All Submission Categories

On the Real Representations of the Poincare Group

Authors: Leonardo Pedro
Comments: 31 Pages.

The formulation of quantum mechanics with a complex Hilbert space is equivalent to a formulation with a real Hilbert space and particular density matrix and observables. We study the real representations of the Poincare group, motivated by the fact that the localization of complex unitary representations of the Poincare group is incompatible with causality, Poincare covariance and energy positivity. We review the map from the complex to the real irreducible representations—finite- dimensional or unitary—of a Lie group on a Hilbert space. Then we show that all the finite-dimensional real representations of the identity component of the Lorentz group are also representations of the parity, in contrast with many complex representations. We show that any localizable unitary representation of the Poincare group, compatible with Poincare covariance, verifies: 1) it is self-conjugate (regardless it is real or complex); 2) it is a direct sum of irreducible representations which are massive or massless with discrete helicity. 3) it respects causality; 4) it is an irreducible representation of the Poincare group (including parity) if and only if it is: a)real and b)massive with spin 1/2 or massless with helicity 1/2. Finally, the energy positivity problem is discussed in a many-particles context.
Category: Mathematical Physics

Extended Electron in Constant Electric Field .

Authors: Hoa van Nguyen
Comments: 19 Pages. 23 figures

This is a theory on the extended model of the electron (which is a version of the screened electron by vacuum polarization) . Part 1 : Determination of the net electric force Fe produced on the extended electron : Fe = F + F'. The effective electric charge Q then can be deduced from Fe : Fe = Q E . Fe and Q vary with velocity of the electron and tend to zero as v tends to c . Part 2 : Radiation process of the extended electron by electric forces . Appendix C : Radiation and absorption of light of the extended electron .
Category: Classical Physics

Exceptional Isomorphisms in the Qi Men Dun Jia Cosmic Board Model

Authors: John Frederick Sweeney
Comments: 6 Pages.

In math, especially within the Lie Algebra groups, there exist a small group of "exceptional isomorphisms" or "accidental isomorphisms." Following the lead of Swiss psychologist Carl Jung, the author does not accept the existence of "exceptional" or "accidental;" instead, these are merely phenomena which heretofore have not been explained satisfactorily by mathematical theory. However, articulation of the Qi Men Dun Jia Cosmic Board Model in a recent and forthcoming paper has helped to explain several of the exceptional isomorphisms.
Category: Algebra

The Projective Line as a Meridian

Authors: Kelly McKennon
Comments: 114 pages and 24 figures.

Descriptions of 1-dimensional projective space in terms of the cross ratio, in one-dimensional geometry as a projective line, in two-dimensional geometry as a circle, and in three-dimensional geometry as a regulus. A characterization of projective 3-space is given in terms of polarity. This paper differs from the original version by addition of a section showing that the circle is distinguished from other meridians by its compactness and the existence of exponential functions.
Category: Geometry

Chisholm-Caianiello-Fubini Identities for S=1 Barut-Muzinich-Williams Matrices

Authors: M. de G. Caldera Cabral, V. V. Dvoeglazov
Comments: 5 Pages. This the modernized version of a EF-UAZ FT-95-14 unpublished preprint of 1995 of the second author. The modifications are due to the Thesis of the first author.

The formulae of the relativistic products are found S=1 Barut-Muzinich-Williams matrices. They are analogs of the well-known Chisholm-Caianiello-Fubini identities. The obtained results can be useful in the higher-order calculations of the high-energy processes with S=1 particles in the framework of the 2(2S+1 Weinberg formalism, which recently attracted attention again. PACS numbers: 02.90.+p, 11.90.+t, 12.20.Ds
Category: High Energy Particle Physics

Self/anti-Self Charge Conjugate States in the Helicity Basis

Authors: V. V.Dvoeglazov
Comments: 4 Pages. Presented in the DGFM-SMF School. December 2012. Puerto Vallarta, Mexico.

We construct self/anti-self charge conjugate (Majorana-like) states for the (1/2,0)+(0,1/2)$ representation of the Lorentz group, and their analogs for higher spins within the quantum field theory. The problem of the basis rotations and that of the selection of phases in the Dirac-like and Majorana-like field operators are considered. The discrete symmetries properties (P, C, T) are studied. Particular attention has been paid to the question of (anti)commutation of the Charge conjugation operator and the Parity in the helicity basis. Dynamical equations have also been presented. In the (1/2,0)+(0,1/2) representation they obey the Dirac-like equation with eight components, which has been first introduced by Markov. Thus, the Fock space for corresponding quantum fields is doubled (as shown by Ziino). The chirality and the helicity (two concepts which are frequently confused in the literature) for Dirac and Majorana states have been discussed.
Category: Mathematical Physics

The Quantum Does not Reduce to Discrete Bits

Authors: Roger Schlafly
Comments: 10 Pages. Submitted to 2013 FQXi Essay Contest

There is no way to reduce physics to information theory. Matter is not just empty space with isolated bits of information. The quantum is not digital data, logic, probability, or information. There is a long history of trying to understand the ethereal mysteries of quantum mechanics by reduction to discrete information, as if the universe were a giant ghostly digital computer without the hardware. These attempts have failed, and should be seen as evasions of the central truths of quantum mechanics. In short, there is no it from bit.
Category: Quantum Physics

It, Bit, Object, Background

Authors: Armin Nikkhah Shirazi
Comments: 8 Pages. Submitted to 2013 FQXi essay contest, "It from bit or bit from it"

In recent years, the notion that information may be the basis for reality, rather than the other way around, has become more popular. Here we consider the issue within the context of a general relation between the role of physical objects against the background in shaping the pattern of distinctions that can then be translated into information. It is found that from this perspective, in classical physics substance is more fundamental than information, while in general relativity they are on an equal footing. Quantum superposition and collapse, on the other hand, introduce new considerations. A foundational principle is introduced to give an explanation for quantum superposition, and from this principle it becomes evident that to the extent that one frames the nature of quantum objects in terms of this dichotomy, in quantum theory information is more fundamental. This implies that the description of quantum objects in a superposition is dependent on features of the background, as these features set boundary conditions on such manifestations. Thus, if this principle really does underlie quantum mechanics, it means that the term "background independent quantum theory" has to be considered a contradiction, which has implications for the search for a quantum theory of gravity.
Category: Quantum Gravity and String Theory

Existence is Difference and is Expressed and Transformed by Information

Authors: Ioannis Hadjidakis
Comments: 9 Pages.

Humans perceive their environment by their senses. The sensitivities of the relevant organs differ for each person and so an individual profile of conceptual senses is formed. This difference of our “inputs” is another factor that deviates our reality according to our sensual organs’ ability. Finally, our conceptual reality is mainly related to the information that reaches us and which is dependent on our position in spacetime. The spacetime position of a physical entity is the data required in order to define any influence of the environment on it. The knowledge of the environment however is a prerequisite that can never be fulfilled. In addition to everything else, environment is also dependent on the entity under examination. This is why Universe reacts as an inseparable system and why reductionism (separable systems) is not the proper method for its study. In this essay we try to explain the findings we get by applying simple ideas to the Natural Coordination System (NCS) we have proposed for the examination of Nature.
Category: Relativity and Cosmology

Reality and Information: It and Bit

Authors: Salvish Goomanee
Comments: 7 Pages.

The present understanding of the relation between reality and information theory is for the time being rather vague. There are many speculations about the fact that the understanding of reality may be beyond our capabilities. However the perception of our observed reality in relation to quantum physics and consciousness as per Wheeler’s theories may lead to the exploration of some new branches of quantum physics and consciousness theory. For many physicists, this may be something rather troubling but what if non – computability was actually part of reality? What if there were some processes or some kind of information that cannot be understood through algorithms and needed new understanding. In this essay the relation between information, reality and consciousness will be briefly discussed.
Category: General Science and Philosophy

What a Wavefunction is

Authors: Chidi Idika
Comments: 12 Pages. Submitted to the FQXi essay contest 2013, an abridged version of a three-part paper

Quantum theory treats rigorously of observables while the term “observer” is hardly itself a rigorous notion. We argue that the uncertainty principle must be understood in the Gödel sense that: any given observer constitutes own practical definition of “the unobservable” (if superposition) or namely length scale, phase space, fundamental frequency etc. Conversely, the observable is definable strictly only in inverse-observer values as, that is, the “wave function collapse” or respectively, inverse-length, phase-point, harmonics. One has thus a picture of the observer that in being participant is also non-local as in Gödel’s “consistency-is-undecidable” or Planck’s “the-constant-is-the-uncertainty” or indeed Einstein’s “speed-of-light-is-information-speed-limit”. Definitive of these three cases, we assert, is Peano’s (and Noether’s?) notion of the constant (our “observer”) as being for any gamut of events the meta-state (“conserved current”). Meaning now, it is the observer per se, and not his observables, which should constitute violation of Bell’s inequality—say, as the infinitesimal/imaginary axis or as the dimensionless/infinite-dimensional etc. We posit: any given observer signifies the virtual exchange of standard model or space-time of GR or just the metric (norm)—defined by the singular trait that it is the de facto “superposition” i.e. natural unit and natural limit of physical information. Observables emerge quite directly thus as the perturbations if “decoherence” or “spontaneous symmetry breaking” of the observer. Now this status of/or the observer we call rather the entity as against hitherto the uncertainty; difference is that we have an ontic as the uncertainty per se. For a prediction we show here an exact value demonstrating man as the entity or “natural unit” for quantum gravity. The idea is that in being to ourselves the most authentic sample of the term observer we should also represent to ourselves the purest sample possible of the term wave function.
Category: Quantum Gravity and String Theory

Mapping the 10B, 9Be, 10Be, 11B, 11C, 12C and 14N Binding Energies with High Precision based Exclusively on the Up and Down Quark Masses

Authors: Jay R. Yablon
Comments: 10 Pages.

We extend the results of two recent letters by expressing the 10B, 9Be, 10Be, 11B, 11C, 12C and 14N binding energies, each independently and each to about parts-per-million or small parts-per-100,000 accuracy in AMU, exclusively as a function of the up and down current quark masses.
Category: Nuclear and Atomic Physics

Spacetime Dipole Waves Pressure and Elemental Particles.

Authors: Policarpo Y. Ulianov
Comments: 14 Pages.

This paper is based on John A. Macken proposal that the universe is only spacetime, and in the dipole waves defined by Macken in context of Quantum Mechanics, that can be seen as a sea of energetic waves, traveling at light speed. From this model the pressure in dipole waves is analyzed in context of kinetic theory of gases. The dipole waves pressure model are used to define a fundamental particle named Ulianov Hole (uhole). One uhole can be associated with an elastic tube that connects two regions of space (or time), generating variations in the dipole wave pressure. Two kinds of uholes are presented, the spatial uhole (uhole-S) that have a property related to the mass, and a time uhole (uhole-T) that have a property related to electric charge. When the Uhole-S is stretched enough, so that the other uhole end (formed by antimatter) is sufficiently distant to avoid an annihilation process, a mass particle will be formed. This paper present a basic analyzes where some mass proprieties are derivate from the dipole wave pressure model proposed by de author, based in the Macken dipole wave model.
Category: High Energy Particle Physics

E8, The Na Yin and the Central Palace of Qi Men Dun Jia

Authors: John Frederick Sweeney
Comments: 21 Pages.

The ancient Chinese divination method called Qi Men Dun Jia is mathematically based on the Clifford Clock, which is a ring of Clifford Algebras related through the Bott Periodicity Theorem. On top of this lies the icosahedra or A5 with its sixty or one hundred twenty elements. A5 in the model functions to account for Time, as well as the Five Elements and the Na Jia, additional elements of Chinese metaphysics used in divination. This icosahedra is composed of three Golden Rectangles. The Golden Rectangles are related to three Fano Planes and the octonions, which are in turn related to the Golden Section. This provides the basis for the Lie Algebra and lattice of E8, again with its own Golden Section properties.
Category: Topology

Radio Waves – Part III: The Photoelectric Effect

Authors: Ionel Dinu, M.Sc.
Comments: 31 Pages. contact details updated

In Part I of this series on Radio Waves I have tried to prove that Maxwell’s theory of electromagnetic waves, claiming that a radio wave travelling in vacuum consists of oscillating electric and magnetic fields mutually inducing one another, is not supported by experiments, being based on assumptions and mathematical manipulations, and is therefore untenable because electric fields cannot exist in vacuum where there are no electric charges to produce them and because experiments have yet to prove that electric fields can be produced in vacuum by changing magnetic fields. In Part II I have expressed the view that light and radio waves are waves in the aether, magnetic in nature, not containing electric waves, being described by the magnetic vector potential A, which corresponds to the velocity v of the flowing aether. In this article I show that the views expressed above give a consistent explanation of the photoelectric effect. I will outline how do the experimental observations of the photoelectric effect summarized in the equation hf = mv2/2 + W, suggest that the photoelectric effect is a Faraday effect of electromagnetic induction. This is significant because, to the best of my knowledge, such an explanation of the photoelectric effect has not been advanced before, and because it proposes a mechanism by which the energy of a light wave is transferred to an electron without being necessary to introduce the hypothesis that light is composed of particles called photons.
Category: Classical Physics

Dark Matter UFO Dust Particles or Quantum Knots in the LHC at CERN ?

Authors: Leo Vuyk
Comments: 21 Pages. 21

Quantum FFF ( Function Follows Form) theory states, that the vacuum is seeded with fast oscillating massless dual Higgs particles, coined Dark Energy of 126 GeV. recently found by the LHC at CERN. Now I try to describe the similarities between the characteristics of energetic Quantum Knots found inside Silicon discharge experiments in the laboratory and so called UFOs (Unidentified Falling Objects) described as “Dust particles” created “somehow” alongside the accelerated proton beam of the LHC, causing beam disruption and automatic beam dumps.
Category: Quantum Physics

The Theory of Relativity and Compressibility Ether

Authors: Hu Chang-Wei
Comments: 12 Pages.

Relativistic and absolute space-time theories are two different space-time theories in nature.
Category: Relativity and Cosmology

Relativistic Problems in the Unitary Quantum View of the World

Authors: Leo G. Sapogin, V. A. Dzhanibekov, Yu. A. Ryabov
Comments: 35 Pages.

The present article discuses the problems of new unitary quantum view of the world in its applications to the different aspects of the reality. There are spectacular examples of the new Unitary Quantum world view considered in the applications for different aspects of reality.
Category: Relativity and Cosmology

New Electromagnetic Phenomenon and the Way it Was Predicted

Authors: Alvydas Jakeliunas
Comments: 5 Pages.

Here I will present electromagnetic phenomenon which can not be explained by known theories. However this phenomenon was found not accidentally. It was predicted by viewpoint very different to modern physics.
Category: Classical Physics

Information Hiding and Modula

Authors: José Francisco García Juliá
Comments: 2 Pages.

The information hiding principle can be applied completely using the Modula language.
Category: Data Structures and Algorithms

Mechanisms of Interaction Between Gravitational Waves.

Authors: Ernesto Lopez Gonzalez
Comments: 6 pages, in spanish

Background: In a previous work ("Matter as gravitational waves." 2012) it was set out that matter could be considered to be formed by gravitational pulsations in a hexadimensional space with anisotropic curvature, since solutions to Einstein's field equations presented many of the characteristics of a particle then. However no way that would allow the interaction between waves was provided. Results: It is shown that standing waves change propagation medium through three non-linear mechanisms: by changing the refractive index, deforming and dragging on propagation medium. Mechanical analogies of all these effects have been provided and later they have been related to Schwarzschild and Kerr metrics. As a demonstration of these ideas particle-pulse's acceleration is calculated for the "weak gravitational fields" case. The solution agrees with Newton's theory. Finally a new interpretation of Michelson-Morley experiment is provided.
Category: Relativity and Cosmology

The Classical Theory of Light Colors: a Paradigm for Description of Particle Interactions

Authors: Nicolae Mazilu; Maricel Agop
Comments: 21 Pages.

The color is an interaction property: of the interaction of light with matter. Classically speaking it is therefore akin to the forces. But while forces engendered the mechanical view of the world, the colors generated the optical view. One of the modern concepts of interaction between the fundamental particles of matter – the quantum chromodynamics – aims to fill the gap between mechanics and optics, in a specific description of strong interactions. We show here that this modern description of the particle interactions has ties with both the classical and quantum theories of light, regardless of the connection between forces and colors. In a word, the light is a universal model in the description of matter. The description involves classical Yang-Mills fields related to color.
Category: High Energy Particle Physics

A 15-Page Collection of Notes on my Mathematical Articles

Authors: Andrew Nassif
Comments: 15 Pages. Resubmitted, please see second PDF for better formatting

This is a collection of some of my notes in mathematical physics and Quantum Field Theory. This also includes the P vs. NP computational proof, the Zeta Function Data graphed, Notes on some common topics in Mathematics and Mathematical Physics, and Computational Mathematics as well as Three Dimensional Data Graphing.
Category: Mathematical Physics

The Search for Yang-Mills Magnetic Monopoles: Might they Actually be Hiding in Plain Sight as Protons And Neutrons?

Authors: Jay R. Yablon
Comments: 64 Pages.

These are lecture slides summarizing the author's four recent published papers advancing the thesis that baryons including protons and neutrons are the magnetic monopoles of non-commuting Yang-Mills gauge theory. These slides should enable the reader to assimilate the primary material in these four papers relatively rapidly. Specifically, these slides review support for the following results: 1) Protons and neutrons are “resonant cavities” with binding energies determined strictly by the masses of the quarks they contain. This is proven true at parts-per million accuracy for each of the 2H, 3H,3He, 4He binding energies and the neutron minus proton mass difference. 2) Respectively, each free proton and neutron contains 7.64 MeV and 9.81 MeV of mass/energy used to confine its quarks. When these nucleons bind, some, never all, of this energy is released and the mass deficit goes into binding. The balance continues to confine quarks. 56Fe releases 99.8429% of this energy for binding, more than any other nuclide. 3) Once we consider the Fermi vev one also finds an entirely theoretical explanation of proton and neutron masses, which also connects within experimental errors to the CKM quark mixing angles. 4) A related GUT explains fermion generation replication based on generator loss during symmetry breaking, and answers Rabi’s question “who ordered this?” 5) Nuclear physics is governed by combining Maxwell’s two classical equations into one equation using non-commuting gauge fields in view of Dirac theory and Fermi-Dirac-Pauli Exclusion. 6) Atoms themselves are core magnetic charges (nucleons) paired with orbital electric charges (electrons and elusive neutrinos), with the periodic table itself revealing an electric/magnetic symmetry of Maxwell’s equations often pondered but heretofore unrecognized for a century and a half.
Category: High Energy Particle Physics

Fitting the 6Li, 7Li, 7Be and 8Be Binding Energies to High Precision based Exclusively on the Up and Down Quark Masses

Authors: Jay R. Yablon
Comments: 12 Pages.

We extend the results of an earlier recent letter by expressing the 6Li, 7Li, 7Be and 8Be binding energies, each independently and each to about parts-per-million or small parts-per-100,000 accuracy, exclusively as a function of the up and down current quark masses.
Category: Nuclear and Atomic Physics

On the Gravitational Mass

Authors: D. G. Kiryan, G. V. Kiryan
Comments: 16 Pages. english

The paper presents a natural definition of gravitational mass without invoking new entities. The approach suggested expands the application field of the law of gravitational interaction between material objects located in a gravitating medium. The paper demonstrates the existence of a functional relationship between the inertial and gravitational masses, which has brought us to a conclusion that the condition under which the inertial and gravitational masses would be equal is rather speculative and not practically realizable. We give here real examples of existence of the negative gravitational mass, as well as natural cases of the gravitational repulsion. Some cases of gravitational dipole as a physical object existing in our natural environment are also presented.
Category: Classical Physics

Relation Between Medieval Renaissance and Today's Open Knowledge Dissemination

Authors: Subhajit Ganguly
Comments: 2 Pages.

Time has shown us how zero control by a handful of individuals over the society and complete control of the community, as a whole, over itself brings about positive changes. Less the control by individuals or groups and more the control of the complete set of individuals, more is the positive change. The history of the printing press is a case in point. While history made a mockery of the control-freaks, it proved right the few individuals, who believed in the intellectual capacity of the masses. Intellectual Nazism should be a thing of the past and we should move away from such self-defeating practices.
Category: History and Philosophy of Physics

Fitting the 2H, 3H, 3He, 4He Binding Energies and the Neutron minus Proton Mass Difference to Parts-Per-Million based Exclusively on the Up and Down Quark Masses

Authors: Jay R. Yablon
Comments: 10 Pages.

We report a method for expressing the 2H, 3H, 3He and 4He binding energies and the neutron minus proton mass difference, each independently and each to about parts-per-million accuracy, exclusively as a function of the up and down current quark masses. In the process, the precision with which these quark masses are predicted is improved by a factor of at least six orders of magnitude beyond the best presently-known data.
Category: Nuclear and Atomic Physics

Unsolved Problems in Special and General Relativity

Authors: Florentin Smarandache (Chief Editor), Fu Yuhua, Zhao Fengjuan (Vice-Chief Editors)
Comments: Pages.

This book includes 21 papers written by 23 authors and co-authors: Hua Di, Li Zifeng, Li Wen-Xiu, Shi Yong-Cheng, Xu Jianmin, Dong Jingfeng, Duan Zhongxiao, Fu Yuhua, Guo Kaizhe, Guo Chongwu, Guo Ying-Huan, Guo Zhen-Hua, Hu Chang-Wei, Jiang Chun-Xuan, Liu Taixiang, Tu Runsheng, Wu Fengming, Yang Shijia, Cao Shenglin, Leo G. Sapogin, V. A. Dzhanibekov, Yu. A. Ryabov, and Florentin Smarandache. The editors hope that all these papers will contribute to the advance of scholarly research on several aspects of Special and General Relativity. This book is suitable for students and scholars interested in studies of physics.
Category: Relativity and Cosmology

Sharp Numerical Coincidences (And the Death of Dark Matter)

Authors: Leonardo Rubino
Comments: 18 Pages.

The anomaly in the rotation curves for galaxies (excess of speed) is not due to any mysterious dark matter, but rather to the tidal effect of the Universe all around the galaxies themselves. Here is the proof.
Category: Astrophysics

Electron Hydro Electric Generator

Authors: Alexander Bolonkin
Comments: 8 Pages. 3 figs

Author offers a new method of getting electric energy from moving water. A special injector injects electrons into water. Water stream picks up the electrons and moves them in the direction of stream which is against the direction of electric field. At some distance from injector a unique grid acquires the electrons, thus charging and producing electricity. This method does not require, as does other water energy devices, strong dams, water turbines, or electric generators. The proposed water installation is very cheap. The area of water braking may be large and produces a great deal of energy. This electron water installation may be in river or ocean stream (as Gulf Stream).
Category: Classical Physics

Electron Super Speed Hydro Propulsion

Authors: Alexander Bolonkin
Comments: 7 Pages. 4 figs

High speed submarines and in particular torpedoes need new propulsion systems which allow the submarine to reach high speeds by cheaper and more efficient methods. Author offers a new propulsion system using electrons for acceleration of the water and having a high efficiency. As this system does not use a water propeller, it does not have the cavitation limitations of conventional water propeller systems. Offered engine can produce a thrust from a zero speed up to high speed. It can work in any liquid planet atmosphere. The system can use apparatus surface for thrust and braking. For energy the system uses high voltage electricity which is not a problem if you have an appropriate electrostatic generator connected with any suitable engine.
Category: Classical Physics

Can CDW Physics Explain Ultra Fast Transitions, and Current Vs. Applied Electric Field Values Seen in the Laboratory?

Authors: A.W. Beckwith
Comments: 4 Pages. additional re do of part of my PhD dissertation

The tunneling Hamiltonian is a proven method to treat particle tunneling between different states represented as wavefunctions in many-body physics. Our problem is how to apply a wave functional formulation of tunneling Hamiltonians to a driven sine-Gordon system. We apply a generalization of the tunneling Hamiltonian to charge density wave (CDW) transport problems in which we consider tunneling between states that are wavefunctionals of a scalar quantum field. We present derived I-E curves that match Zenier curves used to fit data experimentally with wavefunctionals congruent with the false vacuum hypothesis. The open question is whether the coefficients picked in both the wavefunctionals and the magnitude of the coefficients of the driven sine Gordon physical system should be picked by topological charge arguments that in principle appear to assign values that have a tie in with the false vacuum hypothesis first presented by Sidney Coleman. Our supposition is that indeed this is useful and that the topological arguments give evidence as to a first order phase transition which gives credence to the observed and calculated I-E curve as evidence
Category: Condensed Matter

Log N Algorithm for Search from Unstructured List

Authors: Dhananjay P. Mehendale
Comments: 4 pages. Sorting algorithm is added.

The unstructured search problem asks for search of some predefined number, called target, from given unstructured list of numbers. In this paper we propose a novel classical algorithm with complexity ~O(Log N) for searching the target from unstructured list of numbers. We propose a new algorithm, which achieves improvement of exponential order over existing algorithms. Suppose N is the largest number in the list then we consider N dimensional vector space with Euclidean basis. With each of the numbers in the given unstructured list we associate the unique basis vector among the vectors that form together the Euclidean basis. For example suppose j is a number in the list then we associate with this number j the unique basis vector in the above mentioned N-dimensional vector space, namely, |j> = transpose(0, 0, 0, … , 0, 0, 1, 0, 0, … , 0, 0, 0), where the there is entry 1 only at j-th place and every where else there is entry 0. We then divide the given list of numbers in two roughly equal parts (i.e. we divide the given bag containing scrambled numbers in two roughly equal parts and put them in two separate bags, Bag 1 and Bag 2). We represent the list of numbers in Bag 1, Bag 2 in the form of equally weighted superposition of basis vectors associated with the numbers contained in these bags, namely, we represent list in Bag 1 (Bag 2) as a single state formed by equally weighted superposition using orthonormal states forming Euclidean basis corresponding to numbers in the bag B1 (bag B2), namely, |Psi-1> (|Psi-2>). Let t be the target number. It will be represented as |t>. We then find the value of scalar product of target state |t> with |Psi-1> (or Psi-2>). It will revel us whether t belongs to Bag 1 (or Bag 2) which essentially enables us to carry out the binary search and to achieve above mentioned ~O(Log N) complexity!Also, representing list as superposition provides sorting of numbers instantly! One needs to read vector from left to right and prepare the desired sorted list!
Category: Data Structures and Algorithms

Mathematical Proof of Four Color Theorem

Authors: Liu Ran
Comments: 38 Pages.

The method and basic theory are far from traditional graph theory. Maybe they are the key factor of success. K4 regions (every region is adjacent to other 3 regions) are the max adjacent relationship, four-color theorem is true because more than 4 regions, there must be a non-adjacent region existing. Non-adjacent regions can be color by the same color and decrease color consumption. Another important three-color theorem is that the border of regions can be colored by 3 colors. Every region has at least 2 optional colors, which can be permuted.
Category: Topology

Aether Theory with Experimental Verification

Authors: Branislav Pavlovic
Comments: Book is in Serbian. 234 pages.Standard Copyright Licence

In this book I present the main results of my scientific work. My theory is based on the hypothesis of the existence of aether. In my work, I have devoted great attention not only to theoretical considerations but also to the explanation of experiments. I will mention just a few experiments (effects) which I have explained from the standpoint of my aether theory: the Michelson-Morley experiment, the Fizeau experiment, the aberration of light, the Ives-Stilwell experiment, the temperature dependent Pound-Rebka experiment, the Sagnac effect, and so on. Certain anomalies in the GPS system have been analyzed. The Pioneer anomaly has been analysed. 
Category: Relativity and Cosmology

Dual Structures in Cube Nets Disclosed

Authors: Klaus Lange
Comments: 6 Pages. 8 figures

It will be shown how the well known eleven nets for three dimensional cubes, separated in 10 + 1 forms, are hiding a special dual 3-6-1-structure. Implications for space - time models in theoretical physics will be questioned.
Category: Geometry

Energy Conservation Violation by Modulation of Coherent States

Authors: Thomas Alexander Meyer
Comments: 3 Pages.

We present a generalized account of how one might achieve energy conservation violation with quantum coherence effects. The general setup involves a violation of energy conservation by means of a change to the preparation of a coherent quantum mechanical effect which causes a change to the probability distribution of the measurable statistics of an observable. We also present a simple theoretical account of why there is a violation of conservation occurring in this setup.
Category: Quantum Physics

Die Kunst des Wedelns (The Art of Wag) - in German

Authors: Florentin Smarandache, Victor Christianto, Bernd Hutschenreuther
Comments: 18 Pages. This book is a German translation of The Art of Wag book

Wahrscheinlich eines der weltweit bekanntesten Bücher über Strategie ist Sun Tsus „Die Kunst des Krieges“. Es gibt bereits zahlreiche an verschiedenste moderne Aspekte des Managements und andere Themen angepasste Adaptionen dieses Buches. Wir wollen hier nicht diese „neuen“ Kopien wiederholen, sondern haben lieber eine neue Satire geschrieben.
Category: General Science and Philosophy

On the Possibility of N-Topological Spaces

Authors: Kamran Alam Khan
Comments: 4 Pages. Published in International Journal of Mathematical Archive (IJMA)

The notion of a bitopological space as a triple (X,I_1,I_2), where X is a set and I_1and I_2are topologies on X, was first formulated by J.C.Kelly [5]. In this paper our aim is to introduce and study the notion of an N-topological space (X,I_1,I_2,………I_N). We first generalize the notion of an ordinary metric to n variables. This metric will be called K-metric. Then the notion of a quasi-pseudo-K-metric will be introduced. We then follow the approach of Kelly to introduce and study the notion of an N-topological space. An example for such a space is produced using chain topology. And finally we define and study some of the possible separation properties for N-topological spaces.
Category: Topology

A Review of the ZWM Study; What Destroys the Interference?

Authors: Thomas Alexander Meyer
Comments: 9 Pages.

In 1991-1992 three papers were published by the same authors referred to as the ZWM study concerning the subject of induced coherence in photon downconversion. We present a review of these papers which all concern the same experimental arrangement. The central conclusion made by the authors is that interference is destroyed by the in principle knowability of path, that path indistinguishability is fundamental to interference effects. We review these papers with an emphasis on validating this conclusion and attempting to understand the action that is taken in the preparation of the “idler” photon and the subsequent affect that this action has on the interference visibility of the entangled “signal” photon.
Category: Quantum Physics

Unveiling the Conflict of the Speed of Light Postulate: Outlined Mathematical Refutation of the Special Relativity

Authors: Radwan M. Kassir
Comments: 9 pages, 2 figs., PDFLaTeX―[v2-v3]: general editing―[v4]: revised eqs. p.7―[v5]: modified eq. (36)―[v6]: + (discussion notes) pp.6-7―[v7]: amended discussion pp. 2-3―[v8]: revised S. 3.1.1 & S. 4.0

This paper reveals the mathematical contradictory aspects of Einstein’s speed of light postulate and the Lorentz transformation (LT) equations. Essential analyses of the equations, leading to the intelligible refutation of the mathematical foundation of the Special Relativity Theory (SRT), are emphasized in an outlined structure.
Category: Relativity and Cosmology

EPR Paradox Solved by Special Theory of Relativity

Authors: Justin Lee
Comments: 7 Pages.

This paper uses the special theory of relativity (SR) to introduce a novel solution to Einstein-Podolsky-Rosen (EPR) paradox. More specifically, the faster-than-light (FTL) communication is described to explain two types of EPR paradox experiments: photon polarization and electronpositron pair spins. And most importantly, this paper explains why this FTL communication does not violate the SR.
Category: Quantum Physics

Natural Science Education in Germany in 2012 after the 1999 European Bologna Reforms

Authors: Eckhard Hitzer
Comments: 4 Pages. 7 figures. Iin R. Nagaoka (ed.), Proceedings of the Meiji University Symposium on Mathematical Education 2012, Meiji University, Tokyo, 17-18 March 2012, pp. 51-54.

High school teacher education - Education of University Teachers - Research at German Universities - The new structure of university degrees in Germany after the Bologna reforms - The new Bachelor degree - The new Master degree - Acknowledgments - Further literature.
Category: Education and Didactics

The Bottom of Mathematics Education

Authors: Eckhard Hitzer
Comments: 2 Pages. University of Fukui, Faculty Development Forum, Vol. 7, p. 12 (2005).

Arguments for restructuring mathematics education according to the criteria of: (1) Optimal algebraic encoding (2) Coordinate free methodology (3) Optimal uniformity across various domains (4) Smooth articulation with traditional alternative systems (5) Optimal computational efficiency
Category: Education and Didactics

New Ways for Physics Education

Authors: Eckhard Hitzer
Comments: 2 Pages. University of Fukui, Fac. Dev. Forum, Vol. 5, p. 12 (2004).

This article introduces Physics Education Research (PER), which focuses on the connection of teaching and research.
Category: Education and Didactics

Modern Science Emphasizes Mathematics. What the Universe Looks Like When Logic is Emphasized (Maths Has a Vital, But Secondary, Role in This Article).

Authors: Rodney Bartlett
Comments: 21 Pages. This article can also be viewed by going to http://fqxi.org/community/forum/topic/1606 or https://www.researchgate.net/profile/Rodney_Bartlett/?ev=pub_int_doc_dlext

This article had its start with another article, concerned with measuring the speed of gravitational waves - "The Measurement of the Light Deflection from Jupiter: Experimental Results" by Ed Fomalont and Sergei Kopeikin (2003) - The Astrophysical Journal 598 (1): 704–711. This starting-point led to many other topics that required explanation or naturally seemed to follow on – Unification of gravity with electromagnetism and the 2 nuclear forces, Speed of electromagnetic waves, Energy of cosmic rays and UHECRs, Digital string theory, Isolation is an illusion, Dark energy + gravity + binary digits, Cosmic strings and wormholes from Figure-8 Klein bottles, Massless and massive photons and gravitons, Inverse square + quantum entanglement = God + evolution, Binary digits projected to make Prof. Greene’s cosmic holographic movie, Renormalization of infinity, Physically infinite universe, Colliding subuniverses, Unifying cosmic inflation, Theory Of Everything (emphasizing “EVERYthing”) = Bose-Einstein renormalized. The text also addresses (in a nonmathematical way) the wavelength of electromagnetic waves, the frequency of gravitational waves, gravitational and electromagnetic waves having identical speed, the gamma-ray burst designated GRB 090510, the smoothness of space, Self-influence and ESP caused by quantum entanglement in time, and Human involvement in the retrocausality of gravity, electromagnetism and matter. Topics in this article’s PS and PPS include – Gravitational waves actually have a much shorter wavelength than gamma rays, but are extraordinarily weak because almost all that energy goes into the formation of matter – How the Law of Conservation works – Mathematicians, physicists and Richard Feynman – Time travel to the past – Interstellar and intergalactic travel – Nonsupernatural God – 5th dimensional hyperspace – Dark Matter - Variable Speed of Light – Trillions of millennia in the distant future.
Category: Quantum Gravity and String Theory

Speakable and Unspeakable in Special Relativity. I. Synchronization and Clock Rhythms.

Authors: Rodrigo de Abreu, Vasco Guerra
Comments: 22 Pages.

The traditional presentation of special relativity is made from a rupture with previous ideas, such as the notion of absolute motion, emphasizing the antagonism of the Lorentz-Poincaré's views and Einstein's ideas. However, a weaker formulation of the postulates allows to recover all the mathematical results from Einstein's special relativity and reveals that both viewpoints are merely different perspectives of one and the same theory. The apparent contradiction simply stems from different procedures for clock "synchronization," associated with different choices of the coordinates used to describe the physical world. Even very fundamental claims, such as the constancy of the speed of light, relativity of simultaneity and relativity of time dilation, are seen to be no more than a consequence of a misleading language adopted in the description of the physical reality, which confuses clock rhythms with clock time readings. Indeed, the latter depend on the "synchronization" adopted, whereas the former do not. As such, these supposedly fundamental claims are not essential aspects of the theory, as reality is not altered by a mere change of coordinates. The relation between the rhythms of clocks in relative motion is derived with generality. This relation, which is not the standard textbook expression, markedly exposes the indeterminacy of special relativity, connected with the lack of knowledge of the value of the one-way speed of light. Moreover, the theory does not collapse and remains valid if some day the one-way speed of light is truly measured and the indeterminacy is removed. It is further shown that the slow transport method of "synchronization" cannot be seen as distinct from Einstein's procedure.
Category: Relativity and Cosmology

Axioms of Geometric Algebra

Authors: Eckhard Hitzer
Comments: 8 Pages. 3 figures, 1 table. Support Website for the Linear Algebra Lectures of the University of the Air Japan 2004-2008.

Axioms for Geometric Algebra R_{p,q} - Definitions using quadratic form, basic multiplication rules. Grade r subspaces, geometric algebra R_2, complex numbers, reflections and rotations, 2-dim. point groups, geometric algebra R_3 and quaternions.
Category: Algebra

Determinants in Geometric Algebra

Authors: Eckhard Hitzer
Comments: 3 Pages. Support Website for the Linear Algebra Lectures of the University of the Air Japan 2004-2008.

Definition, adjoint and inverse linear mappings, outermorphisms, computation and references.
Category: Algebra

Gram-Schmidt Orthogonalization in Geometric Algebra

Authors: Eckhard Hitzer
Comments: 2 Pages. Support Website for the Linear Algebra Lectures of the University of the Air Japan 2004-2008.

We describe Gram-Schmidt orthogonalization in W.K. Clifford's geometric algebra.
Category: Algebra

The Geometric Product and Derived Products

Authors: Eckhard Hitzer
Comments: 11 Pages. Support Website for the Linear Algebra Lectures of the University of the Air Japan 2004-2008.

The aim of this work is to show how the geometric product of multivectors is defined in general, extending the basic geometric product of vectors given by Clifford. An alternative definition of Clifford geometric algebra, that guarantees existence as quotient algebra of the tensor algebra was given by Chevalley in 1954.[2] We further treat the scalar product, the outer product, the cross product in three dimensions, linear dependence and independence, as well as right- and left contractions. !"#$%
Category: Algebra

The Use of Quadratic Forms in Geometric Algebra

Authors: Eckhard Hitzer
Comments: 6 Pages. Support Website for the Linear Algebra Lectures of the University of the Air Japan 2004-2008.

Definition of geometric algebra with quadratic form - examples of quadratic forms and associated geometric algebras - geometric algebras with degenerate quadratic forms - new interpretation of the geometric algebra of the Minkowski plane - generalizing to the geometric mother algebra with p=q=n.
Category: Algebra

What is an Imaginary Number?

Authors: Eckhard Hitzer
Comments: 4 Pages. Support Website for the Linear Algebra Lectures of the University of the Air Japan 2004-2008.

The previous Japanese emperor is said to have asked this question. Today many students and scientists still ask it, but the traditional canon of mathematics at school and university needs to be widened for the answer.
Category: Algebra

Crystal Cell and Space Lattice Symmetries in Clifford Geometric Algebra

Authors: Eckhard Hitzer, Christian Perwass
Comments: 4 Pages. 2 figures, 2 tables. Iin TE. Simos, G. Sihoyios, C. Tsitouras (eds.), International Conference on Numerical Analysis and Applied Mathematics 2005, Wiley-VCH, Weinheim, 2005, pp. 937-941 (2005).

The structure of crystal cells in two and three dimensions is fundamental for many material properties. In two dimensions atoms (or molecules) often group together in triangles, squares and hexagons (regular polygons). Crystal cells in three dimensions have triclinic, monoclinic, orthorhombic, hexagonal, rhombohedral, tetragonal and cubic shapes. The geometric symmetry of a crystal manifests itself in its physical properties, reducing the number of independent components of a physical property tensor, or forcing some components to zero values. There is therefore an important need to efficiently analyze the crystal cell symmetries. Mathematics based on geometry itself offers the best descriptions. Especially if elementary concepts like the relative directions of vectors are fully encoded in the geometric multiplication of vectors.
Category: Condensed Matter

State Decoding in Multi-Stage Cryptography Protocols

Authors: Sindhu Chitikela
Comments: 9 Pages.

This paper presents a practical method of quantum tomography for decoding the state of photons in a multistage cryptography protocol. This method works if the polarization angles are defined on a fixed plane, as is assumed in several quantum cryptography protocols. We show if there are 2m polarization angles in a fixed plane, we need m number of filters and m2 number of photons through each filter.
Category: General Science and Philosophy

It And Bit

Authors: Juan Ramón González Álvarez
Comments: 7 Pages. Entry for 5th FQXi Essay Contest "It From Bit or Bit From It?"

It is broadly believed that everything in the universe is found to be made from a few basic building blocks called fundamental particles, governed by four fundamental forces. However, physicists such as John Archibald Wheeler suggested that information is fundamental to the physics of the universe. According to this it from bit doctrine, all things physical are information-theoretic in origin. This doctrine is based in the old Copenhagen interpretation of quantum mechanics; an interpretation which is internally inconsistent and no applicable to the cosmos as a whole. Modern consistent interpretations of quantum mechanics eliminate the old myths about measurement processes and observers' consciousness and reintroduce the idea of a wholly physical reality, invalidating the it from bit doctrine. Utilizing a new phase space formulation of quantum mechanics developed recently by the author, the concepts of bit and it are reconsidered. We introduce the new states D as quantum bits and the new Hamiltonians H as quantum its. The new concepts of it and bit introduced in this work have a well-defined and rigorous definition, unlike Wheeler's concepts. Moreover, the new concepts apply on situations where the traditional wavefunction theory does not work. The it H is not derivable from the bit D and, as a consequence, the old it from bit doctrine gets substituted by the new it and bit. After showing why the physical entropy used in the science of thermodynamics is not a measure of the ignorance of human observers, the final part of this Essay is devoted to emphasize the importance that the bit acquires in modern science when confronted to the delicious multiplicity of the far-from-equilibrium regimes, where the certainty of Newtonian and Schrödinger motion begin to fade in favour of a complex non-geometrical, 'living', conception of Nature: an it and bit conception.
Category: Quantum Gravity and String Theory

Einstein a Brilliant Thief

Authors: Gabriela M. Atanasiu
Comments: 3 Pages.

In 1999, the scientific and historical analysis on the birth of the theory of relativity led to the clear conclusion that the true creator of the theory was Henry Poincaré and Einstein's work was a plagiarism. It is difficult to understand how Einstein elaborated a theory of this magnitude in just a few weeks as he hadn’t previously published anything in this regard.
Category: History and Philosophy of Physics

Experimental Evidence for a Non-Globally Trace-Preserving Povm

Authors: Raymond Jensen
Comments: 15 Pages.

Abstract. A well-known experiment from 1986 involving entangled pairs is examined. The data, which until now have not been modeled quantitatively, is shown not to be in agreement with the quantum measurement postulate using von Neumann projectors. On the other hand, the data agree with the postulate using a more general positive operator valued measure (POVM). The peculiarity of the POVM proposed here is that it is only conditionally a POVM; i.e. it is not complete (trace-preserving) on the entire Hilbert space but only on a subset, although the POVM elements are positive semidefinite observables on the entire space. The state vector of the aforementioned experiment is in the subset where completeness holds. An extension of the conditional POVM is then applied to a proposed experiment involving three- particle Greenberger-Horne-Zeilinger (GHZ) entangled states. As with the Aspect experiment, completeness holds for the conditional POVM upon application to the GHZ state. Violation of the Bell inequality in the GHZ experiment does not occur upon application of von-Neumann projectors; however the conditional POVM allows for Bell inequality violation.
Category: Quantum Physics

Its from Bits, Bits from it Nature the Universe and M-Theory-the Physical Theory as a Source of Information

Authors: Michael Muteru
Comments: 8 Pages.

The universe has always been a mystery to the human mind,It has proven to be a multi-faceted enterprise diverse as what it embodies.The Cosmological universe also has its basis too in philosophy,information on the universe is sought in modern ways using the physical theory.The universe displays reality at the deepest level.A Physical universe must also exist in maths,of which the fundamentals are digits/numbers.The universe is herein taken as a physical computer,I reveal The fundamentals that are most likely to make M-theory work-Using it to define the computational parameters that make the universe qualify to be a supercomputer easily capable of Quantum Computing. I take a historical walk from the past to the present displaying the mans quest for Truth about the universe and eventually reality.
Category: Quantum Physics

Strong Relationship Between Prime Numbers and Sporadic Groups

Authors: Klaus Lange
Comments: 18 Pages.

This paper shows a strong relationship between sporadic groups and prime numbers. It starts with new properties for the well known supersingular prime numbers of the moonshine theory. These new properties are only a preparation for the main result of this paper to show that the sporadic groups are strongly connected to prime numbers.
Category: Number Theory

Disposing Classical Field Theory, Part II

Authors: Hans Detlef Hüttenbach
Comments: 4 Pages. Minor upgrade; no fixes

It is shown that the symmetry group of a neutral, energy and momentum conserving particle theory is isomorphic to $SU(3)\times SU(2)\times U(1)$.
Category: Relativity and Cosmology

Proof of Fermat's Theorem

Authors: G. I. Ovchinnikov
Comments: 24 Pages.

In the article showed that the equation of Fermat’s theorem is a transcendental equation. This transcendental equation has no solution in integers. Therefore,Fermat's Last Theorem is true.
Category: Number Theory

Evolutionary Thinking and Changes of the Time Scale in Representations of the World

Authors: Mark Burgin
Comments: 29 Pages.

In this work, emergence of evolutionary thinking is analyzed in the context of the existential triad and system theory of time. This approach shows that emergence of evolutionary thinking is a transition from one type of temporal scale in the mental world representation to another temporal scale. To explain and ground this transition, elements of the system theory of time, which is a far-reaching development of the special relativity theory, are described. One of the main principles of the special relativity theory is that two physical systems that are moving relative to each other have different time and it is necessary to use a correspondence between clocks in these systems to coordinate their time. In accordance with the basic principles of the system theory of time, each system has its own time and sometimes even not a single one. Thus, it is it is necessary to use various techniques to match time in different systems.
Category: Social Science

Interactive 3D Space Group Visualization with CLUCalc and the Clifford Geometric Algebra Description of Space Groups

Authors: Eckhard Hitzer, Christian Perwass
Comments: 27 Pages. 21 figures, 14 tables. Adv. Appl. Clifford Alg., Vol. 20(3-4), pp. 631–658, (2010), DOI 10.1007/s00006-010-0214-z

A new interactive software tool is described, that visualizes 3D space group symmetries. The software computes with Clifford (geometric) algebra. The space group visualizer (SGV) originated as a script for the open source visual CLUCalc, which fully supports geometric algebra computation. Selected generators (Hestenes and Holt, JMP, 2007) form a multivector generator basis of each space group. The approach corresponds to an algebraic implementation of groups generated by reflections (Coxeter and Moser, 4th ed., 1980). The basic operation is the reflection. Two reflections at non-parallel planes yield a rotation, two reflections at parallel planes a translation, etc. Combination of reflections corresponds to the geometric product of vectors describing the individual reflection planes. We first give some insights into the Clifford geometric algebra description of space groups. We relate the choice of symmetry vectors and the origin of cells in the geometric algebra description and its implementation in the SGV to the conventional crystal cell choices in the International Tables of Crystallography (T. Hahn, Springer, 2005). Finally we briefly explain how to use the SGV beginning with space group selection. The interactive computer graphics can be used to fully understand how reflections combine to generate all 230 three-dimensional space groups. Mathematics Subject Classification (2000). Primary 20H15; Secondary 15A66, 74N05, 76M27, 20F55 . Keywords. Clifford geometric algebra, interactive software, space groups, crystallography, visualization.
Category: Condensed Matter

Interactive 3D Space Group Visualization with CLUCalc and Crystallographic Subperiodic Groups in Geometric Algebra

Authors: Eckhard Hitzer, Christian Perwass, Daisuke Ichikawa
Comments: 21 Pages. 11 figures, 7 tables. In G. Scheuermann, E. Bayro-Corrochano (eds.), Geometric Algebra Computing, Springer, New York, 2010, pp. 385-400. DOI: 10.1007/978-1-84996-108-0_18

The Space Group Visualizer (SGV) for all 230 3D space groups is a standalone PC application based on the visualization software CLUCalc. We first explain the unique geometric algebra structure behind the SGV. In the second part we review the main features of the SGV: The GUI, group and symmetry selection, mouse pointer interactivity, and visualization options.We further introduce the joint use with the International Tables of Crystallography, Vol. A [7]. In the third part we explain how to represent the 162 socalled subperiodic groups of crystallography in geometric algebra. We construct a new compact geometric algebra group representation symbol, which allows to read off the complete set of geometric algebra generators. For clarity we moreover state explicitly what generators are chosen. The group symbols are based on the representation of point groups in geometric algebra by versors.
Category: Condensed Matter

Visualization of Fundamental Symmetries in Nature

Authors: Eckhard Hitzer, Christian Perwass
Comments: 6 Pages. 7 figures, 4 tables. Proceedings of Fuzzy System Symposium (FSS 2009), Tsukuba, Japan, 14-16 Jul. 2009.

Most matter in nature and technology is composed of crystals and crystal grains. A full understanding of the inherent symmetry is vital. A new interactive software tool is demonstrated, that visualizes 3D space group symmetries. The software computes with Clifford (geometric) algebra. The space group visualizer (SGV) is a script for the open source visual CLUCalc, which fully supports geometric algebra computation. In our presentation we will first give some insights into the geometric algebra description of space groups. The symmetry generation data are stored in an XML file, which is read by a special CLUScript in order to generate the visualization. Then we will use the Space Group Visualizer to demonstrate space group selection and give a short interactive computer graphics presentation on how reflections combine to generate all 230 three-dimensional space groups.
Category: Geometry

Crystallographic Space Groups: Representation and Interactive Visualization by Geometric Algebra

Authors: Eckhard Hitzer, Christian Perwass
Comments: 6 Pages. 2 figures, 3 tables. submitted to: Proceedings of the 26th Int. Conference on Group Theoretical Methods in Physics, New York, USA, 2006.

We treat the symmetries of crystal space lattices in geometric algebra (GA)~\cite{DH:PGSG}. All crystal cell point groups are generated by geometric multiplication of two or three physical cell vectors. Only one or two relative angles subtended by these vectors need to be known. This treatment extends to space groups by including translations. GA helps to identify optimal multivector generators. As example we take the monoclinic case. New free interactive OpenGL and GA based software visualizes these symmetries.
Category: Condensed Matter

The Hidden Beauty of Gold

Authors: Eckhard Hitzer, Christian Perwass
Comments: 11 Pages. 24 figures. Proc. of Int. Symp. on Adv. Mech. & Power Engin. 2007 (ISAMPE 2007) between Pukyong Nat. Univ. (Kor.), Univ. of Fukui (Jap.) and Univ. of Shanghai for Sci. & Tech. (PRC), Nov. 22-25, 2007, at Univ. of Fukui, pp. 157-167. Figs. 15,16,17,23 rv.

This paper first reviews the history, the economy, the material properties, and the applications of gold. Then the geometry of the face centered cubic (fcc) gold lattice is introduced. Based on the symmetric arrangement of atoms the gold lattice has a rich variety of symmetry transformations, that interchange the positions of atoms, but leave the lattice as a whole invariant. This begins with the point group symmetry of a single fcc lattice cell and is extended by combination with lattice translations to the full space group symmetry of the whole (practically infinite) lattice. We use the newly created interactive Space Group Visualizer (based on geometric algebra) in order to systematically picture all these symmetries. We can thus understand their origin and their relationships. In particular we give a full geometric explanation of the 192 screw symmetries passing through a single fcc cell of the gold lattice.
Category: Condensed Matter

The Space Group Visualizer

Authors: Eckhard Hitzer, Christian Perwass
Comments: 9 Pages. 18 figures, 1 table. Proc. of In. Symp. on Adv. Mech. Eng. 2006 between Pukyong Nat. Univ. (Kor.), Univ. of Fukui (Jap.) and Univ. of Shanghai for Sci. and Techn. (PRC), Oct. 26-29, 2006, at Univ. of Shanghai for Sci. and Techn. pp. 172-181 (2006).

A new free interactive OpenGL software tool is demonstrated, that visualizes all monoclinic, and so far part of the orthorhombic, triclinic and hexagonal space group symmetries. The software computes with Clifford (geometric) algebra. The space group visualizer originated as a script for the open source visual CLUCalc, which fully supports geometric algebra computation. This paper briefly describes the historical and scientific developments leading to the space group visualizer project. Then we step by step demonstrate space group selection and the powerful set of interactive tools, including continuous free interactive 3D rotations, repositioning and resizing of the crystal domain in view. The most prominent feature of the space group visualizer is the full visualization of all spatial symmetries of a crystal domain. Beyond this the user can reduce the view to single symmetry operations or to certain classes of symmetries.
Category: Condensed Matter

Space Group Visualizer for Monoclinic Space Groups

Authors: Eckhard Hitzer, Christian Perwass
Comments: 2 Pages. 4 figures. Bulletin of the Society for Science on Form, 21(1), pp. 38,39 (2006).

A new free interactive OpenGL software tool is demonstrated, that visualizes all monoclinic space group symmetries described by geometric algebra.[1] Keywords: Crystal lattice, space group symmetry, geometric algebra, OpenGL, spacegroup visualizer.
Category: Condensed Matter

Three Vector Generation of Crystal Space Groups in Geometric Algebra

Authors: Eckhard Hitzer, Christian Perwass
Comments: 2 Pages. 1 figure, 1 table. Bulletin of the Society for Science on Form, 21(1), pp. 55,56 (2006).

This paper focuses on the symmetries of crystal space lattices. All two dimensional (2D) and three dimensional (3D) point groups of 2D and 3D crystal cells are exclusively described by vectors (two in 2D, three in 3D for one particular cell) taken from the physical cells. Geometric multiplication of these vectors completely generates all symmetries, including reflections, rotations, inversions, rotary-reflections and rotary-inversions. We then extend this treatment to 3D space groups by including translations, glide reflections and screw rotations. We focus on the monoclinic case as an example. A software demonstration shows the spacegroup visualizer. Keywords: Crystal lattice, space group, geometric algebra, OpenGL, interactive software.
Category: Algebra

Interactive Visualization of Full Geometric Description of Crystal Space Groups

Authors: Christian Perwass, Eckhard Hitzer
Comments: 6 Pages. 9 figures. Proc. of the In. Symp. on Adv. Mech. Eng., between Univ. of Fukui (Japan), Pukyong Nat. Univ. (Korea) and Univ. of Shanghai for Sci. and Techn. (China), 23-26 Nov. 2005, pp. 276-282 (2005).

In this text we present a software tool that visualises the symmetry properties of the space groups of 3D Euclidean space, which play an important role in the investigation of crystalline materials. The main source that lists the properties of all space groups are the "International Tables For Crystallography, Volume A" [1], where the symmetries are shown in three orthographic projections. It is clearly much more intuitive to look at these symmetry properties in a 3D visualisation. The visualisation software presented here (for monoclinic crystals) allows the user to look at the space group symmetries from any view point and to modify lattice parameters in real time. The visualisation software is freely available from www.spacegroup.info.
Category: Condensed Matter

Full Geometric Description of All Symmetry Elements of Crystal Space Groups by the Suitable Choice of Only Three Vectors for Each Bravais Cell or Crystal Family

Authors: Eckhard Hitzer, Christian Perwass
Comments: 7 Pages. 7 figures, 2 tables. Proc. of the Int. Sym. on Adv. Mech. Eng., between Univ. of Fukui (Japan), Pukyong Nat. Univ. (Korea) and Univ. of Shanghai for Sci. and Techn. (China), 23-26 Nov. 2005, pp. 19-25 (2005).

This paper focuses on the symmetries of crystal cells and crystal space lattices. All two dimensional (2D) and three dimensional (3D) point groups of 2D and 3D crystal cells are exclusively described by vectors (two in 2D, three in 3D for one particular cell) taken from the physical cells. Geometric multiplication of these vectors completely generates all symmetries, including reflections, rotations, inversions, rotary-reflections and rotary-inversions. The sets of vectors necessary are illustrated in drawings. We then extend this treatment to 2D and 3D space groups by including translations, glide reflections and screw rotations. For 3D space groups we focus on the monoclinic case as an example. A companion paper [15] describes corresponding interactive visualization software.
Category: Condensed Matter

Crystal Cells in Geometric Algebra

Authors: Eckhard Hitzer, Christian Perwass
Comments: 6 Pages. 5 figures. Proceedings of the International Symposium on Advanced Mechanical Engineering, between University of Fukui (Japan) - Pukyong National University (Korea), 27 Nov. 2004, pp. 290-295 (2004).

This paper focuses on the symmetries of space lattice crystal cells. All 32 point groups of three dimensional crystal cells are exclusively described by vectors (three for one particular cell) taken from the physical cell. Geometric multiplication of these vectors completely generates all symmetries, including reflections, rotations, inversions, rotary-reflections and rotary-inversions. The sets of vectors necessary are illustrated in drawings and all symmetry group elements are listed explicitly as geometric vector products. Finally a new free interactive software tool is introduced, that visualizes all symmetry transformations in the way described in the main geometrical part of this paper.
Category: Condensed Matter

Algorithm for Conversion Between Geometric Algebra Versor Notation and Conventional Crystallographic Symmetry-Operation Symbols

Authors: Eckhard Hitzer, Christian Perwass
Comments: 14 Pages. 6 tables. Preprint (2009).

This paper establishes an algorithm for the conversion of conformal geometric algebra (GA) [3, 4] versor symbols of space group symmetry-operations [6–8, 10] to standard symmetry-operation symbols of crystallography [5]. The algorithm is written in the mathematical language of geometric algebra [2–4], but it takes up basic algorithmic ideas from [1]. The geometric algebra treatment simplifies the algorithm, due to the seamless use of the geometric product for operations like intersection, projection, rejection; and the compact conformal versor notation for all symmetry operations and for geometric elements like lines and planes. The transformations between the set of three geometric symmetry vectors a,b,c, used for generating multivector versors, and the set of three conventional crystal cell vectors a,b,c of [5] have already been fully specified in [8] complete with origin shift vectors. In order to apply the algorithm described in the present work, all locations, axis vectors and trace vectors must be computed and oriented with respect to the conventional crystall cell, i.e. its origin and its three cell vectors.
Category: Condensed Matter

Physical-Layer Encryption on the Public Internet: a Stochastic Approach to the Kish-Sethuraman Cipher

Authors: Lachlan J. Gunn, James M. Chappell, Andrew Allison, Derek Abbott
Comments: 7 pages, 3 figures, to be presented at HotPI-2013

While information-theoretic security is often associated with the one-time pad and quantum key distribution, noisy transport media leave room for classical techniques and even covert operation. Transit times across the public internet exhibit a degree of randomness, and cannot be determined noiselessly by an eavesdropper. We demonstrate the use of these measurements for information-theoretically secure communication over the public internet.
Category: Digital Signal Processing

The Best Theory of Arbitrarily Long Arithmetic Progressions of Primes

Authors: Chun-Xuan Jiang
Comments: 10 Pages. it is very important paper

Using Jiang function we find the best theory of arbitrarily long arithmetic progressions of primes
Category: Number Theory

Arguments and Model for Quantum Consciousness, Modification of Quantum Collapse, and Panpsychism

Authors: Janko Kokosar
Comments: Pages.

As first, a mechanism how quantum coherence in the brain can last long enough is shown. This mechanism is based on very light elementary particles. Then the arguments follow as why consciousness should be a quantum phenomenon and how such an introduction of quantum consciousness modifies the formalism of quantum mechanics. This can also be tested by an experiment. Without use of quantum mechanics it is shown how to atomize consciousness and how to explain the Libet experiment, and why a location of feeling of consciousness is an important paradox. It is also shown that panpsychism is an answer to many questions about consciousness. The author claims that consciousness is physically so fundamental that it is not a result of some complex phenomena, but it is so fundamental as quantum physics and space-time.
Category: Quantum Physics

What is Electron Spin?

Authors: Kamal L Rajpal
Comments: 10 pages, 6 figures

An isolated static electron in free space is not a fixed particle at rest. It is always oscillating in a SHM in its own electromagnetic inertia field, rest frame even at zero kelvin temperature. This is non-thermal, standing wave, resonance Compton frequency, oscillation along a linear path or, along an elliptical or a circular (clockwise or anti-clockwise) path which results in the electron’s intrinsic magnetic moment (spin up or spin down). An electron with spin behaves like a tiny magnet. Intrinsic spin does not imply that a subatomic particle is spinning like a toy-top about its axis. A hypothetical electron without a charge is like the bob of a simple pendulum without a string.
Category: Quantum Physics

Fitzgerald-Lorentz Contraction: Real or Apparent

Authors: Antonio Leon
Comments: 7 Pages.

After a summary introduction to Fitzgerald-Lorentz contraction, and a short revision of some classic and modern opinions on its real or apparent nature, this paper introduces two arguments proving that Fitzgerald-Lorentz contraction can only be apparent. The first of them also proves the deformed appearance disagrees with certain physical laws, pointing to a breaking of Lorentz symmetry that questions the Principle of Relativity. Being also consequences of Lorentz transformation, time dilation and phase difference in synchronization could only be apparent deformations, which open the debate on the physical meaning of Lorentz transformation.
Category: Relativity and Cosmology

What Confinement Really Means in Quantum Chromodynamics

Authors: Syed Afsar Abbas
Comments: 11 Pages. none

In spite of intense efforts it has not been possible to demonstrate that confinement of colour exists consistently in Quantum Chromodynamics. It is therefore one of the most puzzling issues in Quantum Chromodynamics. We study what antisymmetrization in colour space means fundamentally and how this is then matched with the conjugate symmetric state in the rest of the degrees of freedom of the quarks. It is shown that the present understanding, that confinement arises due to a single colour singlet state, is wrong. In this paper we prove that actually there are two independent colour singlet states, both of which are needed simultaneously to provide confinement in QCD. This in turn leads to a fundamental justification of the relativistic bag models and the non-relativistic quark models.
Category: High Energy Particle Physics

Interactive Visualization of Plane Space Groups with the Space Group Visualizer

Authors: Eckhard Hitzer
Comments: 36 Pages. 32 figures, 1 table.

This set of instructions shows how to successfully display the 17 two-dimensional (2D) space groups in the interactive crystal symmetry software Space Group Visualizer (SGV) [6]. The SGV is described in [4]. It is based on a new type of powerful geometric algebra visualization platform [5]. The principle is to select in the SGV a three-dimensional super space group and by orthogonal projection produce a view of the desired plane 2D space group. The choice of 3D super space group is summarized in the lookup table Table 1. The direction of view for the orthographic projection needs to be adapted only for displaying the plane 2D space groups Nos. 3, 4 and 5. In all other cases space group selection followed by orthographic projection immediately displays one cell of the desired plane 2D space group. The full symmetry selection, interactivity and animation features for 3D space groups offered by the SGV software become thus also available for plane 2D space groups. A special advantage of this visualization method is, that by canceling the orthographic projection (remove the tick mark of Orthographic View in drop down menu Visualization), every plane 2D space group is seen to be a subgroup of a corresponding 3D super space group.
Category: Condensed Matter

Tutorial on Reflections in Geometric Algebra

Authors: Eckhard Hitzer
Comments: 22 Pages. 16 figures, 6 tables. In K. Tachibana (ed.) Tutorial on Reflections in Geometric Algebra, Lecture notes of the international Workshop for “Computational Science with Geometric Algebra” (FCSGA2007), Nagoya Univ., Japan, 14-21 Feb. 2007, pp. 34-44 (2007).

This tutorial focuses on describing the implementation and use of reflections in the geometric algebras of three-dimensional (3D) Euclidean space and in the five-dimensional (5D) conformal model of Euclidean space. In the latter reflections at parallel planes serve to implement translations as well. Combinations of reflections allow to implement all isometric transformations. As a concrete example we treat the symmetries of (2D and 3D) space lattice crystal cells. All 32 point groups of three dimensional crystal cells (10 point groups in 2D) are exclusively described by vectors (two for each cell in 2D, three for one particular cell in 3D) taken from the physical cell. Geometric multiplication of these vectors completely generates all symmetries, including reflections, rotations, inversions, rotary reflections and rotary-inversions. The inclusion of translations with the help of the 5D conformal model of 3D Euclidean space allows the full formulation of the 230 crystallographic space groups in geometric algebra. The sets of vectors necessary are illustrated in drawings and all symmetry group elements are listed explicitly as geometric vector products. Finally a new free interactive software tool is introduced, that visualizes all symmetry transformations in the way described in the main geometrical part of this tutorial.
Category: Geometry

Tutorial on Fourier Transformations and Wavelet Transformations in Cliord Geometric Algebra

Authors: Eckhard Hitzer
Comments: 45 Pages. 3 tables. In K. Tachibana (ed.) Tutorial on Fourier Transf. and Wavelet Transf. in Clifford Geometric Algebra, Lect. notes of the Int. Workshop for “Computational Science with Geometric Algebra” (FCSGA2007), Nagoya Univ., JP, Feb. 2007, pp. 65-87 (2007).

First, the basic concept multivector functions and their vector derivative in geometric algebra (GA) is introduced. Second, beginning with the Fourier transform on a scalar function we generalize to a real Fourier transform on GA multivector-valued functions (f : R^3 -> Cl(3,0)). Third, we show a set of important properties of the Clifford Fourier transform (CFT) on Cl(3,0) such as dierentiation properties, and the Plancherel theorem. We round o the treatment of the CFT (at the end of this tutorial) by applying the Clifford Fourier transform properties for proving an uncertainty principle for Cl(3,0) multivector functions. For wavelets in GA it is shown how continuous Clifford Cl(3,0)- valued admissible wavelets can be constructed using the similitude group SIM(3), a subgroup of the ane group of R^3. We express the admissibility condition in terms of the CFT and then derive a set of important properties such as dilation, translation and rotation covariance, a reproducing kernel, and show how to invert the Clifford wavelet transform of multivector functions. We explain (at the end of this tutorial) a generalized Clifford wavelet uncertainty principle. For scalar admissibility constant it sets bounds of accuracy in multivector wavelet signal and image processing. As concrete example we introduce multivector Clifford Gabor wavelets, and describe important properties such as the Clifford Gabor transform isometry, a reconstruction formula, and (at the end of this tutorial) an uncertainty principle for Clifford Gabor wavelets. Keywords: vector derivative, multivector-valued function, Clifford (geometric) algebra, Clifford Fourier transform, uncertainty principle, similitude group, geometric algebra wavelet transform, geometric algebra Gabor wavelets.
Category: Functions and Analysis

The Dark Side of Dark Matter (The Moon and the Dark Matter)

Authors: Leonardo Rubino
Comments: 8 Pages.

The anomaly in the@@ rotation curves for galaxies (excess of speed) is not due to any mysterious dark matter, but rather to the tidal effect of the Universe all around the galaxies themselves. Here is the proof.
Category: Astrophysics

The Clifford Fourier Transform in Real Clifford Algebras

Authors: Eckhard Hitzer
Comments: 21 Pages. 2 figures, 1 table. First published: Proc. of 19th International Conference on the Application of Computer Science and Mathematics in Architecture and Civil Engineering, Weimar, Germany, 04–06 July 2012.

We use the recent comprehensive research [17, 19] on the manifolds of square roots of -1 in real Clifford’s geometric algebras Cl(p,q) in order to construct the Clifford Fourier transform. Basically in the kernel of the complex Fourier transform the imaginary unit j in C (complex numbers) is replaced by a square root of -1 in Cl(p,q). The Clifford Fourier transform (CFT) thus obtained generalizes previously known and applied CFTs [9, 13, 14], which replaced j in C only by blades (usually pseudoscalars) squaring to -1. A major advantage of real Clifford algebra CFTs is their completely real geometric interpretation. We study (left and right) linearity of the CFT for constant multivector coefficients in Cl(p,q), translation (x-shift) and modulation (w-shift) properties, and signal dilations. We show an inversion theorem. We establish the CFT of vector differentials, partial derivatives, vector derivatives and spatial moments of the signal. We also derive Plancherel and Parseval identities as well as a general convolution theorem. Keywords: Clifford Fourier transform, Clifford algebra, signal processing, square roots of -1.
Category: Functions and Analysis

Interactive Visualization of Plane Groups

Authors: Eckhard Hitzer
Comments: 4 Pages. 3 figs, 1 tab. Symm.: Art + Sci., Spec. Iss. of The Jour. of the Int. Soc. For the Interdisc. Study of Symmetry (ISIS): G. Lugosi, D. Nagy (eds.), Proc. of Symm.: Art + Sci., 8th Congr. ISIS, Days of Harmonics, Austr., Aug. 2010, v 2010 (1-4), pp. 80-83.

This contribution shows how to successfully display the 17 two-dimensional space groups (wallpaper groups) in the interactive crystal symmetry software Space Group Visualizer (SGV) (Perwass & Hitzer, 2005). We show examples of four wallpaper groups that contain (as sub patterns, i.e as subgroups) all other 13 wallpaper groups. The SGV is described in (Hitzer & Perwass, 2010). It is based on a new type of powerful geometric algebra visualization platform (Perwass, 2000).
Category: Condensed Matter

Analysis of Point Clouds Using Conformal Geometric Algebra

Authors: Dietmar Hildenbrand, Eckhard Hitzer
Comments: 6 Pages. 6 figures, 1 table. In Braz, J. (ed.), GRAPP 2008, 3rd Int. Conf. on Computer Graphics Theory and Applications. Proc.: Funchal, Madeira, Portugal, January 22-25, 2008, Porto: INSTICC Press, pp. 99-106 (2008). DOI: 10.1.1.151.7539

This paper presents some basics for the analysis of point clouds using the geometrically intuitive mathematical framework of conformal geometric algebra. In this framework it is easy to compute with osculating circles for the description of local curvature. Also methods for the fitting of spheres as well as bounding spheres are presented. In a nutshell, this paper provides a starting point for shape analysis based on this new, geometrically intuitive and promising technology. Keywords: geometric algebra, geometric computing, point clouds, osculating circle, fitting of spheres, bounding spheres.
Category: Data Structures and Algorithms

Clifford Fourier Transform on Multivector Fields and Uncertainty Principles for Dimensions N = 2 (Mod 4) and N = 3 (Mod 4)

Authors: Eckhard Hitzer, Bahri Mawardi
Comments: 24 Pages. 2 tables. Adv. App. Cliff. Alg. Vol. 18, S3,4, pp. 715-736 (2008). DOI: 10.1007/s00006-008-0098-3.

First, the basic concepts of the multivector functions, vector differential and vector derivative in geometric algebra are introduced. Second, we dene a generalized real Fourier transform on Clifford multivector-valued functions ( f : R^n -> Cl(n,0), n = 2,3 (mod 4) ). Third, we show a set of important properties of the Clifford Fourier transform on Cl(n,0), n = 2,3 (mod 4) such as dierentiation properties, and the Plancherel theorem, independent of special commutation properties. Fourth, we develop and utilize commutation properties for giving explicit formulas for f x^m; f Nabla^m and for the Clifford convolution. Finally, we apply Clifford Fourier transform properties for proving an uncertainty principle for Cl(n,0), n = 2,3 (mod 4) multivector functions. Keywords: Vector derivative, multivector-valued function, Clifford (geometric) algebra, Clifford Fourier transform, uncertainty principle.
Category: Functions and Analysis

Uncertainty Principle for Clifford Geometric Algebras Cl(n,0), N = 3 (Mod 4) Based on Clifford Fourier Transform

Authors: Eckhard Hitzer, Bahri Mawardi
Comments: 10 Pages. 1 table. In T. Qian, M.I. Vai, X. Yusheng (eds.), Wavelet Analysis and Applications, Springer (SCI) Book Series Applied and Numerical Harmonic Analysis, Springer, pp. 45-54 (2006). DOI: 10.1007/978-3-7643-7778-6_6.

First, the basic concepts of the multivector functions, vector differential and vector derivative in geometric algebra are introduced. Second, we define a generalized real Fourier transform on Clifford multivector-valued functions (f : Rn -> Cl(n,0), n = 3 (mod 4)). Third, we introduce a set of important properties of the Clifford Fourier transform on Cl(n,0), n = 3 (mod 4) such as differentiation properties, and the Plancherel theorem. Finally, we apply the Clifford Fourier transform properties for proving a directional uncertainty principle for Cl(n,0), n = 3 (mod 4) multivector functions. Keywords. Vector derivative, multivector-valued function, Clifford (geometric) algebra, Clifford Fourier transform, uncertainty principle. Mathematics Subject Classication (2000). Primary 15A66; Secondary 43A32.
Category: Functions and Analysis

Geometric Algebra Illustrated by Cinderella

Authors: Eckhard Hitzer, Luca Redaelli
Comments: 22 Pages. 27 figures. Advances in Applied Clifford Algebras, 13(2), pp. 157-181 (2003). DOI: 10.1007/s00006-003-0013-x .

Conventional illustrations of the rich elementary relations and physical applications of geometric algebra are helpful, but restricted in communicating full generality and time dependence. The main restrictions are one special perspective in each graph and the static character of such illustrations. Several attempts have been made to overcome such restrictions. But up till now very little animated and fully interactive, free, instant access, online material is available. This report presents therefore a set of over 90 newly developed (freely online accessible [1]) JAVA applets. These applets range from the elementary concepts of vector, bivector, outer product and rotations to triangle relationships, oscillations and polarized waves. A special group of 21 applets illustrates three geometrically different approaches to the representation of conics; and even more ways to describe ellipses. Next Clifford's famous circle chain theorem is illustrated. Finally geometric applications important for crystallography and structural mechanics give a glimpse of the vast potential for applied mathematics. The interactive geometry software Cinderella [2] was used for creating these applets. The interactive features of many of the applets invite the user to freely explore by a few mouse clicks as many different special cases and perspectives as he likes. This is of great help in "visualizing" geometry encoded by geometric algebra.
Category: Algebra

Basic Multivector Calculus

Authors: Eckhard Hitzer
Comments: 6 Pages. Proc. of 18th Intelligent Systems Symposium (FAN 2008), 23-24 Oct. 2008, Hiroshima, Japan, pp. 185 – 190 (2008).

We begin with introducing the generalization of real, complex, and quaternion numbers to hypercomplex numbers, also known as Clifford numbers, or multivectors of geometric algebra. Multivectors encode everything from vectors, rotations, scaling transformations, improper transformations (reflections, inversions), geometric objects (like lines and spheres), spinors, and tensors, and the like. Multivector calculus allows to define functions mapping multivectors to multivectors, differentiation, integration, function norms, multivector Fourier transformations and wavelet transformations, filtering, windowing, etc. We give a basic introduction into this general mathematical language, which has fascinating applications in physics, engineering, and computer science.
Category: Functions and Analysis

Symmetry of Orthorhombic Materials and Interactive 3D Visualization in Geometric Algebra

Authors: Daisuke Ichikawa, Eckhard Hitzer
Comments: 11 Pages. 12 figures, 4 tables. Proc. of the Int. Symp. on Adv. Mechanical and Power Engineering 2007, between Univ. of Fukui (Japan), Pukyong Nat. Univ. (Korea) and Univ. of Shanghai for Science and Technology (China), 22--25 Nov. 2007, 302-312 (2007).

The Space Group Visualizer is the main software that we use in this work to show the symmetry of orthorhombic space groups as interactive computer graphics in three dimensions. For that it is necessary to know the features and the classification of orthorhombic point groups and space groups. For representing the symmetry transformations of point groups and space groups, we employ (Clifford) geometric algebra. This algebra results from applying the associative geometric product to the vectors of a vector space. Some major features of the software implementation are discussed. Finally a brief overview of interactive functions of the Space Group Visualizer is given.
Category: Condensed Matter

Foundations of Multidimensional Wavelet Theory: The Quaternion Fourier Transform and its Generalizations

Authors: Eckhard Hitzer
Comments: 3 Pages. E. Hitzer, Foundations of Multidimensional Wavelet Theory: The Quaternion Fourier Transf. and its Generalizations, Preprints of Meeting of the JSIAM, ISSN: 1345-3378, Tsukuba Univ., 16-18 Sep. 2006, Tsukuba, Japan, pp. 66,67.

Keywords: Multidimensional Wavelets, Quaternion Fourier Transform, Clifford geometric algebra
Category: Functions and Analysis

Relativistic Physics as Application of Geometric Algebra

Authors: Eckhard Hitzer
Comments: 12 Pages. 3 figures. In K. Adhav (ed.), Proceedings of the International Conference on Relativity 2005 (ICR2005), University of Amravati, India, January 2005, pp. 71-90 (2005).

This review of relativistic physics integrates the works of Hamilton, Grassmann, Maxwell, Clifford, Einstein, Hestenes and lately the Cambridge (UK) Geometric Algebra Research Group. We start with the geometric algebra of spacetime (STA). We show how frames and trajectories are described and how Lorentz transformations acquire their fundamental rotor form. Spacetime dynamics deals with spacetime rotors, which have invariant and frame dependent splits. Spacetime rotor equations yield the proper acceleration (bivector) and the Fermi (vector) derivative. A first application is given with the relativistic STA formulation of the Lorentz force law, leading to the description of spin precession in magnetic fields and Thomas precession. Now the stage is ready for introducing the STA Maxwell equation, which combines all 4 equations in one single STA equation. STA has procedures to extract from the electromagnetic field strength bivector F, electric and magnetic fields (also for relative motion observers) and field invariants, field momentum and stress-energy tensor. The Leonhard-Wiechert potential gives the retarded field of a point charge. In addition we formulate the Dirac equation in STA, both massless and massive. From the Dirac equation we can derive STA expressions for Dirac observables. Plane wave states are described with the help of rotor decomposition. Finally we briefly review a STA gauge theory of gravity built on displacement and rotation gauge principles.
Category: Relativity and Cosmology

The GeometricAlgebra Java Package – Novel Structure Implementation of 5D Geometric Algebra R_4,1 for Object Oriented Euclidean Geometry, Space-Time Physics and Object Oriented Computer Algebra

Authors: Eckhard Hitzer, Ginanjar Utama
Comments: 13 Pages. 3 figures, 5 tables. Mem. Fac. Eng. Univ. Fukui 53(1), pp. 47-59 (2005).

This paper first briefly reviews the algebraic background of the conformal (homogeneous) model of Euclidean space in Clifford geometric algebra R_4,1= Cl(4,1), concentrating on the subalgebra structure. The subalgebras include space-time algebra (STA), Dirac and Pauli algebras, as well as real and complex quaternion algebras, etc. The concept of the Horosphere is introduced along with the definition of subspaces that intuitively correspond to three dimensional Euclidean geometric objects. Algebraic expressions for the motions of these objects and their set theoretic operations are given. It is shown how 3D Euclidean information on positions, orientations and radii can be extracted. The second main part of the paper concentrates on the GeometricAlgebra Java package implementation of the Clifford geometric algebra R_4,1 = Cl(4,1) and the homogeneous model of 3D Euclidean space. Details are exemplified by looking at the structure and code of the basic MultiVector class and of the 3D Euclidean object model class Sphere. Finally code optimization issues and the ongoing open source project implementation are discussed.
Category: Data Structures and Algorithms

Learning about Conic Sections with Geometric Algebra and Cinderella

Authors: Eckhard Hitzer
Comments: 16 Pages. 8 figures, 1 table. Proc. of the Symposium Innovative Teaching of Mathematics with Geometric Algebra 2003, Nov. 20-22, 2003, RIMS, University of Kyoto, Japan, pp. 89-104 (2003).

Over time an astonishing and sometimes confusing variety of descriptions of conic sections has been developed. This article will give a brief overview over some interesting descriptions, showing formulations in the three geometric algebras of Euclidean three space, projective geometry and the conformal model of Euclidean space. Some illustrations with Cinderella created Java applets will be given. I think a combined geometric algebra & illustration approach can motivate students to explorative learning.
Category: Geometry

Conic Sections Through Five Points Classical, Projective, Conformal

Authors: Eckhard Hitzer
Comments: 6 Pages. 2 figures, 1 table. Proc. of the International Symposium 2003 of Advanced Mechanical Engineering, Pukyong National Univ., Busan, Korea, 22-25 Nov. 2003, pp. 109-114 (2003).

In the so-called conformal model of Euclidean space of geometric algebra, circles receive a very elegant description by the outer product of three general points of that circle, forming what is called a tri-vector. Because circles are a special kind of conic section, the question arises, whether in general some kind of third order outer product of five points on a conic section (or certain linear combinations) may be able to describe other types of conic sections as well. The main idea pursued in this paper is to follow up a formula of Grassmann for conic sections through five points and implement it in the conformal model. Grassmann obviously based his formula on Pascal’s theorem. At the end we consider a simple linear combination of circle tri-vectors.
Category: Geometry

Geometric Calculus – Engineering Mathematics for the 21st Century

Authors: Eckhard Hitzer
Comments: 12 Pages. 13 figures. Mem. Fac. Eng. Fukui Univ. 50(1), pp. 127-137 (2002).

This paper treats important questions at the interface of mathematics and the engineering sciences. It starts off with a quick quotation tour through 2300 years of mathematical history. At the beginning of the 21st century, technology has developed beyond every expectation. But do we also learn and practice an adequately modern form of mathematics? The paper argues that this role is very likely to be played by universal geometric calculus. The fundamental geometric product of vectors is introduced. This gives a quick-and-easy description of rotations as well as the ultimate geometric interpretation of the famous quaternions of Sir W.R. Hamilton. Then follows a one page review of the historical roots of geometric calculus. In order to exemplify the role of geometric calculus for the engineering sciences three representative examples are looked at in some detail: elasticity, image geometry and pose estimation. Next a current snapshot survey of geometric calculus software is provided. Finally the value of geometric calculus for teaching, research and development is commented.
Category: Functions and Analysis

Vector Differential Calculus

Authors: Eckhard Hitzer
Comments: 17 Pages. Mem. Fac. Eng. Fukui Univ. 50(1), pp. 109-125 (2002).

This paper treats the fundamentals of the vector differential calculus part of universal geometric calculus. Geometric calculus simplifies and unifies the structure and notation of mathematics for all of science and engineering, and for technological applications. In order to make the treatment self-contained, I first compile all important geometric algebra relationships, which are necessary for vector differential calculus. Then differentiation by vectors is introduced and a host of major vector differential and vector derivative relationships is proven explicitly in a very elementary step by step approach. The paper is thus intended to serve as reference material, giving details, which are usually skipped in more advanced discussions of the subject matter. Keywords: Geometric Calculus, Geometric Algebra, Clifford Algebra, Vector Derivative, Vector Differential Calculus
Category: Functions and Analysis

Play with Geometry - Animated and Interactive, Free, Instant Access, Online Geometric Algebra Java Applets

Authors: Eckhard Hitzer, Luca Redaelli
Comments: 6 Pages. 18 figures. Proceedings of Fukui University International Congress, International Symposium on Advanced Mechanical Engineering, 11-13 Sep. 2002, pp. 7-12 (2002).

Conventional illustrations of elementary relations and physical applications of geometric algebra are helpful, but restricted in communicating full generality and time dependence. The main restrictions are one special perspective in each graph and the static character of such illustrations. Several attempts have been made to overcome such restrictions. But up till now very little animated and interactive, free, instant access, online material is available. This talk presents therefore a set of well over 60 newly developed (freely online accessible[1]) JAVA applets. These applets range from the elementary concepts of vector, bivector, outer product and rotations to triangle relationships, oscillations and polarized waves. A special group of 21 applets illustrates three geometrically different approaches to the representation of conics; and even more ways to describe ellipses. Finally Clifford's circle chain theorem is illustrated for two to eight primary circles. The interactive geometry software Cinderella[2] was used for creating these applets. Some construction principles will be explained and a number of applets will be demonstrated. The interactive features of many of the applets invite the user to freely explore by a few mouse clicks as many different special cases and perspectives as he likes. This is of great help in "visualizing" the geometry encoded in the concepts and formulas of Geometric Algebra.
Category: Geometry

Geometric Calculus for Engineers

Authors: Eckhard Hitzer
Comments: 8 Pages. 7 figures. Proc. of the Pukyong National University - Fukui University International Symposium 2001 for Promotion of Research Cooperation, Pukyong National University, Busan, Korea, pp. 59-66 (2001).

This paper treats important questions at the interface of mathematics and the engineering sciences. It starts off with a quick quotation tour through 2300 years of mathematical history. At the beginning of the 21st century, technology has developed beyond every expectation. But do we also learn and practice an adequately modern form of mathematics? The paper argues that this role is very likely to be played by (universal) geometric calculus. The fundamental geometric product of vectors is introduced. This gives a quick-and-easy description of rotations as well as the ultimate geometric interpretation of the famous quaternions of Sir W.R. Hamilton. Then follows a one page review of the historical roots of geometric calculus. In order to exemplify the role geometric calculus for the engineering sciences three representative examples are looked at in some detail: elasticity, image geometry and pose estimation. Finally the value of geometric calculus for teaching, research and development and its worldwide impact are commented.
Category: Functions and Analysis

A Real Explanation for Imaginary Eigenvalues and Complex Eigenvectors

Authors: Eckhard Hitzer
Comments: 21 Pages. in T. M. Karade (ed.), Proc. of the Nat. Symp. on Math. Sc., 1-5 March, 2001, Nagpur, India, Einst. Foundation Int. 1, pp. 1-26 (2001).

This paper first reviews how anti-symmetric matrices in two dimensions yield imaginary eigenvalues and complex eigenvectors. It is shown how this carries on to rotations by means of the Cayley transformation. Then the necessary tools from real geometric algebra are introduced and a real geometric interpretation is given to the eigenvalues and eigenvectors. The latter are seen to be two component eigenspinors which can be further reduced to underlying vector duplets. The eigenvalues are interpreted as rotors, which rotate the underlying vector duplets. The second part of this paper extends and generalizes the treatment to three dimensions. The final part shows how all entities and relations can be obtained in a constructive way, purely assuming the geometric algebras of 2-space and 3-space.
Category: Algebra

Antisymmetric Matrices are Real Bivectors

Authors: Eckhard Hitzer
Comments: 16 Pages. Mem. Fac. Eng. Fukui Univ. 49(2), pp. 283-298 (2001).

This paper briefly reviews the conventional method of obtaining the canonical form of an antisymmetric (skew-symmetric, alternating) matrix. Conventionally a vector space over the complex field has to be introduced. After a short introduction to the universal mathematical "language" Geometric Calculus, its fundamentals, i.e. its "grammar" Geometric Algebra (Clifford Algebra) is explained. This lays the groundwork for its real geometric and coordinate free application in order to obtain the canonical form of an antisymmetric matrix in terms of a bivector, which is isomorphic to the conventional canonical form. Then concrete applications to two, three and four dimensional antisymmetric square matrices follow. Because of the physical importance of the Minkowski metric, the canonical form of an antisymmetric matrix with respect to the Minkowski metric is derived as well. A final application to electromagnetic fields concludes the work. Keywords: Geometric Calculus, Geometric Algebra, Clifford Algebra, antisymmetric (alternating, skewsymmetric) matrix, Real Geometry
Category: Algebra

Early Works on the Hagen-Poiseuille Flow

Authors: Eckhard Hitzer
Comments: 14 Pages. 4 figures. Mem. Fac. Eng. Fukui Univ. 49(1), pp. 45-53 (2001).

This paper introduces to the early pioneers in the field of laminar flow described by the Hagen Poiseuille law. After giving some biographical information, the experimental setups are briefly explained and the original data are given in the form of diagrams scaled to modern units. Then the way of argument of Hagen, Poiseuille, Hagenbach and others is reviewed. The early historical development of, corrections to, and the scope and limits of the Hagen Poiseuille law receive thus due attention. Keywords: Hydrodynamics, Laminar Flow, Viscosity, Hagen Poiseuille Flow, Hagenbach Correction
Category: Classical Physics

Classical and Semi-Classical Optics with MAPLE: Investigating a Two-dimensional Light Ray Geometry

Authors: Eckhard Hitzer
Comments: 2 Pages. in C.H. Patterson, J. Nadrchal (eds.), Proceedings of Teaching Computational Physics, 12th Summer School on Computational Techniques in Physics, Trest, Czech Republic, 28 Aug.-2 Sep. 2000, pp. 54-56.

Contents: The Geometry of a Two-dimensional Equiangular Spiral - Solving the Transcendental Light Path Equation (T) with MAPLE’s fsolve - MAPLE Programming of a Simple, Nontrivial Ray Tracing Algorithm - Interactive, Iterative Minimization of Errors - Solving the Transcendental Mode Equations (M) - Iterative Numerical Continuation of Solutions to Transcendental Mode Equations - Visualizing Results with MAPLE Plot Stuctures - Porting the Results to Standard Image Formats - Semi-Classical Optics.
Category: Classical Physics

The Physical Theory of Ball Lightning

Authors: Sergey G. Fedosin, A.S. Kim
Comments: 24 Pages. English version of the paper: Sergey G. Fedosin, A.S. Kim, The Physical Theory of Ball Lightning, Applied physics (Russian Journal), No. 1, 2001, P. 69 – 87.

The analysis of modern models of ball lightning displays, that they are unsatisfactory on a series of tests. The model of ball lightning is offered, which exterior electronic envelope is retained by interior volumetric positive charge. The compounded electron motion in an outer envelope creates the strong magnetic field driving a state of ionized hot air inside ball lightning. The conditions of origin surveyed, the estimates of parameters of ball lightnings of different power are made.
Category: Geophysics

The New Electromagnetics From Matter Waves

Authors: Michael Harney
Comments: 6 Pages.

It is well known that Maxwell’s equations describe electromagnetics at an abstract level – no knowledge about atomic theory or quantum mechanics is required. However, this abstraction also overlooks the physical nature of how electromagnetic fields originate and it may be that our concept of charge needs to be replaced with the more fundamental concept of warped spacetime as described by Einstein, and that matter waves may be the result of all electromagnetic (and possibly gravitational) phenomena.
Category: Quantum Physics

Lucasian Primality Criteria for Specific Classes of Numbers of the Form K2^n-1

Authors: Predrag Terzic
Comments: Pages.

Polynomial time prime testing algorithms for specic classes of numbers of the form k2^n-1 are introduced .
Category: Number Theory

Domain Wall Start to “Inflation” with Contributions to Off Diagonal GR Stress Energy Tensor Terms

Authors: A.W.Beckwith
Comments: 6 Pages. Will be seriously improved upon. This is a preliminary document

We represent how an off diagonal representation of stress energy in GR as given by Dodelson can be affected by an axion style domain wall treatment of a stress energy tensor in GR, as given by Kolb and Turner.We argue that this is a way of presenting how domain wall physics may impact graviton production which in turn has, through Dodelson and his off diagonal stress energy terms consequences as to non uniform evolution of space time cosmology. We close with a treatment of axions (a candidate for DM) as impacting GW, and through Dodelson having consequences which we outline at the end of this document. The off diagonal terms of the stress energy tensor alluded to are allegedly for large scale space-time evolution, but the transition for space-time from the big bang to the Electroweak regime is many thousands of times larger than Planckian space-time, so we argue that the off diagonal relation so used still holds
Category: Quantum Gravity and String Theory

Investigation of the Formalism of Particle Dynamics Under the Framework of Classical Mechanics

Authors: ChiYi Chen
Comments: 10 Pages.

In this paper we reconstruct the formulism of particle dynamics under the framework of classical mechanics according to the causal consistency principle, and obtain a new particle dynamical equation. In this derivation there is a most natural and simple assumption that an absolute background of space exists. Because in essence, the absolute background of space must be distinguished from the relative scales of space. The existence of an absolute background can not only be mostly compatible with the physical logic in special theory of relativity, but also retains the most fundamental elements in our intuitional experience. Certainly, the absolute background of space is also the underlying part of Newton's absolute view of space-time. In the application of the new dynamical equation, inertial reference frames are no longer required and inertial forces are no longer introduced by hand. This new dynamical equation can be directly applied in any reference frame which is irrotational with respect to the absolute background of space, namely a moderate general principle of relativity is realized on particle dynamics. The nature of the inertial force is nothing but the real forces exerted on the reference object. Further analysis illustrates that the new particle dynamical equation is more in line with the empirical laws of classical mechanics experiments, than the traditional theoretical formula of Newton's second law.
Category: Relativity and Cosmology

The Relativistic Space-Time Perspective

Authors: David Grant Taylor
Comments: Pages.

This paper formulates additional relativistic equations examining Einstein’s deductions from a Relativistically Distorted Perspective.  The equations derived from a theoretic ideal “non-Relativistic” velocity distorted in the same manner as length, time, and mass – into an apparent “Relativistic” velocity.  Absolute velocity is a necessary logic component for all Relativity equations – its actual determination is unimportant. Relativity physics equations presume ideals.   The equations that are formulated here examine the absolute/real (no Special Relativistic Perspective Distortion, noSRPD) velocity and use it to determine the distorted (Special Relativistic Perspective Distortion, or SRPD) velocity.  For an observer moving at a Relativistic Speed, some aspects of everything outside that traveller’s immediate environment would appear sped up.  That would include the traveller’s movement through space: meaning an apparently higher Relativistic velocity.

Velocity |v| is one of the valid, theoretic ideals that Classic relativity (all of Physics) relies upon.  Two equations developed in this paper show this relationship.  Independent variables have no relativistic deformation [VnoSRPD||Time], the dependent variable is |Time’| because of relativistic deformation.  Existence/non-existence of ideal values for absolute non-relativistic velocity values are not contested, they are indeterminate real ideals. Two examples of Relativistic Perspective equations are:

            Time‘ = Time / (1 + v_noSRPD²/c²)^.5

This paper reasons an inverse relationship: when an independent variable is the observed velocity from the Relativistically Distorted viewpoints.  The parallel equation from that Relativistic Perspective is:

            Time‘ = Time / (1 + v_noSRPD²/c²)^.5

Time’ is the increase in Time units passing on an undistorted Clock, but observed from the distorted viewpoint.  |Time| is what the value would be were there no distortion.  The above relationship allows for the additional development of eight formulae/equations for the velocity, mass, time, and linear deformations.

Relativistic Perspective equations have been confirmed to be consistent with the Classic equations to 2000 significant digits for 37 velocity values ranging from 1.0E-500m/s to (c – (1.0E-500))m/s. 

Keywords: Perspective, Physical Values, Relativistic Distortion, distorted Velocity, parallel relativistic equations, Time, Mass, Length, distortion, equation confirmation table​

The General Relativistic Perspective

Authors: David Grant Taylor
Comments: 48 Pages.

This paper formulates additional General Relativistic [G.R.] equations. They do not contradict General Relativity. They examine the deductions of Dr. Einstein from a relativistically distorted perspective. The equations examine the distorted escape velocity of a G.R. object, determining its true – not relativistically distorted – escape velocity. In contrast to the variables in the Classical equations of Relativity, they are more specific in their aspect, and in their relationship to escape velocity, not simply the time distortion. The values for the quantities of rate (the Time and the Velocity) are the quantities for zero escape velocity||zero deformation. Because there are fewer seconds for a Relativistic Perspective that has distortion, the perspective equations have a different relation. They calculate higher velocity perceived by the observers in a General relativistically distorted body. The escape velocity would appear to increase in exactly same proportion as time – but the energy needed for that escape velocity would decrease because of the slowing of all Bosons – including the Graviton. The development of the equations is done more completely in this paper, but two examples show the principle. The classic Relativity equation reasoned to show the time distortion relationship is:

Time_Relavistic = Time_Real/(1 - 2GM/rc²)^.5

Because the escape velocity formula is [Velocity_Escape = (2GM/r)^.5], then [Velocity_Escape² = 2GM/r]. So the above |Time| equation could also be expressed as:

Time_Relativistic = Time_Real/(1 - Velocity_Escape²/c²)^.5

That could be reasoned to mean that Escape velocity is limited to light speed, just as Real||non-Relativistic velocity is limited to |c|. Less time will go by when there is a relativistic deformation so all Bosons (including the Graviton) would lose their velocity/mass/energy. The inverse relation would be where the independent variables were the observed velocity from the Relativistic or distorted view. The dependent variable would be the True||non-relativistic||non-distorted Time||Escape_Velocity. The parallel equation for that Relativistic Perspective:

Time_Real = Time_Relativistic/(1 + Relativistic_{Escape_Velocity}²/c²)^.5

This relationship allows the additional development of 2 formula/equations for the Escape velocity. There are a number of other equations for Mass and Radius that will be proposed in a following paper. These equations are all of the two Perspectives. All the equations are confirmed to two thousand decimal places for 35 different values to have a range of

|1.0E-500m/s|

to

|c-(1.0E-500)m/s|

without significant error.

Poster for the Rochester Conference on Quantum Optics and Information

Authors: Peter Cameron
Comments: 1 Page.

Nonlocal reduction of entangled states is clarified by considering the role of background independent scale-invariant quantum impedances in decoherence of the unstable elementary particles, providing simple resolution of the black hole information paradox.
Category: Quantum Physics

Twin Planetary Inertial Reference Frames; an Orbiting ECI frame and Inner Rotating ECRF.

Authors: Peter A Jackson
Comments: 4 Pages.

We propose that the persistent anomalies of Earth's inertial frame with respect to transitions from the barycentric frame and Laser Lunar ranging findings are due to over simplification. Applying the two inertial system rest frames, representing the orbiting and rotating frames, is proposed as being more consistent with findings and able to remove anomalies. Earth's plasmasphere and ionosphere, essentially a single kinetic system of particles, does not rotate but orbits the sun with the planet at 370kps. The dense 'two-fluid' plasma bow shock and magnetotail are the distinctive features of the non rotating system or Earth Centred Inertial (ECI) Frame. Inside this system and across the stratospheres, a zone referred to as the 'ignorosphere' due to our limited exploration, lies the rotating Earth Centred Reference Frame (ECRF) which includes Earth's atmosphere. The 'scattering surface' system mixing zones at the frame transitions, particularly the bow shock effect the transformation with the mechanism of coupling and re-emission at the local c by all particles. The proposal is consistent with the postulates of Einstein Special Theory of Relativity (SR) and is implemented by the Quantum Mechanisms of fermion conjugate pair production (Unruh Effect) and Raman atomic scattering
Category: Astrophysics

Little Green Man Gives Answers to Queensland Plan

Authors: Rodney Bartlett
Comments: 6 Pages.

"THE Queensland Plan will outline our shared vision for the next 30 years and identify local and statewide priorities. It will harness the collective wisdom of Queenslanders and guide future activities delivered by all levels of government, business and the community." That's what the Queensland government says at http://queenslandplan.qld.gov.au/about-the-plan/ (Queensland is one of the states in Australia) These are the 6 questions asked on the "Queensland Plan" website, and their answers as given by a Little Green Man who comes from a different planet. I suspect LGM is secretly using this political website to tell us about the science they have in the universities on 22nd-century Mars.
Category: General Science and Philosophy

Magnetic Theory of Radio, Light, X, Gamma, Delta Radiation, and the Wave Particle Duality of Massless Photons Explained

Authors: Glenn A. Baxter
Comments: Five Pageg

A new quantum magnetic theory to explain all forms radiation, including cosmic background, radio, heat, light, X, Gamma, and Delta radiation, which also explains the wave particle duality of mass-less “photons.”
Category: Quantum Physics

On Lorentz Transformation and Special Relativity: Critical Mathematical Analyses and Findings

Authors: Radwan M. Kassir
Comments: 10 Pages. Published in Physics Essays, Vol. 27, No. 1, March 2014. Post-print available at http://physicsessays.org/browse-journal-2/product/138-3-pdf-radwan-m-kassir-n-lorentz-transformation-and-special-relativity-critical-mathematical-analyses-and-findings.html

In this paper, the Lorentz transformation equations are closely examined in connection with the constancy of the speed of light postulate of the special relativity. This study demonstrates that the speed of light postulate is implicitly manifested in the transformation under the form of space-to-time ratio invariance, which has the implication of collapsing the light sphere to a straight line, and rendering the frames of reference origin-coordinates undetermined with respect to each other. Yet, Lorentz transformation is shown to be readily constructible based on this conflicting finding. Consequently, the formulated Lorentz transformation is deemed to generate mathematical contradictions, thus defying its tenability. A rationalization of the isolated contradictions is then established. An actual interpretation of the Lorentz transformation is presented, demonstrating the unreality of the space-time conversion property attributed to the transformation.
Category: Relativity and Cosmology

Our Current Concept of Locality May be Incomplete (Talk Slides)

Authors: Armin Nikkhah Shirazi
Comments: Pages.

The predictions of Bell's inequalities, and their subsequent experimental verification in the form of correlations between spacelike separated events have led to the prevailing current view that `nature is non-local'. Here we examine the possibility that our current concept of locality may at present not be sufficiently differentiated, and that by using 'nature' synonymously with `spacetime' we may have missed an implication of special relativity which by rendering a more complete conception of locality permits such quantum correlations without either hidden variables or violations of locality.
Category: Quantum Physics

Windowed Fourier Transform of Two-Dimensional Quaternionic Signals

Authors: B. Mawardi, E. Hitzer, R. Ashino, R. Vaillancourt
Comments: 20 Pages. Appl. Math. and Computation, 216, Iss. 8, pp. 2366-2379, 15 June 2010. 6 figures, 1 table.

In this paper, we generalize the classical windowed Fourier transform (WFT) to quaternion-valued signals, called the quaternionic windowed Fourier transform (QWFT). Using the spectral representation of the quaternionic Fourier transform (QFT), we derive several important properties such as reconstruction formula, reproducing kernel, isometry, and orthogonality relation. Taking the Gaussian function as window function we obtain quaternionic Gabor filters which play the role of coefficient functions when decomposing the signal in the quaternionic Gabor basis. We apply the QWFT properties and the (right-sided) QFT to establish a Heisenberg type uncertainty principle for the QWFT. Finally, we briefly introduce an application of the QWFT to a linear time-varying system. Keywords: quaternionic Fourier transform, quaternionic windowed Fourier transform, signal processing, Heisenberg type uncertainty principle
Category: Functions and Analysis

Clifford Algebra Cl(3,0)-valued Wavelets and Uncertainty Inequality for Clifford Gabor Wavelet Transformation

Authors: Mawardi Bahri, Eckhard Hitzer
Comments: 2 Pages. Preprints of Meeting of the Japan Society for Industrial and Applied Mathematics, ISSN: 1345-3378, Tsukuba University, 16-18 Sep. 2006, Tsukuba, Japan, pp. 64,65.

The purpose of this paper is to construct Clifford algebra Cl(3,0)-valued wavelets using the similitude group SIM(3) and then give a detailed explanation of their properties using the Clifford Fourier transform. Our approach can generalize complex Gabor wavelets to multivectors called Clifford Gabor wavelets. Finally, we describe some of their important properties which we use to establish a new uncertainty principle for the Clifford Gabor wavelet transform.
Category: Functions and Analysis

Clifford Algebra Cl(3,0)-valued Wavelet Transformation, Clifford Wavelet Uncertainty Inequality and Clifford Gabor Wavelets

Authors: Mawardi Bahri, Eckhard Hitzer
Comments: 23 Pages. International Journal of Wavelets, Multiresolution and Information Processing, 5(6), pp. 997-1019 (2007). DOI: 10.1142/S0219691307002166, 2 tables.

In this paper, it is shown how continuous Clifford Cl(3,0)-valued admissible wavelets can be constructed using the similitude group SIM(3), a subgroup of the affine group of R^3. We express the admissibility condition in terms of a Cl(3,0) Clifford Fourier transform and then derive a set of important properties such as dilation, translation and rotation covariance, a reproducing kernel, and show how to invert the Clifford wavelet transform of multivector functions. We invent a generalized Clifford wavelet uncertainty principle. For scalar admissibility constant it sets bounds of accuracy in multivector wavelet signal and image processing. As concrete example we introduce multivector Clifford Gabor wavelets, and describe important properties such as the Clifford Gabor transform isometry, a reconstruction formula, and an uncertainty principle for Clifford Gabor wavelets. Keywords: Similitude group, Clifford Fourier transform, Clifford wavelet transform, Clifford Gabor wavelets, uncertainty principle.
Category: Functions and Analysis

The Theory of the Distance-Time

Authors: Keith Maxwell Hardy
Comments: 67 Pages.

Defining space and time in a manner that agrees more with an observer who measures distance and time with particles, I create a quantum theory of space and time which is more accurate than the special theory of relativity. This new theory, called distance-time theory, predicts the following quantum principles: Heisenberg's uncertainty principle, the probabilistic location of a particle, and the collapse of this probability once a particle is observed. These principles are derived mostly independent of traditional quantum theory, and they are intrinsic properties of time and space in distance-time theory. However, special relativity theory always gives a particle's exact location and speed. This relativistic result disagrees with the quantum principles previously discussed, but it agrees with classical physics. Special relativity theory is a classical theory, while distance-time theory is a quantum theory. Nevertheless, distance-time theory still predicts proven special relativistic results, and there are novel testable predictions made by distance-time theory. The most notable predictions are those regarding the speed of quantum tunneling and certain characteristics of light. Also, distance-time theory defines distance as equivalent to a time period according to the equation D = cT.
Category: High Energy Particle Physics

Two-Dimensional Clifford Windowed Fourier Transform

Authors: Mawardi Bahri, Eckhard Hitzer, Sriwulan Adji
Comments: 15 Pages. in G. Scheuermann, E. Bayro-Corrochano (eds.), Geometric Algebra Computing, Springer, New York, 2010, pp. 93-106. 4 figures, 1 table.

Recently several generalizations to higher dimension of the classical Fourier transform (FT) using Clifford geometric algebra have been introduced, including the two-dimensional (2D) Clifford Fourier transform (CFT). Based on the 2D CFT, we establish the two-dimensional Clifford windowed Fourier transform (CWFT). Using the spectral representation of the CFT, we derive several important properties such as shift, modulation, a reproducing kernel, isometry and an orthogonality relation. Finally, we discuss examples of the CWFT and compare the CFT and the CWFT.
Category: Functions and Analysis

An Uncertainty Principle for Quaternion Fourier Transform

Authors: Mawardi Bahri, Eckhard Hitzer, Akihisa Hayashi, Ryuichi Ashino
Comments: 20 Pages. Computer & Mathematics with Applications, 56, pp. 2398-2410 (2008). DOI: 10.1016/j.camwa.2008.05.032, 3 figures, 1 table.

We review the quaternionic Fourier transform (QFT). Using the properties of the QFT we establish an uncertainty principle for the right-sided QFT. This uncertainty principle prescribes a lower bound on the product of the effective widths of quaternion-valued signals in the spatial and frequency domains. It is shown that only a Gaussian quaternion signal minimizes the uncertainty. Key words: Quaternion algebra, Quaternionic Fourier transform, Uncertainty principle, Gaussian quaternion signal, Hypercomplex functions Math. Subj. Class.: 30G35, 42B10, 94A12, 11R52
Category: Functions and Analysis

The Theory of Quantum Wave Sources

Authors: Keith Maxwell Hardy
Comments: 48 Pages.

I replace the Copenhagen Interpretation of quantum mechanics with the Wave Source Interpretation, which I give now. When a quantum wave’s location is observed in a small area, it collapses to a transversal wave source. If this small region is three-dimensional, then the quantum wave would act like a three-dimensional transversal wave source. The three-dimensional transversal wave source has characteristics that parallel leptons’ and hadrons’ characteristics. These properties are derived from the wave sources in this paper without relying on quantum theory. I claim that elementary particles have wave sources as their foundational structure.
Category: High Energy Particle Physics

Clifford Fourier Transformation and Uncertainty Principle for the Clifford Geometric Algebra Cl(3,0)

Authors: Bahri Mawardi, Eckhard Hitzer
Comments: 23 Pages. Advances in Applied Clifford Algebras, 16(1), pp. 41-61 (2006). DOI 10.1007/s00006-006-0003-x , 3 tables.

First, the basic concept of the vector derivative in geometric algebra is introduced. Second, beginning with the Fourier transform on a scalar function we generalize to a real Fourier transform on Clifford multivector-valued functions (f: R^3 -> Cl(3,0)). Third, we show a set of important properties of the Clifford Fourier transform on Cl(3,0) such as differentiation properties, and the Plancherel theorem. Finally, we apply the Clifford Fourier transform properties for proving an uncertainty principle for Cl(3,0) multivector functions. Keywords: vector derivative, multivector-valued function, Clifford (geometric) algebra, Clifford Fourier transform, uncertainty principle.
Category: Functions and Analysis

Reasoning about RFID-tracked Moving Objects in Symbolic Indoor Spaces; in Slides

Authors: Sari Haj Hussein
Comments: 39 Pages.

This is a slide presentation of the paper entitled "Reasoning about RFID-tracked Moving Objects in Symbolic Indoor Spaces".
Category: General Science and Philosophy

The Illusion of Light as Transverse Electromagnetic Waves

Authors: Keith D. Foote
Comments: 6 Pages. V2-minor typo corrections

The interpretation of light as transverse waves is critically examined. ‘Old information’ is updated and combined with ‘new information’ and a new model is presented. The behavior of electromagnetic waves is examined and compared with that of longitudinal sound waves. Synchrotron and Cerenkov radiation are used as supporting evidence showing light waves are not transverse in nature, and are transported by a medium.
Category: Quantum Physics

A Possible Unimportant But Sure Interesting Conjecture About Primes

Authors: Marius Coman
Comments: 2 Pages.

Studying, related to Fermat pseudoprimes, my main object of study, the concatenation and the primes of the form n*p – n + 1, where p is also prime, I found incidentally an interesting possible fact about primes. Because the proof or disproof of the conjecture, and also the consequences in the case that is true, are beyond me, I shall limit myself to enunciate the conjecture and give few examples.
Category: Number Theory

Corrections to 'Energy Theory of Matter & Cosmology' & 'Foundation of Theory of Everything: Non-living & Living Things'

Authors: Mohammad Shafiq Khan
Comments: 25 Pages. These articles were published in Indian Journal of Science & Technology

Consequent upon showing the fallacy of the adopted paradigm of physics an alternative paradigm of physics emerges. These articles are concerned with the basic model of physics under the alternative paradigm of physics according to which space is finite, absolute & filled up with ether, the electric dipoles on the base substance which has been named as ‘energy’ unlike the meaning as applies in the adopted main-stream physics; time is emergent & relative, depending upon the motion of the object/observer with respect to the absolute reference frame of ether at rest, matter is emergent from different electric dipoles with base substance of ‘energy’ and light/radiation is the vibrations of the charge on the electric dipoles of ether which propagates in the medium of ether in the form of longitudinal wave motion. During the process of development of the alternative model of physics changes in the basic model of physics proposed under these two articles had to be incorporated. Besides there were some errors in the printed version of these two articles which are corrected herein for record.
Category: Relativity and Cosmology

Information – Entropy Theory of Physics

Authors: George Rajna
Comments: 7 Pages.

Considering the positive logarithmic values as the measure of entropy and the negative logarithmic values as the measure of information we get the Information – Entropy Theory of Physics, used first as the model of the computer chess program built in the Hungarian Academy of Sciences. Applying this model to physics we have an understanding of the perturbation theory of the QED and QCD as the Information measure of Physics. We have an insight to the current research of Quantum Information Science. The generalization of the Weak Interaction shows the arrow of time in the associate research fields of the biophysics and others. We discuss also the event horizon of the Black Holes, closing the information inside.
Category: Quantum Physics

Solar Magnetism in Little Ice Age, Orbits in Solar Ecliptic, Galactic Centre Cloud G0.253+0.016, Speed of Gravity, Collisions of Universes

Authors: Rodney Bartlett
Comments: 7 Pages.

The beginning of this article is a few years ago, when I wrote about the Little Ice Age of 1645-1715 and how magnetic fields in the Sun restrict the motion of charged particles. This was followed by a 2013 letter in Astronomy magazine that made me wonder why planets orbit in the Sun’s ecliptic plane. I thought about this for awhile and decided my Little Ice Age ideas could help answer the question. Then I read about a solar nebula near the Milky Way’s centre which has approx. 45 times the density of gas needed to initiate star formation but is essentially starless, producing no high-mass stars. After some thought, it occurred to me that the ideas concerning the ecliptic could be extended to explain this strange low-star-formation cloud. The original ideas and their extension embrace an idea of Albert Einstein’s - subatomic particles forming from gravitation. Continuing my astronomical interests, I read an article called “Why the universe has no center”. This inspired a couple of queries (and their possible answers) in my mind – “Can the speed of gravitational waves be both finite and infinite?” and “Can an infinite universe expand?”
Category: Relativity and Cosmology

The Model of Two Spaces.

Authors: Igor Elkin
Comments: 15 Pages. -

We propose the model that gives the explanation of some not entirely clarified chapters of the modern Physics through the use of the elementary formulae. Partly it explains the formation of the inertial and gravitational mass, the cause of the occurring of the gravitation and the divergence of the material points of the Universe, explains the cause of “shortening” of the length in motion, explains Red shift and the cause of changing Hubble constant, that is attributed to the dark energy.
Category: Relativity and Cosmology

The Model of Majorana Particle Travelling at the Speed of Light

Authors: Murod Abdukhakimov
Comments: 5 Pages.

In this paper we present the model of Majorana particle travelling at the speed of light.
Category: High Energy Particle Physics

Manifesto. Galactic Internet

Authors: Alexander M. Ilyanok
Comments: 33 Pages.

On the base of deterministic picture of micro and macro world I made a systematization of large number of known experimental data. I found new functional relations between fundamental physical constants. As a result we obtain new Knowledge, which changes current picture of the world. In proposed new picture the gravitation and electromagnetism are unified. The highest degree of coincidence with experiment and the simplicity of obtained equations are the main proof of obtained picture of the world. It is demonstrated that the velocity of condensed body not exceed 1/500 speed of light, though the speed of elementary particles can reach the speed of light. Low speed of motion for condensed bodies, including astronaut and spaceship, do not allow us to reach the newly discovered extra-solar planets – super-Earths. From the other side it is demonstrated that speed of gravitation interaction is 3.5∙108 times more than speed of light which give us opportunity to create new communication lines for information. We propose to create a new type of receivers and transmitters of gravitation waves, based on macro-quantum coherent phenomena. The application of these devices gives us possibility to made a tomography of Earth as a whole object and to construct the communication system on supraluminal speed. As a result the mankind obtains the possibility in principle to join the world intellect by the galactic Internet. New Earth model, Super-Earth, macro-quantum coherent effects, quantum astronomy, supraluminal communication channels, galactic Internet, fundamental physical constants.
Category: Astrophysics

How Electrical Machine Works

Authors: Mourici Shachter (Shechter)
Comments: 23 Pages.

The induction machine is widely used for about 100 years. The physics of the machine is solved using tensor and large matrices. And the physical explanation sinks into endless mathematical expressions. Tesla the engineer that invented the ac generators did not understood the meaning of the mathematical expressions and because of that he believed that electric power can be transmitted in wireless system like in cellular phones and unfortunately or fortunately is experiment to transmit energy failed. In this paper I arrange sinusoidal function in symmetric group. As a result I don’t need tensor or matrices to describe the induction machine behavior. Really, the first aim of this paper is to explain phenomena's like relative movement as happens in Relativity The second aim is to show that if we choose "good" coordinates we make the solution very short and clear third aim is to show that we can make time depended problem to behave as constants So from this paper one can learn a lot how to simplify physical and mathematical problems. The induction machine is only an example how to "attack" a problem
Category: Classical Physics

"The New si – Another Proposal on the Future Revision of the International System of Units"

Authors: Gocho V. Sharlanov
Comments: 12 Pages.

This article is an alternative to the proposal of 24th meeting of the General Conference on Weights and Measures (CGPM) for a future revision of the International System of units (SI). It concerns the “Resolution 1” of 24th meeting of CGPM and the “Draft Chapter 2 for 9th SI brochure, following redefinitions of the base units”. The article represents a completely new approach for creation of a new SI of proper physical units, based on proper principles of definition. A new SI-structure and new proper units’ definitions are proposed for discussion during the next meeting of the CGPM. Actually, the article represents a concept of next generation SI, oriented to the future.
Category: Classical Physics

Do Photons exist in Spacetime?

Authors: Armin Nikkhah Shirazi
Comments: 6 Pages.

Under our current worldview, it is taken to be so obvious an assumption that objects characterized by $v=c$ exist in spacetime that it is not even bothered to explicitly mention it. This paper will present 4 simple arguments based on the special theory of relativity which at least suggest that this obvious assumption should be put into question. These arguments cannot be considered conclusive, but when considered together they support the case that this question should be seriously investigated.
Category: Relativity and Cosmology

Asymmetry Due to Quantum Collapse (Paper)

Authors: Armin Nikkhah Shirazi
Comments: 6 Pages. This is the paper version, a poster version has also been uploaded

This paper points out an internal tension between quantum collapse and expressions which set eigenstates equal to superposition states in a different basis and thereby imply that pre-measurement and immediate post-measurement states are of the same kind. Its resolution appears to be either to discard the collapse postulate or to consider such states to be of distinct kinds with respect to their association with a superposition of properties.
Category: Quantum Physics

How New Scientists are Brainwashed

Authors: Jeffrey Joseph Wolynski
Comments: 1 Page.

It is given explanation as to how new young scientists are brainwashed to believe what ever their professors want them to believe.
Category: General Science and Philosophy

The Optical Breakdown Density Limit Gamma Giving the Lorentz Transformation Mechanism

Authors: Peter A Jackson
Comments: 6 Pages.

The maximum possible density of conjugate ionized pairs produced by photo-ionization is defined as the optical breakdown (OB) density, which may be considered in terms of minimum wavelength (l) as gamma. Applying Raman atomic scattering to the shocks and transition zones treated as two-fluid plasmas we identify the effects of approaching gamma on the absorption and re-emission process. We theoretically describe how the maximum density and related minimum wavelength limit produce the increasing resistance to electromagnetic (EM) wave permeability at propagation velocities approaching c. The increased ionization with increase speed through the quantum vacuum is found analogous to the Unruh effect and not in conflict with the postulates of Einstein's Special Theory of Relativity (SR). Heat and sound is produced as density and resistance increases to the ion density limit 1021/cm-3. The effect at OB provides a mechanism to implement the Lorentz Transformation (LT) by producing the 'gamma' curve as a resistance curve to matter in motion at increasing speeds in the quantum vacuum due to the bow shock photo-ionisation.
Category: Relativity and Cosmology

The Intelligent Bit

Authors: Peter A Jackson
Comments: 11 Pages.

An intelligent 'IQbit' is found in hierarchical 'Sample Space' sub-sets hidden in the Excluded Middle between binary 0,1 values. Complex but causal distributions of intensity are found equivalent to Gödel's non-integer 'n-valued' or 'Fuzzy' logic, not accessible to binary systems. When tested by asking more than the 'yes/no' limit identified by John Wheeler the IQbit proves surprisingly capable of resolving the EPR paradox causally, without action-at-a-distance or superluminal signalling. New experiments comparing single photon pairs are proposed, predicted to reveal 'cosine curve' distributions from each detector, as John von Neumann proposed. Uncertainty and determinism emerge more consistently superposed. New 'dimensions' and degrees of freedom provide the power, implying new law of nature with a domain limited to only 'real' entities and interactions, giving quantum mechanical statistical probability amplitudes as Bayesian inverse distributions. The law may then be termed the “Law of the Reducing Middle”. Probabilities of any occurrence in an infinite universe are non-zero. A related suggestion emerges; that no two real entities precisely identical at observable scale exist at any time. The fundamental rule of mathematics, also assumed for predicate logic and calculus; A = A is then replaced only for natural phenomena with the 'similar' A~A. The natural 'Dividing Line' discussed by Dirac between entities precisely mathematically describable and the rest is identified, the two parts distinguished as; physical (entities and interactions) and; metaphysical. Only the metaphysical class retains an excluded middle between binary 0,1. The class includes; cardinalised integers, assigned symbols, algebra, finite values and numerical derivatives; speed, frequency, correlations etc. Bell assumed simple binaries precisely modelled reality. 'Squaring' 2D waves creates the 3D IQbit torus wound by helices harnessing orbital angular momentum and describing a helix when translating axially. Field and relative orientations on interaction (detection) varies intensity distribution as the cosine, as Malus's Law.
Category: Relativity and Cosmology

Thermal Neutron Accelerator

Authors: C.Amareshwar Prasad
Comments: 23 Pages.

The main aim of this proposal it to reveal the secrets of the universe by accelerating neutrons. The proposal idea in its abridged version speaks about the possibility of making neutrons accelerate with help of thermal energy and magnetic energy under controlled conditions. Which is helpful in revealing the hidden secrets of the universe like dark energy and in finding Higgs Boson.
Category: High Energy Particle Physics

Understanding the LivMach Framework

Authors: Shreyak Chakraborty
Comments: 4 Pages.

We introduce the alpha version of a C++ Computational Framework to simulate life processes in the body of a living multicellular organism by virtually replicating the data flow of the actual living being in real time. LivMach Framework is an open source project on Sourceforge.net We use various data structures to effectively simulate all components of a living organism 's body. Due to the absence of a Graphical User Interface(GUI), we use special indicator statements to display the flow of data between various parts of the virtual body. Using this code,one can simulate the complete physical,mental and psychological behaviour of simple and complex multicellular organisms on low cost machines.
Category: Data Structures and Algorithms

Asymmetry Due to Quantum Collapse (Poster)

Authors: Armin Nikkhah Shirazi
Comments: 1 Page. Presented at "Quantum Foundations and Quantum Information" Workshop in Vaxjo, Sweden 6.11-6.13

This poster points out an internal tension between quantum collapse and expressions which set eigenstates equal to superposition states in a different basis and thereby imply that pre-measurement and immediate post-measurement states are of the same kind. Its resolution appears to be either to discard the collapse postulate or to consider such states to be of distinct kinds with respect to their association with a superposition of properties.
Category: Quantum Physics

The Splitting Dark Matter- Black Hole- Big Bang and the Cyclic Multiverse.

Authors: Leo Vuyk
Comments: 25 Pages. 25

According to Quantum FFF Theory, the FORM and MICROSTRUCTURE of elementary particles, is supposed to be the origin of FUNCTIONAL differences between Higgs- Graviton- Photon- and Fermion particles. As a result, a NEW paradigm of splitting-, accelerating- and pairing Black Hole seems to be able to accelerate itself by a -Zero Point Energy driven-self created plasma tails ( by a new Quantum Fluctuation process), to form dumbbell systems, of two or even more black holes. Inside Nebula these dumbbell systems are called Herbig Haro systems. Inside the early universe however these systems are observed as dumbbell shaped radio lobes at both sides of early galaxies (Faint B3 radio galaxies). Recent cosmic observations of the infra red and x-ray background radiation of the universe by Chandra and Spitzer space telescopes (CIB and CXB), suggest that even direct after the big bang ABUNDANT black holes already existed. This can be interpreted as a support for a Black Hole splitting Big Bang and a Black Hole pairing Big Crunch before, thus there is reason to propose a cyclic Universe. In Quantum FFF theory, the chirality of the universal vacuum lattice is proposed to be the origin of negative- or positive charged black holes and the origin of the formation of matter over anti-matter around negative charged black holes as in our universe seems to be the case. The chirality of the oscillating Higgs vacuum is supposed to be the origin of preferred Positron attachment with three different shaped monopole Gluon/photons for easy Quark formation without a lot of particle annihilation back into the Higgs vacuum. At the same time, the possibility of a chiral universal vacuum is reason to support the idea of a super symmetric raspberry shaped multiverse, with multiversal copy universes, instant entangled down to all quantum systems as the base for all wavefunction collapses and emergence at the quantum level and above..
Category: Astrophysics

A General Family of Dual to Ratio-Cum-Product Estimator in Sample Surveys

Authors: Rajesh Singh, Mukesh Kumar, Pankaj Chauhan, Nirmala Sawan, Florentin Smarandache
Comments: 8 Pages.

This paper presents a family of dual to ratio-cum-product estimators for the finite population mean. Under simple random sampling without replacement (SRSWOR) scheme, expressions of the bias and mean-squared error (MSE) up to the first order of approximation are derived. We show that the proposed family is more efficient than usual unbiased estimator, ratio estimator, product estimator, Singh estimator (1967), Srivenkataramana (1980) and Bandyopadhyaya estimator (1980) and Singh et al. (2005) estimator. An empirical study is carried out to illustrate the performance of the constructed estimator over others.
Category: Statistics

Connection Between Gravity and Electromagnetism

Authors: Octavian Balaci
Comments: 20 Pages. Octavian Balaci (2014) Connection between Gravity and Electromagnetism, Astronomical Review, 9:2, 4-28, DOI: 10.1080/21672857.2014.11519731

A new interpretation of electrodynamics and gravity is presented, based on the idea that the electromagnetic and gravitational properties of vacuum are connected. The space and time are treated as imaginary concepts. With this, the electrodynamics and gravitational phenomena can be explained with a Galilean invariant vacuum. Also a new way to explain the gravitational attraction will result.
Category: Relativity and Cosmology

Counterfeit/obsolete Equipment and Nuclear Safety Issues of Vver-1000 Reactors at Kudankulam, India

Authors: VT Padmanabhan, R Ramesh, V Pugazhendi, K Sahadevan, Raminder Kaur, Christopher Busby, M Sabir, Joseph Makkolil
Comments: 15 Pages. Keywords: Counterfeit reactor equipment, Nuclear Safety, Global Catastrophic Risk, Reactor Pressure Vessel, Core Damage Frequency, Radiological Disaster, Kudankulam Nuclear Power Plant, VVER-1000, obsolete reactor equipment.

Counterfeit equipment is becoming a major threat to nuclear safety globally. The Kudankulam Nuclear Power Plant (KKNPP) in India housing two VVER-1000 reactors, imported from Russia is being delayed because of counterfeit, substandard and obsolete equipment. The polar crane, the limb of the reactor, is defective as its hoisting capacity is less than 80% of its nameplate capacity. The crane is used for installing the equipment inside the reactor building and also for removing spent fuel. The contract said that there will be no weld in the beltline of the reactor pressure vessel (RPV). The received vessels have two circumferential welds on the beltline. RPV, the heart of the reactor is irreplaceable and hence determines the life of the reactor. RPV and polar crane are safety grade equipment. The core-damage frequency(CDF) of the reactor in the contract was 10e−7reactor-years, while the supplied reactor has a CDF of 10e−5reactor-years. Two units of generator transformers were received as damaged and these were dismantled and reassembled at the site. This paper finds evidences of the unethical practices of sale and use of obsolete and counterfeit reactor equipment and discusses the global catastrophic risks with reference to the international nuclear safety standards.
Category: Nuclear and Atomic Physics

The Hydrogen Atom Relativistic Model

Authors: Mourici Shachter (Shechter)
Comments: 7 Pages.

In this paper the hydrogen atom is solved using Einstein Relativity Theory without any approximation. The solution is very short and simple. What I get is the exact behaviors of the hydrogen atom including Relativity the results are not linear, so linear differential equation like Schrödinger Equation Dirac Equation or Klein Gordon Equation deliver complicate expressions. My solution is just simple and elegant. Most of the result published in the Wikipedia differ from my results and must be checked to establish the correct model
Category: Quantum Physics

The Dimensional Universe. Proving Infinite Dimension and Time.

Authors: Jeremy Michael Poulos
Comments: 4 Pages.

Let's do a little bit of math work. You're given a pattern, and told that there is no other information available to the entire human race at this current time to identify this pattern! The pattern is as follows: 1 2 3 4 5 6 X. Based on this available information, what is the most logical value for x? 7. Now, in our known universe, there also exists a pattern. A point, has a value of infinity^0. It has an area of one POINT. It is one point. The dimension of it, it one point. A line, is an infinite number of points on an X or Y Axis. Infinity ^ 1. An area, is an infinite number of points on an X AND Y axis. Infinity ^ 2. While the number of points do not increase, the limitations on the locations at which these points can exist increases exponentially. As a point has no identifiable area, in any dimension from a point itself, to a cube, there will always be room for infinite points. Now, the complexity constraints of where the points may exist will increase one more time when we move to the third dimension. Infinity ^ 3. Volume! Still, infinite available points, but now, an infinitely larger area to place them. But hey, you can have all the gold cubes in the world, but you can not spend them if time never happened! Why do you think time appears LINEAR to us, when we live in the third dimension? That's because the fourth dimension is also a line. It is a set of points in time, in which, any volumized object can exist. Now, there's another pattern that emerges. For a point to exist, it needs to exist on a line. Why? Because you can not define its location otherwise, and without defining a location, it can not be observed. That which can not be observed within Dimension 2, that exists in dimension 1, doesn't exist, as it's not "part" of the dimension. So, for a point to exist, it needs a location on a line. For a line to exist, you have to locate it on a plane. What is a plane with a thickness of zero? Nothing. It needs a Z value, a thickness, or it is literally, nothing. Now, what logically defines the NEXT LINEAR dimension by which we regularly define the location of matter within our universe? (Note that each advancement in dimensions previously only increased the complexity by a line, or +-infinity, multiplied into the number of existing points.) Everyone experiences a linear travel in this world, by which our physical bodies and all matter moves. It moves through TIME. Therefor, i theorize, that dimension four, is, in fact, time.
Category: General Science and Philosophy

Cálculo de la Cantidad de Números Primos Que Hay Por Debajo de un Número Dado //// How to Calculate the Amount of Prime Numbers that Are Less Than a Given Number

Authors: Germán Paz
Comments: 92 Pages. En español. // In Spanish.

En este documento se explica un procedimiento para calcular la cantidad exacta de números primos que hay por debajo de cualquier número entero mayor que 4. Al momento de escribir este documento, se pensó que se había llegado a un resultado nuevo. Es por eso que este trabajo está escrito describiendo el mencionado procedimiento como algo nuevo. Sin embargo, mucho después de haber escrito este trabajo, se le señaló al autor que el procedimiento en cuestión ya había sido descubierto por Adrien-Marie Legendre.

De todos modos, este documento es útil para quien quiera entender el algoritmo de Legendre para calcular la cantidad exacta de números primos que hay por debajo de un número dado.

Para una demostración de las dos primeras fórmulas que aparecen en la pág. 72 (las cuales describen una de las propiedades del Triángulo de Pascal), ver vixra.org/abs/1303.0163 (Lemas 3 y 6). Combinando lo explicado en la pág. 39 y en las págs. 60 a 72 con las mencionadas fórmulas de la pág. 72, se puede ver la relación que existe entre una de las propiedades del Triángulo de Pascal y el algoritmo de Legendre.

Éste es un trabajo muy antiguo. En algunos casos se usó una simbología distinta a la convencional.

///////////////////

In this paper we explain a procedure to calculate the exact amount of prime numbers that are less than an integer greater than 4. At the time of writing this paper, the author thought he had obtained a new result. This is why in this work the mentioned procedure is described as something new. However, a long time after this work had been written, it was pointed out to its author that the method described had already been discovered by Adrien-Marie Legendre.

Anyway, this paper is useful for anyone who wants to understand Legendre's algorithm to calculate the exact amount of primes that are less than a given number.

For a proof of the first two formulas that appear on page 72, see vixra.org/abs/1303.0163. If we combine what is explained on page 39 and on pages 60 to 72 with the mentioned formulas on page 72, we will see that there exists a relation between one of the properties of Pascal's Triangle and Legendre's algorithm.

This is a very old work.

Critical Analysis of the Bennett–Riedel Attack on the Secure Cryptographic Key Distributions Via the Kirchhoff-Law–Johnson-Noise Scheme

Authors: Laszlo B. Kish, Derek Abbott, Claes-Goran Granqvist
Comments: 33 Pages. Accepted for publication at PLOS ONE

Recently, Bennett and Riedel (BR) (http://arxiv.org/abs/1303.7435v1) argued that thermodynamics is not essential in the Kirchhoff-law–Johnson-noise (KLJN) classical physical cryptographic exchange method in an effort to disprove the security of the KLJN scheme. They attempted to demonstrate this by introducing a dissipation-free deterministic key exchange method with two batteries and two switches. In the present paper, we first show that BR’s scheme is unphysical and that some elements of its assumptions violate basic protocols of secure communication. All our analyses are based on a technically-unlimited Eve with infinitely accurate and fast measurements limited only by the laws of physics and statistics. For non-ideal situations and at active (invasive) attacks, the uncertainly principle between measurement duration and statistical errors makes it impossible for Eve to extract the key regardless of the accuracy or speed of her measurements. To show that thermodynamics and noise are essential for the security, we crack the BR system with 100% success via passive attacks, in ten different ways, and demonstrate that the same cracking methods do not function for the KLJN scheme that employs Johnson noise to provide security underpinned by the Second Law of Thermodynamics. We also present a critical analysis of some other claims by BR; for example, we prove that their equations for describing zero security do not apply to the KLJN scheme. Finally we give mathematical security proofs for each BR-attack against the KLJN scheme and conclude that the information theoretic (unconditional) security of the KLJN method has not been successfully challenged.
Category: Data Structures and Algorithms

Covariant Theory of Gravitation

Authors: Sergey G. Fedosin
Comments: 5 Pages. Essay written for the Gravity Research Foundation 2013 Awards for Essays on Gravitation

The history of appearance and characteristics of covariant theory of gravitation (CTG) and its difference from the general theory of relativity (GTR) are described. CTG is developed as an axiomatic theory based on five axioms using the language of 4-vectors and tensors, and is derived from the principle of least action and through Hamilton equations. In CTG gravitational radiation of any body is based on equation of its motion and has a dipole component. In GTR we proceed from the tensor nature of metric field and take into account all the bodies of considered material system at once, and therefore the basis of gravitational radiation is only the quadrupole component. The CTG Hamiltonian is obtained in two ways – either through 4-velocity or through generalized 4-momentum.
Category: Relativity and Cosmology

Santilli-Jiang Isomathematics for Changing Modern Mathematics

Authors: Chun-Xuan Jiang
Comments: 5 Pages.

To generalise the modern mathematics we establish Santilli-Jiang isomathematics.
Category: Number Theory

A DNA-Binding Protein Gata1 with a Biological Unit Fog1 Zinc Finger Protein Molecule is Synergistic to the Region of the X Chromosome Which Occurred at a 'exome' Splice Site X-Linked Involving the Gata-Type Zinc Finger Domain.

Authors: Mark R. Brenneman
Comments: 3 Pages.

The human ERYF1 gene (summary) NF-E1 DNA-binding protein GATA1, locus Xp11.23
Category: Quantitative Biology

On Space Bombs

Authors: S. Kalimuthu
Comments: 3 Pages. This is only a proposal.And the road to space bombs is TOO and TOO long.

The space is not empty.It is full of energy.According to the law of conversation of energy, one form of energy can be converted in to another form.In this work, the author proposes to make space bombs out of space enrgy.
Category: Nuclear and Atomic Physics

Anti-Semitism as a Part of Anti-Intellectualism: Logical and Religious Outlooks and the Conditional Optimism

Authors: Emanuel Gluskin
Comments: 16 Pages. The presented line of thought makes several, otherwise not unexplained things, including the Holocaust, coherent, and the main warning regarding the dictatory role of intellectualism in modern society is important. All from the mind and heart!

An explanation of Anti-Semitism in terms of the problem that simple people (i.e. those who want to live with a clear mind and be thus respected) have with the intellectual predominance existing in society, i.e. an explanation of Anti-Semitism in terms of the Anti-Intellectualism, is given. The problem of anti-intellectualism is not associated with the "Critique of Pure Reason" again, in any new form, but with protesting the tough (sometimes cruel or even hooligan) dictatorship of the Ruling Intellect. The constructive conclusion is that the media of information, like TV or radio, have to cease making intellectualism the main societal ideal. Human mind should not be overloaded, and it should be "fed" by information that it can well "digest". The thinking ability is given to us (just as any our ability) once and forever, and it has some natural limitations which have to be carefully studied and respected. This point, associated with Anti-Semitism, is the main focus of the discussion in which the author expresses strong sympathy to his nation, but also strong belief that human nature and human society are something good, and tries to be objective with respect to all sides.
Category: Mind Science

Version of Proof of Morley's Trisector Theorem

Authors: Michael Pogorsky
Comments: 2 Pages.

The properties of trisected triangle are utilized in this proof in the way different from other known proofs.
Category: Geometry

How Dirac and Majorana Equations Are Related

Authors: Murod Abdukhakimov
Comments: 4 Pages.

Majorana and Dirac equations are usually considered as two different and mutually exclusive equations. In this paper we demonstrate that both of them can be considered as a special cases of the more general equation.
Category: High Energy Particle Physics

The Universe Rotates And Is No Big Bang

Authors: Dan Visser
Comments: 4 Pages.

I found a ‘quadruple image’ of ‘Hot and Cold Spots’ in the CMB-image, published by the gathered data of the Planck-satellite in 2013, and analyzed by me in the context of the (new) Double Torus cosmology. The ‘quadruple image’ proves the Universe rotates!! The ‘quadruple image’ follows the logic of a ‘dark flow’ in the Double Torus. This ‘dark flow’ is expressed in my (new) dark energy force-formula and astronomically determined. Hence, the Double Torus (until now a hypothesis), is changing into “hitting the right spot”, or in other words: “starts being a real model” !! The new cosmology is extensively described in a series of papers of mine, hosted in the vixra-archive in the category Mathematical Physics.
Category: Mathematical Physics

Nemateria, Ipoteza Smarandache și Fuziunea Informației

Authors: Mircea Monu
Comments: 168 Pages.

Acest volum reuneşte articole scrise de fizicianul si jurnalistul Mircea Monu, cu eliminarea unor paragrafe repetitive. Articolele au apărut în perioada 2009-2012 în publicaţii tipărite („Monitorul de Vâlcea”, „Constelaţii diamantine”, „Semănătorul”) şi reviste online, şi reflectă parte din prodigioasa activitate recentă a omului de ştiinţă şi scriitorului Florentin Smarandache, in special privind termenul de “nematerie” introdus in fizica, “Ipoteza Smarandache” ca nu exista limita de viteza in univers, si cercetari in fuziunea informatiei.
Category: General Science and Philosophy

Six Polynomials in One and Two Variables that Generate Poulet Numbers

Authors: Marius Coman
Comments: 3 Pages.

Fermat pseudoprimes were for me, and they still are, a class of numbers as fascinating as that of prime numbers; over time I discovered few polynomials that generate Poulet numbers (but not only Poulet numbers). I submitted all of them on OEIS; in this paper I get them together.
Category: Number Theory

Electron Wind Generator

Authors: Alexander Bolonkin
Comments: 10 Pages. 4 figs, 1 table.

Author offers a new method of getting electric energy from wind. A special injector injects electrons into the atmosphere. Wind picks up the electrons and moves them in the direction of wind which is also against the direction of electric field. At some distance from injector a unique grid acquires the electrons, thus charging and producing electricity. This method does not require, as does other wind energy devices, strong columns, wind turbines, or electric generators. This proposed wind installation is cheap. The area of wind braking may be large and produces a great deal of energy. Although this electron wind installations may be in a city, the population will not see them.
Category: Classical Physics

Extended Mass Relation for Seven Fundamental Masses and New Evidence of Large Numbers Hypothesis

Authors: Curtis J. Forsythe, Dimitar T. Valev
Comments: 9 pages, minor changes, paper is published in Physics International, 2014, Vol. 5, Issue 2, pp. 152-158

A previously derived mass relation has been extended to seven equidistant fundamental masses covering an extremely large mass range from ~ 10^(-69) kg to ~ 10^53 kg. Six of these masses are successfully identified as mass of the observable universe, Eddington mass limit of the most massive stars, mass of hypothetical quantum “Gravity Atom” whose gravitational potential is equal to electrostatic potential e^2/S, Planck mass, Hubble mass and mass dimension constant relating masses of stable particles with coupling constants of fundamental interactions. The seventh mass, ~ 10^(-48) kg remains unidentified and could be considered as a prediction of the suggested mass relation for an unknown fundamental mass, potentially a yet unobserved light particle. First triad of these masses describes macro objects, the other three masses belong to particle physics masses, and the Planck mass appears intermediate in relation to these two groups. Additionally, new evidences of Dirac Large Numbers Hypothesis (LNH) have been found in the form of series of ratios relating cosmological parameters and quantum properties of space-time. A very large number on the order of 5x10^60 connects mass, density, age and size of the observable universe with Planck mass, density, time and length, respectively.
Category: Relativity and Cosmology

Time and Orbits

Authors: Florentino Muñiz Ania
Comments: 4 pages English (traslation); 4 pages Spanish (original)

This article is a summary of the development of the possibility that the time is quantized further given, along with the graviton and angular momentum, for links between particles and stars. It further believes that all orbits orbit at the same speed, which is the highest for phenomena thermodynamic.
Category: Quantum Gravity and String Theory

Images of Wave Function Solutions for the Electron and Positron Generated by Vectpotential 3D Finite Element Modeling Software

Authors: Declan Traill
Comments: 10 Pages. (c) 2013 Declan Traill

The images [fig 1-9] in this paper are graphical representations of the fields generated by these wave functions using a 3D finite element vector modeling program [ref 1] I wrote to aid in the visualization and testing of proposed wave function solutions.
Category: Quantum Physics

Some Results on Smarandache Groupoids

Authors: H. J. Siamwalla, A.S.Muktibodh
Comments: 7 Pages.

In this paper we prove some results towards classifying Smarandache groupoids which are in Z*(n) and not in Z(n) when n is even and n is odd.
Category: Algebra

Smarandache Half-Groups

Authors: Arun S. Muktibodh
Comments: 5 Pages.

In this paper we introduce the concept of half-groups. This is a totally new concept and demands considerable attention. R.H.Bruck [1] has defined a half groupoid. We have imposed a group structure on a half groupoid wherein we have an identity element and each element has a unique inverse. Further, we have defined a new structure called Smarandache half-group. We have derived some important properties of Smarandache half- groups. Some suitable examples are also given.
Category: Geometry

Smarandache Mukti-Squares

Authors: Arun S. Muktibodh
Comments: 7 Pages.

In [4] we have introduced Smarandache quasigroups which are Smarandache non-associative structures. A quasigroup is a groupoid whose composition table is a Latin square. There are squares in the Latin squares which seem to be of importance to study the structure of Latin Squares. We consider the particular type of squares properly contained in the Latin squares which themselves contain a Latin square. Such Latin squares are termed as Smarandache Mukti-Squares or SMS. Extension of some SMS to Latin squares is also considered.
Category: Algebra

Smarandache Quasigroup Rings

Authors: Arun S. Muktibodh
Comments: 6 Pages.

In this paper, we have introduced Smarandache quasigroups which are Smarandache non- associative structures. W.B.Kandasamy [2] has studied groupoid ring and loop ring. We have de¯ned Smarandache quasigroup rings which are again non-associative structures having two binary operations. Substructures of quasigroup rings are also studied.
Category: Algebra

Smarandache Quasigroups

Authors: Arun S. Muktibodh
Comments: 7 Pages.

In this paper, we have introduced Smarandache quasigroups which are Smaran- dache non-associative structures. W.B.Kandasamy [2] has studied Smarandache groupoids and Smarandache semigroups etc. Substructure of Smarandache quasigroups are also studied.
Category: Algebra

Smarandache Semiquasi Near-Rings

Authors: Arun S. Muktibodh
Comments: 3 Pages.

G. Pilz [1] has dened near-rings and semi-near-rings. In this paper we introduce the concepts of quasi-near ring and semiquasi-near ring. We have also dened Smarandache semiquasi-near-ring. Some examples are constructed. We have posed some open problems.
Category: Algebra

Sequences of Pentagonal Numbers

Authors: Arun S. Muktibodh
Comments: 7 Pages.

Shyam Sunder Gupta [3] has dened Smarandache consecutive and reversed Smarandache sequences of triangular numbers. Delm F.M.Torres and Viorica Teca [1] have further investigated these sequences and dened mirror and symmetric Smarandache sequences of triangular numbers making use of Maple system. Working on the same lines we have de- ned and investigated consecutive, reversed, mirror and symmetric Smarandache sequences of pentagonal numbers of dimension 2 using the Maple system .
Category: General Mathematics

Sequences of Pyramidal Numbers

Authors: Arun Muktibodh, Uzma Sheikh, Dolly Juneja, Rahul Barhate, Yogesh Miglani
Comments: 7 Pages.

Shyam Sunder Gupta [4] has de¯ned Smarandache consecutive and reversed Smarandache sequences of Triangular numbers. Del¯m F.M.Torres and Viorica Teca [1] have further investigated these sequences and de¯ned mirror and symmetric Smarandache sequences of Triangular numbers making use of Maple system. One of the authors A.S.Muktibodh [2] working on the same lines has de¯ned and investigated consecutive, reversed, mirror and symmetric Smarandache sequences of pentagonal numbers of dimension 2 using the Maple system. In this paper we have de¯ned and investigated the s-consecutive, s-reversed, s-mirror and s-symmetric sequences of Pyramidal numbers (Triangular numbers of dimension 3.) using Maple 6.
Category: Number Theory

Chains of Smarandache Semifields

Authors: A.S.Muktibodh, Y.M. Wagh
Comments: 4 Pages.

In this paper we have constructed two chains of semifields. All semifieids in the chains are Smarandache semifields.
Category: General Mathematics

On Spacetime Curvature and Gravity Probe

Authors: S.Kalimuthu
Comments: 3 Pages. Needless to say, the experiment and the out come are consistent

General relativity explains gravity as distortion of the structure of spacetime by matter , affecting the inertial motion of the other matter. General relativity predicts that the path of light is bent in a gravitational field. Light passing a massive body is deflected towards that body. This effect has been confirmed by observing the light of stars or distant quasars being deflected as it passes the sun. In this work , the author experimentally attempts to show that it is not mass which curves spacetime but the attractive force of the mass that warps the spacetime.
Category: Relativity and Cosmology

A Possible Infinite Subset of Poulet Numbers Generated by a Formula Based on Wieferich Primes

Authors: Marius Coman
Comments: 2 Pages.

I was studying the Poulet numbers of the form n*p - n + 1, where p is prime, numbers which appear often related to Fermat pseudoprimes (see the sequence A217835 that I submitted to OEIS) when I discovered a possible infinite subset of Poulet numbers generated by a formula based on Wieferich primes (I pointed out 4 such Poulet numbers).
Category: Number Theory

Extended Prigogine Theorem: Method for Universal Characterization of Complex System Evolution

Authors: Sergey A. Kamenshchikov
Comments: 8 Pages. Published unaltered at Chaos and Complexity Letters, Volume 8, Issue 1, 2014, pp. 63-71. Author: ru.linkedin.com/pub/sergey-kamenshchikov/60/8b1/21a/

Evolution of arbitrary stochastic system was considered in frame of phase transition description. Concept of Reynolds parameter of hydrodynamic motion was extended to arbitrary complex system. Basic phase parameter was expressed through power of energy, injected into system and power of energy, dissipated through internal nonlinear mechanisms. It was found out that basic phase parameter as control parameter must be delimited for two types of system - accelerator and decelerator. It was suggested to select zero state entropy on through condition of zero value for entropy production. Zero state introduces universal principle of disorder characterization. On basis of self organization S – theorem we have derived relations for entropy production behavior in the vicinity stationary state of system. Advantage of these relations in comparison to classical Prigogine theorem is versatility of their application to arbitrary nonlinear systems. It was found out that extended Prigogine theorem introduces two relations for accelerator and decelerator correspondingly, which remarks their quantitative difference. At the same time classic Prigogine theorem makes possible description of linear decelerator only. For unstable motion it corresponds to strange attractor.
Category: Mathematical Physics

Estimates of the Enclosed Mass and Its Distribution for Several Spiral Galaxies

Authors: Geoffrey M. Williams
Comments: 23 Pages.

Recently, high quality rotation curves for several spiral galaxies have become available from THINGS: The HI Nearby Galaxy Survey (Reference 1). This paper analyzes 15 of those galaxy rotation curves using the Newtonian Disk Model (Reference 2). The Model assumes that virtually all the mass of stars, gas, dust and dark-matter is contained as a “flattened” mass within the galactic disk, which extends out to the edge of the observable rotation. Estimates of the enclosed mass and its radial distribution are provided.
Category: Astrophysics

Black Hole and Big Bang: A Simplified Refutation

Authors: Stephen J. Crothers
Comments: 16 Pages. This paper is for the layman and specialist alike. It contains very little mathematics, and where mathematics is employed it does not go beyond high school arithmetic and algebra. Version [3] extends to asymptotically curved spacetimes.

The General Theory of Relativity is notoriously known for its complicated mathematics. This has been a great impediment to many who wish to understand such things as black hole theory and big bang cosmology. However, all the salient facts can be easily understood without any recourse to confusing mathematics. With these facts clearly explained in simple language it becomes easy to understand why black hole theory and big bang cosmology are mutually exclusive and ultimately why General Relativity is itself inconsistent.
Category: Relativity and Cosmology

Event Horizon, Gravitational Lensing, Black Holes, Dark Energy

Authors: Oliver R Jovanovic
Comments: 4 Pages.

"novel" approach on popular subjects: event horizon, gravitational lensing, black holes, dark energy
Category: Relativity and Cosmology

A Phenomenon in Matrix Analysis

Authors: S. Kalimuthu
Comments: 4 Pages. NA

The history of matrices goes back to ancient times! But the term "matrix" was not applied to the concept until 1850."Matrix" is the Latin word for womb, and it retains that sense in English. It can also mean more generally any place in which something is formed or produced. The orgins of mathematical matrices lie with the study of systems of simultaneous linear equations. An important Chinese text from between 300 BC and AD 200, Nine Chapters of the Mathematical Art (Chiu Chang Suan Shu), gives the first known example of the use of matrix methods to solve simultaneous equations. Since their first appearance in ancient China, matrices have remained important mathematical tools. Today, they are used not simply for solving systems of simultaneous linear equations, but also for describing the quantum mechanics of atomic structure, designing computer game graphics, analyzing relationships, and even plotting complicated dance steps! The elevation of the matrix from mere tool to important mathematical theory owes a lot to the work of female mathematician Olga Taussky Todd (1906-1995), who began by using matrices to analyze vibrations on airplanes during World War II and became the torchbearer for matrix theory. In this work, by applying the fundamental concepts of matrices, the author attempts to study the fifth Euclidean postulate problem and Godel’s incompleteness theorems.
Category: Algebra

Space Power: Generation of Electricity from Space

Authors: S. Kalimuthu
Comments: 7 Pages. NA

In this work, a proposal to generate electricity at zero cost from space has been introduced.
Category: Astrophysics

New Concepts of Physics

Authors: S. Kalimuthu
Comments: 9 Pages. NA

After establishing the fundamental physics prizes, Yuri Milner said: “Unlike the Nobel in physics, the Fundamental Physics Prize can be awarded to scientists whose ideas have not yet been verified by experiments, which often occurs decades later. Sometimes a radical new idea “really deserves recognition right away because it expands our understanding of at least what is possible.”. Keeping this mind the author proposes several new concepts of physics such as it is not mass but the attracting force of mass which warps space, electricity can be generated from space at zero cost, making of graviton bombs are for real, it is possible to include gravitons and darkons in to the standard model of particle physics, unification of quantum physics with Einstein’s relativity can be performed on the foundations of a new spherical geometric applications, & new thoughts on big bang theory , particles and pre big bang
Category: Astrophysics

New Concepts of Cosmology Part 2

Authors: S. Kalimuthu
Comments: 5 Pages. NA

In this work, new concepts of physics and cosmology have been proposed
Category: Astrophysics

Femtotechnologies. Step I Atom Hydrogen

Authors: Alexander M. Ilyanok
Comments: 23 Pages. Abstracts of articles have been published in the IV Congress of Belarusian Physicistб, April 2013 http://master.basnet.by/congress2013/sbornik.pdf p / 66-67 /

It is considered unpromising today to study huge interval between nucleus and atom external shell, so called femtoregion, spread from nanometers to femtometers. But without knowledge of atoms spatial structure and their fields it is impossible to construct molecules correctly, and to build nanoobjects further. Femtotechnologies have to lay down in a theoretical basis of nanotechnologies without which development of applied researches is impossible. In work the femtoregion of the simplyest element, atom of hydrogen, is considered. It is shown that the electron in atom of hydrogen has the difficult spatial structure taking which into account allows to specify fundamental constants, such as a constant of thin structure, the speed of light, Bohr radius of an electron. It is shown that on the basis of these constants it is possible to construct the fundamental scales scaling both internal and external fields of atoms. It allows to formulate macroquantum laws that govern the Universe. It means that without research atoms femtoregion it is impossible to eliminate an abyss which arose between gravitation and electromagnetism. It is shown that our model removes a number of theoretical contradictions and is perfectly confirmed by the last astrophysical experiments.
Category: Astrophysics

Moller Formula Fails the Experimental Test

Authors: Dmitri Martila
Comments: 2 Pages.

This formula is believed to be energy good formula. But we forgot ald fashion experiments, how mankind has measured calories in calorimeters to build the Structure of Science-philosophy. I propose to future advance humankind (after Second Coming) to put a cosmic structure into calorimeter! This rough, "rude" way will certainly give the answers to energy problem in General Relativity (GR). One of mind torturing difficulties is hypothesized non-locality of energy [R.J.Epp, Phys.Rev.D, 62, 124018, 2000]. But the GR is local theory. Thus, the formulas are out of GR.
Category: Relativity and Cosmology

On the Logical Analysis of the Foundations of Vector Calculus

Authors: Temur Z. Kalanov
Comments: 8 Pages.

A critical analysis of the foundations of standard vector calculus is proposed. The methodological basis of the analysis is the unity of formal logic and of rational dialectics. It is proved that the vector calculus is incorrect theory because: (a) it is not based on a correct methodological basis – the unity of formal logic and of rational dialectics; (b) it does not contain the correct definitions of “movement”, “direction” and “vector”; (c) it does not take into consideration the dimensions of physical quantities (i.e., number names, denominate numbers, concrete numbers), characterizing the concept of ”physical vector”, and, therefore, it has no natural-scientific meaning; (d) operations on “physical vectors” and the vector calculus propositions relating to the ”physical vectors” are contrary to formal logic.
Category: General Science and Philosophy

An Introduction to an Interesting Naturally Occurring Mathematical Pattern :Piitd Series

Authors: Jatin Patni
Comments: 4 Pages.

This paper introduces a sequence of real number that models a very frequently occurring natural pattern which is observed by everyone. The pattern it tries to model is the angle subtended on the eye of the observer standing at a distance from a long line of equally spaced objects. There are some interesting properties that are captured by this series. It finds a connection with modelling certain aspects of human psychology and can create interesting study areas like stock market price prediction, resource allocations, efficient search algorithms, time versus effort modelling etc.
Category: General Mathematics

Information as the Substance of Gravitational Fields

Authors: Antoine Acke
Comments: 10 Pages. Entry for FQXi essay contest 2013 "It from Bit or Bit from It?"

Gravito-electromagnetism (GEM) describes the gravitational phenomena by introducing a gravitational field that can be viewed as a combination of two fields: a force field and an induction field. It is assumed that this composite field - that serves as a mediator for the gravitational interactions - is isomorphic with the electromagnetic field. In this article we will show that the GEM-description of gravitation can perfectly be explained by the hypothesis that "information carried by informatons" is the substance of the gravitational field. Our starting point is that any material object manifests itself in space by emitting "informatons": granular mass and energy less entities running away with the speed of light and carrying information about the position and the velocity of their emitter. We will show that the cloud of informatons emitted by a material object constitutes its gravitational field.
Category: Classical Physics

On the Singular Series in the Jiang Prime K-Tuple Theorem

Authors: Chun-Xuan Jiang
Comments: 6 Pages.

Using Jiang function we prove the Jiang prime k-tuple theorem.We find true singular series.
Category: Number Theory

Plate Tectonics as Unnecessary

Authors: Jeffrey Joseph Wolynski
Comments: 1 Page.

It is hypothesized that the appearance of tectonic plates can easily be explained by thermodynamic contraction and expansion caused by heating and cooling of the Earth’s mantle underneath the crust.
Category: Geophysics

Electron Air Hypersonic Propulsion

Authors: Alexander Bolonkin
Comments: 7 Pages. 7 ps, 3 figs

Aviation, in general, and aerospace in particular needs new propulsion systems which allow the craft to reach high speeds by cheaper and more efficient methods. Author offers a new propulsion system using electrons for acceleration of the craft and having a high efficiency. As this system does not heat the air, it does not have the heating limitations of conventional air ramjet hypersonic engines. Offered engine can produce a thrust from a zero flight speed up to the desired space apparatus speed. It can work in any planet atmosphere (gas, liquid) and at very high altitude. The system can use apparatus surface for thrust and braking. For energy the system uses high voltage electricity which is not a problem if you have an appropriate electrostatic generator connected with any suitable engine.
Category: Classical Physics

Combined Gravitational Action (IV): Exploitation

Authors: M. E. Hassani
Comments: 24 Pages. 4 Figure; 50 References. A part of this work has already been published in the Galilean Electrodynamics Journal.

In previous papers related to the concept of Combined Gravitational Action (CGA), we have established the theoretical foundations of CGA as an alternative gravity theory that has already allowed us to resolve some unexpected and challenging problems both inside and outside the Solar System. These include the anomalous deceleration of Pioneer 10, the observed secular increase of the Astronomical Unit, the apsidal motion anomaly of eclipsing binary star systems, and the study of CGA-effects in non-compact and compact stellar objects. All of this has been achieved without fully utilizing the CGA-formalism. Therefore, the main purpose of this paper is to thoroughly explore the CGA-equations to investigate, among other things, CGA-spin-orbit coupling precession and the application of CGA to Large-Scale Structures in order to address the issue of galactic rotation curves.
Category: Astrophysics