## Introduction.

The hypothesis of three dimensional time arises from a consideration of the following two principles: -

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*‘If quantum gravity fails, try geometricating the quanta.’*

*‘If quantum gravity fails, try geometricating the quanta.’*

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*‘Probability lies at right angles to time.’*

*‘Probability lies at right angles to time.’*

## Part 1. Geometricating the Quanta.

Gravity resists quantisation because of the equivalence principle. Any particles gravitational/inertial mass depends on its energy; and mass and energy appear as continuously variable rather than as quantised.

Force carrying (boson) particles can transfer accelerations between matter (fermion) particles, and accelerated masses may indeed emit gravitons/gravitational waves. Such accelerations always indicate repulsive and recoil type effects at emission and absorption.

However gravitational ‘forces’ seem best understood as spacetime curvatures as in General Relativity.

Static electromagnetic/electroweak and nuclear ‘forces’ or ‘fields’, that remain conventionally vaguely modelled as mediated by un-quantised ‘virtual’ bosons, may instead arise from special forms of spacetime curvature with which only electrically or colour charged particles interact, and they can have attractive or repulsive effects.

If a particle exhibits multiple properties these properties must arise from yet more fundamental constituents, *or from the dynamic spacetime geometry of the particle*.

If fundamental particles consist of vorticitating hyperspheres (3-spheres or 4-balls) then a number of degrees of freedom exist for their hyperspherical ‘rotations’.

The fourth spatial dimension W, which arises when an object assumes a hypersphere configuration, lies orthogonal to all the other three spatial dimensions and represents the space-curvature. A hypersphere can spin through the spatial planes XY, XZ, YZ, and WX, WY, and WZ, and it can have double spins such as (XY, WZ), (XZ, WY), (YZ, WX).

Additionally with three temporal dimensions (say B, C, D) plus a temporal curvature dimension (say A), a fundamental particle could also have temporal spins corresponding to rotations about the planes BC, BD, CD, and so on.

Alternatively there remains the possibility of spatial spins occurring with respect to any of the 3 temporal dimensions, and perhaps superpositions of such spins to create the threefold character of colour, charge, and flavour/generation.

This potentially provides fundamental particles with enough degrees of rotational freedom to account for a wide range of particle properties and behaviours, as a particle can presumably exist in a superposition of multiple spin states simultaneously.

Hyperspheres spin about planes rather than through axes. One rotation through one fourth-dimensional axis converts a hypersphere into its mirror image; a second rotation through the same plane restores the hypersphere to its original orientation. These rotations can take place in one of two directions for which we have no words but they correspond to something like ‘outside-in’ and’ inside-out’ as they invert/evert the hypersphere with respect to the fourth dimension. In conventional physics notation they correspond to the various conventions of ‘plus’ or ‘minus’ characteristics, and charges. Part two of this paper will set out the case for a spacetime metric composed of 3 dimensions of space and also 3 dimensions of time, with both 3D space and 3D time curved by the geometry of gravity to give hyperspherical space and time.

The Four Dimensional Rotation of Fundamental particles model arises from a consideration of certain symmetries.

Firstly see this elegant display of objects rotated through various dimensions: -

http://eusebeia.dyndns.org/4d/vis/10-rot-1

If we use a line of limited length to represent a ‘one’ dimensional object and then rotate it in a plane and observe it only in that plane, it will appear to shrink to a point and then expand back to its original length but the other way round. (Imagine rotating a thin needle and looking at it in the plane of rotation, it appears to shorten and shrink to a dot as either the point or the blunt end becomes directly orientated towards the observer.

Something similar happens with a ‘two’ dimensional object like a sheet of card rotated towards or away from the observer, when viewed end on it appears to have shrunk into a one dimensional line, which then becomes restored to a sheet as rotation continues.

Of course, neither the needle not the sheet of card have actually expanded or contacted, if viewed from a wider perspective.

If we could observe a cube rotating in one plane through a fourth dimension, and observe it from right angles to that plane, then it would appear to shrink down to a plane before expanding back to a mirror image of itself.

If we could observe a cube rotating simultaneously in all three planes through a fourth dimension it would appear to shrink to a point before expanding again into a mirror image of itself, assuming that we viewed it from less than a full perspective in four dimensions.

Now the main properties of fundamental particles all seem to manifest in a (plus or minus) THREEFOLD FORM: -

**Particle Chiral Spin** – This can lie parallel (or anti-parallel) to the direction of the particles travel, and at lightspeed it must do so, however it can also lie orthogonal to direction of travel at sub-lightspeed, and in practise particles usually appear to travel in superpositions of these states of spin. Conventionally we denote fermion (matter) particle spins as plus or minus one-half units for right or left handed rotation respectively, however it seems simpler to denote this as simply +1 or -1.

**Particle Colour,** (Quantum Chromodynamics),- Hadron particles carry a ‘strong nuclear’ property arbitrarily designated red, blue, or green, or the three corresponding anti-colours.

**Particle Charge** – Electrons and protons conventionally have electric charges of -1 and +1 respectively. However, we have strong grounds for suspecting that a notation of -3 and +3 seems more appropriate because the constituent quarks of hadrons all have electric charges of plus or minus one third or two thirds.

**Particle Flavour** or Generation comes in three varieties and (three anti-varieties) for all matter particles, thus electrons have two heavier short lived variants called muons and tauons, and type one quarks come in three varieties also, down, strange, and bottom. Type 2 quarks also come in three varieties, up, charm and top, the elusive neutrino also comes in three varieties, and antiparticles exist for all types. Curiously, all fermion particles seem to exist to some extent as superpositions of all three of their possible flavours.

Currently it remains unclear which of the possible types of spin correspond to which particle properties, however if colour and charge spins have temporal axes CT symmetry emerges naturally from the model.

**HYPOTHESIS: -** All the above particle properties arise from the various spins that a quantum of spacetime can have.

Particle colour spins and charge spins remain conserved in all particle interactions.

Particle Chiral and Flavour spins do not remain strictly conserved in all particle interactions; they can become converted into other forms of energy such as momentum or angular momentum.

Boson particles consist of certain particle-antiparticle configurations.

The Higg’s mechanism does not confer mass. The Higg’s boson does not exist. Inertial mass arises from a Machian effect.

**PREDICTION:** -

This model describes the photon as consisting of a particle that carries a superposition of plus and minus one units of electric charge spin, and the Z boson as a particle that carries a superposition of plus and minus three units of electric charge spin. A third boson of this type should exist which carries a superposition of plus and minus two units of electric charge spin.

This boson may have already appeared in the anomalous decay of Beryllium 8, and it seems to have a mass-energy of about 17MeV.

## Part 2. Three Dimensional Time and Observed Reality.

A consideration of the mechanisms underlying indeterminacy, entanglement and superposition.

On a macroscopic level the idea that time might have the same three dimensional geometry as space seems at first absurd, the past seems to have happened in one particular way, even if it has become a bit hazy in places, time seems to have a singular moment of the present, even if different observers cannot entirely agree about it, and we expect only one future to manifest, although we can never remain totally confident about which one.

Some physics theories attempt to explain particle behaviours as arising from their activities in extra dimensions of space, however, so as not to upset the rest of macroscopic physics these extra dimensions of space have to have an extreme compactification down to incredibly small sizes and the theories which use them call for an embarrassingly large number of them.

Three dimensional time however can potentially describe particle behaviour and provide a reason for the mysterious existence of the two extra generations of fermions some of which occasionally occur naturally and the rest of which nature allows us to manufacture.

The two additional dimensions of time do not require ‘compactification’. We cannot really ‘see’ the size of one dimensional time, the present seems vanishingly short but the past and future appear potentially quite huge. The present moment doesn’t seem to have a readily discernable ‘length’; although may represent the smallest meaningful or measurable interval, but does it also have a ‘width’?

If time has three dimensions that we cannot see, then perhaps the linear time that we imagine merely consists of an imagined line joining a series of points that need not form a straight line from another perspective. Blindfolded persons wandering across a surface might well insist that they had walked in straight lines, but though those that can see might well disagree.

The existence of three phenomena in particular seems highly suggestive that time may have ‘full size’ orthogonal components, a domain through which probability, superposition and entanglement work.

The apparent indeterminacy that we observe in many physical processes can only arise from some sort of underlying mechanism which has a probability component that yields the still statistically reliable outcomes that we observe in nature. If a plane of time lies orthogonal to the ‘ordinary’ linear timeline which we construct or abstract by memory and expectation then it could conceal a plethora of possible alternatives which wave equations attempt to represent without precise specification. Indeed the relative angles or orientations of events in orthogonal time seem inaccessible to us and perhaps randomly chosen anyway.

Superposition consists of a particle or ensemble of particles apparently occupying two or more mutually exclusive states simultaneously. We cannot observe particles in superposed multiple states but we can infer that they must have come from superposed states immediately before measurement or interaction to account for their actual behaviour. For example an electron does not seem to have a single definable position at any instant as it orbits the nuclei of an atom, but rather it seems to act as though it occupies all points of a wider distribution that we identify as its ‘orbit’ which can extend over several atoms. This means that entire molecules behave as though they exist in two or more different states at the ‘same’ time. Indeed the whole of physical reality seems to exist in superposed states except for the brief instants when particles interact using just one of their superposed states chosen seemingly at random.

Entanglement occurs when two or more particles can remain in some sort of linked quantum state even if separated to arbitrarily large distances. If one then falls out of the quantum state the other(s) then seem instantaneously predisposed to fall out of it in a correlated matter even if no ordinary lightspeed signal could possibly have passed between them.

Whereas superposition consists of multiple events in the same space separated by sideways time, entanglement consists of multiple events at the same time separated by space.

Now the Minkowski formalism usefully allows us to work out spacetime separations by describing ‘ordinary’ time as an ‘imaginary’ form of space using an extension of Pythagoras’ theorem to four dimensions: -

Where means the imaginary number ‘i’, the square root of minus one, multiplied by lightspeed multiplied by the time. This has the effect of turning the temporal part of the spacetime separation or distance into a negative contribution to the separation.

Thus if we consider the spatial distance as just a one dimensional ‘s’ and square out the square root of minus one we obtain: -

This means that something travelling at lightspeed, for example a photon, experiences a zero spacetime separation between its point of emission and its point of absorption. Onboard flight time shrinks towards zero at lightspeed as predicted by Special Relativity and confirmed by experiment.

Now by taking the radical step of designating the orthogonal components of time as ‘imaginary’ or ‘unobservable’ forms of time, i.e. as: -

, then its Pythagorean component comes out as or simply so sideways time can act as type of space which we could regard as some sort of pseudo-space in which superposed states can reside.

Thus we can represent the full spacetime and sideways time separation between two events as: -

where and represent the axes of the plane of orthogonal, ‘sideways’, time.

Or more simply by squaring out and omitting some dimensions for convenience: -

(compact form, one spatial, ordinary temporal and one sideways temporal dimension.)

Now two cases of zero separation become immediately apparent: -

(Entanglement) (Superposition)

In superposition multiple linked events can occupy the same place but remain distinct because they occupy different positions in orthogonal time.

In entanglement multiple linked events can occur at the same time despite any degree of spatial separation.

(Note that this implies that we must not ignore the negative roots, the advanced wave solutions, and that entanglement works by advanced signals travelling backwards in time from the point of quantum state collapse to specify the correlation at the point of emission, as in Cramer’s Transactional Interpretation.)

Superposition implies that the perceived reality of 3D or 4D spacetime and the illusion of ‘substance’ and ‘stuff’ and material reality, with its attendant phenomena of indeterminacy, entanglement and superposition, arises from an interference pattern from quantum wave functions in a much more extensive 6D spacetime.

Moreover, 6D spacetime perhaps provides the skeleton for a ‘unified field theory’ which can accommodate all fundamental ‘forces’ or ‘fields’ as curvatures in spacetime and all fundamental particles as various arrangements of spin of the underlying spacetime quanta.

The questions of how hypersphere antipode length and vorticitation rate give rise to such phenomena as Compton wavelength and frequency and the existence of apparently massless exchange particles receive attention in the following Quantum Hyperspheres paper.