Quantum Gravity and String Theory

Arithmetic Information in Particle Mixing

Authors: M. D. Sheppeard
Comments: 5 pages.

The mutually unbiased bases of quantum information theory are used to study the MNS and CKM mixing matrices. The resulting mixing matrix parameterisation requires only three real parameters, and is thus potentially more constraining than those in current use. We also discuss related results from MINOS and Fermilab.

What Causes the Mass to be Deficit Inside a Nucleus?

Authors: Karunakar Marasakatla
Comments: 4 Pages.

Deficit of mass is a change in the physical characteristics of an object. What corresponding changes, if any, in the nucleus represents the observed deficit in mass?

The Weight Change of a Body in Connection with the Electrical Tension

Authors: H.-J. Hochecker
Comments: 3 Pages.

I stick metal foil on an a 1 square meter large and 10 kilograms heavy dielectric so that a condenser is build. By putting a tension of 10 kV on the condenser or by short-circuiting it I measure a real reduction of the weight of about 0.1 grams each time. This result confirms my theoretical conclusion which says that the weight of a body is related with the movements of its charges (protons and electrons). Keywords: Gravitation, movement of electrical charges, relativity

M-Theory (2)

Authors: Min-Young Yun
Comments: 58 Pages.

The problem of summing of like powers is completely solved by J. Bernoulli's polynomials. Apart from pure mathematics, the Bernoulli numbers appear prominently in perturbative quantum field theory. Here I present a way, using elementary Bernoulli numbers and Riemann zeta function and expanding mathematical meaning then, gain of another physical meaning. The behavior of smallest unit that creating from superstring and quark is indeterminate, but can be described as Unification Theory according to macroscopic-rules. So, it is easy to understand in all ages and countries, at any times and places. Newborns speak out the easiest word 'Mom' at the first time they speaking, which decided the title of the theory

The Cyclotron Notebooks

Authors: Philip Gibbs
Comments: 66 Pages, originally published as a website in March 1996.

The cyclotron note books are a collection of essays about fundamental physics and metaphysics. The central essay is about the principle of event-symmetric space-time, a new theory about how to do quantum gravity. The style is more technical in some parts than in others. Each essay can be read independently but if you find that one of them has terms which you don't understand you may find them explained in an earlier one. The later ones may be too difficult for the layman and even I don't understand the last one.

Thermodynamic Foundations of General Relativity (The Primary Gas Representation of Particle-X)

Authors: V.A.Induchoodan Menon
Comments: 19 pages

The author after introducing the concept of the vean (vacuum energy absorption) process shows that it not only crystallizes the progressive nature of time but also causes gravitation and the red shift of light emitted by far off galaxies [1]. He now shows that the thermodynamics of the primary gas in a gravitational field leads to the principle of equivalence and to its field equations of general relativity. The curvature of the space-time is seen to emerge from the anisotropy of the fluctuations in the Higgs field in the neighborhood of a massive body arising from the vean process. According to him unlike the currently accepted interpretation of general relativity the gravitational field based on the vean process does not exhibit non-linearity.

Using Gravitation to Emulate Electromagnetism.

Authors: S. Halayka
Comments: 3 Pages.

The possibility of Universe-scale black holes living in closed 3D space of constant positive curvature was briefly considered in previous work. Further consideration of this possibility is given here. A possible link between gravitation and electromagnetism is discussed.

Universal Medium ( According to "Hypothesis on MATTER" )

Authors: Nainan K. Varghese
Comments: 17 pages.

Space is a functional entity, presupposed by rational beings, whenever real entities are envisaged. Being a functional entity, space has no structure or form. It can neither physically act nor is able to undergo physical actions. By realising a real entity that fills the entire space as an all-encompassing universal medium, the formless space can be replaced with a structured real entity. This real entity will have positive existence and at the same time, it can have all properties currently assigned to space or to other imaginary entities like; different types of aether, imaginary particles or various types of fields. No actions can be performed at a distance through empty space. An all-encompassing medium is essential to facilitate (apparent) physical actions between matter bodies at a distance. Aether, used in aether-theories is too vague and fails to describe many physical actions of matter bodies, logically. 'Hypothesis on MATTER' envisages an all-encompassing medium, which has only one type of real (postulated) constituent particles and definite properties. Envisaging a universal medium, as described in the concept, helps to logically explain all physical phenomena, related to matter.

Can the Edges of a Complete Graph Form a Radially Symmetric Field in Closed Space of Constant Positive Curvature?

Authors: S. Halayka
Comments: 13 Pages.

In earlier work, it was found that the edges of a complete graph can very nearly form a radially symmetric field at long distance in at 2D and 3D space if the number of graph vertices is great enough. In this work, it is confirmed that the edges of a complete graph can also very nearly form a radially symmetric field in closed 2D and 3D space of constant positive curvature if the graph is small compared to the entirety of the space in which it lives and if the number of graph vertices is great enough.

A Clifford Algebra Realization of Supersymmetry and Its Polyvector Extension in Clifford Spaces

Authors: Carlos Castro
Comments: 15 pages, submitted to Foundations of Physics.

It is shown explicitly how to construct a novel (to our knowledge) realization of the Poincare superalgebra in 2D. These results can be extended to other dimensions and to (extended) superconformal and (anti) de Sitter superalgebras. There is a fundamental difference between the findings of this work with the other approaches to Supersymmetry (over the past four decades) using Grassmannian calculus and which is based on anti-commuting numbers. We provide an algebraic realization of the anticommutators and commutators of the 2D super-Poincare algebra in terms of the generators of the tensor product Cl1,1(R) x A of a two-dim Clifford algebra and an internal algebra A whose generators can be represented in terms of powers of a 3 x 3 matrix Q, such that Q3 = 0. Our realization differs from the standard realization of superalgebras in terms of differential operators in Superspace involving Grassmannian (anticommuting) coordinates θ^α and bosonic coordinates x^μ. We conclude in the final section with an analysis of how to construct Polyvector-valued extensions of supersymmetry in Clifford Spaces involving spinor-tensorial supercharge generators Qμ1μ2.....μn and momentum polyvectors Pμ1μ2....μn. Clifford-Superspace is an extension of Clifford-space and whose symmetry transformations are generalized polyvector-valued supersymmetries.

A More Natural Reference Model Integrating Relativity and Quantum Mechanics

Authors: J Gregory Moxness
Comments: 28 pages, 1 figure, Latex. Original ideas from 1997, latest modifications Nov 22, 2007.

M Theory and/or Loop Quantum Gravity hold the promise of resolving the conflict between general relativity and quantum mechanics but lack experimental connections to predictability in physics. A connection is made to these and other theories vying for the title of a "Theory of Everything" by questioning the value of the traditional Planck unit reference point for the scales at which they operate. It also suggests a cosmological model which has acceleration as being fundamental. It provides for an intuitive understanding of the Standard Model and its relationship to particle masses and the structure of the atom. The prediction of particle mass and lifetimes is a good indicator for its validity.

No-Time-Dilation Corrected Supernovae 1a and GRBs Data and Low-Energy Quantum Gravity

Authors: Michael A. Ivanov
Comments: 5 pages, 2 figures, Latex. Poster contribution to the VI Int. Workshop on the Dark side of the Universe (DSU2010), Guanajuato U., Leon, Mexico, 1-6 June, 2010.

Earlier it was shown that in the model of low-energy quantum gravity by the author, observations of Supernovae 1a and GRBs, which are corrected by observers for characteristic for the standard cosmological model time dilation, may be fitted with the theoretical luminosity distance curve only up to z ~ 0:5; for higher redshifts the predicted luminosity distance is essentially bigger. The model itself has not time dilation due to another redshift mechanism. It is shown here that a correction of observations for no time dilation leads to a good accordance of observations and theoretical predictions for all achieved redshifts.

Hypothesis on Matter

Authors: Nainan K. Varghese
Comments: 14 pages

'Hypothesis on MATTER' is a revolutionary new concept, which explains all physical phenomena based on just one type of (postulated) basic particle - the Quantum of matter. Conception and development of this model is founded on the conviction that there can be only one type of basic entities. They provide substance and create all other real entities in nature. All (apparent) interactions and diverse properties of superior entities are logical developments from inherent properties of the (postulated) quanta of matter. Quanta of matter, by their natural interactions, creates and structure all other entities including an allencompassing medium. A wide array of physical phenomena are explained in the book [1]; from the origin of 3D matter to gravity and subatomic interactions to cosmological events, based on the simple mechanical interactions of quanta of matter. There is no more any need to envisage 'actions at a distance' or to invoke irrational assumptions like diversity of natural forces, mass-energy equivalence, duality of light or constancy of its speed, dual nature of electric charge, singularities, big bang, etc. This new concept will radically alter our understanding of the physical universe and at the same time, explain complex physical phenomena with simple 'Cause and Effect' relationships.

Spacetime Deformations Theory

Authors: Jacek Safuta
Comments: 9 pages

The spacetime deformations theory unifies general relativity with quantum mechanics i.e. unifies all interactions, answers the questions: why particles have mass and what they are, answers the question: what is energy, unifies force fields and matter, implies new theories like spacetime deformations evolution. This is a theory of principle (universal theory delivering description of nature) and not constructive theory (describing particular phenomenon using specific equations). The theory is falsifiable, background independent (space has no fixed geometry), not generating singularities or boundaries. This is hard to believe but a belief has nothing to with it. The real intellectual challenge is to falsify the theory.

M-Theory

Authors: Min-Young Yun
Comments: 55 pages

The behavior of smallest unit that creating from superstring and quark is indeterminate, but can be described as one equation according to macroscopic-rules. So, it is easy to understand in all ages and countries, at any times and places. Newborns speak out the easiest word 'Mom' at the first time they speaking, which Decided the title of the theory.

Relating the Physical Structure and Properties of Quantum Space-Time to Elementary Particles, Gravity, and Relativistic Phenomena

Authors: Gary Heen
Comments: 22 pages

Modern theory states that matter and energy in their most basic form exist in discrete amounts, or quanta. The author proffers that space-time also exists as discrete quanta, and derives a physical model of space-time and elementary particles. The hypothesis for this space-time model is that the quanta for matter and space-time are convertible states of the same elementary building block: the quantum mass unit.

The Galois Solvable Fourth Roots of Reality

Authors: Jack Sarfatti
Comments: 8 pages

Local observers are defined by orthonormal "non-holonomic" (aka "non-coordinate") tetrad gravity fields (Cartan's "moving frames"). The tetrads are spin 1 vector fields under the 6-parameter homogeneous Lorentz group SO1,3 of Einstein's 1905 special relativity. You can think of the tetrad gravity fields as the square roots of Einstein's 1916 spin 2 metric tensor gravity fields. We will see that we must also allow for spin 0 and spin 1 gravity because the spin 1 tetrads, in turn, are Einstein-Podolsky-Rosen entangled quantum states of pairs of 2-component Penrose-Rindler qubits in the quantum pregeometry. The Wheeler-Feynman qubits are the square roots of the advanced and retarded null tetrads and can therefore be called the Galois solvable fourth roots of reality. The spherical wavefront tetrads are then formally the Bell pair states of quantum information theory. Penrose's Cartesian tetrads are a different choice from mine here. The different tetrad choices correspond to the different contours around the photon propagator poles in the complex energy plane of quantum electrodynamics. Both of his spinors in his spin frame are retarded in the same light cone, e.g. the forward cone. It seems that Penrose and Rindler implicitly answered Wheeler's question of how IT comes from BIT, but no one realized it until now.

Using Noetics to Determine the Geometric Limits of 3-Body Alignments that Produce Subtle Energies

Authors: Jeffrey S. Keen
Comments: 7 pages, 5 Figures.

Attempting to link quantum physics with general relativity is one current approach to the comprehension of the structure of the universe. However, this could be an impossible objective as recent theories suggest that gravity is not a fundamental force but a consequence of the way information about material objects is organised in space time (e.g. Reference 27). In this theory, gravity is analogous to the flow of water, and involves a holographic universe, information, entropy, and chaos theory. However, such theories do not explain acts of observations affecting the results of scientific experiments. Many researchers, (e.g. Reference 51), including the author, believe that understanding the structure of the universe lies not just in physics and the above concepts, but in addition involves consciousness and cognitive neuroscience together with understanding the nature and perception of information. As Noetics and dowsing involve all the latter factors, it is proving to be a powerful and relevant research tool. This paper combines these considerations in a non-orthodox, but heuristic approach, linked by geometry. A previous paper, (See Reference 24: http://vixra.org/abs/1001.0004), identified that geometric alignments of three bodies, be they 3 pebbles, 3 circles drawn on paper, or 3 astronomical bodies produce a subtle energy beam that can be detected by the mind and measured. Intriguingly, this beam has a divergence angle involving the inverse of the Fine Structure Constant (137). It has also been shown to instantaneously communicate conscious information across the solar system. These facts suggest, together with other findings, that this "consciousness beam" is linked to the structure of the universe. This avenue of research is now further developed, by quantifying the limits of the alignment of the 3-bodies that is required to produce the subtle energy beam. The findings are that for observations made near the outer of the 3 bodies, the alignment must be less than arcsine 1/4. But for observations near the middle body, this alignment must be within arcsine1/5. This article is a summary of the concepts which are augmented on the author's website http://www.jeffreykeen.co.uk/

The Quantum Uncertainty Principle, Gravitational Waves, and Black Holes

Authors: Willi Penker
Comments: 2 pages

Following the basic rules of the uncertainty principle, gravitation itself becomes uncertain and even massive black holes go into superposition without the possibility of ending up in a real singularity.

Quark Lepton Braids and Heterotic Supersymmetry

Authors: M. D. Sheppeard
Comments: 8 pages. submitted to JPA

A unique matrix is easily assigned to each Bilson-Thompson braid diagram. The quark and lepton matrices are then related to bosons via a twisted quantum Fourier transform, for which fermion and boson multiplets fit the dimension structure of heterotic strings.

Can the External Directed Edges of a Complete Graph Form a Radially Symmetric Field at Long Distance?

Authors: S. Halayka
Comments: 5 Pages.

Using a simple numerical method, the external directed edges of a complete graph are tested for their level of fitness in terms of how well they form a radially symmetric field at long distance (e.g., a test for the inverse square law in 3D space). It is found that the external directed edges of a complete graph can very nearly form a radially symmetric field at long distance if the number of graph vertices is great enough.

Theory of First Force

Authors: Willi Penker
Comments: 3 pages

The effects of forces are well known; however, the basic mechanisms of how forces work and are transmitted remain unexplained. This essay is meant to determine these basic mechanisms.

To Demonstrate that Gravity is Action-at-a-Distance

Authors: Chun-Xuan Jiang
Comments: 14 pages

In this paper we explain the behavior of the entire universe from the smallest to the largest scales. We found the only tachyonic string theory (other string theories all are guesses), find an equation that changed the universe: F-bar = -mc²/R, establish the expansion theory of the universe without dark matter and dark energy, and prove that the principle of equivalence is nonexistent. We demonstrate that gravity is action-at-a-distance and that a gravitational wave is unobservable.We suggest a new universe model.

Objections to Quantum Gravity Theories Based on Causal Dynamical Triangulation

Authors: Ervin Goldfain
Comments: 3 pages, Letter submitted to the Editors of Classical and Quantum Gravity

My letter is in regards to the recently published contribution by R. Loll "The emergence of space-time and quantum gravity on your desktop" 25 (2008) 114006. The article claims that "causal dynamical triangulation" offers a "robust" nonperturbative theory of quantum gravity. On closer examination, the approach is built on many questionable premises.

On Nonlinear Quantum Mechanics, Noncommutative Phase Spaces, Fractal-Scale Calculus and Vacuum Energy

Authors: Carlos Castro
Comments: 18 pages, has been submitted to Foundations of Physics

A novel (to our knowledge) Generalized Nonlinear Schrödinger equation based on the modifications of Nottale-Cresson's fractal-scale calculus and resulting from the noncommutativity of the phase space coordinates is explicitly derived. The modifications to the ground state energy of a harmonic oscillator yields the observed value of the vacuum energy density. In the concluding remarks we discuss how nonlinear and nonlocal QM wave equations arise naturally from this fractal-scale calculus formalism which may have a key role in the final formulation of Quantum Gravity.

Numerical Solution of Quantum Cosmological Model Simulating Boson and Fermion Creation

Authors: V. Christianto, Florentin Smarandache
Comments: 2 pages

A numerical solution of Wheeler-De Witt equation for a quantum cosmological model simulating boson and fermion creation in the early Universe evolution is presented. This solution is based on a Wheeler-DeWitt equation obtained by Krechet, Fil'chenkov, and Shikin, in the framework of quantum geometrodynamics for a Bianchi-I metric.

The Sea of Super-Strong Interacting Gravitons as the Cause of Gravity

Authors: Michael A. Ivanov
Comments: 5 pages, 1 figure, Latex. Contribution to The 3d International Conference on Particle and Fundamental Physics in Space (Space Part'06 ), Beijing, China, 19 - 21 April 2006 (Nuclear Physics B (Proc. Suppl.) 166 (2007) 297-299).

The Newtonian attraction turns out to be the main statistical effect in the sea of super-strong interacting gravitons, with bodies themselves being not sources of gravitons - only correlational properties of in and out fluxes of gravitons in their neighbourhood are changed due to an interaction with bodies. Other quantum effects of low-energy quantum gravity are the following ones: redshifts, their analog - a deceleration of massive bodies, and an additional relaxation of any light flux.

Timeless Microstructural Dynamics with Extra Dimensions: Principles and Overview

Authors: Juno Ryu
Comments: 15 pages

From 70's there have been some indications that theremodynamical physics is deeply related to the gravitational physics with quatum mechanics. [1,2] Recently, works [3,4] showed that there is even good reason to believe that there exists connection between thermodynamical way of thinking and gravitational force. Even though these arguments reveal judicious analogy, they don't provide us physical picture of spacetime. To speak about thermodanamical system, one needs microstructure which we don't have. In order to yield statistical view point on space time, we try to build a model with microstructure in which components have special properties. We will have several interpretations on some physice we know, including particle physics, with the framework of this model. Time is not treated as special dimensional coordinate in this model. We investigate heuristically how the microstructural dynamics can build space and time. This paper will start from several principles and check some property of the model. After that we will study the application of the model from elementary particle physics to cosmological scale quite heuristically. In this work we want to see how a timeless microstructural model can provide framework of physics we know. For motivational reason, This paper is heavily on conceptual statement and analogy rather than mathematical validity.

On N-Ary Algebras, Polyvector Gauge Theories in Noncommutative Clifford Spaces and Deformation Quantization

Authors: Carlos Castro
Comments: 13 Pages. This article has been submitted to Physics Letters B

Polyvector-valued gauge field theories in noncommutative Clifford spaces are presented. The noncommutative binary star products are associative and require the use of the Baker-Campbell-Hausdorff formula. An important relationship among the n-ary commutators of noncommuting spacetime coordinates [X¹,X², ......,Xⁿ] and the poly-vector valued coordinates X^123...n in noncommutative Clifford spaces is explicitly derived and is given by [X¹,X², ......,Xⁿ] = n! X^123...n. It is argued how the large N limit of n-ary commutators of n hyper-matrices X_i1i2...._in leads to Eguchi-Schild p-brane actions when p+1 = n. A noncomutative n-ary generalized star product of functions is provided which is associated with the deformation quantization of n-ary structures. Finally, brief comments are made about the mapping of the Nambu-Heisenberg n-ary commutation relations of linear operators into the deformed Nambu-Poisson brackets of their corresponding symbols.

Prespacetime Model of Elementary Particle, Four Forces & Consciousness

Authors: Huping Hu, Maoxin Wu
Comments: 70 pages.

A prespacetime model of elementary particles, four forces and consciousness has been formulated, which illustrates how the self-referential hierarchical spin structure of the prespacetime provides a foundation for creating, sustaining and causing evolution of elementary particles through matrixing processes embedded in said prespacetime. The prespacetime model reveals the creation, sustenance and evolution of fermions, bosons and spinless entities each comprised of an external wave function or external object and an internal wave function or internal object located respectively in an external world and an internal world of a dual-world universe. The prespacetime model provides a unified causal structure for weak interaction, strong interaction, electromagnetic interaction, gravitational interaction, quantum entanglement, consciousness and brain function. The prespacetime model provides a unique tool for teaching, demonstration, rendering, and experimentation related to subatomic and atomic structures and interactions, quantum entanglement generation, gravitational mechanisms in cosmology, structures and mechanisms of consciousness, and brain functions.

The Causes of Variations When Making Dowsable Measurements Part 4 the Effects of Geometric Alignments and Subtle Energies

Authors: Jeffrey S. Keen
Comments: 24 Pages, 13 Figures, 8 Tables

Comprehension of the structure of the universe requires a theory of quantum gravity. Attempting to link quantum physics with general relativity is one current approach. Many researchers, including the author, believes that the solution lies not just in physics, but involves consciousness and cognitive neuroscience together with understanding the nature and perception of information. As dowsing involves all the latter factors it has proved to be a powerful and relevant research tool. This paper combines these ideas in a non-orthodox approach linked by geometry. This is the fourth of a 5 part complementary series of papers examining several local and non-local factors which affect dowsing measurements, and hence giving an insight into perception and consciousness. Previous papers identified daily, lunar monthly and annual cycles caused by gravity having a significant effect on consciousness and information. Via the use of a standard yardstick, significant discoveries are announced in this paper, including the following: a) Certain geometric alignments of any three bodies, be they 3 pebbles, 3 circles drawn on paper, or 3 astronomical bodies produce significant resonance peaks and troughs that are readily detectable by the yardstick. b) These peaks and troughs are shown to be the varying intensity of a subtle energy beam (of a currently unknown nature). c) Intriguingly, this beam has a divergence angle that includes the inverse of the Fine Structure Constant (137). d) These sharp peaks and troughs augment the slower gravitational changes at new and full moon (identified in Part 2) that affect animal behaviour. e) Properties are measured and comparisons are made between these subtle energies and the more usual earth energies or mind created psi-lines. f) Measurements demonstrate that the sun, earth, and the moon behave identically to these subtle energies when in geometric astronomical alignments (such as new and full moon or eclipses). These finding lead to the following deductions. 1. The structure of the universe, from the Planck level to galaxies, enables 2 or more geometrical bodies to be "aware" of each others existence and precise location. 2. Similarly, the structure of the universe enables 3 geometrical bodies to "know" instantly when they are in perfect alignment. 3. As the same results are obtained for 3 large interacting cosmic bodies as for 3 micro objects, the findings support Global Scaling Theory (GST). 4. Applying GST, quantum entanglement could be explained using the same process involving subtle energy and geometrical alignment as demonstrated for macro objects. 5. Information transfer across the solar system is instantaneous.

"Aspin" Bubbles: Mechanical Project for the Unification of the Forces of Nature

Authors: Yoël Lana-Renault
Comments: 31 pages with 7 figures

This paper describes a mechanical theory for the unification of the basic forces of Nature with a single wave-particle interaction. The theory is based on the hypothesis that the ultimate components of matter are just two kind of pulsating particles. The interaction between these particles immersed in a fluid-like medium (ether) reproduces all the forces in Nature: electric, nuclear, gravitational, magnetic, atomic, van der Waals, Casimir, etc. The theory also designes the internal structure of the atom and of the fundamental particles that are currently known. Thus, a new concept of physics, capable of tackling entirely new problems, is introduced.

Quantum Time is Derived from Motion

Authors: Amrit S. Sorli
Comments: 3 pages

In physics spatial distance d is a product of velocity v and time t : d = v*t . Mathematical formalism x₄ = i*c*t confirms that in Special Theory of Relativity forth coordinate x₄ is spatial too. x₄ is composed out of c light speed, imaginary number i and time t that represents "thick" of a clock. Time t obtained with clocks describes numerical order of material change t₀ ,t₁ ,t₂ .......t_n. Clocks are reference systems for measuring frequency, velocity, numerical order of material changes that run in space. Time t x₄ is running of clocks in space. Clock/time is a measuring reference system for measuring physical events that are running exclusively in space and not in time. Light speed c of light motion is a fundamental speed in the universe on which is calculated basis unit of time "Planck time". This view explains some recent experiments which confirm that time t of physical event can be zero.

A Gravity, U(4) X U(4) Yang-Mills and Matter Unification in Clifford Spaces

Authors: Carlos Castro
Comments: 11 Pages. This article will appear in the special issue of the Invertis Journal of Science and Technology, New Dehli, 2010

A brief review of a Conformal Gravity and U(4) x U(4) Yang-Mills Unification model in four dimensions from a Clifford Gauge Field Theory in C-spaces (Clifford spaces) is presented. It based on the (complex) Clifford Cl(4,C) algebra underlying a complexified four dimensional spacetime (8 real dimensions). The 16 fermions of each generation can be arranged into the 16 entries of a 4 x 4 matrix associated with the A = 1, 2, 3, ....., 16 indices corresponding to the dimensions of the Cl(4) gauge algebra. The Higgs sector is also part of the Cl(4)-algebra polyvector valued gauge field in C-space. The Yukawa couplings which furnish masses to the fermions (after symmetry breaking) admit a C-space geometric interpretation as well.

General Systems and the Unified Field Theory. Part 2

Authors: John A. Gowan
Comments: 22 pages.

The conceptual basis of the Unified Field Theory, as presented in these pages, can be briefly sketched as follows: "Noether's Theorem" states that in a multicomponent field such as the electromagnetic field (or the metric field of spacetime), where one finds a symmetry one finds an associated conservation law, and vice versa. In matter, light's symmetries are conserved by charge and spin; in spacetime, by inertial and gravitational forces. All forms of energy, including the conservation/entropy domain of spacetime, originate as light. During the "Big Bang", the asymmetric interaction of primordial, high energy light with the metric structure of spacetime produces matter; matter carries charges which are the symmetry (and entropy) debts of the light which created it. Charges produce forces which act to return the material system to its original symmetric state (light), paying matter's symmetry/entropy debts. Repayment is exampled by matter-antimatter annihilation reactions, particle and proton decay, the nucleosynthetic pathway of stars, and Hawking's "quantum radiance" of black holes. Identifying the broken symmetries of light associated with each of the 4 forces (and charges) of physics is the first step toward a conceptual unification of those forces.

General Systems and the Unified Field Theory, Part 1

Authors: John A. Gowan
Comments: 21 pages. This paper has also been published as a Google "Knol".

The conceptual basis of the Unified Field Theory, as presented in these pages, can be briefly sketched as follows: "Noether's Theorem" states that in a multicomponent field such as the electromagnetic field (or the metric field of spacetime), where one finds a symmetry one finds an associated conservation law, and vice versa. In matter, light's symmetries are conserved by charge and spin; in spacetime, by inertial and gravitational forces. All forms of energy, including the conservation/entropy domain of spacetime, originate as light. During the "Big Bang", the asymmetric interaction of primordial, high energy light with the metric structure of spacetime produces matter; matter carries charges which are the symmetry (and entropy) debts of the light which created it. Charges produce forces which act to return the material system to its original symmetric state (light), paying matter's symmetry/entropy debts. Repayment is exampled by matter-antimatter annihilation reactions, particle and proton decay, the nucleosynthetic pathway of stars, and Hawking's "quantum radiance" of black holes. Identifying the broken symmetries of light associated with each of the 4 forces (and charges) of physics is the first step toward a conceptual unification of those forces.

A Rationale for Gravitation Gravity is Matter's Memory it Once Was Light

Authors: John A. Gowan
Comments: 4 pages. This paper has also been published as a Google "Knol".

Gravity plays a double conservation role in nature, conserving both: 1) the intrinsic motion of light (by converting it to the intrinsic motion of time - via the annihilation of space and the extraction of a metrically equivalent temporal residue (entropy conservation role); and 2) conserving the non-local distributional symmetry of light's energy (by converting bound to free energy in stars, and via Hawking's "quantum radiance" of black holes (symmetry conservation role). These two conservation roles derive from the double gauge role of "velocity c", which regulates both light's intrinsic motion c (the entropy drive of free electromagnetic energy), and light's non-local distributional symmetry (vanishing time and distance in the direction of propagation). When gravity conserves light's non-local, distributional symmetry (in obedience to "Noether's Theorem"), via gravity's "location" charge, gravity also conserves light's entropy drive by default, since time itself is the active principle of the "location" charge.

Further on the Black Hole War, or to Make the World Deep, Precise and Large Enough for Physics

Authors: Elemér E Rosinger
Comments: 14 pages.

Two somewhat long overdue arguments presented here may help in further clarifying the so called "Black Whole War" and beyond that, may be useful in Physics at large.

12 Summary Points Concerning Gravity

Authors: John A. Gowan
Comments: 8 pages. This paper has also been published as a Google "Knol".

"Local gauge symmetry currents" are forces that maintain the local invariance of universal constants, charges, and other conserved parameters (such as causality and the "Interval") despite the hostile environment of a variable gravitational (or inertial) metric, relative rather than absolute motion, entropy, partial charges, etc. These compensatory forces are due to the activity of the field vectors of the four forces, which not only act (in the long term) to return these asymmetric material systems to their original symmetric state (light), but also act (in the short term) to protect and maintain the invariant values of their symmetry debts (charges), while awaiting a final repayment via antimatter annihilation, proton decay, the "quantum radiance" of black holes, or a universal "Big Crunch". Gravity pays the entropy-interest on the symmetry debt of matter by creating matter's time dimension via the annihilation of space, providing a historical domain within which charge conservation can have significance. Gravitation eventually also pays the energy-principle on matter's symmetry debt, converting bound energy to free energy in stars and via Hawking's "quantum radiance" of black holes.

Global and Local Gauge Symmetry in the "Tetrahedron Model": Part I

Authors: John A. Gowan
Comments: 15 pages. This paper has also been published as a Google "Knol".

1) Noether's Theorem requires the conservation of light's symmetry no less than light's energy. 2) The charges (and spin) of matter are the symmetry debts of light. 3) Charge (and spin) conservation is a temporal, material form of symmetry conservation. 4) Paying (discharging) light's symmetry debt is the role of the 4 forces of physics (field vectors). 5) Charge invariance in time and space (in the service of symmetry conservation) is the key to understanding the local action of the forces ("local gauge symmetry currents"). 6) The field vectors of the forces act as "local gauge symmetry currents" which transform global charge invariance into local charge invariance - serving charge and symmetry conservation, and in the case of gravity, serving energy, symmetry, entropy, and causality conservation (because gravity creates time). 7) Gravity (as gauged by the universal gravitational constant "big G") transforms the global spatial metric of absolute motion and light, as gauged by the universal electromagnetic constant "c", into a local spacetime metric accommodating relative motion and matter. (The local gravitational metric is characterized by "little g".) (Gravity creates time by the annihilation and conversion of space.) 8) Gravity pays the entropy-"interest" on matter's symmetry debt, creating time by the annihilation of metrically equivalent space, decelerating cosmic expansion in consequence. Conversely, the gravitational conversion of bound to free energy (as in the stars and via Hawking's "quantum radiance" of black holes), pays the energy-"principle" on all symmetry and entropy debts, restoring (and hence to all appearances "accelerating") the original cosmic expansion. The radiance of our Sun and the stars represents a completed "circuit" of symmetry conservation. (See: "Currents of Entropy and Symmetry)".

Global-Local Gauge Symmetry: Part III: the Weak Force

Authors: John A. Gowan
Comments: 12 pages. This paper has also been published as a Google "Knol".

The most significant effect of the massive weak force IVBs (Intermediate Vector Bosons) is that they create a specific energy level, a particular unified force symmetric energy state (as "gauged" or scaled by the mass of the Higgs boson), that recreates the original energy-dense primordial environment in which particles were first created and transformed during the early micro-moments of the "Big Bang". This recapitulation ensures that the original and strictly conserved values of charge, mass, energy, etc. are handed on invariant to the next generation of elementary particles: elementary particles created today must be exactly the same in every respect as elementary particles created eons ago during the "Big Bang". These unified force symmetric energy states (for example, the electroweak unified force state, as produced by the "W" IVB) - within which identity transformations are the normal course of events - appear to us as the quantized masses of the IVBs. At the electroweak energy level mediated by the "W" IVB, "ground state" or electromagnetic "species"-level "flavor" identities (electrons vs u,d quarks) are subsumed within a broader "generic"-level identity (leptons vs hadrons); at the next higher GUT energy level (in which the electroweak and strong forces are unified), generic-level identities are subsumed within "family"-level identities - leptons and hadrons become simply fermions or leptoquarks. The final force unification level, the TOE or Planck energy level, incorporates gravity, in which fermions and bosons, particles, light, gravity, and spacetime, are all subsumed within the elemental "order"-level of electromagnetic energy - Gamow's "ylem". (Here I have deliberately employed the terms of the familiar biological taxonomic hierarchy (species, genus, family, order), as it provides a good analogy for the way unfamiliar particle identities and categories are subsumed within the physics hierarchy or energy levels of the unified force symmetric energy states - electromagnetic (ground state), electroweak, GUT, and TOE.) (See: "The Higgs Boson and the Weak Force IVBs".)

Global and Local Gauge Symmetries: Part II (Gravitation)

Authors: John A. Gowan
Comments: 15 pages. This file has also been published as a knol (in two parts)

"Local gauge symmetry currents" are forces that maintain the local invariance of universal constants and other conserved parameters (such as causality and the "Interval") despite the hostile environment of a variable gravitational (or inertial) metric, relative rather than absolute motion, entropy, partial charges, etc. These compensatory forces are due to the activity of the field vectors of the four forces, which not only act (in the long term) to return these asymmetric material systems to their original symmetric state (light), but also act (in the short term) to protect and maintain the invariant values of their symmetry debts while awaiting a final repayment via antimatter annihilation, proton decay, the "quantum radiance" of black holes, or a universal "Big Crunch".

Global and Local Gauge Symmetries: Parts IV and V

Authors: John A. Gowan
Comments: 19 pages.

"Local gauge symmetry currents" are forces that maintain the local invariance of universal constants and other conserved parameters (such as causality and the "Interval") despite the hostile environment of a variable gravitational (or inertial) metric, relative rather than absolute motion, entropy, partial charges, etc. These compensatory forces are due to the activity of the field vectors of the four forces, which not only act (in the long term) to return these asymmetric material systems to their original symmetric state (light), but also act (in the short term) to protect and maintain the invariant values of their symmetry debts while awaiting a final repayment via antimatter annihilation, proton decay, the "quantum radiance" of black holes, or a universal "Big Crunch".

Light and Matter a Synopsis

Authors: John A. Gowan
Comments: 7 pages.

The conceptual basis of the Unified Field Theory, as presented in these pages, can be briefly sketched as follows: "Noether's Theorem" states that in a multi-component field such as the electromagnetic field (or the metric field of spacetime), where one finds a symmetry one finds an associated conservation law, and vice versa. In matter, light's symmetries are conserved by charge and spin; in spacetime, by inertial and gravitational forces. Light's raw energy is conserved as mass and momentum; light's intrinsic motion or entropy drive is conserved as time and gravitation. All forms of energy, including the conservation/entropy domain of spacetime, originate as light. During the "Big Bang", the asymmetric interaction of primordial, high energy light with the metric structure of spacetime produces matter; matter carries charges which are the symmetry (and entropy) debts of the light which created it. Charge invariance is therefore an important corollary of charge and symmetry conservation, maintained in our temporal (gravitational) metric of relative motion by "local gauge symmetry currents" (compensating components of the field vectors, such as magnetism and time). The invariance of "velocity c", the "Interval", and causality (metric analogs of charge) are likewise important corollaries of energy conservation (the "Lorentz Invariance" of Special and General Relativity). Charges produce forces which act to return the material system toward its original symmetric state (light), paying (partially or completely) matter's symmetry/entropy debts. Repayment of matter's symmetry debt (partial and complete) is exampled by: 1) chemical reaction and matter-antimatter annihilation; 2) radioactivity and proton decay; 3) the nucleosynthetic pathway of stars and Hawking's "quantum radiance" of black holes. Identifying the broken symmetries of light associated with each of the 4 charges and forces of physics is the first step toward a conceptual unification of those forces. The charges of matter are the symmetry debts of light.

Orthodox Quantization of Einstein's Gravity: Might Its Unrenormalizability be Technically Fathomable and Physically Innocuous?

Authors: Steven Kenneth Kauffmann
Comments: 6 pages, Also archived as arXiv:0908.3024 [physics.gen-ph].

Many physical constants related to quantized gravity, e.g., the Planck length, mass, curvature, stress-energy, etc., are nonanalytic in G at G = 0, and thus have expansions in powers of G whose terms are progressively more divergent with increasing order. Since the gravity field's classical action is inversely proportional to G, the path integral for gravity-field quantum transition amplitudes shows that these depend on G only through the product ℏG, and are nonanalytic in G at G = 0 for the same reason that all quantum transition amplitudes are nonanalytic in ℏ at ℏ = 0, namely their standard oscillatory essential singularity at the classical 'limit'. Thus perturbation expansions in powers of G of gravity-field transition amplitudes are also progressively more divergent with increasing order, and hence unrenormalizable. While their perturbative treatment is impossible, the exceedingly small value of ℏG makes the semiclassical treatment of these amplitudes extraordinarily accurate, indeed to such an extent that purely classical treatment of the gravity field ought to always be entirely adequate. It should therefore be fruitful to couple classical gravity to other fields which actually need to be quantized: those fields' ubiquitous, annoying ultraviolet divergences would thereupon undergo drastic self-gravitational red shift, and thus be cut off.

Synopsis of the Unification Theory: the System of Matter

Authors: John A. Gowan
Comments: 6 pages.

The conceptual basis of the Unified Field Theory, as presented in these pages, can be briefly sketched as follows: "Noether's Theorem" states that in a multi-component field such as the electromagnetic field (or the metric field of spacetime), where one finds a symmetry one finds an associated conservation law, and vice versa. In matter, light's symmetries are conserved by charge and spin; in spacetime, by inertial and gravitational forces. Light's raw energy is conserved as mass and momentum; light's intrinsic motion or entropy drive is conserved as time and gravitation. All forms of energy, including the conservation/entropy domain of spacetime, originate as light. During the "Big Bang", the asymmetric interaction of primordial, high energy light with the metric structure of spacetime produces matter; matter carries charges which are the symmetry (and entropy) debts of the light which created it. Charge invariance is therefore an important corollary of charge and symmetry conservation, maintained in our temporal (gravitational) metric of relative motion by "local gauge symmetry currents" (compensating components of the field vectors, such as magnetism and time). The invariance of "velocity c", the "Interval", and causality (metric analogs of charge) are likewise important corollaries of energy conservation (the "Lorentz Invariance" of Special and General Relativity). Charges produce forces which act to return the material system toward its original symmetric state (light), paying (partially or completely) matter's symmetry/entropy debts. Repayment of matter's symmetry debt (partial and complete) is exampled by: 1) chemical reaction and matter-antimatter annihilation; 2) radioactivity and proton decay; 3) the nucleosynthetic pathway of stars and Hawking's "quantum radiance" of black holes. Identifying the broken symmetries of light associated with each of the 4 charges and forces of physics is the first step toward a conceptual unification of those forces. The charges of matter are the symmetry debts of light.

Synopsis of Unification Theory

Authors: John A. Gowan
Comments: 6 pages.

The conceptual basis of the Unified Field Theory, as presented in these pages, can be briefly sketched as follows: "Noether's Theorem" states that in a multi-component field such as the electromagnetic field (or the metric field of spacetime), where one finds a symmetry one finds an associated conservation law, and vice versa. In matter, light's symmetries are conserved by charge and spin; in spacetime, by inertial and gravitational forces. Light's raw energy is conserved as mass and momentum; light's intrinsic motion or entropy drive is conserved as time and gravitation. All forms of energy, including the conservation/entropy domain of spacetime, originate as light. During the "Big Bang", the asymmetric interaction of primordial, high energy light with the metric structure of spacetime produces matter; matter carries charges which are the symmetry (and entropy) debts of the light which created it. Charge invariance is therefore an important corollary of charge and symmetry conservation, maintained in our temporal (gravitational) metric of relative motion by "local gauge symmetry currents" (compensating components of the field vectors, such as magnetism and time). The invariance of "velocity c", the "Interval", and causality (metric analogs of charge) are likewise important corollaries of energy conservation (the "Lorentz Invariance" of Special and General Relativity). Charges produce forces which act to return the material system toward its original symmetric state (light), paying (partially or completely) matter's symmetry/entropy debts. Repayment of matter's symmetry debt (partial and complete) is exampled by: 1) chemical reaction and matter-antimatter annihilation; 2) radioactivity and proton decay; 3) the nucleosynthetic pathway of stars and Hawking's "quantum radiance" of black holes. Identifying the broken symmetries of light associated with each of the 4 charges and forces of physics is the first step toward a conceptual unification of those forces. The charges of matter are the symmetry debts of light.

Principles of a Unified Field Theory: a Tetrahedral Model

Authors: John A. Gowan
Comments: 14 pages, This paper has also been published as a Google "Knol".

The tetrahedron diagram is a model of the conversion of free electromagnetic energy (light) into bound electromagnetic energy (matter), and their consequent relationship. So far as we know, the creation of matter has occurred naturally only once, during the very early moments of the "Big Bang", the birth of our Universe. Other examples of the conversion of free to bound energy, not involving the creation of new matter, include the conversion of free energy to "work" and the momentum and kinetic energy of massive particles and organized macroscopic systems, and the simple absorption of photons by the electron shells of atoms (including photosynthesis).

Timeless Quantum Universe in Dynamic Equilibrium

Authors: Amrit S. Sorli
Comments: 3 pages

Original solution of gravity motion is curved 4 dimensional cosmic space. Massive objects move into direction of higher curvature of space. Quantum gravity introduces idea that cosmic space is made out of grains of Planck size. If space has granular structure one can consider space also has its density. More mass in given volume of quantum space less space is dense. Less space is dense more space is curved. Massive objects move always into direction of lover density in higher curvature of quantum space. Gravitational motion of massive objects is result of change of density of quantum space. Change of nsity of quantum space is a physical basis for change of its curvature. In black holes density of mass is extremely high and density of space is extremely low. In a centre of black holes mass is transforming in to quanta of space. In outer space density of mass is extremely low, density of space is extremely high. In outer space quanta of space are transforming onto elementary particles i.e. cosmic rays.

Yang-Mills Interactions and Gravity in Terms of Clifford Algebra

Authors: Wei Lu
Comments: 20 pages, to be published in Advances in Applied Clifford Algebras.

A model of Yang-Mills interactions and gravity in terms of the Clifford algebra Cl_0,6 is presented. The gravity and Yang-Mills actions are formulated as different order terms in a generalized action. The feebleness of gravity as well as the smallness of the cosmological constant and theta terms are discussed at the classical level. The invariance groups, including the de Sitter and the Pati-Salam SU(4) subgroups, consist of gauge transformations from either side of an algebraic spinor. Upon symmetry breaking via the Higgs fields, the remaining symmetries are the Lorentz SO(1,3), color SU(3), electromagnetic U(1)_EM, and an additional U(1). The first generation leptons and quarks are identified with even and odd parts of spinor idempotent projections. There are still several shortcomings with the current model. Further research is needed to fully recover the standard model results.

The Solar Archetype

Authors: John A. Gowan
Comments: 4 pages, This paper has also been published as a Google "Knol".

Gravity has two primary conservation roles in nature: 1) entropy conservation (at all gravitational field strengths), and 2) symmetry conservation (at high gravitational field strengths). Entropy conservation is accomplished by the gravitational annihilation of space, exposing a metrically equivalent temporal residue. Annihilation converts the expansive spatial entropic drive of free energy (the intrinsic motion of light) to the expansive historical entropic drive of bound energy (the intrinsic motion of time). The implicit temporal drive of spatial expansion (recognized as "spacetime") is converted to (and conserved as ) the explicit temporal drive of history - via gravity. Symmetry conservation is accomplished by the gravitational conversion of bound to free energy (mass to light) in stars, and related astrophysical processes, and ultimately and completely, via Hawking's "quantum radiance" of black holes. Sunlight completes the symmetry conservation cycle: light - matter - light, which begins with the conversion of light to matter (free electromagnetic to bound electromagnetic energy) during the "Big Bang" and ends with the gravitational conversion of bound to free energy in stars.

A Conjectured Multiverse String Cosmology in 26 Dimensions

Authors: Richard Ruquist
Comments: 6 pages, Retired physicist, Grafton, Massachusetts, USA

Vafa's (11+1) F theory is extended by means of Bars' 2T holographic theory to yield a 14d Multiverse theory that permeates the brane of a 12d Universe in which both the Universe and the Multiverse have (3+1) spacetimes. Given the 2d toroidal compactification of F theory, we conjecture that the Multiverse has a 4d Cartesian compactification that is filled with 3D+T spacetime via the standard 6d elliptic Calabi-Yau compactification, as in both M and F theory. The result is exemplified using supermassive black hole cosmology.

Quantized Space-Time and Internal Structure of Elementary Particles: a New Model

Authors: Hamid Reza Karimi
Comments: 23 pages.

In this paper we present a model in which the time and length are considered quantized. We try to explain the internal structure of the elementary particles in a new way. In this model a super-dimension is defined to separate the beginning and the end of each time and length quanta from another time and length quanta. The beginning and the end of the dimension of the elementary particles are located in this super-dimension. This model can describe the basic concepts of inertial mass and internal energy of the Elementary particles in a better way. By applying this model, some basic calculations mentioned below, can be done in a new way: 1- The charge of elementary particles such as electrons and protons can be calculated theoretically. This quantity has been measured experimentally up to now. 2- By using the equation of the particle charge obtained in this model, the energy of the different layers of atoms such as hydrogen and helium is calculated. This approach is simpler than using Schrödinger equation. 3- Calculation of maximum speed of particles such as electrons and positrons in the accelerators is given.

Event-Symmetric Space-Time

Authors: Philip Gibbs
Comments: 222 pages, e-book published by Weburbia Press 1998

How much can physics explain? "Event-Symmetric Space-Time" presents a startlingly integrated world view from the forefront of physics. So often we read about the new quantum paradigm which has replaced the old mechanistic philosophy of physics, but seldom do we find "what the paradigm is" spelt out so succinctly. "The universe is made of stories, not of atoms." (Muriel Rukeyser) This is the storyteller's point of view. Through a literal interpretation of those words we transcend causality and determinism to see the quantum multiverse as a whole. Throughout this book, the author returns to the principle of event symmetry - in particle physics, in cosmology, in superstring theory, in epistemology. Coupled to the storyteller's paradigm this new idea of philosophy and physics dares to free us from the constraints of our intuition, to reveal natures truths. We are in the midst of a revolution in our understanding of physics and the universe. This new interpretation of superstring theory is slowly helping to bring physicists' long search for the holy grail of knowledge to fruition. At the debut of the twentieth century Einstein revealed how the laws of nature are independent of any co-ordinate system. According to general relativity, no matter how a reference frame of space-time is turned, pulled and stretched, the laws of physics remain the same because gravity keeps track of the changes. Einstein's only restriction was that he did not allow space-time to tear. You cannot cut out two pieces of space-time and swap them over expecting the forces of nature to compensate, or can you? Research attempting to form a theory of quantum gravity suggests that space-time can tear and reconnect in ways which change its topology. This book suggests that Einstein's symmetry must be extended to allow space-time to be atomised into space-time events which can be pulled apart and recombined in any permutation. The unified forces of nature must permit this "event symmetry" just as gravity already permits the more restricted co-ordinate transformations.

Cosmological Implications of the Tetron Model of Elementary Particles

Authors: Bodo Lampe
Comments: 30 Pages.

Based on a possible solution to the tetron spin problem, a modification of the standard Big Bang scenario is suggested, where the advent of a spacetime manifold is connected to the appearance of tetronic bound states. The metric tensor is constructed from tetron constituents and the reason for cosmic inflation is elucidated. Furthermore, there are natural dark matter candidates in the tetron model. The ratio of ordinary to dark matter in the universe is calculated to be 1:5.

An Introduction to the Papers

Authors: John A. Gowan
Comments: 5 pages, This paper has also been published as a Google "Knol".

Because the papers themselves can be difficult for the uninitiated, in spite of my efforts to make them simple and clear, I have written a series of introductory papers designed as a guide to assist the interested reader in working through them. I will try to bring out the main points of the paper, its relation to the remaining body of work, and perhaps make a few comments on its history and structure. There is almost no mathematics in these papers; for the most part, the papers deal only with conservation principles, although of course I make reference to the mathematical theories which provide the formal basis for the conceptual synthesis of this work (Noether's theorem, Einstein's "Interval" and energy relations, the 1st and 2nd laws of thermodynamics, etc.).

Human Development and Life Stages General Systems Models

Authors: John A. Gowan
Comments: 3 pages, This paper has also been published as a Google "Knol".

Fractal or General Systems models have been extended into the area of human life span development, by myself, deliberately, and earlier by my father, and others, following their own agendas (not intentional GS models). A short discussion with both models is presented below.

The Tetrahedron Model in the Context of a Complete Conservation Cycle

Authors: John A. Gowan
Comments: 6 pages, This paper has also been published as a Google "Knol".

"Noether's Theorem" states that in a multicomponent field such as the electromagnetic field (or the metric field of spacetime), symmetries are associated with conservation laws. In matter, light's (broken) symmetries are conserved by charge and spin; in spacetime, light's symmetries are protected by inertial forces, and conserved (when broken) by gravitational forces. All forms of energy originate as light; matter carries charges which are the symmetry/entropy debts of the light which created it (both concepts are required to fully integrate gravity - which has a double conservation role - with the other forces). Charges produce forces which act to return the material system to its original symmetric state, repaying matter's symmetry/entropy debts. Repayment is exampled by any spontaneous interaction producing net free energy, including: chemical reactions and matter-antimatter annihilation reactions; radioactivity, particle and proton decay; the nucleosynthetic pathway of stars, and Hawking's "quantum radiance" of black holes. Identifying the broken symmetries of light associated with each of the 4 charges and forces of physics is the first step toward a conceptual unification. The charges of matter are the symmetry debts of light.

On a Four Dimensional Unified Field Theory of the Gravitational, Electromagnetic, Weak and the Strong Force.

Authors: Golden Gadzirayi Nyambuya
Comments: 27 pages, first published in the October 2007 Issue of the Aperion Journal. Further work on these ideas is underway.

The Gravitational, Electromagnetic, Weak & the Strong force are here brought together under a single roof via an extension of Reimann geometry to a new geometry (coined Reimann-Hilbert Space); that unlike Reimann geometry, preserves both the length and the angle of a vector under parallel transport. The affine connection of this new geometry - the Reimann-Hilbert Space, is a tensor and this leads us to a geodesic law that truly upholds the Principle of Relativity. The geodesic law emerging from the General Theory of Relativity (GTR) is well known to be in contempt of the Principle of Relativity which is a principle upon which the GTR is founded. The geodesic law for particles in the GTR must be formulated in special (or privileged) coordinate systems i.e. gaussian coordinate systems whereas the Principle of Relativity clearly forbids the existence of special (or privileged) coordinate systems in manner redolent of the way the Special Theory of Relativity forbids the existence of an absolute (or privileged) frame of reference. In the low energy regime and low spacetime curvature the unified field equations derived herein are seen to reduce to the well known Maxwell-Procca equation, the none-abelian nuclear force field equations, the Lorentz equation of motion for charged particles and the Dirac Equation. Further, to the already existing four known forces, the theory predicts the existence of yet another force. We have coined this the super-force and this force obeys SU(4, 4) gauge invariance. Furthermore, unlike in the GTR, gravitation is here represented by a single scaler potential, and electromagnetic field and the nuclear forces are described by the electromagnetic vector potential (A_μ) which describes the metric tensor i.e. g_μν = A_μA_ν. From this (g_μν = A_μA_ν), it is seen that gravity waves may not exist in the sense envisaged by the GTR.

Gravity, Entropy, and Thermodynamics

Authors: John A. Gowan
Comments: 21 pages, This paper has also been published as a Google "Knol".

The intrinsic motions of light, time, and gravity are primordial forms of entropy, causing: 1) the creation, expansion, and cooling of space; 2) the creation, expansion, and aging of history; 3) the creation and expansion of historic spacetime, respectively. The charges of matter are the symmetry debts of light (Noether's Theorem). Gravity pays the entropy-interest on matter's symmetry debt by creating time from space - giving charge conservation an extended significance in the time dimension. Light's spatial entropy drive and expansion funds matter's historical entropy drive and expansion via the gravitational conversion of space to time.

Symmetry Principles of the Unified Field Theory (a "Theory of Everything") Part 2

Authors: John A. Gowan
Comments: 27 pages, This paper has also been published as a Google "Knol".

The conceptual basis of the Unified Field Theory, as presented in these pages, can be briefly sketched as follows: "Noether's Theorem" states that in a multicomponent field such as the electromagnetic field (or the metric field of spacetime), where one finds a symmetry one finds an associated conservation law, and vice versa. In matter, light's symmetries are conserved by charge and spin; in spacetime, by inertial and gravitational forces. All forms of energy, including the conservation/entropy domain of spacetime, originate as light. During the "Big Bang", the asymmetric interaction of primordial, high energy light with the metric structure of spacetime produces matter; matter carries charges which are the symmetry (and entropy) debts of the light which created it. Charges produce forces which act to return the material system to its original symmetric state (light), paying matter's symmetry/entropy debts. Repayment is exampled by matter-antimatter annihilation reactions, particle and proton decay, the nucleosynthetic pathway of stars, and Hawking's "quantum radiance" of black holes. Identifying the broken symmetries of light associated with each of the 4 forces (and charges) of physics is the first step toward a conceptual unification of those forces. In the "global vs local gauge symmetry" representation of the cosmic conservation mechanism, the global symmetry is carried by massless light, space, absolute motion (the intrinsic and invariant motion of light), and "gauged" (regulated) by "c", the universal electromagnetic energy constant. The local symmetry is carried by massive matter, various charges, causal history, relative motion (including the intrinsic but variable motion of time) and gauged by "G", the universal gravitational constant. Connecting these two realms of free vs bound electromagnetic energy (and their conservation domains of space vs history), are the field vectors of the forces, whose function is to translate the invariant symmetry of the global realm into the invariant charges, spin, mass, and "interval" of the local realm, and vice versa, conserving energy, symmetry, entropy, and causality, throughout both conjoined domains. (See: The Tetrahedron Model (diagram)".) I will employ the "global vs local gauge symmetry" representation of the cosmic conservation process (due to the "Standard Model" of "establishment" physics) throughout the following analysis, in combination with certain symmetry principles, as elucidated by the "Tetrahedron Model (text)" originating in these web pages: "the charges of matter are the symmetry debts of light". Four conservation laws and corollaries (energy, entropy, symmetry, causality); Noether's Theorem; and a few invariance principles: (charge, elementary particle mass, velocity c, the "Interval", causality, Lorentz invariance of Special Relativity, etc.), are the key to understanding the operation of the forces and the unified field theory. (See: Global vs Local Gauge Symmetries in the Tetrahedron Model

Symmetry Principles of the Unified Field Theory (a "Theory of Everything") Part I

Authors: John A. Gowan
Comments: 20 pages, This paper has also been published as a Google "Knol".

The conceptual basis of the Unified Field Theory, as presented in these pages, can be briefly sketched as follows: "Noether's Theorem" states that in a multicomponent field such as the electromagnetic field (or the metric field of spacetime), where one finds a symmetry one finds an associated conservation law, and vice versa. In matter, light's symmetries are conserved by charge and spin; in spacetime, by inertial and gravitational forces. All forms of energy, including the conservation/entropy domain of spacetime, originate as light. During the "Big Bang", the asymmetric interaction of primordial, high energy light with the metric structure of spacetime produces matter; matter carries charges which are the symmetry (and entropy) debts of the light which created it. Charges produce forces which act to return the material system to its original symmetric state (light), paying matter's symmetry/entropy debts. Repayment is exampled by matter-antimatter annihilation reactions, particle and proton decay, the nucleosynthetic pathway of stars, and Hawking's "quantum radiance" of black holes. Identifying the broken symmetries of light associated with each of the 4 forces (and charges) of physics is the first step toward a conceptual unification of those forces. In the "global vs local gauge symmetry" representation of the cosmic conservation mechanism, the global symmetry is carried by massless light, space, absolute motion (the intrinsic and invariant motion of light), and "gauged" (regulated) by "c", the universal electromagnetic energy constant. The local symmetry is carried by massive matter, various charges, causal history, relative motion (including the intrinsic but variable motion of time) and gauged by "G", the universal gravitational constant. Connecting these two realms of free vs bound electromagnetic energy (and their conservation domains of space vs history), are the field vectors of the forces, whose function is to translate the invariant symmetry of the global realm into the invariant charges, spin, mass, and "interval" of the local realm, and vice versa, conserving energy, symmetry, entropy, and causality, throughout both conjoined domains. (See: The Tetrahedron Model (diagram)".) I will employ the "global vs local gauge symmetry" representation of the cosmic conservation process (due to the "Standard Model" of "establishment" physics) throughout the following analysis, in combination with certain symmetry principles, as elucidated by the "Tetrahedron Model (text)" originating in these web pages: "the charges of matter are the symmetry debts of light". Four conservation laws and corollaries (energy, entropy, symmetry, causality); Noether's Theorem; and a few invariance principles: (charge, elementary particle mass, velocity c, the "Interval", causality, Lorentz invariance of Special Relativity, etc.), are the key to understanding the operation of the forces and the unified field theory. (See: Global vs Local Gauge Symmetries in the Tetrahedron Model".

The "Tetrahedron Model" vs the "Standard Model" of Physics: a Comparison with Respect to the Unification of Forces

Authors: John A. Gowan
Comments: 19 pages, This paper has also been published as a Google "Knol".

Generally speaking, the "Tetrahedron Model" addresses symmetry breaking/conservation in the macrophysical "rebound" phase of cosmic evolution (the current era of symmetry restoration, in which we live), while the "establishment's" "Standard Model" addresses symmetry breaking/conservation in the microphysical "cascade" phase of cosmic devolution, the period of the "Big Bang" which brings the material cosmos into being.

Nature's Fractal Pathway

Authors: John A. Gowan
Comments: 28 pages, This paper has also been published as a Google "Knol".

A General Systems model of the Universe is presented, based on a fractal paradigm. A 4x3 "metric" or fractal algorithm is proposed as the organizing principle of the Microphysical, Biophysical, Astrophysical, and Metaphysical realms. The algorithm is expressed through the conservation laws and forces of physics, symmetry-breaking and the creation of matter during the "Big Bang", the dimensions of spacetime, the quantum rules of atomic order, the families of elementary particles, the structure of baryons, alpha particles, carbon atoms, carbon's molecular and crystal bonds, DNA, the genetic code, the nucleosynthetic pathway of stars, gravitation, etc. The human mind has discovered this order both intuitively and rationally, where it finds expression in the 4x3 (and 4x4) patterns of mythological, occult, religious, philosophical, and scientific "world systems" and cosmologies. A model of the unified field theory is presented as an example of how the fractal algorithm may be used in system modeling. In its most general form, the 4-part algorithm consists of an input of energy, followed by two complementary conservation modes, concluding with a restorative force which either returns the system to its actual original state, or elevates it to a "harmonic complexion" or resonant analog of the original state. Introduction

Synopsis of the Tetrahedron Model

Authors: John A. Gowan
Comments: 13 pages, This paper has also been published as a Google "Knol".

The "Tetrahedron Model" is a model of the devolution (asymmetric transformation) of light (free energy) into matter (bound energy), that is, of the relationship between the two forms of electromagnetic energy which constitute our Universe. This model revolves around the conversion of light to matter and vice versa, as regulated by four conservation laws: the Conservation of Energy, Entropy, Symmetry, and Causality.

Three-Dimensional Objects Only Consisting of Time-Burdened Space as a Basis of Matter and Its Interactions (Theory of Objects of Space)

Authors: H.-J. Hochecker
Comments: 23 pages, More details and the version in German language can be found on the authors web site (named inside the pdf)

From the constancy of light speed as demanded by the theory of special relativity (SRT) the time dilatation, the length contraction and the unsynchronisation of time arises. These three quantities (values) are not to be applied only to matter but also to the space as such, which is contained by matter. Due to this it yields that space areas can be distinguished from other space areas by these three quantities (values). Since these space areas, which are burdened with SRT values, must be in space again, too, it results that these space areas (burdened with SRT values) can move in space as objects. When these space areas meet then they overlap each other three-dimensionally and by doing this they build overlap areas (OA) with new SRT values. In this way these space areas burdened with SRT values can interact with each other, what for they are named space objects (SOs). It turns out that the SOs are able to interact with each other in the most various ways. How this happens is shown among others in this work. Due to their interactions the SOs are able to form highly complex structures, which we know as matter. Matter in its turn interacts by emitting and absorbing grate numbers of SOs in a field like manner. The great importance of the SOs in our world is underpinned in this work with several interesting examples; with that it is shown how the concept of the definition of the SOs can be used, and that it makes sense to use it. The SOs are the elements upon which all things are based and simultaneous they are the most basic of all elements also (in the time burdened threedimensional space). The "Theory of Space Objects" represents a link between different sections of physics such as gravitation, quantum theory, relativity, electromagnetism, building-up of matter, and much more.

Original Solution of Gravity is Without Gravitational Waves

Authors: Amrit S. Sorli
Comments: 3 pages

Original solution of gravity motion is curved 4 dimensional cosmic space. Massive objects move into direction of higher curvature of space. Quantum gravity introduces idea that cosmic space is made out of grains of Planck size. If space has granular structure one can consider space also has its density. According to the second low of thermodynamics in the universe distribution of energy tends to be homogeneous. More mass in given volume of quantum space less space is dense. Less space is dense more space is curved. Massive objects move always into direction of lover density in higher curvature of quantum space. Gravitational motion of massive objects is result of change of density of quantum space. Change of density of quantum space is a physical basis for change of its curvature.

A Short Course in the Unified Field Theory

Authors: John A. Gowan
Comments: 12 pages, This paper has also been published as a Google "Knol".

The conceptual basis of the Unified Field Theory as presented in these pages is summarized below: "Noether's Theorem" states that in a multicomponent field such as the electromagnetic field (or the metric field of spacetime), symmetries are associated with conservation laws and vice versa. In matter, light's (broken) symmetries are conserved by charge and spin; in spacetime, light's symmetries are protected by inertial forces, and conserved (when broken) by gravitational forces. All forms of energy originate as light; matter carries charges which are the symmetry/entropy debts of the light which created it. The charges of matter are the symmetry debts of light. Charges produce forces which act to return the material system to its original symmetric state, paying matter's symmetry/entropy debts. Payment is exampled by any spontaneous interaction producing net free energy, including: chemical reactions and matter-antimatter annihilation reactions (electromagnetic force); radioactivity, particle and proton decay (weak and strong nuclear forces); the nucleosynthetic pathway of stars, and Hawking's "quantum radiance" of black holes (gravitational force). Identifying the broken symmetries of light associated with each of the 4 charges and forces of physics is the first step toward a conceptual unification. The conservation of energy, symmetry, entropy, and causality, plus the requirement of symmetry-breaking followed by the maintenance of charge invariance (including "local gauge symmetry"), are all key conceptual elements in the formulation of a Unified Field Theory.

The Half-Life of Proton Decay and Its Relation to the "Heat Death" of the Universe

Authors: John A. Gowan
Comments: 13 pages, This paper has also been published as a Google "Knol".

The significance of proton decay is that it is the end-point of temporal entropy for matter, in much the same way we might say the black hole is the end-point of spatial entropy for light. Again we find that "the extremes meet": proton decay is surely commonplace inside black holes, while Hawking's "quantum radiance" returns bound energy to free energy and temporal entropy to spatial entropy. The notion that the ratio of force strengths relates the "heat death" and the "information death" of the Cosmos via proton decay suggests that if we knew one we would know the other; unfortunately, we know neither, and our force ratio is a pure number, without units. Nevertheless, I will use it to make a naive guess at the proton's lifetime. The lower experimental bound on proton decay is currently 10(35) years. According to the hypothesis advanced here, that the proton lifetime reflects the force ratio, in 2.5 x 10(41) seconds all protons will have decayed, which, curiously enough, yields an observational expectation (8 x 10(33) years) not far off the current lower experimental bound.

New Conceptual Foundations for Quantum-Gravity and Quantum-Mechanics

Authors: B N Sreenath
Comments: 71 pages.

Quantum-Gravity (QG) is limited to bodies, which have attained their 'gravitational radius' like Black holes (BH) and Quasars. QG has been explained and solved on entirely new concepts and laws so as to bring within its scope not only unification of all physical interactions including gravitation in its 'distorted' form and electro-magnetism but also other cosmological problems which involve high energy existence like the BH dynamics, dark-energy, etc. This becomes obvious once we go through the BH Chart and the Interaction-Table (IT). In BH Chart and the IT, gravitational radius and the interaction-range are identified thus unifying the phenomena occurring in BH with those of the micro-world. The two laws of QG enunciated give rise to two fundamental constants in physics whose values are reciprocal to the values of 'C'and 'G'. The Quantum-Gravity field is identified with the "Exponentially Varying Accelerated (or Gravity) Field" so that in it both test masses of classical size and micro-particles of quantum size, describe the same 'Logarithmic Spiral Path'. Micro-particles can also describe 'Conical Spiral Path'. Thus QG field is an 'inward spinning field' which involves 'Torsion' and 'Curvature' varying. 'Spinors', which are used to describe the "Logarithmic Spiral Path" in BH, give rise to "Immirzi Parameter". From the concept of 'unitary change in acceleration', atomic transitions are explained and 'Heisenberg's Principle of Indeterminacy' is derived.

On the Density of Space

Authors: Jakob Petelin
Comments: 1 Page

A recent paper came to our attention in which the author makes a striking conclusion about the properties of space. This paper investigates it in detail and demonstrates that upon such conclusion either the General Theory of Relativity is wrong or the mentioned author made some mistakes which have yet to be identified.

Einstein Curvature Tensor and Density Tensor of Quantum Space

Authors: Amrit S. Sorli
Comments: 1 pages

Quantization of the cosmic space allows introduction of density of cosmic space. Medium that has granular structure can also have density. More mass is in a given volume of quantum space, less space is dense. In General Theory of Relativity gravity is generated by change of curvature of cosmic space, here by change of density. The basis for curvature of space is its density. Einstein curvature tensor in a form 1/G is Density tensor of quantum space.

Density/curvature of Quantum Space Generates Gravitational Motion

Authors: Amrit S. Sorli
Comments: 3 pages

Clocks measure a frequency, velocity and numerical order of change. Experimental date confirms that changes and clocks do not run time; they run in quantum space only. Time is not a part of quantum space. Quantum space itself is timeless. In the universe as a whole amount of matter energy and amount of quantum space energy tends to be constant. Density of mass and density of quantum space in a given volume of quantum space tends to be constant. Mass here is considered as a compressed energy of quantum space. Presence of mass in a given volume of quantum space diminishes its density. Massive objects move always into direction of lover density of quantum space. Gravitational motion of massive objects is result of change of density of quantum space. In space with no change of density massive object will not have gravitational motion as in centre of stellar objects or in a flat quantum space where massive objects are far away. Change of density of quantum space corresponds in General Theory of Relativity to the change of the curvature of space. Lower is density of quantum space bigger is its curvature. Here is introduced density/curvature of quantum space.

Mathematical Space-Time, Neuronal Space-Time and Timeless Quantum Space

Authors: Amrit S. Sorli
Comments: 4 pages

The universe is in a continuous change. A change n gets transformed into a change n+1, the change n+1 into a change n+2 and so on. Clocks measure a frequency, velocity and numerical order of change. Experimental date confirms that changes and clocks do not run time; they run in quantum space only. Time is not a part of quantum space. Quantum space itself is timeless. Physical time that is clocks run is man created physical reality. Space-time is a math model merely. Fundamental arena of the universe is timeless quantum space. In the timeless quantum space into which massive bodies and elementary particles move there is no past and no future. Past and future belong to the inner neuronal space-time that is a result of neuronal activity of the brain.

On 2 + 2-Dimensional Spacetimes, Strings, Black-Holes and Maximal Acceleration in Phase Spaces

Authors: Carlos Castro, J. A. Nieto
Comments: 41 Pages. This article appeared in the Int. J. Mod. Phys. A vol 22, no. 11 (2007) 2021.

We study black-hole-like solutions ( spacetimes with singularities ) of Einstein field equations in 3+1 and 2+2-dimensions. In the 3+1-dim case, it is shown how the horizon of the standard black hole solution at r = 2G_NM can be displaced to the location r = 0 of the point mass M source, when the radial gauge function is chosen to have an ultra-violet cutoff R(r = 0) = 2G_NM if, and only if, one embeds the problem in the Finsler geometry of the spacetime tangent bundle (or in phase space) that is the proper arena where to incorporate the role of the physical point mass M source at r = 0. We find three different cases associated with hyperbolic homogeneous spaces. In particular, the hyperbolic version of Schwarzschild's solution contains a conical singularity at r = 0 resulting from pinching to zero size r = 0 the throat of the hyperboloid H² and which is quite different from the static spherically symmetric 3+1-dim solution. Static circular symmetric solutions for metrics in 2+2 are found that are singular at ρ = 0 and whose asymptotic ρ → ∞ limit leads to a flat 1+2-dim boundary of topology S¹ x R². Finally we discuss the 1+1-dim Bars-Witten stringy black-hole solution and show how it can be embedded into our 3 + 1-dimensional solutions with a displaced horizon at r = 0 and discuss the plausible stringy nature of a point-mass, along with the maximal acceleration principle in the spacetime tangent bundle (maximal force in phase spaces). Black holes in a 2 + 2-dimensional "spacetime" from the perspective of complex gravity in 1 + 1 complex dimensions and their quaternionic and octonionic gravity extensions deserve furher investigation. An appendix is included with the most general Schwarzschild-like solutions in D ≥ 4.

On N-Ary Algebras, Branes and Polyvector Gauge Theories in Noncommutative Clifford Spaces

Authors: Carlos Castro
Comments: 25 Pages. This article has been submitted to the J. Math. Phys.

Polyvector-valued gauge field theories in noncommutative Clifford spaces are presented. The noncommutative star products are associative and require the use of the Baker-Campbell-Hausdorff formula. Actions for pbranes in noncommutative (Clifford) spaces and noncommutative phase spaces are provided. An important relationship among the n-ary commutators of noncommuting spacetime coordinates [X¹,X², ......,Xⁿ] with the poly-vector valued coordinates X^123...n in noncommutative Clifford spaces is explicitly derived [X¹,X², ......,Xⁿ] = n! X^123...n. The large N limit of n-ary commutators of n hyper-matrices X_i1i2....in leads to Eguchi-Schild p-brane actions for p + 1 = n. Noncommutative Clifford-space gravity as a poly-vector-valued gauge theory of twisted diffeomorphisms in Clifford spaces would require quantum Hopf algebraic deformations of Clifford algebras.

A Chern-Simons E₈ Gauge Theory of Gravity in D = 15, Grand Unification and Generalized Gravity in Clifford Spaces

Authors: Carlos Castro
Comments: 19 Pages. This article appeared in the International Journal of Geometric Methods in Modern Physics Vol. 4, No. 8 (2007) 1239–1257.

A novel Chern-Simons E₈ gauge theory of gravity in D = 15 based on an octic E₈ invariant expression in D = 16 (recently constructed by Cederwall and Palmkvist) is developed. A grand unification model of gravity with the other forces is very plausible within the framework of a supersymmetric extension (to incorporate spacetime fermions) of this Chern-Simons E₈ gauge theory. We review the construction showing why the ordinary 11D Chern-Simons gravity theory (based on the Anti de Sitter group) can be embedded into a Clifford-algebra valued gauge theory and that an E₈ Yang-Mills field theory is a small sector of a Clifford (16) algebra gauge theory. An E₈ gauge bundle formulation was instrumental in understanding the topological part of the 11-dim M-theory partition function. The nature of this 11-dim E₈ gauge theory remains unknown. We hope that the Chern-Simons E₈ gauge theory of gravity in D = 15 advanced in this work may shed some light into solving this problem after a dimensional reduction.

A Proposal for a Unified Field Theory

Authors: Bruce Rout
Comments: 16 pages

A proposal outlining an approach to a unified field theory is presented. A general solution to the time-dependent Schrödinger Equation using an alternative boundary condition is found to derive the Heisenberg uncertainty formulae. A general relativity/quantum mechanical interaction between a photon and a gravitational field is examined to determine the degree of red shifting of light passing through a gravitational field. The Einstein field equations, complete with an arrangement of Faraday tensors, are presented with suggestions to determine the energy of a photon from Einstein's and Maxwell's equations. Schrödingers Equation is coupled with both the Einstein field equations and Maxwells equations to derive a possible foundation for string theory.

Veneziano Amplitudes, Spin Chains, and String Models

Authors: Arkady L. Kholodenko
Comments: 35 pages

In a series of recently published papers, we reanalyzed the existing treatments of Veneziano and Veneziano-like amplitudes and the models associated with these amplitudes. In this work, we demonstrate that the already obtained new partition function for these amplitudes can be exactly mapped into that for the Polychronakos-Frahm spin chain model. This observation allows us to recover many of the existing string-theoretic models, including the most recent ones.

Polyvector-Valued Gauge Field Theories and Quantum Mechanics in Noncommutative Clifford Spaces

Authors: Carlos Castro
Comments: 13 pages, This article has been submitted to the IJMPA.

The basic ideas and results behind polyvector-valued gauge field theories and Quantum Mechanics in Noncommutative Clifford spaces are presented. The construction of Noncommutative Clifford-space gravity as polyvector-valued gauge theories of twisted diffeomorphisms in Cliffordspaces would require quantum Hopf algebraic deformations of Clifford algebras.

Polyvector Super-Poincare Algebras, M, F Theory Algebras and Generalized Supersymmetry in Clifford-Spaces

Authors: Carlos Castro
Comments: 17 pages, This article appeared in the Int. Journal of Mod. Phys. A 21, no.10 (2005) 2149.

Starting with a review of the Extended Relativity Theory in Clifford-Spaces, and the physical motivation behind this novel theory, we provide the generalization of the nonrelativistic Supersymmetric pointparticle action in Clifford-space backgrounds. The relativistic Supersymmetric Clifford particle action is constructed that is invariant under generalized supersymmetric transformations of the Clifford-space background's polyvector-valued coordinates. To finalize, the Polyvector Super-Poincare and M, F theory superalgebras, in D = 11, 12 dimensions, respectively, are discussed followed by our final analysis of the novel Clifford-Superspace realizations of generalized Supersymmetries in Clifford spaces.

Renormalizable Yang-Mills Tetrad Gravity

Authors: Jack Sarfatti
Comments: 8 pages

Although Yang-Mills theory was developed for non-universal compact internal symmetry groups of subsets of matter fields, it should also work for the universal non-compact symmetry groups of all matter fields implied by the classical Einstein local equivalence principle. We introduce a new class of direct gravity couplings of rotating matter to the electromagnetic field that can be tested in principle especially in rotating superconductors.

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.

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 H^AB 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, p_x); (x, p_y); (x, p_z); (y, p_x), ... 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.

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.

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_∞(w_1+∞) 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_∞(w_1+∞) 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.

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 Cl_C(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^-2_PlanckR^-2 = L^-4_P(L_Planck/R)² ~ 10^-122M⁴_Planck, 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.

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_∞,w_1+∞ 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.

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.

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 q^A, p^A for A = 1, 2, 3, ...n. The latter noncommuting coordinates obey the noncommutative Yang algebra with an ultraviolet L_P (Planck) scale and infrared (R ) scale cutoff. It is shown why our p-brane actions in the "classical" limit ℏ_eff = ℏL_P/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.

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.

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 [Z_a,Z_b] ≠ 0. The Hermitian metric is complex-valued with symmetric and nonsymmetric components and there are two different complex-valued Hermitian Ricci tensors R_μν, S_μν. 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 Z_μ = E_μ^a Z_a as noncommuting p-brane background complex spacetime coordinates is discussed in the conclusion, where E_μ^a is the complex vielbein associated with the Hermitian metric G_μν = g_(μν) + ig_[μν] = E_μ^a Ē_ν^b This could be one of the underlying reasons why string-theory involves gravity.

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 G_μν already encompasses the ordinary spacetime metric g_μν, 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 F_μν through the area momentum Σ^μν in the internal isospin space yields corrections O(1/M²_Planck) 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.

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].

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 z_n = 1/2+iλ_n 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.

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.

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 Ω_M^AB, 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 E_M^A, that gauge the nonabelian translations. Thus, in one-scoop, the vielbein E_M^A 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.

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.

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.

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.

Towards M-Matrix

Authors: Matti Pitkänen
Comments: 732 pages

This book is devoted to a detailed representation 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 S-matrix is replaced with M-matrix identified as time-like entanglement coeficients between positive and negative energy parts of zero energy states. M-matrix is a product of diagonal density matrix and unitary S-matrix. 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. The replacement of massless plane waves with states for which amplitudes are localized at light-rays is suggestive in TGD framework. Twistors could allow lifting of space-time surfaces to surfaces of X x CP₂, where X is 8-D twistor space or its 6-D projective variant. The interpretation of massive particles as massless particles in 8-D sense suggests a generalization of twistors defined using triads of vector and spinor representations of SO(7,1).
5. In TGD Universe bosons are fermion-antifermion bound states. Therefore the action at QFT limit is Dirac action coupled to gauge potentials and bosonic action emerges as part of effective action as one functionally integrates over spinor fields. Coupling constant evolution follows once the UV cutoffs of mass and hyperbolic angle in fermionic loop integrations are fixed. The hyperbolic cutoff motivated by zero energy ontology predicts coupling constant evolution consistent with standard model. The condition that all N-vertices defined by fermiomic loops vanish for N > 3 when incoming particles are massless could fix the hyperbolic cutoff completely.

1. The Clifford algebra of WCW is hyper-finite factor of type II₁ which suggests that M-matrix could be identified as Connes tensor product.
2. In TGD framework dark matter corresponds to ordinary particles with non-standard value of 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.

TGD as a Generalized Number Theory

Authors: Matti Pitkänen
Comments: 604 pages

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 complexifications with Minkowskian signature of metric. Allowed space-time surfaces would correspond to what might be called hyper-quaternionic sub-manifolds of a hyper-octonionic space and mappable to M⁴ x 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 modified gamma matrices but not tangent plane in general. Hence the basic variational principle of TGD would have deep number theoretic content.
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.

Physics in Many-Sheeted Space-Time

Authors: Matti Pitkänen
Comments: 630 pages

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

1. In Part I extremals of Kähler action are discussed and the notions of many-sheeted space-time 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 are basic objects of TGD inspired cosmology. 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 superfluidity.

Physics as Infinite-Dimensional Geometry

Authors: Matti Pitkänen
Comments: 280 pages

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. 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.

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 fl uctuating 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 δM₊⁴ X CP₂, where δM₊⁴ 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.

TGD and Fringe Physics

Authors: Matti Pitkänen
Comments: 296 pages

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.
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.

Topological Geometrodynamics: Overview

Authors: Matti Pitkänen
Comments: 1148 pages

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

1. In the first part of the book I will try to give an overall view about the evolution of TGD and about quantum TGD in its recent form. I cannot avoid the use of various concepts without detailed definitions and my hope is that reader only gets a bird's eye of view about TGD. Two visions about physics are discussed. According to the first vision physical states of the Universe correspond to classical spinor fields in the world of the classical worlds 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. 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.
2. The second part of the book is devoted to the vision about physics as infinite-dimensional configuration space geometry. The basic idea is that classical spinor fields in infinite-dimensional "world of classical worlds", space of 3-surfaces in M⁴ x CP₂ 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. The third part of the book carries title "Algebraic Physics". Classical physics is an exact part of the configuration space geometry and the identification of space-time surfaces as generalized Bohr orbits is not a mere approximation. Path integral is replaced by a functional integral over 3-surfaces and there are reasons to expect that the decomposition of the configuration space to a union of symmetric spaces allows to carry out the functional integral exactly. This together with quantum classical correspondence and Bohr orbit property suggests a generalization of the duality symmetry of hadron models stating that the addition of loops does not affect the physical amplitude assignable to a given diagram. Hopf algebras are used to formulate this symmetry. In the second chapter the profound implications of the fact that configuration space spinors correspond to von Neumann algebras known as hyper-finite factors of type II₁ are considered.
4. The physical applications of TGD are the topic of the fourth part of the book. The cosmological and astrophysical applications of the many-sheeted space-time are summarized and the applications to elementary particle physics are discussed at the general level. TGD explains particle families in terms of generation genus correspondences (particle families correspond to 2-dimensional topologies labelled by genus). The notion of elementary particle vacuum functional is developed leading to an argument that the number of light particle families is three is discussed. The general theory for particle massivation based on p-adic thermodynamics is discussed at the general level. The detailed calculations of elementary particle masses are not however carried out in this book.

The Graviton Background Vs. Dark Energy

Authors: Michael A. Ivanov
Comments: 25 pages, 1 figure. Poster contribution to The Alternative Gravities and Dark Matter Workshop, Edinburgh, UK, 20-22 April 2006

In the model of low-energy quantum gravity by the author, cosmological redshifts are caused by interactions of photons with gravitons. Non-forehead collisions with gravitons will lead to an additional relaxation of any photonic flux. It gives a possibility of another interpretation of supernovae 1a data. Every massive body would be decelerated due to collisions with gravitons that may be connected with the Pioneer 10 anomaly. This mechanism needs graviton pairing and "an atomic structure" of matter for working it. Also an existence of black holes contradicts to the equivalence principle: any black hole should have a gravitational mass to be much bigger - about three orders - than an inertial one.

Gravitational Asymptotic Freedom and Matter Filling of Black Holes

Authors: Michael A. Ivanov
Comments: 2 pages, no figure, Latex. Contribution to the International Meeting "Physical Interpretations of Relativity Theory" (PIRT-09), Moscow, Russia, 6 - 9 July 2009.

The property of asymptotic freedom of the model of low-energy quantum gravity by the author leads to the unexpected consequence: if a black hole arises due to a collapse of a matter with some characteristic mass of particles, its full mass should be restricted from the bottom. For usual baryonic matter, this limit of mass is of the order 107M_☉

Quantum Field Theory in Accelerating Local Reference Frames V.2

Authors: Jack Sarfatti
Comments: 5 pages

Using the Dirac "square root" tetrads of the metric tensor are spin 1 fields that are intrinsically renormalizable for quantum gravity models. On the other hand both the cnumber tetrads and the spin connections in our model are emergent from the eight gluon vacuum condensates of QCD that form in the inflationary phase transition. Their residual micro-quantum operator parts are the spin 1 quantum fields that are responsible for both the dark energy and the dark matter. Spread out dark energy with negative pressure comes from w = -1 random zero point virtual fermion-antifermion vacuum polarization loops that antigravitate because of the equivalence principle. Similarly, clumped dark matter comes from w = -1 random zero point virtual bosons of positive pressure that gravitate and is indistinguishable from w = 0 CDM for the distant observer. New conjectured expressions for important physical observables both at the micro and macro levels in rotating frames are presented. They need to be tested in the laboratory, for example, alleged anomalous gravity from rotating superconductors.

Event-Symmetry for Superstrings

Authors: Philip Gibbs
Comments: 11 pages, Published in Int.J.Theor.Phys.37:1243-1252,1998

I apply the principle of event-symmetry to simple string models and discuss how these lead to the conviction that multiple quantisation is linked to dimension. It may be that string theory has to be formulated in the absence of space-time which will then emerge as a derived property of the dynamics. Another interpretation of the event-symmetric approach which embodies this is that instantons are fundamental. Just as solitons may be dual to fundamental particles instantons may be dual to space-time events. Event-symmetry is then dual to instanton statistics. In that case a unification between particle statistics and gauge symmetry follows on naturally from the principle of event-symmetry. I build algebras which represent symmetries of superstring theories extending event-symmetry but which are also isomorphic to an algebra of creation and annihilation operators for strings of fermionic partons.

The Principle of Event-Symmetry

Authors: Philip Gibbs
Comments: 18 pages, Published in Int.J.Theor.Phys.35:1037-1062,1996.

To accommodate topology change, the symmetry of space-time must be extended from the diffeomorphism group of a manifold, to the symmetric group acting on the discrete set of space-time events. This is the principle of event-symmetric space-time. I investigate a number of physical toy models with this symmetry to gain some insight into the likely nature of event-symmetric space-time. In the more advanced models the symmetric group is embedded into larger structures such as matrix groups which provide scope to unify space-time symmetry with the internal gauge symmetries of particle physics. I also suggest that the symmetric group of space-time could be related to the symmetric group acting to exchange identical particles, implying a unification of space-time and matter. I end with a definition of a new type of loop symmetry which is important in event-symmetric superstring theory.

The Discrete Fourier Transform and the Particle Mixing Matrices

Authors: C. A. Brannen, M. D. Sheppeard
Comments: 8 pages, submitted to New J. Phys.

In quantum mechanics, the Fourier Transform commonly converts from position space to momentum. For finite dimensional Hilbert spaces, the analog is the discrete (or quantum) Fourier transform, which has many applications in quantum information theory. We explore applications of this discrete Fourier transform to the elementary particle generations, and then present a related and elegant new parameterization for unitary 3x3 matrices that is compatible with the tribimaximal MNS matrix.

This Time What a Strange Turn of Events!

Authors: Philip Gibbs
Comments: submission to the 2008 FXQi essay contest on "The Nature Of Time". Published in Presapcetime Journal V2, p162-171

In relativity time is bound to space by the symmetries of spacetime. In the general theory the symmetry is covariance under diffeomorphisms but in string theory this extends to the full permutation group acting on spacetime events. This huge symmetry has profound implications for the nature of time, causality and the way we see our place in the universe.

Conformal Gravity, Maxwell and Yang-Mills Unification in 4D from a Clifford Gauge Field Theory

Authors: Carlos Castro
Comments: recovered from sciprint.org

A model of Emergent Gravity with the observed Cosmological Constant from a BF-Chern-Simons-Higgs Model is revisited which allows to show how a Conformal Gravity, Maxwell and SU(2) x SU(2) x U(1) x U(1) Yang-Mills Unification model in four dimensions can be attained from a Clifford Gauge Field Theory in a very natural and geometric fashion.

What Causes the Mass to be Deficit Inside a Nucleus?

Authors: Karunakar Marasakatla
Comments: 5 Pages.

Mass of an object varies with the change in volume of the object. Mass of a gas nebula will increase when it collapses to form a neutron star or black hole. The cause for an object to exhibit the deficit in mass is the increase in the amount of space in which the particles of that object were occupied. Gas nebula will have more deficit in mass compared to the neutron star formed from the same amount of material. Avogadro number, which establishes a relationship between the mass and the number of atoms within an object, is a baseless notion.

The Cyclotron Notebooks

Authors: Philip Gibbs
Comments: 66 Pages, originally published as a website in March 1996.

The cyclotron note books are a collection of essays about fundamental physics and metaphysics. The central essay is about the principle of event-symmetric space-time, a new theory about how to do quantum gravity. The style is more technical in some parts than in others. Each essay can be read independently but if you find that one of them has terms which you don't understand you may find them explained in an earlier one. The later ones may be too difficult for the layman and even I don't understand the last one.

Using Gravitation to Emulate Electromagnetism.

Authors: S. Halayka
Comments: 3 Pages.

The possibility of Universe-scale black holes living in closed 3D space of constant positive curvature was briefly considered in previous work. Further consideration of this possibility is given here. A possible link between gravitation and electromagnetism is discussed.

Using Gravitation to Emulate Electromagnetism.

Authors: S. Halayka
Comments: 2 Pages.

The possibility of Universe-scale black holes living in closed 3D space of constant positive curvature was briefly considered in previous work. Further consideration of this possibility is given here. A possible link between gravitation and electromagnetism is discussed.

Relating the Physical Structure and Properties of Quantum Space-Time to Elementary Particles, Gravity, and Relativistic Phenomena

Authors: Gary Heen
Comments: 22 pages

Modern theory states that matter and energy in their most basic form exist in discrete amounts, or quanta. The author proffers that space-time also exists as discrete quanta, and derives a physical model of space-time and elementary particles. The hypothesis for this space-time model is that the quanta for matter and space-time are convertible states of the same elementary building block: the quantum mass unit.

Relating the Physical Structure and Properties of Quantum Space-Time to Elementary Particles, Gravity, and Relativistic Phenomena

Authors: Gary Heen
Comments: 22 pages

Modern theory states that matter and energy in their most basic form exist in discrete amounts, or quanta. The author proffers that space-time also exists as discrete quanta, and derives a physical model of space-time and elementary particles. The hypothesis for this space-time model is that the quanta for matter and space-time are convertible states of the same elementary building block: the quantum mass unit.

The Galois Solvable Fourth Roots of Reality

Authors: Jack Sarfatti
Comments: 8 pages

Local observers are defined by orthonormal "non-holonomic" (aka "non-coordinate") tetrad gravity fields (Cartan's "moving frames"). The tetrads are spin 1 vector fields under the 6-parameter homogeneous Lorentz group SO_1,3 of Einstein's 1905 special relativity. You can think of the tetrad gravity fields as the square roots of Einstein's 1916 spin 2 metric tensor gravity fields. We will see that we must also allow for spin 0 and spin 1 gravity because the spin 1 tetrads, in turn, are Einstein-Podolsky-Rosen entangled quantum states of pairs of 2-component Penrose-Rindler qubits in the quantum pregeometry. The Wheeler-Feynman qubits are the square roots of the advanced and retarded null tetrads and can therefore be called the Galois solvable fourth roots of reality. The spherical wavefront tetrads are then formally the Bell pair states of quantum information theory. Penrose's Cartesian tetrads are a different choice from mine here. The different tetrad choices correspond to the different contours around the photon propagator poles in the complex energy plane of quantum electrodynamics. Both of his spinors in his spin frame are retarded in the same light cone, e.g. the forward cone. It seems that Penrose and Rindler implicitly answered Wheeler's question of how IT comes from BIT, but no one realized it until now.

Quark Lepton Braids and Heterotic Supersymmetry

Authors: M. D. Sheppeard
Comments: 8 pages. submitted to JPA

A unique matrix is easily assigned to each Bilson-Thompson braid diagram. The quark and lepton matrices are then related to bosons via a twisted quantum Fourier transform, for which fermion and boson multiplets fit the dimension structure of heterotic strings.

Can the External Directed Edges of a Complete Graph Form a Radially Symmetric Field at Long Distance?

Authors: S. Halayka
Comments: 7 Pages. Added reference McDonald JR, Miller WA. Coupling Non-Gravitational Fields with Simplicial Spacetimes

Using a numerical method, the external directed edges of a complete graph are tested for their level of fitness in terms of how well they form a radially symmetric field at long distance (e.g., a test for the inverse square law in 3D space). It is found that the external directed edges of a complete graph can very nearly form a radially symmetric field at long distance if the number of graph vertices is great enough.

Can the External Directed Edges of a Complete Graph Form a Radially Symmetric Field at Long Distance?

Authors: S. Halayka
Comments: 7 Pages. Clarified discussion about Delaunay-Voronoi tessellations, added related references.

Using a numerical method, the external directed edges of a complete graph are tested for their level of fitness in terms of how well they form a radially symmetric field at long distance (e.g., a test for the inverse square law in 3D space). It is found that the external directed edges of a complete graph can very nearly form a radially symmetric field at long distance if the number of graph vertices is great enough.

Can the External Directed Edges of a Complete Graph Form a Radially Symmetric Field at Long Distance?

Authors: S. Halayka
Comments: 7 Pages. Clarified discussion of bidirected graph. Added discussion about the Delauney triangulation of a 2D shell.

Using a numerical method, the external directed edges of a complete graph are tested for their level of fitness in terms of how well they form a radially symmetric field at long distance (e.g., a test for the inverse square law in 3D space). It is found that the external directed edges of a complete graph can very nearly form a radially symmetric field at long distance if the number of graph vertices is great enough.

Can the External Directed Edges of a Complete Graph Form a Radially Symmetric Field at Long Distance?

Authors: S. Halayka
Comments: 6 Pages. Revised discussion section, included Newtonian gravitational potential.

Using a numerical method, the external directed edges of a complete graph are tested for their level of fitness in terms of how well they form a radially symmetric field at long distance (e.g., a test for the inverse square law in 3D space). It is found that the external directed edges of a complete graph can very nearly form a radially symmetric field at long distance if the number of graph vertices is great enough.

Can the External Directed Edges of a Complete Graph Form a Radially Symmetric Field at Long Distance?

Authors: S. Halayka
Comments: 6 Pages. Expanded discussion to include Schwarzschild black hole properties.

Using a numerical method, the external directed edges of a complete graph are tested for their level of fitness in terms of how well they form a radially symmetric field at long distance (e.g., a test for the inverse square law in 3D space). It is found that the external directed edges of a complete graph can very nearly form a radially symmetric field at long distance if the number of graph vertices is great enough.

Can the External Directed Edges of a Complete Graph Form a Radially Symmetric Field at Long Distance?

Authors: S. Halayka
Comments: 5 Pages. Added references to papers pertaining to event symmetric physics. Changed equation (6) to reflect that an external directed edge vector and its corresponding intersection vertex vector will never give a dot product equal to or less than 0. Uploaded new source code that uses the new version of equation (6). Changed table (4) to reflect the new measurements gained from the new version of equation (6). The fundamental result remains the same -- shrinking the shell S(G_1) to zero size or expanding the shell S(G_2) to infinite size will make the graph G_1 appear to be a single point particle.

Using a numerical method, the external directed edges of a complete graph are tested for their level of fitness in terms of how well they form a radially symmetric field at long distance (e.g., a test for the inverse square law in 3D space). It is found that the external directed edges of a complete graph can very nearly form a radially symmetric field at long distance if the number of graph vertices is great enough.

Can the External Directed Edges of a Complete Graph Form a Radially Symmetric Field at Long Distance?

Authors: S. Halayka
Comments: 5 Pages. Cleared up the notation related to the uniform distribution fitness test (including two spelling errors related to internal edges). Added references.

Using a simple numerical method, the external directed edges of a complete graph are tested for their level of fitness in terms of how well they form a radially symmetric field at long distance (e.g., a test for the inverse square law in 3D space). It is found that the external directed edges of a complete graph can very nearly form a radially symmetric field at long distance if the number of graph vertices is great enough.

Objections to Quantum Gravity Theories Based on Causal Dynamical Triangulation

Authors: Ervin Goldfain
Comments: 2 pages, Letters submitted to the Editors of Classical and Quantum Gravity (v1) and Physics Review Letters (v2).

This memo is in regards to the recently published contribution by Ambjorn J. et al. "Planckian Birth of Quantum de Sitter Universe" PRL 100, 091304 (2008). The article claims that "causal dynamical triangulation" enables a consistent regularization of quantum gravity. A "quantum universe" emerging from a nonperturbative sum over geometries is alleged to recover "with high accuracy a fourdimensional de Sitter space-time". On closer examination, the approach is built on many objectionable premises

On Nonlinear Quantum Mechanics, Noncommutative Phase Spaces, Fractal-Scale Calculus and Vacuum Energy

Authors: Carlos Castro
Comments: 18 pages, has been submitted to Foundations of Physics

A novel (to our knowledge) Generalized Nonlinear Schrödinger equation based on the modifications of Nottale-Cresson's fractal-scale calculus and resulting from the noncommutativity of the phase space coordinates is explicitly derived. The modifications to the ground state energy of a harmonic oscillator yields the observed value of the vacuum energy density. In the concluding remarks we discuss how nonlinear and nonlocal QM wave equations arise naturally from this fractal-scale calculus formalism which may have a key role in the final formulation of Quantum Gravity.

Global and Local Gauge Symmetry in the "Tetrahedron Model": Part I

Authors: John A. Gowan
Comments: 17 pages. This paper has also been published as a Google "Knol".

1) Noether's Theorem requires the conservation of light's symmetry no less than light's energy. 2) The charges (and spin) of matter are the symmetry debts of light. 3) Charge (and spin) conservation is a temporal, material form of symmetry conservation. 4) Paying (discharging) light's symmetry debt is the role of the 4 forces of physics (field vectors). 5) Charge invariance in time and space (in the service of symmetry conservation) is the key to understanding the local action of the forces ("local gauge symmetry currents"). 6) The field vectors of the forces act as "local gauge symmetry currents" which transform global charge invariance into local charge invariance - serving charge and symmetry conservation, and in the case of gravity, serving energy, symmetry, entropy, and causality conservation (because gravity creates time). 7) Gravity (as gauged by the universal gravitational constant "big G") transforms the global spatial metric of absolute motion and light, as gauged by the universal electromagnetic constant "c", into a local spacetime metric accommodating relative motion and matter. (The local gravitational metric is characterized by "little g".) (Gravity creates time by the annihilation and conversion of space.) 8) Gravity pays the entropy-"interest" on matter's symmetry debt, creating time by the annihilation of metrically equivalent space, decelerating cosmic expansion in consequence. Conversely, the gravitational conversion of bound to free energy (as in the stars and via Hawking's "quantum radiance" of black holes), pays the energy-"principle" on all symmetry and entropy debts, restoring (and hence to all appearances "accelerating") the original cosmic expansion. The radiance of our Sun and the stars represents a completed "circuit" of symmetry conservation. (See: "Currents of Entropy and Symmetry)".

Global and Local Gauge Symmetry in the "Tetrahedron Model": Part I

Authors: John A. Gowan
Comments: 15 pages. This paper has also been published as a Google "Knol".

1) Noether's Theorem requires the conservation of light's symmetry no less than light's energy. 2) The charges (and spin) of matter are the symmetry debts of light. 3) Charge (and spin) conservation is a temporal, material form of symmetry conservation. 4) Paying (discharging) light's symmetry debt is the role of the 4 forces of physics (field vectors). 5) Charge invariance in time and space (in the service of symmetry conservation) is the key to understanding the local action of the forces ("local gauge symmetry currents"). 6) The field vectors of the forces act as "local gauge symmetry currents" which transform global charge invariance into local charge invariance - serving charge and symmetry conservation, and in the case of gravity, serving energy, symmetry, entropy, and causality conservation (because gravity creates time). 7) Gravity (as gauged by the universal gravitational constant "big G") transforms the global spatial metric of absolute motion and light, as gauged by the universal electromagnetic constant "c", into a local spacetime metric accommodating relative motion and matter. (The local gravitational metric is characterized by "little g".) (Gravity creates time by the annihilation and conversion of space.) 8) Gravity pays the entropy-"interest" on matter's symmetry debt, creating time by the annihilation of metrically equivalent space, decelerating cosmic expansion in consequence. Conversely, the gravitational conversion of bound to free energy (as in the stars and via Hawking's "quantum radiance" of black holes), pays the energy-"principle" on all symmetry and entropy debts, restoring (and hence to all appearances "accelerating") the original cosmic expansion. The radiance of our Sun and the stars represents a completed "circuit" of symmetry conservation. (See: "Currents of Entropy and Symmetry)".

Global-Local Gauge Symmetry: Part III: the Weak Force

Authors: John A. Gowan
Comments: 12 pages. This paper has also been published as a Google "Knol".

The most significant effect of the massive weak force IVBs (Intermediate Vector Bosons) is that they create a specific energy level, a particular unified force symmetric energy state (as "gauged" or scaled by the mass of the Higgs boson), that recreates the original energy-dense primordial environment in which particles were first created and transformed during the early micro-moments of the "Big Bang". This recapitulation ensures that the original and strictly conserved values of charge, mass, energy, etc. are handed on invariant to the next generation of elementary particles: elementary particles created today must be exactly the same in every respect as elementary particles created eons ago during the "Big Bang". These unified force symmetric energy states (for example, the electroweak unified force state, as produced by the "W" IVB) - within which identity transformations are the normal course of events - appear to us as the quantized masses of the IVBs. At the electroweak energy level mediated by the "W" IVB, "ground state" or electromagnetic "species"-level "flavor" identities (electrons vs u,d quarks) are subsumed within a broader "generic"-level identity (leptons vs hadrons); at the next higher GUT energy level (in which the electroweak and strong forces are unified), generic-level identities are subsumed within "family"-level identities - leptons and hadrons become simply fermions or leptoquarks. The final force unification level, the TOE or Planck energy level, incorporates gravity, in which fermions and bosons, particles, light, gravity, and spacetime, are all subsumed within the elemental "order"-level of electromagnetic energy - Gamow's "ylem". (Here I have deliberately employed the terms of the familiar biological taxonomic hierarchy (species, genus, family, order), as it provides a good analogy for the way unfamiliar particle identities and categories are subsumed within the physics hierarchy or energy levels of the unified force symmetric energy states - electromagnetic (ground state), electroweak, GUT, and TOE.) (See: "The Higgs Boson and the Weak Force IVBs".)

Global and Local Gauge Symmetries: Part II (Gravitation)

Authors: John A. Gowan
Comments: 16 pages. This file has also been published as a knol.

"Local gauge symmetry currents" are forces that maintain the local invariance of universal constants, charges, and other conserved parameters (such as causality and the "Interval") despite the hostile environment of a variable gravitational (or inertial) metric, relative rather than absolute motion, entropy, partial charges, etc. These compensatory forces are due to the activity of the field vectors of the four forces, which not only act (in the long term) to return these asymmetric material systems to their original symmetric state (light), but also act (in the short term) to protect and maintain the invariant values of their symmetry debts (charges), while awaiting a final repayment via antimatter annihilation, proton decay, the "quantum radiance" of black holes, or a universal "Big Crunch". Gravity pays the entropy-interest on the symmetry debt of matter by creating matter's time dimension via the annihilation of space, providing a historical domain within which charge conservation can have significance. Gravitation eventually also pays the energy-principle on matter's symmetry debt, converting bound energy to free energy in stars and via Hawking's "quantum radiance" of black holes.

Global and Local Gauge Symmetries: Part II (Gravitation)

Authors: John A. Gowan
Comments: 15 pages. This file has also been published as a knol.

"Local gauge symmetry currents" are forces that maintain the local invariance of universal constants, charges, and other conserved parameters (such as causality and the "Interval") despite the hostile environment of a variable gravitational (or inertial) metric, relative rather than absolute motion, entropy, partial charges, etc. These compensatory forces are due to the activity of the field vectors of the four forces, which not only act (in the long term) to return these asymmetric material systems to their original symmetric state (light), but also act (in the short term) to protect and maintain the invariant values of their symmetry debts (charges), while awaiting a final repayment via antimatter annihilation, proton decay, the "quantum radiance" of black holes, or a universal "Big Crunch". Gravity pays the entropy-interest on the symmetry debt of matter by creating matter's time dimension via the annihilation of space, providing a historical domain within which charge conservation can have significance. Gravitation eventually also pays the energy-principle on matter's symmetry debt, converting bound energy to free energy in stars and via Hawking's "quantum radiance" of black holes.

Global and Local Gauge Symmetries: Parts IV and V

Authors: John A. Gowan
Comments: 18 pages.

"Local gauge symmetry currents" are forces that maintain the local invariance of universal constants and other conserved parameters (such as causality and the "Interval") despite the hostile environment of a variable gravitational (or inertial) metric, relative rather than absolute motion, entropy, partial charges, etc. These compensatory forces are due to the activity of the field vectors of the four forces, which not only act (in the long term) to return these asymmetric material systems to their original symmetric state (light), but also act (in the short term) to protect and maintain the invariant values of their symmetry debts while awaiting a final repayment via antimatter annihilation, proton decay, the "quantum radiance" of black holes, or a universal "Big Crunch".

Is Entropy Related to the Synchronization of the Input/output Power of a System of Oscillators?

Authors: S. Halayka
Comments: 11 Pages. Added Appendix section (and idea for possible experiment?). Added references related to "quantum graphity"

The objective of this paper is to identify a way to relate entropy with the synchronization of the input/output power of a system of oscillators. This view is ultimately reconciled through an examination of the geometric differences that exist between 2D shell and 3D lattice oscillator arrangements.

Is Entropy Related to the Synchronization of the Input/output Power of a System of Oscillators?

Authors: S. Halayka
Comments: 10 Pages. Changed water ice example with sodium chloride in order to remove ambiguity.

The objective of this paper is to identify a way to relate entropy with the synchronization of the input/output power of a system of oscillators. This view is ultimately reconciled through an examination of the geometric differences that exist between 2D shell and 3D lattice oscillator arrangements.

Towards a Moyal Quantization Program of the Membrane

Authors: Carlos Castro
Comments: 15 Pages. This article has been submitted to the J. Phys. A : Math.

A Moyal deformation quantization approach to a spherical membrane (moving in flat target backgrounds) in the light cone gauge is presented. The physical picture behind this construction relies in viewing the two spatial membrane coordinates σ₁, σ₂ as the two phase space variables q, p, and the temporal membrane coordinate τ as time. Solutions to the Moyal-deformed equations of motion are explicitly constructed in terms of elliptic functions. A knowledge of the Moyal-deformed light-cone membrane's Hamiltonian density H(q, p, τ ) allows to construct a timedependent Wigner function ρ(q, p, τ ) as solutions of the Moyal-Liouville equation, and from which one can obtain the expectation values of the operator < H > = Trace (ρH) that define the quantum average values of the energy density configurations of the membrane at any instant of time. It is shown how a time-dependent quartic oscillator with q⁴, p⁴, q²p² terms plays a fundamental role in the quantum treatment of membranes and displays an important p ↔ q duality symmetry.

Human Development and Life Stages General Systems Models

Authors: John A. Gowan
Comments: 3 pages, This paper has also been published as a Google "Knol".

Fractal or General Systems models have been extended into the area of human life span development, by myself, deliberately, and earlier by my father, and others, following their own agendas (not intentional GS models). A short discussion with both models is presented below.

Nature's Fractal Pathway

Authors: John A. Gowan
Comments: 28 pages, This paper has also been published as a Google "Knol".

A General Systems model of the Universe is presented, based on a fractal paradigm. A 4x3 "metric" or fractal algorithm is proposed as the organizing principle of the Microphysical, Biophysical, Astrophysical, and Metaphysical realms. The algorithm is expressed through the conservation laws and forces of physics, symmetry-breaking and the creation of matter during the "Big Bang", the dimensions of spacetime, the quantum rules of atomic order, the families of elementary particles, the structure of baryons, alpha particles, carbon atoms, carbon's molecular and crystal bonds, DNA, the genetic code, the nucleosynthetic pathway of stars, gravitation, etc. The human mind has discovered this order both intuitively and rationally, where it finds expression in the 4x3 (and 4x4) patterns of mythological, occult, religious, philosophical, and scientific "world systems" and cosmologies. A model of the unified field theory is presented as an example of how the fractal algorithm may be used in system modeling. In its most general form, the 4-part algorithm consists of an input of energy, followed by two complementary conservation modes, concluding with a restorative force which either returns the system to its actual original state, or elevates it to a "harmonic complexion" or resonant analog of the original state. Introduction

Synopsis of the Tetrahedron Model

Authors: John A. Gowan
Comments: 14 pages, This paper has also been published as a Google "Knol".

The "Tetrahedron Model" is a model of the devolution (asymmetric transformation) of light (free energy) into matter (bound energy), that is, of the relationship between the two forms of electromagnetic energy which constitute our Universe. This model revolves around the conversion of light to matter and vice versa, as regulated by four conservation laws: the Conservation of Energy, Entropy, Symmetry, and Causality.

Original Solution of Gravity is Without Gravitational Waves

Authors: Amrit S. Sorli
Comments: 3 pages

Original solution of gravity motion is curved 4 dimensional cosmic space. Massive objects move into direction of higher curvature of space. Quantum gravity introduces idea that cosmic space is made out of grains of Planck size. If space has granular structure one can consider space also has its density. According to the second low of thermodynamics in the universe distribution of energy tends to be homogeneous. More mass in given volume of quantum space less space is dense. Less space is dense more space is curved. Massive objects move always into direction of lover density in higher curvature of quantum space. Gravitational motion of massive objects is result of change of density of quantum space. Change of density of quantum space is a physical basis for change of its curvature.

A Short Course in the Unified Field Theory

Authors: John A. Gowan
Comments: 12 pages, This paper has also been published as a Google "Knol".

"Noether's Theorem" states that in a multicomponent field such as the electromagnetic field (or the metric field of spacetime), symmetries are associated with conservation laws and vice versa. In matter, light's (broken) symmetries are conserved by charge and spin; in spacetime, light's symmetries are protected by inertial forces, and conserved (when broken) by gravitational forces. All forms of energy originate as light; matter carries charges which are the symmetry/entropy debts of the light which created it. The charges of matter are the symmetry debts of light. Charges produce forces which act to return the material system to its original symmetric state, paying matter's symmetry/entropy debts. Payment is exampled by annihilation reactions (electromagnetic force); radioactivity (fission), fusion, particle and proton decay (weak and strong nuclear forces); the nucleosynthetic pathway of stars, and Hawking's "quantum radiance" of black holes (gravitational force). Identifying the broken symmetries of light associated with each of the 4 charges and forces of physics is the first step toward a conceptual unification. The conservation of energy, symmetry, entropy, and causality, plus the requirement of primordial symmetrybreaking followed by the maintenance of charge invariance (including the phenomena of "local gauge symmetry"), are all key conceptual elements in the formulation of a Unified Field Theory.

A Short Course in the Unified Field Theory

Authors: John A. Gowan
Comments: 12 pages, This paper has also been published as a Google "Knol".

"Noether's Theorem" states that in a multicomponent field such as the electromagnetic field (or the metric field of spacetime), symmetries are associated with conservation laws and vice versa. In matter, light's (broken) symmetries are conserved by charge and spin; in spacetime, light's symmetries are protected by inertial forces, and conserved (when broken) by gravitational forces. All forms of energy originate as light; matter carries charges which are the symmetry/entropy debts of the light which created it. The charges of matter are the symmetry debts of light. Charges produce forces which act to return the material system to its original symmetric state, paying matter's symmetry/entropy debts. Payment is exampled by any spontaneous interaction producing net free energy, including: chemical reactions and matter-antimatter annihilation reactions (electromagnetic force); radioactivity, fusion, particle and proton decay (weak and strong nuclear forces); the nucleosynthetic pathway of stars, and Hawking's "quantum radiance" of black holes (gravitational force). Identifying the broken symmetries of light associated with each of the 4 charges and forces of physics is the first step toward a conceptual unification.

A Short Course in the Unified Field Theory

Authors: John A. Gowan
Comments: 10 pages, This paper has also been published as a Google "Knol".

"Noether's Theorem" states that in a multicomponent field such as the electromagnetic field (or the metric field of spacetime), symmetries are associated with conservation laws and vice versa. In matter, light's (broken) symmetries are conserved by charge and spin; in spacetime, light's symmetries are protected by inertial forces, and conserved (when broken) by gravitational forces. All forms of energy originate as light; matter carries charges which are the symmetry/entropy debts of the light which created it. The charges of matter are the symmetry debts of light. Charges produce forces which act to return the material system to its original symmetric state, paying matter's symmetry/entropy debts. Payment is exampled by any spontaneous interaction producing net free energy, including: chemical reactions and matter-antimatter annihilation reactions (electromagnetic force); radioactivity, fusion, particle and proton decay (weak and strong nuclear forces); the nucleosynthetic pathway of stars, and Hawking's "quantum radiance" of black holes (gravitational force). Identifying the broken symmetries of light associated with each of the 4 charges and forces of physics is the first step toward a conceptual unification.

A Short Course in the Unified Field Theory

Authors: John A. Gowan
Comments: 9 pages, This paper has also been published as a Google "Knol".

The conceptual basis of the Unified Field Theory as presented in these pages is summarized below: "Noether's Theorem" states that in a multicomponent field such as the electromagnetic field (or the metric field of spacetime), symmetries are associated with conservation laws and vice versa. In matter, light's (broken) symmetries are conserved by charge and spin; in spacetime, light's symmetries are protected by inertial forces, and conserved (when broken) by gravitational forces. All forms of energy originate as light; matter carries charges which are the symmetry/entropy debts of the light which created it. The charges of matter are the symmetry debts of light. Charges produce forces which act to return the material system to its original symmetric state, paying matter's symmetry/entropy debts. Payment is exampled by any spontaneous interaction producing net free energy (light, electromagnetic radiation), including: chemical reactions and matter-antimatter annihilation reactions (electromagnetic force); radioactivity, particle and proton decay, fusion and fission, (weak and strong nuclear forces); the nucleosynthetic pathway of stars, and Hawking's "quantum radiance" of black holes (gravitational force). Identifying the broken symmetries of light associated with each of the 4 charges and forces of physics is the first step toward a conceptual unification.

Density/curvature of Quantum Space Generates Gravitational Motion

Authors: Amrit S. Sorli
Comments: 5 pages

Clocks measure a frequency, velocity and numerical order of change. Experimental date confirms that changes and clocks do not run time; they run in quantum space only. Time is not a part of quantum space. Quantum space itself is timeless. In the universe as a whole amount of matter energy and amount of quantum space energy is constant. Density of mass and density of quantum space in a given volume of quantum space tends to be constant. Mass here is considered as a compressed energy of quantum space. Presence of mass in a given volume of quantum space diminishes its density. Massive objects move always into direction of lover density of quantum space. Gravitational motion of massive objects is result of change of density of quantum space. In space with no change of density massive object will not have gravitational motion as in centre of stellar objects or in a flat quantum space where massive objects are far away. Change of density of quantum space corresponds in General Theory of Relativity to the change of the curvature of space. Lower is density of quantum space bigger is its curvature. Here is introduced density/curvature of quantum space.

Polyvector-Valued Gauge Field Theories and Quantum Mechanics in Noncommutative Clifford Spaces

Authors: Carlos Castro
Comments: 14 pages, this article has been submitted to Mod Phys Letts A" (instead to IJMPA)

The basic ideas and results behind polyvector-valued gauge field theories and Quantum Mechanics in Noncommutative Clifford spaces are presented. The star products are noncommutative and associative and require the use of the Baker-Campbell-Hausdorff formula. The construction of Noncommutative Clifford-space gravity as polyvector-valued gauge theories of twisted diffeomorphisms in Clifford-spaces would require quantum Hopf algebraic deformations of Clifford algebras.

Polyvector-Valued Gauge Field Theories and Quantum Mechanics in Noncommutative Clifford Spaces

Authors: Carlos Castro
Comments: 13 pages, this article has been submitted to Mod Phys Letts A" (instead to IJMPA)

The basic ideas and results behind polyvector-valued gauge field theories and Quantum Mechanics in Noncommutative Clifford spaces are presented. The star products are noncommutative but associative up to second order only. The construction of Noncommutative Clifford-space gravity as polyvector-valued gauge theories of twisted diffeomorphisms in Clifford-spaces would require quantum Hopf algebraic deformations of Clifford algebras.

Towards M-Matrix

Authors: Matti Pitkänen
Comments: 734 pages

This book is devoted to a detailed representation 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 S-matrix is replaced with M-matrix identified as time-like entanglement coeficients between positive and negative energy parts of zero energy states. M-matrix is a product of diagonal density matrix and unitary S-matrix. 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. The replacement of massless plane waves with states for which amplitudes are localized at light-rays is suggestive in TGD framework. Twistors could allow lifting of space-time surfaces to surfaces of X x CP₂, where X is 8-D twistor space or its 6-D projective variant. The interpretation of massive particles as massless particles in 8-D sense suggests a generalization of twistors defined using triads of vector and spinor representations of SO(7,1).
5. In TGD Universe bosons are fermion-antifermion bound states. Therefore the action at QFT limit is Dirac action coupled to gauge potentials and bosonic action emerges as part of effective action as one functionally integrates over spinor fields. Coupling constant evolution follows once the UV cutoffs of mass and hyperbolic angle in fermionic loop integrations are fixed. The hyperbolic cutoff motivated by zero energy ontology predicts coupling constant evolution consistent with standard model. The condition that all N-vertices defined by fermiomic loops vanish for N > 3 when incoming particles are massless could fix the hyperbolic cutoff completely.

1. The Clifford algebra of WCW is hyper-finite factor of type II₁ which suggests that M-matrix could be identified as Connes tensor product.
2. In TGD framework dark matter corresponds to ordinary particles with non-standard value of 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.

TGD as a Generalized Number Theory

Authors: Matti Pitkänen
Comments: 608 pages

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 complexifications with Minkowskian signature of metric. Allowed space-time surfaces would correspond to what might be called hyper-quaternionic sub-manifolds of a hyper-octonionic space and mappable to M⁴ x 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 modified gamma matrices but not tangent plane in general. Hence the basic variational principle of TGD would have deep number theoretic content.
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.

Physics in Many-Sheeted Space-Time

Authors: Matti Pitkänen
Comments: 640 pages

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

1. In Part I extremals of Kähler action are discussed and the notions of many-sheeted space-time 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 are basic objects of TGD inspired cosmology. 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 superfluidity.

Physics in Many-Sheeted Space-Time

Authors: Matti Pitkänen
Comments: 640 pages

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

1. In Part I extremals of Kähler action are discussed and the notions of many-sheeted space-time 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 are basic objects of TGD inspired cosmology. 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 superfluidity.

Physics as Infinite-Dimensional Geometry

Authors: Matti Pitkänen
Comments: 257 pages

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. 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.

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 fl uctuating 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 δM₊⁴ X CP₂, where δM₊⁴ 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.

TGD and Fringe Physics

Authors: Matti Pitkänen
Comments: 296 pages

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.
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.

Topological Geometrodynamics: Overview

Authors: Matti Pitkänen
Comments: 1148 pages

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

1. In the first part of the book I will try to give an overall view about the evolution of TGD and about quantum TGD in its recent form. I cannot avoid the use of various concepts without detailed definitions and my hope is that reader only gets a bird's eye of view about TGD. Two visions about physics are discussed. According to the first vision physical states of the Universe correspond to classical spinor fields in the world of the classical worlds 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. 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.
2. The second part of the book is devoted to the vision about physics as infinite-dimensional configuration space geometry. The basic idea is that classical spinor fields in infinite-dimensional "world of classical worlds", space of 3-surfaces in M⁴ x CP₂ 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. The third part of the book carries title "Algebraic Physics". Classical physics is an exact part of the configuration space geometry and the identification of space-time surfaces as generalized Bohr orbits is not a mere approximation. Path integral is replaced by a functional integral over 3-surfaces and there are reasons to expect that the decomposition of the configuration space to a union of symmetric spaces allows to carry out the functional integral exactly. This together with quantum classical correspondence and Bohr orbit property suggests a generalization of the duality symmetry of hadron models stating that the addition of loops does not affect the physical amplitude assignable to a given diagram. Hopf algebras are used to formulate this symmetry. In the second chapter the profound implications of the fact that configuration space spinors correspond to von Neumann algebras known as hyper-finite factors of type II₁ are considered.
4. The physical applications of TGD are the topic of the fourth part of the book. The cosmological and astrophysical applications of the many-sheeted space-time are summarized and the applications to elementary particle physics are discussed at the general level. TGD explains particle families in terms of generation genus correspondences (particle families correspond to 2-dimensional topologies labelled by genus). The notion of elementary particle vacuum functional is developed leading to an argument that the number of light particle families is three is discussed. The general theory for particle massivation based on p-adic thermodynamics is discussed at the general level. The detailed calculations of elementary particle masses are not however carried out in this book.

Quantum Field Theory in Accelerating Local Reference Frames V.4

Authors: Jack Sarfatti
Comments: 5 pages

The Dirac "square root" tetrads of the metric tensor are spin 1 fields that are intrinsically renormalizable for quantum gravity models. Spin 2 gravitons are EPR entangled pairs of S-wave spin 1 tetrad quanta. As in superconductors there may be higher P & D wave relative orbital angular momenta as well as S-wave spin 0 and spin 1 micro-quantum corrections that do not show up in the long-range "classical" (macro-quantum coherent) limit. Both the c-number tetrads and the spin connections in our model are emergent from the eight gluon vacuum condensates of QCD that form in the inflationary phase transition. Their residual micro-quantum operator parts are the spin 1 quantum fields that are responsible for both the dark energy and the dark matter. Spread out dark energy with negative pressure comes from w = -1 random zero point virtual bosons of positive energy density that antigravitate because of the equivalence principle. Similarly, clumped dark matter comes from w = -1 random zero point negative energy density fermion-antifermion vacuum polarization loops of positive pressure that gravitate and is indistinguishable from w = 0 CDM for the distant observer. Therefore, the CERN LHC will not detect any exotic real particles that can explain Ω_DM ≈ 0.23 if this theory is correct. New conjectured expressions for important physical observables both at the micro and macro levels in rotating frames are presented. They need to be tested in the laboratory, for example, alleged anomalous gravity from rotating superconductors.

Quantum Field Theory in Accelerating Local Reference Frames V.3

Authors: Jack Sarfatti
Comments: 5 pages

The Dirac "square root" tetrads of the metric tensor are spin 1 fields that are intrinsically renormalizable for quantum gravity models. Spin 2 gravitons are EPR entangled pairs of S-wave spin 1 tetrad quanta. As in superconductors there may be higher P & D wave relative orbital angular momenta as well as S-wave spin 0 and spin 1 micro-quantum corrections that do not show up in the long-range "classical" (macro-quantum coherent) limit. Both the c-number tetrads and the spin connections in our model are emergent from the eight gluon vacuum condensates of QCD that form in the inflationary phase transition. Their residual micro-quantum operator parts are the spin 1 quantum fields that are responsible for both the dark energy and the dark matter. Spread out dark energy with negative pressure comes from w = -1 random zero point virtual fermion-antifermion vacuum polarization loops that antigravitate because of the equivalence principle. Similarly, clumped dark matter comes from w = -1 random zero point virtual bosons of positive pressure that gravitate and is indistinguishable from w = 0 CDM for the distant observer. Therefore, the CERN LHC will not detect any exotic real particles that can explain Ω_DM ≈ 0.23 if this theory is correct. New conjectured expressions for important physical observables both at the micro and macro levels in rotating frames are presented. They need to be tested in the laboratory, for example, alleged anomalous gravity from rotating superconductors.