Einstein's Quest for General Relativity
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Generalization of Lorentz-Poincare Ether Theory to Quantum Gravity
Abstract We present a quantum theory of gravity which is in agreement with observation in the relativistic domain. The theory is not rel- ativistic, but a Galilean invariant generalization of Lorentz-Poincare ether theory to quantum gravity. If we apply the methodological rule that the best available theory has to be preferred, we have to reject the relativistic paradigm and return to Galilean invariant ether theory. arXiv:gr-qc/9706055v1 18 Jun 1997 1 Generalization Of Lorentz-Poincare Ether Theory To Quantum Gravity Ilja Schmelzer∗ September 12, 2021 ... die bloße Berufung auf k¨unftig zu entdeckende Ableitungen bedeutet uns nichts. Karl Popper In quantum gravity, as we shall see, the space-time manifold ceases to exist as an objective physical reality; geometry becomes relational and contextual; and the foundational conceptual categories of prior science – among them, existence itself – become problematized and relativized. Alan Sokal Contents 1 The Problem Of Quantum Gravity 3 2 Introduction 4 3 Generalization Of Lorentz-Poincare Ether Theory To Gra- vity 6 3.1 Elementary Properties Of Post-Relativistic Gravity . 8 3.2 TheCosmologicalConstants . 9 3.2.1 The Observation Of The Cosmological Constants . 9 3.2.2 The Necessity Of Cosmological Constants . 10 3.3 TheGlobalUniverse ....................... 11 3.4 Gravitational Collapse . 12 ∗WIAS Berlin 2 3.5 A Post-Relativistic Lattice Theory . 13 3.6 BetterAtomicEtherTheories . 15 4 Canonical Quantization 16 5 Discussion 17 5.1 Conclusion............................. 18 1 The Problem Of Quantum Gravity We believe that there exists a unique physical theory which allows to describe the entire universe. That means, there exists a theory — quantum gravity — which allows to describe quantum effects as well as relativistic effects of strong gravitational fields. -
A Mathematical Derivation of the General Relativistic Schwarzschild
A Mathematical Derivation of the General Relativistic Schwarzschild Metric An Honors thesis presented to the faculty of the Departments of Physics and Mathematics East Tennessee State University In partial fulfillment of the requirements for the Honors Scholar and Honors-in-Discipline Programs for a Bachelor of Science in Physics and Mathematics by David Simpson April 2007 Robert Gardner, Ph.D. Mark Giroux, Ph.D. Keywords: differential geometry, general relativity, Schwarzschild metric, black holes ABSTRACT The Mathematical Derivation of the General Relativistic Schwarzschild Metric by David Simpson We briefly discuss some underlying principles of special and general relativity with the focus on a more geometric interpretation. We outline Einstein’s Equations which describes the geometry of spacetime due to the influence of mass, and from there derive the Schwarzschild metric. The metric relies on the curvature of spacetime to provide a means of measuring invariant spacetime intervals around an isolated, static, and spherically symmetric mass M, which could represent a star or a black hole. In the derivation, we suggest a concise mathematical line of reasoning to evaluate the large number of cumbersome equations involved which was not found elsewhere in our survey of the literature. 2 CONTENTS ABSTRACT ................................. 2 1 Introduction to Relativity ...................... 4 1.1 Minkowski Space ....................... 6 1.2 What is a black hole? ..................... 11 1.3 Geodesics and Christoffel Symbols ............. 14 2 Einstein’s Field Equations and Requirements for a Solution .17 2.1 Einstein’s Field Equations .................. 20 3 Derivation of the Schwarzschild Metric .............. 21 3.1 Evaluation of the Christoffel Symbols .......... 25 3.2 Ricci Tensor Components ................. -
Interaction Energy of a Charged Medium and Its EM Field in a Curved Spacetime Mayeul Arminjon
Interaction Energy of a Charged Medium and its EM Field in a Curved Spacetime Mayeul Arminjon To cite this version: Mayeul Arminjon. Interaction Energy of a Charged Medium and its EM Field in a Curved Spacetime. Proceedings of the Twentieth International Conference on Geometry, Integrability and Quantization, Ivaïlo M. Mladenov, Jun 2018, Varna, Bulgaria. pp.88-98. hal-01881100 HAL Id: hal-01881100 https://hal.archives-ouvertes.fr/hal-01881100 Submitted on 25 Sep 2018 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. Interaction Energy of a Charged Medium and its EM Field in a Curved Spacetime Mayeul Arminjon Univ. Grenoble Alpes, CNRS, Grenoble INP, 3SR lab., F-38000 Grenoble, France Abstract In the electrodynamics of special relativity (SR) or general relativ- ity (GR), the energy tensors of the charged medium and its EM field add to give the total energy tensor that obeys the dynamical equation without external force. In the investigated scalar theory of gravitation (\SET"), this assumption leads to charge non-conservation, hence an additional, \interaction" energy tensor T inter has to be postulated. The present work aims at constraining this tensor. -
Of the American Mathematical Society August 2017 Volume 64, Number 7
ISSN 0002-9920 (print) ISSN 1088-9477 (online) of the American Mathematical Society August 2017 Volume 64, Number 7 The Mathematics of Gravitational Waves: A Two-Part Feature page 684 The Travel Ban: Affected Mathematicians Tell Their Stories page 678 The Global Math Project: Uplifting Mathematics for All page 712 2015–2016 Doctoral Degrees Conferred page 727 Gravitational waves are produced by black holes spiraling inward (see page 674). American Mathematical Society LEARNING ® MEDIA MATHSCINET ONLINE RESOURCES MATHEMATICS WASHINGTON, DC CONFERENCES MATHEMATICAL INCLUSION REVIEWS STUDENTS MENTORING PROFESSION GRAD PUBLISHING STUDENTS OUTREACH TOOLS EMPLOYMENT MATH VISUALIZATIONS EXCLUSION TEACHING CAREERS MATH STEM ART REVIEWS MEETINGS FUNDING WORKSHOPS BOOKS EDUCATION MATH ADVOCACY NETWORKING DIVERSITY blogs.ams.org Notices of the American Mathematical Society August 2017 FEATURED 684684 718 26 678 Gravitational Waves The Graduate Student The Travel Ban: Affected Introduction Section Mathematicians Tell Their by Christina Sormani Karen E. Smith Interview Stories How the Green Light was Given for by Laure Flapan Gravitational Wave Research by Alexander Diaz-Lopez, Allyn by C. Denson Hill and Paweł Nurowski WHAT IS...a CR Submanifold? Jackson, and Stephen Kennedy by Phillip S. Harrington and Andrew Gravitational Waves and Their Raich Mathematics by Lydia Bieri, David Garfinkle, and Nicolás Yunes This season of the Perseid meteor shower August 12 and the third sighting in June make our cover feature on the discovery of gravitational waves -
Demystifying Special Relativity; the K-Factor Angel Darlene Harb
Demystifying Special Relativity; the K-Factor Angel Darlene Harb University of Texas at San Antonio, TX, U.S.A. ABSTRACT This paper targets upper-level high school students and incoming college freshmen who have been less exposed to Special Relativity (SR). The goal is to spark interest and eliminate any feelings of intimidation one might have about a topic brought forth by world genius Albert Einstein. For this purpose, we will introduce some ideas revolving around SR. Additionally, by deriving the relationship between the k-factor and relative velocity, we hope that students come to an appreciation for the impact of basic mathematical skills and the way these can be applied to quite complex models. Advanced readers can directly jump ahead to the section discussing the k-factor. keywords : relative velocity, world lines, space-time 1 Introduction 1.1 A Morsel of History Throughout time, scientists have searched for ’just the right’ model comprised of laws, assumptions and theories that could explain our physical world. One example of a leading physical law is: All matter in the universe is subject to the same forces. It is important to note, this principle is agreeable to scientists, not because it is empirically true, but because this law makes for a good model of nature. Consequently, this law unifies areas like mechanics, electricity and optics traditionally taught separate from each other. Sir Isaac Newton (1643-1727) contributed to this principle with his ’three laws of motion.’ They were so mathematically elegant, that the Newtonian model dominated the scientific mind for nearly two centuries. -
Einstein's Mistakes
Einstein’s Mistakes Einstein was the greatest genius of the Twentieth Century, but his discoveries were blighted with mistakes. The Human Failing of Genius. 1 PART 1 An evaluation of the man Here, Einstein grows up, his thinking evolves, and many quotations from him are listed. Albert Einstein (1879-1955) Einstein at 14 Einstein at 26 Einstein at 42 3 Albert Einstein (1879-1955) Einstein at age 61 (1940) 4 Albert Einstein (1879-1955) Born in Ulm, Swabian region of Southern Germany. From a Jewish merchant family. Had a sister Maja. Family rejected Jewish customs. Did not inherit any mathematical talent. Inherited stubbornness, Inherited a roguish sense of humor, An inclination to mysticism, And a habit of grüblen or protracted, agonizing “brooding” over whatever was on its mind. Leading to the thought experiment. 5 Portrait in 1947 – age 68, and his habit of agonizing brooding over whatever was on its mind. He was in Princeton, NJ, USA. 6 Einstein the mystic •“Everyone who is seriously involved in pursuit of science becomes convinced that a spirit is manifest in the laws of the universe, one that is vastly superior to that of man..” •“When I assess a theory, I ask myself, if I was God, would I have arranged the universe that way?” •His roguish sense of humor was always there. •When asked what will be his reactions to observational evidence against the bending of light predicted by his general theory of relativity, he said: •”Then I would feel sorry for the Good Lord. The theory is correct anyway.” 7 Einstein: Mathematics •More quotations from Einstein: •“How it is possible that mathematics, a product of human thought that is independent of experience, fits so excellently the objects of physical reality?” •Questions asked by many people and Einstein: •“Is God a mathematician?” •His conclusion: •“ The Lord is cunning, but not malicious.” 8 Einstein the Stubborn Mystic “What interests me is whether God had any choice in the creation of the world” Some broadcasters expunged the comment from the soundtrack because they thought it was blasphemous. -
The State of the Multiverse: the String Landscape, the Cosmological Constant, and the Arrow of Time
The State of the Multiverse: The String Landscape, the Cosmological Constant, and the Arrow of Time Raphael Bousso Center for Theoretical Physics University of California, Berkeley Stephen Hawking: 70th Birthday Conference Cambridge, 6 January 2011 RB & Polchinski, hep-th/0004134; RB, arXiv:1112.3341 The Cosmological Constant Problem The Landscape of String Theory Cosmology: Eternal inflation and the Multiverse The Observed Arrow of Time The Arrow of Time in Monovacuous Theories A Landscape with Two Vacua A Landscape with Four Vacua The String Landscape Magnitude of contributions to the vacuum energy graviton (a) (b) I Vacuum fluctuations: SUSY cutoff: ! 10−64; Planck scale cutoff: ! 1 I Effective potentials for scalars: Electroweak symmetry breaking lowers Λ by approximately (200 GeV)4 ≈ 10−67. The cosmological constant problem −121 I Each known contribution is much larger than 10 (the observational upper bound on jΛj known for decades) I Different contributions can cancel against each other or against ΛEinstein. I But why would they do so to a precision better than 10−121? Why is the vacuum energy so small? 6= 0 Why is the energy of the vacuum so small, and why is it comparable to the matter density in the present era? Recent observations Supernovae/CMB/ Large Scale Structure: Λ ≈ 0:4 × 10−121 Recent observations Supernovae/CMB/ Large Scale Structure: Λ ≈ 0:4 × 10−121 6= 0 Why is the energy of the vacuum so small, and why is it comparable to the matter density in the present era? The Cosmological Constant Problem The Landscape of String Theory Cosmology: Eternal inflation and the Multiverse The Observed Arrow of Time The Arrow of Time in Monovacuous Theories A Landscape with Two Vacua A Landscape with Four Vacua The String Landscape Many ways to make empty space Topology and combinatorics RB & Polchinski (2000) I A six-dimensional manifold contains hundreds of topological cycles. -
Time Dilation of Accelerated Clocks
Astrophysical Institute Neunhof Circular se07117, February 2016 1 Time Dilation of accelerated Clocks The definitions of proper time and proper length in General Rela- tivity Theory are presented. Time dilation and length contraction are explicitly computed for the example of clocks and rulers which are at rest in a rotating reference frame, and hence accelerated versus inertial reference frames. Experimental proofs of this time dilation, in particular the observation of the decay rates of acceler- ated muons, are discussed. As an illustration of the equivalence principle, we show that the general relativistic equation of motion of objects, which are at rest in a rotating reference frame, reduces to Newtons equation of motion of the same objects at rest in an inertial reference system and subject to a gravitational field. We close with some remarks on real versus ideal clocks, and the “clock hypothesis”. 1. Coordinate Diffeomorphisms In flat Minkowski space, we place a rectangular three-dimensional grid of fiducial marks in three-dimensional position space, and assign cartesian coordinate values x1, x2, x3 to each fiducial mark. The values of the xi are constants for each fiducial mark, i. e. the fiducial marks are at rest in the coordinate frame, which they define. Now we stretch and/or compress and/or skew and/or rotate the grid of fiducial marks locally and/or globally, and/or re-name the fiducial marks, e. g. change from cartesian coordinates to spherical coordinates or whatever other coordinates. All movements and renamings of the fiducial marks are subject to the constraint that the map from the initial grid to the deformed and/or renamed grid must be differentiable and invertible (i. -
A Brief History of Gravitational Waves
universe Review A Brief History of Gravitational Waves Jorge L. Cervantes-Cota 1, Salvador Galindo-Uribarri 1 and George F. Smoot 2,3,4,* 1 Department of Physics, National Institute for Nuclear Research, Km 36.5 Carretera Mexico-Toluca, Ocoyoacac, C.P. 52750 Mexico, Mexico; [email protected] (J.L.C.-C.); [email protected] (S.G.-U.) 2 Helmut and Ana Pao Sohmen Professor at Large, Institute for Advanced Study, Hong Kong University of Science and Technology, Clear Water Bay, Kowloon, 999077 Hong Kong, China 3 Université Sorbonne Paris Cité, Laboratoire APC-PCCP, Université Paris Diderot, 10 rue Alice Domon et Leonie Duquet, 75205 Paris Cedex 13, France 4 Department of Physics and LBNL, University of California; MS Bldg 50-5505 LBNL, 1 Cyclotron Road Berkeley, 94720 CA, USA * Correspondence: [email protected]; Tel.:+1-510-486-5505 Academic Editors: Lorenzo Iorio and Elias C. Vagenas Received: 21 July 2016; Accepted: 2 September 2016; Published: 13 September 2016 Abstract: This review describes the discovery of gravitational waves. We recount the journey of predicting and finding those waves, since its beginning in the early twentieth century, their prediction by Einstein in 1916, theoretical and experimental blunders, efforts towards their detection, and finally the subsequent successful discovery. Keywords: gravitational waves; General Relativity; LIGO; Einstein; strong-field gravity; binary black holes 1. Introduction Einstein’s General Theory of Relativity, published in November 1915, led to the prediction of the existence of gravitational waves that would be so faint and their interaction with matter so weak that Einstein himself wondered if they could ever be discovered. -
The Multiverse: Conjecture, Proof, and Science
The multiverse: conjecture, proof, and science George Ellis Talk at Nicolai Fest Golm 2012 Does the Multiverse Really Exist ? Scientific American: July 2011 1 The idea The idea of a multiverse -- an ensemble of universes or of universe domains – has received increasing attention in cosmology - separate places [Vilenkin, Linde, Guth] - separate times [Smolin, cyclic universes] - the Everett quantum multi-universe: other branches of the wavefunction [Deutsch] - the cosmic landscape of string theory, imbedded in a chaotic cosmology [Susskind] - totally disjoint [Sciama, Tegmark] 2 Our Cosmic Habitat Martin Rees Rees explores the notion that our universe is just a part of a vast ''multiverse,'' or ensemble of universes, in which most of the other universes are lifeless. What we call the laws of nature would then be no more than local bylaws, imposed in the aftermath of our own Big Bang. In this scenario, our cosmic habitat would be a special, possibly unique universe where the prevailing laws of physics allowed life to emerge. 3 Scientific American May 2003 issue COSMOLOGY “Parallel Universes: Not just a staple of science fiction, other universes are a direct implication of cosmological observations” By Max Tegmark 4 Brian Greene: The Hidden Reality Parallel Universes and The Deep Laws of the Cosmos 5 Varieties of Multiverse Brian Greene (The Hidden Reality) advocates nine different types of multiverse: 1. Invisible parts of our universe 2. Chaotic inflation 3. Brane worlds 4. Cyclic universes 5. Landscape of string theory 6. Branches of the Quantum mechanics wave function 7. Holographic projections 8. Computer simulations 9. All that can exist must exist – “grandest of all multiverses” They can’t all be true! – they conflict with each other. -
Towards a Theory of Gravitational Radiation Or What Is a Gravitational Wave?
Recent LIGO announcement Gravitational radiation theory: summary Prehistory: 1916-1956 History: 1957-1962 Towards a theory of gravitational radiation or What is a gravitational wave? Paweł Nurowski Center for Theoretical Physics Polish Academy of Sciences King’s College London, 28 April 2016 1/48 Recent LIGO announcement Gravitational radiation theory: summary Prehistory: 1916-1956 History: 1957-1962 Plan 1 Recent LIGO announcement 2 Gravitational radiation theory: summary 3 Prehistory: 1916-1956 4 History: 1957-1962 2/48 Recent LIGO announcement Gravitational radiation theory: summary Prehistory: 1916-1956 History: 1957-1962 LIGO detection: Its relevance the first detection of gravitational waves the first detection of a black hole; of a binary black-hole; of a merging process of black holes creating a new one; Kerr black holes exist; black holes with up to 60 Solar masses exist; the most energetic process ever observed important test of Einstein’s General Theory of Relativity new window: a birth of gravitational wave astronomy 3/48 Recent LIGO announcement Gravitational radiation theory: summary Prehistory: 1916-1956 History: 1957-1962 LIGO detection: Its relevance the first detection of gravitational waves the first detection of a black hole; of a binary black-hole; of a merging process of black holes creating a new one; Kerr black holes exist; black holes with up to 60 Solar masses exist; the most energetic process ever observed important test of Einstein’s General Theory of Relativity new window: a birth of gravitational wave astronomy -
Equivalence Principle (WEP) of General Relativity Using a New Quantum Gravity Theory Proposed by the Authors Called Electro-Magnetic Quantum Gravity Or EMQG (Ref
WHAT ARE THE HIDDEN QUANTUM PROCESSES IN EINSTEIN’S WEAK PRINCIPLE OF EQUIVALENCE? Tom Ostoma and Mike Trushyk 48 O’HARA PLACE, Brampton, Ontario, L6Y 3R8 [email protected] Monday April 12, 2000 ACKNOWLEDGMENTS We wish to thank R. Mongrain (P.Eng) for our lengthy conversations on the nature of space, time, light, matter, and CA theory. ABSTRACT We provide a quantum derivation of Einstein’s Weak Equivalence Principle (WEP) of general relativity using a new quantum gravity theory proposed by the authors called Electro-Magnetic Quantum Gravity or EMQG (ref. 1). EMQG is manifestly compatible with Cellular Automata (CA) theory (ref. 2 and 4), and is also based on a new theory of inertia (ref. 5) proposed by R. Haisch, A. Rueda, and H. Puthoff (which we modified and called Quantum Inertia, QI). QI states that classical Newtonian Inertia is a property of matter due to the strictly local electrical force interactions contributed by each of the (electrically charged) elementary particles of the mass with the surrounding (electrically charged) virtual particles (virtual masseons) of the quantum vacuum. The sum of all the tiny electrical forces (photon exchanges with the vacuum particles) originating in each charged elementary particle of the accelerated mass is the source of the total inertial force of a mass which opposes accelerated motion in Newton’s law ‘F = MA’. The well known paradoxes that arise from considerations of accelerated motion (Mach’s principle) are resolved, and Newton’s laws of motion are now understood at the deeper quantum level. We found that gravity also involves the same ‘inertial’ electromagnetic force component that exists in inertial mass.