Specularium A Site exploring the hypothesis of Three-Dimensional Time

HD8. HYPERSPIN EIGHT DIMENSIONAL.

This paper attempts to describe the suite of all experimentally confirmed fundamental particles in terms of various spins of the six dimensional axes of space and time about the curvature axes of space and time. It makes some testable predictions. 

Warning , Hypothesis Under Continuous Construction!
"DON’T QUANTISE GRAVITY, GEOMETRICATE THE QUANTA!" 

The development of a unified theory which can model all of the phenomena currently described by both quantum theories and the special and general theories of relativity presents humanity with one of its greatest intellectual challenges. For over half a century the expected marriage between an incomplete understanding of fundamental particles and our understanding of gravity has remained overdue.
A unified theory would probably complete our understanding of both fundamental particles and gravity and would almost certainly tell us a great deal about cosmology and the mechanisms that may or may not allow the construction of starships. The hypotheses advanced in the following paper argue for a description of all fundamental "forces" as spins subtending curvatures within a six dimensional spacetime, consisting of three spatial and three temporal dimensions. The curvatures of space and time themselves constitute another two dimensions in a sense, making eight dimensions in all, see the VHC papers.

The model of fundamental particles, and their associated field and wave/particle boson interactions presented in this paper, seeks to augment the standard model by describing particles as singularities in a six dimensional space-time. This model provides a number of testable predictions within current or near future experimental capabilities. The belief that we can explain the behaviour of the universe with simple formulae of algebra/geometry such as F = ma, or
E = mc^2 informs this model. Such inelegant manifestations of mathematics as non-integral factors do not appear in it, despite their facility in its construction. Thus whilst quantitative data have elucidated qualitative mechanisms, only the latter, which interest the author, appear in their simplest algebraic form here.

2. The Hyperspin 8D model.

If a particle exhibits multiple properties these properties must arise from as yet more fundamental constituents, or from the spacetime geometry of the particle.
If, like space, time has three dimensions, and all spatial dimensions have equal orthogonality to all temporal dimensions, then fundamental particles can have the following spins and spacetime geometries to account for their various properties.

The ‘spin’ of a spatial or temporal axis against the fourth dimensional curvature axis basically consists of an inversion and then a restoration of the direction of that axis. Thus the particle rotates or ‘vorticitates’ into and out of its mirror image in either a ‘left’ (-) or ‘right’ (+) direction through the unobserved fourth dimensions of space or time.

Fig 1.Spins about various axes, and particle properties. Where s1, s2, s3 = spatial axes, t1, t2, t3 = temporal axes, and where s4 and t4 represent the curvature axes of space and time respectively.
 

Four codes for particle properties, S, spin, C, colour, E, electroweak, and G, generation, will frequently appear in the remainder of this paper.

Three-dimensional time need not conflict with our experiences and observations, rather it may provide a basis for the probabilistic behaviour of matter and energy.

To simplify this paper numerically, the smallest unit of fundamental fermion chiral spin, h / 4 pi will appear as 1 rather than the conventional ½. The electroweak charge on an electron will appear as -3 instead of the conventional -1, and thus the electroweak charges on quarks and anti-quarks will appear as -1 or 2 and 1 or -2 respectively.

The application of five principles to the spacetime spins shown in fig.1 can explain the manifestation and much of the behaviour of all observed particles to date: -

a) Spin Conservation. All particle reactions conserve all spins. Chiral spins can interconvert with orbital angular momenta.

b) Phenomenisation. A fundamental particle must have both S and G spins to exist. A particle must displace a finite amount of both space and time to exist.

c) T axis Neutrality. All particles must have +3, or -3, or 0, t-axis spins. Since both C and E "charges" have t axes, we thus only observe C1 E-1 and C1 E2 quarks and C-1 E1 and C-1 E-2 anti-quarks. Amongst the leptons we thus observe only the C0 E0 neutrinos and the C0 E-3 electrons, and C0 E3 positrons. This principle also generates predictions, see later. This principle thus defines the types of particle that can exist in each generation and it has a further effect on colour bearing particles. The colour spins carry more energy than the electroweak spins, and colour bearing particles will configure themselves together to achieve a further 'colour t axis neutrality' thus producing the familiar baryon quark triplet, with 3 colour t axes (or -3 in the case of anti-quarks) and meson quark anti-quark doublets with 0 colour t axes. A third and weaker manifestation of t axis neutrality occurs in respect to electroweak t axes in baryons, in that only baryons with electroweak charges of 0, 3 or -3 such as neutrons and protons and exhibit stability.
 
d) The inertial and gravitational components of mass arises from the total spacetime distortions of S,C, E, and G spins and from the orbital angular momentum, in short from the total energy. Colour and electroweak spins also subtend higher dimensional spacetime distortions that interact only with themselves. All spins occur about the s4 and t4 axes of spacetime curvature that we recognise as gravity in general relativity.

e) Bosons consist of 'particle / anti-particle' components that can carry any amount of mass / energy as orbital angular momentum. The anti-particle components of bosons correspond to the normally discarded advanced wave solutions to Maxwell's equations. Bosons arise as distortions in fields when fermions undergo quantum jumps and accelerations.

3.Particle Properties in the Hyperwarp 6D model
A brief description follows of the types of spin as shown in fig.1.
a) Chiral spin S.
The purely spatial spin of a particle could appear in Cartesian co-ordinates as z / xy, x / yz, or y /xz. Space has no preferred direction but we conventionally designate the direction of measurement / observation / interaction as z. Obviously a particle can only have a single purely spatial spin, designated s1 or s2 or s3, in this model. At lightspeed a particles chiral spin must align parallel or anti parallel to the direction of travel, at sub-light speeds it can orient itself transversely as well. All fermions (except neutrinos) can have + or - (right or left handed) chiral spins. In neutrinos and anti-neutrinos only chirality differentiates between particle and anti-particle. Note that in this model chiral spin undergoes spatial but not temporal reversal. The neutrino component of charged weak bosons dictates their chirality. Other bosons can have both chiralities.

b) Colour Spin, C.
A particle can have only one of the three possible purely temporal spins t1 or t2 or t3 against t4, which in quantum chromodynamics carry the arbitrary designations, in no particular order, of red, green, and blue or their anti-colours for anti-particles. Because of the temporal axis, colour charge undergoes temporal but not spatial reversal, with anti-particles carrying anti-spin and hence anti-colour.

c) Electroweak Spin, E.
A particle can have (within the limits of 't' axis neutrality) spins of the spatial axes s1, s2, or s3 about the temporal axis t4. Having a temporal axis, E undergoes temporal, but not spatial reversal to yield anti-particles of opposite electroweak charge.

d) Generational Spin, G.
A particle can have spin of a temporal axes t1, t2, or t3 about each of the spatial axis s4. Having a spatial axis, G undergoes spatial reversal not temporal reversal. Both particles and antiparticles can have a G spin of either type, rather as they can have chiral spins of either type. This explains the apparent non-conservation of generation in particle reactions because we cannot simply ascribe positive generation to particles and negative generation to antiparticles.

To account for the experimentally observed behaviour of the phenomena of mass and gravity we can make the following assumption:- All spins subtend a spacetime curvature in proportion to the energy they embody. All so-called "fields" consist of such curvatures. Colour and electroweak spins also subtend higher dimensional curvatures that interact only with themselves. The overall basic spacetime curvature (gravity) resists the acceleration and movement of all forms of mass and energy. This particular expression of Mach's Principle can account for the apparent equivalence of inertial and gravitational mass and explain the phenomena currently within the models of special and general relativity.

4. Apparent Asymmetries.
A universe with a net total of zero spins has great philosophical elegance, yet the universe appears to contain little anti-matter. Now t-axis neutrality energetically favours t +3 or t -3 configurations over t 0 configurations achieved by t +1 plus t -1. (Thus d quarks undergo beta decay into u quarks and free neutrons decay into protons). The problem of the apparent lack of anti-matter basically reduces to the lack of anti-colour spins. The universe has taken the lower energy route in splitting symmetry as R+G+B=O rather than C+ plus C- =O. We inhabit a colour neutral and electrically neutral universe, that does not require an equal mass of antimatter for neutrality.
The matter dominated universe still has overall G-spin neutrality due to the spatial reversibility of G. The Universe does not contain much antimatter for the same reason it contains few 2nd and 3rd generation particles, energy considerations do not favour it.

 

5. Particles, Fields, and Bosons in the Hyperwarp 6D model.
Fig.2.

Hyperspin Type

Fermion

Field

Boson

1

Neutrino

Graviton?

S

C

E

G

S

C

E

G

-1

1,2,3

&2

@1

2

Forbidden

Electroweak

Photon

S

C

E

G

&2

@1

@1

3

Forbidden

Electroweak

?

4

Electron

Electroweak

Z Boson

S

C

E

G

S

C

E

G

&1

-3

1,2,3

&2

@3

@1

W Bosons

S

C

E

G

&2

&3

@1

5

Forbidden

Colour

Gluon

S

C

E

G

&2

@1

@1

6

Quark Type 1

Colour / Electroweak

(mesons)

S

C

E

G

&1

1

-1

1,2,3

7

Quark Type 2

Colour / Electroweak

(mesons)

S

C

E

G

&1

1

2

1,2,3

KEY.. S, C, E, G indicate chiral, colour, electroweak, and generational spins, as in fig.1. & indicates plus or minus. @ indicates plus and minus existing together in a condition of non-annihilatory cancellation in bosons and mesons. Anti-neutrinos have an opposite chiral spin to neutrinos, other anti-fermions (not shown) have opposite C & E spins to the corresponding fermions. Mesons comprise quark/antiquark pairs, many combinations exist, and they may play some role in binding nucleons.
Many mesons do not have the S&2,G@1 characteristics of bosons, nor do they behave quite like bosons. This model does not exclude type 3 bosons, some evidence exists for a boson of this type, see Confirmation page. The Z boson has components corresponding to an electron / position pair whilst the W- and W+ bosons have components equivalent to electron / anti-neutrino and position / neutrino pairs respectively. All weak bosons carry a large mass / energy in the form of orbital angular momentum between particle and anti-particle components because of the highly energetic processes that create them, and they all couple strongly with elecroweak fields, thus severely restricting their range. Gluons, as true wave / particle bosons would have prodigious mass / energies and would interact very strongly with strong nuclear fields and thus we observe only the field manifestation. Some Weak force bosons may carry G&2 or perhaps other values.

6. Further Considerations upon Fields and Bosons.

Fields consist of the spacetime curvature centred on fermions that extends indefinitely from fermions in the case of electromagnetism and gravity, but only acts at close range for the colour force. Fields exist non locally as curvatures of space-time. Bosons however can only propagate at light speed or less.
When a fermion quantum jumps or becomes accelerated across a spatial interval, it creates a boson with a wavelength proportional to the jump energy.
A quantum jump somehow creates a particle/antiparticle configuration with a double spin and concealed (+AND -) spacetime curvatures which exhibit no overall "charges" except for the W+& W-. Some sort of action-reaction mechanism seems to operate here. However, charged weak bosons and possibly leptoquarks that have asymmetric particle anti-particle components can still exhibit colour or electroweak charge.
Bosons can carry any amount of energy in the form of orbital angular momentum between the particle and anti-particle components. This orbital angular motion creates the phenomena of wavelength and frequency in bosons.
Fields as spacetime curvatures can have attractive or repulsive effects, real bosons always have repulsive effects, and virtual bosons do not exist.

7. Problems and Questions Arising.

Three dimensional time need not create any conflict with experience and observation. We can only perceive and hence measure infinitesimally small 'instants of now', and then string them together by effort of memory and expectation, or by records and calculation, to create an apparent time 'line'. However, such a time line could arise from selecting points from within a three dimensional matrix. Indeed the probabilistic nature of reality, which appears with respect to the indeterminate future of personal experience, and with respect to the indeterminate future and past in the quantum behaviour of particles, suggests that reality evolves through a three dimensional rather than a linear time frame.
It means very little to say that an electron, for example, can 'be' in two places at once or even that an electron 'was' in two places at once. Rather we should perhaps say that electrons behave as though more than one history seems to have contributed to their behaviour at the moment of observation /interaction.
The whole problem of the collapse of wave functions may find a resolution based on the idea that whilst particles can only interact at a definite point in time, their history and future requires three rather than one temporal co-ordinates to give a complete specification.
The two 'extra' dimensions of time suggested in this model, which in effect provide a plane of time (or possibility) orthogonal to linear classical relativistic time, as we commonly conceptualise it, may offer scope for the construction of a more general expression of Heisenburg's uncertainty principle. Indeed the 'imaginary' factors that yield appropriate probabilistic values in Schrodinger's wave equations suggest that the universe has more dimensions than the conventional four.
The Exclusion Principle. The Pauli exclusion principle, which partially models the atomic architecture and differentiates between the behaviour of fermions and bosons associated with it, appears in the HD8 model as follows; No two fermions with identical or completely opposite spins and curvatures can occupy the same quantum state.

Bosons do not interact with each other or resist each others passage where they have a net of zero spacetime spins, thus for example the concealed electroweak charges in photons to not interact with those in other photons.

Singularities and Renormalisation. The infinities that the standard theory re-normalises away also appear in the HD8 model in the sense that the warping of 8D space-time becomes theoretically infinite if we calculate it for zero dimensional point sources. Any calculation which creates an infinity plainly contains a mistake. HD8 thus strongly implies a quantisation of spacetime itself. 

Generational Parity Reversal As a consequence of its spatial axis, generation,G, undergoes parity reversal, so reversing the direction of travel of a particle changes the sign of its generational charge, in the same way that its chiral spin becomes reversed. Thus a sufficiently energetic collision between a neutrino and an antineutrino can produce a Z boson with S2 and G@1, but a collision between 2 neutrinos (or between 2 antineutrinos) can lead to an annihilation creating 2 photons or new pairs of neutrinos of other generations. Collisions between charged or colour bearing particles  will not lead to annihilations as the charges or colours cannot cancel. However as any two particles of the same type can have opposite G if travelling in opposite directions, the universe can exhibit overall generational neutrality without antimatter.

Fig.3. Neutrino(n), and antineutrino(a) S and G values with respect to the directions > and <.

The Origin of Mass. In the HD8 hypothesis mass arises from the intrinsic hyperspins of particles, which subtend a spacetime curvature. Its existence does not require a Higg’s field mediated mechanism. I suspect that no simple algorithm can exist to predict particle masses because the various spins fit together in complicated ways that require inputs of energy that vary due to many factors. I do not consider the lack of a simple particle mass algorithm any more surprising than the lack of a simple algorithm that can predict the stable isotopes of the periodic table.

Predictions from the HD8 model

a) No more generations of particles can exist. (Subject only to falsification)
b) No Higgs particle exists. (Subject only to falsification)
c) As it seems that no known natural process except, perhaps, neutron star or black hole collisions could cause a sufficiently large quantity of matter to undergo a sufficient acceleration to produce graviton bosons in detectable quantities, we shall never easily detect gravity waves (subject only to falsification).
d) The principle of t-axis neutrality does permit the existence of a number of exotic bosons corresponding to configurations such as :
d-quark/positron, or d-antiquark/electron or any type of quark/antineutrino or antiquark/neutrino
Within HD8 theory a "leptoquark boson" does not really represent a fifth force of nature, anymore than weak (W-, W+, or Z) bosons represent anything other than a special case of electromagnetism.
e) The quantisation of particle properties in terms of spacetime curvature implies a quantisation of spacetime itself and the top quark represents the maximum possible curvature at any point.
f) Neutrinos can annihilate against neutrinos in head on collisions. Antineutrinos can likewise annihilate against antineutrinos. Such collisions could create photon pairs or pairs of neutrinos of other generations. This controversial proposition lies open to experimental confirmation. It may also contribute a solution to the solar neutrino problem.
h) Neutrons can annihilate against other neutrons in sufficiently energetic collisions. Although we cannot currently accelerate or steer neutrons to do this, it provides a potential method of converting mass directly and completely into energy. It also prevents neutron stars collapsing into black holes or singularities.

Overview.
The hypotheses advanced above extend the general relativistic principle of a gravitational field as a distortion of space-time to the idea that all fields exist as various kinds of space-time distortion. Gravity has a special status in that it couples to all types of charge and spin and also resists, in Machian fashion, the acceleration of such spins and curvatures.
The three dimensional time hypothesis at least has the virtue of describing all known fundamental particles as arising from a single mechanism, spin, and it does not invoke swarms of as yet undetected particles. However, it differs from both the Copenhagen interpretation and the multiple universe model in that it implies that the probabilistic future and past of an event arise from extra temporal properties which we do not otherwise notice. Thus although events actually occur at a singular point in time, much as they do at a singular point in space, they appear to have multiple 'universe' pasts and futures. By analogy, a single frame high speed camera photograph of a cannon ball in flight gives no information about its trajectory. If, by an extension of the Minkowski metric, we consider the two temporal dimensions 'orthogonal' to the 'direction' of measurement as 'imaginary forms of imaginary time' in the mathematical sense then we can use real rather than imaginary numbers to describe them in which case they behave mathematically and for the purposes of visualisation, rather like an extra spatial plane.

Epilogue.
What 'are' Fermions, Fields, and Bosons?
Science should not pretend to answer questions about ontology or meaning. The studious avoidance of concepts of 'is-ness' or 'being' in this paper reflects this principle. Science should only attempt to discern quantity, mechanism, similarity and difference.

This model suggests that we can usefully consider fermions as vorticitating units of quantised space-time subtending curvatures affecting other fermions at a distance (giving rise to what we call fields). Secondly that the quantum jumping or acceleration of fermions can cause energy to propagate across space-time, (giving rise to what we call bosons).
None of these phenomena submit to easy visual analogy. None of these phenomena resemble anything in the domain of our everyday experience. We can never know what they 'are', for they resemble only themselves. We can only strive to improve our models of what they seem to do, and what we can do with them..
The author thanks those physicists who have offered insights and criticisms that have helped formulate the above hypotheses, and welcomes further criticism and collaboration, particularly to flesh out the algebra implied. In a later paper I hope to address the problems of quantum indeterminacy, superposition, and entanglement, in terms of three dimensional time. Superposition in particular may arise from 3D time pasts and futures which "collapse" to a 1D time present moment of observation.