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Symmetry and Gravity
universe Article Making a Quantum Universe: Symmetry and Gravity Houri Ziaeepour 1,2 1 Institut UTINAM, CNRS UMR 6213, Observatoire de Besançon, Université de Franche Compté, 41 bis ave. de l’Observatoire, BP 1615, 25010 Besançon, France; [email protected] or [email protected] 2 Mullard Space Science Laboratory, University College London, Holmbury St. Mary, Dorking GU5 6NT, UK Received: 05 September 2020; Accepted: 17 October 2020; Published: 23 October 2020 Abstract: So far, none of attempts to quantize gravity has led to a satisfactory model that not only describe gravity in the realm of a quantum world, but also its relation to elementary particles and other fundamental forces. Here, we outline the preliminary results for a model of quantum universe, in which gravity is fundamentally and by construction quantic. The model is based on three well motivated assumptions with compelling observational and theoretical evidence: quantum mechanics is valid at all scales; quantum systems are described by their symmetries; universe has infinite independent degrees of freedom. The last assumption means that the Hilbert space of the Universe has SUpN Ñ 8q – area preserving Diff.pS2q symmetry, which is parameterized by two angular variables. We show that, in the absence of a background spacetime, this Universe is trivial and static. Nonetheless, quantum fluctuations break the symmetry and divide the Universe to subsystems. When a subsystem is singled out as reference—observer—and another as clock, two more continuous parameters arise, which can be interpreted as distance and time. We identify the classical spacetime with parameter space of the Hilbert space of the Universe. -
Kaluza-Klein Gravity, Concentrating on the General Rel- Ativity, Rather Than Particle Physics Side of the Subject
Kaluza-Klein Gravity J. M. Overduin Department of Physics and Astronomy, University of Victoria, P.O. Box 3055, Victoria, British Columbia, Canada, V8W 3P6 and P. S. Wesson Department of Physics, University of Waterloo, Ontario, Canada N2L 3G1 and Gravity Probe-B, Hansen Physics Laboratories, Stanford University, Stanford, California, U.S.A. 94305 Abstract We review higher-dimensional unified theories from the general relativity, rather than the particle physics side. Three distinct approaches to the subject are identi- fied and contrasted: compactified, projective and noncompactified. We discuss the cosmological and astrophysical implications of extra dimensions, and conclude that none of the three approaches can be ruled out on observational grounds at the present time. arXiv:gr-qc/9805018v1 7 May 1998 Preprint submitted to Elsevier Preprint 3 February 2008 1 Introduction Kaluza’s [1] achievement was to show that five-dimensional general relativity contains both Einstein’s four-dimensional theory of gravity and Maxwell’s the- ory of electromagnetism. He however imposed a somewhat artificial restriction (the cylinder condition) on the coordinates, essentially barring the fifth one a priori from making a direct appearance in the laws of physics. Klein’s [2] con- tribution was to make this restriction less artificial by suggesting a plausible physical basis for it in compactification of the fifth dimension. This idea was enthusiastically received by unified-field theorists, and when the time came to include the strong and weak forces by extending Kaluza’s mechanism to higher dimensions, it was assumed that these too would be compact. This line of thinking has led through eleven-dimensional supergravity theories in the 1980s to the current favorite contenders for a possible “theory of everything,” ten-dimensional superstrings. -
Geometrodynamics of Gauge Fields on the Geometry of Yang-Mills and Gravitational Gauge Theories
springer.com Physics : Classical and Quantum Gravitation, Relativity Theory Mielke, Eckehard W. Geometrodynamics of Gauge Fields On the Geometry of Yang-Mills and Gravitational Gauge Theories A comprehensive revision of a classic text relating geometic field theory to modern physics Offers an up-to-date overview of geometrodynamics including minimal topological models Contains new chapters on teleparalelism, Chern-Simons-induced topological 3D gravity and supergravity, quantization via topological ghosts, constrained BF model with SL (5, R) gauge group, and chiral and trace anomalies Provides a detailed exposition of frame bundles in gravity Springer This monograph aims to provide a unified, geometrical foundation of gauge theories of 2nd ed. 2017, XVII, 373 p. elementary particle physics. The underlying geometrical structure is unfolded in a coordinate- 2nd 18 illus., 8 illus. in color. free manner via the modern mathematical notions of fibre bundles and exterior forms. Topics edition such as the dynamics of Yang-Mills theories, instanton solutions and topological invariants are included. By transferring these concepts to local space-time symmetries, generalizations of Einstein's theory of gravity arise in a Riemann-Cartan space with curvature and torsion. It Printed book provides the framework in which the (broken) Poincarégauge theory, the Rainich geometrization Hardcover of the Einstein-Maxwell system, and higher-dimensional, non-abelian Kaluza-Klein theories are Printed book developed. Since the discovery of the Higgs boson, concepts of spontaneous symmetry breaking in gravity have come again into focus, and, in this revised edition, these will be Hardcover exposed in geometric terms. Quantizing gravity remains an open issue: formulating it as a de ISBN 978-3-319-29732-3 Sitter type gauge theory in the spirit of Yang-Mills, some new progress in its topological form is £ 109,99 | CHF 141,50 | 119,99 € | presented. -
On the Covariant Representation of Integral Equations of the Electromagnetic Field
On the covariant representation of integral equations of the electromagnetic field Sergey G. Fedosin PO box 614088, Sviazeva str. 22-79, Perm, Perm Krai, Russia E-mail: [email protected] Gauss integral theorems for electric and magnetic fields, Faraday’s law of electromagnetic induction, magnetic field circulation theorem, theorems on the flux and circulation of vector potential, which are valid in curved spacetime, are presented in a covariant form. Covariant formulas for magnetic and electric fluxes, for electromotive force and circulation of the vector potential are provided. In particular, the electromotive force is expressed by a line integral over a closed curve, while in the integral, in addition to the vortex electric field strength, a determinant of the metric tensor also appears. Similarly, the magnetic flux is expressed by a surface integral from the product of magnetic field induction by the determinant of the metric tensor. A new physical quantity is introduced – the integral scalar potential, the rate of change of which over time determines the flux of vector potential through a closed surface. It is shown that the commonly used four-dimensional Kelvin-Stokes theorem does not allow one to deduce fully the integral laws of the electromagnetic field and in the covariant notation requires the addition of determinant of the metric tensor, besides the validity of the Kelvin-Stokes theorem is limited to the cases when determinant of metric tensor and the contour area are independent from time. This disadvantage is not present in the approach that uses the divergence theorem and equation for the dual electromagnetic field tensor. -
Gravitation Law and Source Model in the Anisotropic Geometrodynamics
Gravitation law and source model in the anisotropic geometrodynamics Sergey Siparov State University of Civil Aviation, 38 Pilotov str., St-Petersburg, 196210; Research Institute for Hyper Complex Systems in Geometry and Physics, 3 bg 1 Zavodskoy pr., Fryazino, Moscow region, 141190; Russian Federation Abstract. The GRT modification taking into account the dependence of metric on the velocities of the sources is built. It is shown that this dependence follows from the equivalence principle and from the inseparability of the field equations and geodesics equations. As it is known, the latter are the conditions of the field equations solvability, and their form coincides with Newtonian one only in the lowest approximation. The obtained modification provides the explanation for the flat character of the rotation curves of spiral galaxies, for Tully-Fisher law, for some specific features of globular clusters behavior and for the essential excess of the observable gravitational lens effect over the predicted one. Neither dark matter nor arbitrary change of dynamics equations appeared to be needed. Important cosmological consequences are obtained. Keywords: modified theory of gravity, rotation curves, Tully-Fisher law, anisotropic metric PACS: 04.20.Cv, 04.50.Kd, 95.30.Sf, 98.20.Gm, 98.52.Nr, 98.80.Es 1. INTRODUCTION The flat character of the rotation curves (RC) of spiral galaxies is the most pronounced problem of the known GRT problems on the galactic scale. This is a simple, not small and statistically verified effect which doesn’t find explanation not only in the GRT but in Newton gravity as well. It is to the fact that the orbital velocities of stars in the spiral galaxies don’t tend to zero with the distance from the center but approach constant values of the order 105m/s for all galaxies. -
Do Global Virtual Axionic Gravitons Exist?
NeuroQuantology | March 2014 | Volume 12 | Issue 1 | Page 35-39 35 Glinka LA., Do global virtual axionic gravitons exist? Do Global Virtual Axionic Gravitons Exist? Lukasz Andrzej Glinka ABSTRACT Recently, the author has proposed the global one-dimensionality conjecture which, throughout making use of the method of the primary canonical quantization of General Relativity according to the Dirac-Arnowitt-Deser-Misner Hamiltonian formulation, formally avoids the functional differential nature which is the basic obstacle of quantum geometrodynamics, a model of quantum gravity based on the Wheeler-DeWitt equation and resutling from quantization of the Einstein field equations. The emergent quantum gravity model is straightforwardly integrable in terms of the Riemann-Lebesgue integral, has an unambiguous physical interpretation within quantum theory, and introduces a consistent concept of global graviton. In this article, the axionic nature of the global gravitons, that is the hypothetical particles responsible for gravitation in the global one-dimensional quantum gravity model, is shortly described and, making use of fundamental methods of quantum field theory, the virtual states of such gravitons are generated. Key Words: global one-dimensionality conjecture; quantum gravity; quantum geometrodynamics; graviton; axion DOI Number: 10.14704/nq.2014.12.1.716 NeuroQuantology 2014; 1: 35-39 1. Introduction1 results in replacement of the functional Recently the Wheeler-DeWitt equation was evolution parameter which is the metric of considered in the framework of the global one- space by a variable which is the metric dimensionality conjecture (Glinka, 2012; 2010). determinant. The ramifications of this change Recall that this conjecture formally reduces the are highly non-trivial. -
Gravitational Waves and Binary Black Holes
Ondes Gravitationnelles, S´eminairePoincar´eXXII (2016) 1 { 51 S´eminairePoincar´e Gravitational Waves and Binary Black Holes Thibault Damour Institut des Hautes Etudes Scientifiques 35 route de Chartres 91440 Bures sur Yvette, France Abstract. The theoretical aspects of the gravitational motion and radiation of binary black hole systems are reviewed. Several of these theoretical aspects (high-order post-Newtonian equations of motion, high-order post-Newtonian gravitational-wave emission formulas, Effective-One-Body formalism, Numerical-Relativity simulations) have played a significant role in allowing one to compute the 250 000 gravitational-wave templates that were used for search- ing and analyzing the first gravitational-wave events from coalescing binary black holes recently reported by the LIGO-Virgo collaboration. 1 Introduction On February 11, 2016 the LIGO-Virgo collaboration announced [1] the quasi- simultaneous observation by the two LIGO interferometers, on September 14, 2015, of the first Gravitational Wave (GW) event, called GW150914. To set the stage, we show in Figure 1 the raw interferometric data of the event GW150914, transcribed in terms of their equivalent dimensionless GW strain amplitude hobs(t) (Hanford raw data on the left, and Livingston raw data on the right). Figure 1: LIGO raw data for GW150914; taken from the talk of Eric Chassande-Mottin (member of the LIGO-Virgo collaboration) given at the April 5, 2016 public conference on \Gravitational Waves and Coalescing Black Holes" (Acad´emiedes Sciences, Paris, France). The important point conveyed by these plots is that the observed signal hobs(t) (which contains both the noise and the putative real GW signal) is randomly fluc- tuating by ±5 × 10−19 over time scales of ∼ 0:1 sec, i.e. -
Electromagnetic Particles Guy Michel Stephan
Electromagnetic particles Guy Michel Stephan To cite this version: Guy Michel Stephan. Electromagnetic particles. 2017. hal-01446417 HAL Id: hal-01446417 https://hal.archives-ouvertes.fr/hal-01446417 Preprint submitted on 2 Feb 2017 HAL is a multi-disciplinary open access L’archive ouverte pluridisciplinaire HAL, est archive for the deposit and dissemination of sci- destinée au dépôt et à la diffusion de documents entific research documents, whether they are pub- scientifiques de niveau recherche, publiés ou non, lished or not. The documents may come from émanant des établissements d’enseignement et de teaching and research institutions in France or recherche français ou étrangers, des laboratoires abroad, or from public or private research centers. publics ou privés. Electromagnetic particles. G.M. St´ephan 26, Chemin de Quo Vadis 22730, Tregastel email : [email protected] 25 janvier 2017 R´esum´e The covariant derivative of the 4-components electromagnetic potential in a flat Minkowski space- time is split into its antisymmetric and symmetric parts. While the former is well known to describe the electromagnetic field, we show that the latter describes the associated particles. When symmetry principles are applied to the invariants in operations of the Poincar´egroup, one finds equations which describe the structure of the particles. Both parts of the tensor unify the concept of matter-wave duality. Charge and mass are shown to be associated to the potential. 1 Introduction. When Born and Infeld published their work[1] on the foundations of non linear electromagnetism in the year 1934, their aim was to describe the electron and more generally the physical world from a purely electromagnetic theory. -
Plasma Modes in Surrounding Media of Black Holes and Vacuum Structure - Quantum Processes with Considerations of Spacetime Torque and Coriolis Forces
COLLECTIVE COHERENT OSCILLATION PLASMA MODES IN SURROUNDING MEDIA OF BLACK HOLES AND VACUUM STRUCTURE - QUANTUM PROCESSES WITH CONSIDERATIONS OF SPACETIME TORQUE AND CORIOLIS FORCES N. Haramein¶ and E.A. Rauscher§ ¶The Resonance Project Foundation, [email protected] §Tecnic Research Laboratory, 3500 S. Tomahawk Rd., Bldg. 188, Apache Junction, AZ 85219 USA Abstract. The main forces driving black holes, neutron stars, pulsars, quasars, and supernovae dynamics have certain commonality to the mechanisms of less tumultuous systems such as galaxies, stellar and planetary dynamics. They involve gravity, electromagnetic, and single and collective particle processes. We examine the collective coherent structures of plasma and their interactions with the vacuum. In this paper we present a balance equation and, in particular, the balance between extremely collapsing gravitational systems and their surrounding energetic plasma media. Of particular interest is the dynamics of the plasma media, the structure of the vacuum, and the coupling of electromagnetic and gravitational forces with the inclusion of torque and Coriolis phenomena as described by the Haramein-Rauscher solution to Einstein’s field equations. The exotic nature of complex black holes involves not only the black hole itself but the surrounding plasma media. The main forces involved are intense gravitational collapsing forces, powerful electromagnetic fields, charge, and spin angular momentum. We find soliton or magneto-acoustic plasma solutions to the relativistic Vlasov equations solved in the vicinity of black hole ergospheres. Collective phonon or plasmon states of plasma fields are given. We utilize the Hamiltonian formalism to describe the collective states of matter and the dynamic processes within plasma allowing us to deduce a possible polarized vacuum structure and a unified physics. -
Vacuum Energy
Vacuum Energy Mark D. Roberts, 117 Queen’s Road, Wimbledon, London SW19 8NS, Email:[email protected] http://cosmology.mth.uct.ac.za/ roberts ∼ February 1, 2008 Eprint: hep-th/0012062 Comments: A comprehensive review of Vacuum Energy, which is an extended version of a poster presented at L¨uderitz (2000). This is not a review of the cosmolog- ical constant per se, but rather vacuum energy in general, my approach to the cosmological constant is not standard. Lots of very small changes and several additions for the second and third versions: constructive feedback still welcome, but the next version will be sometime in coming due to my sporadiac internet access. First Version 153 pages, 368 references. Second Version 161 pages, 399 references. arXiv:hep-th/0012062v3 22 Jul 2001 Third Version 167 pages, 412 references. The 1999 PACS Physics and Astronomy Classification Scheme: http://publish.aps.org/eprint/gateway/pacslist 11.10.+x, 04.62.+v, 98.80.-k, 03.70.+k; The 2000 Mathematical Classification Scheme: http://www.ams.org/msc 81T20, 83E99, 81Q99, 83F05. 3 KEYPHRASES: Vacuum Energy, Inertial Mass, Principle of Equivalence. 1 Abstract There appears to be three, perhaps related, ways of approaching the nature of vacuum energy. The first is to say that it is just the lowest energy state of a given, usually quantum, system. The second is to equate vacuum energy with the Casimir energy. The third is to note that an energy difference from a complete vacuum might have some long range effect, typically this energy difference is interpreted as the cosmological constant. -
Gravitational Waves
Bachelor Project: Gravitational Waves J. de Valen¸caunder supervision of J. de Boer 4th September 2008 Abstract The purpose of this article is to investigate the concept of gravita- tional radiation and to look at the current research projects designed to measure this predicted phenomenon directly. We begin by stat- ing the concepts of general relativity which we will use to derive the quadrupole formula for the energy loss of a binary system due to grav- itational radiation. We will test this with the famous binary pulsar PSR1913+16 and check the the magnitude and effects of the radiation. Finally we will give an outlook to the current and future experiments to measure the effects of the gravitational radiation 1 Contents 1 Introduction 3 2 A very short introduction to the Theory of General Relativ- ity 4 2.1 On the left-hand side: The energy-momentum tensor . 5 2.2 On the right-hand side: The Einstein tensor . 6 3 Working with the Einstein equations of General Relativity 8 4 A derivation of the energy loss due to gravitational radiation 10 4.1 Finding the stress-energy tensor . 10 4.2 Rewriting the quadrupole formula to the TT gauge . 13 4.3 Solving the integral and getting rid of the TT’s . 16 5 Testing the quadrupole radiation formula with the pulsar PSR 1913 + 16 18 6 Gravitational wave detectors 24 6.1 The effect of a passing gravitational wave on matter . 24 6.2 The resonance based wave detector . 26 6.3 Interferometry based wave detectors . 27 7 Conclusion and future applications 29 A The Einstein summation rule 32 B The metric 32 C The symmetries in the Ricci tensor 33 ij D Transversal and traceless QTT 34 2 1 Introduction Waves are a well known phenomenon in Physics. -
Einstein's Quadrupole Formula from the Kinetic-Conformal Horava Theory
Einstein’s quadrupole formula from the kinetic-conformal Hoˇrava theory Jorge Bellor´ına,1 and Alvaro Restucciaa,b,2 aDepartment of Physics, Universidad de Antofagasta, 1240000 Antofagasta, Chile. bDepartment of Physics, Universidad Sim´on Bol´ıvar, 1080-A Caracas, Venezuela. [email protected], [email protected] Abstract We analyze the radiative and nonradiative linearized variables in a gravity theory within the familiy of the nonprojectable Hoˇrava theories, the Hoˇrava theory at the kinetic-conformal point. There is no extra mode in this for- mulation, the theory shares the same number of degrees of freedom with general relativity. The large-distance effective action, which is the one we consider, can be given in a generally-covariant form under asymptotically flat boundary conditions, the Einstein-aether theory under the condition of hypersurface orthogonality on the aether vector. In the linearized theory we find that only the transverse-traceless tensorial modes obey a sourced wave equation, as in general relativity. The rest of variables are nonradiative. The result is gauge-independent at the level of the linearized theory. For the case of a weak source, we find that the leading mode in the far zone is exactly Einstein’s quadrupole formula of general relativity, if some coupling constants are properly identified. There are no monopoles nor dipoles in arXiv:1612.04414v2 [gr-qc] 21 Jul 2017 this formulation, in distinction to the nonprojectable Horava theory outside the kinetic-conformal point. We also discuss some constraints on the theory arising from the observational bounds on Lorentz-violating theories. 1 Introduction Gravitational waves have recently been detected [1, 2, 3].