Predicted fundamental force strengths, all observable particle masses, and cosmology from a simple causal mechanism of vector boson exchange radiation, based on the existing mainstream quantum field theory

Solution to a problem with general relativity: A Yang-Mills mechanism for quantum field theory exchange-radiation dynamics, with prediction of gravitational strength, space-time curvature, Standard Model parameters for all forces and particle masses, and cosmology, including comparisons to other research and experimental tests

(For an introduction to quantum field theory concepts, see The physics of quantum field theory.)

‘It has been said that more than 200 theories of gravitation have been put forward; but the most plausible of these have all had the defect that they lead nowhere and admit of no experimental test.’ - Sir Arthur Eddington, Space Time and Gravitation, Cambridge University Press, 1921, p64.

The Physical Relationship between General Relativity and Newtonian gravity
    1. Newtonian gravity

      2. Let’s begin with a look at the Newtonian gravity law F = mMG/r2, which is based on empirical evidence, not a speculative theory (remember Newton’s claim: hypotheses non fingo!). The inverse square law is based on Kepler’s empirical laws, which were obtained by Brahe’s detailed observations of motion of the planet Mars. The mass dependence was more of a guess by Newton, since he didn’t actually calculate gravitational forces (he did not know or even write the symbol for G, which arrived long after from the pen of Laplace). However, Newton’s other empirical law, F = ma, was strong evidence for a linear dependence of force on mass, and there was some evidence from the observation of the Moon’s orbit. The Moon was known to be about 250,000 miles away and to take about 30 days to orbit the earth, so it’s centripetal acceleration could be calculated from Newton’s law, a = v2/r. This could confirm Newton’s law in two ways. First, since 250,000 miles is about 60 times the radius of the Earth, the acceleration due to gravity from the Earth should, from the inverse-square law, be 602 times weaker at the Moon than it is at the Earth’s surface where it is 9.8 m/s2.

      Hence it was possible to check the inverse-square law in Newton’s day. Newton also made a good guess at the average density of the earth, which indicates G fairly accurately using Galileo’s measurement of the gravitational acceleration at the Earth’s surface and - applied also to the Moon (assumed to have a similar density to the Earth) gives a very approximate justification for the assumption of Newton’s that gravitational force is directly proportional to the product of the two masses involved. Newton worked out geometrically proofs for using his law. For example, the mass of the Earth is not located in a point at its centre, but is distributed over a large three-dimensional volume. Newton proved that you can treat the entire mass of the earth as being in a small place in the centre of the Earth for the purpose of making calculations, and this proof is as clever as his demonstration that the inverse square law applies to elliptical planetary orbits (Hooke showed that it applied to circular orbits, which is much easier). Newton treated the mass of the earth as a series of uniform shells of small thickness. He proved that outside the shell, the gravitational field is identical, at any radius from the middle of the shell, to the gravitational field from an equal mass all located in a small lump in the middle. This proof also applies to the quantum gravity mechanism (below).

      Cavendish produced a more accurate evaluation of G by measuring the twisting force (torsion) in a quartz fibre due to the gravitational attraction of two heavy balls of known mass located a known distance apart.

    2. General relativity as a modification needed to include relativistic phenomena

Eventually failures in the Newtonian law became apparent. Because orbits of planets are elliptical with the sun at one focus, the planets speed up when near the sun, and this causes effects like time dilation and it also causes their mass to increase due to relativistic effects (this is significant for Mercury, which is closest to the sun and orbits fastest). Although this effect is insignificant over a single orbit, so it didn’t affect the observations of Brahe or Kepler’s laws upon which Newton’s inverse square law was based, the effect accumulates and is substantial over a period of centuries, because it the perhelion of the orbit precesses. Only part of the precession is due to relativistic effects, but it is still an important anomaly in the Newtonian scheme. Einstein and Hilbert developed general relativity to deal with such problems. Significantly, the failure of Newtonian gravity is most important for light, which is deflected by gravity twice as much when passing the sun as that predicted by Newton’s a = MG/r2.

Einstein recognised that gravitational acceleration and all other accelerations are represented by a curved worldline on a plot of distance travelled versus time. This is the curvature of spacetime; you see it as the curved line when you plot the height of a falling apple versus time.

Einstein then used tensor calculus to represent such curvatures by the Ricci curvature tensor, Rab, and he tried to equate this with the source of the accelerative field, the tensor Tab, which represents all the causes of accelerations such as mass, energy, momentum and pressure. In order to represent Newton’s gravity law a = MG/r2 with such tensor calculus, Einstein began with the assumption of a direct relationship such as Rab = Tab. This simply says that mass-energy tells is directly proportional to curvature of spacetime. However, it is false since it violates the conservation of mass-energy. To make it consistent with the experimentally confirmed conservation of mass-energy, Einstein and Hilbert in November 1915 realised that you need to subtract from Tab on the right hand side the product of half the metric tensor, gab, and the trace, T (the sum of scalar terms, across the diagonal of the matrix for Tab).

Hence

Rab = Tab - (1/2)gabT.

[This is usually re-written in the equivalent form, Rab - (1/2)gabR = Tab.]

There is a very simple way to demonstrate some of the applications and features of general relativity. Simply ignore 15 of the 16 terms in the matrix for Tab, and concentrate on the energy density component, T00, which is a scalar (it is the first term in the diagonal for the matrix) so it exactly equal to its own trace:

T00 = T.

Hence, Rab = Tab - (1/2)gabT becomes

Rab = T00 - (1/2)gabT, and since T00 = T, we obtain

Rab = T[1 - (1/2)gab]

The metric tensor gab = ds2/(dxadxb), and it depends on the relativistic Lorentzian metric gamma factor, (1 - v2/c2)-1/2, so in general gab falls from about 1 towards 0 as velocity increases from v = 0 to v = c.

Hence, for low speeds where, approximately, v = 0 (i.e., v << c), gab is generally close to 1 so we have a curvature of

Rab = T[1 - (1/2)(1)] = T/2.

For high speeds where, approximately, v = c, we have gab = 0 so

Rab = T[1 - (1/2)(0)] = T.

The curvature experienced for an identical gravity source if you are moving at the velocity of light is therefore twice the amount of curvature you get at low (non-relativistic) velocities. This is the explanation as to why a photon moving at speed c gets twice as much curvature from the sun’s gravity (i.e., it gets deflected twice as much) as Newton’s law predicts for low speeds. It is important to note that general relativity doesn’t supply the physical mechanism for this effect. It works quantitatively because is its a mathematical package which accounts accurately for the use of energy.

However, it is clear from the way that general relativity works that the source of gravity doesn’t change when such velocity-dependent effects occur. A rapidly moving object falls faster than a slowly moving one because of the difference produced in way the moving object is subject to the gravitational field, i.e., the extra deflection of light is dependent upon the Lorentz-FitzGerald contraction (the gamma factor already mentioned), which alters length (for a object moving at speed c there are no electromagnetic field lines extending along the direction of propagation whatsoever, only at right angles to the direction of propagation, i.e., transversely). This increases the amount of interaction between the electromagnetic fields of photon and the gravitational field. Clearly, in a slow moving object, half of the electromagnetic field lines (which normally point randomly in all directions from matter, apart from minor asymmetries due to magnets, etc.), will be pointing in the wrong direction to interact with gravity, and so slow moving objects only experience half the curvature that fast moving ones do, in a similar gravitational field.

Some issues with general relativity are focussed on the assumed accuracy of Newtonian gravity which is put into the theory as the low speed, weak field solution normalization. As we shall show below, this is incompatible with a Yang-Mills (Standard Model type) quantum gravity theory for reasons other than the renormalization problems usually assumed to exist. First, over very large distances in an expanding universe, the exchange of gravitons weakens gravitons because redshift reduces the frequency and thus the energy of radiation dramatically over cosmological sized distances. This eliminates curvature over such distances, explaining the lack of gravitational deceleration in supernova data. This is falsely explained by the mainstream by adding an epicycle, i.e.,

(gravitational deceleration without redshift of gravitons in general relativity) + (acceleration due to small positive cosmological constant due to some kind of dark energy) = (observed, non-decelerating, recession of supernovae)

instead of the simpler quantum gravity explanation (predicted in 1996, two years ahead of observation):

(general relativity with G falling for large distances due to redshift of exchange gravitons reducing the energy of gravitational interactions) = (observed, non-decelerating, recession of supernovae).

So there is no curvature of spacetime at extremely big distances! On small scales, too, general relativity is false, because the tensor describing the source of gravity uses an average density to smooth out the real discontinuities resulting from the quantized, discrete nature of particles which have mass! The smoothness of a curvature in general relativity is false in general on small scales due to the input assumption - required for the stress-energy tensor to work (it is a summation of continuous differential terms, not discrete terms for each fundamental particle). So on both very large and very small scales, general relativity is a fiddle. But this is not a problem when you understand the physical dynamics and know the limitations of the theory. It only becomes a problem when people take a lot of discrete fundamental particles representing a real mass causing gravity, average their masses over space to get an average density, and then calculate the curvature from the average density, getting a smooth result and claiming that this proves that curvature is really smooth on small scales. Of course it isn’t. That argument is like averaging the number of kids per household and getting 2.5, then claiming that the average proves that one third of kids are born with only half of their bodies. But there is also a problem with quantum gravity as usually believed (see the previous post, and also this comment, on Cosmic Variance blog, by Professor John Baez).

Symmetry groups which include gravity

We will show how you can make checkable predictions for quantum gravity in this post. In the previous two posts, here and here, the inclusion of gravity in the standard model was shown to require a change of the electroweak force SU(2) x U(1) to SU(2) x SU(2) where the three electroweak gauge bosons (W+, W-, and Zo) occur in both short-ranged massive versions and massless, infinite-range versions with the charged ones producing electromagnetic force and the neutral one producing gravitation, and the issues in calculating the outward force of the big bang were described. Depending on how the Higgs mechanism for mass will be modified, this SU(2) x SU(2) electro-weak-gravity may be replacable by a new version of a single SU(2). In the existing Standard Model, SU(3) x SU(2) x U(1), only one handedness of fundamental particles respond to the SU(2) weak force, so if you change the electroweak groups SU(2) x U(1) to SU(2) x SU(2) it can lead to a different way of understanding chiral symmetry and electroweak symmetry breaking. See also this earlier post, which discusses with quantum force effects as Hawking radiation emissions.)

The understanding of the correct symmetry model behind the Standard Model requires a physical understanding of what quarks are, how they arise, etc. For instance, bring 3 electrons close together and you start getting problems with the exclusion principle. But if you could somehow force a triad of such particles together, the net charge would be 3 times stronger than normal, so the vacuum shielding veil of polarized pair-production fermions will be also 3 times stronger, shielding the bare core charges 3 times more efficently. (Imagine it like 3 communities combining their separate castles into one castle with walls 3 times thicker. The walls provide 3 times as much shielding; so as long as they can all fit inside the reinforced castle, all benefit.) This means that the long range (shielded) charge from each of the three charges of the triad will be -1/3 instead of -1. Since pair-production, and polarization of electric charges cancelling out part of the electric field, are experimentally validated phenomena, this mechanism for fractional charges is real. Obviously, while it is easy to explain the downquark this way, you need a detailed knowledge of electroweak phenomena like the weak charges of quarks compared to leptons (which have chiral features) and also the strong force, to explain physically what is occurring with upquarks that have a +2/3 charge. Some interesting although highly abstract mathematical assaults on trying to understand particles have been made by Dr Peter Woit in http://arxiv.org/abs/hep-th/0206135 which generates all the Standard Model particles using a U(2) spin representation (see also his popular non-mathematical introduction, Not Even Wrong: The Failure of String Theory and the Continuing Challenge to Unify the Laws of Physics), which can be compared to the more pictorial preon models of particles advocated by loop quantum gravity theorists like Dr Lee Smolin. Both approaches are suggesting that there is a deep simplicity, with the different quarks, leptons, bosons and neutrinos arising from a common basic entity by means of symmetry transformations or twists of braids:

‘There is a natural connection, first discovered by Eugene Wigner, between the properties of particles, the representation theory of Lie groups and Lie algebras, and the symmetries of the universe. This postulate states that each particle "is" an irreducible representation of the symmetry group of the universe.’ -Wiki. (Hence there is a simple relationship between leptons and fermions; more later on.)

Introduction to the basis for the dynamics of quantum gravity

You can treat the empirical Hubble recession law, v = HR, as describing a variation in velocity with respect to observable distance R, because as we look to greater distances in the universe, we’re seeing an earlier era, because of the time taken for the light to reach us. That’s spacetime: you can’t have distance without time. Because distance R = ct where c is the velocity of light and t is time, Hubble’s law can be written v = HR = Hct which clearly shows a variation of velocity as a function of time! A variation of velocity with time is called acceleration. By Newton’s 2nd law, the acceleration of matter produces force. This view of spacetime is not new:

‘The views of space and time which I wish to lay before you have sprung from the soil of experimental physics, and therein lies their strength. They are radical. Henceforth space by itself, and time by itself, are doomed to fade away into mere shadows, and only a kind of union of the two will preserve an independent reality.’ - Herman Minkowski, 1908.

To find out what the acceleration is, we remember that velocity is defined as v = dR/dt, and this rearranges to give dt = dR/v, which can be substituted into the definition of acceleration, a = dv/dt, giving a = dv/(dR/v) = v.dv/dR, into which we can insert Hubble’s empirical law v = HR, giving a = HR.d(HR)/dR = H2R.

The outward motion of matter produces a force which for simplicity for the present (we will discuss correction factors for density variation and redshift effects below; see also this previous post) will be approximated by Newton’s 2nd law in the form

F = ma

= [(4/3)πR3r].[dv/dt],

and since dR/dt = v = HR, it follows that dt = dR/(HR), so

F = [(4/3)πR3r].[d(HR)/{dR/(HR)}]

= [(4/3)πR3r].[H2R.dR/dR]

= [(4/3)πR3r].[H2R]

= 4πR4rH2/3.

Fig. 1: Mechanism for quantum gravity (a tiny falling test mass is located in the middle of the universe, which experiences isotropic graviton radiation - not necessarily spin 2 gravitons, preferably spin 1 gravitons which cause attraction by simply pushing things as this allows predictions as wel shall see - from all directions except that where there is an asymmetry produced by the mass which shields that radiation) . By Newton’s 3rd law the outward force of the big bang has an equal inward force, and gravity is equal to the proportion of that inward force covered by the shaded cone in this diagram:

(force of gravity) = (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).

Later in this post, this will be evaluated proving 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 HR = c gives R/c = 1/H so

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

This 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.

Quantization of mass

However, it is significant qualitatively that this gives a force of gravity proportional not to M1M2 but instead to M2, because this is evidence for the quantization of mass. We are dealing with unit masses, fundamental particles. (Obviously ‘large masses’ are just composites of many fundamental particles.) M2 should only arise if the ultimate building blocks of mass (the ‘charge’ in a theory of quantum gravity) are quantized, because it shows that two units of mass are identical. This tells us about the way the mass-giving field particles, the ‘Higgs bosons’, operate. Instead of there being a cloud of an indeterminate number of Higgs bosons around a fermion giving rise to mass, what happens is that each fermion acquires a discrete number of such mass-giving particles. (These ‘Higgs bosons’ surrounding the fermion acquire inertial and gravitational mass by interacting with the external gravitational field, which explains why mass increases with velocity but electric charge doesn’t. The core of a fermion doesn’t interact with the inertial/gravitational field, only with the massive Higgs bosons surrounding the core, which in turn do interact with the inertial/gravitational field. The core of the fermion only interacts with Standard Model forces, namely electromagnetism, weak force, and in the case of pairs or triads of closely confined fermions - quarks - the strong nuclear force. Inertial mass and gravitational mass arise from the Higgs bosons in the vacuum surrounding the fermion, and gravitons only interact with Higgs bosons, not directly with the fermions.)

This is explicable simply in terms of the vacuum polarization of matter and the renormalization of charge and mass in quantum electrodynamics, and is confirmed by an analysis of all relatively stable (half life of 10-23 second or more) known particles, as discussed in an earlier post here (for a table of the mass predictions compared to measurements see Table 1). (Note that the simple description of polarization of the vacuum as two shells of virtual fermions, a positive one close to the electron core and a negative one further away, depicted graphically on those sites, is a simplification for convenience in depicting the net physical effect for the purpose of understanding what is going on for making accurate calculations. Obviously, in reality, all the virtual positive fermions and all the virtual negative fermions will not be located in two shells; they will be all over the place but on the average the virtual charges of like sign to the real particle core will be further away from the core than the virtual charges of unlike sign.)

Table 1: Comparison of measured particle masses with predicted particle masses using a physical model for the renormalization of mass (both mass and electric charge are renormalized quantities in quantum electrodynamics, due to the polarization of pairs of charged virtual fermions in the electron’s strong electric field, see previous posts such as this). Anybody wanting a high quality, printable PDF version of this table can find it here. (The theory of masses here was inspired by an arXiv paper by Drs. Rivero and de Vries, and on a related topic I gather than Carl Brannen is using density operators to explain theoretically and extend the application of Yoshio Koide’s empirical formula, which states that the sum of the masses of the 3 leptons electron, muon and tau, multiplied by 1.5, is equal to the square of the sum of the square roots of the masses of those three particles. If that works it may well be compatible with this mass mechanism. Although the mechanism predicts the possible quantized masses fairly accurately as first approximations, it is good to try to understand better how the actual masses are picked out. The mechanism which produced the table produced a formula containing two integers which predicts a lot of particles which are too short-lived to occur. Why are some configurations more stable than others? What selection principle picks out the proton as being particularly stable - if not completely stable? We know that the nuclei of heavy elements aren’t chaotic bags of neutrons and protons, but have a shell structure to a considerable extent, with ‘magic numbers’ which determine relative stability, and which are physically explained by the number of nucleons taken to completely fill up successive nuclear shells. Probably some similar effect plays a part to some extent in the mass mechanism, so that some configurations have magic numbers which are stable, while nearby ones are far less stable and decay quickly. This if true of the quantized vacuum surrounding fundamental particles, would lead to a new quantum theory of such particles, with similar gimmicks explaining the original ‘anomalies’ of the periodic table, viz. isotopes explaining non-integer masses, etc.)

Particle mass predictions: the gravity mechanism implies quantized unit masses. As proved, the 1/a = 137.036… number is the electromagnetic shielding factor for any particle core charge by the surrounding polarised vacuum.

This shielding factor is obtained by working out the bare core charge (within the polarized vacuum) as follows. Heisenberg’s uncertainty principle says that the product of the uncertainties in momentum and distance is on the order h-bar. The uncertainty in momentum p = mc, while the uncertainty in distance is x = ct. Hence the product of momentum and distance, px = (mc).(ct) = Et where E is energy (Einstein’s mass-energy equivalence). Although we have had to assume mass temporarily here before getting an energy version, this is just what Professor Zee does as a simplification in trying to explain forces with mainstream quantum field theory (see previous post). In fact this relationship, i.e., product of energy and time equalling h-bar, is widely used for the relationship between particle energy and lifetime. The maximum possible range of the particle is equal to its lifetime multiplied by its velocity, which is generally close to c in relativistic, high energy particle phenomenology. Now for the slightly clever bit:

px = h-bar implies (when remembering p = mc, and E = mc2):

x = h-bar /p = h-bar /(mc) = h-bar*c/E

so E = h-bar*c/x

when using the classical definition of energy as force times distance (E = Fx):

F = E/x = (h-bar*c/x)/x

= h-bar*c/x2.

So we get the quantum electrodynamic force between the bare cores of two fundamental unit charges, including the inverse square distance law! This can be compared directly to Coulomb’s law, which is the empirically obtained force at large distances (screened charges, not bare charges), and such a comparison tells us exactly how much shielding of the bare core charge there is by the vacuum between the IR and UV cutoffs. So we have proof that the renormalization of the bare core charge of the electron is due to shielding by a factor of a. The bare core charge of an electron is 137.036… times the observed long-range (low energy) unit electronic charge. All of the shielding occurs within a range of just 1 fm, because by Schwinger’s calculations the electric field strength of the electron is too weak at greater distances to cause spontaneous pair production from the Dirac sea, so at greater distances there are no pairs of virtual charges in the vacuum which can polarize and so shield the electron’s charge any more.

One argument that can superficially be made against this calculation (nobody has brought this up as an objection to my knowledge, but it is worth mentioning anyway) is the assumption that the uncertainty in distance is equivalent to real distance in the classical expression that work energy is force times distance. However, since the range of the particle given, in Yukawa’s theory, by the uncertainty principle is the range over which the momentum of the particle falls to zero, it is obvious that the Heisenberg uncertainty range is equivalent to the range of distance moved which corresponds to force by E = Fx. For the particle to be stopped over the range allowed by the uncertainty principle, a corresponding force must be involved. This is more pertinent to the short range nuclear forces mediated by massive gauge bosons, obviously, than to the long range forces.

It should be noted that the Heisenberg uncertainty principle is not metaphysics but is solid causal dynamics as shown by Popper:

‘… the Heisenberg formulae can be most naturally interpreted as statistical scatter relations, as I proposed [in the 1934 German publication, ‘The Logic of Scientific Discovery’]. … There is, therefore, no reason whatever to accept either Heisenberg’s or Bohr’s subjectivist interpretation of quantum mechanics.’ – Sir Karl R. Popper, Objective Knowledge, Oxford University Press, 1979, p. 303. (Note: statistical scatter gives the energy form of Heisenberg’s equation, since the vacuum contains gauge bosons carrying momentum like light, and exerting vast pressure; this gives the foam vacuum effect at high energy where nuclear forces occur.)

Experimental evidence:

‘… we 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.

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. (Levine and Koltick experimentally found a 7% increase in the strength of Coulomb’s/Gauss’ force field law when hitting colliding electrons at an energy of 80 GeV or so. The coupling constant for electromagnetism is 1/137 at low energies but was found to be 1/128.5 at 80 GeV or so. This rise is due to the polarised vacuum being broken through. We have to understand Maxwell’s equations in terms of the gauge boson exchange process for causing forces and the polarised vacuum shielding process for unifying forces into a unified force at very high energy. If you have one force (electromagnetism) increase, more energy is carried by virtual photons at the expense of something else, say gluons. So the strong nuclear force will lose strength as the electromagnetic force gains strength. Thus simple conservation of energy will explain and allow predictions to be made on the correct variation of force strengths mediated by different gauge bosons. When you do this properly, you learn that stringy supersymmetry first isn’t needed and second is quantitatively plain wrong. At low energies, the experimentally determined strong nuclear force coupling constant which is a measure of effective charge is alpha = 1, which is about 137 times the Coulomb law, but it falls to 0.35 at a collision energy of 2 GeV, 0.2 at 7 GeV, and 0.1 at 200 GeV or so. So the strong force falls off in strength as you get closer by higher energy collisions, while the electromagnetic force increases! Conservation of gauge boson mass-energy suggests that energy being shielded form the electromagnetic force by polarized pairs of vacuum charges is used to power the strong force, allowing quantitative predictions to be made and tested, debunking supersymmetry and existing unification pipe dreams.)

Related to this exchange radiation, are the Feynman’s path integrals of quantum field theory:

‘I like Feynman’s argument very much (although I have not thought about the virtual charges in the loops bit bit). The general idea that you start with a double slit in a mask, giving the usual interference by summing over the two paths… then drill more slits and so more paths… then just drill everything away… leaving only the slits… no mask. Great way of arriving at the path integral of QFT.’ - Prof. Clifford V. Johnson’s comment, here

‘The world is not magic. The world follows patterns, obeys unbreakable rules. We never reach a point, in exploring our universe, where we reach an ineffable mystery and must give up on rational explanation; our world is comprehensible, it makes sense. I can’t imagine saying it better. There is no way of proving once and for all that the world is not magic; all we can do is point to an extraordinarily long and impressive list of formerly-mysterious things that we were ultimately able to make sense of. There’s every reason to believe that this streak of successes will continue, and no reason to believe it will end. If everyone understood this, the world would be a better place.’ – Prof. Sean Carroll, here

As for the indeterminancy of electron locations in the atom, the fuzzy picture is not a result of multiple universes interacting but simply the Poincare manybody problem, whereby Newtonian physics fails when you have more than 2 bodies of similar mass or charge interacting at once (the failure is that you lose deterministic solutions to the equations, having to resort instead to statistical descriptions like the Schroedinger equation and annihilation-creation operators in quantum field theory produce many pairs of charges randomly in location and time in strong fields, deflecting particle motions chaotically on small scales, similarly to Brownian motion; this is the ‘hidden variable’ causing indeterminancy in quantum theory, not multiverses or entangled states). Entanglement is a false interpretation physically of Aspect’s (and related) experiments: Heisenberg’s uncertainty principle only applies to slower than light velocity particles like massive fermions. Aspect’s experiment stems from the Einstein-Rosen-Polansky suggestion to measure the spins of two molecules; if the correlate in a certain way then that would prove entanglement, because molecular spin are subject to the indeterminancy principle. Aspect used photons instead of molecules. Photons cannot change polarization when measured as they are frozen in nature due to their velocity, c. Therefore, the correlation of photon polarizations observed merely confirms that Heisenberg’s uncertainty principle does not apply to photons, rather than implying that (believing that Heisenberg’s uncertainty principle does apply to photons) the photons ‘must’ have an entangled polarization until measured! Aspect’s results in fact discredits entanglement.

‘… the ‘inexorable laws of physics’ … were never really there … Newton could not predict the behaviour of three balls … In retrospect we can see that the determinism of pre-quantum physics kept itself from ideological bankruptcy only by keeping the three balls of the pawnbroker apart.’

Gravity is basically a boson shielding effect, while the errors of LeSage’s infamous pushing-gravity model are due to fermion radiation assumptions, so they did not get anywhere. Once again, gravity is a massless boson - integer spin - exchange radiation effect. LeSage (or Fatio, whose ideas LeSage borrowed), assumed that very small material particles - fermions in today’s language - were the force-causing exchange radiation. Massless bosons don’t obey the exclusion principle and they don’t interact with one another like massive bosons and all fermions (fermions do obey the exclusion principle, so they always interact with one another). Hence, LeSage’s attractive force mechanism is only valid for short-ranged particles like pions, which produce the strong nuclear attractive force between nucleons. Therefore, the ‘errors’ people found in the past when trying to use LeSage’s mechanism for gravity - the mutual interactions between the particles which equalize the force in the shadow region after a mean-free-path - don’t apply to bosonic radiation which doesn’t obey the exclusion principle. The short-range of LeSage’s gravity becomes an advantage in explaining the pion mediated strong nuclear force. LeSage - or actually Newton’s friend Fatio, whose ideas were allegedly plagarised by LeSage - made a mess of it. The LeSage attraction mechanism is predicted to have a short range on the order of a mean free path of scatter before radiation pressure equalization in the shadows quenches the attractive force. This short range is real for nuclear forces, but not for gravity or electromagnetism:

(Source: http://www.mathpages.com/home/kmath131/kmath131.htm.)

The Fatio-LeSage mechanism is useless because it makes no prediction for the strength of gravity whatsoever, and it is plain wrong because it assumes gas molecules or fermions are the exchange radiation, instead of gauge bosons. The falsehood of the Fatio-LeSage mechanism is that the gravity force range would be short ranged, since the material pressure of the fermion particles (which bounce off each other due to the Pauli exclusion principle) or gas molecules causing gravity, would get diffused into the shadows within a short distance; just as air pressure is only shielded by a solid for a distance on the order of a mean free path of the gas molecules. Hence, to get a rubber suction cup to be pushed strongly to a wall by air pressure, the wall must be smooth, and it must be pushed firmly. Such a short ranged attractive force mechanism may be useful in making pion-mediated Yukawa strong nuclear force calculations, but is not gravity.

(Some of the ancient objections to LeSage are plain wrong and in contradiction of Yang-Mills theories such as the standard model. For example, it was alleged that gravity couldn’t be the result of an exchange radiation force because the exchange radiation would heat up objects until they all glowed. This is wrong because the mechanisms by which radiation interact with matter don’t necessarily transfer that energy into heat; classically all energy is usually degraded to waste heat in the end, but the gravitational field energy cannot be directly degraded to heat. Masses don’t heat up just because they are exchanging radiation, the gravitational field energy. If you drop a mass and it hits another mass hard, substantial heat is generated, but this is an indirect effect. Basically, many of the arguments against physical mechanisms are bogus. For an object to heat up, the charged cores of the electrons must gain and radiate heat energy; but the gravitational gauge boson radiation isn’t being exchanged with the electron bare core. Instead, the fermion core of the electron has no mass, and since quantum gravity charge is mass, the lack of mass in the core of the electron means it can’t interact with gravitons. The gravitons interact with some vacuum particles like ‘Higgs bosons’, which surround the electron core and produce inertial and gravitational forces indirectly. The electron core couples to the ‘Higgs boson’ by electromagnetic field interactions, while the ‘Higgs boson’ at some distance from the electron core interacts with gravitons. This indirect transfer of force can smooth out the exchange radiation interactions, preventing that energy from being degraded into heat. So objections - if correct - would also have to debunk the Standard Model which is based on Yang-Mills exchange radiation, and which is well tested experimentally. Claiming that exchange radiation would heat things up until they glowed is similar to the Ptolemy followers claiming that if the Earth rotated daily, clouds would fly over the equator at 1000 miles/hour and people would be thrown off the ground! It’s a political-style junk objection and doesn’t hold up to any close examination in comparison to experimentally-determined scientific facts.)

When a mass-giving black hole (gravitationally trapped) Z-boson (this is the Higgs particle) with 91 GeV energy is outside an electron core, both its own field (it is similar to a photon, with equal positive and negative electric field) and the electron core have alpha shielding factors, and there are also smaller geometric corrections for spin loop orientation, so the electron mass is:

Mza2 /(1.5*2p) = 0.51 MeV

If, however, the electron core has more energy and can get so close to a trapped Z-boson that both are inside and share the same overlapping polarised vacuum veil, then the geometry changes so that the 137 shielding factor operates only once, predicting the muon mass:

Mza/(2p ) = 105.7 MeV

The muon is thus an automatic consequence of a higher energy state of the electron. As Dr Thomas Love of California State University points out, although the muon doesn’t decay directly into an electron by gamma ray emission, apart from its higher mass it is identical to an electron, and the muon can decay into an electron by emitting electron and muon neutrinos. The general equation the mass of all particles apart from the electron is:

Men(N + 1)/(2a) = 35n(N+1) Mev.

(For the electron, the extra polarised shield occurs so this should be divided by the 137 factor.) Here the symbol n is the number of core particles like quarks, sharing a common, overlapping polarised electromagnetic shield, and N is the number of Higgs or trapped Z-bosons. Lest this be dismissed as ad hoc coincidence (as occurred in criticism of Dalton’s early form of the periodic table), remember we have a physical mechanism unlike Dalton, and we below make additional predictions and tests for all the other observable particles in the universe, and compare the results to experimental measurements. There is a similarity in the physics between these vacuum corrections and the Schwinger correction to Dirac’s 1 Bohr magneton magnetic moment for the electron: corrected magnetic moment of electron = 1 + a/(2p) = 1.00116 Bohr magnetons. Notice that this correction is due to the electron interacting with the vacuum field, similar to what we are dealing with here. Also note that Schwinger’s correction is only the first (but is by far the biggest numerically and thus the most important, allowing the magnetic moment to be accurately predicted to 6 significant figures of accuracy) of an infinite series of correction terms involving higher powers of a for more complex vacuum field interactions. Each of these corrections is depicted by a different Feynman diagram. (Basically, quantum field theory is a mathematical correction for the probability of different reactions. The more classical and obvious things generally have the greatest probability by far, but stranger interactions occasionally occur in addition, so these also need to be included in calculations which give a prediction which is statistically very accurate.)

This kind of gravitational calculation also allows us to predict the gravitational coupling constant, G, as will be proved below. We know that the inward force is carried by gauge boson radiation, because all forces are due to gauge boson radiation according to the Standard Model of particle physics, which is the best-tested physical theory of all time and and has made thousands of accurately confirmed predictions from an input of just 19 empirical parameters (don’t confuse this with the bogus supersymmetric standard model, which even in its minimal form requires 125 adjustable parameters and has a large landscape of possibilities, making no definite or precise predictions whatsoever). The Standard Model is a Yang-Mills theory in which the exchange of gauge bosons between relevant charges for the force (i.e., colour charges for quantum chromodynamic forces, electric charges for electric forces, etc.) causes the force.

What happens is that Yang-Mills exchange radiation pushes inward, coming from the surrounding, expanding universe. Since spacetime, as recently observed, isn’t boundless (there’s no observable gravity retarding the recession of the most distant galaxies and supernovae, as discovered in 1998, and so there is no curvature at the greatest distances), the universe is spherical and is expanding without slowing down. The expansion is caused by the physical pressure of the gauge boson radiation. This radiation exerts momentum p = E/c. Gauge boson radiation is emitted towards us by matter which is receding: the reason is Newton’s 3rd law. Because, as proved above, the Hubble recession in spacetime is an acceleration of matter outwards, the matter receding has an outward force by Newton’s 2nd empirical law F = ma, and this outward force has an equal and opposite reaction, just like the exhaust of a rocket. The reaction force is carried by gauge boson radiation.

What, you may ask, is the mechanism behind Newton’s 3rd law in this case? Why should the outward force of the universe be accompanied by an inward reaction force? I dealt with this in a paper in May 1996, made available via the letters page of the October 1996 issue of Electronics World. Consider the source of gravity, the gravitational field (actually gauge boson radiation), to be a frictionless perfect fluid. As lumps of matter, in the form of the fundamenta particles of galaxies, accelerate away from us, they leave in their wake a volume of vacuum which was previously occupied but is now unoccupied. The gravitational field doesn’t ignore spaces which are vacated when matter moves: instead, the gravitational field fills them. How does this occur?

What happens is like the situation when a ship moves along. It doesn’t suck in water from behind it to fill its wake. Instead, water moves around from the front to the back. In fact, there is a simple physical law: there is an equal volume of water moving to the ship’s displacement moving continuously in the opposite direction to the ship’s motion.

This water fills in the void behind the moving ship. For a moving particle, the gravitational field of spacetime does the same. It moves around the particle. If it did anything else, we would see the effects of that: for example, if the gravitational field piled up in front of a moving object instead of flowing around it, the pressure would increase with time and there would be drag on the object, slowing it down. The fact that Newton’s 1st law, inertia, is empirically based tells us that the vacuum field does flow frictionlessly around moving particles instead of slowing them down. The vacuum field does however exert a net force when an object accelerates; this causes increases the mass of the object and causes a flattening of the object in the direction of motion (FitzGerald-Lorentz contraction). However, this is purely a resistance to acceleration, and there is drag to motion unless the motion is accelerative.

‘… the source of the gravitational field can be taken to be a perfect fluid…. A fluid is a continuum that "flows" … A perfect fluid is defined as one in which all antislipping forces are zero, and the only force between neighboring fluid elements is pressure.’ - Bernard Schutz, General Relativity, Cambridge University Press, 1986, pp89-90.

‘Popular accounts, and even astronomers, talk about expanding space. But how is it possible for space … to expand? … ‘Good question,’ says [Steven] Weinberg. ‘The answer is: space does not expand. Cosmologists sometimes talk about expanding space – but they should know better.’ [Martin] Rees agrees wholeheartedly. ‘Expanding space is a very unhelpful concept’.’ – New Scientist, 17 April 1993, pp32-3. (The volume of spacetime expands, but the fabric of spacetime, the gravitational field, flows around moving particles as the universe expands.)

Fig. 2: The general all-round pressure from the gravitational field does of course produce physical effects. The radiation is received by mass almost equally from all directions, coming from other masses in the universe; the radiation is in effect reflected back the way it came if there is symmetry that prevents the mass from being moved. The result is a compression of the mass by the amount mathematically predicted by general relativity, i.e., the radial contraction is by the small distance MG/(3c²) = 1.5 mm for the Earth; this was calculated by Feynman using general relativity in his famous Feynman Lectures on Physics. The reason why nearby, local masses shield the force-carrying radiation exchange, causing gravity, is because the distant masses in the universe is in high speed recession, but the nearby mass is not receding significantly. By Newton’s 2nd law the outward force (according of a nearby mass which is not receding (in spacetime) from you is F = ma = m.dv/dt = 0. Hence, by Newton’s 3rd law, the inward force of gauge bosons coming towards you from a local, non-receding mass is also zero; there is no action and so there is no reaction. As a result, the local mass shields you rather than exchanging gauge bosons with you, so you get pushed towards it. This is why apples fall.

Since there is very little shielding area (fundamental particle shielding cross-sectional areas are small compared to the Earth’s area) so the Earth doesn’t block all of the gauge boson radiation being exchanged between you and the masses in the receding galaxies beyond the other far side of the Earth. The shielding by the Earth is by fundamental particles in it, specifically the fundamental particles which give rise to mass (supposed to be some form of Higgs bosons which surround fermions, giving them mass) by interacting with the gravitational field of exchange radiation. Although each local fundamental particle over its shielding cross-sectional area stops the gauge boson radiation completely, most of Earth’s volume is devoid of fundamental particles because they are so small. Consequently, the Earth as a whole is an inefficient shield. There is little probability of different fundamental particles in the earth being directly behind one another (i.e., overlapping of shielded areas) because they are so small. Consequently, the gravitational effect from a large mass like the Earth is just the simple sum of the contributions from the fundamental particles which make the mass up, so the total gravity is proportional to the number of particles, which is proportional to the mass.

The point is that nearby masses, which are not receding from you significantly, don’t fire gauge boson radiation towards you, because there is no reaction force! However, they still absorb gauge bosons, so they shield you, creating an asymmetry. You get pushed towards such masses by the gauge bosons coming from the direction opposite to the mass. For example, standing on the Earth, you get pushed down by the asymmetry; the upward beam of gauge bosons coming through the earth is very slightly shielded. The shielding effect is very small, because it turns out that the effective cross-sectional shielding area of an electron (or other fundamental particle) for gravity is equal to πR2 where R = 2GM/c2 which is the event horizon radius of an electron. This is a result of the calculations, as is a prediction of the Newtonian gravitational parameter G! Now let’s prove it.

Approach 1

Referring to Fig. 1 above, we can evaluate the gravity force (which is the proportion of the total force indicated by the dark-shaded cone; the observer is in the middle of the diagram at the apex of each cone). The force of gravity is not simply the total inward force, which is equal to the total outward force. Gravity is only the proportion of the total force which is represented by the dark cone.

The total force, as proved above, is = 4πR4rH2/3. The fraction of this which is represented by the dark cone is equal to the volume of the cone (XR/3, where X is the area of the end of the cone), divided by volume (4πR3/3), of the sphere of radius R (the radius of the observable spacetime universe defined by R = ct = c/H). Hence,

Force of gravity = (4πR4rH2/3).(XR/3)/(4πR3/3)

= R2rH2X/3,

where the area of the end of the cone, X, is observed in Fig. 1 to be geometrically equal to the area of the shield, A, multiplied by (R/r)2.

X = A(R/r)2.

Hence the force of gravity is R2rH2[A(R/r)2]/3

= (1/3)R4rH2A/r2.

(Of course you get exactly the same result if you take the fraction of the total force delivered in the cone to be the area of the base of the cone, X, divided into the surface area, 4πR2, of the sphere of radius R.)

If we assume that the shield area is A = π(2GM/c2)2, i.e., the cross-sectional area of the event horizon of a black hole, then the formula above for the force of gravity, when set equal to the Newtonian law, F = mMG/r2, gives for m = M and c/R = H, the result is the prediction that

G = (3/4)H2/(rπ).

This is of course equal to twice the false amount you get from rearranging the ‘critical density’ formula of general relativity (without a cosmological constant), but what is more interesting is that we do not need to assume that the shield area is A = π(2GM/c2)2. The critical density formula, and other cosmological applications of general relativity, is false because it ignores the quantum gravity dynamics which become important on very large scales due to recession of masses in the universe, because the gravitational interaction is a product of the cosmological expansion; both are caused by gauge boson exchange radiation (the radiation pushes masses apart over large, cosmological distance scales, while pushing things together on small scales; this is because the uniform gauge boson pressure between masses causes them to recede from all surrounding masses and fill the expanding volume of space like raisins in an expanding cake receding from one another, where the gauge boson radiation pressure is represented by the pressure of the dough of the cake as it expands; there is no contradiction whatsoever between this effect and the local gravitational attraction which occurs when two currants are close enough that there is no dough between them and plenty of dough around them, pushing them towards one another like gravity).

We get the same result by an independent method, which does not assume that the shield area is the event horizon cross section of a black hole. Now we shall prove it.

Approach 2

As in the above approach, the outward force of the universe is 4πR4rH2/3, and there is an equal inward force. The fraction of the inward force which is shielded is now calculated as the mass, Y, of those atoms in shaded cone in Fig. 1 which actually emit the gauge boson radiation that hits the shield, divided by the mass of the universe.

The important thing here is that Y is not simply the total mass of the universe in the shaded cone. (If it were, Y would be the density of the universe multiplied by volume of the cone.)

That total mass inside the shaded cone of Fig.1 is not important because part of the gauge boson radiation it emits misses the shield, because it hits other intervening masses in the universe. (See Fig. 3.)

The mass in the shaded cone which actually produces the gauge boson radiation which we are concerned with (that which causes gravity) is equal to the mass of the shield multiplied up geometrically by the ratio of the area of the base of the cone to the area of the shield, i.e., Y = M(R/r)2, because of the geometric convergence of the inward radiation from many masses within the cone towards the center. This is illustrated in Fig. 3.

Hence, the force of gravity is:

(4πR4rH2/3)Y/[mass of universe]

= (4πR4rH2/3).[M(R/r)2]/(4πR3r/3)

= R3H2m/r2.

Comparing this to Newton’s law F = mMG/r2, gives us

G = R3H2/[mass of universe]

= (3/4)H2/(rπ).

Fig. 3: The mass multiplication scheme basis of Approach 2.

So we get precisely the same result as the previous method where we assumed that the shield area of an electron was the cross-sectional area of the black hole event horizon! This result for G has been produced entirely without the need for an assumption about what numerical value to take for the shielding cross-sectional area of a particle. Yet it is the same result as that derived above in the previous method when assuming that a fundamental particle has a shielding cross-sectional area for gravity-causing gauge boson radiation equal to the event horizon of a black hole. Hence, this result justifies and substantiates that assumption. We get two major quantitative results from this study of quantum gravity: a formula of G, and a formula of the cross-sectional area of a fundamental particle for gravitational interactions.

The exact formula for G, including photon redshift and density variation

The toy model above began by assuming that the inward force carried by the gauge boson radiation is identical to the outward force represented the simple product of mass and acceleration in Newton’s 2nd law, F = ma. In fact, taking the density of the universe to be the local average around us (at a time of 14,000 million years after the big bang) is an error, because the density increases as we look back in time with increasing distance, seeing earlier epochs which have higher density. This effect tends to increase the effective outward force of the universe, by increasing the density. In fact, the effective mass would go to infinity unless there was another factor, which tends to reduce the force imparted by gravity causing gauge bosons from the greatest distances. This second effect is redshift. This problem of how to evaluate the extent to which these two effects partly offset one another is discussed in detail in the earlier post on this blog, here. It is shown there that the effective inward force should take some more complex form, so that the inward force is no longer simply F = ma but some integral (depending on the way that the redshift is modelled, and there are several alternatives) like

F = ma = mH2r

= ò(4πr2r )(1 – rc-1H)-3(1 – rc-1H)H2r [1 + {1.1*10-13 (H -1 - r/c )}-1 ]-1 dr

= 4 π r c2 ò r [ {c/(Hr) } – 1 ]-2 [1 + {1.1*10-13 (H -1 - r/c )}-1 ]-1 dr.

Where r is the local density, i.e., the density of spacetime at 14,000 million years after the big bang. I have not completed the evaluation of such integrals (some of them give an infinite answer, so it is possible to rule those out as either wrong or missing some essential factor in the model). However, an earlier idea, to take account of the rise in density with increasing spacetime around us, at the same time taking account of the redshift as a divergence of the universe, is to set up a more abstract model.

Density variation with spacetime and divergence of matter in universe (causing the redshift of gauge bosons by an effect which is quantitatively similar to gauge boson radiation being ’stretched out’ over the increasing volume of space while in transit between receding masses in the expanding universe) can be modelled by the well-known equation for mass continuity (based on the conservation of mass in an expanding gas, etc):

dρ/dt + Ñ (ρv) = 0

Or: dρ/dt = -Ñ (ρv)

Where divergence term

-Ñ .(ρv) = -[{d(ρv)x/dx} + {d(ρv)y/dy} + {d(ρv)z/dz}]

For the observed spherical symmetry of the universe we see around us

d(ρv)x/dx = d(ρv)y/dy = d(ρv)z/dz = d(ρv)R/dR

where R is radius.

Now we insert the Hubble equation v = HR:

dρ/dt = -Ñ (ρv) = -Ñ.(ρHR) = -[{d(ρHR)/dR} + {d(ρHR)/dR} + {d(ρHR)/dR}]

= -3d(ρHR)/dR

= -3ρHdR/dR

= -3ρH.

So dρ/dt = -3ρH. Rearranging:

-3Hdt = (1/ρ) dρ. Integrating:

ò-3Hdt = ò(1/ρ) dρ.

The solution is:

-3Ht = (ln ρ1) – (ln ρ). Using the base of natural logarithms e to get rid of the ln’s:

e-3Ht = ρ1/ρ

Because H = v/R = c/[radius of universe, R] = 1/[age of universe, t] = 1/t, we find:

e-3Ht = ρ1/ρ = e-3(1/t)t = e-3.

Therefore

ρ = ρ1e3 ~ 20.0855 ρ1.

Therefore, if this analysis is a correct abstract model for the combined effect of graviton redshift (due to the effective ’stretching’ of radiation as a result of the divergence of matter across spacetime caused by the expansion of the universe) and density variation of the universe across spacetime, our earlier result of G = (3/4)H2/(rπ) should be corrected for spacetime density variation and redshift of gauge bosons, to:

G = (3/4)H2/(rπe3),

which is a factor of ~10 smaller than the rearranged traditional ‘critical density’ formula of general relativity, G = (3/8)H2/(rπ). Therefore, this theory predicts gravity quantitatively and checkably, and it dispenses with the need for an enormous amount of unobserved dark matter. (There is clearly some dark matter, as neutrinos are known to have some mass, but this can be assessed from the rotation curves for spiral galaxies and other observational checks.)

Experimental confirmation for the black hole size as the cross-sectional area for fundamental particles in gravitational interactions

In additional to the theoretical evidence above, there is independent experimental evidence. If the core of an electron is gravitationally trapped Heaviside-Poynting electromagnetic energy current, it is a black hole and it has a magnetic field which is a torus (see Electronics World, April 2003).

Experimental evidence for why an electromagnetic field can produce gravity effects involves the fact that electromagnetic energy is a source of gravity (think of the stress-energy tensor on the right hand side of Einstein’s field equation). There is also the capacitor charging experiment. When you charge a capacitor, practically the entire electrical energy entering it is electromagnetic field energy (Heaviside-Poynting energy current). The amount of energy carried by electron drift is negligible, since the electrons have a kinetic energy of half the product of their mass and the square of their velocity (typically 1 mm/s for a 1 A current).

So the energy current flows into the capacitor at light speed. Take the capacitor to be simple, just two parallel conductors separated by a dielectric composed of just a vacuum (free space has a permittivity, so this works). Once the energy goes along the conductors to the far end, it reflects back. The electric field adds to that from further inflowing energy, but most of the magnetic field is cancelled out since the reflected energy has a magnetic field vector curling the opposite way to the inflowing energy. (If you have a fully charged, ’static’ conductor, it contains an equilibrium with similar energy currents flowing in all possible directions, so the magnetic field curls all cancel out, leaving only an electric field as observed.)

The important thing is that the energy keeps going at light velocity in a charged conductor: it can’t ever slow down. This is important because it proves experimentally that static electric charge is identical to trapped electromagnetic field energy. If this can be taken to the case of an electron, it tells you what the core of an electron is (obviously, there will be additional complexity from the polarization of loops of virtual fermions created in the strong field surrounding the core, which will attenuate the radial electric field from the core as well as the transverse magnetic field lines, but not the polar radial magnetic field lines).

You can prove this if you discharge any conductor x metres long which is charged to v volts with respect to ground, through a sampling oscilloscope. You get a square wave pulse which has a height of v/2 volts and a duration of 2 x/c seconds. The apparently ’static’ energy of v volts in the capacitor plate is not static at all; at any instant, half of it, at v/2 volts, is going eastward at velocity c and half is going westward at velocity c. When you discharge it from any point, the energy already by chance headed towards that point immediately begins to exit at v/2 volts, while the remainder is going the wrong way and must proceed and reflect from one end before it exits. Thus, you always get a pulse of v/2 volts which is 2 x metres long or 2 x/c seconds in duration, instead of a pulse at v volts and x metres long or x/c seconds in duration, which you would expect if the electromagnetic energy in the capacitor was static and drained out at light velocity by all flowing towards the exit.

This was investigated by Catt, who used it to design the first crosstalk (glitch) free wafer scale integrated memory for computers, winning several prizes for it. Catt welcomed me when I wrote an article on him for the journal Electronics World, but then bizarrely refused to discuss physics with me, while he complained that he was a victim of censorship. However, Catt published his research in IEEE and IEE peer-reviewed journals. The problem was not censorship, but his refusal to get into mathematical physics far enough to sort out the electron.

It’s really interesting to investigate why classical (not quantum) electrodynamics is totally false in many ways: Maxwell’s model is wrong. Some calculations of quantum gravity based on a simple, empirically-based model (no ad hoc hypotheses), which yields evidence (which needs to be independently checked) that the proper size of the electron is the black hole event horizon radius.

There is also the issue of a chicken-and-egg situation in QED where electric forces are mediated by exchange radiation. Here you have the gauge bosons being exchanged between charges to cause forces. The electric field lines between the charges have to therefore arise from the electric field lines of the virtual photons being continually exchanged.

How do you get an electric field to arise from neutral gauge bosons? It’s simply not possible. The error in the conventional thinking is that people incorrectly rule out the possibility that electromagnetism is mediated by charged gauge bosons. You can’t transmit charged photons one way because the magnetic self-inductance of a moving charge is infinite. However, charged gauge bosons will propagate in an exchange radiation situation, because they are travelling through one another in opposite directions, so the magnetic fields are cancelled out. It’s like a transmission line, where the infinite magnetic self-inductance of each conductor cancels out that of the other conductor, because each conductor is carrying equal currents in opposite directions.

Hence you end up with the conclusion that the electroweak sector of the Standard Model is in error: Maxwellian U(1) doesn’t describe electromagnetism properly. It seems that the correct gauge symmetry is SU(2) with three massless gauge bosons: positive and negatively charged massless bosons mediate electromagnetism and a neutral gauge boson (a photon) mediates gravitation. See Fig. 4.

Fig. 4: 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. See Fig. 5.

Fig. 5: 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. 5).

Experimentally checkable consequences of this gravity mechanism, and consistency with known physics
    1. Universal gravitational parameter, G

G = (3/4)H2/(rπe3), derived in stages above, where e3 is the cube of the base of natural logarithms (the correction factor due to the effects of redshift and density variation in spacetime), is a quantitative prediction. In the previous post here, the best observational inputs for Hubble parameter H and local density of universe r were identified: ‘The WMAP satellite in 2003 gave the best available determination: H = 71 +/- 4 km/s/Mparsec = 2.3*10-18 s-1. Hence, if the present age of the universe is t = 1/H (as suggested from the 1998 data showing that the universe is expanding as R ~ t, i.e. no gravitational retardation, instead of the Friedmann-Robertson-Walker prediction for critical density of R ~ t2/3 where the 2/3 power is the effect of curvature/gravity in slowing down the expansion) then the age of the universe is 13,700 +/- 800 million years. … The Hubble space telescope was used to estimate the number of galaxies in a small solid area of the sky. Extrapolating this to the whole sky, we find that the universe contains approximately 1.3*1011 galaxies, and to get the density right for our present time after the big bang we use the average mass of a galaxy at the present time to work out the mass of the universe. Taking our Milky Way as the yardstick, it contains about 1011 stars, and assuming that the sun is a typical star, the mass of a star is 1.9889*1030 kg (the sun has 99.86% of the mass of the solar system). Treating the universe as a sphere of uniform density and radius R = c/H, with the above mentioned value for H we obtain a density for the universe at the present time (~13,700 million years) of about 2.8*10-27 kg/m3.’

Putting H = 2.3*10-18 s-1 and r = 2.8*10-27 kg/m3 into G = (3/4)H2/(rπe3), gives a result of G = 2.2*10-11 m3 kg-1 s-2 which is one third of the experimentally determined value of G = 6.673*10-11 m3 kg-1 s-2. This factor of 3 error is within the error bars for the estimates of the density because of uncertainties in estimating the average mass of a galaxy. To put the accuracy of this prediction into perspective, try reading the statement by Eddington (quoted at the top of this blog post): how many other theories based entirely on observably verified facts like Hubble’s law and Newton’s laws, predict the strength of gravity? Alternatively, compare it to the classical (and incorrect) ‘critical density’ prediction from general relativity (which ignores the mechanism of gravitation), which rearranges to give a formula for G which is e3/2 or 10 times bigger, thus the critical density is 3.3 times bigger than the experimental data.

This is actually an unfair comparison, because the rough estimate for the density is about 3 times too high. Most astronomers suggest that the observable density is 5-20% of the critical density, i.e, 10% with a factor of 2 error limit. This would put the density at r = 10-27 kg/m3 and our prediction is then exact, with a factor of 2 experimental error limit. The abundance of dark matter is not experimentally measured. There is some observational evidence for dark matter, and theoretically there are some solid reasons why there should be such matter in a dark, non luminous form (neutrinos have mass, as do black holes). The mainstream takes the critical density formula from general relativity and the measured density for luminous matter and uses the disagreement to claim that the difference is dark matter. That argument is weak, because general relativity is in error for cosmological purposes through ignoring quantum gravity effects which become important on large scales in an expanding universe (i.e., redshift of gravitons weaking the force gravity over large distances, the nature of the Yang-Mills exchange radiation dynamical mechanism for gravity in which gravity is a result of radiation exchange with the other masses in the expanding universe, etc.). Another argument for a lot of dark matter is the flattening of galactic rotation curves, Cooperstock and Tieu have explained galactic rotation ‘evidence’ for dark matter as not being due to dark matter, but a GR effect which was not taken into account by the people who originally applied Newtonian dynamics to analyse galactic rotation:

‘One might be inclined to question how this large departure from the Newtonian picture regarding galactic rotation curves could have arisen since the planetary motion problem is also a gravitationally bound system and the deviations there using general relativity are so small. The reason is that the two problems are very different: in the planetary problem, the source of gravity is the sun and the planets are treated as test particles in this field (apart from contributing minor perturbations when necessary). They respond to the field of the sun but they do not contribute to the field. By contrast, in the galaxy problem, the source of the field is the combined rotating mass of all of the freely-gravitating elements themselves that compose the galaxy.’

Professor Sean Carroll writes a lot about cosmology, and is author of a very useful book on general relativity. However, in writing about the discovery of direct evidence for dark matter on his blog post http://cosmicvariance.com/2006/08/21/dark-matter-exists/ he does perhaps cause confusion. He starts by stating without evidence that 5% of the universe is ordinary matter, 25% dark matter and 70% dark energy. He then explains that the direct evidence for dark matter proves that mainstream cosmologists are not fooling themselves. The problem is that the direct evidence for dark matter doesn’t say how much dark matter there is: it’s not quantitative. It does not allow any confirmation of the theoretical guesswork for the statement he makes that there is 5 times as much dark matter as visible matter. He does then go on to discuss whether some kind of ‘modified Newtonian dynamics,’ rather than dark matter, could resolve the problems - and he writes that he would prefer some objective resolution of that type rather than in effect inventing ‘dark matter’ epicycles as convenient fixes which cannot be readily checked even in principle, but it is all wishy-washy because he does not state a definite proposal which is concrete and solves the quantum gravity facts, such as this mechanism.
    1. Small size of the cosmic background radiation ripples
      2.

      The prediction of gravity by this mechanism appears to be accurate to within experimental data, which is accurate to within a factor of approximately two. The second major prediction of this mechanism is the small size in the sound-like ripples in angular distribution of the cosmic background radiation which is the earliest directly observable radiation in the universe, whose emitted power peaked at 370,000 years after the big bang when the temperature was 3,500 Kelvin, and redshifted or ’stretched out’ due to cosmic expansion which reduces its temperature to 2.7 Kelvin.

      Because radiation and matter were in thermal equilibrium (an ionised gas) at the time the cosmic background radiation was emitted, the radiation carries an imprint of the nature of the matter at that time. The cosmic background radiation was found to be of extremely uniform temperature, far more uniform than expected at 370,000 years after the big bang, when conventional models of galaxy formation implied that should have been big ripples to indicate the ’seeding’ of lumps that could become stars and galaxies.

      This is called the ‘horizon problem’ or ‘isotropy problem’, because the microwave background radiation from opposite directions in the sky is similar to within 0.01%, and in the mainstream models gravity always has the same strength and would have caused bigger non-uniformities within 370,000 years of the big bang. A mainstream attempt to solve this problem is ‘inflation’ whereby the universe expanded at a faster than light speed for a small fraction of a second after the big bang, making the density of the universe uniform all over the sky before gravity had a chance to magnify irregularities in the expansion process.

      This ‘horizon problem’ is closely related to the ‘flatness problem’ which is the issue that in general relativity, the universe depending on its density has three possible geometries: open, flat, and closed. At the critical density it will be flat, with gravitation causing its radius to increase in proportion to the two-thirds power of time after the big bang. Mainstream consensus was that the universe was probably flat - which means of critical density, five to twenty times more than the observable density. The flatness problem is that if the universe was not completely flat, but of slightly different density across the universe, then the variation in density would be greatly magnified by the expansion of the universe and would be obvious today. The absense of any such large anisotropy is widely believed, by the mainstream, to be evidence for a flat geometry.

      The mechanism for gravity solves these problems. It solves the flatness problem by showing that the critical density (distinguishing the open, flat, and closed solutions to the Friedmann-Robertson-Walker metric of general relativity, which is applied to cosmology) is false for ignoring quantum gravity effects: there ars no long range gravitational influences in an expanding universe because the graviton exchange radiation of quantum gravity is becomes severely redshifted like light, and cannot produce curvature effects like forces on large distances. So the whole existing mainstream structure of using general relativity to work out cosmology falls apart.

      The horizon problem as to why the cosmic background is so smooth is solved by this model in an interesting way. It is very simple. The relationship giving the gravity parameter G is directly proportional to the age of the universe. The older the universe gets, the stronger gravity gets. At 370,000 years after the big bang, G was 40,000 times smaller than it is now, and at earlier times it was even smaller. The ripples in the cosmic background radiation are extremely small, because the gravitational force was so small.

      As proved earlier, the Hubble acceleration is a = dv/dt = H2R = H2ct, where t is time past when the light was emitted but can be set equal to the age of the universe for our purposes here. Hence the outward force F = ma = mH2ct, is proportional to the age of the universe, as is the equal inward force according to Newton’s 3rd law of motion.

      We can also see proportionality to time in the result G = (3/4)H2/(rπe3), since H2 = 1/t2 and r is mass of universe divided by volume (which is proportional to the cube of radius, i.e., the cube of the product ct), so this formula implies that G is proportional to (1/t2)/(1/t3) which is of course directly proportional to time.

      Dirac did not have a mechanism for a time-dependence of G but he guessed that G might vary. Unfortunately, lacking this mechanism, Dirac guessed that G was falling with time when it is actually increasing, and he did not realise that it is not just the strength constant for gravity that varies, but all the strength coupling constants vary in the same way. This disproves Edward Teller’s claim (based on just G varying) that if it were true, the sun’s radiant power would vary with time in a way incompatible with life (e.g., he calculated that the oceans would have been literally boiling during the Cambrian era if Dirac’s assumption was true).

      It also disproves another claim that G is constant based on nucleosythesis in the big bang, in the same way. The argument here is that nuclear fusion in stars and in the big bang depends on gravity to cause the basic compressive force, causing electrically charged positive particles to collide hard enough to sufficiently break through the ‘barrier’, caused by the repulsive electric Coulomb force, so that the short-ranged strong attractive force can then fuse the particles together. The big bang nucleosynthesis model correctly predicts the observed abundances of unfused hydrogen and fusion products like helium, assuming that G is constant. Because the result is correct, it is often claimed (even by students of Professor Carroll) that G must have had a value at 1 minutes after the big bang that is no more than 10% different to today’s value for G. The obvious fallacy here is that both electromagnstism and gravity vary the same way. If you double both the Coulomb force and the gravity force, the fusion rate doesn’t vary, because the Coulomb force is opposing fusion while gravity is causing fusion, and both are inverse square forces. The effect of G varying is not manifested in a change to the fusion rate in the big bang or in a star, because the corresponding change in the Coulomb force offsets it.

      For a discussion of why the different forces unify by scaling similarly (it is due to vacuum polarization dynamics) see this earlier post: http://nige.wordpress.com/2007/03/17/the-correct-unification-scheme/

      Louise Riofrio has investigated the dimensionally correct relationship GM = tc3 which was discussed earlier on this blog here, here and here where M is the mass of the universe and t is its age. This is algebraically equivalent to G = (3/4)H2/(rπ), i.e, the gravity prediction without a dimensionless redshift-density correction factor of e3. It is interesting that it can be derived on the basis of energy based methods, as first pointed out by John Hunter who suggested setting E = mc2 = mMG/R, i.e, setting rest mass energy equal to gravitational potential energy.

      Since the electromagnetic charge of the electron is massless bosonic energy trapped as a black hole, the gravitational potential energy would have to be equal, to keep it trapped.

      This rearranges to give the equations of Riofrio and Rabinowitz, although physically it is obviously missing some dimensionless multiplication constant because the gravitational potential energy cannot be E = mMG/R, where R is the radius of the universe. It is evident that this equation describes the gravitational potential energy which would be released if the universe were (somehow) to collapse. However, the average radial distance of the mass of the universe M will be less than the radius of the universe R. This brings up the density variation problem: gravitons and light both go at velocity c so we see them coming from times in the past when the density was greater (density is proportional to the reciprocal of the cube of the age of the universe due to expansion). So you cannot assume constant density and get a simple solution. You really also need to take account of the redshift of gravitons from the greatest distances, or the density will cause you problems due to tending towards infinity at radii approaching R. Hence, this energy-based approach to gravity is analogous to the physical mechanism described above. See also the derivation, by mathematician Dr Thomas R. Love of California State University, of Kepler’s law at http://nige.wordpress.com/2006/09/30/keplers-law-from-kinetic-energy/ which demonstrates that you can indeed treat problems generally by assuming that the rest mass energy of the spinning, otherwise static fundamental particle or the kinetic energy of the orbiting body, is being trapped by gravitation.

      This leads to to a concrete basis for John Hunter’s suggestions published as a notice in the 12 July 2003 issue of New Scientist, page 17: he suggested that if E = mc2 = mMG/R, then the effective value of G depends on distance since G = Rc2/M, which is algebraically equivalent to the expression we obtained above for the gravity mechanism, and published in the article ‘Electronic Universe, Part 2′, Electronics World, April 2003 (excluding the suggested e-cube correction for density variation with distance and graviton redshift, which was published in a letter to Electronics World in 2004). Hunter’s July 2003 notice in New Scientist indicated that this solves the horizon problem of cosmology (thus not requiring the speculative mainstream extravagances of Alan Guth’s inflation theory). Hunter pointed out in his notice that his E = mc2 = mMG/R, when applied to the earth, should include another term for the influence of the nearby mass of the sun, leading to E = mc2 = mMG/R + mM’G/r where m is mass of Earth, M is mass of universe, R is radius of universe (which is inaccurate as pointed out since the average distance of the mass of the surrounding universe can hardly be the radius of the universe, but must be a smaller distance, leading to the problem of the time-variation of density and thus also the redshift of the gravitons causing gravity), M’ is the mass of the Sun, and r is the distance of the Earth from the sun. Hunter argued that since r varies and is 3.4% bigger in July than in January (when Earth is closest to the sun), this leads to a suggestion for a definite experiment to test the theory: ‘Prediction: the weight of objects on the Earth will vary by 3.3 parts in 10 billion over a year, as the Earth to Sun distance changes.’ (My only problem with this prediction is simply that it is virtually impossible to test, just like the ‘not even wrong’ Planck scale unification supersymmetry ‘prediction’. Because the Earth is constantly vibrating due to seismic effects, you can never really hope to make such accurate measurements of weight. Anyone who has tried to make measurements of masses beyond a few significant figures for quantitative chemical analysis knows how difficult such a mass measurement is: making sensitive instruments is a problem, but the increased sensitivity multiplies up background vibrations so the instrument just becomes a seismograph. However, maybe some space-based precise measurements with clever experimentalist/observationist tricks will one day be able to check this to some extent.)

    2. Electric force constant (permittivity), Hubble parameter, etc.
      3.

      The proof [above] predicts gravity accurately, with G = ¾ H2/(pre3). Electromagnetic force (discussed above and in the April 2003 Electronics World article) in quantum field theory (QFT) is due to ‘virtual photons’ which cannot be seen except via forces produced. The mechanism is continuous radiation from spinning charges; the centripetal acceleration of a = v2/r causes the emission energy emission which is naturally in exchange equilibrium between all similar charges, like the exchange of quantum radiation at constant temperature. This exchange causes a ‘repulsion’ force between similar charges, due to recoiling apart as they exchange energy (two people firing guns at each other recoil apart). In addition, an ‘attraction’ force occurs between opposite charges that block energy exchange, and are pushed together by energy being received in other directions (shielding-type attraction). The attraction and repulsion forces are equal for similar net charges. The net inward radiation pressure that drives electromagnetism is similar to gravity, but the addition is different. The electric potential adds up with the number of charged particles, but only in a diffuse scattering type way like a drunkards walk, because straight-line additions are cancelled out by the random distribution of equal numbers of positive and negative charge. The addition only occurs between similar charges, and is cancelled out on any straight line through the universe. The correct summation is therefore statistically equal to the square root of the number of charges of either sign multiplied by the gravity force proved above.

      Hence F(electromagnetism) = mMGN1/2/r2 = q1q2/(4per2) (Coulomb’s law), where G = ¾ H2/(pre3) as proved above, and N is as a first approximation the mass of the universe (4pR3r/3= 4p(c/H)3r/3) divided by the mass of a hydrogen atom. This assumes that the universe is hydrogen. In fact it is 90% hydrogen by atomic abundance as a whole, although less near stars (only 70% of the solar system is hydrogen, due to fusion of hydrogen into helium, etc.). Another problem with this way of calculating N is that we assume the fundamental charges to be electrons and protons, when in fact protons contain two up quarks (each +2/3) and one downquark (-1/3), so there are twice as many fundamental particles. However, the quarks remain close together inside a nucleon and behave for most electromagnetic purposes as a single fundamental charge. With these approximations, the formulae above yield a prediction of the strength factor e in Coulomb’s law of:

      e = qe2e2.7…3[r/(12pme2mprotonHc3)]1/2 F/m.

      Using old data as in the letter published in Electronics World some years ago which gave the G formula (r = 4.7 x 10-28 kg/m3 and H = 1.62 x 10-18 s-1 for 50 km.s-1Mpc-1), gives e = 7.4 x 10-12 F/m which is only 17% low as compared to the measured value of 8.85419 x 10-12 F/m.

      Rearranging this formula to yield r, and rearranging also G = ¾ H2/(pre3) to yield r allows us to set both results for r equal and thus to isolate a prediction for H, which can then be substituted into G = ¾ H2/(pre3) to give a prediction for r which is independent of H:

      H = 16p2Gme2mprotonc3e2/(qe4e2.7…3) = 2.3391 x 10-18 s-1 or 72.2 km.s-1Mpc-1, so 1/H = t = 13,550 million years. This is checkable against the WMAP result that the universe is 13,700 million years old; the prediction is well within the experimental error bar.

      r = 192p 3Gme4mproton2c6e4/(qe8e2.7…9) = 9.7455 x 10-28 kg/m3.

      Again, these predictions of the Hubble constant and the density of the universe from the force mechanisms assume that the universe is made of hydrogen, and so are first approximations. However they clearly show the power of this mechanism-based predictive method.

      Furthermore, calculations show that Hawking radiation from electron-mass black holes has the right force as exchange radiation of electromagnetism: http://nige.wordpress.com/2007/03/08/hawking-radiation-from-black-hole-electrons-causes-electromagnetic-forces-it-is-the-exchange-radiation/

      4. Particle masses

      Fig. 6: Particle mass mechanism. The ‘polarized vacuum’ shell exists between IR and UV cutoffs. We can work out the shell outer radius from either using the IR cutoff energy as the collision energy to calculate the distance of closest approach in a particle scattering event (like Coulomb scattering, which predominates at low energies) or we use Schwinger’s formula for the minimum static electric field strength which is needed to cause pair-productions of fermion-antifermion pairs to pop out of the Dirac sea in the vacuum. The outer radius of the polarized vacuum around a unit charge by either calculation is on the order 1 fm. This scheme doesn’t just explain and predict masses, it also replaces supersymmetry with a proper physical, checkable prediction of what happens to Standard Model forces at extremely high energy. The following text is an extract from an earlier blog post here:

      ‘The pairs you get produced by an electric field above the IR cutoff corresponding to 10^18 v/m in strength, i.e., very close (<1 fm) to an electron, have direct evidence from Koltick’s experimental work on polarized vacuum shielding of core electric charge published in the PRL in 1997. Koltick et al. found that electric charge increases by 7% in 91 GeV scattering experiments, which is caused by seeing through the part of polarized vacuum shield (observable electric charge is independent of distance only at beyond 1 fm from an electron, and it increases as you get closer to the core of the electron, because you have less polarized dielectric between you and the electron core as you get closer, so less of the electron’s core field gets cancelled by the intervening dielectric).

      ‘There is no evidence whatsoever that gravitation produces pairs which shield gravitational charges (masses, presumably some aspect of a vacuum field such as Higgs field bosons). How can gravitational charge be renormalized? There is no mechanism for pair production whereby the pairs will become polarized in a gravitational field. For that to happen, you would first need a particle which falls the wrong way in a gravitational field, so that the pair of charges become polarized. If they are both displaced in the same direction by the field, they aren’t polarized. So for mainstream quantum gravity ideas work, you have to have some new particles which are capable of being polarized by gravity, like Well’s Cavorite.

      ‘There is no evidence for this. Actually, in quantum electrodynamics, both electric charge and mass are renormalized charges, with only the renormalization of electric charge being explained by the picture of pair production forming a vacuum dielectric which is polarized, thus shielding much of the charge and allowing the bare core charge to be much greater than the observed value. However, this is not a problem. The renormalization of mass is similar to that of electric charge, which strongly suggests that mass is coupled to an electron by the electric field, and not by the gravitational field of the electron (which is way smaller by many orders of magnitude). Therefore mass renormalization is purely due to electric charge renormalization, not a physically separate phenomena that involves quantum gravity on the basis that mass is the unit of gravitational charge in quantum gravity.

      ‘Finally, supersymmetry is totally flawed. What is occurring in quantum field theory seems to be physically straightforward at least regarding force unification. You just have to put conservation of energy into quantum field theory to account for where the energy of the electric field goes when it is shielded by the vacuum at small distances from the electron core (i.e., high energy physics).

      ‘The energy sapped from the gauge boson mediated field of electromagnetism is being used. It’s being used to create pairs of charges, which get polarized and shield the field. This simple feedback effect is obviously what makes it hard to fully comprehend the mathematical model which is quantum field theory. Although the physical processes are simple, the mathematics is complex and isn’t derived in an axiomatic way.

      ‘Now take the situation where you put N electrons close together, so that their cores are very nearby. What will happen is that the surrounding vacuum polarization shells of both electrons will overlap. The electric field is two or three times stronger, so pair production and vacuum polarization are N times stronger. So the shielding of the polarized vacuum is N times stronger! This means that an observer more than 1 fm away will see only the same electronic charge as that given by a single electron. Put another way, the additional charges will cause additional polarization which cancels out the additional electric field!

      ‘This has three remarkable consequences. First, the observer at a long distance (>1 fm) who knows from high energy scattering that there are N charges present in the core, will see only a 1 charge at low energy. Therefore, that observer will deduce an effective electric charge which is fractional, namely 1/N, for each of the particles in the core.

      ‘Second, the Pauli exclusion principle prevents two fermions from sharing the same quantum numbers (i.e., sharing the same space with the same properties), so when you force two or more electrons together, they are forced to change their properties (most usually at low pressure it is the quantum number for spin which changes so adjacent electrons in an atom have opposite spins relative to one another; Dirac’s theory implies a strong association of intrinsic spin and magnetic dipole moment, so the Pauli exclusion principle tends to cancel out the magnetism of electrons in most materials). If you could extend the Pauli exclusion principle, you could allow particles to acquire short-range nuclear charges under compression, and the mechanism for the acquisition of nuclear charges is the stronger electric field which produces a lot of pair production allowing vacuum particles like W and Z bosons and pions to mediate nuclear forces.

      ‘Third, the fractional charges seen at low energy would indicate directly how much of the electromagnetic field energy is being used up in pair production effects, and referring to Peter Woit’s discussion of weak hypercharge on page 93 of the U.K. edition of Not Even Wrong, you can see clearly why the quarks have the particular fractional charges they do. Chiral symmetry, whereby electrons and quarks exist in two forms with different handedness and different values of weak hypercharge, explains it.

      ‘The right handed electron has a weak hypercharge of -2. The left handed electron has a weak hypercharge of -1. The left handed downquark (with observable low energy, electric charge of -1/3) has a weak hyper charge of 1/3, while the right handed downquark has a weak hypercharge of -2/3.

      ‘It’s totally obvious what’s happening here. What you need to focus on is the hadron (meson or baryon), not the individual quarks. The quarks are real, but their electric charges as implied from low energy physics considerations, are totally fictitious for trying to understand an individual quark (which can’t be isolate anyway, because that takes more energy than making a pair of quarks). The shielded electromagnetic charge energy is used in weak and strong nuclear fields, and is being shared between them. It all comes from the electromagnetic field. Supersymmetry is false because at high energy where you see through the vacuum, you are going to arrive at unshielded electric charge from the core, and there will be no mechanism (pair production phenomena) at that energy, beyond the UV cutoff, to power nuclear forces. Hence, at the usually assumed so-called Standard Model unification energy, nuclear forces will drop towards zero, and electric charge will increase towards a maximum (because the electron charge is then completely unshielded, with no intervening polarized dielectric). This ties in with representation theory for particle physics, whereby symmetry transformation principles relate all particles and fields (the conservation of gauge boson energy and the exclusion principle being dynamic processes behind the relationship of a lepton and a quark; it’s a symmetry transformation, physically caused by quark confinement as explained above), and it makes predictions.

      ‘It’s easy to calculate the energy density of an electric field (Joules per cubic metre) as a function of the electric field strength. This is done when electric field energy is stored in a capacitor. In the ele