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Predicted Force Strengths and All Nuclear Particle Masses from a Causal Mechanism
Nigel Cook
SUMMARY OF RESULTS PROVING CAUSALITY
H = 16
p 2Gme2mprotonc3 e 2/(qe4e2.7…3) = 2.3391 x 10-18 s-1 or 72.2 km.s-1Mpc-1, so 1/H = t = 13.55 Gyr.r
= 192p 3Gme4mproton2c6 e 4/(qe8e2.7…9) = 9.7455 x 10-28 kg/m3.Heisenberg’s uncertainty (based on impossible gamma ray microscope thought experiment): pd = h/(2.Pi), where p is uncertainty in momentum and d is uncertainty in distance. The product pd is physically equivalent to Et, where E is uncertainty in energy and t is uncertainty in time. Since, for light speed, d = ct, we obtain: d = hc/(2.Pi.E). This is the formula the experts generally use to relate the range of the force, d, to the energy of the gauge boson, E.Notice that both d and E are really uncertainties in distance and energy, rather than real distance and energy, but the formula works for real distance and energy, because we are dealing with a definite ratio between the two. Hence for 80 GeV mass-energy W and Z intermediate vector bosons, the force range is on the order of 10^-17 m.Since the formula d = hc/(2.Pi.E) therefore works for d and E as realities, we can introduce work energy as E = Fd, which gives us the strong nuclear force law: F = hc/(2.Pi.d^2). The range of this force is of course d = hc/(2.Pi.E).
The vacuum is full of 'virtual' particles - particles that we feel only as forces such as inertial resistance to acceleration, nuclear confinement of charged particles, electromagnetism and gravity.
Aound any particle core some of these particles will be attracted, forming a polarised veil which acts like a dielectric, shielding the charge of the core. Electron cores tend to attract virtual positrons, leaving behind an outer zone of virtual electrons. This shields the real electron core charge by a factor of 137, the 'magic number' of QED. For the massive quarks, you get virtual quark pairs polarising around them. This limits the range of the colour charge of quantum chromodynamics. Gravity is just the shielding of a background pressure of the virtual particles in the vacuum. Because all energy has speed c, as per Einstein's E=mc^2, gravity goes at c.
We can visualise an emerging unified force as a progressive shielding effect by the polarised vacuum on the particle core. The strong nuclear force is the basic force, and gets progressively filtered down by the polarised virtual charges of the vacuum around the particle core until we get through electromagnetism, weak force, and finally gravity. No extra dimensions!
‘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.
Dr Peter Woit has very interesting ideas on the problem of the actual particles themselves: http://www.arxiv.org/abs/hep-th/0206135
Traditionally, the ‘delta-double-plus’ particle is used to justify the existence of three types of quark charge, which are referred to arbitrarily as ‘colours’. This was proposed because the delta-double-plus contains identical three quarks spinning the same way, which violates the Pauli exclusion principle (which prohibits two or more particles from having the same set of quantum numbers, which include spin). This appears to be correct because the mechanism for the Pauli exclusion principle may be linked to the intrinsic magnetism of spinning charged particles forcing adjacent particles to be paired up with opposite spin (however, there are problems to be resolved). According to quantum chromodynamics (QCD, the analogy to quantum electrodynamics, QED) any proton contains one green, one red, and one blue quark, making the proton as a whole colourless, the nuclear force equivalent of an atom with equal positive and negative charge. The three quarks also have electric charges of +2/3, +2/3 and –1/3 (two upquarks and one downquark), so the net electric charge is +1. The strong force depends on the colour charge, which is short ranged and operates somewhat like the short-range ‘Van der Waals force’ of chemistry that binds some electrically neutral atoms together. (This is really a geometric effect of the locations of the shells of charge with can be polarised to allow a net electromagnetic force to be felt over short distances.) While the QED force is mediated by photons, the QCD force is mediated by ‘gluons’, of which 8 different types exist. Gluons attract (or shield) each other as well as the quarks. There is also a field of other virtual particles around each quark, just as there is a field of ‘virtual’ fermions around an electron, which partly shield the charge of the core. Colour charge has very indirect evidence. While it is a fine example of how usefully predictive ad hoc modifications can be made to physics, it is crass to take it as evidence discrediting causality. A clearer illustration is to consider the weak nuclear force, which has been unified with the electromagnetic force. QCD may similarly be unified with electro-weak force when more is known. The problem with colour charge is that it is vague with respect to which of the two otherwise-identical upquarks in a proton has which colour and why: colour charge is not a fundamental property like electric charge. Is it real, or just a useful corrective epicycle for some more subtle physics?
(Dr Leonard Susskind is quoted in a recent issue of New Scientist suggesting that the Casimir force reality issue should be solved by banning physicists from using the word ‘real’, which is kind of sweet, useful to him and other string theorists! While you are about it, why also not ‘ban’ all physics experiments and people that might possibly damage string theory? Dr D.R. Lunsford objects in English and also in Latin.)
The physical mechanism does give rise to a lot of mathematics, but not the same type of useless mathematics that ‘string theory’ generates. Because ‘string theory’ falsely is worshipped as a religion, naturally the productive facts are ridiculed. The accurate predictions include the strengths of gravity, electroweak and strong nuclear forces, as well as solutions to the problems of cosmology and the correct ratios of some fundamental particles. Feynman correctly calculates the huge ratio of gravity attraction force to the repulsive force of electromagnetism for two electrons as 1/(4.17 x 1042 ). He then says: ‘It is very difficult to find an equation for which such a fantastic number is a natural root. Other possibilities have been thought of; one is to relate it to the age of the universe.’ He then says that the ratio of the time taken by light to cross the universe to the time taken by light to cross a proton is about the same huge factor. After this, he chucks out the idea because gravity would vary with time, and the sun’s radiating power varies as the sixth power of the gravity constant G. The error here is that there is no mechanism for Feynman’s idea about the times for light to cross things. Where you get a mechanism is for the statistical addition of electric charge (virtual photons cause electric force) exchanged between similar charges distributed around the universe. This summation does not work in straight lines, as equal numbers of positive and negative charges will be found along any straight line. So only a mathematical drunkard’s walk, where the net result is the charge of one particle times the square root of the number of particles in the universe, is applicable: http://members.lycos.co.uk/nigelbryancook/Image11.jpg.
This means that the electric force is equal to gravity times the square root of the number of particles. Since the number of particles is effectively constant, the electric force varies with the gravity force! This disproves Feynman: suppose you double the gravity constant. The sun is then more compressed, but does this mean it releases 26 = 64 times more power? No! It releases the same. What happens is that the electric force between protons – which is called the Coulomb barrier – increases in the same way as the gravity compression. So the rise in the force of attraction (gravity) is offset by the rise in the Coulomb repulsion (electric force), keeping the proton fusion rate stable! However, Feynman also points out another effect, that the variation in gravity will also alter the size of the Earth’s orbit around the sun, so the Earth will get a bit hotter due to the distance effect if G rises, although he admits: ‘such arguments as the one we have just given are not very convincing, and the subject is not completely closed.’ Now the smoothness of the cosmic background radiation is explained by the lower value of G in the past (see discussion of the major predictions, further on). Gravity constant G is directly proportional to the age of the universe, t. Let’s see how far we get playing this game (I’m not really interested in it, but it may help to test the theory even more rigorously). The gravity force constant G and thus t are proportional to the electric force, so that if charges are constant, the electric permittivity varies as ‘1/t’, while the magnetic permeability varies directly with t. By Weber and Maxwell, the speed of light is c =1/(square root of the product of the permittivity and the permeability). Hence, c is proportional to 1/ [square root of {(1/t).(t)}] = constant. Thus, the speed of light goes NOT vary in any way with the age of the universe. The strong nuclear force strength, basically F = hc/(2p
d2 ) at short distances, is varying like gravity and electroweak forces, results in the implication that h is proportional to G and thus also to t.
Many ‘tests’ for variations in G assume that h is a constant. Since this is not correct, and G is proportional to h, the interpretations of such ‘tests’ are total nonsense, much as the Michelson-Morley experiment does not disprove the existence of the sea of gauge bosons that cause fundamental forces! At some stage this model will need to be applied rigorously to very short times after the big bang by computer modelling. For such times, the force ratios vary not merely because the particles of matter have sufficient energy to smash through the shielding veils of polarised virtual particles which surround the cores of particles, but also because the number of fundamental particles was increasing significantly at early times! Thus, soon after the big bang, the gravity and electromagnetic forces would have been similar. The strong nuclear force, because it is identical in strength to the unshielded electroweak force, would also have been the same strength because the energy of the particles would break right through the polarised shields. Hence, this is a unified force theory that really works! Nature is beautifully simple after all. Lunsford’s argument that gravity is a residual of the other forces is right.
Predicted masses of all nuclear particles
The problem is that people are used to looking to abstruse theory due to the success of QFT in some areas, and looking at the data is out of fashion. If you look at history of chemistry there were particle masses of atoms and it took school teachers like Dalton and a Russian to work out periodicity, because the bigwigs were obsessed with vortex atom maths, the ‘string theory’ of that age. Eventually, the obscure school teachers won out over the mathematicians, because the vortex atom (or string theory equivalent) did nothing, but empirical analysis did stuff. It was eventually explained theoretically!
There was a crude empirical equation for their masses by A.O. Barut, PRL, v. 42 (1979), p. 1251. We can extend the basic idea to hadrons. The muon is 1.5 units on this scale but this is heuristically explained by a coupling of the core (mass 1) with a virtual particle, just as the electron couples increasing its magnetic moment to about 1 + 1/(2.Pi.137). The mass increase of a muon is 1 + 1/2 because Pi is due to spin and the 137 shielding factor doesn’t apply to bare particles cores in proximity, as it is due to the polarised vacuum veil at longer ranges. This is why unification of forces is approached with higher energy interactions, which penetrate the veil. This idea predicts that a particle core with n fundamental particles (n=1 for leptons, n = 2 for mesons, and obviously n=3 for baryons) coupling to N virtual vacuum particles (N is an integer) will have an associative inertial mass of Higgs bosons of: (0.511 Mev).(137)n(N + 1)/2 = 35n(N +1) Mev.
Accuracy tested against data for mass of muon and all ‘long-lived’ hadrons:
LEPTON (n=1)
Muon (N=2): 105 Mev (105.66 Mev measured), 0.6% error!
HADRONS
Mesons (contain n=2 quarks):
Pions (N=1): 140 Mev (139.57 and 134.96 actual), 0.3% and 3.7% errors!
Kaons (N=6): 490 Mev (493.67 and 497.67 actual), 0.7% and 1.6% errors!
Eta (N=7): 560 Mev (548.8 actual), 2% error!
Baryons (contain n=3 quarks):
Nucleons (N=8): 945 Mev (938.28 and 939.57 actual), 0.7% and 0.6% errors!
Lambda (N=10): 1155 Mev (1115.60 actual), 3.5% error!
Sigmas (N=10): 1155 Mev (1189.36, 1192.46, and 1197.34 actual), 3.0%, 3.2% and 3.7% errors!
Xi (N=12): 1365 Mev (1314.9 and 1321.3 actual), 3.8% and 3.3% errors!
Omega (N=15): 1680 Mev (1672.5 actual), 0.4% error!
The mechanism is that the charge of the bare electron core is 137 times the Coulomb (polarisation-shielded) value, so vacuum interactions of bare cores of fundamental particles attract 137 times as much virtual mass from the vacuum, increasing the inertia similarly. It is absurd that these close fits, with only a few percent deviation, are random chance, and this can be shown by statistical testing using random numbers as the null hypothesis. So there is empirical evidence that this heuristic interpretation is on the right lines, whereas the ‘renormalisation’ is bogus: http://www.cgoakley.demon.co.uk/qft/
INTRODUCTION
Gravity is the effect of inward directed graviton radiation pressure of the inflow of the fabric of spacetime inwards to fill the volume left empty by the outward acceleration of galaxies in the big bang. LeSage-Feynman shadowing of the spacetime fabric – which is a light velocity radiation on the 4 dimensional spacetime we observe – pushes us downward. You can’t stop space with an umbrella, as atoms are mainly void through which space pressure propagates!
Newton’s 3rd empirical law states outward force has an equal and opposite reaction (inward or implosive force). The bomb dropped on Nagasaki used TNT around plutonium, an ‘implosion’ bomb. Half the force acted inward, an implosion that compressed the plutonium. The inward or implosion force of the big bang is apparently physical space pressure. Fundamental particles behave as small black holes (electrons, quarks) which shield space pressure. They are therefore pressed from all sides equally except the shielded side, so they are pushed towards masses. The proof (below) predicts gravity. A calculation using black hole electrons and quarks gives identical results.
This inward pressure makes the radius of the earth contract by a distance of 1.5-mm. This was predicted by Einstein’s general relativity, which Einstein in 1920 at Leyden University said proved that: ‘according to the general theory of relativity, space without ether [physical fabric] is unthinkable.’ The radius contraction, discussed further down this page, is GM/(3c2). (Professor Feynman makes a confused mess of it in his relevant volume of Lectures, c42 p6, where he gives his equation 42.3 correctly for excess radius being equal to predicted radius minus measured radius, but then on the same page in the text says ‘… actual radius exceeded the predicted radius …’ Talking about ‘curvature’ when dealing with radii is not helpful and probably caused the confusion. The use of Minkowski light ray diagrams and string ‘theory’ to obfuscate the cause of gravity with talk over ‘curved space’ stems to the false model of space by the surface of a waterbed, in which heavy objects roll towards one another. This model when extended to volume type, real, space shows that space has a pressurised fabric which is shielded by mass, causing gravity.) But despite this insight, Einstein unfortunately overlooked the Hubble acceleration problem and failed to make the link with the big bang, the mechanism of gravity, which is proved below experimentally with step by step mathematics. The gravitational contraction is radial only, not affecting the circumference, so there a difference between the true radius and that calculated by Euclidean geometry. Thus curved space using non-Euclidean geometry, or you can seek the physical basis of the pressure in the surrounding universe.
There is strong evidence from electromagnetic theory that every fundamental particle has black-hole properties. The effective shielding radius of a black hole of mass M is equal to 2GM/c2. A shield, like the planet earth, is composed of very small, sub-atomic particles. The very small shielding area per particle means that there will be an insignificant chance of the fundamental particles within the earth ‘overlapping’ one another by being directly behind each other. The total shield area is therefore directly proportional to the total mass: the total shield area is equal to the area of shielding by 1 fundamental particle, multiplied by the total number of particles. (Newton showed that a spherically symmetrical arrangement of masses, say in the earth, by the inverse-square gravity law is similar to the gravity from the same mass located at the centre, because the mass within a shell depends on its area and the square of its radius.) The earth’s mass in the standard model is due to particles associated with up and down quarks: the Higgs field. From the illustration above, the total outward force of the big bang, (total outward force) = ma = (mass of universe).(Hubble acceleration, see below), while the gravity force is the shielded inward reaction (by Newton’s 3rd law the outward force has an equal and opposite reaction): F = (total outward force).(cross-sectional area of shield projected to radius R) / (total spherical area with radius R). The cross-sectional area of shield projected to radius R is equal to the area of the fundamental particle (
p multiplied by the square of the radius of the black hole of similar mass), multiplied by the (R/r)2 which is the inverse-square law for the geometry of the implosion. The total spherical area with radius R is simply four times p, multiplied by the square of R. Inserting simple Hubble law results c = RH and R/c = 1/H give us F = (4/3)p r G2M2/(Hr)2. We then set this equal to F=Ma and solve, getting G = (3/4)H2/(p r ). When the effect of the higher density in the local universe at the great distance R is included, this becomes G = (3/4)H2/(p r (local) e3), which is accurate and identical to that obtained in the older analysis.
Evidence of black-hole properties of fundamental particles.
Maxwell’s classical electromagnetism was first found to be hard to reconcile with quantum theory by Planck. Bohr later proposed that the classical theory of Maxwell should co-exist with quantum theory, without any endeavour to discover and correct whatever error there might be in Maxwell’s equations. For this reason, the substance of Maxwell’s differential equations of classical electromagnetism has remained intact over the years although Heaviside, in 1893, expressed them in vector calculus, and Einstein expressed them in six-vector form (for compatibility with general relativity) in 1916. In 1978, Catt, Davidson and Walton published a paper showing that the central innovation made by Maxwell, the ‘extra current’ required for continuity of current in charging and discharging capacitors with a vacuum insulator, is not a true continuous differential equation, but quantum leaps, or a stepwise variation. This results from the fact that energy charges up the capacitor at light speed for the insulator, spreading across the capacitor plates and reflecting back to collide with more in-flowing energy. Each collision nearly doubles the voltage as a discrete jump on each reflection passage. Maxwell’s model wrongly ignores the energy flowing along the capacitor plates (it is based on a false model to explain the charging of a capacitor by means of a mechanical space filled with idler wheels and gear cogs). The problem was eventually highlighted by ‘glitches’ due to cross-talk (mutual inductance) in high-speed digital computers during the 1960s, and the solution was discovered in 1978. The proof that charge in a ‘static’ charged capacitor is light-speed reciprocating electromagnetic energy implies that the charge of the electron and proton is composed of such energy, implying a light speed energy model for fundamental charges which makes testable predictions for the strength of gravity and electromagnetism, confirmed experimentally.
Next: for mass continuity, dr/dt = -Ñ.(rv) = -3rH. Hence, r = rlocal e3 (early visible universe has higher density). The reason for multiplying the local measured density of the universe up by a factor of about 20 (the number e3 , the cube of the base of natural logarithms) is because it is the denser, more distant universe which contains most of the mass which is producing most of the inward pressure. Because we see further back in time with increasing distance, we see a more compressed age of the universe. Gravitational push comes to us at light speed, with the same velocity as the visible light that shows the stars. Therefore we have to take account of the higher density at earlier times. What counts is what we see, the spacetime in which distance is directly linked to time past, not the simplistic picture of a universe at constant density, because we can never see or experience gravity from such a thing due to the finite speed of light. The mass continuity equation d
r/dt = -Ñ.(rv) is simple hydrodynamics based on Green’s theorem and allows the Hubble law (v = HR) to be inserted and solved. An earlier method of calculation for this the notes of CERN preprint EXT-2004-007, is to set up a formula for the density at any particular time past, so as to calculate red-shifted contributions to inward spacetime fabric pressure from a series of shells surrounding the observer. This is the same as the result r = rlocal e3.
Notice that the big bang recession velocity rises with observed distance. We always see the sun 8.3 minutes ago, the next nearest stars over 4 years ago and so on. But because of recession during this travel time, the observed distance is not the real distance (which increases while the light is on the way to us!). All we can directly work out is the time in the past when the light was emitted (hence distances expressed as light years). Edwin Hubble, 1929, claimed to observe constant ‘speed/distance’ or 1/time. In fact, he should have reported constant ‘observed speed/observed time past’ or acceleration of the big bang. Therefore from Newton’s 2nd empirical law (mass times acceleration is force) the big bang is a real explosion with a force of 7 x 1043 Newtons. Now examine the consequences of Hubble’s serious error.
Georges Louis LeSage, between 1747-82, explained gravity classically as a shadowing effect of space pressure by masses. The speculative, non-quantitative mechanism was published in French and is available online (G.L. LeSage, Lucrece Newtonien, Nouveaux Memoires De L’Academie Royal de Sciences et Belle Letters, 1782, pp. 404-31). Because gravity depends on the mass within the whole earth’s volume, LeSage predicted that the atomic structure was mostly void, a kind of nuclear atom which was confirmed by Rutherford’s work in 1911. LeSage argued that there is some kind of pressure in space, and that masses shield one another from the space pressure, thus being pushed together by the unshielded space pressure on the opposite side. Feynman explained that the major advance of general relativity, the contraction term, shortens the radius of every mass. He does not derive the equation, but we will do so below.
The velocity needed to escape from the gravitational field of a mass (ignoring atmospheric drag), beginning at distance x from the centre of mass, by Newton’s law will be v = (2GM/x)1/2, so v2 = 2GM/x. The situation is symmetrical; ignoring atmospheric drag, the speed that a ball falls back and hits you is equal to the speed with which you threw it upwards (the conservation of energy). Therefore, the energy of mass in a gravitational field at radius x from the centre of mass is equivalent to the energy of an object falling there from an infinite distance, which by symmetry is equal to the energy of a mass travelling with escape velocity v. By Einstein’s principle of equivalence between inertial and gravitational mass, this gravitational acceleration field produces an identical effect to ordinary motion. Therefore, we can place the square of escape velocity (v2 = 2GM/x) into the Fitzgerald-Lorentz contraction, giving g = (1 – v2/c2)1/2 = [1 – 2GM/(xc2)]1/2. However, there is an important difference between this gravitational transformation and the usual Fitzgerald-Lorentz transformation, since length is only contracted in one dimension with velocity, whereas length is contracted equally in 3 dimensions (in other words, radially outward in 3 dimensions, not sideways between radial lines!), with spherically symmetric gravity. Using the binomial expansion to the first two terms of each:
Fitzgerald-Lorentz contraction effect: g = x/x0 = t/t0 = m0/m = (1 – v2/c2)1/2 = 1 – ˝v2/c2 + ...
Gravitational contraction effect: g = x/x0 = t/t0 = m0/m = [1 – 2GM/(xc2)]1/2 = 1 – GM/(xc2) + ...,
where for spherical symmetry ( x = y = z = r), we have the contraction spread over three perpendicular dimensions not just one as is the case for the FitzGerald-Lorentz contraction: x/x0 + y/y0 + z/z0 = 3r/r0. Hence the radial contraction of space around a mass is r/r0 = 1 – GM/(xc2) = 1 – GM/[(3rc2]
Therefore, clocks slow down not only when moving at high velocity, but also in gravitational fields, and distance contracts in all directions toward the centre of a static mass. The variation in mass with location within a gravitational field shown in the equation above is due to variations in gravitational potential energy. The contraction of space is by (1/3) GM/c2. This is the 1.5-mm contraction of earth’s radius Feynman obtains, as if there is pressure in space. An equivalent pressure effect causes the Lorentz-FitzGerald contraction of objects in the direction of their motion in space, similar to the wind pressure when moving in air, but without viscosity. Feynman was unable to proceed with the LeSage gravity and gave up on it in 1965. However, we have a solution.
The big bang causes an outward force (Newton’s 2nd law) that results in an equal inward force (Newton’s 3rd law) which causes gravity as an inward force, Higgs field pressure. Where partially shielded by mass, the inward pressure causes gravity. Apples are pushed downwards towards the earth, a shield.
In quantum gravity, the big error in physics is that Edwin Hubble in 1929 divided the Doppler shift determined recession speeds by the apparent distances to get his constant, v/R = H. In fact, the distances increase while the light and gravity effect are actually coming back to us. What he should have done is to represent it as a variation in speed with time past. The whole point about space-time is precisely that there is equivalence between seeing thing at larger distances, and seeing things further back in time. You cannot simply describe the Hubble effect as a variation in speed with distance, because time past is involved! Whereas H has units s-1 (1/age of universe), the directly observed Hubble ratio is equal to v/t = HR/(1/H) = RH2 (and therefore has units of ms-2, acceleration). In the big bang, the recession velocities from here outward vary from v = 0 towards v = c, and the corresponding times after the big bang vary from 15,000 million years (t = 1/H) towards zero time. Hence, the apparent acceleration as seen in space-time is
a = (variation in velocity)/(variation in time) = c / (1/H) = cH = 6 x 10-10 ms-2.
Although a small acceleration, a large mass of the universe is involved so the outward force (F = ma) is very large. The 3rd law of motion implies equal inward force like an implosion, which in LeSage gravity gives the right value for G, disproving the ‘critical density’ formula of general relativity by ˝ e3 = 10 times. This disproves most speculative ‘dark matter’. Since gravity is the inward push caused by the graviton/Higgs field flowing around the moving fundamental particles to fill in the void left in their wake, there will only be a gravitational ‘pull’ (push) where there is a surrounding expansion. Where there is no surrounding expansion there is no gravitational retardation to slow matter down. This is in agreement with observations that there is no slowing down (a fictitious acceleration is usually postulated to explain the lack of slowing down of supernovae).
Current teaching of general relativity, as causing a flat surface like a rubber sheet to curve into a manifold, is unhelpful to further progress in unifying quantum space with gravitation, since physical space fills volume, not surface area.
‘… 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, pp. 89-90.
The sound wave is longitudinal and has pressure variations. Half a cycle is compression (overpressure) and the other half cycle of a sound wave is underpressure (below ambient pressure). When a spherical sound wave goes outward, it exerts outward pressure which pushes on you eardrum to make the noises you hear. Therefore the sound wave has outward force F = PA where P is the sound wave pressure and A is the area it acts on.
Note the outward force and equal and opposite inward force. This is Newton’s 3rd law. The same happens in explosions, except the outward force is then a short tall spike (due to air piling up against the discontinuity and going supersonic), while the inward force is a longer but lower pressure. A nuclear implosion bomb relies upon Newton’s 3rd law for TNT surrounding a plutonium core to compress the plutonium. The same effect in the Higgs field surrounding outward-going quarks in the ‘big bang’ produces an inward force which gives gravity, including the compression of the earth's radius (1/3)MG/c2 = 1.5 mm (the contraction term effect in general relativity). Fundamental physical force mechanisms have been developed as a consequence.
It is possible that some deep things in nature can be explained by simple maths, just as Bohr’s atomic equation for energy levels matches spectroscopic line positions, and Restricted Relativity equations are good. But deep down, the maths is more complex, so Bohr’s vulgar atomic model is replaced by quantum mechanics, while Einstein replaced his own simplistic Restricted (‘Special’) Relativity with general relativity which is mathematically complex but describes absolute motions called accelerations!
Taking things simply, the virtual vacuum surrounding each charge core is polarised, which screens the core charge. This is geometrical. The virtual positron-electron pairs in the vacuum are polarised: the virtual positive charges are attracted closer to the negative core than the virtual electrons, which are repelled to greater distances. Hence the real negative core has a positive virtual shell just around it, with a negative virtual shell beyond it, which falls off to neutral at great distances. This virtual particle or heuristic (trial and error) explanation is used in the Feynman approach to quantum field theory, and was validated experimentally in 1997, by firing leptons together at high energy to penetrate the virtual shield and observe the greater charge nearer the bare core of an electron.
Some 99.27 % of the inward-directed electric field from the electron core is cancelled by the outward-directed electric field due to the shells of virtual charges polarised in the vacuum by the electron core. Traditionally, the normal mathematics of quantum field theory has had the issue of having to be ‘renormalised’ to stop the electron core from interacting with an infinite number of virtual charges. The renormalisation process force-fits limits the size of the integral for each coupling correction, which would otherwise be infinity. Heuristically, renormalisation is limiting each coupling correction (Feynman diagram) to one virtual charge at one time. Hence, for the first coupling correction (which predicts the electron’s magnetism right to 5 decimals or 6 significant figures), the electron core charge is weakened by the polarised charge (positron shell) and is 137 times weaker when associating with 1 virtual electron in the space around the positive shell. The paired magnetic field is 1 + 1/(2.Pi.137) = 1.00116 Bohr magnetons, first term is the unshielded magnetism of the real electron core, and the second is the contribution from the paired virtual electron in the surrounding space, allowing for the transverse direction of the core magnetic field lines around the electron loop equator (the magnetic field lines are radial at the poles). My understanding now is that the transverse magnetic field surrounding the core of the electron is shielded by the 137 factor, and it is this shielded transverse field which couples with a virtual electron. The radial magnetic field lines emerging from the electron core poles are of course not attenuated, since they don’t cross electric field lines in the polarised vacuum, but merely run parallel to electric field lines. (This is a large step forward in heuristic physics from that a couple of weeks back.)
The pairing is the Pauli-exclusion process. Because an electron has a spin, it is a magnet. Every two adjacent electrons in the atom have opposite spin directions (up or down). There are two natural ways tou can put two magnets together, end to end or side to side. The side to side arrangement, with one North pole facing up and the other down, is most stable, so it occurs in the atom where the electrons are in chaotic orbits. The only way you can measure the spin of an electron is by using a magnetic field, which automatically aligns the electron, so the spin can only take two possible values (up or down), so the magnetism is either adding to or subtracting from the background field. You can flip the electron over by adding the energy needed for it to add to the magnetic field. None of this is mystical, any more than playing with magnets and finding they naturally align in certain (polar) ways only. The Pauli exclusion principle states that the four quantum numbers (including spin) are unique for every electron in the atom. Spin was the last quantum number to be accepted.
In order to heuristically explain the abstruse 1 + 1/(2.Pi.137) = 1.00116 first coupling correction for the electron’s magnetism in QED, we suggested on Motl’s blog that the electron core magnetism is not attenuated by the polarised vacuum of space, while the electric field is attenuated by a factor of 137. The 2.Pi factor comes from the way a virtual electron in the vacuum couples with the real core electron, both of which are spinning. (Magnetism is communicated via the spin of virtual particles in the vacuum, according to Maxwell’s electromagnetism.) The coupling is related to the mechanism of the Pauli exclusion principle. The coupling is weakened by the 137 factor because the polarisation of virtual charges creates an inner virtual positron shell around the real electron core, with an outer virtual electrons shell. The polarised vacuum shields the core charge by a factor of 137.
The extra mass-energy of a muon means that interacts not only with virtual electrons and positrons, but also more energetic virtual particles in the vacuum. This very slightly affects the measured magnetic moment of the muon, since it introduces extra coupling corrections that don’t occur for an electron.
Could it be that the effect on the electron’s mass is greater for the same reason, but that the effect for mass is greater than magnetic field, because it doesn’t involve the 137-attenuation factor? Somehow you get the feeling that we are going towards a ‘bootstrap’ physics approach; the muon is more 207 times more massive than the electron, because the greater mass causes it to interact more with the spacetime fabric, which adds mass! (‘I pulled myself upward by my own bootstraps.’) I’ll come back to this at the end of this paper, with a list of tested predictions of particle masses that it yields.
The gravity mechanism has been applied to electromagnetism that has both attractive and repulsive forces, and nuclear attractive forces. These are all powered by the gravity mechanism in a simple way. Spinning charges in heuristic quantum field theory all radiate and exchange energy as virtual photons, which gets red-shifted when travelling large distances in the universe, due to the big bang. As a result, the exchange of energy between nearby similar charges, where the expansion of the universe does not occur between the charges, is strong and they recoil apart (repulsion), like two people accelerating in opposite directions due to exchanging streams of lead bullets from machine-guns! (Thank God for machine guns and big bangs, or physics would seem daft.) As a virtual photon leaves any electron, the electron must recoil, like a rifle firing a bullet. According to the uncertainty principle, the range of the virtual photon is half its wavelength. Since the inverse-square law is simple geometric divergence (of photons over increasing areas) with no range limit (infinite range), the wavelength of the virtual photons in electromagnetism is infinite. Hence, they are continuous energy flow, not oscillating. This is why you can’t hear steady electromagnetic forces on a radio: there is no oscillation to jiggle the electrons and introduce a resonate current. (Planck’s formula E = hf implies that zero net energy is carried when f = 0, which is due to the Prevost exchange mechanism of 1792 that also applies to quantum energy exchange at constant temperatures, where cooling objects are in equilibrium, receiving as much as they radiate each second.) When we accelerate a charge, we then get a detectable photon with a definite frequency. The spin of a loop electron is continuous not a periodic phenomena so it radiates energy with no frequency, just like a trapped electric TEM wave in a capacitor plate.
Electric attraction occurs between opposite charges, which stop virtual photons from each other’s direction, and so are pushed together like gravity, but the force is multiplied up from gravity by a factor of about 10^40, due to the drunkard’s walk (statistical zig-zag path) of energy between similar charges in the universe. This ‘displacement current’ of electromagnetic energy can’t travel in a straight line or it will statistically encounter similar numbers of equal and opposite charges, cancelling out the net electric field. Thus mathematical physics only permits a drunkard’s walk, in which the sum is gravity times the square root of the number of similar charges in the universe. A diagram here http://members.lycos.co.uk/nigelbryancook/Image11.jpg proves that the electric repulsion force is equal to the attraction force for equal charges, but has opposite directions depending on whether the two charges are similar in sign or different:
Hence F(electromagnetism) = mMGN1/2/r2 = q1q2/(4
p e r2) (Coulomb’s law)where G = ľ H2/(
p r e3) as proved above, and N is as a first approximation the mass of the universe (4p R3 r /3= 4p (c/H)3 r /3) divided by the mass of a hydrogen atom. This assumes that the universe is hydrogen. In fact it is 90% hydrogen by atomic abundance as a whole, although less near stars (only 70% of the solar system is hydrogen, due to fusion of hydrogen into helium, etc.). Another problem with this way of calculating N is that we assume the fundamental charges to be electrons and protons, when in fact protons contain two up quarks (each +2/3) and one downquark (-1/3), so there are twice as many fundamental particles. However, the quarks remain close together inside a nucleon and behave for most electromagnetic purposes as a single fundamental charge. With these approximations, the formulae above yield a prediction of the strength factor e in Coulomb’s law of:e
= qe2e2.7…3 [r /(12p me2mprotonHc3)]1/2 F/m.Testing this with the PRL and other data used above (
r = 4.7 x 10-28 kg/m3 and H = 1.62 x 10-18 s-1 for 50 km.s-1Mpc-1), gives e = 7.4 x 10-12 F/m which is only 17% low as compared to the measured value of 8.85419 x 10-12 F/m. This relatively small error reflects the hydrogen assumption and quark effect. Rearranging this formula to yield r , and rearranging also G = ľ H2/(p r e3) to yield r allows us to set both results for r equal and thus to isolate a prediction for H, which can then be substituted into G = ľ H2/(p r e3) to give a prediction for r which is independent of H:H = 16
p 2Gme2mprotonc3 e 2/(qe4e2.7…3) = 2.3391 x 10-18 s-1 or 72.2 km.s-1Mpc-1, so 1/H = t = 13.55 Gyr.r
= 192p 3Gme4mproton2c6 e 4/(qe8e2.7…9) = 9.7455 x 10-28 kg/m3.Again, these predictions of the Hubble constant and the density of the universe from the force mechanisms assume that the universe is made of hydrogen, and so are first approximations. However they clearly show the power of this mechanism-based predictive method. Tony Smith has predictions of quark masses: http://www.valdostamuseum.org/hamsmith/
Dr Peter Woit has some sensible ideas on how to proceed with the Standard Model: ‘Supersymmetric quantum mechanics, spinors and the standard model’, Nuclear Physics, v. B303 (1988), pp. 329-42; ‘Topological quantum theories and representation theory’, Differential Geometric Methods in Theoretical Physics: Physics and Geometry, Proceedings of NATO Advanced Research Workshop, Ling-Lie Chau and Werner Nahm, Eds., Plenum Press, 1990, pp. 533-45:
‘… [it] should be defined over a Euclidean signature four dimensional space since even the simplest free quantum field theory path integral is ill-defined in a Minkowski signature. If one chooses a complex structure at each point in space-time, one picks out a U(2)
Ì SO(4) (perhaps better thought of as a U(2) Ì Spinc(4)) and … it is argued that one can consistently think of this as an internal symmetry. Now recall our construction of the spin representation for Spin(2n) as L *(‘Under U(2), the spin representation has the quantum numbers of a standard model generation of leptons… A generation of quarks has the same transformation properties except that one has to take the ‘vacuum’ vector to transform under the U(1) with charge 4/3, which is the charge that makes the overall average U(1) charge of a generation of leptons and quarks to be zero. The above comments are … just meant to indicate how the most basic geometry of spinors and Clifford algebras in low dimensions is rich enough to encompass the standard model and seems to be naturally reflected in the electro-weak symmetry properties of Standard Model particles…
‘This article has attempted to present some fragmentary ideas relating representation theory and quantum theory in the hope that they will lead to new ways of thinking about quantum field theory and particle physics and ultimately to progress in going beyond the Standard Model of particle physics. … 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.’ – Dr P. Woit, Quantum Field Theory and Representation Theory: A Sketch (2002),
http://arxiv.org/abs/hep-th/0206135.These comments hit the nail on the head: to get quantum gravity and particle physics, ‘string theory’ is useless.
D.R. Lunsford has a paper on ‘Gravitation and Electrodynamics over SO(3,3)’ on
CERN document server, EXT-2003-090: ‘an approach to field theory is developed in which matter appears by interpreting source-free (homogeneous) fields over a 6-dimensional space of signature (3,3), as interacting (inhomogeneous) fields in spacetime. The extra dimensions are given a physical meaning as ‘coordinatized matter’. The inhomogeneous energy-momentum relations for the interacting fields in spacetime are automatically generated by the simple homogeneous relations in 6-D. We then develop a Weyl geometry over SO(3,3) as base, under which gravity and electromagnetism are essentially unified via an irreducible 6-calibration invariant Lagrange density and corresponding variation principle. The Einstein-Maxwell equations are shown to represent a low-order approximation, and the cosmological constant must vanish in order that this limit exist.’ Lunsford begins with an enlightening overview of attempts to unify electromagnetism and gravitation:‘The old goal of understanding the long-range forces on a common basis remains a compelling one. The classical attacks on this problem fell into four classes:
‘1. Projective theories (Kaluza, Pauli, Klein)
‘2. Theories with asymmetric metric (Einstein-Mayer)
‘3. Theories with asymmetric connection (Eddington)
‘4. Alternative geometries (Weyl)
‘All these attempts failed. In one way or another, each is reducible and thus any unification achieved is purely formal. The Kaluza theory requires an ad hoc hypothesis about the metric in 5-D, and the unification is non-dynamical. As Pauli showed, any generally covariant theory may be cast in Kaluza’s form. The Einstein-Mayer theory is based on an asymmetric metric, and as with the theories based on asymmetric connection, is essentially algebraically reducible without additional, purely formal hypotheses.
‘Weyl’s theory, however, is based upon the simplest generalization of Riemannian geometry, in which both length and direction are non-transferable. It fails in its original form due to the non-existence of a simple, irreducible calibration invariant Lagrange density in 4-D. One might say that the theory is dynamically reducible. Moreover, the possible scalar densities lead to 4th order equations for the metric, which, even supposing physical solutions could be found, would be differentially reducible. Nevertheless the basic geometric conception is sound, and given a suitable Lagrangian and variational principle, leads almost uniquely to an essential unification of gravitation and electrodynamics with the required source fields and conservation laws.’ Again, the general concepts involved are very interesting: ‘from the current perspective, the Einstein-Maxwell equations are to be regarded as a first-order approximation to the full calibration-invariant system.
‘One striking feature of these equations that distinguishes them from Einstein’s equations is the absent gravitational constant – in fact the ratio of scalars in front of the energy tensor plays that role. This explains the odd role of G in general relativity and its scaling behaviour. The ratio has conformal weight 1 and so G has a natural dimensionfulness that prevents it from being a proper coupling constant – so the theory explains why general relativity, even in the linear approximation and the quantum theory built on it, cannot be regularised.’ [Lunsford goes on to suggest gravity is a residual of the other forces, which is one way to see it.]