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SU(2)xSU(3) particle physics based on solid facts, giving quantum gravity predictions
Hubble’s law: v = dR/dt = HR. => Acceleration: a = dv/dt = d(HR)/dt = (H*dR/dt) + (R*dH/dt) = Hv + 0 = RH2. 0 < a < 6*10-10 ms-2. Outward force: F = ma. Newton’s 3rd law: equal inward reaction force (via gravitons). Since non-receding nearby masses don’t cause reaction, they cause an asymmetry, predicting gravity and in 1996 this theory predicted the ‘cosmological acceleration’ discovered in 1998.
Above: how the flux of Yang-Mills gravitational exchange radiation (gravitons) being exchanged between all the masses in the universe physically creates an observable gravitational acceleration field directed towards a cosmologically nearby or non-receding mass, labelled ’shield’. (The Hubble expansion rate and the distribution of masses around us are virtually isotropic, i.e., radially symmetric.) The mass labelled ’shield’ creates an asymmetry for the observer in the middle of the sphere, since it shields the graviton flux because it doesn’t have an outward force relative to the observer (in the middle of the circle shown), and thus doesn’t produce a forceful graviton flux in the direction of the observer according to Newton’s 3rd law (action and reaction, an empirical fact, not a speculative assumption).
Hence, any mass that is not at a vast cosmological distance (with significant redshift) physically acts as a shield for gravitons, and you get pressed towards that shield from the unshielded flux of gravitons on the other side. Gravitons act by pushing, they have spin-1. In the diagram, r is the distance to the mass that is shielding the graviton flux from receding masses located at the far greater distance R. As you can see from the simple but subtle geometry involved, the effective size of the area of sky which is causing gravity due to the asymmetry of mass at radius r is equal to the cross-sectional area of the mass for quantum gravity interactions (detailed calculations, included later in this post, show that this cross-section turns out to be the area of the event horizon of a black hole for the mass of the fundamental particle which is acting as the shield), multiplied by the factor (R/r)2, which is how the inverse square law, i.e., the 1/r2 dependence on gravitational force, occurs.
Because this mechanism is built on solid facts of expansion from redshift data that can’t be explained any other way than recession, and on experiment and observation based laws of nature such as Newton’s, it is not just a geometric explanation of gravity but it uniquely makes detailed predictions including the strength of gravity, i.e., the value of G, and the cosmological expansion rate; it is a simple theory as it uses spin-1 gravitons which exert impulses that add up to an effective pressure or force when exchanged between masses. It is quite a different theory to the mainstream model which ignores graviton interactions with other masses in the surrounding universe.
The mainstream model in fact can’t predict anything at all. It begins by ignoring all the masses in the universe except for two masses, such as two particles. It then represents gravity interactions between those two masses by a Lagrangian field equation which it evaluates by a Feynman path integral. It finds that if you ignore all the other masses in the universe, and just consider two masses, then spin-1 gauge boson exchange will cause repulsion, not attraction as we know occurs for gravity. It then ‘corrects’ the Lagrangian by changing the spin of the gauge boson to spin-2, which has 5 polarizations. This new ‘corrected’ Lagrangian with 5 tensor terms for the 5 polarizations of the spin-2 graviton being assumed, gives an always-attractive force between two masses when put into the path integral and evaluated. However, it doesn’t say how strong gravity is, or make any predictions that can be checked. Thus, the mainstream first makes one error (ignoring all the graviton interactions between masses all over the universe) whose fatally flawed prediction (repulsion instead of attraction between two masses) it ‘corrects’ using another error, a spin-2 graviton.
So one reason why the actual spin-2 gravitons don’t cause masses to repel is because the path integral isn’t just a sum of interactions between two gravitational charges (composed of mass-energy) when dealing with gravity; it’s instead a sum of interactions between all mass-energy in the universe. The reason why mainstream people don’t comprehend this is that the mathematics being used in the Lagrangian and path integral are already fairly complex, and they can’t readily include the true dynamics so they ignore them and believe in a fiction instead. (There is a good analogy with the false mathematical epicycles of the Earth-centred universe. Whenever the theory was in difficulty, they simply added another epicycle to make the theory more complex, ‘correcting’ the error. Errors were actually celebrated and simply re-labelled being ‘discoveries’ that nature must contain more epicycles.)
Some papers here,
home page here. CERN Doc Server
deposited draft preprint paper EXT-2004-007,
15/01/2004 (this is now
obsolete and can’t be updated to the revised version such as something
similar to the discussion and mathematical proof below, because CERN now only
accepts feed through arXiv.org which is blocked (even
to some string theorists who work on non-mainstream ideas) by mainstream
(M-theory) string ‘theorists’ (who have no testable predictions and no checkable
theory, and so are not theorists in a scientific sense): ‘String theory has the remarkable property
of predicting gravity.’ - Dr
Edward Witten, M-theory originator, Physics Today, April 1996. What
Witten’s claimed ‘prediction of gravity’ is, is the spin-2 graviton and it isn’t
a falsifiable prediction, unlike all the predictions made and subsequently
confirmed by the spin-1 gravity idea. To grasp Dr Woit’s assessment of the “not
even wrong” spin-2 graviton idea, try the following passage:
“For the last eighteen years particle theory has been dominated by a single approach to the unification of the Standard Model interactions and quantum gravity. This line of thought has hardened into a new orthodoxy that postulates an unknown fundamental supersymmetric theory involving strings and other degrees of freedom with characteristic scale around the Planck length. [...] It is a striking fact that there is absolutely no evidence whatsoever for this complex and unattractive conjectural theory. There is not even a serious proposal for what the dynamics of the fundamental ‘M-theory’ is supposed to be or any reason at all to believe that its dynamics would produce a vacuum state with the desired properties. The sole argument generally given to justify this picture of the world is that perturbative string theories have a massless spin two mode and thus could provide an explanation of gravity, if one ever managed to find an underlying theory for which perturbative string theory is the perturbative expansion.” – Quantum Field Theory and Representation Theory: A Sketch (2002), http://arxiv.org/abs/hep-th/0206135.
Gravity gets weaker than the inverse square over massive distances in this universe. This is because gravity is mediated by gravitons which get redshifted and thus the quanta lose energy when exchanged between masses which are receding at relativistic velocities, i.e. well apart in this expanding universe, which would reduce the effective value of G over immense distances. Additionally, from empirical facts (see the calculations below in this blog post), the mechanism of gravity depends on surrounding recession of masses around any point. This means that if general relativity is just a classical approximation to quantum gravity (due to the graviton redshift effect just explained, which implies that spacetime is not curved over cosmological distances), we have to treat spacetime as finite and not bounded, so that what you see is what you get and the universe may be approximately analogous to a simple expanding fireball.
Masses near the real ‘outer edge’ (the radial distance in spacetime which corresponds to the time of big bang, i.e. 13,700 million light-years distance) of such a fireball (remember that since gravity doesn’t act over cosmological distances due to graviton redshift when exchanged between receding masses, there is no spacetime curvature causing gravitation over such distances) get an asymmetry in the exchange of gravitons: exchanging them on one side only (the side facing the core of the fireball, where other masses are located).
Hence such masses tend to just get pushed outward, instead of suffering the usual gravitational attraction, which is of course caused by shielding of all-round graviton pressure. In such an expanding fireball where gravitation is a reaction to surrounding expansion due to exchange of gravitons, you will get both expansion and gravitation as results of the same fundamental process: exchange of gravitons. The pressure of gravitons will cause attraction (due to mutual shadowing) between masses which are relatively nearby, but over cosmological distances the whole collection of masses will be expanding (masses receding from one another) due to the momentum imparted in the process of exchanging gravitons. This prediction was put forward via the October 1996 Electronics World, two years before evidence from Perlmutter’s supernovae observations which confirmed that the universe is not decelerating contrary to the standard predictions of cosmology at that time (i.e., that the expansion of the universe looks as if there is a small positive cosmological constant - of predictable magnitude - offsetting gravitational deceleration over cosmological distances).
I’ve been preparing a Google or U-tube video about physical mechanisms, physical forces in the fireballs in the 1962 nuclear tests at high altitude (particularly the amazing films of the fireball dynamics in the Bluegill test), and exchange radiation which will make the material and figures in the post here easier to grasp. It was a study of fireball phenomenology, the break down of general relativity due to a weakening of the gravity coupling constant in an expanding universe (gravitons exchanged between relativistically receding masses - quantum gravity charges - in an expanding universe are redshifted, reducing the effective strength of gravitational interactions in proportion to amount of redshift of the gravitons and the visible light observed, since energy is related to frequency by E = hf) and the analogy to the big bang which suggested the mechanism of gravity in 1996. In an air blast wave, Newton’s 3rd law - the equality of action and reaction forces - always holds. Initially, there is extremely high pressure throughout the fireball, communicating reaction forces in spherical symmetry, i.e., the Northward portion of the shock wave exerts a net outward force equal to its pressure times its surface area, and the reaction force is found in the Southward portion of the shock wave.
But after a while, the amount of air in the shock front is so compressed that the density falls in the central region, which cools and loses pressure. Hence, the central region can no longer mediate the reaction force of the shock wave in different directions. What happens at this stage is that a negative pressure wave, directed inward towards the centre of the explosion, then develops which has lower pressures but longer duration, allowing a reaction force to be exerted. A shock wave cannot exert outward pressure (and thus force, being equal to pressure times area) without satisfying Newton’s 3rd law of action and reaction. The reversed phase of the blast wave (with pressure acting towards the point of the explosion, i.e., suction or ‘negative pressure’ - below the ambient 14.7 psi/101 kPa normal air pressure phase) is vital for maintaining Newton’s 3rd law of motion in a shock wave.
The negative pressure phase consists of an inner shell of blast with a force directed inward in response to the outward force at the shock front. This feature is vital in implosion systems used to actually cause a nuclear explosion in the first place: the implosion relies on the fact that half the force of an explosion is initially directed inward within the mass of exploding material (the inward-travelling shock wave reflects back when it reaches the centre, and the rebounded shock wave travels outward, but in the meantime it squashes very effectively anything placed at the core, like a lump of subcritical fissile material). Implosion is also a feature of the big bang:
The product rule of differentiation is: d(uv)/dx = (v*du/dx) + (u*dv/dx)
Hence the observationally based 1929 Hubble law, v = HR, differentiates as follows:
dv/dt = d(RH)/dt = (H*dR/dt) + (R*dH/dt)
The second term here, R*dH/dt, is zero because in the Hubble law v = HR the term H is a constant from our standpoint in spacetime, so H doesn’t vary as a function of R and thus it also doesn’t vary as a function of apparent time past t = R/c. In the spacetime trajectory we see as we look out to greater distances, R/t is always in the fixed ratio c, because when we see things at distance R the light from that distance has to travel that distance at velocity c to get to us, so when we look out to distance R we’re automatically looking back in time to time t = R/c seconds ago.
Hence R*dH/dt = R*dH/d[R/c] = Rc*dH/dR = Rc*0 = 0.
This is because dH/dR = 0. I.e., there is no variation of the Hubble constant as a function of observable spacetime distance R.
Thus, the acceleration of any distant, receding lump of matter as we perceive it in spacetime, is
a = dv/dt = d(RH)/dt = H*dR/dt = H*v = H*[RH] = R*H^2.
Now the outward acceleration, a, is very small. It reaches only about 6*10^{-10} ms^{-2} for the most distant receding objects. But because the mass of the receding universe is really big, that comes to an outward force on the order of say 7*10^43 Newtons. Newton’s 3rd law tells us there should be an equal and opposite reaction force. According to what is physically known about the possible particles and fields that exist, this inward reaction force might be carried by spin-1 gravitons (non-string theory gravitons; string theory hype supposes spin-2 gravitons), which cause all gravitational field and observed general relativity (contraction, etc.) effects physically by exerting pressure as a quantum field of exchange radiation.
When we calculate the universal gravitational parameter, G, by this theory we get a figure that’s good (within available experimental data). There are complexities because what counts in spacetime for graviton exchange is the observable density of the universe as a function of distance/time past, which increases towards infinity as we look back to immense distances (approaching time zero); however this massive increase in effective outward force is cancelled out by the fact that the reaction force is mediated by gravitons which are extremely redshifted from such locations where the recession velocities are very close to the velocity of light (i.e., relativistic).
One way to imagine the mechanism for why an outward-accelerating particle should fire back gravitons as a reaction force to satisfy Newton’s 3rd law of motion is very simple: walk down a corridor and observe what happens to air that vacates the region in front of you and fills in the region behind you as you walk. Or better, push a ball along while holding it underwater. There is a resistance due to motion against the water (which is a crude model for moving an electron or other object having rest mass in a graviton field in the vacuum of spacetime), which compresses the ball slightly in the direction of motion. There is then a flow of the field quanta (water in the analogy) around the particle from front to back. This flow permits things to move, and because the field flow - once set up after effort (against resistance) - has momentum, it adds inertia to the moving object. (Ships and submarines are hard to stop suddenly because they have extra momentum - not just the usual momentum, but momentum from the water field’s motion around them. This hints that the intrinsic momentum of any moving mass is due to a similar effect involving the vacuum graviton field flowing around individual fundamental particles. As Einstein pointed out, inertial and gravitational masses are indistinguishable.)
Hence, as a 70 kg (70 litre) person walks down a corridor at 1 m/s, some 70 litres of air moving at a net velocity of 1 m/s in the opposite direction flows into the void the person is vacating. (In internet discussions, some ingenious bigots claimed that when you walk, you attract air from behind which follows you to fill the volume of space you are vacating. If that were true, the air pressure along the corridor would become ever more become unequal because of (1) air becoming compressed in front of you (instead of flowing around you to fill in the void behind), and (2) air pressure being reduced still further behind you as air expands to fill in the void. This doesn’t happen. In any case, the example with water makes it clear what happens: water flows from the front to the back of a moving object.
If the object accelerates, the surrounding field responds similarly if the motion of the particles in it is adequately fast that it can respond. (Air molecules have an average velocity of only 500 m/s, but spin-1 gravitons travel at 300 Mm/s.) Hence, if you have a long line of people walking in one direction only along a corridor, you have a current flowing in that direction, which is compensated for by a net flow of the surrounding field (air) in the opposite direction. Although the individual air molecules are going at about 500 m/s, the net flow of the bulk ‘field’ composed of air is equal to the speed of the current of people moving, while the net volume of the field which is effectively flowing is equal to the volume of the people who are moving.
Similarly, when matter moves away from us in the big bang, the graviton field around that matter responds by moving in the other direction at the same time, causing the graviton reaction force as described quantitatively by Newton’s 3rd law.
I’ll insert the video into a blog post on this site in the near future, along with a free PDF download link for the accompanying book. In the meanwhile, please make do with the posts on this page, especially this, this, this, this, this, this, this, this, this, this, this, and this.
To understand why mainstream hype of unchecked stringy theory with its non-falsifiable speculative extra dimensions, multiverse/landscape, and so on are destructive, see this link. The mechanism proved in detail below does work, although it is still very much in a nascent stage. The problems are (1) that it leads to interesting applications in so many directions in physics that it absorbs a great deal of time, (2) it is extremely unpopular because “mechanisms” are sneered at out of prejudice (in favour of mechanism-less mathematical “models”) , and are regarded as being “crazy” by essentially all mainstream physicists, i.e. most professional physicists. People like LeSage and Maxwell (who developed a mechanical model of space which was flawed), with false, half-baked ideas have permanently damaged the credibility of mechanisms in fundamental physics, not to mention the metaphysical (non-falsifiable) hidden variable “interpretation” of quantum mechanics.
The absurdity of this situation is demonstrated by the fact that quantum field theory postulates gauge boson radiations being exchanged in the vacuum between charges in order to mediate force fields (i.e., causing forces), yet the attitude is to believe in this without searching for the underlying physical mechanism! It’s exactly like religion where you allowed to believe things without investigating them scientifically. Moreover, the majority of people in the world actually want to hero-worship religious beliefs in science, in place of supporting accurate, predictive physical mechanisms based on solid facts: people are today using modern physics as an alternative religion. They have (1) abandoned the search for reality, (2) lied that it is not possible to understand physics by mechanisms (it is), and (3) embarked on a campaign to censor out the facts and replace them with false speculations. Differential equations describing smooth curvatures and continuously variable fields in general relativity and mainstream quantum field theory are wrong except for very large numbers of interactions, where statistically they become good approximations to the chaotic (particle interactions) which are producing accelerations (spacetime curvatures, i.e. forces). See http://nige.wordpress.com/2007/07/04/metrics-and-gravitation/ and in particular see Fig. 1 of the post: http://nige.wordpress.com/2007/06/13/feynman-diagrams-in-loop-quantum-gravity-path-integrals-and-the-relationship-of-leptons-to-quarks/.
Think about air pressure as an analogy. Air pressure can be represented mathematically as a continuous force acting per unit area: P = F/A. However, air pressure is not a continuous force, it is due to impulses delivered by discrete random, chaotic strikes by air molecules (travelling at average speeds of 500 m/s in sea level air) against surfaces. If therefore you take a very small area of surface, you will not find a continuous uniform pressure P acting on it. Instead, you will find a series of chaotic impulses due to individual air molecules striking the surface! This is an example of how a useful mathematical fiction on large scales like air pressure, loses its accuracy if applied on small scales. It is well demonstrated by Brownian motion. The motion of an electron in an atom is subjected to the same thing simply because the small size doesn’t allow large numbers of interactions to be averaged out. Hence, on small scales, the smooth solutions predicted by mathematical models are flawed. Calculus assumes that spacetime are endlessly divisible, which is not true when calculus is used to represent a curvature (acceleration) due to a quantum field! Instead of perfectly smooth curvature as modelled by calculus, the path of a particle in a quantum field is affected by a series of discrete impulses from individual quantum interactions. The summation of all these interactions gives you something that is approximated in calculus by the “path integral” of quantum field theory. The whole reason why you can’t predict deterministic paths of electrons in atoms, etc., using differential equations is that their applicability breaks down for individual quantum interaction phenomena. You should be summing impulses from individual quantum interactions to get a realistic “path integral” to predict quantum field phenomena. The total and utter breakdown of mechanistic research in modern physics has instead led to a lot of nonsense, based on sloppy thinking, lack of calculations, and the failure to make checkable, falsifiable predictions and obtain experimental confirmation of them. The abusiveness and hatred directed towards people like myself by those “brane”-washed with failed ideas from Dr Witten et al., is not unique to modern physics. It’s a mixture of snobbish hatred of innovation based on simple ideas, and a lack of real interest in physics by people who claim to be physicists but are in fact only crackpot mathematicians.
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.
Here’s an outline of the basic ‘idea’ (actually it is well-established 100% factual evidence just assembled in a 100% new way, and it is not merely a personal idea, not a speculation, not guesswork, not a pet ‘theory’, but it is scientific fact pure and simple) behind the new mechanistic physics involved (described in detail on this page and more recent pages of this blog):
Galaxy recession velocity in spacetime (Hubble’s empirical law): v = dR/dt = HR. Acceleration: a = dv/dt = d(HR)/dt = H.dR/dt = Hv = H(HR) = RH2 so: 0 < a < 6*10-10 ms-2. Outward force: F = ma by Newton’s 2nd empirical law. Newton’s empirical 3rd law predicts equal inward force (which according to the possibilities in quantum field theory, will be carried by gravitons, exchange radiation between gravitational charges in quantum gravity): but non-receding nearby masses don’t give rise to any reaction force according to this mechanism, so they act as shields and thus cause an asymmetry, producing gravity. This predicts the strength of gravity and electromagnetism, particle physics and cosmology. In 1996 it predicted the lack of deceleration at large redshifts.
The underlying symmetry group physics which follows from this mechanism is to replace SU(2)xU(1) + Higgs sector in the Standard Model with simply a version of SU(2) where the 22 -1 = 3 gauge bosons can exist in both massless and massive forms. Some field in the vacuum (different to the Higgs field in detail, but similar in that it provides rest mass to particles) gives masses to some of each of the 3 massless gauge bosons of SU(2), and the massive versions are the massive neutral Z, charged W-, and charged W+ weak gauge bosons just as occur in the Standard Model. However, the massless versions of Z, W- and W+ are the gauge bosons of gravity, negative electromagnetic fields, and positive electromagnetic fields, respectively.
The basic method for electromagnetic repulsion is the exchange of similar massless W- gauge bosons between negative charges, or massless W+ gauge bosons between positive charges. The charges recoil apart because they get hit repeatedly by radiation emitted by the other charge. But for a pair of opposite charges, like a negative electron and positive nucleus, you get attraction because each charge can only interact with similar charges, so the effect is opposite charges on one another is to simply shadow them from radiation coming in from other charges in the surrounding universe. A simple vector force diagram (published in Electronics World in April 2003) shows that in this mechanism the magnitudes of the attraction and repulsion forces of electromagnetism are identical. The fact that electromagnetism is on the order of 1040 times as strong as gravity for fundamental charges (the precise figure depends on which fundamental charge are compared), is due to the fact that in this mechanism radiation is only exchanged between similar charges, so you get a statistical-type “random walk” vector summation across the similar charges distributed in the universe. This was also illustrated in the April 2003 Electronics World article. Because gravity is carried by neutral (uncharged) gauge bosons, it’s net force doesn’t add up this way, so it turns out that gravity is weaker than electromagnetism by a factor equal to the square root of the number of similar charges of either sign in the universe. Since 90% of the universe is hydrogen, composed of two negative charges (electron and downquark) and two positive charges (two upquarks), it is easy to make approximate calculations of such numbers, using the density and size of the universe.
Obviously, massless charged radiation is a non-starter in classical physics because it won’t propagate due to it’s magnetic self-inductance; however for Yang-Mills theory (exchange radiation causing forces) this objection doesn’t hold because the transit of similar radiation in two opposite directions along a path at the same time cancels out the magnetic field vectors, allowing propagation. In a different context, we see this effect every day in normal electricity, say computer logic signals (Heaviside signals), which require two conductors each carrying charged currents flowing in opposite directions to enable a signal (or pulse, or logic step, or net energy flow) to propagate: the magnetic fields of each charged current (one on each conductor in the pair of conductors) cancel one another out, preventing the infinite self-inductance problem and thus allowing propagation of charged energy currents. Thus the analogy of electricity propagating in a pair of conductors when a switch is closed shows how charged exchange radiation works.
Abstract
The objective is to unify the Standard Model and General Relativity with a causal mechanism for gauge boson mediated forces which makes checkable predictions. In very brief outline, Hubble recession: v = HR = dR/dt, so dt = dR/v, hence outward acceleration a = dv/dt = d[HR]/[dR/v] = vH = RH2 and outward force F = ma ~ 1043 Newtons. Newton’s 3rd law implies an inward force, which from the possibilities available seems to be carried by gauge boson radiation (gravitons), which predicts gravitational curvature, other fundamental forces, cosmology and particle masses. Non-receding (local) masses don’t cause a reaction force, because they don’t present an outward force, so they act as a shield and cause an asymmetry that we experience as the attraction effect of gravity: see Fig. 1.
The symmetrical inward pressure of graviton radiation (see Fig. 2) exerts a pressure on masses (acting on masses, i.e., what is referred to as ‘Higgs field quanta’, which act on the interaction cross-sectional areas of fundamental particles, and not on the macroscopic surface area of a planet) which causes the gravitational contraction predicted by general relativity, i.e., Earth’s radius is contracted by (1/3)MG/c2 = 1.5 mm by this graviton exchange radiation hitting masses, imparting momentum p = E/c, and then reflecting back (in the process causing another impulse on the mass, by the recoil effect, equal to p = E/c, so that the total imparted momentum is obviously p = 2E/c). (This ‘reflection’ is not the literal mechanism, because although a ball thrown against a wall can bounce back, a photon ‘reflected’ from a mirror actually undergoes a complex series of interactions, the sum of which (or path integral) is merely equivalent to a simple reflection: the photon is absorbed by the mirror and a new photon then gets emitted. Similarly with gauge boson radiations, the interactions involved are far more complex in detail than a simple reflection, although that is a useful approximation to the total process, under some circumstances.) Applying this contraction to motions, we find that the same behaviour of the gravitational field causes inertial force which resists acceleration, because of Einstein’s equivalence principle whereby inertial mass = gravitational mass!
To understand the picture of writing the Hubble expansion rate as an expansion in a time dimension, think of time (age of universe) as 1/Hubble constant (until 1998 it was assumed to be 0.67/Hubble constant with the 2/3 factor due to gravitational deceleration, but that gravitational deceleration was debunked by supernovae observations made by Perlmutter and published in Nature that year; so either gravitons are redshifted over large cosmological distances and lose energy by E = hf, being thus unable to slow down the expansion of the universe, or else there is some “dark energy” which produces an outward acceleration that offsets the inward acceleration of gravity).
If the Hubble constant was different in different directions, the age of the universe, 1/H, would be different in different directions. Hence the isotropy of the big bang we observe around us: there are three effective time dimensions, each corresponding to an expanding spatial dimension. (The redshift of radiation exchanged between receding masses in an expanding universe prevents thermal equilibrium being established, and therefore provides an endless heatsink.) Because of the isotropy, we see the 3 effective time dimensions as always being equal, so they are identical and can be represented by SO(3,1), hence we observe effectively 4 different dimensions including one of time and 3 of space.
Lunsford (discussed and cited below) has proved that the 3 spatial and 3 time dimension spin orthagonal group, SO(3,3) unifies gravity and electrodynamics correctly without the reducible problems of the old Kaluza-Klein unification. I’ve shown that this is reasonable because 3 spatial dimensions are contracted by gravity in general relativity (for example, in general relativity the Earth’s radius is contracted by the amount 1.5 millimetres), while 3 time dimensions are continuously expanding: this means that the Hubble expansion should be written in terms of velocity as a function of time, not distance:
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. So we have a real outward acceleration in Hubble’s law!
We then use Newton’s 2nd empirical law F=ma to estimate outward force of big bang, and then his 3rd empirical law to estimate the inward recation force carried by gauge bosons exchanged between local and distant receding masses. This makes quantum gravity quantitative and we can calculate the strength of gravity and lots of other things from the resulting mechanism. This post concentrates on gravity’s mechanism.
The Physical Relationship between General Relativity and Newtonian gravity
(1) Newtonian gravity
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, or as a variation of velocity with respect to time past, 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.
Radial distance elements are equal for the Hubble recession in all directions around us,
H = dv/dr = dv/dx = dv/dy = dv/dz
implying
t(age of universe), 1/H = dr/dv = dx/dv = dy /dv = dz/dv
implying
dv/H = dr = dx = dy = dx
1/H is a way to measure the age of the universe. If the universe were at critical density and being gravitationally slowed down with no cosmological constant to offset this gravity effect by providing repulsive long range force and an outward acceleration to cancel out the gravitational inward deceleration assumed by the mainstream (i.e., the belief until 1998), then the age of the universe would be (2/3)/H where 2/3 is the compensation factor for gravitational retardation.
This makes spacetime easier to understand and allows a new unification scheme! The expanding universe has three orthagonal expanding time-like dimensions (we usually refer to astronomical dimensions in time units like ‘lightyears’ anyway, since we are observing the past with increasing distance, due to the travel time of light) in addition to three spacetime dimensions describing matter. Surely this contradicts general relativity? No, because all three time dimensions are usually equal, and so can be represented by a single time element, dt, or its square. To do this, we take dr = dx = dy = dz and convert them all into time-like equivalents by dividing each distance element by c, giving:
(dr)/c = (dx)/c = (dy)/c = (dz)/c
which can be written as:
dtr = dtx = dty = dtz
So, because the age of the universe (ascertained by the Hubble parameter) is the same in all directions, all the time dimensions are equal! This is why we only need one time to describe the expansion of the universe. If the Hubble expansion rate was found to be different in directions x, y and x, then the age of the universe would appear to be different in different directions. Fortunately, the age of the universe derived from the Hubble recession seems to be the same (within observational error bars) in all directions: time appears to be isotropic! This is quite a surprising result as some hostility to this new idea from traditionalists shows.
But the three time dimensions which are usually hidden by this isotropy are vitally important! Replacing the Kaluza-Klein theory, Lunsford has a 6-dimensional unification of electrodynamics and gravitation which has 3 time-like dimensions and appears to be what we need. It was censored off arXiv after being published in a peer-reviewed physics journal, “Gravitation and Electrodynamics over SO(3,3)”, International Journal of Theoretical Physics, Volume 43, Number 1 / January, 2004, Pages 161-177, which can be downloaded here. The mass-energy (i.e., matter and radiation) has 3 spacetime which are different from the 3 cosmological spacetime dimensions: cosmological spacetime dimensions are expanding, while the 3 spacetime dimensions are bound together but are contractable in general relativity. For example, in general relativity the Earth’s radius is contracted by the amount 1.5 millimetres.
This sorts out ‘dark energy’ and predicts the strength of gravity accurately within experimental data error bars, because when we rewrite the Hubble recession in terms of time rather than distance, we get acceleration which by Newton’s 2nd empirical law of motion (F = ma) implies an outward force of receding matter, which in turn implies by Newton’s 3rd empirical law of motion an inward reaction force which - it turns out - is the mechanism behind gravity.
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 - spin 1 gravitons which cause attraction by simply pushing things as this allows predictions as we 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.)
This prediction doesn’t strictly demand perfect integers to be observable, because it’s possible that effects like isotopes to exist, where the different individuals of the same type of meson or baryon can be surrounded by different integer numbers of Higgs field quanta, giving non-integer average masses. (The number would be likely to actually change during a high-energy interaction, where particles are broken up.)
The early attempts of Dalton and others to work out an atomic theory were regularly criticised and even ridiculed by the fact that the measured mass of chlorine is 35.5 times the mass of hydrogen, i.e., nowhere near an integer! Here is a summary of the rules:
If a particle is a baryon, it’s mass should in general be close to an integer when expressed in units of 105 MeV (3/2 multiplied by the electron mass divided by alpha: 1.5*0.511*137 = 105 MeV).
If it is a meson, it’s mass should in general be close to an integer when expressed in units of 70 MeV (2/2 multiplied by the electron mass divided by alpha: 1*0.511*137 = 70 MeV).
If it is a lepton apart from the electron (the electron is the most complex particle), it’s mass should in general be close to an integer when expressed in units of 35 MeV (1/2 multiplied by the electron mass divided by alpha: 0.5*0.511*137 = 35 MeV).
This scheme has a simple causal mechanism in the quantization of the ‘Higgs field’ which supplies mass to fermions and bosons. By itself the mechanism just predicts that mass comes in discrete units, depending on how strong the polarized vacuum is in shielding the fermion core from the Higgs field quanta.
To predict specific masses (apart from the fact they are likely to be near integers if isotopes don’t occur), regular QCD ideas can be used. This prediction doesn’t replace lattice QCD predictions, it just suggests how masses are quantized by the ‘Higgs field’ rather than being a continuous variable.
Every mass apart form the electron is predictable by the simple expression: mass = 35n(N+1) MeV, where n is the number of real particles in the particle core (hence n = 1 for leptons, n = 2 for mesons, n = 3 for baryons), and N is is the integer number of ‘Higgs field’ quanta giving mass to that fermion (lepton or baryon) or meson (boson) core.
From analogy to the shell structure of nuclear physics where there are highly stable or ‘magic number’ configurations like 2, 8 and 50, and we can use n = 1, 2, and 3, and N = 1, 2, 8 and 50 to predict the most stable masses of fermions besides the electron, and also the masses of bosons (mesons):
For leptons, n = 1 and N = 2 gives the muon: 35n(N+1) = 105 MeV.
For mesons, n = 2 and N = 1 gives the pion: 35n(N+1) = 140 MeV.
For baryons, n = 3 and N = 8 gives nucleons: 35n(N+1) = 945 MeV.
For leptons, n = 1 and N = 50 gives tauons: 35n(N+1) = 1785 MeV.
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: statistically, 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.
Plus, in particular:
‘All charges are surrounded by clouds of virtual photons, which spend part of their existence dissociated into fermion-antifermion pairs. The virtual fermions with charges opposite to the bare charge will be, on average, closer to the bare charge than those virtual particles of like sign. Thus, at large distances, we observe a reduced bare charge due to this screening effect.’ – I. Levine, D. Koltick, et al., Physical Review Letters, v.78, 1997, no.3, p.424.
(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 91 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.’
– Dr Tim Poston and Dr Ian Stewart, ‘Rubber Sheet Physics’ (science article) in Analog: Science Fiction/Science Fact, Vol. C1, No. 129, Davis Publications, New York, November 1981.
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 (discussed by Feynman in the video here). 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.
(Consider motion in the Dirac sea, which is incompressible owing to the Pauli exclusion principle: all states are filled: this predicted antimatter successfully. Nobody wants to hear of modelling physical effects of particles moving in the Dirac sea. Why? A good analogy is the particle-and-hole theory used in semiconductor electronics, solid state physics. Now plug in cosmology: both positive and negative real charges are streaming away from us in all directions. Hence virtual charges in the Dirac sea will stream inward. Moving fermions can’t occupy the same space as virtual fermions, they get shoved out of the way due to the Pauli exclusion principle. It is pretty obvious to anyone that the outward force of matter in the expanding universe is balanced by equal inward Dirac sea force, according to Newton’s 3rd law. Similarly, in a a corridor, a person of 70 litre volume moving at velocity v is compensated for by 70 litres of fluid air moving at velocity -v, or the same speed but in the opposite direction to the person’s motion. This is pretty obvious because if the surronding fluid didn’t displace around the person to fill in the volume they are vacating, there would be a vacuum left behind them and the 14.7 psi air pressure in front would exert 144*14.7 ~ 2,100 pounds of pressure per square foot of the person which would prevent the person being able to walk. It is absolutely crucial for the person that air is a fluid which flows around and fills in the space being vacated behind. The lack of this mechanism explains why you need to apply substantial force to remove large suction plungers from smooth surfaces against air pressure. However, to my cost, I have found that this argument using the air pressure analogy or Dirac sea analogy is fruitless. Mainstream crackpots claim that it is all wrong and by deliberately misunderstanding the analogy they can create endless rows which have nothing to do with the point, the gravitational mechanism. As an analogy to this misunderstanding of a simple point, think about Feynman’s remark that energy was misunderstood even by the author of physics school textbook who claimed that ‘energy’ makes everything go. Taking up Feynman’s argument, if you calculate the energy of the air in your room, the air molecules have a mean velocity of about 500 m/s, and there is 1.2 kg of air per cubic metre of your room. Let’s say you are in a small room with 10 cubic metres of air in it, 12 kg of air. The kinetic energy that air possesses is half the mass multiplied by the square of the mean speed, i.e., 1.5 MJ. However, that ‘energy’ is useless to you unless you have a way of extracting it. You can’t power your laptop from the energy of air pressure and temperature! You could of course use it like a battery if you had a big vacuum chamber with a fan powering a generator at a hole in the wall of the vacuum chamber, so that the in-rushing air would turn the fan and generate electricity. But the power it takes to create such a vacuum is more than the energy you can possibly get out of the collapsing vacuum. So the simple idea of ‘energy’ is misleading to mainstream crackpots. What counts is not gross energy, but usable energy! This is why most of the gauge boson radiation energy has nothing to do with the energy we use. Because the gauge boson radiation energy, such as ‘gravitons’, comes from all directions, most of it is not useful energy and cannot do work. Only the small asymmetries in it result in work, by creating the fundamental forces we experience!)
‘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/ 
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