Gauge theory mechanisms

Gauge symmetry: whenever the motion or charge or angular momentum of spin, or some other symmetry, is altered, it is a consequence of conservation laws in physics that radiation is emitted or received. This is Noether’s theorem, which was applied to quantum physics by Weyl. (Illustration credit: http://hyperphysics.phy-astr.gsu.edu/hbase/particles/expar.html. Unfortunately the arrow they show for the antineutrino in this diagram points the wrong way: the antineutrino is emitted in beta decay.)

Noether’s theorem (discovered 1915) connects the symmetry of the action of a system (the integral over time of the Lagrangian equation for the energy of a system) with conservation laws. In quantum field theory, the Ward-Takahashi identity expresses Noether’s theorem in terms of the Maxwell current (a moving charge, such as an electron, can be represented as an electric current since that is the flow of charge). Any modification to the symmetry of the current involves the use of energy, which (due to conservation of energy) must be represented by the emission or reception of photons, e.g. field quanta. (For an excellent introduction to the simple mathematics of the Lagrangian in quantum field theory and its role in symmetry modification for Noether’s theorem, see chapter 3 of Ryder’s Quantum Field Theory, 2nd ed., Cambridge University Press, 1996.)

So, when the symmetry of a system such as a moving electron is modified, such a change of the phase of an electron’s electromagnetic field (which together with mass is the only feature of the electron that we can directly observe) is accompanied by a photon interaction, and vice-versa. This is the basic gauge principle relating symmetry transformations to energy conservation. E.g., modification to the symmetry of the electromagnetic field when electrons accelerate away from one another implies that they emit (exchange) virtual photons.

All fundamental physics is of this sort: the electromagnetic, weak and strong interactions are all examples of gauge theories in which symmetry transformations are accompanied by the exchange of field quanta. Noether’s theorem is pretty simple to grasp: if you modify the symmetry of something, the act of making that modification involves the use or release of energy, because energy is conserved. When the electron’s field undergoes a local phase change to its symmetry, a gauge field quanta called a ’virtual photon’ is exchanged. However, it is not just energy conservation that comes into play in symmetry. Conservation of charge and angular momentum are involved in more complicated interactions. In the Standard Model of particle physics, there are three basic gauge symmetries, implying different types of field quanta (or gauge bosons) which are radiation exchanged when the symmetries are modified in interactions:

1. Electric charge symmetry rotation. This describes the electromagnetic interaction. This is supposedly the most simple gauge theory, the Abelian U(1) electromagnetic symmetry group with one element, invoking just one charge and one gauge boson. To get negative charge, a positive charge is represented as travelling backwards in time, and vice-versa. The gauge boson of U(1) is mixed up with the neutral gauge boson of SU(2), to the amount specified by the empirically based Weinberg mixing angle, producing the photon and the neutral weak gauge boson. U(1) represents not just electromagnetic interactions but also weak hypercharge.

The U(1) maths is based on a type of continuous group defined by Sophus Lie in 1873. Dr Woit summarises this very clearly in Not Even Wrong (UK ed., p47): ‘A Lie group … consists of an infinite number of elements continuously connected together. It was the representation theory of these groups that Weyl was studying.

‘A simple example of a Lie group together with a representation is that of the group of rotations of the two-dimensional plane. Given a two-dimensional plane with chosen central point, one can imagine rotating the plane by a given angle about the central point. This is a symmetry of the plane. The thing that is invariant is the distance between a point on the plane and the central point. This is the same before and after the rotation. One can actually define rotations of the plane as precisely those transformations that leave invariant the distance to the central point. There is an infinity of these transformations, but they can all be parametrised by a single number, the angle of rotation.

Argand diagram showing rotation by an angle on the complex plane. Illustration credit: based on Fig. 3.1 in Not Even Wrong.

‘If one thinks of the plane as the complex plane (the plane whose two coordinates label the real and imaginary part of a complex number), then the rotations can be thought of as corresponding not just to angles, but to a complex number of length one. If one multiplies all points in the complex plane by a given complex number of unit length, one gets the corresponding rotation (this is a simple exercise in manipulating complex numbers). As a result, the group of rotations in the complex plane is often called the ‘unitary group of transformations of one complex variable’, and written U(1).

‘This is a very specific representation of the group U(1), the representation as transformations of the complex plane … one thing to note is that the transformation of rotation by an angle is formally similar to the transformation of a wave by changing its phase [by Fourier analysis, which represents a waveform of wave amplitude versus time as a frequency spectrum graph showing wave amplitude versus wave frequency by decomposing the original waveform into a series which is the sum of a lot of little sine and cosine wave contributions]. Given an initial wave, if one imagines copying it and then making the copy more and more out of phase with the initial wave, sooner or later one will get back to where one started, in phase with the initial wave. This sequence of transformations of the phase of a wave is much like the sequence of rotations of a plane as one increases the angle of rotation from 0 to 360 degrees. Because of this analogy, U(1) symmetry transformations are often called phase transformations. …

‘In general, if one has an arbitrary number N of complex numbers, one can define the group of unitary transformations of N complex variables and denote it U(N). It turns out that it is a good idea to break these transformations into two parts: the part that just multiplies all of the N complex numbers by the same unit complex number (this part is a U(1) like before), and the rest. The second part is where all the complexity is, and it is given the name of special unitary transformations of N (complex) variables and denotes SU(N). Part of Weyl’s achievement consisted in a complete understanding of the representations of SU(N), for any N, no matter how large.

‘In the case N = 1, SU(1) is just the trivial group with one element. The first non-trivial case is that of SU(2) … very closely related to the group of rotations in three real dimensions … the group of special orthagonal transformations of three (real) variables … group SO(3). The precise relation between SO(3) and SU(2) is that each rotation in three dimensions corresponds to two distinct elements of SU(2), or SU(2) is in some sense a doubled version of SO(3).’

2. Isospin symmetry rotation. This describes the weak interaction of quarks, controlling the transformation of quarks within one family of quarks. E.g., in beta decay a neutron decays into a proton by the transformation of a downquark into an upquark, and this transformation involves the emission of an electron (conservation of charge) and an antineutrino (conservation of energy and angular momentum). Neutrinos were a falsifiable prediction made by Pauli on 4 December 1930 in a letter to radiation physicists in Tuebingen based on the spectrum of beta particle energies in radioactive decay (’Dear Radioactive Ladies and Gentlemen, I have hit upon a desperate remedy regarding … the continous beta-spectrum … I admit that my way out may seem rather improbable a priori … Nevertheless, if you don’t play you can’t win … Therefore, Dear Radioactives, test and judge.’ - Pauli’s letter, quoted in footnote of page 12, http://arxiv.org/abs/hep-ph/0204104). The total amount of radiation emitted in beta decay could be determined from the difference in mass between the beta radioactive material and its decay product, the daughter material. The amount of energy carried in readily detectable ionizing beta particles could be measured. However, the beta particles were emitted with a continuous spectrum of energies up to a maximum upper energy limit (unlike the line spectra of gamma ray energies): it turned out that the total energy lost in beta decay was equal to the upper limit of the beta energy spectrum, which was three times the mean beta particle energy! Hence, on the average, only one-third of the energy loss in beta decay was accounted for in the emitted beta particle energy.

Pauli suggested that the unobserved beta decay energy was carried by neutral particles, now called antineutrinos. Because they are weakly interacting, it takes a great intensity of beta decay in order to detect the antineutrinos. They were first detected in 1956 coming from intense beta radioactivity in the fission product waste of a nuclear reactor. By conservation laws, Pauli had been able to predict the exact properties to be expected. The beta decay theory was developed soon after Pauli’s suggestion in the 1930s by Enrico Fermi, who then invented the nuclear reactor used to discover the antineutrino. However, Fermi’s theory has a neutron decay directly into a beta particle plus an antineutrino, whereas in the 1960s the theory of beta decay had to be expressed in terms of quarks. Glashow, Weinberg and Salam discovered that to make it a gauge theory there had to be a massive intermediate ‘weak gauge boson’. So what really happens is more complicated than in Fermi’s theory of beta decay. A downquark interacts with a massive W_- weak field gauge boson, which then decays into an electron and an antineutrino. The massiveness of the field quanta is needed to explain the weak strength of beta decay (i.e., the relatively long half-lives of beta decay, e.g. a free neutron is radioactive and has a beta half life of 10.3 minutes, compared with the tiny lifetimes of a really small fraction of a second for hadrons which decay via the strong interaction). The massiveness of the weak field quanta was a falsifiable prediction, and in 1983 CERN discovered the weak field quanta with the predicted energies, confirming SU(2) weak interaction gauge theory.

There are two relative types or directions of isospin, by analogy to ordinary spin in quantum mechanics (where spin up and spin down states are represented by +1/2 and –1/2 in units of h-bar). These two isospin charges are modelled by the Yang-Mills SU(2) symmetry, which has (2*2)-1 = 3 gauge bosons (with positive, negative and neutral electric charge, respectively). Because the interaction is weak, the gauge bosons must be massive and as a result they have a short range, since massive virtual particles don’t exist for long in the vacuum, and can’t travel far in that short life time. The two isospin charge states allow quark-antiquark pairs, or doublets, to form, called mesons. The weak isospin force only acts on particles with left-handed spin. At high energy, all weak gauge bosons will be massless, allowing weak and electromagnetic forces become symmetric and unify. But at low energy, the weak gauge bosons acquire mass, supposedly from a Higgs field, breaking the symmetry. This Higgs field has not been observed, and the general Higgs models don’t predict a single falsifiable prediction (there are several possibilities).

3. Colour symmetry rotation. This changes the colour charge of a quark, in the process releasing colour charged gluons as the field quanta. Strong nuclear interactions (which bind protons into a nucleus against very strong electromagnetic repulsion, which would be expected to make nuclei explode in the absence of this strong binding force) are described by quantum chromodynamics, whereby quarks have a symmetry due to their strong nuclear or ‘colour’ charges. This originated with Gell-Mann’s SU(3) eightfold way of arranging the known baryons by their properties, a scheme which successfully predicted the existence of the Omega Minus in before it was experimentally observed in 1964 at Brookhaven National Laboratory, confirming the SU(3) symmetry of hadron properties. The understanding (and testing) of SU(3) as a strong interaction Yang-Mills gauge theory in terms of quarks with colour charges and gluon field quanta was a completely radical extension of the original convenient SU(3) eightfold way hadron categorisation scheme.

Experiments in scattering very high energy electrons off neutrons and protons first showed evidence that each nucleon had a more complex structure than a simple point in the 1950s, and therefore the idea that these nucleons were simply fundamental particles was undermined. Another problem with nucleons being fundamental particles was that of the magnetic moments of neutrons and protons. Dirac in 1929 initially claimed that the antiparticle his equation predicted for the electron was the already-known proton (the neutron was still undiscovered until 1932), but because he couldn’t explain why the proton is more massive than the electron, he eventually gave up on this idea and predicted the unobserved positron instead (just before it was discovered). The problem with the proton being a fundamental particle was that, by analogy to the positron, it would have a magnetic moment of 1 nuclear magneton, whereas in fact the measured value is 2.79 nuclear magnetons. Also, for the neutron, you would expect zero magnetic moment for a neutral spinning particle, but the neutron was found to have a magnetic moment of -1.91 nuclear magnetons. These figures are inconsistent with neutrons being fundamental particles, but are consistent with quark structure:

‘The fact that the proton and neutron are made of charged particles going around inside them gives a clue as to why the proton has a magnetic moment higher than 1, and why the supposedly neutral neutron has a magnetic moment at all.’ - Richard P. Feynman, QED, Penguin, London, 1990, p. 134.

To explain hadron physics, Zweig and Gell-Mann suggested the theory that baryons are composed of three quarks. But there was immediately the problem the Omega Minus would contain three identical strange quarks, violating the Pauli exclusion principle that prevents particles from occupying the same set of quantum numbers or states. (Pairs of otherwise identical electrons in an orbital have opposite spins, giving them different sets of quantum numbers, but because there are only two spin states, you can’t make three identical charges share the same orbital by having different spins. Looking at the measured 3/2-spin of the Omega Minus, all of its 1/2-spin strange quarks would have the same spin.) To get around this problem in the experimentally discovered Omega Minus, the quarks must have an additional quantum number, due to the existence of a new charge, namely the colour charge of the strong force that comes in three types (red, blue and green). The SU(3) symmetry of colour force gives rise to (3*3)-1 = 8 gauge bosons, called gluons. Each gluon is a charged combination of a colour and the anticolour of a different colour, e.g. a gluon might be charged blue-antigreen. Because gluons carry a charge, unlike photons, they interact with one another and also with with virtual quarks produced by pair production due to the intense electromagnetic fields near fermions. This makes the strong force vary with distance in a different way to that of the electromagnetic force. At small distances from a quark, the net colour charge increases in strength with increasing distance, which the opposite of the behaviour of the electromagnetic charge (which gets bigger at smaller distances, due to less intervening shielding by the polarized virtual fermions caused in pair production). The overall result is that quarks confined in hadrons have asymptotic freedom to move about over a certain range of distances, which gives nucleons their size. Before the quark theory and colour charge had been discovered, Yukawa discovered a theory of strong force attraction that predicted the strong force was due to pion exchange. He predicted the mass of the pion, although unfortunately the muon was discovered before the pion, and was originally inaccurately identified as Yukawa’s exchange radiation. Virtual pions and other virtual mesons are now understood to mediate the strong interaction between nucleons as a relatively long-range residue of the colour force.

Above: the electroweak charges of the Standard Model of mainstream particle physics. The argument we made is that U(1) symmetry isn’t real and must be replaced by SU(2) with two charges and massless versions of the weak boson triplet (we do this by replacing the Higgs mechanism with a simpler mass-giving field that gives predictions of particle masses).  The two charged gauge bosons simply mediate the positive and negative electric fields of charges, instead of having neutral photon gauge bosons with 4 polarizations. The neutral gauge boson of the massless SU(2) symmetry is the graviton. The lepton singlet with right handed spin in the standard model table above is not really a singlet: because SU(2) is now being used for electromagnetism rather than U(1), we have automatically a theory that unites quarks and leptons. The problem of the preponderance of matter over antimatter is also resolved this way: the universe is mainly hydrogen, one electron, two quarks and one downquark. The electrons are not actually produced alone. The downquark, as we will demonstrate below, is closely related to the electron.

The fractional charge is due to vacuum polarization shielding, with the accompanying conversion of electromagnetic field energy into short-ranged virtual particle mediated nuclear fields. This is a predictive theory even at low energy because it can make predictions based on conservation of field quanta energy where vacuum polarization attenuates a field, and the conversion of leptons into quarks requires higher energy than existing experiments have had access to. So electrons are not singlets: some of them ended up being converted into quarks in the big bang in very high energy interactions. The antimatter counterpart for the electrons in the universe is not absent but is present in nuclei, because those positrons were converted into the upquarks in hadrons. The handedness of the weak force relates to the fact that in the early stages of the big bang, for each two electron-positron pairs that were produced by pair production in the intense, early vacuum fields of the universe, both positrons but only one electron were confined to produce a proton. Hence the amount of matter and antimatter in the universe is identical, but due to reactions related to the handedness of the weak force, all the anti-positrons were converted into upquarks, but only half of the electrons were converted into downquarks. We’re oversimplifying a little because some neutrons were produced, and quite a few other minor interactions occurred, but this is approximately the overall result of the reactions. The Standard Model table of particles above is in error because it assumes that leptons and quarks are totally distinct. For a more fundamental level of understanding, we need to alter the electroweak portion of the Standard Model.

The apparent deficit of antimatter in the universe is simply a miss-observation: the antimatter has simply been transformed from leptons into quarks, which from a long distance display different properties and interactions to leptons (due to cloaking by the polarized vacuum and to close confinement causing colour charge to physically appear by inducing asymmetry; the colour charge of a lepton is invisible because it is symmetrically distributed over three preons in a lepton, and cancels out to white unless an enormous field strength due to the extremely close proximity of another particle is present, creating an asymmetry in the preon arrangement is produced, allowing a net colour charge to operate on the other nearby particle), so it isn’t currently being acknowledged for what it really is. (Previous discussions of the relationship of quarks to leptons on this blog include http://nige.wordpress.com/2007/06/13/feynman-diagrams-in-loop-quantum-gravity-path-integrals-and-the-relationship-of-leptons-to-quarks/ and http://nige.wordpress.com/2007/07/17/energy-conservation-in-the-standard-model/ where suggestions by Carl Brannen and Tony Smith are covered.)

Considering the strange quarks in the Omega Minus, which contains three quarks each of electric charge -1/3, vacuum polarization of three nearby leptons would reduce the -1 unit observable charge per lepton to -1/3 observable charge per lepton, because the vacuum polarization in quantum field theory which shields the core of a particle occurs out to about a femtometre or so, and this zone will overlap for three quarks in a baryon like the Omega Minus. The overlapping of the polarization zone will make it three times more effective at shielding the core charges than in the case of a single charge like a single electron. So the electron’s observable electric charge (seen from a great distance) is reduced by a factor of three to the charge of a strange quark or a downquark. Think of it by analogy a couple sharing blankets which act as shields, reducing the emission of thermal radiation. If each of the couple contribute one blanket, then the overlap of blankets will double the heat shielding. This is basically what happens when N electrons are brought close together so that they share a common (combined) vacuum polarization shell around the core charges: the shielding gives each charge in the core an apparent charge (seen from outside the vacuum polarization, i.e., more than a few femtometres away) of 1/N charge units. In the case of upquarks with apparent charges of +2/3, the mechanism is more complex, since the -1/3 charges in triplets are the clearest example of the mechanism whereby shared vacuum polarization shielding transforms properties of leptons into those of quarks. The emergence of colour charge when leptons are confined together also appears to have a testable, falsifiable mechanism because we know how much energy becomes available for the colour charge as the observable electric charge falls (conservation of energy suggests that the attenuated electromagnetic charge gets converted into colour charge energy). For the mechanism of the emergence of colour charge in quarks from leptons, see the suggestions of Tony Smith and Carl Brannen, outlined at http://nige.wordpress.com/2007/07/17/energy-conservation-in-the-standard-model/.

In particularly, the Cabibbo mixing angle in quantum field theory indicates a strong universality in reaction rates for leptons and quarks: the strength of the weak force when acting on quarks in a given generation is similar to that for leptons to within 1 part in 25. The small 4% difference in reaction rates arises, as explained by Cabibbo in 1964, due to the fact that a lepton has only one way to decay, but a quark has two decay routes, with probabilities of 96% and 4% respectively. The similarity between leptons and quarks in terms of their interactions is strong evidence that they are different manifestations of common underlying preons, or building blocks.

Above: Coulomb force mechanism for electric charged massless gauge bosons. The SU(2) electrogravity mechanism. Think of two flak-jacket protected soldiers firing submachine guns towards one another, while from a great distance other soldiers (who are receding from the conflict) fire bullets in at both of them. They will repel because of net outward force on them, due to successive impulses both from bullet strikes received on the sides facing one another, and from recoil as they fire bullets. The bullets hitting their backs have relatively smaller impulses since they are coming from large distances and so due to drag effects their force will be nearly spent upon arrival (analogous to the redshift of radiation emitted towards us by the bulk of the receding matter, at great distances, in our universe). That explains the electromagnetic repulsion physically. Now think of the two soldiers as comrades surrounded by a mass of armed savages, approaching from all sides. The soldiers stand back to back, shielding one another’s back, and fire their submachine guns outward at the crowd. In this situation, they attract, because of a net inward acceleration on them, pushing their backs toward towards one another, both due to the recoils of the bullets they fire, and from the strikes each receives from bullets fired in at them. When you add up the arrows in this diagram, you find that attractive forces between dissimilar unit charges have equal magnitude to repulsive forces between similar unit charges. This theory holds water!

This predicts the right strength of gravity, because the charged gauge bosons will cause the effective potential of those fields in radiation exchanges between similar charges throughout the universe (drunkard’s walk statistics) to multiply up the average potential between two charges by a factor equal to the square root of the number of charges in the universe. This is so because any straight line summation will on average encounter similar numbers of positive and negative charges as they are randomly distributed, so such a linear summation of the charges that gauge bosons are exchanged between cancels out. However, if the paths of gauge bosons exchanged between similar charges are considered, you do get a net summation.

Above: Charged gauge bosons mechanism and how the potential adds up, predicting the relatively intense strength (large coupling constant) for electromagnetism relative to gravity according to the path-integral Yang-Mills formulation. For gravity, the gravitons (like photons) are uncharged, so there is no adding up possible. But for electromagnetism, the attractive and repulsive forces are explained by charged gauge bosons. Notice that massless charge electromagnetic radiation (i.e., charged particles going at light velocity) is forbidden in electromagnetic theory (on account of the infinite amount of self-inductance created by the uncancelled magnetic field of such radiation!) only if the radiation is going solely in only one direction, and this is not the case obviously for Yang-Mills exchange radiation, where the radiant power of the exchange radiation from charge A to charge B is the same as that from charge B to charge A (in situations of equilibrium, which quickly establish themselves). Where you have radiation going in opposite directions at the same time, the handedness of the curl of the magnetic field is such that it cancels the magnetic fields completely, preventing the self-inductance issue. Therefore, although you can never radiate a charged massless radiation beam in one direction, such beams do radiate in two directions while overlapping. This is of course what happens with the simple capacitor consisting of conductors with a vacuum dielectric: electricity enters as electromagnetic energy at light velocity and never slows down. When the charging stops, the trapped energy in the capacitor travels in all directions, in equilibrium, so magnetic fields cancel and can’t be observed. This is proved by discharging such a capacitor and measuring the output pulse with a sampling oscilloscope.

The price of the random walk statistics needed to describe such a zig-zag summation (avoiding opposite charges!) is that the net force is not approximately 10⁸⁰ times the force of gravity between a single pair of charges (as it would be if you simply add up all the charges in a coherent way, like a line of aligned charged capacitors, with linearly increasing electric potential along the line), but is the square root of that multiplication factor on account of the zig-zag inefficiency of the sum, i.e., about 10⁴⁰ times gravity. Hence, the fact that equal numbers of positive and negative charges are randomly distributed throughout the universe makes electromagnetism strength only 10⁴⁰/10⁸⁰ = 10^-40 as strong as it would be if all the charges were aligned in a row like a row of charged capacitors (or batteries) in series circuit. Since there are around 10⁸⁰ randomly distributed charges, electromagnetism as multiplied up by the fact that charged massless gauge bosons are Yang-Mills radiation being exchanged between all charges (including all charges of similar sign) is 10⁴⁰ times gravity. You could picture this summation by the physical analogy of a lot of charged capacitor plates in space, with the vacuum as the dielectric between the plates. If the capacitor plates come with two opposite charges and are all over the place at random, the average addition of potential works out as that between one pair of charged plates multiplied by the square root of the total number of pairs of plates. This is because of the geometry of the addition. Intuitively, you may incorrectly think that the sum must be zero because on average it will cancel out. However, it isn’t, and is like the diffusive drunkard’s walk where the average distance travelled is equal to the average length of a step multiplied by the square root of the number of steps. If you average a large number of different random walks, because they will all have random net directions, the vector sum is indeed zero. But for individual drunkard’s walks, there is the factual solution that a net displacement does occur. This is the basis for diffusion. On average, gauge bosons spend as much time moving away from us as towards us while being exchanged between the charges of the universe, so the average effect of divergence is exactly cancelled by the average convergence, simplifying the calculation. This model also explains why electromagnetism is attractive between dissimilar charges and repulsive between similar charges.

Fig. 1a: Feynman diagrams for quantum gravity interactions discussed in this post. M₁ and M₂ are two masses which accelerate towards one another. Note that in the spin-1 graviton model, the accelerating expansion of the universe is maintained by the long-range Yang-Mills exchange of gravitons between all of the masses in the universe because the emission of gravitons causes the recoil of those masses further away from one another, and when gravitons are received they also help to knock receding masses further apart.  The overall effect is accelerative recession of masses.

This same mechanism, i.e. the exchange of gravitons between masses, which causes the acceleration of the universe and the Hubble expansion, also causes gravitational attraction between masses which are not substantially red-shifted relative to one another. This effect is due to the fact that nearby masses don’t recede substantially from one another, so they don’t exchange gravitons forcefully.  The whole basis for graviton exchange is that masses must be receding. This recession leads to outward acceleration of one mass relative to another of a = dv/dt = d(HR)/dt = Hv = H(Hv), which results in outward force of one mass from another of F = ma = mRH² (the Hubble recession law is v = HR, which can be differentiated to find acceleration).

By Newton’s 3rd law Law of Motion, it follows that there is an equal reaction force, which - from the possibilities implied by the Standard Model and gravitational physics - turns out to be mediated by gravitons.  Hence non-receding masses don’t have any outward force relative to one another, and thus no inward directed graviton-mediated reaction force.  In other words, the physics tells us that non-receding masses (or masses which are not receding from one another at immense, relativistic velocities) actually shield one another from gravitons exchanged with the rest of the universe (which is radially symmetrically distributed around the sky at the greatest distances for which graviton exchange contributions are most important, i.e. it leads to isotropic incoming graviton exchange-radiation).  Hence, we are pushed down to Earth because the Earth shields us from gravitons in the downward direction, creating a small amount of asymmetry in the exchange of gravitons between us and the surrounding universe (the cross-section for graviton shielding by an electron is only its black hole event horizon cross-sectional area, i.e. 5.75*10^-114 square metres). The special quasi-compressive effects of gravitons on masses accounts for the ‘curvature’ effects of general relativity, such as the fact that the Earth’s radius is 1.5 mm less than the figure given by Euclidean geometry (Feynman Lectures on Physics, c42 p6, equation 42.3).

In the big bang (see http://www.astro.ucla.edu/~wright/tiredlit.htm for evidence that the big bang is the only scientifically defensible interpretation of the redshift of distant matter in the universe), the relative radial outward motion of matter away from us at velocity v = dR/dt = H*R (Hubble’s recession law) leads to outward cosmological acceleration of matter a = dv/dt = d(H*R)/dt = (H*dR/dt) + (R*dH/dt) = H*v = R*H².

This is the cosmological acceleration observed, and also gives us an outward force of receding matter (Newton’s 2nd law, F=dp/dt ~ ma), which by Newton’s 3rd law leads to an equal-inward directed reaction force (which it turns out is mediated by gravitons, which predicts the strength of gravity as proved below). Notice that the path integral for non-loop quantum gravity interactions (those important at low energy, e.g. for determining the model of discrete-interaction quantum gravity which replaces the classical differential geometry approximation used in the theory of general relativity), is very simple. We need only to sum the simple (non-loop) exchanges of gravitons between masses. Because the model denies that you get substantially forceful graviton exchange between masses which aren’t receding at relativistic velocities, it follows that all relatively nearby (non-redshifted) masses like the sun act as a shield of gravitons, towards which we are pushed by the unimpeded gravitons from other directions. Unlike LeSage’s original idea, this model is substantiated by a fully predictive, falsifiable physical analysis and actually predicts the strength of gravity and other checkable facts such as the acceleration of the universe (see Fig. 3 below for a simplified version of the analysis).

The mainstream spin-2 graviton speculation is not even wrong

The mainstream spin-2 graviton model firstly makes the error of considering only two regions of energy or mass and ignoring all the other masses in the entire universe in the analysis! So it assumes - with no evidence for this whatsoever - that gravitons are only exchanged between the two masses which are attracted together. Actually, as explained above, this is the opposite of what occurs. There is no reason, in any case, why gravitons are not being exchanged with the rest of the masses in the universe. The fraction of the mass of the universe contained in an apple and the Earth is trivial. The omission from the physical model used by the mainstream of graviton exchanges with the mass of the surrounding universe causes a massive error. (A good analogy to this error is Sternglass’s confusion over low-level radiation effects, where he similarly begins with a false assumption and then turns the false assumption into a fact-like arguing point to interpret his evidence wrongly. As with Sternglass and low-level radiation hype, the facts gain absolutely no publicity when published, and Sternglass does not retract and apologise any more than string theorists do, and the media continues to make a living from selling lies.)

But that is not all. Because all gravitational charge is positive (mass and energy), the mainstream compounds this error by arguing that spin-1 exchange radiation would cause repulsion between such similar charges. We know that similar masses appear to attract, not repel, so there is an error somewhere in the assumptions made. But the mainstream, rather than finding the real error (which is that it is ignoring the effects of contributions from all the mass in the surrounding universe which is also exchanging spin-1 gravitons with the two relkatively small masses of interest for the calculation!!), has instead (since the 1930s!!) followed into stringy fairyland a 1930s suggestion by Pauli and Fierz that the faulty assumption is just the spin of the graviton, and that if the graviton is spin-2 instead of being spin-1, it will cause universal attraction between similar charges (just as spin-1 causes universal repulsion between similar charges).

So, compounding the first error of ignoring almost all of the mass in the universe when writing down its path-integral for quantum gravity, the mainstream then adds to that error by making the second error of fraudulently ‘correcting’ the false prediction of repulsion that would occur using spin-1 graviton exchange between two regions of mass-energy, by fraudulently adjusting the assumed spin properties of the mediating graviton to make the force attractive instead. Using spin-2 gives a 5-polarisation graviton with a 5-component tensor in the Lagrangrian, which when evaluated in a Feynman path integral would make two masses always attract. The failure here, aside from predicting nothing checkable unlike the spin-1 graviton, is that it is false in the first place to assume that gravitons are only going to be exchanged between two masses. Why on Earth should the gravitons from other masses in the rest of the universe not be exchanged with the two masses you are considering when calculating gravitation? Of course they should be! It’s obvious to one who is concerned with the mathematical physics, rather than ignorantly working mathematical machinery with no concern in the physics.

As soon as you do include masses in the surrounding universe (which are far bigger even though they are further away, i.e., the mass of the Earth and an apple is only 1 part in 10²⁹ of the mass of the universe, and all masses are gravitational charges which exchange gravitons with all other masses and with energy!), you begin to see what is really occurring. Spin-1 gauge bosons are gravitons!

The correct model is radical and extremely predictive and checkable unlike the ‘not even wrong’ spin-2 graviton belief system which leads to the stringy landscape of pseudoscience: in simple outline, receding (v = HR Hubble law) masses have an acceleration dv/dt = d(H*R)/dt = H*dR/dt + R*dH/dt = Hv + 0 = H(H*R) and thus carry an outward force F = m*dv/dt which has, by Newton’s 3rd law, an inward reaction force which is mediated by gravitons. Cosmologically distant masses push one another apart by exchanging gravitons, explaining the lack of gravitational deceleration observed in the universe. But masses which are nearby in cosmological terms (not redshifted much relative to one another) are pushed together by gravitons from the surrounding (highly redshifted) distant universe, because they don’t exert an outward force relative to one another, and so don’t fire a recoil force (mediated by spin-1 gravitons) towards one another. They, in other words, shield each other. Think of the exchange simply as bullets bouncing off particles. If bullets are firing in from all directions, the proximity of a nearby mass which isn’t shooting at you will act as a shield, and you’d be pushed towards that shield (which is why things fall towards large masses). This is a quantitative prediction, predicting the strength of the gravitational coupling which can be checked. So this mechanism, which predicted the lack of gravitational deceleration in the big bang in 1996 (observed in 1998 by Saul Perlmutter’s automated CCD telescope software) ,also predicts gravitation, quantitatively.

It should be noted that in this diagram we have drawn the force-causing gauge or vector boson exchange radiation in the usual convention as a horizontal wavy line (i.e., the gauge bosons are shown as being instantly exchanged, not as radiation propagating at the velocity of light and thus taking time to propagate). In fact, gauge bosons don’t propagate instantly and to be strictly accurate we would need to draw inclined wavy lines as shown in Fig. 2 below. The exchange of the gauge bosons as a kind of reflection process (which imparts an impulse in the case where it causes the mass to accelerate) would make the diagram more complex. Conventionally, Feynman diagrams are shorthand for categories of interactions, not for specific individual interactions. Therefore, they are not depicting all the similar interactions that occur when two particles attract or repel; they are way oversimplified in order to make the basic concept lucid.

Loops in Feynman diagrams and the associated infinite perturbative expansion

Because the gravitational phenomena we have observed manifested in checked aspects of general relativity are at low energy, phenomena such as loops (whereby bosonic field quanta undergo pair production and briefly become fermionic pairs which soon annihilate back into bosons, but become briefly polarized during their existence and in so doing modify the field) which are described by the infinite series of Feynman diagrams each representing one term in the infinite series of terms in the perturbative expansion to a Feynman path integral, can be ignored (this is discussed later in this post).  So the direct exchange of gauge bosons such as gravitons, gives us only a few possible types of Feynman diagrams for non-loop, simple, direct exchange of field quanta between charges.

The illustration above summarises a few of the basic (widely ignored) points about the failure of existing general relativity to represent quantum fields (by making clear that curvature is an approximation of a lot of little deflections caused by lots of individual, discrete, quantum gravity interactions), and the failure of the mainstream quantum gravity model to include graviton exchange with surrounding masses in the rest of the universe.  When receding masses appear to be accelerating radially away relative to us (as observed in spacetime), they are emitting gravitons which travel towards us at the same velocity as the visible light we observe from such receding galaxies.  The recoil and impulses created by the emission and reception of such gravitons explain both gravitation and the acceleration of the universe in one go, as shown in the 3rd Feynman diagram of Fig. 1 above, and in the more technical mathematics below in this blog post.  (I’ve only completed the first two sections in chapter 1 so far: book draft version 1.23.)

Fig. 1b: an illustration of some of the Feynman diagrams corresponding to successive terms in the perturbative expansion for electron-electron scattering (illustration credit: http://www.answers.com/topic/feynman-diagram?cat=technology). The first Feynman diagram shown represents the low energy (non-loop) approximation, i.e. Coulomb’s law in Maxwell’s equations (Gauss’s law in the Maxwell’s equations describes the diverging electric field from a charge and is physically equivalent to Coulomb’s law). This simple Feynman diagram contains no loops as it has only two vertices (it is second-order). All of the other Feynman diagrams in the illustration have four vertices and thus are fourth-order; these are the ‘loop’ corrections.

It is very important to recognise that the simplest (non-loop) Feynman diagram is of overwhelming importance for calculations in low-energy physics! It is the simplest Feynman diagram which corresponds to the classical approximation (the low-energy or long-distance asymptotic limit to a quantum field theory). Although the presence of loops does cause charge and mass renormalization, whereby the apparent values of these parameters at low energy is different to their values at high energy (due to the shielding or anti-shielding of the respective force field by pair-production virtual particles which arise in relatively intense fields), it is a fact that at low energy coupling parameters are constant.

This means that we can analyse the low-energy limit to a quantum field theory of gravity and electromagnetism without complex calculations of looped Feynman diagrams. For example, the first loop Feynman diagram for the calculation of the magnetic moment of the electron, only increases the simple (Dirac equation) non-loop calculation of the magnetic moment of the electron from 1 Bohr magneton to about 1.00116 Bohr magnetons. In other words, the most important loop Feynman diagram only varies the calculated result by 0.116%. This itself is quite a trivial correction, and in general the more complex the Feynman diagram, the less likely it is to occur and so the smaller the contribution it makes to a prediction of what will be observed in experiments. For this reason, we can ignore loops when we analyse the path-integrals for fundamental forces. This means that the path integral has a simple approximate solution for the non-loop factor, and omits the complex perturbative expansion of looped diagram terms.

This makes the calculations extremely straightforward and soluble by simple geometric methods, such as asymmetry analysis (see Fig. 3 below for a calculation of the force of gravity by this method of analyzing non-loop contributions to path integrals geometrically).

Fig. 1c: an illustration from a paper by Reinhard Alkofer demonstrating the complexity of loops in feynman diagrams. This demonstrates the simple cancellation of non-loop Feynman diagrams, as opposed to the non-cancellation you get when loops occur.  Generally, loops occur when a boson (an oscillatory electromagnetic wave, with as much negative electric field as positive electric field), when in a strong (>1.3*10^18 volts/metre) electric field, briefly becomes two virtual (short-lived) fermions, one positive and one negative.  The fermions quickly (as predicted by the energy-versus-time version of the Heisenberg uncertainty principle, a simple scattering law) recombine and annihilate back into bosonic field quanta. But during the brief phase as virtual fermions, the virtual fermions move in opposite directions in the original electric field, introducing an electric dipole which tends to oppose and partially screen the original electric field (i.e., the observable charge, which is determined from the observed electric field, since nobody can see the core charge directly). Hence, the existence of loops in electric fields tend to shield those fields as seen from a great distance. In the case of colour charge fields in QCD, the virtual charges can increase the field strength rather than shielding it. Loops are important in high-energy, short-ranged fields.  For low-energy, long-range electromagnetic and gravitational physics, loops don’t exist in spacetime far from charges because the field strengths are too weak to allow pair-production phenomena. Generally, field strengths must exceed Schwinger’s threshold before there is any pair-production. As far as quantum gravity field loops are concerned, there is no experimental evidence that they even exist, although they are assumed in vacuous string theory to exist very close to gravitational charges, as a means of making the weak force of gravity ‘unify’ with other forces at high energy (however, that stringy approach to numerological ‘unification’ of coupling constants ignores the conservation of energy as discussed in a previous post, and it is not a physical unification of different force fields, which has been demonstrated by different means using a physical mechanism).

For more simple discussion on loops in quantum fields, see this paper and this paper. This blog post is concerned primarily with non-loop interactions, i.e., force fields in low energy physics, i.e. the classical limit for quantum field theory, where quantum field effects are relatively simple and therefore, as shown below, simply don’t require the kind of very sophisticated mathematics required to accommodate loop effects.

“The cloud of virtual particles acts like a screen or curtain that shields the true value of the central core. As we probe into the cloud, getting closer and closer to the core charge, we ’see’ less of the shielding effect and more of the core. This means that the electromagnetic force from the electron as a whole is not constant, but rather gets stronger as we go through the cloud and get closer to the core. Ordinarily when we look at or study an electron, it is from far away and we don’t realize the core is being shielded.” - Professor David Koltick.

Unlike the electromagnetic field which is shielded by the vacuum and gets stronger than predicted by the Coulomb inverse-square law as you approach the core of a fermion, the strong nuclear force - which is the “glue” that holds together elementary particles such as protons - actually gets weaker closer to the core charge. “Because the electromagnetic charge is in effect becoming stronger as we get closer and the strong force is getting weaker, there is a possibility that these two forces may at some energy be equal. Many physicists have speculated that when and if this is determined, an entirely new and unique physics may be discovered.” - Professor David Koltick, quoted at http://findarticles.com/p/articles/mi_m1272/is_n2625_v125/ai_19496192

‘… we [experimentally] find that the electromagnetic coupling grows with energy. This can be explained heuristically by remembering that the effect of the polarization of the vacuum … amounts to the creation of a plethora of electron-positron pairs around the location of the charge. These virtual pairs behave as dipoles that, as in a dielectric medium, tend to screen this charge, decreasing its value at long distances (i.e. lower energies).’ - arxiv hep-th/0510040, p 71.

Plus, in particular:

‘All charges are surrounded by clouds of virtual photons, which spend part of their existence dissociated into fermion-antifermion pairs. The virtual fermions with charges opposite to the bare charge will be, on average, closer to the bare charge than those virtual particles of like sign. Thus, at large distances, we observe a reduced bare charge due to this screening effect.’ – I. Levine, D. Koltick, et al., Physical Review Letters, v.78, 1997, no.3, p.424.

Fig. 2: Feynman diagrams (left) by convention make various simplifications: the gauge boson radiation is not actually transmitted instantly between charges, contrary to the convention as depicted in places like http://hyperphysics.phy-astr.gsu.edu/hbase/particles/expar.html.  Instead, as the diagram on the right shows, it takes time for radiation to be transferred between charges.  If gravitons went instantly (i.e. as a horizontal wavy line on a diagram where the vertical axis depicts time), then gravity would act instantly instead of being constrained by the velocity of light.  The errors introduced by oversimplification of Feynman diagrams helps to keep mainstream physicists insulated from reality, and concentrating on non-existent ‘problems’ like working out ways to avoid the difficulties in renormalizing a spin-2 graviton theory.  If they concentrated on the fact that gravitons are spin-1, as demonstrated by the empirical, observed evidence, the entire problem could be sorted out straight away as shown below.

They don’t want to be heretics, however.  Groupthink wins: ’Groupthink is a type of thought exhibited by group members who try to minimize conflict and reach consensus without critically testing, analyzing, and evaluating ideas. During Groupthink, members of the group avoid promoting viewpoints outside the comfort zone of consensus thinking. A variety of motives for this may exist such as a desire to avoid being seen as foolish, or a desire to avoid embarrassing or angering other members of the group. Groupthink may cause groups to make hasty, irrational decisions, where individual doubts are set aside, for fear of upsetting the group’s balance.’ - Wikipedia.  ‘[Groupthink is a] mode of thinking that people engage in when they are deeply involved in a cohesive in-group, when the members’ strivings for unanimity override their motivation to realistically appraise alternative courses of action.’ - Irving Janis.

Fig. 3: This is the key diagram working out, without a fancy path integral formulation, the net sum of spin-1 graviton contributions.  The first few logical steps are included:

1. Outward force of receding matter (recession velocity v = HR where H is Hubble constant and R is apparent distance) is F = ma = m.dv/dt = m.d(HR)/dt = m[H.dR/dt + R.dH/dt] = m[Hv + 0] = mH(HR) = mRH^2.  This is on the order of F = 10^43 Newtons, but there is a correction to be applied for the apparent increase in density as we look back to earlier times (great distances in spacetime), and for relativistic mass increase of receding matter.  But for simplicity, to see how the maths works, ignore the correction:

F = ma = [(4/3)πR³r].[dv/dt] = [(4/3)πR³r].[H²R] = 4πR⁴rH²/3. 

2. Inward force (which must be carried by gravitons or the spacetime fabric, as explained in the book draft and here), is equal to the outward force (action and reaction are equal and opposite - Newton’s 3rd law).  However, there is a redshift of gravitons approaching us from relativistically receding, extremely redshifted masses, which reduces the effective graviton energy when received.  (This redshift effect offsets the infinity-approaching outward force effects of relativistic mass increase and the increasing density of the earlier universe at ever greater distances.)

3. Gravity force, F =  (total inward force).(cross sectional area of shield projected out to radius R, i.e., the area of the base of the cone marked x, which is the product of the shield’s cross-sectional area and the ratio R²/r²) / (total spherical area with radius R).

In an earlier post, it is proved that the shield’s cross-sectional area is the cross-sectional area of the event horizon for a black hole, π(2GM/c²)². But at present, to get the feel for the physical dynamics, we will assume this is the case without proving it. This gives

(force of gravity) = (4πR⁴rH²/3).(π(2GM/c²)²R²/r²)/(4πR²)

= (4/3)πR⁴rH²G²M²/(c⁴r²)

We can simplify this using the Hubble law because at great distances/early times (where the density of the universe is highest) it is a good approximation to put HR = c, which gives R/c = 1/H, so:

(force of gravity) = (4/3)πrG²M²/(H²r²)

This key result ignores both the density variation in spacetime (the distant, earlier universe having higher density) and the effect of redshift in reducing the energy of gravitons and weakening quantum gravity contributions from extreme distance, because the momentum of a graviton will be p = E/c and where E is reduced by redshift since E = hf, but it does demonstrate three important things about this line of research:

1. Quantization of mass: the force of gravity is proportional not to M₁M₂ but instead to M², which is a vital result because this is evidence for the quantization of mass. We are dealing with unit masses, fundamental particles.  Lepton and hadron masses beyond the electron are nearly all integer denominations of 0.5*0.511*137 = 35 MeV where 0.511 MeV is the electron’s mass and 137.036… is the well known Feynman dimensioness factor in charge renormalization (discovered much earlier in quantum mechanics by Sommerfeld); furthermore, quark doublet or meson masses are close to multiples of twice this or 70 MeV while quark triplet or baryon masses are close to multiples of three times this or 105 MeV; it appears that the simplest possible model, which predicts masses of new as yet unobserved particles as well as explaining existing particle masses, is that the vacuum particle which is the building block of mass is 91 GeV like the Z weak boson; the muon mass for instance is 91,000 divided by the product of 137 and twice Pi, which is a combination of a 137 vacuum polarization shielding factor, and twice Pi which is a dimensionless geometric shield factor, e.g. spinning a particle or a missile in flight reduces the radiant exposure per unit area of its spinning surface by Pi as compared to a non-spinning particle or missile, because the entire surface area of the edge of a loop or cylinder is Pi times the cross-sectional area seen side-on, while a spin-1/2 fermion must rotate twice, i.e., by 720 not 360 degrees  - like drawing a line right around the single-surface of the Möbius strip - to expose its entire surface to observation and reset its symmetry.  This is analysed in an earlier blog post, showing how all masses are built up from only one type of fundamental massive particle in the vacuum, and making checkable predictions.  Polarized vacuum veils around particles reduce the strength of the coupling between the massive 91 GeV vacuum particles (which interact with gravitons) and the SU(2) x SU(3) particle core of interest (which doesn’t directly interact with gravitons), accounting for the observed discrete spectrum of fundamental particle masses.

The correct mass giving field is different in some ways to the electroweak symmetry breaking Higgs field of the conventional Standard Model (which gives the standard model charges as well as the 3 weak gauge bosons their symmetry-breaking mass at low energies by ‘miring’ them or resisting their acceleration): a discrete number of the vacuum mass particles (gravitational charges) become associated with leptons and hadrons, either within the vacuum polarized region which surrounds them (strong coupling to the massive particles, hence large effective masses) or outside it (where the coupling, which presumably relies on the electromagnetic interaction, is shielded and weaker, giving lower effective masses to particles).  In the case of the deflection of light by gravity, the photons have zero rest mass so it is their energy content which is causing deflection.  The mass-giving field in the vacuum still mediates effects of gravitons, but the photon has no net electric charge (it has equal amounts of positive and negative electric field density), it has zero effective rest mass.  The quantum mechanism by which light gets deflected as predicted by general relativity has been analysed in an earlier post: due to the FitzGerald-Lorentz contraction, a photon’s field lines are all in a plane perpendicular to the direction of propagation.  This means that twice the electric field’s energy density in a photon (or other light velocity particle) is parallel to a gravitational field line that the photon is crossing at normal incidence, compared to the case for a slow-moving charge with an isotropic electric field.  The strength of the coupling between the photon’s electric field and the mass-giving particles in the vacuum is generally not quantized, unless the energy of the photon is quantized.

If you are firmly attached to an accelerating horse, you will accelerate at the specific rate that the horse accelerates at.  But if you are less firmly attached, the acceleration you get depends on your adhesion to the saddle.  If you slide back as the horse accelerates, your acceleration is somewhat less than that of the horse you are sitting on.  Particles with rest mass are firmly anchored to vacuum gravitational charges, the particles with fixed mass that replace the traditional role of Higgs bosons.  But particles like photons, which lack rest mass, are not firmly attached  to the massive vacuum field, and the quantized gravitational interactions - like a fixed acceleration of a horse - is not automatically conveyed upon the photon.  The result is that a photon gets deflected more classically by ‘curved spacetime’ created by the effect of gravitons upon the Higgs-like massive bosons in the vacuum, than particles with rest mass such as electrons.

2. The inverse square law, for distance r.

3. Many checked and checkable quantitative predictions.  Because the Hubble constant and the density of the universe can be quantitatively measured (within certain error bars, like all measurements), you can use this to predict the value of G.  As astronomy gets better measurements, the accuracy of the prediction gets better and can be checked experimentally.

In addition, the mechanism predicts the expansion of the universe: the reason why Yang-Mills exchange radiation is redshifted to lower energy by bouncing off distant masses is that energy from gravitons is being used to cause the distant masses to speed up.  This makes quantitative predictions, and is a firm test of the theory. (The outward force of a receding galaxy of mass m is F = mH²R, which requires power P = dE/dt = Fv = mH³R², where E is energy.)

In 1996 (published via the letters pages of the Oct. 1996 issue of the British-based journal Electronics World) the mechanism also predicted the lack of deceleration at large redshifts, which was confirmed by Perlmutter’s observations on distant supernovae redshifts in 1998.  Another prediction, which occurs when you apply the same mechanism in detail to electromagnetism, is that the coupling constant for the electromagnetic interaction is bigger than that of gravitation by the square root of the number of charges in the universe.  This again is accurate to within available data, and is a falsifiable prediction because, as the input data inproves, the prediction becomes more accurate and can be compared in more detail to observation.

It should be noted that the gravitons in this model would have a mean free path (average distance between interactions) of 3.10 x 10^77 metres in water, as calculated in the earlier post here. These are able to produce gravity by interacting with the the Higgs-like vacuum field, due to the tremendous flux of gravitons involved.  The radially symmetric, isotropic outward force of the receding universe is on the order 10^43 Newtons, and by Newton’s 3rd law this produces a similar equal and opposite (inward) reaction force.  This is the immense field behind gravitation.  Only a trivial asymmetry in the normal equilibrium of such immense forces is enough to produce gravity.  Cosmologically nearby masses are pushed together because they aren’t receding much, and so don’t exert a forceful flux of graviton exchange radiation in the direction of other (cosmologically) nearby masses.  Because (cosmologically) nearby masses therefore don’t exert graviton forces upon each other as exchange radiation, they are shielding one another in effect, and therefore get pushed together by the forceful exchange of gravitons which does occur with the receding universe on the unshielded side, as illustrated in Fig. 1 above.

Some other posts, besides the key one, that are useful to grasping the details are this, this, this, this, this and this.  Some of the earlier posts contain omissions or errors which have later been corrected in later posts, or by comments added to the post.  Science is not a religion or political business where a dogma or policy is agreed upon and then fixed forever.  Where omissions or errors occur, they should be corrected.

Update: I’ve decided that in the finished book, every right-hand page will be simply a full-page illustration (using diagrams, graphs, etc.) of the technical content of the text on the left-hand page.  Otherwise the book will rely on appealing to people who have the time to read a lot of technical text, which most people do not have.  Hopefully the technical illustrations on all right-hand pages will provide the ‘reader’ with the ability to grasp all the main points in a few seconds visually, and then they can refer to the text on the facing page if they want further particulars.  I’ll probably wait until I finish the text for each chapter, before designing and inserting the full page illustrations.

As of 10 February 2008, I’ve changed the banner of this blog from SU(2) x SU(3) to “U(1) x SU(2) x SU(3) quantum field theory: Is electromagnetism mediated by charged, massless SU(2) gauge bosons?  Is the weak hypercharge interaction mediated by the neutral massless SU(2) weak gauge boson?  Is gravity mediated by the spin-1 gauge boson of U(1)?  This blog provides the evidence and predictions for this introduction of gravity into the Standard Model of particle physics.” This is driven by the fact, explained in the comments to this post, that:

… SU(2) x SU(3), … [it] seems too difficult to make SU(2) account for weak hypercharge, weak isospin charge, electric charge and gravity.I thought it would work out by changing the Higgs field so that some massless versions of the 3 weak gauge bosons exist at low energy and cause electromagnetism, weak hypercharge and gravity.However, since the physical model I’m working on uses the two electrically charged but massless SU(2) gauge bosons for electromagnetism, that leaves only the electrically neutral massless SU(2) gauge boson to perform both the role of weak hypercharge and gravity. That doesn’t work out, because the gravitational charges (masses) are evidently going to be different to the weak hypercharge which is only a factor of two different between an electron and a neutrino. Clearly, an electron is immensely more massive than a neutrino. So the SU(2) x SU(3) model must be wrong.The only possibility left seems to be similar to the Standard Model U(1) x SU(2) x SU(3), but with differences from the Standard Model. U(1) would model gravitational charge (mass) and spin-1 (push) gravitons. The massless neutral SU(2) gauge boson in the model I’m working on would then mediate weak hypercharge only, instead of mediating gravitation as well.The whole point about my approach is that I’m working from fact-based predictive mechanisms for fundamental forces, and in this world view the symmetry group is just a mathematical model which is found to describe the symmetries suggested by the mechanisms.  Here are some links to some online basic information about hypercharge, weak hypercharge and SU(2) isospin.  Ryder’s book Quantum Field Theory (2nd ed., 1996), chapters 1-3 and 8-9, contains the best (physically understandable) introduction to the basic mathematics including Lagrangians, path integrals, Yang-Mills theory and the Standard Model.  From my perspective, the symmetry groups are the end product of the physics; they summarise the symmetries of the interactions.  The end product can change when the understanding of the details producing it changes. I’ve revised the latest draft book manuscript PDF file accordingly.

Dr Thomas Love of California State University has pointed out:

‘The quantum collapse [in the mainstream interpretation of of quantum mechanics, which has wavefunction collapse occur when a measurement 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.’

That looks like a factual problem, undermining the mainstream interpretation of the mathematics of quantum mechanics. If you think about it, sound waves are composed of air molecules, so you can easily write down the wave equation for sound and then - when trying to interpret it for individual air molecules - come up with the idea of wavefunction collapse occurring when a measurement is made for an individual air molecule.

Feynman writes on a footnote printed on pages 55-6 of my (Penguin, 1990) copy of his book QED:

‘… 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 … If you get rid of all the old-fashioned ideas and instead use the [path integral] ideas that I’m explaining in these lectures - adding arrows for all the ways an event can happen - there is no need for an uncertainty principle!’

Feynman on p85 points out that the effects usually attributed to the ‘uncertainty principle’ are actually due to interferences from virtual particles or field quanta in the vacuum (which don’t exist in classical theories but must exist in an accurate quantum field theory):

‘But when the space through which a photon moves becomes too small (such as the tiny holes in the screen), these [classical] rules fail - we discover that light doesn’t have to go in straight lines, there are interferences created by two holes … 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 there is no main path, no ‘orbit’; there are all sorts of ways the electron could go, each with an amplitude. The phenomenon of intereference becomes very important, and we have to sum the arrows to predict where an electron is likely to be.’

Hence, in the path integral picture of quantum mechanics - according to Feynman - all the indeterminancy is due to interferences. It’s very analogous to the indeterminancy of the motion of a small grain of pollen (less than 5 microns in diameter) due to jostling by individual interactions with air molecules, which represent the field quanta being exchanged with a fundamental particle.

The path integral then makes a lot of sense, as it is the statistical resultant for a lot of interactions, just as the path integral was actually used for brownian motion (diffusion) studies in physics before its role in QFT. The path integral still has the problem that it’s unrealistic in using calculus and averaging an infinite number of possible paths determined by the continuously variable lagrangian equation of motion in a field, when in reality there are not going to be an infinite number of interactions taking place. But at least, it is possible to see the problems, and entanglement may be a red-herring:

‘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, BBC Books, 1965, pp. 57-8.

copy of a comment:

http://asymptotia.com/2008/02/17/tales-from-the-industry-xvii-jump-thoughts/

Hi Clifford,

Thanks for these further thoughts about being science advisor [...] for what is (at least partly) a sci fi film. It’s fascinating.

“What I like to see first and foremost in these things is not a strict adherence to all known scientific principles, but instead internal consistency.”

Please don’t be too hard on them if there are apparent internal inconsistencies. Such alleged internal inconsistencies don’t always matter, as Feynman discovered:

“… take the exclusion principle … it turns out that you don’t have to pay much attention to that in the intermediate states in the perturbation theory. I had discovered from empirical rules that if you don’t pay attention to it, you get the right answers anyway …. Teller said: “… It is fundamentally wrong that you don’t have to take the exclusion principle into account.” …

“… Dirac asked “Is it unitary?” … Dirac had proved … that in quantum mechanics, since you progress only forward in time, you have to have a unitary operator. But there is no unitary way of dealing with a single electron. Dirac could not think of going forwards and backwards … in time …

” … 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 …” - Feynman, quoted at http://www.tony5m17h.net/goodnewsbadnews.html#badnews

I agree with you that: “Entertainment leading to curiosity, real questions, and then a bit of education …”

Update (23 February 2008): via Dr Woit’s blog Not Even Wrong, see the recent review of Smolin’s book in the Times Literary Review,

“… Smolin has launched a controversial attack on those working on the dominant model in theoretical physics. He accuses string theorists of racism, sexism, arrogance, ignorance, messianism and, worst of all, of wasting their time on a theory that hasn’t delivered.”

- Richard Lea, ”Too attached”, The Times Literary Review, 1 February 2008,
 http://tls.timesonline.co.uk/article/0,,25372-2650590_1,00.html

Update (28 February 2008): via Woit, the latest hype for string is ‘rock guitars could hold secret to the universe’. It might sound like just more pathetic spin, but actually, the analogy of string theory hype to that of a community of rock groupies is sound.

Update (2 March 2008): The rock guitar string promoter referred to just above is Dr Lewney who has the site http://www.doctorlewney.com/.  He writes on Dr Woit’s blog:

‘I’m actually very open to ideas as to how best to communicate physics to schoolkids.’

Dr Lewney, if you want to communicate real, actual physics rather than useless blathering and lies to schoolkids, that’s really excellent. But please just remember that physics is not uncheckable speculation, and that twenty years of mainstream hype of string theory in British TV, newspapers and the New Sceintist has by freak ‘coincidence’ (don’t you believe it) correlated with a massive decline in kids wanting to do physics.  Maybe they’re tired of sci fi dressed up as physics or something.

http://www.buckingham.ac.uk/news/newsarchive2006/ceer-physics-2.html:

‘Since 1982 A-level physics entries have halved. Only just over 3.8 per cent of 16-year-olds took A-level physics in 2004 compared with about 6 per cent in 1990.

‘More than a quarter (from 57 to 42) of universities with significant numbers of physics undergraduates have stopped teaching the subject since 1994, while the number of home students on first-degree physics courses has decreased by more than 28 per cent. Even in the 26 elite universities with the highest ratings for research the trend in student numbers has been downwards.

‘Fewer graduates in physics than in the other sciences are training to be teachers, and a fifth of those are training to be maths teachers. A-level entries have fallen most sharply in FE colleges where 40 per cent of the feeder schools lack anyone who has studied physics to any level at university.’

http://www.math.columbia.edu/~woit/wordpress/?p=651#comment-34820:

‘One thing that is clear is that hype of speculative uncheckable string theory has at least failed to encourage a rise in student numbers over the last two decades, assuming that such speculation itself is not actually to blame for the decline in student interest.

‘However, it’s clear that when hype fails to increase student interest, everyone will agree to the consensus that the problem is a lack of hype, and if only more hype of speculation was done, the problem would be addressed.’

Professor John Conway, a physicist at the University of California, has written a post called ‘What’s the (Dark) Matter?’ where someone has referred to my post here as my ‘belief’ that gravitons are of spin-1. Actually, this isn’t a ‘belief’. It’s a fact (not a belief) that so far, spin-2 graviton ideas are at best uncheckable speculation that is ‘not even wrong‘, and it’s a fact (not a belief) that this post shows that spin-1 gravitons do reproduce gravitation as already known from the checked and confirmed results of general relativity, plus quantitatively predicting more stuff such as the strength of gravity. This is not a mere ‘personal belief’, such as the gut feeling that is used by string theorists, politicians and priests to justify hype in religion or politics. It is instead fact-based, not belief-based, and it makes accurate predictions so far as the difficult calculations and the imperfect experimental data to date can be used to check it, so there’s no belief system here, just cold hard fact. This is why I’m writing about it, and why censoring it is wrong. If science is to be based on mainstream groupthink, then it is reduced to a religion or to politics, i.e., a dictatorship of the majority over minorities which is enforced not by solid physical reasoning from facts determined in nature, but by the political tools of censorship.

On the subject of dark matter, my analysis of the gravity coupling constant G shows that the usual critical density formula (for a flat universe) from general relativity, implies a density which is too high, simply because of quantum gravity effects on G which are ignored by general relativity which is classical on large scales.  Sure there is some dark matter (neutrinos and large black holes which give off little Hawking radiation, for example), but it is nowhere near the amount suggested by general relativity’s quantum-gravity-ignoring Friedmann-Robertson-Walker metric.  Actually, with graviton exchange between masses being the source of gravity, there is a difference between the classical approximation you get for fairly short range effects (like an apple falling to the earth, and the earth orbiting the sun), and very long range effects in cosmology where the masses involved are actually receding with motion that is relativistic (approaching c velocity).  The latter case involves gravitons being received in a redshifted condition, i.e. with lower energy than is the case over shorter distances where masses aren’t receding so rapidly.  This, and related effects, could easily be included in the usual framework of general relativity by reducing the value of G for long ranges to an effective value that allows for this graviton redshift effect.  General relativity is only a classical approximation, but it needn’t be completely wrong for cosmological scales: by building in corrections for physical mechanism, it can be made to approximate cosmology far better. 

To explain the apparent dark matter manifested in the flattened shapes of observed galactic rotation curves showing orbit velocity versus radial distance from the centre of a rotating galaxy, I recommend that the reader should check a page on John Hunter’s website, http://www.gravity.uk.com/galactic_rotation_curves.html.  I first came across Hunter’s idea after he published a quarter-page notice in the New Scientist a few years ago, and we corresponded.  Hunter is apparently not too interested in quantum gravity (spin-1 graviton exchange as a mechanism), just with making a mathematical conjecture and checking it, but his simple idea is mathematically equivalent to the physical mechanism of graviton exchange I worked out (I didn’t investigate the idea of inertial and gravitational potential energy equivalence and its consequences for about galactic rotation curves). Hunter starts off with the conjecture that the rest mass of any object, mc^2, is equivalent to the gravitational potential energy GMm/R with respect to distant matter of mass M at distance R, which is important (see comment 18 of this blog post) from my standpoint because general relativity rests on the principle of equivalence between inertial and gravitational masses.  Since inertial mass has an energy equivalent via Einstein’s famous formula, and gravitational mass also has an energy equivalent (the gravitational potential energy of that mass with respect to the surrounding universe, i.e. the energy which would be released by that mass via the gravitational field if the universe collapsed). Einstein failed to apply the equivalence principle (for inertial and gravitational masses in general relativity) to the energy equivalents of those respective inertial and gravitational masses, which are known from special relativity and from classical gravitation:

Fig. 4: John Hunter’s result: ‘So stars moving at a constant velocity at different radii means a constant m/r ratio. … For any given radius r, if the mass within this radius is such that the m/r value is higher than an average value (k), then the effective gravitational constant is lowered. This allows rotating matter to drift away from the centre, thus reducing the m/r ratio at this radius.  If m/r < k (for any given radius r) then the effective gravitational constant is higher than average attracting more matter to within this radius, increasing the m/r ratio at this radius. In this way a constant m/r ratio for spiral galaxies can be maintained for different r, resulting in the constant velocity of stars and the flat shape of the rotation graphs. A reduction in the value of G at the centre of galaxies, … may lead to the phenomenon of active galactic nuclei and the emergence of jets.’

Notice that Hunter is oversimplifying the mass distribution in the universe, since due to the big bang the effective density increases with spacetime distance (the earlier universe had higher density) and he is not including all graviton interaction effects, but the basic conjecture and some of its consequences are mathematically similar to the physical mechanism of graviton exchange I’m working on. The normal equilibrium of radiated graviton power, which occurs via the exchange of gravitons between any given mass and the rest of the universe, produces the immense pressure on each mass which keeps it confined to a small as a tiny black hole; fermions are charged bosons which are trapped by gravitation.  It is because of this graviton exchange equilibrium that the rest mass energy of a fundamental particle is equal to the gravitational potential energy of that mass with respect to the other masses in the surrounding universe: equilibrium of graviton exchange between one mass and all the other masses in the surrounding universe is the cause of the equality between inertial and gravitational masses/energies.  It also shows why masses contract in the direction of motion and gain mass when in motion (as predicted by special relativity): acceleration of mass alters the exchange equilibrium, the resistance being the force of inertia, and the pressure effect of encountering gravitons in the direction of motion causes the Lorentz contraction.

If you look at Hunter’s conjecture mc^2 = mMG/R, since in spacetime R = ct, this immediately gives you Louise Riofrio’s fundamental equation, namely tc^3 = MG.  Louise Riofrio is a physicist who has investigated whether this formula suggests that c is inversely proportional to the cube-root of the age of the universe.  The quantum gravity mechanism gives the same equation (ignoring dimensionless multiplication factors for redshift and varying density effects) and suggests that c isn’t varying; instead the effective value of G varies for various reasons as already discussed (see also discussion here and updates in comments at that post).

Update (3 March 2008): in Figure 4, John Hunter states that the basic result from his equivalence, G = R(c^2)/M, provides an explanation for the flatness problem.  This is something I also obtained from the graviton interaction mechanism, as you can see in the detailed post here.  From Hunter’s way of writing the formula, because it is so simplified (in certain ways it is oversimplified), is maybe easier to grasp why the universe is so flat at the greatest distances (earliest times): gravitation was weaker then.  Gravitation coupling G increases in direct proportion to the age of the universe, G = R(c^2)/M = ct(c^2)/M.  This formula is oversimplified because it ignores various subtle but important physical effects like the variation in the density of the universe with distance in spacetime (the density tends towards infinity at the greatest distances and hence earliest times after the big bang), and the effect of graviton exchange in an expanding universe which quenches certain aspects of gravitation over immense distances because gravitons received as a result of exchange between two receding masses arrive at each mass in a redshifted state, weaking that interaction.

Because the effective value of G at early times after the big bang is so small from our spacetime perspective, we see small gravitational effects: the universe looks very flat, i.e., gravity was so weak it was unable to clump matter very much at 400,000 years after the big bang, which is the time of our information on flatness, i.e. the time that the closely studied cosmic background radiation was emitted.  The mainstream ad hoc explanation for this kind of observation is a non-falsifiable (endlessly adjustable) idea from Alan Guth that the universe expanded or ‘inflated’ at a speed faster than light for a small fraction of a second, which would have allowed the limited total mass to get very far dispersed very quickly, which would have reduced the curvature of the universe and suppressed the effects of gravitation at subsequent times in the early universe.

Hence, the ‘peer’ review mainstream has blocked the proper publication of Hunter’s research just as it blocks mine, because non-falsifiable mainstream ideas are in place and as Dr Stanley Brown, editor of PRL, emailed me in January 2004, checkable ‘alternatives’ to uncheckable mainstream speculation are unpublishable in mainstream journals due to the attitude of ‘peer’ reviewers.

On the topic of variations in G, Edward Teller falsely claimed in a 1948 paper that if G had varied as Dirac suggested a few years earlier, then the gravitationally caused compression in the early universe and in stars including the sun would vary with time, affecting fusion rates dramatically because fusion is highly sensitive to the amount of compression (which he knew from his Los Alamos studies on the difficulty of producing a hydrogen bomb at that time).  However, the Yang-Mills mechanism of electromagnetism (whose role in fusion is the Coulomb repulsion of protons, i.e., the stronger electromagnetism is, the less fusion you get because protons approach less closely because they are repelled more strongly, so the short-ranged strong force which causes protons to fuse together ends up causing less fusion), shows that it will vary with time in the same way that gravitation does.

This invalidates Teller’s theory, because if you for example halve the value of G (making fusion more difficult by reducing the compression of protons long ago), you simultaneously get an electromagnetic coupling charge which is halved, and the effect of the latter is to increase fusion by reducing the Coulomb barrier which protons need to overcome in order to fuse.  The two effects - reduced G which tends to reduce fusion by reducing compression, and reduced Coulomb charge which allows protons to approach closer before being repelled, and therefore increases fusion - offset one another. Dirac wrongly suggested that G falls with time, because he believed that at early times G was as strong as electromagnetism and numerically ‘unified’; actually all attempts to explain the universe by claiming that the fundamental forces including gravity are the same at a particular very early time/high energy, are physically flawed and violate the conservation of energy - the whole reason why the strong force charge strength falls at higher energies is because it is being caused by pair-production of virtual particles including virtual quarks accompanied by virtual gluons.  This pair-production is a result of the electromagnetic charge, which increases at higher energy.

The electromagnetic force has been proved to cause pair-production (this is a major source of shielding of gamma rays above 1.022 MeV by nuclei with a high Coulomb charge like lead, and this has been very carefully observed studied for eighty years now using all the gear of particle physics from the obsolete Wilson cloud chamber onwards) which produces the virtual particles including mesons and gluons which mediate the short-range interactions.  By the principle of conservation of mass-energy, you can work out and predict exactly how the this works.  Electromagnetic charge increases with collision energy (and thus decreasing distance between particles) if the collision energy exceeds that which takes the particles close enough so that their electric field strengths exceed 1.3 x 10^18 v/m, Schwinger’s threshold for pair-production in the vacuum.  Where the electric field exceeds this value, virtual fermions form a dielectric medium of polarized dipoles which on average tend to align to oppose the electric charge of the real particle core, reducing the value of the latter as observed from a large distance.  The energy density of an electromagnetic field is precisely known from electromagnetism.  Integrating it over successive radial distances, r + dr, where the charge is varying, tells you how much energy is being shielded by the polarized vacuum and is becoming available to power short-ranged nuclear forces at any particular distance.  Conservation of mass-energy tells you, therefore, exactly how much energy is being used to create pairs of polarized charges at any given distance from a particle’s core.  The textbook equations of quantum field theory don’t investigate this obvious physical approach to explaining the different forces; they instead simply find a logarithmic variation of effecive charge as a function of energy between two cutoffs for the Standard Model forces.  The lower energy or ‘infrared’ cutoff must physically correspond to Schwinger’s pair-production threshold electric field strength, and the upper energy or ‘ultraviolet’ cutoff physically corresponds to some kind of ‘grain size’ in the Dirac sea, or - far more likely - to a minimum physical distance scale that is required for pair production charges to become polarized before they annihilate back into bosonic field quanta.  When two particles get very close, the strong nuclear charge decreases because there is less shielding of the electromagnetic charge between them, and therefore less electromagnetic energy is being transformed by pair production into strong force mediating pions and gluons.  This is the physics, and it’s a checkable prediction because you can calculate the details to see if they work out if you have the time.

Mainstream string gatherings have the allure of attending a rock concert, i.e. social entertainment, while also maintaining some features of religious dogma and political inertia and reluctance to listen to or investigate new ideas, except new ideas building on the mainstream speculations such as string theory.  When ‘peer’ reviewers are mainstream faith-based physicists, they are not the ‘peers’ of those who build on empirically confirmed facts; they are in competition with them. Expecting such ‘peers’ to behave ethically (i.e. recommend the publication of facts that don’t fit in with uncheckable mainstream Party speculation) is as irrational and misguided as expecting honest and decent behaviour from politicians or sellers of religious dogmas: they’re bored and repelled by physics of the down-to-earth fact based, checkable type.

‘A Party member … is supposed to live in a continuous frenzy of hatred of foreign enemies and internal traitors … The discontents produced by his bare, unsatisfying life are deliberately turned outwards and dissipated by such devices as the Two Minutes Hate, and the speculations which might possibly induce a skeptical or rebellious attitude are killed in advance by his early acquired inner discipline … called, in Newspeak, crimestop. Crimestop means the faculty of stopping short, as though by instinct, at the threshold of any dangerous thought. It includes the power of not grasping analogies, of failing to perceive logical errors, of misunderstanding the simplest arguments if they are inimical to Ingsoc, and of being bored or repelled by any train of thought which is capable of leading in a heretical direction. Crimestop, in short, means protective stupidity.’ - Orwell, 1984.

Update (25 March 2008):

Maybe part of the problem here is that most people (including Catt) don’t grasp the fault in Maxwell’s electromagnetism:

Fig. 5: Maxwell’s error in electromagnetic theory and how it physically maps classical electromagnetism on to quantum field theory.

VITAL POINTS TO NOTE:

1. Maxwell and Heaviside claimed that a vacuum “displacement current” of polarized virtual charges occurs, with the process of polarization being a “displacement current” which closes the open circuit between the two conductors before the logic step has completed the full circuit (i.e., while the logic step is moving along the circuit at light velocity for the insulator which must be  presumed to be a “dielectric”, even if a vacuum).

2. Julian Schwinger worked out that the quantum field theory vacuum only undergoes any polarization in electric fields above 1.3*10^18 v/m.  Such fields don’t occur in computers, but they still work!

3. In each conductor, as the energy step passes a given location, the relatively loosely bound (conduction band) electrons get accelerated from a mean of zero to their full mean drift speed.  This causes them to radiate and swap EM energy!!!  This is the physical mechanism for what happens, replacing Maxwell’s mistaken “displacement current” with tested physics.

As Fig. 5 indicates, the electrons accelerate in opposite directions along each of the two conductors, so each conductor radiates a waveform of EM radiation which is the exact inversion of that from the other conductor.  Hence, at distances from the transmission line, there is perfect cancellation or interference, cancelling any detectable signal!  Thus, no net energy loss occurs due to the radiation.  The sole effect of this radiation (ignored by Catt and leading to a serious argument between us, even after I wrote an Electronics World cover-story about Catt’s best invention) is that it is exchanged between the two conductors.  This is the physical mechanism that does the same job that Maxwell’s false pet theory of “displacement current” (which doesn’t exist, because as Nobel Laureate Schwinger proved, the quantum field theory vacuum doesn’t polarize in electrif fields below 1.3*10^18 volts/metre, and you don’t get that kind of field strength in radio waves or computers, where field strengths are very much lower).

(I’ve uploaded some vital background information on Catt’s vital background work to this blog here, here, here, here, here, here, here and here, since Wikipedia entries are being vandalised and some of Catt’s web pages are now disappearing owing to his long hospitalization.)

This changes the physical understanding of Maxwell’s equations: from it, we know that wherever Maxwell claimed “displacement currents” to exist, exchange radiation is occurring which produces the same forces and energy transfers but tells us about the previously hidden quantum field theory mechanism behind the quantum electromagnetic interaction.

Surely the quantum gravitational charge, mass, can be expected to behave as a first approximation like electric charge when accelerated.

Whereas the acceleration of electric charge produces an asymmetry in the field (which itself is mediated by gauge boson exchange radiation) that ripples outward as an observable transverse EM wave (mediated by numerous gauge bosons or field quanta), with gravity what you are doing is accelerating a mass (a unit gravitational charge), which introduces an asymmetry into the graviton exchange mechanism, that propagates as a gravitational wave (mediated by numerous gravitons, or field quanta).

Why introduce additional complexity?  It looks as if the mechanism for gravitational waves is a perfect analogy to electromagnetic waves, and that the relative weakness of the gravitational waves is simply due to the relatively weakness of the gravitational coupling, as compared to electromagnetism.

Update (31 March 2008):

Fig. 6: Simplified depiction of the coupling scheme for mass to be given to Standard Model particles by a separate field, which is the man-in-the-middle between graviton interactions and electromagnetic interactions.  A more detailed analysis of the model, with a couple of mathematical variations and some predictions of masses for different leptons and hadrons, is given in the earlier post here and there are updates in other recent posts on this blog.  In the case of quarks, the cores are so close together that they share the same ‘veil’ of polarized vacuum, so N quarks in close proximity (asymptotic freedom inside hadrons) boosts its electric charge shielding factor by a factor N, so if you have three quarks of  bare charge -j each and normal vacuum polarization shielding factor j, the total charge is not -jN but is -jN/N, where the N in the denominator is there to account for the increased vacuum shielding.  Obviously -jN/N = -j, so 3 electron-charge quarks in close proximity will only exhibit the combined charge of 1 electron, as seen at a distance beyond 33 fm from the core.  Hence, in such a case, the apparent electric charge contribution per quark is only -1/N = -1/3, which is the exactly what happens in the Omega Minus particle (which has 3 strange quarks of apparent charge -1/3 each, giving the Omega Minus a total apparent electric charge as observed beyond 33 fm of -1 unit).  More impressively, this model predicts the masses of all leptons and hadrons, and also makes falsifiable predictions about the variation in coupling constants as a function of energy which result from the conversion of electromagnetic field energy into short range nuclear force field quanta as a result of pair-production of particles including weak gauge bosons, virtual quarks and gluons in the electromagnetic field at high energy (short distances from the particle core).  The energy lost from the electromagnetic field, due to vacuum polarization opposing the electric charge core, gets converted into short range nuclear force fields.  From the example of the Omega Minus particle, we can see that the electric charge per quark observable at long ranges is reduced from -1 to -1/3 unit due to the close proximity of three similarly charge quarks, as compared to a single particle core surrounded by polarized vacuum, i.e. a lepton (the Omega Minus is a unique, very simple situation; usually things are far and away more complicated because hadrons generally contain pairs or triplets of quarks of different flavour).  Hence, 2/3rds of the electric field energy that occurs when only one particle is alone in a polarized vacuum (i.e. a lepton) is used to generate short-ranged weak and strong nuclear force fields when three such particles are closely confined.

As discussed in earlier posts, the similarity of leptons and quarks has been known since 1964, when it was discovered by the Italian physicist Nicola Cabibbo: the rates of lepton interactions are identical to those of quarks to within just 4%, or one part in 25.  The weak force when acting on quarks within one generation of quarks is identical to within 1 part in 25 of that when acting on leptons (although if the interaction is between two quarks of different generations, the interaction is weaker by a factor of 25).  This similarity of quarks and leptons is called ‘universality’.  Cabibbo brilliantly suggested that the slight (4%) difference between the action of the weak force on leptons and quarks is due to the fact that a lepton has only one way to decay, whereas a quark has two possible decay routes, with relative probabilities of 1/25 and 24/45, the sum being of course (1/25) + (24/25) = 1 (the same as that for a lepton).  But because only the one quark decay route or the other (1/25 or 24/25) is seen in an experiment, the effective rate of quark interactions are lower than those for leptons.  If the weak force involves an interaction between just one generation of quarks, it is 24/25 or 96% as strong as between leptons, but if it involves two generations of quarks, it is only 1/25th as strong as when mediating a similar interaction for leptons.

This is very strong evidence that quarks and leptons are fundamentally the same thing, just in a different disguise due to the way they are paired or tripleted and ’dressed’ by the surrounding vacuum polarization (electric charge shielding effects, and the use of energy to mediate short-range nuclear forces).

A quick but vital update about my research (particularly updating the confusion in some of the comments to this blog post): I’ve obtained the physical understanding which was missing from the QFT textbooks I’ve been studying by Weinberg, Ryder and Zee, from the 2007 edition of Professor Frank Close’s nicely written little book The Cosmic Onion, Chapter 8, ‘The Electroweak Force’.

Close writes that the field quanta of U(1) in the standard model is not the photon, but is a B₀ field quanta.

SU(2) gives rise to field quanta W₊, W_- and W₀. The photon and the Z₀ both result from the Weinberg ‘mixing’ of the electrically neutral W₀ from SU(2) with the electrically neutral B₀ from U(1).

This is precisely the information I was looking for, which was not clearly stated in the QFT textbooks. It enables me to get a physical feel for how the mathematics works.

The Weinberg mixing angle determines how W₀ from SU(2) and B₀ from U(1) mix together to yield the photon (textbook electromagnetic field quanta) and the Z₀ massive neutral weak gauge boson.

If the Weinberg mixing angle were zero, then W₀ = Z₀ and B₀ = electromagnetic photon. However, this simple scheme fails (although this failure is not made clear in any of the QFT textbooks I’ve read, which have obfuscated instead), and an ad hoc or fudged mixing angle of about 26 degrees (this is the angle between the Z₀ and W₀ phase vectors) is required.

This mixing angle is physically unexplained in the Standard Model, it’s just an epicycle needed to make it represent the experimentally known facts well enough to predict other things accurately (like Ptolemiac epicycles), just as force coupling constants and particle masses have to be put in by hand. Because neutrinos also mix as they propagate (changing flavour), there are mixing parameters there too. The Standard Model has 19 parameters which have to be put in by hand. My objective to to get away from such fiddled factors and to get a theory which does more while requiring less speculative assertion. The total number of parameters that need to be supplied is far smaller than the Standard Model requires, because the model predicts masses of leptons and quarks, and force coupling parameters.

I haven’t had time yet to analyse the Weinberg mixing yet. My first reaction is that it is a failure of the Standard Model that you need to mix up the U(1) field quanta with the usually massive weak electrically neutral field quanta from SU(2) in order to arrive at empirically useful descriptions of the electromagnetic field quanta and the weak field quanta. This is definitely being covered-up by the textbooks, which obfuscate it terribly. In fact, the mixing angle is an epicycle or fudge factor which is needed to force an inaccurate physical description of electromagnetism to work. It has no natural explanation.

However, it is vital to understand what the existing theory is in order to get a complete grasp on what needs to go in its place. This is getting very interesting. Unfortunately, I will have no time for several weeks to work on this further.

Note that Professor Close was kind enough to email me back this evening within four hours of my emailing him an error I spotted in his book (however if I had sent a longer email with a paper or a request for him to spend valuable time on my pet ideas, it would predictably have been a very different story):

From: Frank Close
To: Nigel Cook

Sent: Monday, March 31, 2008 10:48 PM

Subject: RE: The Cosmic Onion, 2007 ed., Fig 11.3 page 156

yes. well spotted. pythagaros requires 1+24 =25 (all over 25)

—–Original Message—–
From: Nigel Cook
Sent: Mon 3/31/2008 7:06 PM
To: Frank Close
Subject: The Cosmic Onion, 2007 ed., Fig 11.3 page 156

Dear Professor Close,

Should the small square in Fig 11.3 on p 156 of The Cosmic Onion (2007 ed.) be labelled 1/25 rather than 1/5? It seems to be a printing error.

Thanks for your clear discussion of universality in that book which I only discovered very recently.  I’ve only done undergraduate physics at university, and am interested in quantum field theory, so it’s great to get some semi-popular discussions of basic stuff to supplement the more mathematical works by Weinberg, Ryder, Zee, et al.

Kind regards,

Nige Cook
http://quantumfieldtheory.org/

Update (23 April 2008): Below is the text of a comment, summarising what is missing from existing quantum mechanics and quantum field theory, in the moderation queue to:

http://egregium.wordpress.com/2008/03/30/legendary-lectures-on-qft-by-sidney-coleman/

Geroch’s Special Topics in Particle Physics are very concise and begin in a simple way, but soon become extremely technical.

Coleman’s notes on QFT (as written up by Tong) are slightly longer and more detailed, and in some ways address the key questions I have with QFT a lot better.

As a latecomer to QFT (I’ve only recently read Zee, Weinberg vI and vII, and Ryder), it’s amazing that the structure of the theory is entirely based on classical field equations for the lagrangian. I had read (previous to seeing the maths of QFT) that in principle the path integral can be used to model the motion of orbital electrons.  Feynman gives an illustration of this in his book QED: the random exchange of discrete Coulomb field quanta between electrons and the proton cause the chaotic motion and indeterminancy according to Feynman: fields are quantized so they aren’t classical.

‘… when seen on a large scale, they [electrons, photons, etc.] travel like particles, on definite paths. But on a small scale, such as inside an atom, the space is so small that 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 [from quantum interactions, each represented by a Feynman diagram] becomes very important, and we have to sum the arrows [amplitudes] to predict where an electron is likely to be.’

- R. P. Feynman, QED, Penguin, 1990, page 84-5.

This implies that the physical difference between Bohr’s atomic model and quantum mechanics is that the Coulomb field should be quantized properly. If you derived the Bohr model using a Coulomb force equation that correctly modelled the fluctuations in the electric attractive force on small scales (in atoms), the key problem of Bohr’s incorrect quantum mechanics would be solved.

Instead of that, quantum mechanics leaves the classical Co