real benefit from promoting a false interpretation of his results. If IC was genuinely famous for a discovery which turned out to be misinterpreted, he would have some unethical but at least “logical” reason to censor out attempts to improve the theoretical analysis of his results. He has no such fame to lose, his self-promotion on the internet by having several “personal name” websites exploits his unusual name to give high ranking google results when his name is searched, but if you look at the webcounters on his sites, he gets little interest. Few people google his name in the first place. If I buy a domain called “zzzuuuyy”, and it gets top rank results on google when searching for that “name”, it doesn’t mean anything because nobody will search for it.

I regularly write that groupthink fashion and popularity are no measure of science. But that doesn’t mean that writing such useless and boring material is a measure of helpfulness! IC should aim to write in a useful way, which unfortunately for him means confronting the depressing fact that his research work is relevant to path integrals in quantum field theory. Remaining prejudiced against QFT is irrational. The only way to destroy classical Maxwellian lies about light is to do so using the best replacement theory, Feynman’s QFT. By the time IC ever tries that, it will be too late and he will have polluted the world with too much boring, vacuous drivel to be taken seriously. There are only so many times you can cry wolf and get away with it. The best thing you can say about IC is that, with friends like him, who needs enemies?

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