Loop Quantum Gravity - Spin Foam Vacuum

... a spin foam is a four-dimensional graph made out of two-dimensional faces that represents one of the configurations that must be summed to obtain Feynman's path integral (functional integration) describing the alternative formulation of quantum gravity known as loop gravity or loop quantum gravity. ...

"In loop quantum gravity there are some results from a possible canonical quantization of general relativity at the Planck scale. Any path integral formulation of the theory can be written in the form of a spin foam model, such as the Barrett-Crane model. Spin network is defined as a diagram (like Feynman diagram) which make a basis of connections between the elements of a differentiable manifold for the Hilbert spaces defined over them. Spin network provides a representation for computations of amplitudes between two different hypersurfaces of the manifold. Any evolution of spin network provides a spin foam over a manifold of one dimensional higher than the dimensions of the corresponding spin network. A spin foam may be viewed as a quantum history. ...

"Spacetime is considered as a quantic superposition of spin foams, which is a generalized Feynman diagram where instead of a graph we use a higher-dimensional complecies. In topology this sort of space is called a 2-dimensional complex." - Wikipedia

PHYSICAL REALITY OF A SPIN FOAM VACUUM (in addition to the maths, not replacing it), http://feynman137.tripod.com/:

Maxwell’s 1873 Treatise on Electricity and Magnetism, Articles 822-3: ‘The ... action of magnetism on polarised light [discovered by Faraday not Maxwell] leads ... to the conclusion that in a medium ... is something belonging to the mathematical class as an angular velocity ... This ... cannot be that of any portion of the medium of sensible dimensions rotating as a whole. We must therefore conceive the rotation to be that of very small portions of the medium, each rotating on its own axis [spin] ... The displacements of the medium, during the propagation of light, will produce a disturbance of the vortices ... We shall therefore assume that the variation of vortices caused by the displacement of the medium is subject to the same conditions which Helmholtz, in his great memoir on Vortex-motion [of 1858; sadly Lord Kelvin in 1867 without a fig leaf of empirical evidence falsely applied this vortex theory to atoms in his paper ‘On Vortex Atoms’, Phil. Mag., v4, creating a mathematical cult of vortex atoms just like the mathematical cult of string theory now; it created a vast amount of prejudice against ‘mere’ experimental evidence of radioactivity and chemistry that Rutherford and Bohr fought], has shewn to regulate the variation of the vortices [spin] of a perfect fluid.’

‘… 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.’ – Professor Bernard Schutz, General Relativity, Cambridge University Press, 1986, pp. 89-90.

‘In this chapter it is proposed to study the very interesting dynamical problem furnished by the motion of one or more solids in a frictionless liquid. The development of this subject is due mainly to Thomson and Tait [Natural Philosophy, Art. 320] and to Kirchhoff [‘Ueber die Bewegung eines Rotationskörpers in einer Flüssigkeit’, Crelle, lxxi. 237 (1869); Mechanik, c. xix]. … it appeared that the whole effect of the fluid might be represented by an addition to the inertia of the solid. The same result will be found to hold in general, provided we use the term ‘inertia’ in a somewhat extended sense.’ – Sir Horace Lamb, Hydrodynamics, Cambridge University Press, 6th ed., 1932, p. 160. (Hence, the gauge boson radiation of the gravitational field causes inertia. This is also explored in the works of Drs Rueda and Haisch: see http://arxiv.org/abs/physics/9802031 http://arxiv.org/abs/gr-qc/0209016 , http://www.calphysics.org/articles/newscientist.html and http://www.eurekalert.org/pub_releases/2005-08/ns-ijv081005.php .)

So the Feynman problem with virtual particles in the spacetime fabric retarding motion does indeed cause the FitzGerald-Lorentz contraction, just as they cause the radial gravitationally produced contraction of distances around any mass (equivalent to the effect of the pressure of space squeezing things and impeding accelerations). What Feynman thought may cause difficulties is really the mechanism of inertia!

At http://www.valdostamuseum.org/hamsmith/cnfGrHg.html, Tony Smith quotes Feynman:

Richard Feynman’s book Lectures on Gravitation (1962-63 lectures at Caltech), Addison-Wesley 1995, contains a section on Quantum Gravity by Brian Hatfield, who says: ‘... Feynman ... felt ... that ... the fact that a massless spin-2 field can be interpreted as a metric was simply a ‘coincidence’ ... In order to produce a static force and not just scattering, the emission or absorption of a single graviton by either particle [of a pair of particles] must leave both particles in the same internal state ... Therefore the graviton must have integer spin. ... when the exchange particle carries odd integer spin, like charges repel and opposite charges attract ... when the exchanged particle carries even integer spin, the potential is universally attractive ... If we assume that the exchanged particle is spin 0, then we lose the coupling of gravity to the spin-1 photon ... the graviton is massless because gravity is a long ranged force and it is spin 2 in order to be able to couple the energy content of matter with universal attraction ...’.

http://feynman137.tripod.com/:

General relativity, absolute causality

Professor Georg Riemann (1826-66) stated in his 10 June 1854 lecture at Gottingen University, On the hypotheses which lie at the foundations of geometry: ‘If the fixing of the location is referred to determinations of magnitudes, that is, if the location of a point in the n-dimensional manifold be expressed by n variable quantities x₁, x₂, x₃, and so on to x_n, then … ds =

Ö [å (dx)²] … I will therefore term flat these manifolds in which the square of the line-element can be reduced to the sum of the squares … A decision upon these questions can be found only by starting from the structure of phenomena that has been approved in experience hitherto, for which Newton laid the foundation, and by modifying this structure gradually under the compulsion of facts which it cannot explain.’

Riemann’s suggestion of summing dimensions using the Pythagorean sum ds² =

å (dx²) could obviously include time (if we live in a single velocity universe) because the product of velocity, c, and time, t, is a distance, so an additional term d(ct)² can be included with the other dimensions dx², dy², and dz². There is then the question as to whether the term d(ct)² will be added or subtracted from the other dimensions. It is clearly negative, because it is, in the absence of acceleration, a simple resultant, i.e., dx² + dy² + dz² = d(ct)², which implies that d(ct)² changes sign when passed across the equality sign to the other dimensions: ds² = å (dx²) = dx² + dy² + dz² – d(ct)² = 0 (for the absence of acceleration, therefore ignoring gravity). This formula, ds² = å (dx²) = dx² + dy² + dz² – d(ct)², is known as the ‘Riemann metric’. It is important to note that it is not the correct spacetime metric, which is precisely why Riemann did not discover general relativity back in 1854. [The algebraic Newtonian-equivalent (for weak fields) approximation in general relativity is the Schwarzschild metric, which, ds² = (1 – 2GM/r)^-1 (dx² + dy² + dz² ) – (1 – 2GM/r) d(ct)².]

Professor Gregorio Ricci-Curbastro (1853-1925) took up Riemann’s suggestion and wrote a 23-pages long article in 1892 on ‘absolute differential calculus’, developed to express differentials in such a way that they remain invariant after a change of co-ordinate system. In 1901, Ricci and Tullio Levi-Civita (1873-1941) wrote a 77-pages long paper on this, Methods of the Absolute Differential Calculus and Their Applications, which showed how to represent equations invariantly of any absolute co-ordinate system. This relied upon summations of matrices of differential vectors. Ricci expanded Riemann’s system of notation to allow the Pythagorean dimensions of space to be defined by a dimensionless ‘Riemann metric’ (named the ‘metric tensor’ by Einstein in 1916)..... continued at http://feynman137.tripod.com/

‘The special theory of relativity … does not extend to non-uniform motion … The laws of physics must be of such a nature that they apply to systems of reference in any kind of motion. Along this road we arrive at an extension of the postulate of relativity… The general laws of nature are to be expressed by equations which hold good for all systems of co-ordinates, that is, are co-variant with respect to any substitutions whatever (generally co-variant). … We call four quantities A_v the components of a covariant four-vector, if for any arbitrary choice of the contravariant four-vector B^v, the sum over v, å A_v B^v = Invariant. The law of transformation of a covariant four-vector follows from this definition.’ – Albert Einstein, ‘The Foundation of the General Theory of Relativity’, Annalen der Physik, v49, 1916.

Professor Morris Kline describes the situation after 1911, when Einstein began to search for more sophisticated mathematics to build gravitation into space-time geometry: ‘Up to this time Einstein had used only the simplest mathematical tools and had even been suspicious of the need for "higher mathematics", which he thought was often introduced to dumbfound the reader. However, to make progress on his problem he discussed it in Prague with a colleague, the mathematician Georg Pick, who called his attention to the mathematical theory of Ricci and Levi-Civita. In Zurich Einstein found a friend, Marcel Grossmann (1878-1936), who helped him learn the theory; and with this as a basis, he succeeded in formulating the general theory of relativity.’ (M. Kline, Mathematical Thought from Ancient to Modern Times, Oxford University Press, 1990, vol. 3, p. 1131.)

Let us examine the developments Einstein introduced to accomplish general relativity, which aims to equate the mass-energy in space to the curvature of motion (acceleration) of an small test mass, called the geodesic path. Readers who want a good account of the full standard tensor manipulation should see the page by

Dr John Baez or Sir Kevin Aylward

We will give perhaps a slightly more practical and physical interpretation of the basics here. Ricci introduced a tensor, the Ricci tensor, which deals with a change of co-ordinates by using Fitzgerald-Lorentz contraction factor,

g = (1 – i>v²/c²)^1/2. Light is accelerated by gravity exactly twice as much as predicted by Newton’s law. General relativity is a mathematical accounting system and this factor of two comes into it from the energy considerations ignored by Newtonian physics, due to the light speed of the gravitational field itself. When gravity deflects an object with rest mass that is moving perpendicularly to the gravitational field lines, it speeds up the object. Because light is already travelling at its maximum velocity, it cannot be speeded up. Therefore, that half of the gravitational potential energy that goes into speeding up an object with rest mass cannot do so in the case of light and must go instead into additional directional change (downward acceleration). This is the mathematical physics why light is deflected twice the amount suggested by Newton’s law.

The contraction of materials only in the direction of their motion through the physical fabric of space, and their contraction due to the space pressure of gravity in the outward (radial) direction from the centre of a mass indicates a physical nature of space consistent with the 377 ohm property of the vacuum in electronics. Feynman’s approach to quantum electrodynamics, showing that interference creates the illusion that light always travels along the shortest route, accords with this model of space. However, Feynman fails to examine radio wave transmission, which cannot be treated by quantum theory as the waves are continuous and of macroscopic size easily examined and experimented with. The emission of radio is due to the accelerations of electrons as the electric field gradient varies in the transmitter aerial. Because electrons are naturally spinning, even still electrons have centripetal acceleration and emit energy continuously. The natural exchange of such energy creates a continuous, non-periodic equilibrium that is only detectable as electromagnetic forces. Photon emission as described by Feynman is periodic emission of energy. Thus in a sheet of glass there are existing energy transfer processes passing energy around at light speed before light enters. The behaviour of light therefore depends on how it is affected by the existing energy flow inside the glass, which depends on its thickness. Feynman explains in his 1985 book QED that ‘When a photon comes down, it interacts with electrons throughout the glass, not just on the surface. The photon and electrons do some kind of dance, the net result of which is the same as if the photon hit only the surface.’ Feynman in the same book concedes that his path-integrals approach to quantum mechanics explains the chaos of the atomic electron as being simply a Bohm-type interference phenomenon: ‘when the space through which a photon moves becomes too small (such as the tiny holes in the screen) … we discover that … there are interferences created by the two holes, and so on. The same situation exists with electrons: when seen on a large scale, they travel like particles, on definite paths. But on a small scale, such as inside an atom, the space is so small that … interference becomes very important.’ Thus Feynman suggests that a single hydrogen atom (one electron orbiting a proton, which can never be seen without an additional particle as part of the detection process) would behave classically, and it is the presence of a third particle (say in the measuring process) which interrupts the electron orbit by interference, creating the 3+ body chaos of the Schroedinger wave electron orbital.

QFT heuristically explained with a classical model of a polarised virtual charge dielectric

‘As I proceeded with the study of Faraday, I perceived that his method of conceiving the phenomena was also a mathematical one, though not exhibited in the conventional form of mathematical symbols. I also found that these methods were capable of being expressed in the ordinary mathematical forms … For instance, Faraday, in his mind’s eye, saw lines of force transversing all space where the mathematicians saw centres of force attracting at a distance: Faraday saw a medium where they saw nothing but distance: Faraday sought the seat of the phenomena in real actions going on in the medium, they were satisfied that they had found it in a power of action at a distance…’ – Dr J. Clerk Maxwell, Preface, A Treatise on Electricity and Magnetism, 1873.

‘In fact, whenever energy is transmitted from one body to another in time, there must be a medium or substance in which the energy exists after it leaves one body and before it reaches the other… I think it ought to occupy a prominent place in our investigations, and that we ought to endeavour to construct a mental representation of all the details of its action…’ – Dr J. Clerk Maxwell, conclusion, A Treatise on Electricity and Magnetism, 1873 edition.

Analogy of the ‘string theory’ to ‘Copenhagen Interpretation’ quantum mechanics math

‘Statistical Uncertainty. This is the kind of uncertainty that pertains to fluctuation phenomena and random variables. It is the uncertainty associated with ‘honest’ gambling devices…

‘Real Uncertainty. This is the uncertainty that arises from the fact that people believe different assumptions…’ – H. Kahn & I. Mann, Techniques of systems analysis, RAND, RM-1829-1, 1957.

Let us deal with the physical interpretation of the periodic table using quantum mechanics very quickly. Niels Bohr in 1913 came up with an orbit quantum number, n, which comes from his theory and takes positive integer values (1 for first or K shell, 2 for second or M shell, etc.). In 1915, Arnold Sommerfeld (of 137-number fame) introduced an elliptical-shape orbit number, l, which can take values of n –1, n – 2, n – 3, … 0. Back in 1896 Pieter Zeeman introduced orbital direction magnetism, which gives a quantum number m with possible values l, l – 1, l – 2, …, 0, … - (l- 2), -(l – 1), -l. Finally, in 1925 George Uhlenbeck and Samuel Goudsmit introduced the electron’s magnetic spin direction effect, s, which can only take values of +1/2 and –1/2. (Back in 1894, Zeeman had observed the phenomenon of spectral lines splitting when the atoms emitting the light are in a strong magnetic field, which was later explained by the fact of the spin of the electron. Other experiments confirm electron spin. The actual spin is in units of h/(2

p ), so the actual amounts of angular spin are + ½ h/(2p ) and – ½ h/(2p

). ) To get the periodic table we simply work out a table of consistent unique sets of quantum numbers. The first shell then has n, l, m, and s values of 1, 0, 0, +1/2 and 1, 0, 0, -1/2. The fact that each electron has a different set of quantum numbers is called the ‘Pauli exclusion principle’ as it prevents electrons duplicating one another. (Proposed by Wolfgang Pauli in 1925; note the exclusion principle only applies to fermions with half-integral spin like the electron, and does not apply to bosons which all have integer spin, like light photons and gravitons. While you use fermi-dirac statistics for fermions, you have to use bose-einstein statistics for bosons, on account of spin. Non-spinning particles, like gas molecules, obey maxwell-boltzmann statistics.) Hence, the first shell can take only 2 electrons before it is full. (It is physically due to a combination of magnetic and electric force effects from the electron, although the mechanism must be officially ignored by order of the Copenhagen Interpretation ‘Witchfinder General’, like the issue of the electron spin speed.)

For the second shell, we find it can take 8 electrons, with l = 0 for the first two (an elliptical subshell is we ignore the chaos effect of wave interactions between multiple electrons), and l = 1 for next other 6.

Experimentally we find that elements with closed full shells of electrons, i.e., a total of 2 or 8 electrons in these shells, are very stable. Hence, helium (2 electrons) and Argon (2 electrons in first shell and 8 electrons filling second shell) will not burn

Let us now examine how fast the electrons go in the atom in their orbits, neglecting spin speed. Assuming simple circular motion to begin with, the inertial ‘outward’ force on the electron is F = ma = mv²/R, which is balanced by electric ‘attractive’ inward force of F = (q_e/R)²/(4

p e ). Hence, v = ½q_e /(p e

Rm)^1/2.

Now for Werner Heisenberg’s ‘uncertainty principle’ of 1927. This is mathematically sound in the sense that the observer always disturbs the signals he observes. If I measure my car tyre pressure, some air leaks out, reducing the pressure. If you have a small charged capacitor and try to measure the voltage of the energy stored in it with an old fashioned analogue volt meter, you will notice that the volt meter itself drains the energy in the capacitor pretty quickly. A digital meter contains an amplifier, so the effect is less pronounced, but it is still there. A geiger counter held in fallout area absorbs some of the gamma radiation it is trying to measure, reducing the reading, as does the presence of the body of the person using it. A blind man searching for a golf ball by swinging a stick around will tend to disturb what he finds. When he feels and hears the click of the impact of his stick hitting the golf ball, he knows the ball is no longer where it was when he detected it. If he prevents this by not moving the stick, he never finds anything. So it is a reality that the observer always tends to disturb the evidence by the very process of observing the evidence. If you even observe a photograph, the light falling on the photograph very slightly fades the colours. With something as tiny as an electron, this effect is pretty severe. But that does not mean that you have to make up metaphysics to stagnate physics for all time, as Bohr and Heisenberg did when they went crazy. Really, Heisenberg’s law has a simple causal meaning to it, as I’ve just explained. If I toss a coin and don’t show you the result, do you assume that the coin is in a limbo, indeterminate state between two parallel universes, in one of which it is heads and in the other of which it landed tails? (If you believe that, then maybe you should have yourself checked into a mental asylum where you can write your filthy equations all over the walls with a crayon held between your big ‘TOEs’ or your ‘theories of everything’.)

For the present, let’s begin right back before QFT, in other words with the classic theory back in 1873:

Fiat Lux:

‘Let there be Light’

Michael Faraday, Thoughts on Ray Vibrations, 1846. Prediction of light without numbers by the son of a blacksmith who became a bookseller’s delivery boy aged 13 and invented electric motor, generator, etc.

James Clerk Maxwell, A Dynamical Theory of the Electromagnetic Field, 1865. Fiddles with numbers.

I notice that the man (J.C. Maxwell) most often attributed with Fiat Lux wrote in his final (1873) edition of his book A Treatise on Electricity and Magnetism, Article 110:

‘... we have made only one step in the theory of the action of the medium. We have supposed it to be in a state of stress, but we have not in any way accounted for this stress, or explained how it is maintained...’

In Article 111, he admits further confusion and ignorance:

‘I have not been able to make the next step, namely, to account by mechanical considerations for these stresses in the dielectric [spacetime fabric]... When induction is transmitted through a dielectric, there is in the first place a displacement of electricity in the direction of the induction...’

First, Maxwell admits he doesn’t know what he’s talking about in the context of ‘displacement current’. Second, he talks more! Now Feynman has something about this in his lectures about light and EM, where he says idler wheels and gear cogs are replaced by equations. So let’s check out Maxwell's equations.

One source is A.F. Chalmers’ article, ‘Maxwell and the Displacement Current’ (Physics Education, vol. 10, 1975, pp. 45-9). Chalmers states that Orwell’s novel 1984 helps to illustrate how the tale was fabricated:

‘… history was constantly rewritten in such a way that it invariably appeared consistent with the reigning ideology.’

Maxwell tried to fix his original calculation deliberately in order to obtain the anticipated value for the speed of light, proven by Part 3 of his paper, On Physical Lines of Force (January 1862), as Chalmers explains:

‘Maxwell’s derivation contains an error, due to a faulty application of elasticity theory. If this error is corrected, we find that Maxwell’s model in fact yields a velocity of propagation in the electromagnetic medium which is a factor of

Ö

2 smaller than the velocity of light.’

It took three years for Maxwell to finally force-fit his ‘displacement current’ theory to take the form which allows it to give the already-known speed of light without the 41% error. Chalmers noted: ‘the change was not explicitly acknowledged by Maxwell.’

Weber, not Maxwell, was the first to notice that, by dimensional analysis (which Maxwell popularised), 1/(square root of product of magnetic force permeability and electric force permittivity) = light speed.

Maxwell after a lot of failures (like Keplers trial-and-error road to planetary laws) ended up with a cyclical light model in which a changing electric field creates a magnetic field, which creates an electric field, and so on. Sadly, his picture of a light ray in Article 791, showing in-phase electric and magnetic fields at right angles to one another, has been accused of causing confusion and of being incompatible with his light-wave theory (the illustration is still widely used today!).

GENERAL RELATIVITY’S HEURISTICALLY EXPLAINED PRESSURE-CONTRACTION EFFECT AND INERTIAL ACCELERATION-RESISTANCE CONTRACTION

Penrose’s Perimeter Institute lecture is interesting: ‘Are We Due for a New Revolution in Fundamental Physics?’ Penrose suggests quantum gravity will come from modifying quantum field theory to make it compatible with general relativity…I like the questions at the end where Penrose is asked about the ‘funnel’ spatial pictures of blackholes, and points out they’re misleading illustrations, since you’re really dealing with spacetime not a hole or distortion in 2 dimensions. The funnel picture really shows a 2-d surface distorted into 3 dimensions, where in reality you have a 3-dimensional surface distorted into 4 dimensional spacetime. In his essay on general relativity in the book ‘It Must Be Beautiful’, Penrose writes: ‘… when there is matter present in the vicinity of the deviating geodesics, the volume reduction is proportional to the total mass that is surrounded by the geodesics. This volume reduction is an average of the geodesic deviation in all directions … Thus, we need an appropriate entity that measures such curvature averages. Indeed, there is such an entity, referred to as the Ricci tensor …’ Feynman discussed this simply as a reduction in radial distance around a mass of (1/3)MG/c² = 1.5 mm for Earth. It’s such a shame that the physical basics of general relativity are not taught, and the whole thing gets abstruse. The curved space or 4-d spacetime description is needed to avoid Pi varying due to gravitational contraction of radial distances but not circumferences.

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 – ½v²/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 Generic Fundamental Particle

‘I think the important and extremely difficult task of our time is to try to build up a fresh idea of reality.’ – W. Pauli, letter to Fierz, 12 August 1948.

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

‘... the view of the status of quantum mechanics which Bohr and Heisenberg defended - was, quite simply, that quantum mechanics was the last, the final, the never-to-be-surpassed revolution in physics ... physics has reached the end of the road.’ – Sir Karl Popper, Quantum Theory and the Schism in Physics, Rowman and Littlefield, NJ, 1982, p. 6.

‘To try to stop all attempts to pass beyond the present viewpoint of quantum physics could be very dangerous for the progress of science and would furthermore be contrary to the lessons we may learn from the history of science … Besides, quantum physics … seems to have arrived at a dead end. This situation suggests strongly that an effort to modify the framework of ideas in which quantum physics has voluntarily wrapped itself would be valuable …’ – Professor Louis de Broglie, Foreword to Dr David Bohm’s book, Causality and Chance in Modern Physics, Routledge and Kegan Paul, London, 2^nd ed., 1984, p. xiv.

‘Niels Bohr brain-washed a whole generation of physicists into believing that the problem had been solved fifty years ago.’ – Murray Gell-Mann, in The Nature of the Physical Universe, Wiley, New York, 1979, p. 29.

Before analysing general relativity and quantum field theory, let’s show how the Heaviside mechanism of electricity suggests the spin speed of static charge, giving a model for the electron.

How physically, can you picture this sort of mathematics? Is it not better to deny that it is possible to understand mathematics in terms of simplicity and causality? In the 1960s while at Motorola, Catt (born 1935, B.Eng. 1959) charged up a 1 m length of coaxial cable to 10 volts, and then discharged it, measuring with a Tektronix 661sampling osclloscope with 4S1 and 4S2 (100 picosecond) plug-ins, finding an output of a 2 m long 5 v pulse. In any static charge, the energy is found to be moving at the speed of light for the adjacent insulator; when discharged, the 50% of the energy already moving towards the exit point leaves first, while the remaining 50% first goes in the opposite direction, reflects back off the far edge, and then exits, creating a pulse of half the voltage and twice the duration needed light to transit the length. Considering a capacitor reduced to simply two oppositely charged particles separated by a vacuum, e.g., an atom, we obtain the particle spin speed.

So the electromagnetic energy of charge is trapped at light speed in any ‘static’ charge situation. David Ash, BSc, and Peter Hewitt, MA, in their 1994 book reviewing electron spin ideas, The Vortex (Gateway, Bath, page 33), stated: ‘… E = mc² shows that mass (m) is equivalent to energy (E). The vortex goes further: it shows the precise form of energy in matter. A particle of matter is a swirling ball of energy … Light is a different form of energy, but it is obvious from Einstein’s equation that matter and light share a common movement. In E = mc², it is c, the speed of light, which related matter to energy. From this, we can draw a simple conclusion. It is obvious: the speed of movement in matter must be the speed of light.’ However, Ash and Hewitt don’t tackle the big issue: ‘It had been an audacious idea that particles as small as electrons could have spin and, indeed, quite a lot of it. … the ‘surface of the electron’ would have to move 137 times as fast as the speed of light. Nowadays such objections are simply ignored.’ – Professor Gerard t’Hooft, In Search of the Ultimate Building Blocks, Cambridge University Press, 1997, p27. In addition, quantum mechanical spin, given by Lie’s mathematics, is generally obscure, and different fundamental particles have different spins. Fermions have half-integer spin while bosons have integer spin. Neutrinos and antineutrinos do have a spin around their propagation axis, but the maths of spin for electrons and quarks is obscure. The twisted paper loop, the Mobius strip, illustrates how a particle can have different quantum mechanical spins in a causal way. If you half twist a strip of paper and then glue the ends, forming a loop, the result has only one surface: in the sense that if you draw a continuous line on the looped paper, you find it will cover both sides of the paper! Hence, a Mobius strip must be spun around twice to get back where it began! The same effect would occur in a spinning fundamental particle, where the trapped energy vector rotates while spinning.

Magnetism, in Maxwell’s mechanical theory of spinning virtual particles in space, may be explained akin to vortices, like whirlpools in water. If you have two whirlpools of similar spin (either both being clockwise, or both being anticlockwise), they attract. If the two whirlpools have opposite spins, they repel. In 1927, Samuel Goudsmit and George Uhlenbeck introduced the spin quantum number. But under Bohr’s and Heisenberg’s ‘Machian’ (‘non-observables like atoms and viruses are not real’) paranoid control, it was subsumed into Lie algebra as a mathematical trick, not a physical reality, despite Dirac’s endorsement of the ‘aether’ in predicting antimatter. Apart from the spin issue above that we resolved by the rotation of the Heaviside-Poynting vector like a Mobius strip, there is also the issue that the equator of the classical spherical electron would revolve 137.03597 times faster than light. Taking Ivor Catt’s work, the electron is not a classical sphere at all, but a Heaviside-Poynting energy current trapped gravitationally into a loop, and it goes at light speed, which is the ‘spin’ speed.

If the electron moves at speed v as a whole in a direction orthogonal (perpendicular) to the plane of the spin, then the c speed of spin will be reduced according to Pythagoras: v² + x² = c² where x is the new spin speed. For v = 0 this gives x = c. What is interesting is that this model gives rise to the Lorentz-FitzGerald transformation naturally, because: x = c(1 - v² / c² )^1/2 . Since all time is defined by motion, this (1 - v² / c² )^1/2 factor of reduction of fundamental particle spin speed is therefore the time-dilation factor for the electron when moving at speed v. So there is no metaphysics in such ‘time travel’! Mass increase occurs due to the snowplough effect of the fabric of spacetime ahead of the particle, since it doesn’t have time to flow out of the way when the speed is great.

The light photon has a spin angular momentum is cmr where the effective mass m is of course energy equivalent, m = E/c² (from E = mc² ). Using Planck’s E = hf = hc/

l where f is frequency and l is wavelength (l = 2p r ), we find that the spin angular momentum is cmr = ½ h/p , which is well verified experimentally. Since the unit of atomic angular momentum is ½ h/p

, we find the light boson has a spin or 1 unit, or is a spin-1 boson, obeying Bose-Einstein statistics. The electron, however, has only half this amount of spin, so it is like half a photon (the negative electric field oscillation of a 1.022 MeV gamma ray, to be precise). The electron is called a fermion as it obeys Fermi-Dirac statistics, which applies to half-integer spins. (The spins of two fermions can, of course, under some special conditions ‘add up’ to behave as a boson, hence the ‘Bose-Einstein condensate’ at very low temperatures.)

I corresponded on these topics with Dr Arnold C. Lynch, who later gave the IEE Centenary Lecture on Sir J. J. Thomson’s discovery of the electron in 1997, and he also presented the Catt Anomaly to the IEE in HEE/26 the next year. Lynch had been chosen to give the lecture on the electron because J. J. Thomson (1856-40) told him about it in Cambridge. (J. J. Thomson had always favoured a vortex picture of the fundamental particle, but had been caught up in Kelvin’s mythical ‘vortex atom’ speculations, which were falsely promoted as mathematically beautiful just like string theory today, and so ‘queered the pitch’ for any attempt to develop vortex fundamental particle ideas, just as Maxwell had ‘queered the pitch’ on aether by making errors and false predictions disproved in the Michelson-Morley experiment of 1887.) Sir J. J. Thomson wrote in his 1884 Treatise on the Motion of Vortex Rings: ‘… the vortex theory of matter is of a much more fundamental character than the ordinary solid particle theory.’ Notice that he does not automatically and outrageously jump to the unproved claim that the vortices are atoms, thus he paves the way for his own discovery of 1897 that the atoms are not fundamental particles, but contain fundamental particles. Back in 1875, James Clerk Maxwell had falsely written in his famous article on ‘The Atom’ in Encyclopaedia Britannica: ‘… the vortex ring of Helmholtz … satisfies more of the conditions than any atom hitherto imagined.’ This was just hype, because it was pushing speculation that ignores the chemical facts and that has not a fig leaf of empirical evidence to support it (exactly like string theory claims today). It offered no testable prediction for the masses of different atoms (just as ‘string theory’ today offers absolutely no testable prediction of the masses of different fundamental particles today).

I don’t really want to discuss vortex theory in detail, because like string theory, most of it is speculative and not useful. Lord Kelvin (William Thomson who became Lord Kelvin in 1892, not to be confused with Sir J. J. Thomson) introduced vortex in a lecture to the Royal Society of Edinburgh on 18 February 1867, in which he claimed matter is moving vortices in the aether of space. (‘The Vortex Theory of Ether’, Pro. Roy. Soc. Edin., v6, 1867, pp 94-105; Phil. Mag., v34, 1867, pp 15-24.) He used chemical smoke rings in the air to dramatically produce smoke rings, which were stable and would diffract around knives without being cut, and bounce off walls! The chemical smoke was produced by mixing acid with ammonia in a box with a flexible wall at one end and a circular hole in the other. By hitting the flexible end of the box, a smoke ring-vortex was produced from the hole that propagated outward. Using two smoke boxes with the holes facing one another, vortex collisions could be produced and studied: they bounced and recoiled! Thus, they did not break up when colliding. They just shook like rubber rings, sending off eddy air currents (a bit like light being generated by colliding particles), so they behaved like atoms.

Obviously the problem is that they do eventually dissipate, so smoke vortices, whirlpools, hurricanes, anti-cyclones and tornadoes are not permanent, despite a brief period of stability. Herman von Helmholtz (1821-94) in 1858 showed that in a frictionless or ‘perfect’ fluid, vortices would not dissipate: Ueber Integrale der hydrodynamischen Gleichungen, welche den Wirbelbewegungen entsprechen. This added to the vortex crazy of Victorian mathematics.

The only widely known attempt to introduce some kind of causal fluid dynamics into quantum mechanics was by Professor David Bohm and Professor J. P. Vigier in their paper ‘Model of the Causal Interpretation of Quantum Theory in Terms of a Fluid with Irregular Fluctuation’ (Physical Review, v 96, 1954, p 208). This paper showed that the Schroedinger equation of quantum mechanics arises as a statistical description of the effects of Brownian motion impacts on a classically moving particle. However, the whole Bohm approach is wrong in detail, as is the attempt of de Broglie (his ‘non-linear wave mechanics’) to guess a classical potential that mimics quantum mechanics on the small scale and deterministic classical mechanics at the other size regime. The whole error here is due to the Poincaré chaos introduced by the three-body problem, which destroys determinism (but not causality) in classical, Newtonian physics:

‘… 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.’ – Tim Poston and Ian Stewart, Analog, November 1981.

So it is not quantum physics that is the oddity, but actually classical physics. The normal teaching of Newtonian physics at low levels falsely claims that it allows the positions of the planets to be exactly calculated (determinism) when it does not. Newton’s laws do not contain any exact solution for more than two bodies, and there are more than two bodies in our solar system. So the problem to address is the error in classical, Newtonian physics, which explains why quantum mechanics is the way it is. Bohm’s approach was to try to obtain a classical model of quantum mechanics, which is the wrong approach, since classical physics is the fiddle. What you first have to admit is that Newton only dealt with two bodies, so his laws simply don’t apply to reality.

Henri Poincaré’s work shows that in any atom, you will have chaos whenever you observe it, even in the Newtonian mechanics framework. The simplest atom is hydrogen, with an electron going around a proton. As soon as you try to observe it, you must introduce another particle like a photon or electron, which gives rise to a 3-body situation! Therefore the chaotic, statistical behaviour of the situation gives rise to the statistical Schroedinger wave equation of the atom without any need to introduce explanations based on ‘hidden variables’. The only mediation is the force gauge boson, which is well known in quantum field theory, and is not exactly a ‘hidden variable of the sort Bohm looked for. Newton’s error is restricting his theory to the oversimplified case of only two bodies, when in fact this is a bit like Euclidean geometry, missing a vital ingredient. (Sometimes you do really have to deepen the foundations to build a taller structure.)

In 1890, Poincaré published a 270-pages book, On the problem of Three Bodies and the Equations of Dynamics. He showed that two bodies of similar mass have predictable, deterministic orbital motion because their orbits trace out closed, repeating loops in space. But he found that three bodies of similar mass in orbit trace out irregular, continuously changing unclosed loops and tangles throughout a volume of space, not merely in the flat plane they began in. The average radius of a chaotic orbit that is equal to the classical (deterministic) radius, and the probability of finding the particle beyond average radius diminishes, so giving the basis of the Schroedinger model, where the probability of finding the electron peaks at the classical radius and diminishes gradually elsewhere. Computer programs approximate chaotic motion roughly by breaking up a three body problem, ABC, into steps AB, AC, and BC, and then cyclically calculating motions of each pair of bodies brief period of time while ignoring the other body for that brief period. This is not exact, but is a useful approximation for understanding how chaos occurs and what statistical variations are possible over a period of time. It disproves determinism! Because most of the physicists working in quantum mechanics have not studied the mathematical application of chaos to classical atomic electrodynamics, they have no idea that Newtonian physics is crackpot off the billiard table, and can’t describe the solar system in the way it claims, and that the ‘contradiction’ usually presented as existing between classical and quantum physics is not a real contradiction but is down to the falsehood that classical physics is supposed to be deterministic, when it is not.