Quantum Gravity and String Theory

Lanczos-Lovelock and F ( R ) Gravity from Clifford Space Geometry

Authors: Carlos Castro
Comments: 15 Pages. Submitted to the Int. Jour. of Theor. Physics

A rigorous construction of Clifford-space Gravity is presented which is compatible with the Clifford algebraic structure and permits the derivation of the generalized connections in Clifford spaces ( C-space) in terms of derivatives of the C-space metric. We continue by arguing how Lanczos-Lovelock higher curvature gravity can be embedded into gravity in Clifford spaces and suggest how this might also occur for extended gravitational theories based on f ( R ), f ( R_{\mu \nu} ), .... actions, for polynomial-valued functions. Black-strings and black-brane metric solutions in higher dimensions D > 4 play an important role in finding specific examples.
Category: Quantum Gravity and String Theory

Theory for Quantization of Gravity

Authors: Patrick Linker
Comments: 7 Pages.

The unification of Einstein's field equations with Quantum field theory is a problem of theoretical physics. Many models for solving this problem were done, i.e. the String Theory or Loop quantum gravity were introduced to describe gravity with quantum theory. The main problem of this theories is that they are mathematically very complicated. In this research text, there is given another description of gravity unified with Quantum field theory. In this case, gravity is described so that for weak gravitational fields the (semi)classical gravity desciption is equivalent.
Category: Quantum Gravity and String Theory

Foundations of Physics: Edward Witten Versus Joy Christian Versus Stephen Wolfram

Authors: David Brown
Comments: 4 Pages.

The pioneers of string theory have not convinced such critics as Philip Anderson, Sheldon Glashow, Robert B. Laughlin, and Burton Richter. Does nondeterministic M-theory need to be replaced by deterministic M-theory according to the ideas of J. Christian? Does nondeterministic M-theory need to be replaced by modified M-theory with Wolfram’s mobile automaton operating on a network of information below the Planck scale? If X is to M-theory as Kepler’s laws are to Newton’s theory of gravity, then what is X? There is overwhelming empirical evidence in favor of the Rañada-Milgrom effect because of two things: (1) the work of Milgrom, McGaugh, and Kroupa and (2) an easy scaling argument. Are the ideas of Witten, Christian, and Wolfram essential for understanding Milgrom’s acceleration law in terms of the foundations of physics?
Category: Quantum Gravity and String Theory

Is Christian’s Parallelized 7-Sphere Model Essential for the Physical Interpretation of M-Theory?

Authors: David Brown
Comments: 8 Pages.

In 1991 with Abner Shimony as thesis advisor, J. Christian obtained his PhD in the foundations of quantum theory. As of 2012, he is affiliated with both Wolfson College of the University of Oxford and the Perimeter Institute in Toronto. From 2007 to 2012 Christian published some highly controversial work related to Bell’s theorem. Christian has proposed a parallelized 7-sphere model for a local, realistic theory that replaces quantum theory. This communication considers how his model might be relevant to a physical interpretation of M-theory. There is overwhelming empirical evidence in favor of the Rañada-Milgrom effect, at least as an approximation. Christian’s theory of local realism might be empirically valid if and only if the Rañada-Milgrom effect is empirically valid.
Category: Quantum Gravity and String Theory

The Inverse Square Root Law of Gravity

Authors: Meir Amiram
Comments: 10 Pages. This article is based on the essay "Modified Wheelerian Perspective of Gravity" submitted to the Gravity Research Foundation 2012 Awards for Essays on Gravitation

John Wheeler’s famous statement “Matter tells space how to curve space tells matter how to move” converges into a surprising underlying machinery, through a discussion of the questions “is gravity space or within space”, “does force cause motion, or maybe motion causes force” and “what is the real gradient law of gravitational fields”. I conclude that space is gravity, and it consists of two ingredients, the concentration gradient of one of them among the other is the gradient of gravitational fields. The Newtonian inverse square law is a phenomenologically based interpretation of a real inverse square root law.
Category: Quantum Gravity and String Theory

A Possible Theory for Particle Composition of Matter Based on Only Three Functional Quantum Particles

Authors: Emmanuel Markakis, Christopher Provatidis
Comments: 43 Pages.

This work presents the possibility of revising the standard model of subatomic composition of matter, extending the “inverse square law” from gravity and electric fields to also the thermal effects. It is shown that assuming only three proposed particles and only three relevant interactions, simple explanations can be provided for all natural phenomena, particularly those in which the existing theory does not provide documental and convincing answers. The paper starts with the description of a unique reaction between two types of the proposed subatomic particles thus producing the so-called ‘thermions’ that finally form an elastic Cubic Energy Grid under mechanical stress. Then the existence of the three known phases of matter is explained. The meaning of ‘heat’ is redefined without focusing on the usual kinetic energy of atoms and molecules. The elimination of anomalies in a closed system is explained through an asymmetrical oscillation. Also, the paper attempts a new interpretation of the creation of the universe from a huge electric discharge based on the simultaneous creation of the three subatomic particles. It describes ‘monopoles’ as the first quantized agglomerates of pure energy and explains why they bound to form ‘dipoles’, which later progressively form larger agglomerates. In the sequence, it describes the crystallization as a first resistance line that the nature foresight to avoid the self-destruction of the universe. The paper closes with possible models of electron and positron as well as of neutron and proton based on only the three proposed subatomic particles. At the same time, the equivalent mass of a thermion as well as the quanta of positive and negative electric charges is determined.
Category: Quantum Gravity and String Theory

Quantum Electric Gravity

Authors: Rad H Dabbaj
Comments: 16 Pages.

This paper proposes a new theory of gravity called quantum electric gravity (QEG) based entirely on electromagnetic and quantum electrodynamics (QED) principles. Neutral atoms contain equal amount of absolute positive and negative charge such that they interact by both attractive and repulsive forces. In classical electromagnetism the absolute magnitudes of these forces are exactly and symmetrically identical. However, from a quantum mechanical/QED perspective the picture is subtly different. In QED the electric and magnetic forces are mediated by the exchange of virtual particles and are subject to the quantum mechanical rules of probabilities and Heisenberg Uncertainty principle. Quantum electric gravity introduces an appropriate quantum parameter to classical electromagnetic forces in order to improve compatibility with quantum mechanics. There are compelling observations and experiments to suggest that the quantum parameters for attractive and repulsive forces are not exactly and symmetrically identical. This leads the symmetry to breakdown and leaves a clear non-zero net force synonymous with and indistinguishable from the force of gravity. This asymmetry between forces proved crucial in securing inverse square law in line with Newton’s and general relativity. Interestingly, quantum electric gravity theoretically derives the underlying formula for the gravitational “constant” G and predicts its nonlinear behaviour at high field intensities. Quantum electric gravity is compatible with quantum mechanics, QED and the special theory of relativity.
Category: Quantum Gravity and String Theory

Deduction of New Gravitation Formula$-M*c^2/R$

Authors: chun-xuan jiang
Comments: 3 Pages. 3

We prove that gravity is the tachyon centripetal force and deduce a new gravitation formula $-m*c^2/R$.Beyond the Newtonian gravitational theory and deny the Einstein gravitational theory. This paper is the first human to a true descriptionof gravitation.Anyone can understand gravity.
Category: Quantum Gravity and String Theory

University Alliance Quantum Entanglement Separable Control of Time and Space

Authors: James Dunn
Comments: 12 Pages. A system of developments to characterize quantum entanglement.

Electricity at one time was magical; and now mundane. The same is true of space and time. Once the foundations of space and time are understood as described in Chapter 5 – “Pathway”, the methodologies for controlling space, time, and gravity become understandable and attainable. Additional developments are available that provide greater detail, but the intent here is to formulate and initiate a system of efforts for the characterizing of quantum entanglements with regard to relativity in uniform fields of physics such as gravity, centripetal force, acceleration… while providing the administrative influence to sustain economic growth. The pathway itself provides for predictable systems of opportunities and career pathways to elevate students in higher education as scientists/engineers to become business development professionals as well.
Category: Quantum Gravity and String Theory

Control of Time and Space

Authors: James Dunn
Comments: 33 Pages.

Separable Control of Space, Time, Gravity, Energy, and more Functioned Quantum Entangled Singularities (QES) Relativistic Matter as entanglements amongst Higgs-Boson & Gravity moderators
Relativistic Energy from relationships of Space, Time, and Gravity
Relativistic Gravity from Entanglement Moderators Space from Scalar Functioned Entanglements Time from Causal Functioned Entanglements
Systems of Quantum Aliasing with Transfer Functions providing “Probability Aliasing” Singularity Mechanics supporting superposition of Relativistic Mechanics Sub-atomic particles formed by systems of functioned quantum entanglements This QESdunn Theory of Everything (TOE) is based in modern experimentation techniques and a practical methodology pathway is provided herein that provides the tools to easily prove wrong the proposed relationships. Such attempts are encouraged. QESdunn unifies not only Electromagnetism and Gravity, but also instantaneous properties of entanglement and gravitational aberration, as well as all anomalies of physics.
Category: Quantum Gravity and String Theory

Seiberg-Witten M-Theory as an Almost Successful Predictive Theory

Authors: David Brown
Comments: 5 Pages.

Seiberg, Witten, and many other string theorists have suggested that superstring theory might lead to spacetime as an emergent approximation. Seiberg-Witten M-theory predicts supersymmetry in the form of particles. If nature is finite and digital and the Rañada-Milgrom effect fully explains so-called dark matter, then supersymmetry might exist in the form of symmetry principles within Wolfram’s mobile automaton. This hypothetical automaton is qualitatively described in Wolfram’s “A New Kind of Science”, Chapter 9. M-theory with the infinite nature hypothesis suggests questions and hypotheses based upon a curling-up (or compactification) of the 11-dimensional fundamental domain. Modified M-theory with the finite nature hypothesis suggests questions and hypotheses based upon a building-up of an approximation to the 11-dimensional domain. This hypothetical approximation is the result of the Wolframian updating parameter gradually building up time, space, and energy from Fredkin-Wolfram information below the Planck scale. If Wolfram is correct, then the monster group and the 6 pariah groups are essential for understanding the foundations of physics. If nature is finite and digital then the precise values of the free parameters of the Standard Model should be completely predictable. Modified M-theory with Wolfram’s automaton might underlie quantum field theory.
Category: Quantum Gravity and String Theory

Maxwell's Theory of Gravity and Thermodynamics

Authors: Mohammed Alzain Mohammed Ali
Comments: 7 Pages.

We argue that the entropic origin of gravitation correctly reproduced general relativity and quantum mechanics, with a particular treatment, where entropic gravity can be viewed as Maxwell's theory of gravity and thermodynamics. And this application will give us more detailed knowledge on the origin of gravity
Category: Quantum Gravity and String Theory

The Physics of Unification

Authors: Steven Howard Snyder
Comments: 126 Pages.

To date, a unification is needed with the application of Planck units which unifies not only the force of Newtonian gravity with the electromagnetic force and the strong and weak nuclear forces, but also one which includes quantum field theory and relativity. Herein, a unification as such is accomplished in which the mathematical terms of the conventional fields and the corresponding forces are unified into one general function in Planck units, and the geometry (including internal structure) and functionality of certain aspects of the respective unified field constructed therefrom are described. Accordingly, the geometry and functionality of the unified field are applied for describing certain aspects of electromagnetic, gravitational, and nuclear interaction along with certain aspects of elementary particles (including antiparticles), atoms, molecules, and at the macroscopic scale, astronomical bodies.
Category: Quantum Gravity and String Theory

New Excited Levels of the Bottom and Anti Bottom Mesons in Integral Charge Quark Susy

Authors: U.V.S.Seshavatharam, S.Lakshminarayana
Comments: 10 Pages.

Considering the `molar electron mass' an attempt is made to study the 4 interactions in a unified manner. Charged leptons, nucleons and (integral charge) quark masses were fitted in a unified scheme. Based on the modified SUSY, Higgs charged fermion, its boson and the quark baryon and quark meson masses were fitted. Finally an attempt is made to fit and predict the new excited levels of the bottom and anti bottom mesons.
Category: Quantum Gravity and String Theory

A Physical Interpretation of String Theory?

Authors: Dirk J. Pons
Comments: 4 Pages.

This note identifies similarities between the cordus conjecture and string theory, and suggests opportunity for new research directions. To fully define a cordus particule requires 11 geometric independent-variables. This is the same number of dimensions predicted by some variants of string theory. There is also a similarity in the structural models, e.g. for the photon. The cordus model is physically descriptive and built with conceptual-design principles, whereas string theory provides a family of abstract mathematical models. Perhaps they are describing the same thing from different perspectives? Therefore we invite string theorists to consider whether the orthogonal spatial dimensions in their models could instead be interpreted as geometric independent-variables. Doing so would create new ways for interpreting string theories. Perhaps string theory might yet be a tool for the development of physically meaningful explanations for fundamental physics?
Category: Quantum Gravity and String Theory

The God Particle: the Higgs Boson, Extra Dimensions and the Particle in a Box

Authors: A.Garcés Doz
Comments: 10 Pages.

In this paper we show as the lightest Higgs boson, is directly linked to the existence of seven dimensions compacted Kaluza-Klein type, and four extended. The model of a particle in a box allows us to calculate, using the extra dimensions as entries in the well-known equations of this model, the mass of the lightest Higgs boson. This estimate coincides with complete accuracy with that obtained in our previous work, "God and His Creation: The Universe", using the well known quantum mechanical model of a particle in a spherically symmetric potential. Both load match and result in a mass for the lightest Higgs boson of 126.23 Gev - 126.17 Gev
Category: Quantum Gravity and String Theory

Today, Atheism is Reasonable and Scientific. Tomorrow, Mathematics and Physics Will Show that Atheism is Mistaken.

Authors: Rodney Bartlett
Comments: 21 Pages.

We begin 600 years in the future, looking back and forth in time until we arrive in the next millennium … where science explains Infinity, Eternity and God. Subheadings in this article are – The 27th Century, Electrical Engineering, Relatively Short-Term Benefits, Gravitational-Electromagnetic Equivalence, Unified Field Theory, Resurrection To Eternal Life, Time Travel And Teleporting, The 30th Century, < Doctor Who … Mathematical Hyperspace And Quantum Spin >, Mobius Loop, Localized Unified Field, The Matrix And The Figure-8 Klein Bottle, Real / Imaginary / Negative, 1000 Years+, Quantum Mechanical God’s-Eye View, Unification Explains Infinity And Eternity And God, Hidden Variables, Virtual Particles
Category: Quantum Gravity and String Theory

Role of the `molar Electron Mass' in Coupling the Strong, Weak and Gravitational Interactions

Authors: U.V.S.Seshavatharam, S.Lakshminarayana
Comments: 5 Pages. Searching, collecting, sorting and compiling the cosmic code is an essential part of unification

Considering the `molar electron mass' an attempt is made to understand the strong, weak and gravitational interactions in a unified approach. Muon \& tau rest masses, nuclear characteristic size, proton size, nucleon rest masses and magnetic moments were fitted. Obtained SEMF energy coefficients are 16.28, 19.36, 0.7681, 23.76 and 11.88 MeV respectively.
Category: Quantum Gravity and String Theory

Fermi Energy of Proton and the Semf Energy Coefficients

Authors: U.V.S.Seshavatharam, S.Lakshminarayana
Comments: 3 Pages.

Considering the Avogadro number as a scaling factor an attempt is made to understand the origin of the strong, weak and electromagnetic interactions in a unified approach. Nuclear characteristic size, proton size, nucleon rest masses and magnetic moments were fitted. It is noticed that, nuclear binding energy can be understood with the `molar electron mass' and `fermi energy' concepts.
Category: Quantum Gravity and String Theory

The 3 Atomic Forces and the Strong Coupling Constant

Authors: U.V.S.Seshavatharam, S.Lakshminarayana
Comments: 3 Pages.

Key conceptual link that connects the gravitational force and non-gravitational forces is - the classical force limit, $F_C \cong \left(\frac{c^{4} }{G} \right)$. Nuclear weak force magnitude is $F_W \cong \frac{F_C}{N^2}$ where $N$ is the Avogadro number. Relation between the nuclear strong force and weak force magnitudes can be expressed as $\sqrt{\frac{F_S}{F_W}} \cong 2 \pi \ln \left(N^2\right).$ It is noticed that there exists simple relations in between the nuclear strong force, weak force and the force on the revolving electron in the Bohr radius of the Hydrogen atom. An attempt is made to couple the strong coupling constant with these 3 forces.
Category: Quantum Gravity and String Theory

Quaternionic-Valued Gravitation in 8D, Grand Unification and Finsler Geometry

Authors: Carlos Castro
Comments: 15 Pages. Submitted to the Int. Jour. of Theor. Physics

A unification model of 4D gravity and SU(3) x SU(2) x U(1) Yang-Mills theory is presented. It is obtained from a Kaluza-Klein compactification of 8D quaternionic gravity on an internal CP^2 = SU (3)/U(2) symmetric space . We proceed to explore the nonlinear connection A^a_\mu ( x, y ) formalism used in Finsler geometry to show how ordinary gravity in D = 4 + 2 dimensions has enough degrees of freedom to encode a 4D gravitational and SU (5) Yang-Mills theory. This occurs when the internal two-dim space is a sphere S^2 . This is an appealing result because SU (5) is one of the candidate GUT groups. We conclude by discussing how the nonlinear connection formalism of Finsler geometry provides an infinite hierarchical extension of the Standard Model within a six dimensional gravitational theory due to the embedding of SU (3) x SU (2) x U(1) \subset SU ( 5 ) \subset SU ( \infty ) .
Category: Quantum Gravity and String Theory

An Investigation of Kaluza Theory with Weak Scalar Field

Authors: Robert Watson
Comments: 12 Pages.

Kaluza's 1921 theory of gravity and electromagnetism using a fifth wrapped-up spatial dimension is at the root of many modern attempts to develop new physical theories. However it has a number of foundational problems. These issues are clearly of interest to researchers developing new theories based on Kaluza's approach. One of these issues is that it offers only null electromagnetic solutions unless there is also a scalar field. A standard fix is to set the scalar field large so its variations make little difference to the resulting field equations, however this is arbitrary and begs explanation. Without setting the scalar field large, the stress-energy tensor is different from the Einstein-Maxwell tensor and the usual derivation of the Lorentz force law or even Maxwell's equations can not be assumed. In this paper we derive Maxwell's laws and the Lorentz force law for varying scalar field solutions, where the scalar field is no different in magnitude from other diagonal elements of the 5 dimensional metric. The result is that Kaluza's theory included static electric fields all along. This is done by weakening the usual constraints slightly and making other assumptions precise. The amazing thing is that electromagnetism survives the addition in all important respects, though testable differences in terms of stress-energy do become apparent. Charge is shown to be quite naturally equivalent to fifth dimensional momentum. The argument is made rigorous contrary to previous indicative investigations by allowing for matter and charge models that make it possible to compare momentum and charge in ways analogous to the process of identifying momentum with elements of the stress-energy tensor in general relativity.
Category: Quantum Gravity and String Theory

Quantum Theory, String Theory, Strong Gravity and the Avogadro Number

Authors: U.V.S.Seshavatharam, S.Lakshminarayana
Comments: 29 Pages.

Nucleon behaves as if it constitutes molar electron mass. In a unified way nucleon's mass, size and other characteristic properties can be studied with this idea. If strong interaction is really $10^{39}$ times stronger than the strength of gravity, this proposal can be given a chance. Key conceptual link that connects the gravitational force and non-gravitational forces is - the classical force limit, $F_C \cong \left(\frac{c^{4} }{G} \right)$. It can be considered as the upper limit of the cosmic string tension. Weak force magnitude $F_W$ can be considered as the characteristic nuclear weak string tension. Until the measurement of $\left(F_C \;\&\; F_W\right)-$ it can be assumed that $\frac{F_C}{F_W}\cong N^2$ where $N$ is Avogadro like number.
Category: Quantum Gravity and String Theory

Does the Rañada-Milgrom Effect Explain the Flyby Anomaly?

Authors: David Brown
Comments: 2 Pages.

In 2007, the JPL researchers Anderson, Campbell, Ekelund, Ellis, and Jordan found an empirical prediction formula which describes anomalous orbital-energy changes for six Earth flybys. The Rañada-Milgrom effect might explain the empirical prediction formula found by these JPL researchers.
Category: Quantum Gravity and String Theory

Does the Rañada-Milgrom Effect Explain the Ecliptic Alignment of CMB Anisotropy?

Authors: David Brown
Comments: 2 Pages.

The cosmic microwave background (CMB) radiation yields a precise probe of the universe’s largest structures. The Wilkinson Microwave Anisotropy Probe (WMAP) data revealed anomalies at the largest angular scales (> 60º). Statistical analysis showed that there exist statistically significant correlations between features of the microwave sky and both the motion of the solar system and the orientation of the plane of the ecliptic. From a qualitative viewpoint, these anomalous statistical correlations are what one would expect if Sun-caused gravitational lensing were slightly different from the predictions of general relativity theory. Thus, there is a qualitative indication that the Rañada-Milgrom effect is empirically valid.
Category: Quantum Gravity and String Theory

The Everlasting Theory and Special Number Theory

Authors: Sylwester Kornowski
Comments: 147 Pages.

The Kasner solution for the flat anisotropic model (1921) described within the General Theory of Relativity is the common platform for the gravity and quantum theory. The scales for the charges in the generalized Kasner solution lead to the phase transitions of the fundamental spacetime and to the transition which caused the exit of the early Universe from the black-hole state. There is the ultimate equation which ties masses of sources of all types of interactions.
Category: Quantum Gravity and String Theory

Dirac Singletons in a Quantum Theory Over a Galois Field

Authors: Felix M. Lev
Comments: 37 Pages. Well known results on singletons in standard theory are generalized to the case of a quantum theory over a Galois field.

Dirac singletons are exceptional irreducible representations (IRs) of the so(2,3) algebra found by Dirac. As shown in a seminal work by Flato and Fronsdal, the tensor product of singletons can be decomposed into massless IRs of the so(2,3) algebra and therefore each massless particle (e.g. the photon) can be represented as a composite state of singletons. This poses a fundamental problem of whether only singletons can be treated as true elementary particles. However, in standard quantum theory (based on complex numbers) such a possibility encounters difficulties since one has to answer the following questions: a) why singletons have not been observed and b) why the photon is stable and its decay into singletons has not been observed. We show by direct calculations that in a quantum theory over a Galois field (GFQT), the decomposition of the tensor product of singletons IRs contains not only massless IRs but also special massive IRs which have no analogs in standard theory. In the case of supersymmetry we explicitly construct a complete set of IRs taking part in the decomposition of the tensor product of supersingletons. Then in GFQT one can give natural explanations of a) and b).
Category: Quantum Gravity and String Theory

Anomalous Gravitational Acceleration and the Opera Neutrino Anomaly (Updated)

Authors: David Brown
Comments: 4 Pages.

In September 2011, OPERA researchers observed muon neutrinos that seemed to travel faster than the speed of light, but in February 2012, re-analysis suggested that a loose fiber optic cable might have caused the problem. The explanation of the OPERA neutrino anomaly might have 3 alternatives: (1) There are one or more serious experimental errors. (2) Quantum field theory is slightly wrong. (3) General relativity theory is slightly wrong. Is alternative (3) known to be true? Overwhelming empirical evidence shows that Milgrom is the Kepler of modern cosmology. Combination of the ideas of Fernández-Rañada and Milgrom might explain the OPERA neutrino anomaly, because the GPS timing differs slightly from the predictions of general relativity theory. Professor Antonio Fernández-Rañada and I have exchanged e-mails on the Rañada-Milgrom effect and he wants to be more thorough before going into print. He and I might, or might not, be regarded as implicit collaborators. His ideas seem to indicate that the Rañada-Milgrom effect is approximately correct, but my ideas favor the effect as a precise indication of the existence of alternate universes.
Category: Quantum Gravity and String Theory

Finite Nature Hypothesis and Space Roar Profile Prediction

Authors: David Brown
Comments: 3 Pages.

In 2006, a NASA team with Alan Kogut as principal investigator used a balloon-borne radiometer named ARCADE to measure the temperature of the cosmic microwave background (CMB) at centimeter wavelengths. ARCADE searched the sky for faint traces of heat from first generation stars in the very early universe, but ARCADE found a pervasive electromagnetic noise about 6 times louder than predicted. The NASA team named this pervasive electromagnetic noise “the space roar.” Highly speculative hypotheses based upon the failure of Einstein’s equivalence principle for virtual mass-energy might yield a way of testing the hypothesis that nature is finite and digital. The finite nature hypothesis might yield a Space Roar Profile Prediction suitable for empirical tests.
Category: Quantum Gravity and String Theory

Earth Magnetic Monopole Field Interactionwith Cyclotron-Synchrotron Electrons and Muon Conversion Used for Levitation Systems

Authors: Leo Vuyk
Comments: 18 Pages. 18

Quantum FFF (Function Follows Form) theory states, that the vacuum is seeded with fast oscillating massless Higgs particles, oscillating along a complex chiral tetrahedral vacuum lattice, which has the ability to transfer Photon and Graviton information in bunches of oscillations, through the vacuum lattice with the local speed of light. As a consequence there are no attraction forces on propeller shaped Fermions. Only the sum of the different kinds of vacuum impulses from all directions on Fermions are responsible for all energetic phenomena in the universe. Quantum Gravity can be interpreted as the statistical result of opposing impulse differences of two radiation fields, the massless Higgs field and the massless graviton field. Magnetism seems to be the statistical result of opposing impulse differences of the massless magnetic North monopole array field and the opposing magnetic South monopole array field. As a consequence magnetic levitation should be possible by Lorentz force creation by electron cyclotron interaction with earth magnetic monopole array fields. Graviton or Higgs field screening for levitation is not supported by “double LeSage gravity” described in Q-FFF theory. Only inertial effects through rotational mass differences such as is the case in Muonic decay in compact storage rings with a Muon-positron recycling possibility, called electron-muon-electron conversion, seems to be a promise for future solutions
Category: Quantum Gravity and String Theory

Planck-Scale Physics: Facts and Beliefs

Authors: Diego Meschini
Comments: 14 Pages. Published in Foundations of Science, 12, 277-294, 2007.

The relevance of the Planck scale to a theory of quantum gravity has become a worryingly little examined assumption that goes unchallenged in the majority of research in this area. However, in all scientific honesty, the significance of Planck's natural units in a future physical theory of spacetime is only a plausible, yet by no means certain, assumption. The purpose of this article is to clearly separate fact from belief in this connection.
Category: Quantum Gravity and String Theory

Is Empty Spacetime a Physical Thing?

Authors: Diego Meschini, Markku Lehto
Comments: 23 Pages. Published in Foundations of Physics, 36, 1193-1216, 2006.

This article deals with empty spacetime and the question of its physical reality. By "empty spacetime" we mean a collection of bare spacetime points, the remains of ridding spacetime of all matter and fields. We ask whether these geometric objects -- themselves intrinsic to the concept of field -- might be observable through some physical test. By taking quantum-mechanical notions into account, we challenge the negative conclusion drawn from the diffeomorphism invariance postulate of general relativity, and we propose new foundational ideas regarding the possible observation -- as well as conceptual overthrow -- of this geometric ether.
Category: Quantum Gravity and String Theory

Geometry, Pregeometry and Beyond

Authors: Diego Meschini, Markku Lehto, Johanna Piilonen
Comments: 41 Pages. Published in Stud. in Hist. and Phil. of Mod. Phys., 36, 435-464, 2005.

This article explores the overall geometric manner in which human beings make sense of the world around them by means of their physical theories; in particular, in what are nowadays called pregeometric pictures of Nature. In these, the pseudo-Riemannian manifold of general relativity is considered a flawed description of spacetime and it is attempted to replace it by theoretical constructs of a different character, ontologically prior to it. However, despite its claims to the contrary, pregeometry is found to surreptitiously and unavoidably fall prey to the very mode of description it endeavours to evade, as evidenced in its all-pervading geometric understanding of the world. The question remains as to the deeper reasons for this human, geometric predilection--present, as a matter of fact, in all of physics--and as to whether it might need to be superseded in order to achieve the goals that frontier theoretical physics sets itself at the dawn of a new century: a sounder comprehension of the physical meaning of empty spacetime.
Category: Quantum Gravity and String Theory

A Metageometric Enquiry Concerning Time, Space, and Quantum Physics

Authors: Diego Meschini
Comments: 285 Pages. Ph.D. thesis, Department of Physics, University of Jyväskylä, 2008.

An enquiry into the physical nature of time and space and into the ontology of quantum mechanics from a metageometric perspective, resulting from the belief that geometric thought and language are powerless to farther understanding of these issues, restricting instead physical progress.

The nature and assumptions of quantum gravity are analysed critically, including misgivings about the relevance of the Planck scale to it and its lack of observational referent in the natural world.

The anthropic foundations of geometry are investigated. The exclusive use of geometric thought from antiquity to present-day physics is found to permeate all new attempts towards better theories, including quantum gravity and, within it, even pregeometry.

The problem of the ether is found to have perpetuated itself up to the present by transmuting its form from mechanical, through metric, to geometric.

A clarification is made of the physical, mathematical, and psychological foundations of relativity and quantum theories. The former is founded geometrically on measurement-based clock-reading separations ds. The latter is founded metageometrically on the experiment-based concepts of premeasurement and transition things, inspired in the physically unexplored aspect of time as a consciousness-related product. A concept of metageometric time is developed and coordinate time t is recovered from it. Discovery of the connection between quantum-mechanical metageometric time elements and general-relativistic clock time elements ds is deemed necessary for a combined understanding of time.

Time is conjectured to be the missing link between general relativity and quantum mechanics.

Anomalous Gravitational Acceleration and the Opera Neutrino Anomaly

Authors: David Brown
Comments: 2 Pages.

In September 2011, OPERA researchers observed muon neutrinos that seemed to travel faster than the speed of light, but in February 2012, re-analysis suggested that a loose fiber optic cable might have caused the problem. The explanation of the OPERA neutrino anomaly might have 3 alternatives: (1) There are one or more serious experimental errors. (2) Quantum field theory is slightly wrong. (3) General relativity theory is slightly wrong. Is alternative (3) known to be true? Overwhelming empirical evidence shows that Milgrom is the Kepler of modern cosmology. Combination of the ideas of Fernández-Rañada and Milgrom might explain the OPERA neutrino anomaly, because the GPS timing differs slightly from the predictions of general relativity theory.
Category: Quantum Gravity and String Theory

God and His Creation: the Universe

Authors: A. Garcés Doz
Comments: 89 Pages.

In this paper we demonstrate how the universe has to be caused or created by an intelligent being: God. And as the multiverse theory, mainly based on the random generation of states infinite universe is very poorly posed from the mathematical point of view, and how this failure leads to the demonstration of its impossibility. The anthropic principle called not taken into account, it is a mere philosophical statement without any physical-mathematical foundation, and therefore lacking the minimum necessary scientific validity. The main parameters are obtained: densities of baryons, vacuum energy density, mass of the lightest Higgs boson, neutrino mass, mass of the graviton, among others. Deducting finally naturally within the theory, the inflation factor of the universe. Similarly, the theory implies necessarily the "creation" of matter.
Category: Quantum Gravity and String Theory

Mathematical Foundations of the Relativistic Theory of Quantum Gravity

Authors: Fran De Aquino
Comments: 76 Pages.

Starting from the action function, we have derived a theoretical background that leads to the quantization of gravity and the deduction of a correlation between the gravitational and the inertial masses, which depends on the kinetic momentum of the particle. We show that the strong equivalence principle is reaffirmed and, consequently, Einstein's equations are preserved. In fact, such equations are deduced here directly from this new approach to Gravitation. Moreover, we have obtained a generalized equation for the inertial forces, which incorporates the Mach's principle into Gravitation. Also, we have deduced the equation of Entropy; the Hamiltonian for a particle in an electromagnetic field and the reciprocal fine structure constant directly from this new approach. It was also possible to deduce the expression of the Casimir force and to explain the Inflation Period and the Missing Matter, without assuming existence of vacuum fluctuations. This new approach to Gravitation will allow us to understand some crucial matters in Cosmology.
Category: Quantum Gravity and String Theory

The Universal Quantum Fluid

Authors: Fran De Aquino
Comments: 8 Pages.

The quantization of gravity showed that the matter is also quantized, and that there is an elementary quantum of matter, indivisible, whose mass is 3.9 X 10-73kg. This means that any body is formed by a whole number of these particles (quantization). It is shown here that these elementary quanta of matter should fill all the space in the Universe forming a Quantum Fluid continuous and stationary. In addition, it is also explained why the Michelson-Morley experiment was not able to detect this Universal Quantum Fluid.
Category: Quantum Gravity and String Theory

Gravity Control by Means of Modified Electromagnetic Radiation

Authors: Fran De Aquino
Comments: 6 Pages.

Here a new way for gravity control is proposed that uses electromagnetic radiation modified to have a smaller wavelength. It is known that when the velocity of a radiation is reduced its wavelength is also reduced. There are several ways to strongly reduce the velocity of an electromagnetic radiation. Here, it is shown that such a reduction can be done simply by making the radiation cross a conductive foil.
Category: Quantum Gravity and String Theory

Accelerating Universe and the Expanding Atom-2

Authors: U .V . S. Seshavatharam, S. Lakshminarayana
Comments: 7 Pages.

Bohr radius of hydrogen atom, quanta of the angular momentum and the strong interaction range - are connected with the large scale structure of the massive universe. In the accelerating universe, as the space expands, in hydrogen atom, distance between proton and electron increases and is directly proportional to the size of the universe. Obtained value of the present Hubble constant is 70.75 Km/sec/Mpc. `Rate of decrease in fine structure ratio' is a measure of cosmic rate of expansion. Considering the integral nature of number of protons (of any nucleus), integral nature of `hbar' can be understood.
Category: Quantum Gravity and String Theory

Algebraic Braids, Sub-Manifold Braid Theory, and Generalized Feynman Diagrams

Authors: Matti Pitkänen
Comments: 37 Pages.

The basic challenge of quantum TGD is to give a precise content to the notion of generalization Feynman diagram and the reduction to braids of some kind is very attractive possibility inspired by zero energy ontology. The point is that no n>2-vertices at the level of braid strands are needed if bosonic emergence holds true.

1. For this purpose the notion of algebraic knot is introduced and the possibility that it could be applied to generalized Feynman diagrams is discussed. The algebraic structrures kei, quandle, rack, and biquandle and their algebraic modifications as such are not enough. The lines of Feynman graphs are replaced by braids and in vertices braid strands redistribute. This poses several challenges: the crossing associated with braiding and crossing occurring in non-planar Feynman diagrams should be integrated to a more general notion; braids are replaced with sub-manifold braids; braids of braids ....of braids are possible; the redistribution of braid strands in vertices should be algebraized. In the following I try to abstract the basic operations which should be algebraized in the case of generalized Feynman diagrams.
2. One should be also able to concretely identify braids and 2-braids (string world sheets) as well as partonic 2-surfaces and I have discussed several identifications during last years. Legendrian braids turn out to be very natural candidates for braids and their duals for the partonic 2-surfaces. String world sheets in turn could correspond to the analogs of Lagrangian sub-manifolds or two minimal surfaces of space-time surface satisfying the weak form of electric-magnetic duality. The latter opion turns out to be more plausible. Finite measurement resolution would be realized as symplectic invariance with respect to the subgroup of the symplectic group leaving the end points of braid strands invariant. In accordance with the general vision TGD as almost topological QFT would mean symplectic QFT. The identification of braids, partonic 2-surfaces and string world sheets - if correct - would solve quantum TGD explicitly at string world sheet level in other words in finite measurement resolution.
3. Also a brief summary of generalized Feynman rules in zero energy ontology is proposed. This requires the identification of vertices, propagators, and prescription for integrating over al 3-surfaces. It turns out that the basic building blocks of generalized Feynman diagrams are well-defined.
4. The notion of generalized Feynman diagram leads to a beautiful duality between the descriptions of hadronic reactions in terms of hadrons and partons analogous to gauge-gravity duality and AdS/CFT duality but requiring no additional assumptions. The model of quark gluon plasma as s strongly interacting phase is proposed. Color magnetic flux tubes are responsible for the long range correlations making the plasma phase more like a very large hadron rather than a gas of partons. One also ends up with a simple estimate for the viscosity/entropy ratio using black-hole analogy.

Evolution of TGD

Authors: Matti Pitkänen
Comments: 36 Pages.

A summary about how various ideas about TGD have developed is given. This is a response to a request of Mark McWilliams. I try to represent the development chronologically but I must confess that I have forgotten precise dates so that the chronology is not exact. Very probably I have also forgotten many important ideas and many side tracks which led nowhere. Unavoidably the emphasis is on the latest ideas and there is of course the risk that some of them are not here to stay. Even during writing process some ideas developed into more concrete form. A good example is the vision about what happens in quantum jump and what the unitarity of U-matrix really means, how M-matrices generalize to form Kac-Moody type algebra, and how the notion of quantum jump in zero energy ontology (ZEO) reproduces the basic aspects of quantum measurement theory. Also a slight generalization of quantum arithmetics suggested itself during the preparation of the article.
Category: Quantum Gravity and String Theory

Ulianov String Theory a New Representation for Fundamental Particles

Authors: Policarpo Yōshin Ulianov
Comments: 15 Pages.

This article introduces a new model for fundamental particles representation, named Ulianov String Theory (UST). In the UST model, the space is composed of eight dimensions, being four of them “rolled up” dimensions while the other four are ”ordinary” dimensions. Moreover, in the UST, time dimension is modeled as a complex variable and can also be “rolled up”. This new string model also defines point-like particles named Ulianov Holes (uholes), which, from the imaginary time collapse, is transformed into strings. These strings allow generation of a series of structures, which can be associated to configurations of the observed matter and energy in our universe.
Category: Quantum Gravity and String Theory

A Ribbon Dark Sector and Koide Triplets

Authors: M. D. Sheppeard
Comments: 7 Pages.

Riofrio predicted a basic total dark sector density fraction, and hypothesised an exact $1:3$ ratio for the matter and dark energy components, consistent with observations. It is suggested that the color quantum number for quark states is responsible for the factor of 3, whereby dark sector properties are a consequence of a non local quark and lepton complementarity. This factor of 3 also appears as the proton mass scale in a quark Koide triplet.
Category: Quantum Gravity and String Theory

Cosmo-Logical Origin of Electromagnetic and Strong Interactions

Authors: U .V . S. Seshavatharam, S. Lakshminarayana
Comments: 1 Page. Abstract only

If mass of the present universe is, $M_0 \cong \frac{c^3}{2GH_0} \cong 9\times10^{52}$ Kg and ($m_e$ \& $m_p$) represents the rest masses of electron and proton, it is noticed that $\hbar \cong \frac{Gm_p\sqrt{M_0m_e}}{c}.$ Considering the integral nature of number of protons in the nucleus, integral nature of $\hbar$ can be understood. With reference to the classical force limt $\frac{c^{4} }{G},$ minimum distance between (point electron) and (point universe) is $d_e \cong \frac{G\sqrt{M_0m_e}}{c^2}\cong 0.213$ fm. Similarly minimum distance between (point proton) and (point universe) is $d_p \cong \frac{G\sqrt{M_0m_p}}{c^2}\cong 9.11$ fm. Geometric mean of $d_e$ and $d_p$ is 1.39 fm.
Category: Quantum Gravity and String Theory

Earth Magnetic Monopole Array Field Interaction with Cyclotron Electrons Used for Levitation Systems.

Authors: Leo Vuyk
Comments: 15 Pages. 15

Quantum FFF theory states, that the vacuum is seeded with fast oscillating massless Higgs particles, oscillating along a complex chiral tetrahedral vacuum lattice, which has the ability to transfer Photon and Graviton information in bunches of oscillations, through the vacuum lattice with the local speed of light. As a consequence there are no attraction forces on propeller shaped Fermions. Only the sum of the different kinds of vacuum impulses from all directions on Fermions are responsible for all energetic phenomena in the universe. Quantum Gravity can be interpreted as the statistical result of opposing impulse differences of two radiation fields, the massless Higgs field and the massless graviton field. Magnetism seems to be the statistical result of opposing impulse differences of the massless magnetic North monopole array field and the opposing magnetic South monopole array field. As a consequence magnetic levitation should be possible by Lorentz force creation by electron cyclotron interaction with earth magnetic monopole array fields. Graviton or Higgs field screening for levitation is not supported by “double LeSage gravity” in Q-FFF theory. Only inertial effects through rotational mass differences such as is the case in cyclotron Muonic decay, seems to be a promise for future solutions.
Category: Quantum Gravity and String Theory

Toward a Quantum Conception of the Gravity

Authors: Jorge Gabriel Ales Corona
Comments: 7 Pages.

The quantum treatment of the gravity has resisted for over fifty years. The efforts were centered fundamentally in the search of the concept of “quantum gravitational field”. This article presents a new road that can allow solving this enigma. The gravitation would not have to be described with this concept; that is to say, a quantum gravitational field doesn't exist. In their place the gravity would be a simple stochastic phenomenon. The phenomena tend to occur in places of higher probability. The particles move, to be detected, to the places of greatest concentration of particles.
Category: Quantum Gravity and String Theory

To Unify the String Theory and the Strong Gravity

Authors: U .V . S. Seshavatharam, S. Lakshminarayana
Comments: 15 Pages. Please circulate this article.

Key conceptual link that connects the gravitational force and non-gravitational forces is - the classical force limit,
Category: Quantum Gravity and String Theory

Is the Threshold Curvature that Corresponds to the Onset of the Uselessness of Mass-Energy for Work a Variable Measure?

Authors: Shawn Halayka
Comments: 2 Pages.

A duality between entropy and curvature is discussed.
Category: Quantum Gravity and String Theory

Neutrinos Faster Than Light Speed

Authors: Stein Sivertsen
Comments: 4 Pages.

The OPERA neutrino anomaly is the detection by the OPERA experiment of subatomic particles, neutrinos, that appear to travel faster than light. This result was publicly announced on September 2011. The apparent finding is a subject of inquiry and debate. It is considered anomalous since speeds higher than that of light in a vacuum are generally thought to violate special relativity. In this paper I offer an explanation of this anomaly based upon my article: http://www.vixra.org/pdf/1010.0035v4.pdf (A Philosophical And Mathematical Theory Of Everything.
Category: Quantum Gravity and String Theory

To Implemet the Gravitational Constant and the Avogadro Number in Atomic, Nuclear and Particle Physics

Authors: U .V . S. Seshavatharam, S. Lakshminarayana
Comments: 15 Pages. Role of Avogadro number in grand unification. Hadronic Journal. Vol-33, No 5, 2010 Oct. p513.

It is very clear that, to unify 2 interactions if 5 dimensions are required, for unifying 4 interactions 10 dimensions are required. For 3+1 dimensions if there exists 4 (observed) interactions, for 10 dimensions there may exist 10 (observable) interactions. To unify 10 interactions 20 dimensions are required. From this idea it can be suggested that- with `n' new dimensions `unification' problem can not be resolved. By implementing the gravitational constant in atomic and nuclear physics, independent of the CGS and SI units, Avogadro number can be obtained very easily and its order of magnitude is $\cong N \cong 6 \times 10^{23}$ but not $6 \times 10^{26}.$ If $M_P$ is the Planck mass and $m_e$ is the rest mass of electron, semi empirically it is observed that, $M_g \cong N^{\frac{2}{3}}\cdot \sqrt{M_Pm_e} \cong 1.0044118 \times 10^{-3} \; Kg.$ If $m_{p} $ is the rest mass of proton it is noticed that $\ln \sqrt{\frac{e^{2} }{4\pi \varepsilon _{0} Gm_{P}^{2} } } \cong \sqrt{\frac{m_{p} }{m_{e} } -\ln \left(N^{2} \right)}.$ Key conceptual link that connects the gravitational force and non-gravitational forces is - the classical force limit $\left(\frac{c^{4} }{G} \right)$. For mole number of particles, if strength of gravity is $\left(N.G\right),$ any one particle's weak force magnitude is $F_{W} \cong \frac{1}{N} \cdot \left(\frac{c^{4} }{N.G} \right)\cong \frac{c^{4} }{N^{2} G} $. Ratio of `classical force limit' and `weak force magnitude' is $N^{2} $. Assumed relation for strong force and weak force magnitudes is $\sqrt{\frac{F_{S} }{F_{W} } } \cong 2\pi \ln \left(N^{2} \right)$. From SUSY point of view, `integral charge quark fermion' and `integral charge quark boson' mass ratio is $\Psi=2.262218404$ but not unity. With these advanced concepts an ``alternative" to the `standard model' can be developed.
Category: Quantum Gravity and String Theory

3 Dimensional String Theory

Authors: George Rajna
Comments: 6 Pages.

This paper examines the possibility to origin the spontaneously broken symmetries from the Planck distribution law. In this way we get for example a unification of the strong, electromagnetic and weak interactions from the interference occurrences of oscillators.
Category: Quantum Gravity and String Theory

Units Independent Avogadro Number and Its Applications in Unification

Authors: U .V . S. Seshavatharam, S. Lakshminarayana
Comments: 16 Pages. Avogadro number couples the gravitational and non-gravitational interactions

By implementing the gravitational constant in atomic and nuclear physics, independent of the CGS and SI units, Avogadro number can be obtained very easily. It is observed that, either in SI system of units or in CGS system of units, value of the order of magnitude of Avogadro number $\cong N \cong 6 \times 10^{23}$ but not $6 \times 10^{26}.$ Key conceptual link that connects the gravitational force and non-gravitational forces is - the classical force limit $\left(\frac{c^{4} }{G} \right)$. For mole number of particles, if strength of gravity is $\left(N.G\right),$ any one particle's weak force magnitude is $F_{W} \cong \frac{1}{N} \cdot \left(\frac{c^{4} }{N.G} \right)\cong \frac{c^{4} }{N^{2} G} $. Ratio of `classical force limit' and `weak force magnitude' is $N^{2} $. This may be the beginning of unification of `gravitational and non-gravitational interactions'.
Category: Quantum Gravity and String Theory

Gravitational Constant in Nuclear Interactions

Authors: U .V . S. Seshavatharam, S. Lakshminarayana
Comments: 13 Pages. Strange relations can not be ignored.

Till today no atomic principle implemented the gravitational constant in nuclear physics. Considering the electromagnetic and gravitational force ratio of electron and proton a simple semi empirical relation is proposed for estimating the strong coupling constant. Obtained value is $\alpha_s \cong 0.117378409.$ It is also noticed that $\alpha_s\cong \ln\left(r_Ur_D\right)$ where $r_U$ and $r_D$ are the geometric ratios of Up and Down quark series respectively. It is noticed that proton rest mass is equal to $\left(\frac{1}{\alpha}+\frac{1}{\alpha_s}\right)\sqrt{UD}.$ With reference to the the electromagnetic and gravitational force ratio of electron, 137 can be fitted at $r_U $ and 128 can be fitted at $r_D.$ Finally semi empirical mass formula energy constants are fitted.
Category: Quantum Gravity and String Theory

A Proposed New Model

Authors: Paul Karl Hoiland
Comments: 6 Pages.

I examine a slight modification to the so-called Higgless models that allows for a real Higg’s particle and some cosmological constant that varies over time via vacuum decay. In this Model you find Dark Matter as a Higg's decay mode, and a variable cosmological constant resulting from dark matters uncoupling from the EW scale.
Category: Quantum Gravity and String Theory

A 10-Dimensional and 11-Dimensional Hidden Variables Duality Model of a ‘D-Brane and Type I String Structure’

Authors: Gary Heen
Comments: 24 Pages.

In this paper a 'hidden variables' interpretation of the quantum world is presented. A hidden variables explanation assumes current quantum mechanical theories are imperfect in that they do not incorporate a physical reality to the quantum world. At the Solvay conference of 1927, Louis De Broglie presented a hypothesis which was to be the forerunner to hidden variables theory: at the quantum level, a 'matter wave' steered particles. Under the powerful influence of Neils Bohr, Louis De Broglie's matter wave was disregarded in favor of the 'Copenhagen Interpretation' championed by Bohr himself, and the Copenhagen interpretation became the de facto accepted theory of quantum mechanics. In 1932, John Von Neumann presented a supposed "proof" that no hidden variables theory could properly describe the quantum world. He was first shown to be wrong by Grete Hermann, but she was largely ignored do to Neumann's immense stature as a mathematician. Later in 1966, John Bell further established that the proof was flawed, and the hidden variables interpretation has since seen a renewal of interest amongst researchers. The model presented in this paper incorporates d-branes and Type I strings into a hidden variables quantum structure; this physical structure can be interpreted as both 10-dimensional and 11- dimensional, and is designated: the D-string.
Category: Quantum Gravity and String Theory

The Physical Interpretation of the Energy-Momentum Transport Wave Function for the Gravitational and Electrostatic Interactions

Authors: Mirosław J. Kubiak
Comments: 4 Pages.

In the paper [1] we have presented simple model of the energy-momentum transport wave function (EMTWF). In this paper we will discuss the physical interpretation of the EMTWF for the elementary quanta of action connected with the gravitational and electrostatic interactions.
Category: Quantum Gravity and String Theory

Gews Interactions in Strong Nuclear Gravity

Authors: U .V . S. Seshavatharam, S. Lakshminarayana
Comments: 32 Pages. To be published in the Hadronic journal.

In the atomic or nuclear space, till today no one measured the value of the gravitational constant. To bring down the planck mass scale to the observed elementary particles mass scale a large scale factor is required. Ratio of planck mass and electron mass is close to $\textrm{Avogadro number}/8 \pi\cong N/8 \pi$. The idea of strong gravity originally referred specifically to mathematical approach of Abdus Salam of unification of gravity and quantum chromo-dynamics, but is now often used for any particle level gravity approach. In this connection it is suggested that, key conceptual link that connects the gravitational force and non-gravitational forces is - the classical force limit $\left(\frac{c^{4} }{G} \right)$. For mole number of particles, if strength of gravity is $\left(N.G\right),$ any one particle's weak force magnitude is $F_{W} \cong \frac{1}{N} \cdot \left(\frac{c^{4} }{N.G} \right)\cong \frac{c^{4} }{N^{2} G} $. Ratio of `classical force limit' and `weak force magnitude' is $N^{2} $. This is another significance of Avogadro number. If $R_0\cong 1.21$ fermi is the nuclear charge radius, to a very good accuracy it is noticed that in Hydrogen atom, ratio of total energy of electron and nuclear potential is equal to the electromagnetic and gravitational force ratio of electron where the operating gravitational constant is $N^2G_C$ but not $G_C.$ Square root of ratio of strong and weak force magnitudes can be expressed as $2 \pi \ln\left(N^2\right).$ With the defined strong and weak force magnitudes observed elementary particles masses and their magnetic moments can be generated. Interesting application is that: characteristic building block of the cosmological ‘dark matter’ can be quantified in terms of fundamental physical constants. No extra dimensions are required in this new approach.
Category: Quantum Gravity and String Theory

Nuclear Mass Density in Strong Gravity and Grand Unification

Authors: U.V.S.Seshavatharam, S.Lakshminarayana
Comments: 5 Pages. Poster presentation in the 3rd Galileo - Xu Guangqi meeting, Beijing, China, October, 2011.

It is noticed that, when the black hole mass density reaches the nuclear mass density, mass of the black hole approaches to $1.81\times 10^{31} \rm{\;Kg\;} \cong 9.1M_\odot.$ This characteristic mass can be called as the Fermi black hole mass. This proposed mass unit plays an interesting role in grand unification and primordial black holes. Mass ratio of Fermi black hole mass and Chandrasekhar's mass limit is $2\pi.$ Mass ratio of Fermi black hole mass and neutron star mass limit is $\sqrt{2\pi}.$ Considering strong nuclear gravity, Fermi black hole mass can be obtained in a grand unified approach.
Category: Quantum Gravity and String Theory

Strong Nuclear Gravity a Very Brief Report

Authors: U V Satya Seshavatharam, S Lakshminarayana
Comments: 2 Pages. Full paper to be published in the Hadronic journal.

Key conceptual link that connects the gravitational force and non-gravitational forces is - the classical force limit $\left(\frac{c^{4} }{G} \right)$. For mole number of particles, if strength of gravity is $\left(N.G\right),$ any one particle's weak force magnitude is $F_{W} \cong \frac{1}{N} \cdot \left(\frac{c^{4} }{N.G} \right)\cong \frac{c^{4} }{N^{2} G} $. Ratio of `classical force limit' and `weak force magnitude' is $N^{2} $. This can be considered as the beginning of `strong nuclear gravity'. Assumed relation for strong force and weak force magnitudes is $\sqrt{\frac{F_{S} }{F_{W} } } \cong 2\pi \ln \left(N^{2} \right)$. If $m_{p} $ is the rest mass of proton it is noticed that $\ln \sqrt{\frac{e^{2} }{4\pi \varepsilon _{0} Gm_{P}^{2} } } \cong \sqrt{\frac{m_{p} }{m_{e} } -\ln \left(N^{2} \right)}.$ From SUSY point of view, `integral charge quark fermion' and `integral charge quark boson' mass ratio is $\Psi=2.262218404$ but not unity. With these advanced concepts starting from nuclear stability to charged leptons, quarks, electroweak bosons and charged Higgs boson's origin can be understood. Finally an ``alternative" to the `standard model' can be developed.
Category: Quantum Gravity and String Theory

Nucleus in Strong Nuclear Gravity

Authors: U V Satya Seshavatharam, S Lakshminarayana
Comments: 2 Pages. DAE Symposium on Nuclear Physics, December 26-30, 2011, India.

Based on strong nuclear gravity, $N$ being the Avogadro number and $\left(\frac{c^4}{N^2G}\right)$ being the weak force magnitude, electron`s gravitational mass generator $= X_{E} \cong m_{e} c^{2} \div \sqrt{\frac{e^{2} }{4\pi \varepsilon _{0} } \left(\frac{c^4}{N^2G}\right) } \cong 295.0606338$. Weak coupling angle is $\sin \theta _{W} \cong \frac{1}{\alpha X_{E} } \cong 0.464433353\cong \frac{{\rm Up}\; {\rm quark}\; {\rm mass}}{{\rm Down}\; {\rm quark}\; {\rm mass}} $. $X_{S} \cong \ln \left(X_{E}^{2} \sqrt{\alpha } \right)\cong 8.91424\cong \frac{1}{\alpha _{s} } $ can be considered as `inverse of the strong coupling constant'.The proton-nucleon stability relation is $A_{S} \cong 2Z+\frac{Z^{2} }{S_{f} }$ where $S_{f} \cong X_{E} -\frac{1}{\alpha } -1\cong 157.0246441$. With reference to proton rest energy, semi empirical mass formula coulombic energy constant is $E_{c} \cong \frac{\alpha }{X_{S} } \cdot m_{p} c^{2} \cong \alpha \cdot \alpha _{s} \cdot m_{p} c^{2} \cong {\rm 0}.7681\; MeV.$ Pairing energy constant is $E_{p} \cong \frac{m_{p} c^{2} +m_{n} c^{2} }{S_{f} } \cong 11.959\; {\rm M}eV$ and asymmetry energy constant is $E_{a} \cong 2E_{p} \cong 23.918\; {\rm M}eV$. It is also noticed that, $\frac{E_{a} }{E_{v} } \cong 1+\sin \theta _{W} $ and $\frac{E_{a} }{E_{s} } \cong 1+\mathop{\sin }\nolimits^{2} \theta _{W} $. Thus $E_{v} \cong 16.332$ MeV and $E_{s} \cong 19.674\; {\rm M}eV.$ Nuclear binding energy can be fitted with 2 terms. In scattering experiments minimum distance between electron and the nucleus is $R_0 \cong \left(\frac{\hbar c}{\left(N.G\right)m_e^2}\right)^2 \frac{2Gm_e}{c^2}.$
Category: Quantum Gravity and String Theory

Integral Charge Susy in Strong Nuclear Gravity

Authors: U V Satya Seshavatharam, S Lakshminarayana
Comments: 2 Pages. Poster presentation in DAE Symposium on Nuclear Physics, December 26-30, 2011, India.

‘Quark flavor’ is a property of ‘strong interaction charge’ and nowhere connected with ‘fermions’ or ‘bosons’. There exists nature friendly ‘integral charge quark flavors’. If a ‘charged quark flavor’ rests in a ‘fermionic container’ it is a ‘quark fermion’. Similarly if a ‘charged quark flavor’ rests in a ‘bosonic container’ it is a ‘quark boson’. Strong interaction charge contains ‘multiple flavors’ and can be called as the ‘hybrid charge quark’. No 3 quark fermions couples together to form a baryon and no 2 quark fermions couples together to form a meson. In super symmetry, quark fermion and quark boson mass ratio is $\Psi \cong 2.262218404$ but not unity. Quark fermions convert into quark baryons and effective quark fermions convert into effective quark baryons. Similarly quark bosons convert into quark mesons. Effective quark baryons generates charged and unstable multi flavor baryons and light quark bosons couples with these charged baryons and generates doublets or triplets. Any two oppositely charged quark mesons generates neutral and unstable mesons. <br> Based on strong nuclear gravity and super symmetry it is suggested that: charged $W$ boson is the super symmetric boson of top quark fermion and charged Higgs boson pair generates the neutralized $Z$ boson. Rest energy of Higgs charged boson is 45586 MeV. It is noticed that charged SUSY Higgs fermion, and nuclear charge radius play a crucial role in the emission of electron in Beta decay. Recently discovered neutral boson of rest energy 120 to 160 MeV seems to be composed of Higgs charged boson and W boson. Its obtained mass is 126 GeV}.
Category: Quantum Gravity and String Theory

Understanding the Particle Mass Spectrum (100 1860 Mev)

Authors: Robert L. Oldershaw
Comments: 16 Pages. comments welcome

The goal of the research presented below is to provide a basic and general first approximation explanation for the unique patterns of masses and stabilities found at the lower end of the subatomic particle mass spectrum, where the patterns are most restricted, unique and diagnostic. The Standard Model of particle physics has achieved limited success in this effort, but only by resorting to putting the hypothetical “quark” masses and numerous other parameters into the analysis “by hand”. This way of doing science is ad hoc “model-building”, at best, and possibly borders on Ptolemaic pseudo-science. Discrete Scale Relativity, on the other hand, may offer a more realistic potential for understanding how nature actually works in the Atomic Scale domain, and how the unique particle mass spectrum is the product of fundamental physics: General Relativity, Quantum Mechanics and Discrete Cosmological Self-Similarity.
Category: Quantum Gravity and String Theory

Nuclear Binding Energy in Strong Nuclear Gravity

Authors: U V Satya Seshavatharam, S Lakshminarayana
Comments: 26 Pages. Journal of Vectorial Relativity, JVR 6 (2011) 3 . (To be published online)

It is noticed that ratio of coulombic energy coefficient and proton rest energy is close to the product of fine structure ratio and the strong coupling constant. Strong coupling constant plays a crucial role in binding energy saturation. Based on strong nuclear gravity, semi empirical mass formula and with reference to the gravitational mass generator,$X_E \cong 295.0606338,$ an expression is proposed for neutron and proton rest masses at quantum numbers n =1 and 2. Nuclear binding energy can be fitted with 2 terms and one energy constant. For these 2 terms, coulombic energy constant $E_c \cong0.7681 $ MeV is applied. Another attempt is made to fit the nuclear binding energy with a product of 5 factors with 0.7681 MeV. At Z = 2 and A = 4 obtained binding energy is 28.8 MeV. For any Z error in binding energy is very small near the stable mass number and increasing above and below the stable mass number. In these two methods new nuclear stability factor $S_f \cong 157.025$ plays a crucial role in proton-neutron stability.
Category: Quantum Gravity and String Theory

Speculation on the Higg's

Authors: Paul Karl Hoiland
Comments: 2 Pages.

I take a look at the rumored Higg’s at 125 GeV and abstract a bit with a Non-Standard decay of a metastable vacuum state. In this model you end up with a Cold Dark Matter state that while appearing as the Neutralino, is actually more a decayed Higg’s resultant.
Category: Quantum Gravity and String Theory

The Simple Universe

Authors: Alireza Malekzadeh
Comments: 16 Pages, 13 Figures

This paper presents a unified theory for the universe which encompasses the dominant theories of physics. Our work is strictly based on the philosophy that the work of the universe is extremely simple in the fundamental level. We provide a minimal set of elements as the fundamental constituents of the universe, and demonstrate that all natural phenomena can be explained by a minimum number of laws governing these fundamental elements and their minimal set of properties.
Category: Quantum Gravity and String Theory

Are the Concepts of Mass in Quantum Theory and in General Relativity the Same?

Authors: Armin Nikkhah Shirazi
Comments: 5 Pages.

The predominant approaches to understanding how quantum theory and General Relativity are related to each other implicitly assume that both theories use the same concept of mass. Given that despite great efforts such approaches have not yet produced a consistent falsifiable quantum theory of gravity, this paper entertains the possibility that the concepts of mass in the two theories are in fact distinct. It points out that if the concept of mass in quantum mechanics is defined such that it always exists in a superposition and is not a gravitational source, then this sharply segregates the domains of quantum theory and of general relativity. This concept of mass violates the equivalence principle applied to active gravitational mass, but may still produce effects consistent with the equivalence principle when applied to passive gravitational mass (in agreement with observations) by the correspondence principle applied to a weak field in the appropriate limit. An experiment that successfully measures the gravity field of quantum objects in a superposition, and in particular of photons, would not only falsify this distinction but also constitute the first direct empirical test that gravity must in fact be described fundamentally by a quantum theory.
Category: Quantum Gravity and String Theory

U(1) X SU(2) X Su(3) Quantum Gravity Successes

Authors: Nige Cook
Comments: 63 Pages.

See paper for technical abstract. Paper covers checked predictions for a theory which modifies the Standard Model's electroweak group representations to include quantum gravity, replacing the Higgs mechanism with checkable predictions. The model correctly predicted the cosmological acceleration in 1996. Full references, analysis, and feedback from peer-reviewed string theory dominated journals is included.
Category: Quantum Gravity and String Theory

On the Zero Point Field

Authors: Paul Karl Hoiland
Comments: 5 Pages.

Via a look at the Ricci and Weyl curvature tensors I show that from a quantum perspective the Zero Point Field or ZPF is the origin of both inertia and gravity. I also point out that accelerated expansion of the cosmos and a observational slow down of C should have been expected.
Category: Quantum Gravity and String Theory

Inertia

Authors: Meir Amiram
Comments: 12 Pages.

I indicate that the key factor in the mechanism of inertia is the proximity of any elementary particle to itself, and consequently show that Newton laws of motion are derivatives of Newton's inverse square law of gravity. Inertia is originated in the microscopic realm, in the particle's diameter scale of reality, and is the response of an elementary particle to the gravitational field of itself, nothing more or less. Experimental evidences and several consequences of the discovery are discussed.
Category: Quantum Gravity and String Theory

Dark Matter, Dark Energy, and Elementary Particles and Forces

Authors: Thomas J. Buckholtz
Comments: 39 pages

Patterns link properties of six quarks and three leptons, the set of fundamental forces, and possible properties of dark matter and dark energy.
Category: Quantum Gravity and String Theory

Condensation States and Landscaping with the Theory of Abstraction

Authors: Subhajit Ganguly
Comments: 11 pages

The Abstraction theory is applied in landscaping. A collection of objects may be made to be vast or meager depending upon the scale of observations. This idea may be developed to unite the worlds of the great vastness of the universe and the minuteness of the sub-atomic realm. Keeping constant a scaling ratio for both worlds, these may actually be converted into two self-same representatives with respect to scaling. The Laws of Physical Transactions are made use of to study Bose-Einstein condensation. As the packing density of concerned constituents increase to a certain critical value, there may be evolution of energy from the system.
Category: Quantum Gravity and String Theory

Geometric Quantum Gravity

Authors: Antony Ryan
Comments: 37 pages

Naturally existing geometry that describes the Pre-Big Bang singularity is derived, reconciling the three paradoxes of cosmogony; infinite regression, causality and the conservation laws. The geometry unifies the forces of nature, explains the Arrow of Time, Baryon Asymmetry, Cosmic Inflation, Neutrino Oscillations and interprets Quantum Entanglement and the Double Slit Experiment by illustrating what spin and wave function collapse are. Further, it explains Dark Energy and Dark Matter, the mechanism of Black Hole formation from Neutron Stars, the origin and fate of the Universe, and why we have three spatial dimensions. The point where two equal spheres of any size touch is infinitesimally small, like a singularity. This is analogous to the Newton Number Problem (1), but without a central sphere. We get what I would describe as the Quantum Newton Number Problem, from which geometries for the 36 Standard Model Elementary particles are derived. Applying the Koide formula (2) to the Electron, Proton and Neutron masses, with simple logical adjustments taken from the geometry, predicts a 1/2 and obtains a 0.49999994 result. Further the geometry matches the quantum mechanical cosine predictions for entangled spin measurements perfectly. The theory is potentially testable too.
Category: Quantum Gravity and String Theory

Quantum Arithmetics and the Relationship Between Real and P-Adic Physics

Authors: Matti Pitkänen
Comments: 32 pages

p-Adic physics involves two only partially understood questions.

1. Is there a duality between real and p-adic physics? What is its precice mathematic formulation? In particular, what is the concrete map p-adic physics in long scales (in real sense) to real physics in short scales? Can one find a rigorous mathematical formulation of canonical identification induced by the map p→ 1/p in pinary expansion of p-adic number such that it is both continuous and respects symmetries.

2. What is the origin of the p-adic length scale hypothesis suggesting that primes near power of two are physically preferred? Why Mersenne primes are especially important?

A possible answer to these questions relies on the following ideas inspired by the model of Shnoll effect. The first piece of the puzzle is the notion of quantum arithmetics formulated in non-rigorous manner already in the model of Shnoll effect.

1. Quantum arithmetics is induced by the map of primes to quantum primes by the standard formula. Quantum integer is obtained by mapping the primes in the prime decomposition of integer to quantum primes. Quantum sum is induced by the ordinary sum by requiring that also sum commutes with the quantization.

2. The construction is especially interesting if the integer defining the quantum phase is prime. One can introduce the notion of quantum rational defined as series in powers of the preferred prime defining quantum phase. The coefficients of the series are quantum rationals for which neither numerator and denominator is divisible by the preferred prime.

3. p-Adic--real duality can be identified as the analog of canonical identification induced by the map p→ 1/p in the pinary expansion of quantum rational. This maps maps p-adic and real physics to each other and real long distances to short ones and vice versa. This map is especially interesting as a map defining cognitive representations.

Quantum arithmetics inspires the notion of quantum matrix group as counterpart of quantum group for which matrix elements are ordinary numbers. Quantum classical correspondence and the notion of finite measurement resolution realized at classical level in terms of discretization suggest that these two views about quantum groups are closely related. The preferred prime p defining the quantum matrix group is identified as p-adic prime and canonical identification p→ 1/p is group homomorphism so that symmetries are respected.

1. The quantum counterparts of special linear groups SL(n,F) exists always. For the covering group SL(2,C) of SO(3,1) this is the case so that 4-dimensional Minkowski space is in a very special position. For orthogonal, unitary, and orthogonal groups the quantum counterpart exists only if quantum arithmetics is characterized by a prime rather than general integer and when the number of powers of p for the generating elements of the quantum matrix group satisfies an upper bound characterizing the matrix group.

2. For the quantum counterparts of SO(3) (SU(2)/ SU(3)) the orthogonality conditions state that at least some multiples of the prime characterizing quantum arithmetics is sum of three (four/six) squares. For SO(3) this condition is strongest and satisfied for all integers, which are not of form n= 2^2r(8k+7)). The number r₃(n) of representations as sum of squares is known and r₃(n) is invariant under the scalings n→ 2^2rn. This means scaling by 2 for the integers appearing in the square sum representation.

3. r₃(n) is proportional to the so called class number function h(-n) telling how many non-equivalent decompositions algebraic integers have in the quadratic algebraic extension generated by (-n)^1/2.

The findings about quantum SO(3) suggest a possible explanation for p-adic length scale hypothesis and preferred p-adic primes.

1. The basic idea is that the quantum matrix group which is discrete is very large for preferred p-adic primes. If cognitive representations correspond to the representations of quantum matrix group, the representational capacity of cognitive representations is high and this kind of primes are survivors in the algebraic evolution leading to algebraic extensions with increasing dimension.

2. The preferred primes correspond to a large value of r₃(n). It is enough that some of their multiples do so (the 2^2r multiples of these do so automatically). Indeed, for Mersenne primes and integers one has r₃(n)=0, which was in conflict with the original expectations. For integers n=2M_m however r₃(n) is a local maximum at least for the small integers studied numerically.

3. The requirement that the notion of quantum integer applies also to algebraic integers in quadratic extensions of rationals requires that the preferred primes (p-adic primes) satisfy p=8k+7. Quite generally, for the integers n=2^2r(8k+7) not representable as sum of three integers the decomposition of ordinary integers to algebraic primes in the quadratic extensions defined by (-n)^1/2 is unique. Therefore also the corresponding quantum algebraic integers are unique for preferred ordinary prime if it is prime also in the algebraic extension. If this were not the case two different decompositions of one and same integer would be mapped to different quantum integers. Therefore the generalization of quantum arithmetics defined by any preferred ordinary prime, which does not split to a product of algebraic primes, is well-defined for p=2^2r(8k+7).

4. This argument was for quadratic extensions but also more complex extensions defined by higher polynomials exist. The allowed extensions should allow unique decomposition of integers to algebraic primes. The prime defining the quantum arithmetics should not decompose to algebraic primes. If the algebraic evolution leadis to algebraic extensions of increasing dimension it gradually selects preferred primes as survivors.

Is Kähler Action Expressible in Terms of Areas of Minimal Surfaces?

Authors: Matti Pitkänen
Comments: 5 pages

The general form of ansatz for preferred extremals implies that the Coulombic term in Kähler action vanishes so that it reduces to 3-dimensional surface terms in accordance with general coordinate invariance and holography. The weak form of electric-magnetic duality in turn reduces this term to Chern-Simons terms.

The strong form of General Coordinate Invariance implies effective 2-dimensionality (holding true in finite measurement resolution) so that also a strong form of holography emerges. The expectation is that Chern-Simons terms in turn reduces to 2-dimensional surface terms.

The only physically interesting possibility is that these 2-D surface terms correspond to areas for minimal surfaces defined by string world sheets and partonic 2-surfaces appearing in the solution ansatz for the preferred extremals. String world sheets would give to Kähler action an imaginary contribution having interpretation as Morse function. This contribution would be proportional to their total area and assignable with the Minkowskian regions of the space-time surface. Similar but real string world sheet contribution defining Kähler function comes from the Euclidian space-time regions and should be equal to the contribution of the partonic 2-surfaces. A natural conjecture is that the absolute values of all three areas are identical: this would realize duality between string world sheets and partonic 2-surfaces and duality between Euclidian and Minkowskian space-time regions.

Zero energy ontology combined with the TGD analog of large N_c expansion inspires an educated guess about the coefficient of the minimal surface terms and a beautiful connection with p-adic physics and with the notion of finite measurement resolution emerges. The t'Thooft coupling λ should be proportional to p-adic prime p characterizing particle. This means extremely fast convergence of the counterpart of large N_c expansion in TGD since it becomes completely analogous to the pinary expansion of the partition function in p-adic thermodynamics. Also the twistor description and its dual have a nice interpretation in terms of zero energy ontology. This duality permutes massive wormhole contacts which can have off mass shell with wormhole throats which are always massive (also for the internal lines of the generalized Feynman graphs).

An Attempt to Understand Preferred Extremals of Kähler Action

Authors: Matti Pitkänen
Comments: 23 pages

There are pressing motivations for understanding the preferred extremals of Kähler action. For instance, the conformal invariance of string models naturally generalizes to 4-D invariance defined by quantum Yangian of quantum affine algebra (Kac-Moody type algebra) characterized by two complex coordinates and therefore explaining naturally the effective 2-dimensionality. One problem is how to assign a complex coordinate with the string world sheet having Minkowskian signature of metric. One can hope that the understanding of preferred extremals could allow to identify two preferred complex coordinates whose existence is also suggested by number theoretical vision giving preferred role for the rational points of partonic 2-surfaces in preferred coordinates. The best one could hope is a general solution of field equations in accordance with the hints that TGD is integrable quantum theory.

A lot is is known about properties of preferred extremals and just by trying to integrate all this understanding, one might gain new visions. The problem is that all these arguments are heuristic and rely heavily on physical intuition. The following considerations relate to the space-time regions having Minkowskian signature of the induced metric. The attempt to generalize the construction also to Euclidian regions could be very rewarding. Only a humble attempt to combine various ideas to a more coherent picture is in question.

The core observations and visions are following.

1. Hamilton-Jacobi coordinates for M⁴ > define natural preferred coordinates for Minkowskian space-time sheet and might allow to identify string world sheets for X⁴ as those for M⁴. Hamilton-Jacobi coordinates consist of light-like coordinate m and its dual defining local 2-plane M²⊂ M⁴ and complex transversal complex coordinates (w,w*) for a plane E²_x orthogonal to M²_x at each point of M⁴. Clearly, hyper-complex analyticity and complex analyticity are in question.

2. Space-time sheets allow a slicing by string world sheets (partonic 2-surfaces) labelled by partonic 2-surfaces (string world sheets).

3. The quaternionic planes of octonion space containing preferred hyper-complex plane are labelled by CP₂, which might be called CP₂^mod. The identification CP₂=CP₂^mod motivates the notion of M⁸--M⁴× CP₂. It also inspires a concrete solution ansatz assuming the equivalence of two different identifications of the quaternionic tangent space of the space-time sheet and implying that string world sheets can be regarded as strings in the 6-D coset space G₂/SU(3). The group G₂ of octonion automorphisms has already earlier appeared in TGD framework.

4. The duality between partonic 2-surfaces and string world sheets in turn suggests that the CP₂=CP₂^mod conditions reduce to string model for partonic 2-surfaces in CP₂=SU(3)/U(2). String model in both cases could mean just hypercomplex/complex analyticity for the coordinates of the coset space as functions of hyper-complex/complex coordinate of string world sheet/partonic 2-surface.

The considerations of this section lead to a revival of an old very ambitious and very romantic number theoretic idea.

1. To begin with express octonions in the form o=q₁+Iq₂, where q_i is quaternion and I is an octonionic imaginary unit in the complement of fixed a quaternionic sub-space of octonions. Map preferred coordinates of H=M⁴× CP₂ to octonionic coordinate, form an arbitrary octonion analytic function having expansion with real Taylor or Laurent coefficients to avoid problems due to non-commutativity and non-associativity. Map the outcome to a point of H to get a map H→ H. This procedure is nothing but a generalization of Wick rotation to get an 8-D generalization of analytic map.

2. Identify the preferred extremals of Kähler action as surfaces obtained by requiring the vanishing of the imaginary part of an octonion analytic function. Partonic 2-surfaces and string world sheets would correspond to commutative sub-manifolds of the space-time surface and of imbedding space and would emerge naturally. The ends of braid strands at partonic 2-surface would naturally correspond to the poles of the octonion analytic functions. This would mean a huge generalization of conformal invariance of string models to octonionic conformal invariance and an exact solution of the field equations of TGD and presumably of quantum TGD itself.

The Master Formula for the U-Matrix Finally Found?

Authors: Matti Pitkänen
Comments: 12 pages

In zero energy ontology U-matrix replaces S-matrix as the fundamental object characterizing the predictions of the theory. U-matrix is defined between zero energy states and its orthogonal rows define what I call M-matrices, which are analogous to thermal S-matrices of thermal QFTs. M-matrix defines the time-like entanglement coefficients between positive and negative energy parts of the zero energy state. M-matrices identifiable as hermitian square roots of density matrices. In this article it is shown that M-matrices form in a natural manner a generalization of Kac-Moody type algebra acting as symmetries of M-matrices and U-matrix and that the space of zero energy states has therefore Lie algebra structure so that quantum states act as their own symmetries. The generators of this algebra are multilocal with respect to partonic 2-surfaces just as Yangian algebras are multilocal with respect to points of Minkowski space and therefore define generalization of the Yangian algebra appearing in the Grassmannian twistor approach to N=4 SUSY.
Category: Quantum Gravity and String Theory

Final Book on Fundamental Theoretical Physics

Authors: G. Quznetsov
Comments: Book, 174 pages

This book title is "Final Book on Fundamental Theoretical Physics" because it offers full logic explanation of all fundamental notions and statements of theoretical physics: Time and Space, Quantum Physics, Quarks and Gravitation.
Category: Quantum Gravity and String Theory

Lanczos-Lovelock and F ( R ) Gravity from Clifford Space Geometry

Authors: Carlos Castro
Comments: 15 Pages. Submitted to the Int. J. of Theor. Phys.

A rigorous construction of Clifford-space Gravity is presented which is compatible with the Clifford algebraic structure and permits the derivation of the generalized connections in Clifford spaces ( C-space) in terms of derivatives of the C-space metric. We continue by arguing how Lanczos-Lovelock higher curvature gravity can be embedded into gravity in Clifford spaces and suggest how this might also occur for extended gravitational theories based on f ( R ), f ( R_{\mu \nu} ), .... actions, for polynomial-valued functions. Black-strings and black-brane metric solutions in higher dimensions D > 4 play an important role in finding specific examples.
Category: Quantum Gravity and String Theory

Is Christian’s Parallelized 7-Sphere Model Essential for the Physical Interpretation of M-Theory?

Authors: David Brown
Comments: 8 Pages.

In 1991 with Abner Shimony as thesis advisor, J. Christian obtained his PhD in the foundations of quantum theory. As of 2012, he is affiliated with both Wolfson College of the University of Oxford and the Perimeter Institute in Waterloo, Ontario. From 2007 to 2012 Christian published some highly controversial work related to Bell’s theorem. Christian has proposed a parallelized 7-sphere model for a local, realistic theory that replaces quantum theory. This communication considers how his model might be relevant to a physical interpretation of M-theory. There is overwhelming empirical evidence in favor of the Rañada-Milgrom effect, at least as an approximation. Christian’s theory of local realism might be empirically valid if and only if the Rañada-Milgrom effect is empirically valid.
Category: Quantum Gravity and String Theory

Maxwell's Theory of Gravity and Thermodynamics

Authors: Mohammed Alzain Mohammed Ali
Comments: 7 Pages.

We argue that the entropic origin of gravitation correctly reproduced general relativity and quantum mechanics, with a particular treatment, where entropic gravity can be viewed as Maxwell's theory of gravity and thermodynamics. And this application will give us more detailed knowledge on the origin of gravity
Category: Quantum Gravity and String Theory

The Physics of Unification

Authors: Steven Howard Snyder
Comments: 128 Pages.

To date, a unification is needed with the application of Planck units which unifies not only the force of Newtonian gravity with the electromagnetic force and the strong and weak nuclear forces, but also one which includes quantum field theory and relativity. Herein, a unification as such is accomplished in which the mathematical terms of the conventional fields and the corresponding forces are unified into one general function in Planck units, and the geometry (including internal structure) and functionality of certain aspects of the respective unified field constructed therefrom are described. Accordingly, the geometry and functionality of the unified field are applied for describing certain aspects of electromagnetic, gravitational, and nuclear interaction along with certain aspects of elementary particles (including antiparticles), atoms, molecules, and at the macroscopic scale, astronomical bodies.
Category: Quantum Gravity and String Theory

God and His Creation: the Universe

Authors: A. Garcés Doz
Comments: 91 Pages. Improving the translation from Spanish to English. Added a new subsection. Fixed minor errors

In this paper we demonstrate how the universe has to be caused or created by an intelligent being: God. And as the multiverse theory, mainly based on the random generation of states infinite universe is very poorly posed from the mathematical point of view, and how this failure leads to the demonstration of its impossibility. The anthropic principle called not taken into account, it is a mere philosophical statement without any physical-mathematical foundation, and therefore lacking the minimum necessary scientific validity. The main parameters are obtained: density of baryons, vacuum energy density, mass of the lightest Higgs boson, neutrino mass, mass of the graviton, among others. Deducting finally naturally within the theory, the inflation factor of the universe. Similarly, the theory implies necessarily the "creation" of matter
Category: Quantum Gravity and String Theory

Accelerating Universe and the Expanding Atom-2

Authors: U.V. S. Seshavatharam, S. Lakshminarayana
Comments: 15 Pages.

In the cosmic Euclidean volume, inverse of the fine structure ratio is equal to the natural logarithm of ratio of number of (electrons or positrons) and the Avogadro number. Bohr radius of hydrogen atom, quanta of the angular momentum and the strong interaction range - are connected with the large scale structure of the massive universe. In the accelerating universe, as the space expands, in hydrogen atom, distance between proton and electron increases and is directly proportional to the size of the universe. Obtained value of the present Hubble constant is 70.75 Km/sec/Mpc. `Rate of decrease in fine structure ratio' is a measure of cosmic rate of expansion. Considering the integral nature of number of protons (of any nucleus), integral nature of `hbar' can be understood.
Category: Quantum Gravity and String Theory

The Unifying of the Forces of Nature

Authors: Bertrand Wong
Comments: 9 Pages. The conclusion of this paper contains a number of new and important points.

This paper takes a look at the formulating of the unified field theory and the theory of everything. It shows how a unified field theory and theory of everything may be obtained.
Category: Quantum Gravity and String Theory

Accelerating Universe and the Increasing Bohr Radius

Authors: U.V. S. Seshavatharam, S. Lakshminarayana
Comments: 11 Pages.

It seems that- Bohr radius of hydrogen atom, quanta of the angular momentum and the strong interaction range - are connected with the large scale structure of the massive universe. In the accelerating universe, as the space expands, in hydrogen atom, distance between proton and electron increases and is directly proportional to the mass of the universe (which is the product of critical density and the Hubble volume). `Rate of decrease in fine structure ratio' is a measure of cosmic rate of expansion. Considering the integral nature of number of protons (of any nucleus), integral nature of `hbar' can be understood.
Category: Quantum Gravity and String Theory

Virtual Event Horizons: is the Threshold Curvature that Corresponds to the Onset of the Uselessness of Mass-Energy for Work a Variable Measure?

Authors: S Halayka
Comments: 3 Pages. Added paragraph about energy scale and degrees of freedom.

The duality between entropy and curvature is discussed. The possibility of a gravity-mediated local UV cutoff is discussed.
Category: Quantum Gravity and String Theory

Virtual Event Horizons: is the Threshold Curvature that Corresponds to the Onset of the Uselessness of Mass-Energy for Work a Variable Measure?

Authors: Shawn Halayka
Comments: 3 Pages. Changed the title a little.

The duality between entropy and curvature is discussed. The possibility of a gravity-mediated local UV cutoff is discussed.
Category: Quantum Gravity and String Theory

Is the Threshold Curvature that Corresponds to the Onset of the Uselessness of Mass-Energy for Work a Variable Measure?

Authors: S Halayka
Comments: 3 Pages. Toned down the babble.

The duality between entropy and curvature is discussed. The possibility of a gravity-mediated local UV cutoff is discussed.
Category: Quantum Gravity and String Theory

Is the Threshold Curvature that Corresponds to the Onset of the Uselessness of Mass-Energy for Work a Variable Measure?

Authors: S Halayka
Comments: 2 Pages. Make a few implied things explicit.

A duality between entropy and curvature is discussed.
Category: Quantum Gravity and String Theory

Avogadro Number the 11 Dimensions Alternative

Authors: U.V. S. Seshavatharam, S. Lakshminarayana
Comments: 15 Pages. Role of Avogadro number in grand unification. Hadronic Journal. Vol-33, No 5, 2010 Oct. p513.

It is very clear that, to unify 2 interactions if 5 dimensions are required, for unifying 4 interactions 10 dimensions are required. For 3+1 dimensions if there exists 4 (observed) interactions, for 10 dimensions there may exist 10 (observable) interactions. To unify 10 interactions 20 dimensions are required. From this idea it can be suggested that- with `n' new dimensions `unification' problem can not be resolved. By implementing the gravitational constant in atomic and nuclear physics, independent of the CGS and SI units, Avogadro number can be obtained very easily and its order of magnitude is $\cong N \cong 6 \times 10^{23}$ but not $6 \times 10^{26}.$ If $M_P$ is the Planck mass and $m_e$ is the rest mass of electron, semi empirically it is observed that, $M_g \cong N^{\frac{2}{3}}\cdot \sqrt{M_Pm_e} \cong 1.0044118 \times 10^{-3} \; Kg.$ If $m_{p} $ is the rest mass of proton it is noticed that $\ln \sqrt{\frac{e^{2} }{4\pi \varepsilon _{0} Gm_{P}^{2} } } \cong \sqrt{\frac{m_{p} }{m_{e} } -\ln \left(N^{2} \right)}.$ Key conceptual link that connects the gravitational force and non-gravitational forces is - the classical force limit $\left(\frac{c^{4} }{G} \right)$. For mole number of particles, if strength of gravity is $\left(N.G\right),$ any one particle's weak force magnitude is $F_{W} \cong \frac{1}{N} \cdot \left(\frac{c^{4} }{N.G} \right)\cong \frac{c^{4} }{N^{2} G} $. Ratio of `classical force limit' and `weak force magnitude' is $N^{2} $. Assumed relation for strong force and weak force magnitudes is $\sqrt{\frac{F_{S} }{F_{W} } } \cong 2\pi \ln \left(N^{2} \right)$. From SUSY point of view, `integral charge quark fermion' and `integral charge quark boson' mass ratio is $\Psi=2.262218404$ but not unity. With these advanced concepts an ``alternative" to the `standard model' can be developed.
Category: Quantum Gravity and String Theory

Dark Matter, Dark Energy, and Elementary Particles and Forces

Authors: Thomas J. Buckholtz
Comments: 41 Pages.

Patterns link properties of six quarks and three leptons, the set of fundamental forces, and possible properties of dark matter and dark energy.
Category: Quantum Gravity and String Theory

Advancements Over a Geometrodynamical Model

Authors: Sandro Antonelli
Comments: 15 Pages.

This article is mainly conceived to gain more interest into a recent trustworthy development. The dynamics of the relativistic Space-Time structure, as discussed in the model, exhibits unforeseen analogies with the electromagnetic theory. As direct continuation of the analysis of the gravitational wave propagation in free space, one should realize (unlike Lorentz gauge in General Relativity) that the polarization state is mixture of six independent modes as many as the independent components of the Riemann tensor determining the tide forces, although one can always recover two polarizations for particular symmetry conditions on the direction of propagation and observation. Actually, in this gravitational framework, for one polarization state, transverse waves propagate causing equal in-phase deformation displacement, not counterphase as expected in gravitational interferometry experiments at present status. Calculation of gravitational power losses for the keplerian system PSR 1913+16 in the solution by approximations of inhomogeneous problem is worked out at first order, which allows the assessment of a new gravitational constant.
Category: Quantum Gravity and String Theory

Quantum Arithmetics and the Relationship Between Real and P-Adic Physics

Authors: Matti Pitkänen
Comments: 37 Pages.

p-Adic physics involves two only partially understood questions.

1. Is there a duality between real and p-adic physics? What is its precice mathematic formulation? In particular, what is the concrete map p-adic physics in long scales (in real sense) to real physics in short scales? Can one find a rigorous mathematical formulation of canonical identification induced by the map p→ 1/p in pinary expansion of p-adic number such that it is both continuous and respects symmetries.

2. What is the origin of the p-adic length scale hypothesis suggesting that primes near power of two are physically preferred? Why Mersenne primes are especially important?

A possible answer to these questions relies on the following ideas inspired by the model of Shnoll effect. The first piece of the puzzle is the notion of quantum arithmetics formulated in non-rigorous manner already in the model of Shnoll effect.

1. Quantum arithmetics is induced by the map of primes to quantum primes by the standard formula. Quantum integer is obtained by mapping the primes in the prime decomposition of integer to quantum primes. Quantum sum is induced by the ordinary sum by requiring that also sum commutes with the quantization.

2. The construction is especially interesting if the integer defining the quantum phase is prime. One can introduce the notion of quantum rational defined as series in powers of the preferred prime defining quantum phase. The coefficients of the series are quantum rationals for which neither numerator and denominator is divisible by the preferred prime.

3. p-Adic--real duality can be identified as the analog of canonical identification induced by the map p→ 1/p in the pinary expansion of quantum rational. This maps maps p-adic and real physics to each other and real long distances to short ones and vice versa. This map is especially interesting as a map defining cognitive representations.

Quantum arithmetics inspires the notion of quantum matrix group as counterpart of quantum group for which matrix elements are ordinary numbers. Quantum classical correspondence and the notion of finite measurement resolution realized at classical level in terms of discretization suggest that these two views about quantum groups are closely related. The preferred prime p defining the quantum matrix group is identified as p-adic prime and canonical identification p→ 1/p is group homomorphism so that symmetries are respected.

1. The quantum counterparts of special linear groups SL(n,F) exists always. For the covering group SL(2,C) of SO(3,1) this is the case so that 4-dimensional Minkowski space is in a very special position. For orthogonal, unitary, and orthogonal groups the quantum counterpart exists only if quantum arithmetics is characterized by a prime rather than general integer and when the number of powers of p for the generating elements of the quantum matrix group satisfies an upper bound characterizing the matrix group.

2. For the quantum counterparts of SO(3) (SU(2)/ SU(3)) the orthogonality conditions state that at least some multiples of the prime characterizing quantum arithmetics is sum of three (four/six) squares. For SO(3) this condition is strongest and satisfied for all integers, which are not of form n= 2^2r(8k+7)). The number r₃(n) of representations as sum of squares is known and r₃(n) is invariant under the scalings n→ 2^2rn. This means scaling by 2 for the integers appearing in the square sum representation.

3. r₃(n) is proportional to the so called class number function h(-n) telling how many non-equivalent decompositions algebraic integers have in the quadratic algebraic extension generated by (-n)^1/2.

The findings about quantum SO(3) suggest a possible explanation for p-adic length scale hypothesis and preferred p-adic primes.

1. The basic idea is that the quantum matrix group which is discrete is very large for preferred p-adic primes. If cognitive representations correspond to the representations of quantum matrix group, the representational capacity of cognitive representations is high and this kind of primes are survivors in the algebraic evolution leading to algebraic extensions with increasing dimension.

2. The preferred primes correspond to a large value of r₃(n). It is enough that some of their multiples do so (the 2^2r multiples of these do so automatically). Indeed, for Mersenne primes and integers one has r₃(n)=0, which was in conflict with the original expectations. For integers n=2M_m however r₃(n) is a local maximum at least for the small integers studied numerically.

3. The requirement that the notion of quantum integer applies also to algebraic integers in quadratic extensions of rationals requires that the preferred primes (p-adic primes) satisfy p=8k+7. Quite generally, for the integers n=2^2r(8k+7) not representable as sum of three integers the decomposition of ordinary integers to algebraic primes in the quadratic extensions defined by (-n)^1/2 is unique. Therefore also the corresponding quantum algebraic integers are unique for preferred ordinary prime if it is prime also in the algebraic extension. If this were not the case two different decompositions of one and same integer would be mapped to different quantum integers. Therefore the generalization of quantum arithmetics defined by any preferred ordinary prime, which does not split to a product of algebraic primes, is well-defined for p=2^2r(8k+7).

4. This argument was for quadratic extensions but also more complex extensions defined by higher polynomials exist. The allowed extensions should allow unique decomposition of integers to algebraic primes. The prime defining the quantum arithmetics should not decompose to algebraic primes. If the algebraic evolution leadis to algebraic extensions of increasing dimension it gradually selects preferred primes as survivors.

Quantum Arithmetics and the Relationship Between Real and P-Adic Physics

Authors: Matti Pitkänen
Comments: 33 Pages.

p-Adic physics involves two only partially understood questions.

1. Is there a duality between real and p-adic physics? What is its precice mathematic formulation? In particular, what is the concrete map p-adic physics in long scales (in real sense) to real physics in short scales? Can one find a rigorous mathematical formulation of canonical identification induced by the map p→ 1/p in pinary expansion of p-adic number such that it is both continuous and respects symmetries.

2. What is the origin of the p-adic length scale hypothesis suggesting that primes near power of two are physically preferred? Why Mersenne primes are especially important?

A possible answer to these questions relies on the following ideas inspired by the model of Shnoll effect. The first piece of the puzzle is the notion of quantum arithmetics formulated in non-rigorous manner already in the model of Shnoll effect.

1. Quantum arithmetics is induced by the map of primes to quantum primes by the standard formula. Quantum integer is obtained by mapping the primes in the prime decomposition of integer to quantum primes. Quantum sum is induced by the ordinary sum by requiring that also sum commutes with the quantization.

2. The construction is especially interesting if the integer defining the quantum phase is prime. One can introduce the notion of quantum rational defined as series in powers of the preferred prime defining quantum phase. The coefficients of the series are quantum rationals for which neither numerator and denominator is divisible by the preferred prime.

3. p-Adic--real duality can be identified as the analog of canonical identification induced by the map p→ 1/p in the pinary expansion of quantum rational. This maps maps p-adic and real physics to each other and real long distances to short ones and vice versa. This map is especially interesting as a map defining cognitive representations.

Quantum arithmetics inspires the notion of quantum matrix group as counterpart of quantum group for which matrix elements are ordinary numbers. Quantum classical correspondence and the notion of finite measurement resolution realized at classical level in terms of discretization suggest that these two views about quantum groups are closely related. The preferred prime p defining the quantum matrix group is identified as p-adic prime and canonical identification p→ 1/p is group homomorphism so that symmetries are respected.

1. The quantum counterparts of special linear groups SL(n,F) exists always. For the covering group SL(2,C) of SO(3,1) this is the case so that 4-dimensional Minkowski space is in a very special position. For orthogonal, unitary, and orthogonal groups the quantum counterpart exists only if quantum arithmetics is characterized by a prime rather than general integer and when the number of powers of p for the generating elements of the quantum matrix group satisfies an upper bound characterizing the matrix group.

2. For the quantum counterparts of SO(3) (SU(2)/ SU(3)) the orthogonality conditions state that at least some multiples of the prime characterizing quantum arithmetics is sum of three (four/six) squares. For SO(3) this condition is strongest and satisfied for all integers, which are not of form n= 2^2r(8k+7)). The number r₃(n) of representations as sum of squares is known and r₃(n) is invariant under the scalings n→ 2^2rn. This means scaling by 2 for the integers appearing in the square sum representation.

3. r₃(n) is proportional to the so called class number function h(-n) telling how many non-equivalent decompositions algebraic integers have in the quadratic algebraic extension generated by (-n)^1/2.

The findings about quantum SO(3) suggest a possible explanation for p-adic length scale hypothesis and preferred p-adic primes.

1. The basic idea is that the quantum matrix group which is discrete is very large for preferred p-adic primes. If cognitive representations correspond to the representations of quantum matrix group, the representational capacity of cognitive representations is high and this kind of primes are survivors in the algebraic evolution leading to algebraic extensions with increasing dimension.

2. The preferred primes correspond to a large value of r₃(n). It is enough that some of their multiples do so (the 2^2r multiples of these do so automatically). Indeed, for Mersenne primes and integers one has r₃(n)=0, which was in conflict with the original expectations. For integers n=2M_m however r₃(n) is a local maximum at least for the small integers studied numerically.

3. The requirement that the notion of quantum integer applies also to algebraic integers in quadratic extensions of rationals requires that the preferred primes (p-adic primes) satisfy p=8k+7. Quite generally, for the integers n=2^2r(8k+7) not representable as sum of three integers the decomposition of ordinary integers to algebraic primes in the quadratic extensions defined by (-n)^1/2 is unique. Therefore also the corresponding quantum algebraic integers are unique for preferred ordinary prime if it is prime also in the algebraic extension. If this were not the case two different decompositions of one and same integer would be mapped to different quantum integers. Therefore the generalization of quantum arithmetics defined by any preferred ordinary prime, which does not split to a product of algebraic primes, is well-defined for p=2^2r(8k+7).

4. This argument was for quadratic extensions but also more complex extensions defined by higher polynomials exist. The allowed extensions should allow unique decomposition of integers to algebraic primes. The prime defining the quantum arithmetics should not decompose to algebraic primes. If the algebraic evolution leadis to algebraic extensions of increasing dimension it gradually selects preferred primes as survivors.

Is Kähler Action Expressible in Terms of Areas of Minimal Surfaces?

Authors: Matti Pitkänen
Comments: 5 Pages.

The general form of ansatz for preferred extremals implies that the Coulombic term in Kähler action vanishes so that it reduces to 3-dimensional surface terms in accordance with general coordinate invariance and holography. The weak form of electric-magnetic duality in turn reduces this term to Chern-Simons terms.

The strong form of General Coordinate Invariance implies effective 2-dimensionality (holding true in finite measurement resolution) so that also a strong form of holography emerges. The expectation is that Chern-Simons terms in turn reduces to 2-dimensional surface terms.

The only physically interesting possibility is that these 2-D surface terms correspond to areas for minimal surfaces defined by string world sheets and partonic 2-surfaces appearing in the solution ansatz for the preferred extremals. String world sheets would give to Kähler action an imaginary contribution having interpretation as Morse function. This contribution would be proportional to their total area and assignable with the Minkowskian regions of the space-time surface. Similar but real string world sheet contribution defining Kähler function comes from the Euclidian space-time regions and should be equal to the contribution of the partonic 2-surfaces. A natural conjecture is that the absolute values of all three areas are identical: this would realize duality between string world sheets and partonic 2-surfaces and duality between Euclidian and Minkowskian space-time regions.

Zero energy ontology combined with the TGD analog of large N_c expansion inspires an educated guess about the coefficient of the minimal surface terms and a beautiful connection with p-adic physics and with the notion of finite measurement resolution emerges. The t'Thooft coupling λ should be proportional to p-adic prime p characterizing particle. This means extremely fast convergence of the counterpart of large N_c expansion in TGD since it becomes completely analogous to the pinary expansion of the partition function in p-adic thermodynamics. Also the twistor description and its dual have a nice interpretation in terms of zero energy ontology. This duality permutes massive wormhole contacts which can have off mass shell with wormhole throats which are always massive (also for the internal lines of the generalized Feynman graphs).

An Attempt to Understand Preferred Extremals of Kähler Action

Authors: Matti Pitkänen
Comments: 23 Pages.

There are pressing motivations for understanding the preferred extremals of Kähler action. For instance, the conformal invariance of string models naturally generalizes to 4-D invariance defined by quantum Yangian of quantum affine algebra (Kac-Moody type algebra) characterized by two complex coordinates and therefore explaining naturally the effective 2-dimensionality. One problem is how to assign a complex coordinate with the string world sheet having Minkowskian signature of metric. One can hope that the understanding of preferred extremals could allow to identify two preferred complex coordinates whose existence is also suggested by number theoretical vision giving preferred role for the rational points of partonic 2-surfaces in preferred coordinates. The best one could hope is a general solution of field equations in accordance with the hints that TGD is integrable quantum theory.

A lot is is known about properties of preferred extremals and just by trying to integrate all this understanding, one might gain new visions. The problem is that all these arguments are heuristic and rely heavily on physical intuition. The following considerations relate to the space-time regions having Minkowskian signature of the induced metric. The attempt to generalize the construction also to Euclidian regions could be very rewarding. Only a humble attempt to combine various ideas to a more coherent picture is in question.

The core observations and visions are following.

1. Hamilton-Jacobi coordinates for M⁴ > define natural preferred coordinates for Minkowskian space-time sheet and might allow to identify string world sheets for X⁴ as those for M⁴. Hamilton-Jacobi coordinates consist of light-like coordinate m and its dual defining local 2-plane M²⊂ M⁴ and complex transversal complex coordinates (w,w*) for a plane E²_x orthogonal to M²_x at each point of M⁴. Clearly, hyper-complex analyticity and complex analyticity are in question.

2. Space-time sheets allow a slicing by string world sheets (partonic 2-surfaces) labelled by partonic 2-surfaces (string world sheets).

3. The quaternionic planes of octonion space containing preferred hyper-complex plane are labelled by CP₂, which might be called CP₂^mod. The identification CP₂=CP₂^mod motivates the notion of M⁸--M⁴× CP₂. It also inspires a concrete solution ansatz assuming the equivalence of two different identifications of the quaternionic tangent space of the space-time sheet and implying that string world sheets can be regarded as strings in the 6-D coset space G₂/SU(3). The group G₂ of octonion automorphisms has already earlier appeared in TGD framework.

4. The duality between partonic 2-surfaces and string world sheets in turn suggests that the CP₂=CP₂^mod conditions reduce to string model for partonic 2-surfaces in CP₂=SU(3)/U(2). String model in both cases could mean just hypercomplex/complex analyticity for the coordinates of the coset space as functions of hyper-complex/complex coordinate of string world sheet/partonic 2-surface.

The considerations of this section lead to a revival of an old very ambitious and very romantic number theoretic idea.

1. To begin with express octonions in the form o=q₁+Iq₂, where q_i is quaternion and I is an octonionic imaginary unit in the complement of fixed a quaternionic sub-space of octonions. Map preferred coordinates of H=M⁴× CP₂ to octonionic coordinate, form an arbitrary octonion analytic function having expansion with real Taylor or Laurent coefficients to avoid problems due to non-commutativity and non-associativity. Map the outcome to a point of H to get a map H→ H. This procedure is nothing but a generalization of Wick rotation to get an 8-D generalization of analytic map.

2. Identify the preferred extremals of Kähler action as surfaces obtained by requiring the vanishing of the imaginary part of an octonion analytic function. Partonic 2-surfaces and string world sheets would correspond to commutative sub-manifolds of the space-time surface and of imbedding space and would emerge naturally. The ends of braid strands at partonic 2-surface would naturally correspond to the poles of the octonion analytic functions. This would mean a huge generalization of conformal invariance of string models to octonionic conformal invariance and an exact solution of the field equations of TGD and presumably of quantum TGD itself.

The Master Formula for the U-Matrix Finally Found?

Authors: Matti Pitkänen
Comments: 11 Pages.

In zero energy ontology U-matrix replaces S-matrix as the fundamental object characterizing the predictions of the theory. U-matrix is defined between zero energy states and its orthogonal rows define what I call M-matrices, which are analogous to thermal S-matrices of thermal QFTs. M-matrix defines the time-like entanglement coefficients between positive and negative energy parts of the zero energy state. M-matrices identifiable as hermitian square roots of density matrices. In this article it is shown that M-matrices form in a natural manner a generalization of Kac-Moody type algebra acting as symmetries of M-matrices and U-matrix and that the space of zero energy states has therefore Lie algebra structure so that quantum states act as their own symmetries. The generators of this algebra are multilocal with respect to partonic 2-surfaces just as Yangian algebras are multilocal with respect to points of Minkowski space and therefore define generalization of the Yangian algebra appearing in the Grassmannian twistor approach to N=4 SUSY.
Category: Quantum Gravity and String Theory

Final Book on Fundamental Theoretical Physics

Authors: Gunn Quznetsov
Comments: 180 Pages. Publ. American Research Press, Rehoboth (NM), 2011, ISBN 978-1-59973-172-8

This book title is "Final Book on Fundamental Theoretical Physics" because it offers full logic explanation of all fundamental notions and statements of theoretical physics: Time and Space, Quantum Physics, Quarks and Gravitation.
Category: Quantum Gravity and String Theory