The Apophenion: A Chaos Magick Paradigm - Peter J. Carroll 2008

Three-dimensional time and quantum geometry
Appendix

Part 1.

The Prologue to a Quantum Geometry

Two theories describe the four fundamental material forces that seem to characterise this universe at the time of writing.

The theory of General Relativity describes how gravity works in terms of spacetime curvature, and this seems to work fairly well, and rather more precisely than Newton's theory of gravity, when it comes to working out how things interact with big objects like planets and stars. However it doesn't seem to give correct answers for the behaviour of whole galaxies and its predictions for the whole universe remain rather open ended.

The Quantum theories describe how the strong nuclear force works (this holds the nuclei of atoms together), and the electromagnetic force (this controls how atoms behave chemically and how they interact with light). They also describe the weak nuclear force which theorists now regard as specialised aspect of the electromagnetic force, so they tend to refer to a single electro-weak force nowadays. Quantum theories model these forces as mediated by 'real' particles and fields that supposedly consist of 'virtual' particles.

Unfortunately the Relativity and Quantum theories do not fit comfortably together, indeed they seem to contradict each other completely in principle. Relativity implies a continuously divisible and ultimately causal and determinate universe with strict temporal and spatial locality which does not allow anything to exceed lightspeed or to travel backwards in time. Thus relativity remains an essentially classical theory in which we can model the universe geometrically, even though we have to accept that a large concentration of mass or energy, or an extreme acceleration can distort the geometry of spacetime. (The earlier and simpler theory of Special Relativity describes how velocity alone can create spacetime distortion).

Quantum theories on the other hand imply that nature does not exhibit continuous divisibility, at some point we must encounter the smallest possible pieces of mass and energy and probably of space and time as well. Moreover the quantum perspective implies that the usual classical rules of causality and locality do not apply, or at least not very strictly.

For over seventy years theorists have attempted to reconcile the underlying conflict between these two rival descriptions. The conflict goes beyond physics into the realms of metaphysics, the realm of our basic beliefs about how reality actually works in principle. Because quantum theories can model three out of the four fundamental forces, attention has tended to focus on developing a quantum type theory of gravity. This quest has so far proved fruitless, the supersymmetry particles predicted by the simplest quantum gravity theories have failed to appear in experiments. The more sophisticated Superstring and Brane theories have failed to produce testable predictions, and the quantum gravity particles theoretically responsible for mass and gravity, the Higg's Boson and the Graviton, remain undetected.

Thus perhaps we should consider geometricating the quanta instead of trying to quantise gravity.

Three dimensions of time, plus curvature, together with the accepted three of space, plus curvature, seem to provide exactly the required degrees of freedom to accommodate the known

suite of particle behaviours. In this model, particle properties arise from rotations of the three spatial and the three temporal dimensions about the fourth (curvature) axes of space and time.

Part 2.

Fundamental particles in eight dimensions

In this model called Hyperspin Eight Dimensional, or HD8 for short, the six space and time axes of a fundamental particle can rotate through the fourth dimensions. As all eight dimensions lie orthogonal, (at right angles) to each other, the spatial and temporal axes can rotate relative to either the spatial or temporal fourth dimensions

I do not know 'what' actually spins, but I suspect that fundamental particles consist of the quanta of spacetime itself somehow endowed with spin. This quantisation appears to occur at the level of the so-called Planck scale, of about 10^-33 metres and 10^-44 seconds, so fundamental quanta appear as virtually zero size points in particle mode.

We can designate the dimensions of space and time as s1, s2, s3, and t1, t2, t3, and the fourth curvature dimensions as s4 and t4.

Anchoring the rotations on the curvature axes explains in principle the origin of mass and gravity, for spacetime curvature corresponds to what we perceive as mass and gravity. Increasing the number of axes rotating about the fourth dimensions generally increases the mass of the fundamental particle as the rotations act as a store of energy, however no simple algorithm for particle masses arises from this model as yet.

Complete rotations relative to the fourth (curvature) dimensions of space and time have the effect of making a 3D object turn into its mirror image and back again.

Consider a six-sided dice. Swapping over the faces marked six and one creates a mirror image of the original dice which no kind of rotation in three dimensions can restore to its original form. Similarly, swapping all three pairs of opposite faces also creates the mirror image of the original dice.

Swapping any two pairs of opposite faces however merely has the same effect as rotating the dice in three dimensions. We can see this effect manifest in the suite of observed fundamental particles; none of them exhibits two axes of the same type rotating against one of the fourth dimensional axes on their own.

The dice analogy does fail to show a particular feature of rotation in a fourth dimension, it can occur either clockwise or anticlockwise in the fourth dimension, even though the result looks the same because the fourth dimension remains invisible to us. Thus the rotations of the six dimensions about the fourth dimensions can each occur clockwise or anticlockwise, corresponding to the positive and negative generational, electroweak, and colour charges.

Consequently the following classes of spin become possible:

By applying a few simple rules to the above scheme we can account for the whole suite of observed particles.

1) A particle must have at least one rotation in space and one in time. This amounts to no more than saying that it must create a finite amount of spacetime curvature.

2) A particle must exhibit 't4-axis neutrality' which means that it can only have either zero or +3 or _3 rotations about t4.

3) Bosons (energy particles) consist of particle-antiparticle doublets that have aligned chiral spins, thus giving them twice the spin of Fermions (matter particles).

4) Particles cannot have more than one spatial rotation against s4 or more than one temporal rotation against t4. The s4/s2 and s4/s3 spins denote chiral spins transverse to the direction of propagation. The three spins t4/t1, t4/t2, and t4/t3 denote the colour charges of red, blue and green and their anti-colours when reversed, of which quarks and gluon 'halves' can only carry one.

This simple scheme can model all the particles and antiparticles we observe and also clarify some of their peculiarities. The principle of 't4-axis neutrality' means that electrons have to exhibit 3 units of electro-weak charge, (conventionally denoted as minus 1). The principle applies twice over to quarks. Quarks always have to appear in triplets as hadrons such as the familiar proton and neutron, or as meson doublets to preserve t4-axis neutrality. Quarks also have an electroweak charge of either +or _ 1/3, or + or _ 2/3 of the electron charge, to maintain t4-axis neutrality as they can only carry one colour charge each. Thus at each generation two types of quark (and antiquark) exist, the familiar Up and Down quarks that make up most of the matter in the universe, and also the Strange and Charm, and lastly the supermassive Bottom and Top varieties.

HD8 does not give a mass algorithm for calculating particle masses but it implies that the addition of spins with increasing charge causes increasing distortion of spacetime and thus requires a higher energy input which appears as mass, although not in any easily quantifiable way.

HD8 does explain the apparent non-conservation of generation in particle interaction. The generational characteristic has spatial reversibility, not temporal reversibility. It also explains the apparent parity violation of neutrinos and the W+ and W- bosons.

All neutrinos appear left-handed and all anti-neutrinos appear right-handed because only the direction of their s1 spins differentiates them. W- bosons consist of electron-antineutrino doublets whilst W+ bosons consist of positron-neutrino doublets.

According to HD8, neutrinos should annihilate in head on collision and liberate energy for new particle creation. The hypothesis also strongly suggests that neutrons behave in the same way at high enough energies, as they have overall colour and electroweak neutrality. Thus Black Holes and singularities do not form in galactic cores, only neutron stars form, and at high densities these stars begin to annihilate neutrons against each other, shedding matter and radiation back into space.

HD8 allows the existence of a wide range of massive and inconsequential bosons that will probably only have a fleeting existence, and it specifically predicts that the Higgs Boson does not exist. Mass arises as an intrinsic quality of particles as a consequence of their fourth dimensional nature.

The suite of known fundamental particles exhausts all possible spin combinations, and mass arises from spacetime curvatures subtended by these spins. The acceleration of charge certainly produces bosons, but I suspect that static fields consist of spacetime curvatures that propagate instantaneously and do not require so called virtual bosons to mediate them.

This proposition seems difficult if not impossible to falsify, even though it apparently contradicts special relativity, yet we could hardly use it for signalling purposes.

Gravitons thus probably exist in the form of a 'neutrino-antineutrino' type bosons caused by cataclysmic mass accelerations such as neutron star collisions but gravitational fields remain the product of spin induced spacetime curvatures, and both strong nuclear and electroweak static fields result from higher dimensional curvatures in spacetime.

Particle Physics buffs may care to adumbrate the spins which characterise each type of particle in the above scheme, the entire chart looks rather large, so I'll just present a few examples:-

(Photon showing both particle and antiparticle components)

Note that the photon consists of particle and antiparticle components, thus it has double the chiral spin of fermions, and no overall electroweak or generational charge.

Part 3.

Summary.

The above technical digression hopefully serves to show that the three-dimensional time posited in General Metadynamics also has considerable explanatory power in the field of particle physics as well as in modelling quantum and magical effects.

Strange quarks occasionally feature in reality for the same reason that Magic occasionally features in reality _ because reality has 3 dimensional time.

Chapter 6 and its appendix will examine the case for three-dimensional time on the cosmic scale, where it has profound implications for our whole philosophy on such topics as infinity, eternity, creation, eschatology, life, the universe, and the meanings that we may choose to abstract from it.

In passing it seems worth noting that the ratio of any of the six dimensions to its curvature dimension has the value of One to Pi. (See Hypersphere material). Now as an irrational and transcendental number Pi might just supply the chaotic basis for the apparently random collapse of quantum states.