DOCSLIB.ORG

Quantum Pre-Geometry Models for Quantum Gravity

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
Quantum Pre-Geometry Models for Quantum Gravity Quantum pre-geometry models for Quantum Gravity by Francesco Caravelli A thesis presented to the University of Waterloo in fulfillment of the thesis requirement for the degree of Doctor of Philosophy in Physics Waterloo, Ontario, Canada, 2012 © Francesco Caravelli 2012 AUTHOR’S DECLARATION I hereby declare that I am the sole author of this thesis. This is a true copy of the thesis, including any required final revisions, as accepted by my examiners. I understand that my thesis may be made electronically available to the public. ii ABSTRACT In this thesis we review the status of an approach to Quantum Gravity through lattice toy models, Quantum Graphity. In particular, we describe the two toy models introduced in the literature and describe with a certain level of details the results obtained so far. We emphasize the connection between Quantum Graphity and emergent gravity, and the relation with Variable Speed of Light theories. iii ACKNOWLEDGEMENTS A long list of sincere thanks has to be given here. First of all, to my supervisors, Fotini Markopoulou and Lee Smolin, for the continuous and discrete support during the PhD. Then, a sincere thanks goes to the people I have closely collaborated with (and friends), Leonardo Modesto, Alioscia Hamma and Simone Severini, Arnau Riera, Dario Benedetti, Daniele Oriti, Lorenzo Sindoni, Razvan Gurau, Olaf Dreyer, Emanuele Alesci, Isabeau Premont-Schwarz,´ Sylvain Carrozza and Cosimo Bambi. A particular thanks goes also to my family (Mamma, Papa´ e le sorelline), for continuous support, moral and economi- cal. Then a long list of friends goes here. Having shared a double life between Waterloo (Canada) and Berlin (Germany), a list of people from all over the world follows! In Wa- terloo, I have to thank my buddy Cozmin(/Cozster Cosniverse Cosferatu) Ududec and my dear friend Mitzy Herrera, Owen Cherry (on top), Cohl Fur(e)y, Coco Escobedo, John Daly and Jessica Phillips, Jonathan Hackett and Sonia Markes . In Berlin I have to thank my russian friend Sasha Latnikova, die kleine Marina Zygelman, Anja Rogacheva, Sara Pernbrunner, Cosimo Restuccia, Ivano Pallante, to my not-girlfriend Elena Bruno, to the si-culo Marco Scalisi for many discussions about all-but-physics, to the puzzling and mis- terious friend Carlos Guedes and to la francesina Estelle de Tournadre in the good and the iv bad (and the bad and the sad). I thank in particular Isabeau, who kindly gave me his thesis in order to use his Latex style. Research at Perimeter Institute is supported by the Government of Canada through Industry Canada and by the Province of Ontario through the Ministry of Research & In- novation. Part of this research has been also funded by the Templeton Foundation. Part of the numerical work was made possible by the facilities of the Shared Hierarchical Aca- demic Research Computing Network (SHARCNET:www.sharcnet.ca). Also, hospitality at the Santa Fe Institute and the Albert Einstein Institute of Berlin have been much appre- ciated. v DEDICATION Ancora alla mia famiglia e ai miei amici, a qualcun altro che dimentico, e a qualcun altro che non voglio ricordare (Again to my family and my friends, to somebody else I forgot, and to somebody I do not want to remember) vi CONTENTS Author’s Declaration ii Abstract iii Acknowledgements iv Dedication vi 1 Introduction 1 I General Relativity: a troubled son 9 2 General Relativity and its problems 10 2.1 General Relativity . 10 2.1.1 Conceptual problems of GR . 15 2.1.2 Breakdown of General Relativity: singularities . 15 2.2 Why quantizing gravity? . 17 2.3 First attempt of quantization . 20 vii 2.3.1 QFT: linearized theory and divergences . 20 3 Motivations for an analogue description of General Relativity 29 3.1 Condensed Matter, Quantum Mechanics and Analogue models . 30 3.2 Variable Speed of Light theories and the major cosmological problems . 32 II Graph models 38 4 Quantum Graphs without matter 39 4.1 Graph Models . 40 4.2 A brief review of the String-Net condensation . 41 4.3 Graph theory preliminaries . 45 4.4 Quantum mechanics preliminaries . 46 4.5 The Hamiltonian . 49 4.5.1 Valence term . 50 4.5.2 Closed Paths . 51 4.5.3 Interaction Terms . 52 4.6 Extensions with More Degrees of Freedom and String-Net condensation . 52 4.7 Lieb-Robinson Bounds and (non-)locality . 57 4.7.1 Locality and non-locality . 57 4.7.2 Lieb-Robinson Bounds and the emergent speed of sound . 59 4.7.3 Lieb-Robinson Bound for the emergent U(1) model . 60 4.8 Mean field theory approximation at Low Temperature . 63 viii 4.8.1 Graphs and Line Graphs . 63 4.8.2 The line graph representation . 65 4.8.3 Mean field theory approximation and low temperature expansion . 75 4.9 The cosmological horizon problem and the speed of propagation of signals 86 4.10 Problems with this model and the external bath . 87 5 Quantum Graphs with matter 88 5.1 Bose-Hubbard model on Dynamical Graphs . 88 5.1.1 The Bose-Hubbard model . 91 5.1.2 Promoting the edges of the lattice to a quantum degree of freedom . 96 5.1.3 Discussion of the model . 104 5.1.4 Setting of the model . 111 5.1.5 Numerical analysis . 115 5.2 Markov chains analysis of the model . 121 III Emergence 135 6 Geometry and Emergence 136 6.1 Foliated and rotationally invariant graphs . 138 6.1.1 Foliated graphs . 138 6.1.2 Rotationally invariant graphs . 143 6.2 Regions of high connectivity as trapped surfaces . 145 6.2.1 Classical trapping . 146 ix 6.2.2 Quantum case: the KN configuration . 147 6.3 Correspondence between graph connectivity and curved geometry . 156 6.3.1 Restriction of the time-dependent Schrodinger¨ equation to the set of classical states . 156 6.3.2 Dispersion relation and continuum limit . 161 6.3.3 Lieb-Robinson bound for hopping bosons . 163 6.4 Model with parametrized fall-off of connectivity . 166 6.4.1 The Model . 166 6.4.2 Trapped surface . 167 6.5 Emergence of the mass for the scalar field . 169 6.5.1 Emergence of the mass from disordered locality . 169 6.5.2 Emergence of the mass from multi-particles interactions . 191 Appendix A Random Walk 208 Bibliography 216 x ”You can know the name of a bird in all the languages of the world, but when you’re finished, you’ll know absolutely nothing whatever about the bird. So let’s look at the bird and see what it’s doing - that’s what counts. I learned very early the difference between knowing the name of something and knowing something.” Richard Feynman ”Phantasie / Vorstellungskraft ist wichtiger als Wissen, denn Wissen ist begrenzt.” (Imagination is more important than knowledge, because knowledge is limited.) Albert Einstein ”Ero giovanissimo, avevo l’illusione che l’intelligenza umana potesse arrivare a tutto. E percio´ m’ero ingolfato negli studi oltremisura.” (I was young, I had the illusion that human intelligence could get anywhere. For this reason I focused on studies beyond measure.) Enrico Fermi Thanks. xi Chapter 1 Introduction General Relativity is one of the most intriguing physical theories, since it deals with the nature of space and time, and our perception of reality. Using the Planck constant ~, the Newton constant G and the speed of light c, we can build a constant with the dimension of an energy. This is the Planck energy, given by: r 5 ~c 19 Ep = 10 GeV: G ≈ When a gravitational process has an energy of the order of the Planck energy, using the intuition we gained by quantizing the other three known forces, we expect another theory, a Quantum Theory of Gravity, to replace General Relativity. As we will discuss later in detail, this process of quantization is very troublesome. So far, no fully satisfactory quantization of General Relativity exists. What is a Quantum Theory of Gravity? A quantum theory of gravity is a theory which describes gravitational phenomena up to the Planck scale and such that in the 1 limit ~ 0, reduces to a gravitational theory, and that at energies much smaller then the ! Planck energy, reduces to Einstein’s General Relativity. Given this, it is rather compli- cated to describe a theory which do not exist yet. It is true that there are many proposals, but many of these are yet not fully convincing, or cannot predict a valuable and testable phenomenon[45]. Quantum mechanics is one of the milestones of the physics of the last century. It describes the physics of elementary particles and of atoms and molecules and has been tested extensively. General relativity is the other milestone of the past century. It describes the physics of spacetime and it works very well in describing the motion of celestial bod- ies in our solar system, in galaxies and in our Universe. However, when we put the two together and when we try to quantize gravity as it has been done for other forces, many obstructions appear. In spite of progresses in several directions, finding this new theory has proven a chal- lenging problem for several decades. In particular, there are several approaches propos- ing a quantization of gravity [33, 1, 120, 148]. In particular, Loop Quantum Gravity[33] (LQG) is a promising quantization of Gen- eral Relativity. It establishes that spacetime is a foam, in which atoms of space are con- structed on Wilson gauge lines, or spin networks. Many results have been obtained, as the spectrum of the area and volume operators [47] and the Bekenstein-Hawking Area- Entropy law[46].
Load more

Recommended publications
  • Arxiv:Hep-Ph/9912247V1 6 Dec 1999 MGNTV COSMOLOGY IMAGINATIVE Abstract
    IMAGINATIVE COSMOLOGY ROBERT H. BRANDENBERGER Physics Department, Brown University Providence, RI, 02912, USA AND JOAO˜ MAGUEIJO Theoretical Physics, The Blackett Laboratory, Imperial College Prince Consort Road, London SW7 2BZ, UK Abstract. We review1 a few off-the-beaten-track ideas in cosmology. They solve a variety of fundamental problems; also they are fun. We start with a description of non-singular dilaton cosmology. In these scenarios gravity is modified so that the Universe does not have a singular birth. We then present a variety of ideas mixing string theory and cosmology. These solve the cosmological problems usually solved by inflation, and furthermore shed light upon the issue of the number of dimensions of our Universe. We finally review several aspects of the varying speed of light theory. We show how the horizon, flatness, and cosmological constant problems may be solved in this scenario. We finally present a possible experimental test for a realization of this theory: a test in which the Supernovae results are to be combined with recent evidence for redshift dependence in the fine structure constant. arXiv:hep-ph/9912247v1 6 Dec 1999 1. Introduction In spite of their unprecedented success at providing causal theories for the origin of structure, our current models of the very early Universe, in partic- ular models of inflation and cosmic defect theories, leave several important issues unresolved and face crucial problems (see [1] for a more detailed dis- cussion). The purpose of this chapter is to present some imaginative and 1Brown preprint BROWN-HET-1198, invited lectures at the International School on Cosmology, Kish Island, Iran, Jan.
    [Show full text]
  • Engineering the Quantum Foam
    Engineering the Quantum Foam Reginald T. Cahill School of Chemistry, Physics and Earth Sciences, Flinders University, GPO Box 2100, Adelaide 5001, Australia [email protected] _____________________________________________________ ABSTRACT In 1990 Alcubierre, within the General Relativity model for space-time, proposed a scenario for ‘warp drive’ faster than light travel, in which objects would achieve such speeds by actually being stationary within a bubble of space which itself was moving through space, the idea being that the speed of the bubble was not itself limited by the speed of light. However that scenario required exotic matter to stabilise the boundary of the bubble. Here that proposal is re-examined within the context of the new modelling of space in which space is a quantum system, viz a quantum foam, with on-going classicalisation. This model has lead to the resolution of a number of longstanding problems, including a dynamical explanation for the so-called `dark matter’ effect. It has also given the first evidence of quantum gravity effects, as experimental data has shown that a new dimensionless constant characterising the self-interaction of space is the fine structure constant. The studies here begin the task of examining to what extent the new spatial self-interaction dynamics can play a role in stabilising the boundary without exotic matter, and whether the boundary stabilisation dynamics can be engineered; this would amount to quantum gravity engineering. 1 Introduction The modelling of space within physics has been an enormously challenging task dating back in the modern era to Galileo, mainly because it has proven very difficult, both conceptually and experimentally, to get a ‘handle’ on the phenomenon of space.
    [Show full text]
  • A Different Derivation of the Calogero Conjecture
    1 A Different Derivation of the Calogero Conjecture Ioannis Iraklis Haranas Physics and Astronomy Department York University 314 A Petrie Science Building Toronto – Ontario CANADA E mail: [email protected] Abstract: In a study by F. Calogero [1] entitled “ Cosmic origin of quantization” an expression was derived for the variability of h with time, and its consequences if any, of such an idea in cosmology were examined. In this paper we will offer a different derivation of the Calogero conjecture based on a postulate concerning a variable speed of light, [2] in conjuction with Weinberg’s relationship for the mass of an elementary particle. Introduction: Recently, Calogero studied and reconsidered the “ universal background noise which according to Nelsons’s stohastic mechanics [3,4,5] is the basis for the quantum behaviour. The position that Calogero took was that there might be a physical origin for this noise. He immediately pointed his attention to the gravitational interactions with the distant masses in the universe. Therefore, he argued for the case that Planck’s constant can be given by the following expression: 1/ 2 h ≈α G1/ 2m3/ 2[]R(t) (1) where α is a numerical constant = 1, G is the Newtonian gravitational constant, m is the mass of the hydrogen atom which is considered as the basic mass unit in the universe, and finally R(t) represents the radius of the universe or alternatively: “part of the universe which is accessible to gravitational interactions at time t.” [6]. We can obtain a rough estimate of the value of h if we just take into account that R(t) is the radius of the -28 universe evaluated at the present time t0 ie.
    [Show full text]
  • Table of Contents (Print)
    PERIODICALS PHYSICAL REVIEW D Postmaster send address changes to: For editorial and subscription correspondence, American Institute of Physics please see inside front cover Suite 1NO1 „ISSN: 0556-2821… 2 Huntington Quadrangle Melville, NY 11747-4502 THIRD SERIES, VOLUME 66, NUMBER 4 CONTENTS 15 AUGUST 2002 RAPID COMMUNICATIONS Density of cold dark matter (5 pages) ................................................... 041301͑R͒ Alessandro Melchiorri and Joseph Silk Shape of a small universe: Signatures in the cosmic microwave background (4 pages) . 041302͑R͒ R. Bowen and P. G. Ferreira Nonlinear r-modes in neutron stars: Instability of an unstable mode (5 pages) . 041303͑R͒ Philip Gressman, Lap-Ming Lin, Wai-Mo Suen, N. Stergioulas, and John L. Friedman Convergence and stability in numerical relativity (4 pages) . 041501͑R͒ Gioel Calabrese, Jorge Pullin, Olivier Sarbach, and Manuel Tiglio Stabilizing textures with magnetic ®elds (5 pages) . 041701͑R͒ R. S. Ward Friction in in¯aton equations of motion (5 pages) . 041702͑R͒ Ian D. Lawrie Singularity threshold of the nonlinear sigma model using 3D adaptive mesh re®nement (5 pages) . 041703͑R͒ Steven L. Liebling ARTICLES Neutrino damping rate at ®nite temperature and density (11 pages) . 043001 Eduardo S. Tututi, Manuel Torres, and Juan Carlos D'Olivo Numerical and analytical predictions for the large-scale Sunyaev-Zel'dovich effect (13 pages) . 043002 Alexandre Refregier and Romain Teyssier In¯ation, cold dark matter, and the central density problem (12 pages) . 043003 Andrew R. Zentner and James S. Bullock Size of the smallest scales in cosmic string networks (4 pages) . 043501 Xavier Siemens, Ken D. Olum, and Alexander Vilenkin Semiclassical force for electroweak baryogenesis: Three-dimensional derivation (9 pages) .
    [Show full text]
  • Variable Planck's Constant
    Variable Planck’s Constant: Treated As A Dynamical Field And Path Integral Rand Dannenberg Ventura College, Physics and Astronomy Department, Ventura CA [email protected] [email protected] January 28, 2021 Abstract. The constant ħ is elevated to a dynamical field, coupling to other fields, and itself, through the Lagrangian density derivative terms. The spatial and temporal dependence of ħ falls directly out of the field equations themselves. Three solutions are found: a free field with a tadpole term; a standing-wave non-propagating mode; a non-oscillating non-propagating mode. The first two could be quantized. The third corresponds to a zero-momentum classical field that naturally decays spatially to a constant with no ad-hoc terms added to the Lagrangian. An attempt is made to calibrate the constants in the third solution based on experimental data. The three fields are referred to as actons. It is tentatively concluded that the acton origin coincides with a massive body, or point of infinite density, though is not mass dependent. An expression for the positional dependence of Planck’s constant is derived from a field theory in this work that matches in functional form that of one derived from considerations of Local Position Invariance violation in GR in another paper by this author. Astrophysical and Cosmological interpretations are provided. A derivation is shown for how the integrand in the path integral exponent becomes Lc/ħ(r), where Lc is the classical action. The path that makes stationary the integral in the exponent is termed the “dominant” path, and deviates from the classical path systematically due to the position dependence of ħ.
    [Show full text]
  • Variable Planck's Constant
    Preprints (www.preprints.org) | NOT PEER-REVIEWED | Posted: 29 January 2021 doi:10.20944/preprints202101.0612.v1 Variable Planck’s Constant: Treated As A Dynamical Field And Path Integral Rand Dannenberg Ventura College, Physics and Astronomy Department, Ventura CA [email protected] Abstract. The constant ħ is elevated to a dynamical field, coupling to other fields, and itself, through the Lagrangian density derivative terms. The spatial and temporal dependence of ħ falls directly out of the field equations themselves. Three solutions are found: a free field with a tadpole term; a standing-wave non-propagating mode; a non-oscillating non-propagating mode. The first two could be quantized. The third corresponds to a zero-momentum classical field that naturally decays spatially to a constant with no ad-hoc terms added to the Lagrangian. An attempt is made to calibrate the constants in the third solution based on experimental data. The three fields are referred to as actons. It is tentatively concluded that the acton origin coincides with a massive body, or point of infinite density, though is not mass dependent. An expression for the positional dependence of Planck’s constant is derived from a field theory in this work that matches in functional form that of one derived from considerations of Local Position Invariance violation in GR in another paper by this author. Astrophysical and Cosmological interpretations are provided. A derivation is shown for how the integrand in the path integral exponent becomes Lc/ħ(r), where Lc is the classical action. The path that makes stationary the integral in the exponent is termed the “dominant” path, and deviates from the classical path systematically due to the position dependence of ħ.
    [Show full text]
  • Does LIGO Prove General Relativity?
    Does LIGO Prove General Relativity? by Clark M. Thomas © May 12, 2016; modified Sept. 11, 2016 ABSTRACT LIGO-detected "gravitational waves" are very real. This successful experiment in early 2016 did open up a new form of astronomy. Despite the hype, the initial explanation for what was discovered neither confirms nor denies Einstein's full theory of General Relativity, including the concept of gravity membranes (branes). The LIGO discovery can be explained by a model somewhat similar to de Broglie-Bohm quantum pilot waves. LIGO-detected "gravitational waves" are real. The successful experiment in early 2016 did open up a new form of astronomy. However, despite the hype, the initial explanation for what was discovered neither confirms nor denies Einstein's full theory of Page !1 of !11 General Relativity, including the concept of gravity membranes (branes). It merely confirms his 2016 guess that gravity waves should be generated, and that they potentially could be detected and measured. That’s a long way from the core of his GR thesis.1 “Spacetime” is a cool idea, but it merely records the timely effects of motion within a 3D Universe, making up frame-specific 4D spacetimes – with seemingly infinite discrete inertial frames of reference.2 Einstein's idea of "c" being the somewhat mystical absolute limit of measured speed in any direction simply acknowledges the initial acceleration of electromagnetic particle strings from their graviton base within a frame of reference. Speed of light within a vacuum is only the initial burst of acceleration for each yin/yang photon string as it leaves its graviton “mother ship.”3 A better explanation for the waves detected by LIGO is a 21st century paradigm of push/shadow gravity – within a 3D set sea of “quantum foam” (primarily Yin/Yang particles, Y/Y strings, Y/Y graviton rings, and some larger particles).
    [Show full text]
  • Fine Structure Constant| and Variable Speed of Light
    Apeiron, Vol. 17, No. 2, April 2010 126 Fine Structure Constant| and Variable Speed of Light Guoyou HUANG 1. Geoscience institute, Guilin University of echnology No. 12, Jiangan St. Guilin, Guangxi. 541004 P.R. CHINA 2. Geophysics research institute, No.274 Geological Corp. No.69, Gaode St. Beihai, Guangxi. 536000 P.R.CHINA Email: [email protected] The fine structure constant has been proved to be no change even if the speed of light varies in gravitation field or in the history of cosmos. Lorentz transformation has also been proved to be a transformation of physical units between two different frames. This transformation implies a variable speed of light in gravitational field. Base on this variable speed of light, a new VSL cosmology model was established so as to solve the flatness problem and horizon problem in Standard Cosmology. Keywords: Fine structure constant, Lorentz Transformation, Variable Speed of Light, Flatness Problem, Horizon © 2010 C. Roy Keys Inc. — http://redshift.vif.com Apeiron, Vol. 17, No. 2, April 2010 127 1. Introduction The thinking of natural constants change with time was first made by Paul Dirac in 1937 [1] known as the Dirac Large Numbers Hypothesis, in which the gravitational constant was proposed to be inversely proportional to the age of universe in order to explain the relative weakness of the gravitational force compared to electrical forces. A group studying distant quasars claimed to have detected a variation in the fine structure constant [2], other groups claimed no detectable variation at much higher sensitivities [3][4][5][6]. Variable Speed of Light (VSL) cosmology has also been proposed by several authors [7][8][9][10] as an alternative choice for the well developed Inflationary Theory to explain the horizon problem and other puzzles in Standard Cosmology.
    [Show full text]
  • Quantum Geometrodynamics with Intrinsic Time Development
    2nd LeCosPA International Symposium, Nat.Taiwan U. (December 17th 2015) Quantum geometrodynamics with intrinsic time development 許 Chopin Soo 祖 斌 Department of Physics, Nat. Cheng Kung U, Taiwan Everything? What about (let’s not forget) the `problem of time’ ? A very wise man once said “What then is time? If no one asks me, I know what it is. If I wish to explain it to him who asks, I do not know”, pondering the mystery of what time really is, Saint Augustine (of Hippo) (354-430 A.D.) wrote in his Confessions《懺悔錄》, “Si nemo ex me quaerat scio; Si quaerente explicare velim, nescio ’’ Time: We all have some intuitive understanding of time. But what is time? Where does it comes from? Physical theory of space and time Einstein’s GR: Classical space-time <-> (pseudo-Riemannian)Geometry Quantum Gravity: “`Spacetime’ - a concept of limited applicability” ---J. A. Wheeler What, if anything at all, plays the role of “time” in Quantum Gravity? Importance of time: 1)Quantum probabilities are normalized at fixed instances of time 2)Time <-> Hamiltonian as generator of time translation/evolution Hamiltonian <-> Energy Time: Is it 1) fundamental (present even in Quantum Gravity)? 2) emergent (present in the (semi)-classical context only)? 3) an illusion (!)? … Nemeti, Istvan et al. arXiv:0811.2910 [gr-qc] Getting to know Einstein’s theory Spacetime tells matter how to move; matter tells spacetime how to curve John Wheeler, in Geons, Black Holes, and Quantum Foam p.235 This saying has seeped into popular culture and public discourse; but with all due respect to Wheeler, it is the Hamiltonian which tells everything (including the metric) how to move! from The Early Universe (E.
    [Show full text]
  • Quantum Information Hidden in Quantum Fields
    Preprints (www.preprints.org) | NOT PEER-REVIEWED | Posted: 21 July 2020 Peer-reviewed version available at Quantum Reports 2020, 2, 33; doi:10.3390/quantum2030033 Article Quantum Information Hidden in Quantum Fields Paola Zizzi Department of Brain and Behavioural Sciences, University of Pavia, Piazza Botta, 11, 27100 Pavia, Italy; [email protected]; Phone: +39 3475300467 Abstract: We investigate a possible reduction mechanism from (bosonic) Quantum Field Theory (QFT) to Quantum Mechanics (QM), in a way that could explain the apparent loss of degrees of freedom of the original theory in terms of quantum information in the reduced one. This reduction mechanism consists mainly in performing an ansatz on the boson field operator, which takes into account quantum foam and non-commutative geometry. Through the reduction mechanism, QFT reveals its hidden internal structure, which is a quantum network of maximally entangled multipartite states. In the end, a new approach to the quantum simulation of QFT is proposed through the use of QFT's internal quantum network Keywords: Quantum field theory; Quantum information; Quantum foam; Non-commutative geometry; Quantum simulation 1. Introduction Until the 1950s, the common opinion was that quantum field theory (QFT) was just quantum mechanics (QM) plus special relativity. But that is not the whole story, as well described in [1] [2]. There, the authors mainly say that the fact that QFT was "discovered" in an attempt to extend QM to the relativistic regime is only historically accidental. Indeed, QFT is necessary and applied also in the study of condensed matter, e.g. in the case of superconductivity, superfluidity, ferromagnetism, etc.
    [Show full text]
  • Evolutionary Physical Constants in Einstein's Field Equations and the Redshift
    Preprints (www.preprints.org) | NOT PEER-REVIEWED | Posted: 10 April 2019 doi:10.20944/preprints201904.0119.v1 Evolutionary physical constants in Einstein’s field equations and the redshift Rajendra P. Gupta Macronix Research Corporation, 9 Veery Lane, Ottawa, ON Canada K1J 8X4; [email protected] Abstract We have shown that the use of evolutionary gravitational constants G, the speed of light c, and cosmological constant Λ in the Einstein’s field equations leads to a very simple model that fits the supernovae Ia data with a single parameter as well as the standard ΛCDM model with two parameters, and has the predictive capability superior to the latter. We have shown that at the current time G and c both increase as dG/dt = 5.4GH0 and dc/dt = 1.8cH0 with H0 as the Hubble constant, and Λ decreases as dΛ/dt = -1.2ΛH0. Negative finding on the variation of G with time derived from the analysis of lunar laser ranging data in several studies has been attributed to the fact that these studies did not consider the variation of c simultaneously with G. Keywords: cosmology: theory, cosmological parameters – galaxies: distances and redshifts – variable physical constants 1 INTRODUCTION final section, Sec. 6, we will discuss our findings and present conclusions. Varying physical constant theories have been in existence The essence of this work is that the new model implicitly since time immemorial, especially since Dirac (1937, 1938) includes the cosmological constant (that is varying) and it can suggested such variation based on his large number fit the supernovae Ia data with a single parameter almost as hypothesis.
    [Show full text]
  • Variable Time and the Variable Speed of Light Edward G
    Variable Time and the Variable Speed of Light Edward G. Lake Independent Researcher August 14, 2018 [email protected] Abstract: Einstein’s Special and General Theories of Relativity state that time is a variable depending upon motion and gravity. The theories also state that the speed of light is variable. Einstein’s theories are being verified virtually every day. Yet, a few physicists still argue that time does not vary, and many physicists appear to inexplicably argue that Einstein’s theories state that the speed of light is invariable. This is an attempt to clarify what Einstein wrote and show how experiments routinely confirm that the speed of light is variable. Key words: Speed of Light; Time; Time Dilation; Relativity; Einstein. I. Measuring the speed of light. The fact that the speed of light is variable is demonstrated almost every day. No matter where you measure the speed of light, if you measure it correctly, you will get a result of 299,792,458 meters per second. Does this mean that the speed of light is the same everywhere? No. It means the speed of light per second is the same everywhere. And, according to Einstein’s Theories of Special and General Relativity, the length of a second can be different almost everywhere. That means that if you measure the speed of light to be 299,792,458 meters per second in one location, and if you also measure it to be 299,792,458 meters per second in another location, if the length of a second is different at those two locations, then the speed of light is also different.
    [Show full text]