Quantum Gravity and String Theory

0908 Submissions

[25] viXra:0908.0112 [pdf] submitted on 30 Aug 2009

On Holography and Quantum Mechanics in Yang's Noncommutative Spacetime with a Lower and Upper Scale

Authors: Carlos Castro
Comments: 14 pages, This article appeared in Progress in Physics vol. 2 April (2006) 86-92.

We explore Yang's Noncommutative space-time algebra (involving two length scales) within the context of QM defined in Noncommutative spacetimes; the Holographic principle and the area-coordinates algebra in Clifford spaces. Casimir invariant wave equations corresponding to Noncommutative coordinates and momenta in d-dimensions can be recast in terms of ordinary QM wave equations in d+2-dimensions. It is conjectured that QM over Noncommutative spacetimes (Noncommutative QM) may be described by ordinary QM in higher dimensions. Novel Moyal-Yang-Fedosov-Kontsevich star products deformations of the Noncommutative Poisson Brackets (NCPB) are employed to construct star product deformations of scalar field theories. Finally, generalizations of the Dirac-Konstant and Klein-Gordon-like equations relevant to the physics of D-branes and Matrix Models are presented.
Category: Quantum Gravity and String Theory

[24] viXra:0908.0111 [pdf] submitted on 28 Aug 2009

On Modified Weyl-Heisenberg Algebras, Noncommutativity Matrix-Valued Planck Constant and QM in Clifford Spaces

Authors: Carlos Castro
Comments: 22 pages, This article appeared in the Journal of Physics A : Math. Gen 39 (2006) 14205-14229.

A novel Weyl-Heisenberg algebra in Clifford-spaces is constructed that is based on a matrix-valued HAB extension of Planck's constant. As a result of this modifiedWeyl-Heisenberg algebra one will no longer be able to measure, simultaneously, the pairs of variables (x, px); (x, py); (x, pz); (y, px), ... with absolute precision. New Klein-Gordon and Dirac wave equations and dispersion relations in Clifford-spaces are presented. The latter Dirac equation is a generalization of the Dirac-Lanczos-Barut-Hestenes equation. We display the explicit isomorphism between Yang's Noncommutative space-time algebra and the area-coordinates algebra associated with Clifford spaces. The former Yang's algebra involves noncommuting coordinates and momenta with a minimum Planck scale λ (ultraviolet cutoff) and a minimum momentum p = ℏ/R (maximal length R, infrared cutoff ). The double-scaling limit of Yang's algebra λ → 0, R → ∞, in conjunction with the large n → ∞ limit, leads naturally to the area quantization condition λR = L2 = nλ2 ( in Planck area units ) given in terms of the discrete angular-momentum eigenvalues n. It is shown how Modified Newtonian dynamics is also a consequence of Yang's algebra resulting from the modified Poisson brackets. Finally, another noncommutative algebra ( which differs from the Yang's algebra ) and related to the minimal length uncertainty relations is presented . We conclude with a discussion of the implications of Noncommutative QM and QFT's in Clifford-spaces.
Category: Quantum Gravity and String Theory

[23] viXra:0908.0108 [pdf] submitted on 29 Aug 2009

The Dirac Equation in a Gravitational Field

Authors: Jack Sarfatti
Comments: 7 pages

Einstein's equivalence principle implies that Newton's gravity force has no local objective meaning. It is an inertial force, i.e. a contingent artifact of the covariantly tensor accelerating (non-zero g's) Local Non-Inertial Frame (LNIF) detector. Indeed, Newton's gravity force disappears in a locally coincident non-accelerating (zero g) Local Inertial Frame (LIF). The presence or absence of tensor spacetime curvature is completely irrelevant to this fact. In the case of an extended test body, these remarks apply only to the Center of Mass (COM). Stresses across separated parts of the test body caused by the local objective tensor curvature are a logically independent separate issue. Garbling this distinction has generated not-even-wrong critiques of the equivalence principle among "philosophers of physics" and even among some venerable confused theoretical physicists. Non-standard terms coupling the spin-connection to the commutator of the Dirac matrices and to the Lorentz group Lie algebra generators are conjectured.
Category: Quantum Gravity and String Theory

[22] viXra:0908.0107 [pdf] submitted on 28 Aug 2009

Gauge Theories of Kac-Moody Extensions of W Algebras as Effective Field Theories of Colored W Strings

Authors: Carlos Castro
Comments: 11 pages, This article appeared in Advanced Studies in Theoretical Physics, 2, no. 17, (2008) 825 - 835.

A novel invariant gauge field theory realization of Kac-Moody extensions of w(w1+∞) algebras and based on a Lie group G is constructed. The most relevant physical feature of this theory is that it describes an effective field theory of "colored" internal w(w1+∞) strings when G = SU(3). We conclude with a discussion of how these theories might provide infinite higher conformal-spins extensions of Grand Unified Models and the Standard Model in four dimensions.
Category: Quantum Gravity and String Theory

[21] viXra:0908.0106 [pdf] submitted on 28 Aug 2009

The Extended Relativity Theory in Born-Clifford Phase Spaces with a Lower and Upper Length Scales and Clifford Group Geometric Unification

Authors: Carlos Castro
Comments: 61 pages, This article appeared in Foundations of Physics vol 35, no.6 (2005) 971.

We construct the Extended Relativity Theory in Born-Clifford-Phase spaces with an upper R and lower length λ scales (infrared/ultraviolet cutoff ). The invariance symmetry leads naturally to the real Clifford algebra Cl(2, 6,R) and complexified Clifford ClC(4) algebra related to Twistors. A unified theory of all Noncommutative branes in Clifford-spaces is developed based on the Moyal-Yang star product deformation quantization whose deformation parameter involves the lower/upper scale (ℏλ/R). Previous work led us to show from first principles why the observed value of the vacuum energy density (cosmological constant ) is given by a geometric mean relationship ρ ~ L-2PlanckR-2 = L-4P(LPlanck/R)2 ~ 10-122M4Planck, and can be obtained when the infrared scale R is set to be of the order of the present value of the Hubble radius. We proceed with an extensive review of Smith's 8D model based on the Clifford algebra Cl(1,7) that reproduces at low energies the physics of the Standard Model and Gravity, including the derivation of all the coupling constants, particle masses, mixing angles, ....with high precision. Geometric actions are presented like the Clifford-Space extension of Maxwell's Electrodynamics, and Brandt's action related to the 8D spacetime tangentbundle involving coordinates and velocities ( Finsler geometries ). Finally we outline the reasons why a Clifford-Space Geometric Unification of all forces is a very reasonable avenue to consider and propose an Einstein-Hilbert type action in Clifford-Phase spaces (associated with the 8D Phase space) as a Unified Field theory action candidate that should reproduce the physics of the Standard Model plus Gravity in the low energy limit.
Category: Quantum Gravity and String Theory

[20] viXra:0908.0104 [pdf] submitted on 27 Aug 2009

Strings and Membranes from Einstein Gravity, Matrix Models and W Gauge Theories as paths to Quantum Gravity

Authors: Carlos Castro
Comments: 49 pages, This article appeared in the Int. J. Mod. Phys. A 23, no. 24 (2008) 3891

It is shown how w,w1+∞ Gauge Field Theory actions in 2D emerge directly from 4D Gravity. Strings and Membranes actions in 2D and 3D originate as well from 4D Einstein Gravity after recurring to the nonlinear connection formalism of Lagrange-Finsler and Hamilton-Cartan spaces. Quantum Gravity in 3D can be described by aW1 Matrix Model in D = 1 that can be solved exactly via the Collective Field Theory method. We describe why a quantization of 4D Gravity could be attained via a 2D Quantum W gauge theory coupled to an infinite-component scalar-multiplet. A proof that non-critical W (super) strings are devoid of BRST anomalies in dimensions D = 27 (D = 11), respectively, follows and which coincide with the critical (super) membrane dimensions D = 27 (D = 11). We establish the correspondence between the states associated with the quasi finite highest weights irreducible representations of W,W algebras and the quantum states of the continuous Toda molecule. Schroedinger-like QM wave functional equations are derived and solutions are found in the zeroth order approximation. Since higher-conformal spin W symmetries are very relevant in the study of 2D W Gravity, the Quantum Hall effect, large N QCD, strings, membranes, ...... it is warranted to explore further the interplay among all these theories.
Category: Quantum Gravity and String Theory

[19] viXra:0908.0102 [pdf] submitted on 27 Aug 2009

On Generalized Yang-Mills Theories and Extensions of the Standard Model in Clifford (Tensorial) Spaces

Authors: Carlos Castro
Comments: 31 pages, This article appeared in Annals of Physics vol. 321, no.4 (2006) 813-839.

We construct the Clifford-space tensorial-gauge fields generalizations of Yang-Mills theories and the Standard Model that allows to predict the existence of new particles (bosons, fermions) and tensor-gauge fields of higher-spins in the 10 Tev regime. We proceed with a detailed discussion of the unique D4 - D5 - E6 - E7 - E8 model of Smith based on the underlying Clifford algebraic structures in D = 8, and which furnishes all the properties of the Standard Model and Gravity in four-dimensions, at low energies. A generalization and extension of Smith's model to the full Clifford-space is presented when we write explictly all the terms of the extended Clifford-space Lagrangian. We conclude by explaining the relevance of multiple-foldings of D = 8 dimensions related to the modulo 8 periodicity of the real Cliford algebras and display the interplay among Clifford, Division, Jordan and Exceptional algebras, within the context of D = 26, 27, 28 dimensions, corresponding to bosonic string, M and F theory, respectively, advanced earlier by Smith. To finalize we describe explicitly how the E8 X E8 Yang-Mills theory can be obtained from a Gauge Theory based on the Clifford ( 16 ) group.
Category: Quantum Gravity and String Theory

[18] viXra:0908.0100 [pdf] submitted on 26 Aug 2009

Noncommutative (Super) P-Branes and Moyal-Yang Star Products with a Lower and Upper Scale

Authors: Carlos Castro
Comments: 8 pages, This article appeared in Phys. Letts B 626 (2005) 209.

Noncommutative p-brane actions, for even p+1 = 2n-dimensional world-volumes, are written explicitly in terms of the novel Moyal-Yang ( Fedosov-Kontsevich ) star product deformations of the Noncommutative Nambu Poisson Brackets (NCNPB) that are associated with the noncommuting world-volume coordinates qA, pA for A = 1, 2, 3, ...n. The latter noncommuting coordinates obey the noncommutative Yang algebra with an ultraviolet LP (Planck) scale and infrared (R ) scale cutoff. It is shown why our p-brane actions in the "classical" limit ℏeff = ℏLP/R → 0 still acquire nontrivial noncommutative corrections that differ from ordinary p-brane actions. Super p-branes actions in the light-cone gauge are also amenable to Moyal-Yang star product deformations as well due to the fact that p-branes moving in flat spacetime backgrounds, in the light-cone gauge, can be recast as gauge theories of volume-preserving diffeomorphisms. The most general construction of noncommutative super p-branes actions based on non ( anti ) commuting superspaces and quantum group methods remains an open problem.
Category: Quantum Gravity and String Theory

[17] viXra:0908.0095 [pdf] submitted on 25 Aug 2009

An Exceptional E8 Gauge Theory of Gravity in D = 8, Clifford Spaces and Grand Unification

Authors: Carlos Castro
Comments: 22 pages, This article will appear in the Int J. Geom. Meth in Mod Phys vol 6 , no. 6 (Sept 2009)

A candidate action for an Exceptional E8 gauge theory of gravity in 8D is constructed. It is obtained by recasting the E8 group as the semi-direct product of GL(8,R) with a deformed Weyl-Heisenberg group associated with canonical-conjugate pairs of vectorial and antisymmetric tensorial generators of rank two and three. Other actions are proposed, like the quartic E8 group-invariant action in 8D associated with the Chern-Simons E8 gauge theory defined on the 7-dim boundary of a 8D bulk. To finalize, it is shown how the E8 gauge theory of gravity can be embedded into a more general extended gravitational theory in Clifford spaces associated with the Cl(16) algebra and providing a solid geometrical program of a grand-unification of gravity with Yang-Mills theories. The key question remains if this novel gravitational model based on gauging the E8 group may still be renormalizable without spoiling unitarity at the quantum level.
Category: Quantum Gravity and String Theory

[16] viXra:0908.0094 [pdf] submitted on 25 Aug 2009

Complex Gravitational Theory and Noncommutative Gravity

Authors: Carlos Castro
Comments: 11 pages, This article appeared in Phys Letts B 675, (2009) 226-230

Born's reciprocal relativity in flat spacetimes is based on the principle of a maximal speed limit (speed of light) and a maximal proper force (which is also compatible with a maximal and minimal length duality) and where coordinates and momenta are unified on a single footing. We extend Born's theory to the case of curved spacetimes and construct a deformed Born reciprocal general relativity theory in curved spacetimes (without the need to introduce star products) as a local gauge theory of the deformed Quaplectic group that is given by the semi-direct product of U(1,3) with the deformed (noncommutative) Weyl-Heisenberg group corresponding to noncommutative generators [Za,Zb] ≠ 0. The Hermitian metric is complex-valued with symmetric and nonsymmetric components and there are two different complex-valued Hermitian Ricci tensors Rμν, Sμν. The deformed Born's reciprocal gravitational action linear in the Ricci scalars R, S with Torsion-squared terms and BF terms is presented. The plausible interpretation of Zμ = Eμa Za as noncommuting p-brane background complex spacetime coordinates is discussed in the conclusion, where Eμa is the complex vielbein associated with the Hermitian metric Gμν = g(μν) + ig[μν] = Eμa Ēνb This could be one of the underlying reasons why string-theory involves gravity.
Category: Quantum Gravity and String Theory

[15] viXra:0908.0090 [pdf] submitted on 24 Aug 2009

On the Noncommutative and Nonassociative Geometry of Octonionic Spacetime, Modified Dispersion Relations and Grand Unification

Authors: Carlos Castro
Comments: 23 pages, This article appeared in the J. Math. Phys, 48, no. 7 (2007) 073517.

The Octonionic Geometry (Gravity) developed long ago by Oliveira and Marques is extended to Noncommutative and Nonassociative Spacetime coordinates associated with octonionic-valued coordinates and momenta. The octonionic metric Gμν already encompasses the ordinary spacetime metric gμν, in addition to the Maxwell U(1) and SU(2) Yang-Mills fields such that implements the Kaluza-Klein Grand Unification program without introducing extra spacetime dimensions. The color group SU(3) is a subgroup of the exceptional G2 group which is the automorphism group of the octonion algebra. It is shown that the flux of the SU(2) Yang-Mills field strength Fμν through the area momentum Σμν in the internal isospin space yields corrections O(1/M2Planck) to the energy-momentum dispersion relations without violating Lorentz invariance as it occurs with Hopf algebraic deformations of the Poincare algebra. The known Octonionic realizations of the Clifford Cl(8),Cl(4) algebras should permit the construction of octonionic string actions that should have a correspondence with ordinary string actions for strings moving in a curved Clifford-space target background associated with a Cl(3, 1) algebra.
Category: Quantum Gravity and String Theory

[14] viXra:0908.0089 [pdf] submitted on 24 Aug 2009

The Large N Limit of Exceptional Jordan Matrix Models and M, F Theory

Authors: Carlos Castro
Comments: 14 pages, This article appeared in the Journal of Geometry and Physics, 57 (2007) 1941-1949

The large N → ∞ limit of the Exceptional F4,E6 Jordan Matrix Models of Smolin-Ohwashi leads to novel Chern-Simons Membrane Lagrangians which are suitable candidates for a nonperturbative bosonic formulation of M Theory in D = 27 real, complex dimensions, respectively. Freudenthal algebras and triple Freudenthal products permits the construction of a novel E7 X SU(N) invariant Matrix model whose large N limit yields generalized nonlinear sigma models actions on 28 complex dimensional backgrounds associated with a 56 real-dim phase space realization of the Freudenthal algebra. We argue why the latter Matrix Model, in the large N limit, might be the proper arena for a bosonic formulation of F theory. To finalize we display generalized Dirac-Nambu-Goto membrane actions in terms of 3 X 3 X 3 cubic matrix entries that match the number of degrees of freedom of the 27-dim exceptional Jordan algebra J3[0].
Category: Quantum Gravity and String Theory

[13] viXra:0908.0088 [pdf] submitted on 24 Aug 2009

On the Riemann Hypothesis and Tachyons in Dual String Scattering Amplitudes

Authors: Carlos Castro
Comments: 13 pages, This article appeared in the International Journal of Geometric Methods in Modern Physics (IJGMMP) vol 3, no. 2 (2006) 187-199.

It is the purpose of this work to pursue a novel physical interpretation of the nontrivial Riemann zeta zeros and prove why the location of these zeros zn = 1/2+iλn corresponds physically to tachyonic-resonances/tachyonic-condensates, originating from the scattering of two on-shell tachyons in bosonic string theory. Namely, we prove that if there were nontrivial zeta zeros (violating the Riemann hypothesis) outside the critical line Real z = 1/2 (but inside the critical strip), these putative zeros do not correspond to any poles of the bosonic open string scattering (Veneziano) amplitude A(s, t, u). The physical relevance of tachyonic-resonances/tachyonic-condensates in bosonic string theory, establishes an important connection between string theory and the Riemann Hypothesis. In addition, one has also a geometrical interpretation of the zeta zeros in the critical line in terms of very special (degenerate) triangular configurations in the upper-part of the complex plane.
Category: Quantum Gravity and String Theory

[12] viXra:0908.0084 [pdf] submitted on 22 Aug 2009

The Extended Relativity Theory in Clifford Spaces

Authors: Carlos Castro, M. Pavšič
Comments: 65 pages, This article appeared in Progress in Physics vol 1 (April 2005) 31-64

An introduction to some of the most important features of the Extended Relativity theory in Clifford-spaces (C-spaces) is presented whose "point" coordinates are non-commuting Clifford-valued quantities which incorporate lines, areas, volumes, hyper-volumes.... degrees of freedom associated with the collective particle, string, membrane, p-brane,... dynamics of p-loops (closed p-branes) in target Ddimensional spacetime backgrounds. C-space Relativity naturally incorporates the ideas of an invariant length (Planck scale), maximal acceleration, non-commuting coordinates, supersymmetry, holography, higher derivative gravity with torsion and variable dimensions/signatures. It permits to study the dynamics of all (closed) p-branes, for all values of p, on a unified footing. It resolves the ordering ambiguities in QFT, the problem of time in Cosmology and admits superluminal propagation ( tachyons ) without violations of causality. A discussion of the maximalacceleration Relativity principle in phase-spaces follows and the study of the invariance group of symmetry transformations in phase-space allows to show why Planck areas are invariant under acceleration-boosts transformations . This invariance feature suggests that a maximal-string tension principle may be operating in Nature. We continue by pointing out how the relativity of signatures of the underlying n-dimensional spacetime results from taking different n-dimensional slices through C-space. The conformal group in spacetime emerges as a natural subgroup of the Clifford group and Relativity in C-spaces involves natural scale changes in the sizes of physical objects without the introduction of forces nor Weyl's gauge field of dilations. We finalize by constructing the generalization of Maxwell theory of Electrodynamics of point charges to a theory in C-spaces that involves extended charges coupled to antisymmetric tensor fields of arbitrary rank. In the concluding remarks we outline briefly the current promising research programs and their plausible connections with C-space Relativity.
Category: Quantum Gravity and String Theory

[11] viXra:0908.0083 [pdf] submitted on 22 Aug 2009

The Exceptional E8 Geometry of Clifford (16) Superspace and Conformal Gravity Yang-Mills Grand Unification

Authors: Carlos Castro
Comments: 33 pages, This article appeared in the IJGMMP vol 6, no. 3 (2009) 385.

We continue to study the Chern-Simons E8 Gauge theory of Gravity developed by the author which is a unified field theory (at the Planck scale) of a Lanczos-Lovelock Gravitational theory with a E8 Generalized Yang-Mills (GYM) field theory, and is defined in the 15D boundary of a 16D bulk space. The Exceptional E8 Geometry of the 256-dim slice of the 256 X 256-dimensional flat Clifford (16) space is explicitly constructed based on a spin connection ΩMAB, that gauges the generalized Lorentz transformations in the tangent space of the 256-dim curved slice, and the 256 X 256 components of the vielbein field EMA, that gauge the nonabelian translations. Thus, in one-scoop, the vielbein EMA encodes all of the 248 (nonabelian) E8 generators and 8 additional (abelian) translations associated with the vectorial parts of the generators of the diagonal subalgebra [Cl(8) ⊗ Cl(8)]diag ⊂ Cl(16). The generalized curvature, Ricci tensor, Ricci scalar, torsion, torsion vector and the Einstein-Hilbert-Cartan action is constructed. A preliminary analysis of how to construct a Clifford Superspace (that is far richer than ordinary superspace) based on orthogonal and symplectic Clifford algebras is presented. Finally, it is shown how an E8 ordinary Yang-Mills in 8D, after a sequence of symmetry breaking processes E8 → E7 → E6 → SO(8, 2), and performing a Kaluza-Klein-Batakis compactification on CP2, involving a nontrivial torsion, leads to a (Conformal) Gravity and Yang-Mills theory based on the Standard Model in 4D. The conclusion is devoted to explaining how Conformal (super) Gravity and (super) Yang-Mills theory in any dimension can be embedded into a (super) Clifford-algebra-valued gauge field theory.
Category: Quantum Gravity and String Theory

[10] viXra:0908.0081 [pdf] submitted on 21 Aug 2009

The Clifford Space Geometry of Conformal Gravity and U(4) X U(4) Yang-Mills Unification

Authors: Carlos Castro
Comments: 22 pages, This article will appear in the Int J. of Mod. Phys A.

It is shown how a Conformal Gravity and U(4) X U(4) Yang-Mills Grand Unification model in four dimensions can be attained from a Clifford Gauge Field Theory in C-spaces (Clifford spaces) based on the (complex) Clifford Cl(4,C) algebra underlying a complexified four dimensional spacetime (8 real dimensions). Upon taking a real slice, and after symmetry breaking, it leads to ordinary Gravity and the Standard Model in four real dimensions. A brief conclusion about the Noncommutative star product deformations of this Grand Unified Theory of Gravity with the other forces of Nature is presented.
Category: Quantum Gravity and String Theory

[9] viXra:0908.0080 [pdf] submitted on 21 Aug 2009

P-Branes as Antisymmetric Nonabelian Tensorial Gauge Field Theories of Diffeomorphisms in P + 1 Dimensions

Authors: Carlos Castro
Comments: 44 pages, This article has been submitted to the Journal of Mathematical Physics, Aug 2009

Long ago, Bergshoeff, Sezgin, Tanni and Townsend have shown that the light-cone gauge-fixed action of a super p-brane belongs to a new kind of supersymmetric gauge theory of p-volume preserving diffeomorphisms (diffs) associated with the p-spatial dimensions of the extended object. These authors conjectured that this new kind of supersymmetric gauge theory must be related to an infinite-dim nonabelian antisymmetric gauge theory. It is shown in this work how this new theory should be part of an underlying antisymmetric nonabelian tensorial gauge field theory of p+1-dimensional diffs (upon supersymmetrization) associated with the world volume evolution of the p-brane. We conclude by embedding the latter theory into a more fundamental one based on the Clifford-space geometry of the p-brane configuration space.
Category: Quantum Gravity and String Theory

[8] viXra:0908.0077 [pdf] submitted on 21 Aug 2009

Dark Energy is Needed for the Consistency of Quantum Electrodynamics Heisenberg's Biggest Blunder?

Authors: Jack Sarfatti
Comments: 4 pages

The argument that virtual photons can be globally gauged away I think is spurious. Indeed, the inconsistency with the boson commutation rules in Heisenberg and Pauli's historic 1929 attempt to quantize the electromagnetic field disappears once one uses the recently discovered dark energy density.
Category: Quantum Gravity and String Theory

[7] viXra:0908.0023 [pdf] replaced on 2014-09-28 01:48:24

Genes and Memes

Authors: Matti Pitkänen
Comments: 658 Pages.

The first part of book discusses the new physics relevant to biology and the vision about Universe as topological quantum computer (tqc).

  1. The notion of many-sheeted DNA and a model of genetic code inspired by the notion of Combinatorial Hierarchy predicting what I call memetic code are introduced. The almost exact symmetries of the code table with respect to the third letter inspire the proposal that genetic code could have evolved as fusion of two-letter code and single-letter code.
  2. A model for how genome and cell membrane could act as tqc is developed. Magnetic flux tubes containing dark matter characterized by large value of Planck constant would make living matter a macroscopic quantum system. DNA nucleotides and lipids of the cell membrane would be connected by magnetic flux tubes and the flow of the 2-D liquid formed by lipids would induce dynamical braiding defining the computation.
  3. The net of magnetic flux tubes could explain the properties of gel phase. Phase transitions reducing Planck constant would induce a contraction of the flux tubes explaining why bio-molecules manage to find each other in a dense soup of bio-molecules. The topology of the net would be dynamical and ADP ↔ ATP transformation could affect it. The anomalies related to ionic currents, nerve pulse activity, and interaction of ELF radiation with vertebrate brain find an explanation in this framework. The number theoretic entanglement entropy able to have negative values could be seen as the real quintenssence associated with the metabolic energy transfer, and the poorly understood high energy phosphate bond could be interpreted in terms of negentropic entanglement rather than ordinary bound state entanglement.
  4. The discoveries of Peter Gariaev about interaction of ordinary and laser light with genome combined with ideas about dark matter and water memory lead to a model for the interaction of photons with DNA. Dark ↔ ordinary transformation for photons could allow to "see" dark matter by allowing ordinary light to interact with DNA.
  5. A physical model for genetic code emerged from an attempt to understand the mechanism behind water memory. Dark nuclei which sizes zoomed up to atomic size scale could represent genes. The model for dark nucleon consisting of three quarks predicts counterparts of 64 DNAs, 64 RNAs, and 20 aminoacids and allows to identify genetic code as a natural mapping of DNA type states to amino-acid type states and consistent with vertebrate genetic code.

The third part of the book discusses number theoretical models of the genetic code based on p-adic thermodynamics and maximization of entropy or negentropy. These models reproduce the genetic code but fail to make killer predictions.
Category: Quantum Gravity and String Theory

[6] viXra:0908.0019 [pdf] replaced on 2013-09-09 07:09:54

Towards M-Matrix

Authors: Matti Pitkänen
Comments: 1119 Pages.

This book is devoted to a detailed representation of the recent state of quantum TGD.

The first part of the book summarizes quantum TGD in its recent form.

  1. General coordinate invariance and generalized super-conformal symmetries are the basic symmetries of TGD and Equivalence Principle can be generalized using generalized coset construction.
  2. In zero energy ontology the basis of classical WCW spinors fields forms unitary U-matrix having M-matrices as its orthogonal rows. M-matrix defines time-like entanglement coefficients between positive and negative energy parts of the zero energy states. M-matrix is a product of a hermitian density matrix and unitary S-matrix commuting with it. The hermitian density matrices define infinite-dimensional Lie-algebra extending to a generalization of Kac-Moody type algebra with generators defined as products of hermitian density matrices and powers of S-matrix. Yangian type algebra is obtained if only non-negative powers of S are allowed. The interpretation is in terms of the hierarchy of causal diamonds with size scales coming as integer multiples of CP2 size scale. Zero energy states define their own symmetry algebra. For generalized Feynman diagrams lines correspond to light-like 3-surfaces and vertices to 2-D surfaces.
  3. Finite measurement resolution realized using fractal hierarchy of causal diamonds (CDs) inside CDs implies a stringy formulation of quantum TGD involving replacement of 3-D light-like surfaces with braids representing the ends of strings. Category theoretical formulation leads to a hierarchy of algebras forming an operad.
  4. Twistors emerge naturally in TGD framework and several proposal for twistorialization of TGD is discussed in two chapters devoted to the topic. Twistorial approach combined with zero energy ontology, bosonic emergence, and the properties of the Chern-Simons Dirac operator leads to the conjecture that all particles -also string like objects- can be regarded as bound states of massless particles identifiable as wormhole throats. Also virtual particles would consist of massles wormhole throats but bound state property is not assumed anymore and the energies of wormhole throats can have opposite signs so that space-like momentum exchanges become possible. This implies extremely strong constraints on loop momenta and manifest finiteness of loop integrals.

    An essential element of the formulation is exact Yangian symmetry obtained by replacing the loci of multilocal symmetry generators of Yangian algebra with partonic 2-surfaces so that conformal algebra of Minkowski space is extened to infinite-dimensional algebra bringing in also the conformal algebra assigned to the partonic 2-surfaces. Yangian symmetry requires the vanishing of both UV and IR divergences achieved if the physical particles are bound states of massless wormhole throats.

    Rather general arguments suggest the formulation of TGD in terms of holomorphic 6-surfaces in the product CP3× CP3 of twistor spaces leading to a unique partial differential equations determining these surfaces in terms of homogenous polynomials of the projective complex coordinates of the two twistor spaces.

Second part of the book is devoted to hyper-finite factors and hierarchy of Planck constants.

  1. The Clifford algebra of WCW is hyper-finite factor of type II1. The inclusions provide a mathematical description of finite measurement resolution. The included factor is analogous to gauge symmetry group since the action of the included factor creates states not distinguishable from the original one. TGD Universe would be analogous to Turing machine able to emulate any internally consistent gauge theory (or more general theory) so that finite measurement resolution would provide TGD Universe with huge simulational powers.
  2. In TGD framework dark matter corresponds to ordinary particles with non-standard value of Planck constant. The simplest view about the hierarchy of Planck constants is as an effective hierarchy describable in terms of local, singular coverings of the imbedding space. The basic observation is that for Kähler action the time derivatives of the imbedding space coordinates are many-valued functions of canonical momentum densities. If all branches for given values of canonical momentum densities are allowed, one obtains the analogs of many-sheeted Riemann surfaces with each sheet giving same contribution to the Kähler action so that Planck constant is effectively a multiple of the ordinary Planck constant. Dark matter could be in quantum Hall like phase localized at light-like 3-surfaces with macroscopic size and analogous to black-hole horizons.

Category: Quantum Gravity and String Theory

[5] viXra:0908.0018 [pdf] replaced on 2014-09-26 04:44:22

TGD as a Generalized Number Theory

Authors: Matti Pitkänen
Comments: 856 Pages. Updating

The focus of this book is the number theoretical vision about physics. This vision involves three loosely related parts.

  1. The fusion of real physic and various p-adic physics to a single coherent whole by generalizing the number concept by fusing real numbers and various p-adic number fields along common rationals. Extensions of p-adic number fields can be introduced by gluing them along common algebraic numbers to reals. Algebraic continuation of the physics from rationals and their their extensions to various number fields (generalization of completion process for rationals) is the key idea, and the challenge is to understand whether how one could achieve this dream. A profound implication is that purely local p-adic physics would code for the p-adic fractality of long length length scale real physics and vice versa, and one could understand the origins of p-adic length scale hypothesis.
  2. Second part of the vision involves hyper counterparts of the classical number fields defined as subspaces of their complexificationsnwith Minkowskian signature of metric. Allowed space-time surfaces would correspond to what might be callednhyper-quaternionic sub-manifolds of a hyper-octonionic space and mappable to M4× CP2 in natural manner. One could assign to each point of space-time surface a hyper-quaternionic 4-plane which is the plane defined by the induced or modified gamma matrices defined by the canonical momentum currents of Kähler action. Induced gamma matrices seem to be preferred mathematically: they correspond to modified gamma matrices assignable to 4-volume action, and one can develop arguments for why Kähler action defines the dynamics.

    Also a general vision about preferred extremals of Kähler action emerges. The basic idea is that imbedding space allows octonionic structure and that field equations in a given space-time region reduce to the associativity of the tangent space or normal space: space-time regions should be quaternionic or co-quaternionic. The first formulation is in terms of the octonionic representation of the imbedding space Clifford algebra and states that the octonionic gamma "matrices" span a complexified quaternionic sub-algebra. Another formulation is in terms of octonion real-analyticity. Octonion real-analytic function f is expressible as f=q1+Iq2, where qi are quaternions and I is an octonionic imaginary unit analogous to the ordinary imaginary unit. q2 (q1) would vanish for quaternionic (co-quaternionic) space-time regions. The local number field structure of the octonion real-analytic functions with composition of functions as additional operation would be realized as geometric operations for space-time surfaces. The conjecture is that these two formulations are equivalent.

  3. The third part of the vision involves infinite primes identifiable in terms of an infinite hierarchy of second quantized arithmetic quantum fields theories on one hand, and as having representations as space-time surfaces analogous to zero loci of polynomials on the other hand. Single space-time point would have an infinitely complex structure since real unity can be represented as a ratio of infinite numbers in infinitely many manners each having its own number theoretic anatomy. Single space-time point would be in principle able to represent in its structure the quantum state of the entire universe. This number theoretic variant of Brahman=Atman identity would make Universe an algebraic hologram.

    Number theoretical vision suggests that infinite hyper-octonionic or -quaternionic primes could could correspond directly to the quantum numbers of elementary particles and a detailed proposal for this correspondence is made. Furthermore, the generalized eigenvalue spectrum of the Chern-Simons Dirac operator could be expressed in terms of hyper-complex primes in turn defining basic building bricks of infinite hyper-complex primes from which hyper-octonionic primes are obtained by dicrete SU(3) rotations performed for finite hyper-complex primes.

Besides this holy trinity I will discuss in the first part of the book loosely related topics such as the relationship between infinite primes and non-standard numbers.

Second part of the book is devoted to the mathematical formulation of the p-adic TGD. The p-adic counterpart of integration is certainly the basic mathematical challenge. Number theoretical universality and the notion of algebraic continuation from rationals to various continuous number fields is the basic idea behind the attempts to solve the problems. p-Adic integration is also a central problem of modern mathematics and the relationship of TGD approach to motivic integration and cohomology theories in p-adic numberfields is discussed.

The correspondence between real and p-adic numbers is second fundamental problem. The key problem is to understand whether and how this correspondence could be at the same time continuous and respect symmetries at least in discrete sense. The proposed explanation of Shnoll effect suggests that the notion of quantum rational number could tie together p-adic physics and quantum groups and could allow to define real-p-adic correspondence satisfying the basic conditions.

The third part is develoted to possible applications. Included are category theory in TGD framework; TGD inspired considerations related to Riemann hypothesis; topological quantum computation in TGD Universe; and TGD inspired approach to Langlands program.
Category: Quantum Gravity and String Theory

[4] viXra:0908.0017 [pdf] replaced on 2014-09-26 04:40:40

Physics in Many-Sheeted Space-Time

Authors: Matti Pitkänen
Comments: 877 Pages. Updating

This book is devoted to what might be called classical TGD.

  1. Classical TGD identifies space-time surfaces as kind of generalized Bohr orbits. It is an exact part of quantum TGD.
  2. The notions of many-sheeted space-time, topological field quantization and the notion of field/magnetic body, follow from simple topological considerations. Space-time sheets can have arbitrarily large sizes and their interpretation as quantum coherence regions implies that in TGD Universe macroscopic quantum coherence is possible in arbitrarily long scales. Also long ranged classical color and electro-weak fields are predicted.
  3. TGD Universe is fractal containing fractal copies of standard model physics at various space-time sheets and labeled by p-adic primes assignable to elementary particles and by the level of dark matter hierarchy characterized partially by the value of Planck constant labeling the pages of the book like structure formed by singular covering spaces of the imbedding space M4× CP2 glued together along four-dimensional back. Particles at different pages are dark relative to each other since local interactions defined in terms of the vertices of Feynman diagram involve only particles at the same page.

    The simplest view about the hierarchy of Planck constants is as an effective hierarchy describable in terms of local, singular coverings of the imbedding space. The basic observation is that for Kähler action the time derivatives of the imbedding space coordinates are many-valued functions of canonical momentum densities. If all branches for given values of canonical momentum densities are allowed, one obtains the analogs of many-sheeted Riemann surfaces with each sheet giving same contribution to the Kähler action so that Planck constant is effectively a multiple of the ordinary Planck constant.

  4. Zero energy ontology brings in additional powerful interpretational principle.

The topics of the book are organized as follows.

  1. In Part I extremals of Kähler action are discussed and the notions of many-sheeted space-time, topological field quantization, and topological condensation and evaporation are introduced.
  2. In Part II many-sheeted-cosmology and astrophysics are summarized. p-Adic and dark matter hierarchies imply that TGD inspired cosmology is fractal. Cosmic strings and their deformations giving rise to magnetic flux tubes are basic objects of TGD inspired cosmology. Magnetic flux tubes can in fact be interpreted as carriers of dark energy giving rise to accelerated expansion via negative magnetic "pressure". The study of imbeddings of Robertson-Walker cosmology shows that critical and over-critical cosmology are unique apart from their duration. The idea about dark matter hierarchy was originally motivated by the observation that planetary orbits could be interpreted as Bohr orbits with enormous value of Planck constant, and this picture leads to a rather detailed view about macroscopically quantum coherent dark matter in astrophysics and cosmology.

  3. Part III includes old chapters about implications of TGD for condensed matter physics. The phases of CP2 complex coordinates could define phases of order parameters of macroscopic quantum phases manifesting themselves in the properties of living matter and even in hydrodynamics. For instance, Z0 magnetic gauge field could make itself visible in hydrodynamics and Z0 magnetic vortices could be involved with super-fluidity.

Category: Quantum Gravity and String Theory

[3] viXra:0908.0016 [pdf] replaced on 2014-09-26 04:42:43

Physics as Infinite-Dimensional Geometry

Authors: Matti Pitkänen
Comments: 480 Pages. Updating

The topics of this book is a vision about physics as infinite-dimensional Kähler geometry of the "world of classical worlds" (WCW), with "classical world" identified either as light-like 3-D surface X3 of a unique Bohr orbit like 4-surface X4(X3) or X4(X3) itself. The non-determinism of Kähler action defining Kähler function forces to generalize the notion of 3-surface. Zero energy ontology allows to formulate this generalization elegantly using a hierarchy of causal diamonds (CDs) defined as intersections of future and past directed light-cones, and a geometric realization of coupling constant evolution and finite measurement resolution emerges.

The general vision about quantum dynamics is that the basis for WCW spinor fields defines in zero energy ontology unitary U-matrix having as orthogonal rows M-matrices. Given M-matrix is expressible as a product of hermitian square root of density matrix and S-matrix. M-matrices define time-like entanglement coefficients between positive and negative energy parts of zero energy states represented by the modes of WCW spinor fields.

One encounters two challenges.

  1. Provide WCW with Kähler geometry consistent with 4-dimensional general coordinate invariance. Clearly, the definition of metric must assign to given light-like 3-surface X3 a 4-surface X4(X3) as kind of Bohr orbit.
  2. Provide WCW with spinor structure. The idea is to express configuration space gamma matrices using super algebra generators expressible using second quantized fermionic oscillator operators for induced free spinor fields at X4(X3). Isometry generators and contractions of Killing vectors with gamma matrices would generalize Super Kac-Moody algebra.

The condition of mathematical existence poses stringent conditions on the construction.

  1. The experience with loop spaces suggests that a well-defined Riemann connection exists only if this space is union of infinite-dimensional symmetric spaces. Finiteness requires that vacuum Einstein equations are satisfied. The coordinates labeling these symmetric spaces do not contribute to the line element and have interpretation as non-quantum fluctuating classical variables.
  2. The construction of the Kähler structure requires the identification of complex structure. Direct construction of Kähler function as action associated with a preferred extremal for Kähler action leads to a unique result. The group theoretical approach relies on direct guess of isometries of the symmetric spaces involved. Isometry group generalizes Kac-Moody group by replacing finite-dimensional Lie group with the group of symplectic transformations of δ M4+× CP2, where δ M4+ is the boundary of 4-dimensional future light-cone. The generalized conformal symmetries assignable to light-like 3-surfaces and boundaries of causal diamonds bring in stringy aspect and Equivalence Principle can be generalized in terms of generalized coset construction.
  3. Configuration space spinor structure geometrizes fermionic statistics and quantization of spinor fields. Quantum criticality can be formulated in terms of the modified Dirac equation for induced spinor fields allowing a realization of super-conformal symmetries and quantum gravitational holography.
  4. Zero energy ontology combined with the weak form of electric-magnetic duality led to a breakthrough in the understanding of the theory. The boundary conditions at light-like wormhole throats and at space-like 3-surfaces defined by the intersection of the space-time surface with the light-like boundaries of causal diamonds reduce the classical quantization of Kähler electric charge to that for Kähler magnetic charge. The integrability of field equations for the preferred extremals reduces to the condition that the flow lines of various isometry currents define Beltrami fields for which the flow parameter by definition defines a global coordinate. The assumption that isometry currents are proportional to the instanton current for Kähler action reduces Kähler function to a boundary term which by the weak form of electric-magnetic duality reduces to Chern-Simons term. This realizes TGD as almost topological QFT.
  5. There are also number theoretical conjectures about the character of the preferred extremals. The basic idea is that imbedding space allows octonionic structure and that field equations in a given space-time region should reduce to the associativity of the tangent space or normal space so that space-time regions should be quaternionic or co-quaternionic. The first formulation is in terms of the octonionic representation of the imbedding space Clifford algebra and states that the octonionic gamma "matrices" span a quaternionic sub-algebra. Another formulation is in terms of octonion real-analyticity. Octonion real-analytic function f is expressible as f=q1+Iq2, where qi are quaternions and I is an octonionic imaginary unit analogous to the ordinary imaginary unit. q2 (q1) would vanish for quaternionic (co-quaternionic) space-time regions. The local number field structure of octonion real-analytic functions with composition of functions as additional operation would be realized as geometric operations for space-time surfaces. The conjecture is that these two formulations are equivalent.
  6. An important new interpretational element is the identification of the Kähler action from Minkowskian space-time regions as a purely imaginary contribution identified as Morse function making possible quantal interference effects. The contribution from the Euclidian regions interpreted in terms of generalized Feynman graphs is real and identified as Kähler function. These contributions give apart from coefficient identical Chern-Simons terms at wormhole throats and at the space-like ends of space-time surface: it is not clear whether only the contributions these 3-surfaces are present.
  7. Effective 2-dimensionality suggests a reduction of Chern-Simons terms to a sum of real and imaginary terms corresponding to the total areas of of string world sheets from Euclidian and Minkowskian string world sheets and partonic 2-surfaces, which are an essential element of the proposal for what preferred extremals should be. The duality between partonic 2-surfaces and string world sheets suggests that the total area of partonic 2-surfaces is same as that for string world sheets.
  8. The approach leads also to a highly detailed understanding of the Chern-Simons Dirac equation at the wormhole throats and space-like 3-surfaces and Kähler Dirac equation in the interior of the space-time surface. The effective metric defined by the anticommutators of the modified gamma matrices has an attractive interpretation as a geometrization for parameters like sound velocity assigned with condensed matter systems in accordance with effective 2-dimensionality and strong form of holography.

Category: Quantum Gravity and String Theory

[2] viXra:0908.0015 [pdf] replaced on 2014-09-26 04:33:55

TGD and Fringe Physics

Authors: Matti Pitkänen
Comments: 458 Pages. Updating

The topics of this book could be called fringe physics involving claimed phenomena which do not have explanation in terms of standard physics.

Many-sheeted space-time with p-adic length scale hierarchy, the predicted dark matter hierarchy with levels partially characterized by quantized dynamical Planck constant, and the prediction of long ranged color and weak forces alone predict a vast variety of new physics effects. Zero energy ontology predicts that energy can have both signs and that classical signals can propagate in reversed time direction at negative energy space-time sheets and an attractive identification for negative energy signals would be as generalizations of phase conjugate laser beams. This vision leads to a coherent view about metabolism, memory, and bio-control and it is natural to ask whether the reported anomalies might be explained in terms of the mechanisms giving hopes about understanding the behavior of living matter.

  1. The effects involving coin words like antigravity, strong gravity, and electro-gravity motivate the discussion of possible anomalous effects related to long range electro-weak fields and many-sheeted gravitation. For instance, TGD leads to a model for the strange effects reported in rotating magnetic systems.
  2. Tesla did not believe that Maxwell's theory was an exhaustive description of electromagnetism. He claimed that experimental findings related to pulsed systems require the assumption of what he called scalar waves not allowed by Maxwell's electrodynamics. TGD indeed allows scalar wave pulses propagating with light velocity. The dropping of particles to larger space-time sheets liberating metabolic energy, transformation of ordinary charged matter to dark matter and vice versa, dark photons, etc... might be needed to explain Tesla's findings. Also phase conjugate, possibly dark, photons making possible communications with geometric past might be involved.
    These speculative ideas receive unexpected support from the TGD inspired view about particle physics. The recent TGD inspired view about Higgs mechanism suggests strongly that photon eats the remaining component of Higgs boson and in this manner gets longitudinal polarization and small mass allowing to avoid infrared divergences of scattering amplitudes.
  3. The reports about ufos represent a further application for TGD based view about Universe. Taking seriously the predicted presence of infinite self hierarchy represented by dark matter hierarchy makes it almost obvious that higher civilizations are here, there, and everywhere, and that their relationship to us is like that of our brain to its neurons, so that Fermi paradox (Where are they all?) would disappear. Although the space travel might be quite too primitive idea for the civilizations at higher levels of hierarchy, ufos might be real objects representing more advanced technology rather than plasmoid like life forms serving as mediums in telepathic communications.

Category: Quantum Gravity and String Theory

[1] viXra:0908.0014 [pdf] replaced on 2014-09-26 04:51:06

Topological Geometrodynamics: Overview

Authors: Matti Pitkänen
Comments: 1157 Pages. Updating

This book tries to give an overall view about quantum TGD as it stands now. The topics of this book are following.

  1. Part I: An overall view about the evolution of TGD and about quantum TGD in its recent form. Two visions about physics are discussed at general level. According to first vision physical states of the Universe correspond to classical spinor fields in the world of the classical worlds (WCW) identified as 3-surfaces or equivalently as corresponding 4-surfaces analogous to Bohr orbits and identified as special extrema of Kähler action. TGD as a generalized number theory vision leading naturally also to the emergence of p-adic physics as physics of cognitive representations is the second vision.
  2. Part II: The vision about physics as infinite-dimensional configuration space geometry. The basic idea is that classical spinor fields in WCW describe the quantum states of the Universe. Quantum jump remains the only purely quantal aspect of quantum theory in this approach since there is no quantization at the level of the configuration space. Space-time surfaces correspond to special extremals of the Kähler action analogous to Bohr orbits and define what might be called classical TGD discussed in the first chapter. The construction of the configuration space geometry and spinor structure are discussed in remaining chapters.
  3. Part III: Physics as generalized number theory. Number theoretical vision involves three loosely related approaches: fusion of real and various p-adic physics to a larger whole as algebraic continuations of what might be called rational physics; space-time as a hyper-quaternionic surface of hyper-octonion space, and space-time surfaces as a representations of infinite primes.
  4. Part IV: The first chapter summarizes the basic ideas related to von Neumann algebras known as hyper-finite factors of type II1 about which configuration space Clifford algebra represents canonical example. Second chapter is devoted to the basic ideas related to the hierarchy of Planck constants and related generalization of the notion of imbedding space to a book like structure.
  5. Part V: Physical applications of TGD. Cosmological and astrophysical applications are summarized and applications to elementary particle physics are discussed at the general level. TGD explains particle families in terms of generation-genus correspondence (particle families correspond to 2-dimensional topologies labeled by genus). The general theory for particle massivation based on p-adic thermodynamics is discussed at the general level.

Category: Quantum Gravity and String Theory