I am a proponent of what I call TGD (Topological Geometrodynamics), which could be seen as a generalisation of superstring models obtained by replacing strings with 3-D surfaces representing 3-spaces at microscopic level: space time is a surface in 8-D H=M4xCP2. TGD could be also seen as a solution to the energy problem of General Relativity: the notion of four-momentum is ill-defined in GRT since the symmetries of empty Minkowski space of special relativity are lost so that Noether's Theorem does not apply (NT says that every infinitesimal symmetry corresponds to conserved quantity).
I am not involved with tetryonic geometry although I have proposed a model correlating Platonic (icosahedral and tetrahedral) geometries, music (12-note scale--number of icosahedral vertices), and genetic code (20 amino-acids-20 icosahedral faces and 64 DNA codons as 3-chords of bioharmony). The model predicts correctly vertebrate genetic code and predicts also alternative code realized in biology involving 21st and 22nd amino-acids.
One obtains rather beatiful sounding chord artificial music as random sequences of chords of bio-harmonies assuming that subsequent chords have at least one note in common. An exciting possibility is that this rule could apply to real DNA sequences: this is a testable prediction. There are 256 different bio-harmonies obtained as combinations of 3 basic harmonies of different types defined by icosahedral Hamiltonian cycles with symmetries for which symmetry group is cyclic Zn, n=6,4,2: hexagon, square, line segment) and defines the type of the harmony: the number of cycles is 11+11=22 when one counts also the direction in which one goes through the cycle. A single step along cycle corresponds to quint. These harmonies are rather complex since there are 64 basic 3-chords (rock'n roll harmony has three chords whereas simplest songs for children make it with two chords;-)).
Below brief answers to the questions.
- How do you cover the tachyon?
Tachyon does not belong to the spectrum of real particles in TGD. Tachyonic ground states are possible for elementary particles but physical states are non-tachyonic.
- How do you cover the graviton?
Graviton is one particular particle: all the particles predicted by TGD have similar topological and geometric structure of string like object - closed magnetic flux tube carrying monopole flux- and are accompanied by string world sheet- now imbedded inside 4-D space-time surface.
- How do you handle color from QCD?
Color corresponds to isometries of CP2 factor of the 8-D imbedding space H= M4xCP2 in which space-times are 4-surfaces. TGD predicts that also leptons can have coloured excitations and they could be light. Color is in TGD like orbital angular momentum whereas in QCD in it is like spin. Standard model symmetries are geometrized in terms of isometric and vielbein group of H. Weak gauge potentials are projections of components of CP2 spinor connection. Color gauge potentials those of CP2 Killing vector fields.
Many-sheeted space-time approximated by GRT space-time by replacing sheets with single slightly curved region of M4 gives the ordinary gauge potentials as sums of induced spinor connections for sheets. Also the metric of GRT space-time is obtained in analogous manner from the metrics of space-time sheets.
- When you describe the proton and neutron the fact that the number of quanta in the base tetrahedra can be more - does this imply that there are heavier versions of protons and neutrons.
My model of proton and neutron does not involve tetrahedra. It involves color magnetic flux tubes carrying most of the rest mass of baryon and currents quark masses are very low. I have considered also a dual description based on static quarks giving most of the baryon mass. Static valence quark would correspond to current quark plus associated flux tube.
- What is your view on Dark Matter?
Dark matter in TGD framework correspond to a hierarchy of ordinary matter in phases in which Planck constant heff=n× h is integer multiple of ordinary Planck constant. These phases are macroscopically quantum coherent for large values of heffand play central role in biology by making macroscopic quantum coherence possible since quantum scales are scaled up by n=heff/h. Dark matter would make living matter living.
Galactic dark matter does not form 3-D large halo but one has necklace like structures: a thread representing cosmic string (magnetic flux tube) and carrying dark energy as magnetic energy containing galaxies like pearls in necklace. Constant velocity spectrum for distant starts follows automatically from the gravitational potential of the cosmic string: the motion along cosmic string direction is free, this is a specific prediction).
A model Pioneer and Flyby anomalies allows to conclude that dark matter can be concentrate on 2-D surfaces with universal density .8 kg/m2. The estimate for effective surface density in galactic nucleus is essentially same. TGD makes also predictions: for instance, in Earth Moon system the analog of Pioneer anomaly should be observed. TGD explains all findings (that I know) appearing as anomalies in CDM and MOND models.
- What is your view on Dark Energy and the Cosmological Constant?
Dark energy correspond to magnetic energy at magnetic flux quanta (tubes and sheets: space-time sheets of particular kind) carrying dark matter as large heff phases. Cosmological constant provides effective description at GRT limit of TGD, which I briefly summarised above.
At more microscopic limit the negative "pressure" associated with magnetic flux tubes allows to understand the accelerated expansion. There is an accelerating expansion also during the TGD counterpart of inflationary phase identifiable as a transition period from a phase in which one has gas of string like objects (2-D M4 projection) to a phase in which one has space-time sheets (4-D M4 projection).
Periods of accelerating expansion would quite generally correspond to periods of criticality and imbeddable-to-H critical cosmologies are unique apart from duration.
- How do you cover the anyon as proposed for hidden variables by people such as Bryan Sanctuary from Mc Gill University (Youtube videos kIysfrByZHE, vXRq1QTrtSg, ABnIvcvn2bc, PcwQWa-rV9Y)
I have proposed a model of anyons and FHE based on dark variants of electrons having thus non-standard Planck constant heff=n×h explaining fractional charges.
- In 'A Hidden Dimension, Clifford Algebra, and Centauro Events - 0703.0053v1.pdf' by Carl Brannen the particle 'Binon' is described. Is this the same as the quanta that you refer to?
No. TGD predicts a hierarchy of scaled up versions of standard model physics both weak and QCD type physics. Also leptonic variants of QCD type physics for which there exists evidence from anomalies discovered in heavy ion collisions already at seventies. These copies are labelled by Mersenne primes Mn= 2n-1. Ordinary hadron physics corresponds to M107 and at LHC energies a copy labelled by M89 should be discovered and this year is particularly exciting at LHC. There is already now evidence for M89 hadron physics, for instance the anomalous behaviour of what was thought to be QCD plasma (already at RHIC and later at LHC). The mass scale of hadrons of this physics is roughly 512 that of ordinary hadrons. In Centauro events hadrons of M89 hadron physics would be created and decay to ordinary hadrons.
- What is your attitude to Bohm Pilot Wave theory?
Pilot wave theory was an attempt to save determinism of classical physics. This was very natural at the time when Pilot Wave theory was proposed. This is however also ironic since Bohm took consciousness seriously and one might have expected that he accepts free will.
The idea was to reproduce by pilot wave approach the basic (and classically extremely strange looking) facts of quantum measurement theory. The attempt failed. The approach has also fatal mathematical problems: the non-linear structure involved in separation of modules and phase of Schroedinger amplitude produces horrible singularities in quantum field theory and fermionic statistics is an insurmountable problem.