Preprints from viXra.org site http://viXra.org/ Tue Jun 18 20:14:12 BST 2013 Tue Jun 18 20:14:12 BST 2013 http://viXra.org/abs/1306.0144 2013-06-18 07:39:43 Digital Signal Processing reference: viXra:1306.0144v1
title: 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
category: Digital Signal Processing
type: submission
date: 2013-06-18 07:39:43
abstract: 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. ]]> http://viXra.org/abs/1306.0143 2013-06-18 03:59:05 Number Theory reference: viXra:1306.0143v1
title: The Best Theory of Arbitrarily Long Arithmetic Progressions of Primes
authors: chun-xuan jiang
category: Number Theory
type: submission
date: 2013-06-18 03:59:05
abstract: Using Jiang function we find the best theory of arbitrarily long arithmetic progressions of primes ]]> http://viXra.org/abs/1306.0142 2013-06-17 13:14:29 Quantum Physics reference: viXra:1306.0142v1
title: Arguments and Model for Quantum Consciousness, Modication of Quantum Collapse, and Panpsychism
authors: Janko Kokosar
category: Quantum Physics
type: submission
date: 2013-06-17 13:14:29
abstract: 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. ]]> http://viXra.org/abs/1306.0141 2013-06-17 13:28:25 Quantum Physics reference: viXra:1306.0141v1
title: What is Electron Spin?
authors: Kamal L Rajpal
category: Quantum Physics
type: submission
date: 2013-06-17 13:28:25
abstract: 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, corresponding to 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. ]]> http://viXra.org/abs/1306.0140 2013-06-17 22:35:48 Relativity and Cosmology reference: viXra:1306.0140v1
title: A Note On Olber's Paradox
authors: Joseph Catania
category: Relativity and Cosmology
type: submission
date: 2013-06-17 22:35:48
abstract: Olber's Paradox predicts a bright night sky. Big Bang theorists reason this bright sky away by accounting for the dark night sky with increasing redshift with distance. In this Note I derive a dark night sky without use of expansion or redshifting. ]]> http://viXra.org/abs/1306.0139 2013-06-17 23:33:37 Relativity and Cosmology reference: viXra:1306.0139v1
title: Fitzgerald-Lorentz Contraction: Real or Apparent?
authors: Antonio Leon
category: Relativity and Cosmology
type: submission
date: 2013-06-17 23:33:37
abstract: After reviewing some classical and modern opinions on the 'notorious controversy' on the real or apparent nature of FitzGerald-Lorentz contraction, this paper analyzes a conflicting relativistic situation related to the mechanical tension of an elastic cord stretched by a hanging mass. A sliding pulley divides the cord into a vertical and a horizontal section. Thanks to a metric scale printed on the cord, FitzGerald-Lorentz contraction makes each section appear with different mechanical tension when observed in relative motion parallel to one of the sections of the elastic cord. By sliding the pulley on its horizontal support the length of the stretched cord changes while it is always stretched by the same hanging mass. ]]> http://viXra.org/abs/1306.0138 2013-06-18 00:03:59 General Mathematics reference: viXra:1306.0138v1
title: Not so Rational
authors: Antonio Leon
category: General Mathematics
type: submission
date: 2013-06-18 00:03:59
abstract: In the year 1874 Cantor proved the set of rational numbers is denumerable. An immediate consequence of this result is the impossibility of non-countable partitions of the real line, also proved by Cantor in 1885. Inspired by Cantor 1874 and 1885 proofs, the following argument defines a partition of an interval of positive rational numbers whose successive parts are defined a la Cantor by means of the successive elements of an w-ordered sequence of positive rational numbers that contains all positive rational numbers. It is then proved each part of the partition contains positive rational numbers that are not members of the defining sequence. ]]> http://viXra.org/abs/1306.0137 2013-06-18 00:37:59 High Energy Particle Physics reference: viXra:1306.0137v1
title: What Confinement Really Means in Quantum Chromodynamics
authors: Syed Afsar Abbas
category: High Energy Particle Physics
type: submission
date: 2013-06-18 00:37:59
abstract: 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. ]]> http://viXra.org/abs/1306.0136 2013-06-18 01:07:32 Social Science reference: viXra:1306.0136v1
title: JFK, the November Coup D'etat and de Tocqueville
authors: John Frederick Sweeney
category: Social Science
type: submission
date: 2013-06-18 01:07:32
abstract: In 1835, Alexis de Tocqueville warned that democracies had the potential to turn into tyrannies of greater evil than Rome, since the organs of control were less manifest and more powerful than those used by Roman emperors. In the wake of the Edward Snowden incident, this paper traces how the USA became a tyranny with the assassination of President John F. Kennedy in November 1963, and how the assassination conspiracy has since been covered up by succeeding presidents, all of whom either benefited directly or were blackmailed into silence by JFK's murder. Tocqueville's warning has come to pass, and Snowden has provided the incontrovertible evidence for such. ]]> http://viXra.org/abs/1306.0135 2013-06-17 05:02:34 Condensed Matter reference: viXra:1306.0135v1
title: Interactive Visualization of Plane Space Groups with the Space Group Visualizer
authors: Eckhard Hitzer
category: Condensed Matter
type: submission
date: 2013-06-17 05:02:34
abstract: 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. ]]> http://viXra.org/abs/1306.0134 2013-06-17 05:10:48 Geometry reference: viXra:1306.0134v1
title: Tutorial on Reflections in Geometric Algebra
authors: Eckhard Hitzer
category: Geometry
type: submission
date: 2013-06-17 05:10:48
abstract: 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. ]]> http://viXra.org/abs/1306.0133 2013-06-17 05:21:04 Functions and Analysis reference: viXra:1306.0133v1
title: Tutorial on Fourier Transformations and Wavelet Transformations in Cliord Geometric Algebra
authors: Eckhard Hitzer
category: Functions and Analysis
type: submission
date: 2013-06-17 05:21:04
abstract: 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. ]]> http://viXra.org/abs/1306.0132 2013-06-16 16:21:30 Astrophysics reference: viXra:1306.0132v1
title: The Dark Side of Dark Matter (The Moon and the Dark Matter)
authors: Leonardo Rubino
category: Astrophysics
type: submission
date: 2013-06-16 16:21:30
abstract: 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. ]]> http://viXra.org/abs/1306.0131 2013-06-16 23:30:28 Classical Physics reference: viXra:1306.0131v1
title: Modifying Maxwell's Third Law
authors: Victor Mark Battaglia
category: Classical Physics
type: submission
date: 2013-06-16 23:30:28
abstract: This paper deals solely with classical electrodynamics, specifically Maxwell's third law. The law deals with a magnetic field, and the electric field it induces. The scope of this paper is to to mathematically derive Maxwell's third law. Along the way, the paper makes a modification to the law. ]]> http://viXra.org/abs/1306.0130 2013-06-17 01:29:18 Functions and Analysis reference: viXra:1306.0130v1
title: The Clifford Fourier Transform in Real Clifford Algebras
authors: Eckhard Hitzer
category: Functions and Analysis
type: submission
date: 2013-06-17 01:29:18
abstract: 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. ]]> http://viXra.org/abs/1306.0129 2013-06-17 01:41:53 Condensed Matter reference: viXra:1306.0129v1
title: Interactive Visualization of Plane Groups
authors: Eckhard Hitzer
category: Condensed Matter
type: submission
date: 2013-06-17 01:41:53
abstract: 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). ]]> http://viXra.org/abs/1306.0128 2013-06-17 01:49:37 Data Structures and Algorithms reference: viXra:1306.0128v1
title: Analysis of Point Clouds Using Conformal Geometric Algebra
authors: Dietmar Hildenbrand, Eckhard Hitzer
category: Data Structures and Algorithms
type: submission
date: 2013-06-17 01:49:37
abstract: 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. ]]> http://viXra.org/abs/1306.0127 2013-06-17 01:59:58 Functions and Analysis reference: viXra:1306.0127v1
title: 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
category: Functions and Analysis
type: submission
date: 2013-06-17 01:59:58
abstract: 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. ]]> http://viXra.org/abs/1306.0126 2013-06-17 02:09:49 Functions and Analysis reference: viXra:1306.0126v1
title: Uncertainty Principle for Clifford Geometric Algebras Cl(n,0), N = 3 (Mod 4) Based on Clifford Fourier Transform
authors: Eckhard Hitzer, Bahri Mawardi
category: Functions and Analysis
type: submission
date: 2013-06-17 02:09:49
abstract: 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. ]]> http://viXra.org/abs/1306.0125 2013-06-17 02:20:49 Algebra reference: viXra:1306.0125v1
title: Geometric Algebra Illustrated by Cinderella
authors: Eckhard Hitzer, Luca Redaelli
category: Algebra
type: submission
date: 2013-06-17 02:20:49
abstract: 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. ]]> http://viXra.org/abs/1306.0124 2013-06-17 02:53:25 Functions and Analysis reference: viXra:1306.0124v1
title: Basic Multivector Calculus
authors: Eckhard Hitzer
category: Functions and Analysis
type: submission
date: 2013-06-17 02:53:25
abstract: 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. ]]> http://viXra.org/abs/1306.0123 2013-06-17 03:00:32 Condensed Matter reference: viXra:1306.0123v1
title: Symmetry of Orthorhombic Materials and Interactive 3D Visualization in Geometric Algebra
authors: Daisuke Ichikawa, Eckhard Hitzer
category: Condensed Matter
type: submission
date: 2013-06-17 03:00:32
abstract: 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. ]]> http://viXra.org/abs/1306.0122 2013-06-17 03:06:17 Functions and Analysis reference: viXra:1306.0122v1
title: Foundations of Multidimensional Wavelet Theory: The Quaternion Fourier Transform and its Generalizations
authors: Eckhard Hitzer
category: Functions and Analysis
type: submission
date: 2013-06-17 03:06:17
abstract: Keywords: Multidimensional Wavelets, Quaternion Fourier Transform, Clifford geometric algebra ]]> http://viXra.org/abs/1306.0121 2013-06-17 03:12:32 Relativity and Cosmology reference: viXra:1306.0121v1
title: Relativistic Physics as Application of Geometric Algebra
authors: Eckhard Hitzer
category: Relativity and Cosmology
type: submission
date: 2013-06-17 03:12:32
abstract: 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. ]]> http://viXra.org/abs/1306.0120 2013-06-17 03:19:30 Data Structures and Algorithms reference: viXra:1306.0120v1
title: 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
category: Data Structures and Algorithms
type: submission
date: 2013-06-17 03:19:30
abstract: 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. ]]> http://viXra.org/abs/1306.0119 2013-06-17 03:27:06 Geometry reference: viXra:1306.0119v1
title: Learning about Conic Sections with Geometric Algebra and Cinderella
authors: Eckhard Hitzer
category: Geometry
type: submission
date: 2013-06-17 03:27:06
abstract: 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. ]]> http://viXra.org/abs/1306.0118 2013-06-17 03:33:05 Geometry reference: viXra:1306.0118v1
title: Conic Sections Through Five Points Classical, Projective, Conformal
authors: Eckhard Hitzer
category: Geometry
type: submission
date: 2013-06-17 03:33:05
abstract: 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. ]]> http://viXra.org/abs/1306.0117 2013-06-17 03:56:01 Functions and Analysis reference: viXra:1306.0117v1
title: Geometric Calculus – Engineering Mathematics for the 21st Century
authors: Eckhard Hitzer
category: Functions and Analysis
type: submission
date: 2013-06-17 03:56:01
abstract: 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. ]]> http://viXra.org/abs/1306.0116 2013-06-17 04:00:42 Functions and Analysis reference: viXra:1306.0116v1
title: Vector Differential Calculus
authors: Eckhard Hitzer
category: Functions and Analysis
type: submission
date: 2013-06-17 04:00:42
abstract: 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 ]]> http://viXra.org/abs/1306.0115 2013-06-17 04:05:54 Geometry reference: viXra:1306.0115v1
title: Play with Geometry - Animated and Interactive, Free, Instant Access, Online Geometric Algebra Java Applets
authors: Eckhard Hitzer, Luca Redaelli
category: Geometry
type: submission
date: 2013-06-17 04:05:54
abstract: 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. ]]> http://viXra.org/abs/1306.0114 2013-06-17 04:13:56 Functions and Analysis reference: viXra:1306.0114v1
title: Geometric Calculus for Engineers
authors: Eckhard Hitzer
category: Functions and Analysis
type: submission
date: 2013-06-17 04:13:56
abstract: 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. ]]> http://viXra.org/abs/1306.0113 2013-06-17 04:25:16 Algebra reference: viXra:1306.0113v1
title: A Real Explanation for Imaginary Eigenvalues and Complex Eigenvectors
authors: Eckhard Hitzer
category: Algebra
type: submission
date: 2013-06-17 04:25:16
abstract: 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. ]]> http://viXra.org/abs/1306.0112 2013-06-17 04:30:00 Algebra reference: viXra:1306.0112v1
title: Antisymmetric Matrices are Real Bivectors
authors: Eckhard Hitzer
category: Algebra
type: submission
date: 2013-06-17 04:30:00
abstract: 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 ]]> http://viXra.org/abs/1306.0111 2013-06-17 04:35:04 Classical Physics reference: viXra:1306.0111v1
title: Early Works on the Hagen-Poiseuille Flow
authors: Eckhard Hitzer
category: Classical Physics
type: submission
date: 2013-06-17 04:35:04
abstract: 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 ]]> http://viXra.org/abs/1306.0110 2013-06-17 04:42:40 Classical Physics reference: viXra:1306.0110v1
title: Classical and Semi-Classical Optics with MAPLE: Investigating a Two-dimensional Light Ray Geometry
authors: Eckhard Hitzer
category: Classical Physics
type: submission
date: 2013-06-17 04:42:40
abstract: 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. ]]> http://viXra.org/abs/1306.0109 2013-06-16 05:41:34 Geophysics reference: viXra:1306.0109v1
title: The Physical Theory of Ball Lightning
authors: Sergey G. Fedosin, A.S. Kim
category: Geophysics
type: submission
date: 2013-06-16 05:41:34
abstract: 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. ]]> http://viXra.org/abs/1306.0108 2013-06-15 20:03:26 Quantum Physics reference: viXra:1306.0108v1
title: The New Electromagnetics From Matter Waves
authors: Michael Harney
category: Quantum Physics
type: submission
date: 2013-06-15 20:03:26
abstract: 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. ]]> http://viXra.org/abs/1306.0107 2013-06-15 22:58:16 Number Theory reference: viXra:1306.0107v1
title: Lucasian Primality Criteria for Specific Classes of Riesel Numbers
authors: Predrag Terzic
category: Number Theory
type: submission
date: 2013-06-15 22:58:16
abstract: Polynomial time prime testing algorithms for specific classes of Riesel numbers are introduced . ]]> http://viXra.org/abs/1306.0106 2013-06-16 00:10:10 Quantum Gravity and String Theory reference: viXra:1306.0106v1
title: Domain Wall Start to “Inflation” with Contributions to Off Diagonal GR Stress Energy Tensor Terms
authors: A.W.Beckwith
category: Quantum Gravity and String Theory
type: submission
date: 2013-06-16 00:10:10
abstract: 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 ]]> http://viXra.org/abs/1306.0105 2013-06-15 10:59:55 Classical Physics reference: viXra:1306.0105v1
title: An Interpretation of the Essence of the Inertial Force
authors: ChiYi Chen
category: Classical Physics
type: submission
date: 2013-06-15 10:59:55
abstract: In this article we discuss the formulism of particle dynamics under the framework of classical mechanics. But we propose a new dynamical equation (5) which has significant advantages than Newton's second law. The essence of the inertial force is also interpreted in a very simple and natural way. Firstly, we remove the concept of inertial reference frame from particle dynamics and the equation (5) can be directly applied in any reference frame. Secondly, we prove that the essence of inertial forces is the real force exerted on the reference object, which must be deducted in a relative counting of forces between the object under study and the reference object. Finally, the general principle of relativity is first time realized on the particle dynamics. In one word, the new form of dynamical law (5) is more general and presents a more concise physical picture than Newton's second law. ]]> http://viXra.org/abs/1306.0104 2013-06-15 12:03:17 Relativity and Cosmology reference: viXra:1306.0104v1
title: The Relativistic Space-Time Perspective
authors: D.G. Taylor
category: Relativity and Cosmology
type: submission
date: 2013-06-15 12:03:17
abstract: This paper formulates additional Relativistic equations. They do not contradict Special Relativity. They examine the deductions of Dr. Einstein from a relativistically distorted perspective. It reasons that the REAL||non-Relativistic velocity value can be distorted just as the Length|Time|Mass values are. The equations examine the both the true/Real (not Special Relativistically Distorted||noSRD) Velocity of an object and use it to determine the distorted (Special Relativistically Distorted||SRD) Velocity for the same object. It also derives opposite equations that calculate the noSRD velocity||VelocitynoSRD from the SRD velocity||VelocitySRD. The values of non-Relativistic Velocity and the apparent Velocity relativistic deformation puts on are it equally valid: they are simply from different perspectives. In contrast to the variables in the Classical equations of Relativity, they are more specific in their aspect. The values for the physical quantities (the length and the mass) and the quantities of rate (the time and the velocity) are the quantities for zero Velocity||zero deformation – the non-Relativistic aspects. More REAL seconds go by when you are under Relativistic distortion. That does not mean that as a Relativistically distorted traveller you would observe that your actions are moving more slowly – it would be that everything else outside was going faster. 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 on the object in passage. The Velocity would appear to increase in exactly the same proportion as the others. The development of the equations is done more completely in the paper, but two examples show the principle. The equations show the relation of two points of view. The independent variables have no Relativistic deformation |VelocitynoSRD| and the dependent variable would be the value||velocity reasoned to be observed because of the Relativistic deformation |VelocitySRD|. Like the Mass or the Time, the velocity would appear to increase: VelocitySRD = VelocitynoSRD/(1 - VelocitynoSRD^2/c^2)^½ Less Time will go by when there is a relativistic deformation, so the Velocity will appear distorted just as the Length/Time/Mass are. The inverse relation would be where the independent variables were the observed Velocity from the Relativistic or distorted view |VelocitySRD|. The dependent variable would be the True/non-Relativistic/non-distorted Velocity |VelocitynoSRD|. The parallel equation for that Relativistic Perspective: VelocitynoSRD= VelocitySRD /(1 + VelocitySRD^2/c^2)^½ This relationship allows the additional development of 8 formula/equations for the velocity, the mass, the Time, and the linear deformation. These equations are all of the two Perspectives. All the equations are confirmed to two thousand decimal places for 35 different values ranging from |1.0E-500|m/s to |c – (1.0E-500)|m/s without significant error. Those tables are available on request. ]]> http://viXra.org/abs/1306.0103 2013-06-15 12:18:19 Relativity and Cosmology reference: viXra:1306.0103v1
title: The General Relativistic Perspective
authors: D.G. Taylor
category: Relativity and Cosmology
type: submission
date: 2013-06-15 12:18:19
abstract: 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. The values of non-Relativistic velocity and the apparent escape velocity relativistic deformation puts on are it equally true. 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 – the non-Relativistic aspects. 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 the paper, but two examples show the principle. The equations show the relation of two points of view: the independent variables had non-deformation and the depending variable would be the value observed because of the deformation. The equation reasoned to show to this relationship is: Time’ = Time/(1 – 2GM/rc^2)^½ Because escape velocity [VelocityEscape = (2GM/r)½], then [VelocityEscape2 = 2GM/r)]. So the above |Time| equation could also be expressed as: Time’ = Time/(1 – Velocity_Escape^2/c^2)^½ – 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 = Time’/(1 + Relativistic_Escape_Velocity^2/c^2)^½ 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 to thousand figures for 35 different values to have a range of 1.0E-500 m/s to c-(1.0E-500) m/s without the significant error. These tables are available on request. ]]> http://viXra.org/abs/1306.0102 2013-06-15 05:02:17 Quantum Physics reference: viXra:1306.0102v1
title: Poster for the Rochester Conference on Quantum Optics and Information
authors: Peter Cameron
category: Quantum Physics
type: submission
date: 2013-06-15 05:02:17
abstract: 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. ]]> http://viXra.org/abs/1306.0101 2013-06-14 12:13:17 Astrophysics reference: viXra:1306.0101v1
title: Twin Planetary Inertial Reference Frames; an Orbiting ECI frame and Inner Rotating ECRF.
authors: Peter A Jackson
category: Astrophysics
type: submission
date: 2013-06-14 12:13:17
abstract: 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 ]]> http://viXra.org/abs/1306.0100 2013-06-15 00:16:17 General Science and Philosophy reference: viXra:1306.0100v1
title: Little Green Man Gives Answers to Queensland Plan
authors: Rodney Bartlett
category: General Science and Philosophy
type: submission
date: 2013-06-15 00:16:17
abstract: "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. ]]> http://viXra.org/abs/1306.0099 2013-06-14 09:37:10 Quantum Physics reference: viXra:1306.0099v1
title: Magnetic Theory of Radio, Light, X, Gamma, Delta Radiation, and the Wave Particle Duality of Massless Photons Explained
authors: Glenn A. Baxter
category: Quantum Physics
type: submission
date: 2013-06-14 09:37:10
abstract: 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.” ]]> http://viXra.org/abs/1306.0098 2013-06-17 06:01:28 Relativity and Cosmology reference: viXra:1306.0098v3
title: On Lorentz Transformation and Special Relativity: Critical Mathematical Analyses and Findings
authors: Radwan M. Kassir
category: Relativity and Cosmology
type: replacement
date: 2013-06-17 06:01:28
abstract: 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. ]]> http://viXra.org/abs/1306.0098 2013-06-17 00:29:04 Relativity and Cosmology reference: viXra:1306.0098v2
title: On Lorentz Transformation and Special Relativity: Critical Mathematical Analyses and Findings
authors: Radwan M. Kassir
category: Relativity and Cosmology
type: replacement
date: 2013-06-17 00:29:04
abstract: 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. ]]> http://viXra.org/abs/1306.0098 2013-06-14 09:59:51 Relativity and Cosmology reference: viXra:1306.0098v1
title: On Lorentz Transformation and Special Relativity: Critical Mathematical Analyses and Findings
authors: Radwan M. Kassir
category: Relativity and Cosmology
type: submission
date: 2013-06-14 09:59:51
abstract: 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. ]]> http://viXra.org/abs/1306.0097 2013-06-15 04:38:20 Quantum Physics reference: viXra:1306.0097v2
title: Our Current Concept of Locality May be Incomplete (Talk Slides)
authors: Armin Nikkhah Shirazi
category: Quantum Physics
type: replacement
date: 2013-06-15 04:38:20
abstract: 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. ]]>