DOCSLIB.ORG

PMEM and Unification

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
PMEM and Unification Pre-metric electromagnetism as a path to unification. DAVID DELPHENICH Independent researcher Spring Valley, OH 45370, USA [email protected] It is shown that the pre-metric approach to Maxwell’s equations provides an alternative to the traditional Einstein- Maxwell unification problem, namely, that electromagnetism and gravitation are unified in a different way that makes the gravitational field a consequence of the electromagnetic constitutive properties of spacetime, by way of the dispersion law for the propagation of electromagnetic waves. Keyw ords: Pre-metric electromagnetism, Einstein-Maxwell unification problem, line geometry, electromagnetic constitutive laws 1. The Einstein-Maxwell unification problem. fundamental distinctions between them, as well. In particular, the analogy between mass and Ever since Einstein succeeded in accounting for charge was not complete, since at the time (and the presence of gravitation in the universe by to this point in time, as well), no one had ever showing how it was a natural consequence of the observed what one might call “negative” mass or curvature of the Levi-Civita connection that one “anti-gravitation.” Of course, the possibility that derived from the Lorentzian metric on the such a unification of gravitation and spacetime manifold, he naturally wondered if the electromagnetism might lead to such tantalizing other fundamental force of nature that was consequences has been an ongoing source of known at the time – namely, electromagnetism – impetus for the search for that theory. could also be explained in a similar way. Since Several attempts followed by Einstein and the best-accepted theory of electromagnetism at others (cf., e.g., [1] and part II of [2]) at the time (as well as the best-accepted “classical” achieving such a unification. They seemed to theory to this day) was Maxwell’s theory, that fall into two basic categories: Extensions of g gave rise to what one might called the Einstein- with a four-dimensional spacetime and Maxwell unification problem: Find some extensions of spacetime to something higher- intrinsic (presumably geometric) structure on dimensional. The former models included spacetime (suitably extended) that will teleparallelism 1 and the Einstein-Schrödinger decompose into (or at least lead to) the theory [2], while the latter include the Kaluza- Lorentzian metric tensor g and the Klein models [1, 2, 4, 5], and some of the electromagnetic field strength 2-form F, along attempts to extend the tangent bundle of the four- with a set of field equations for that extended dimensional spacetime manifold to an geometric structure that would imply the anholonomic (i.e., non-integrable) rank-4 sub- Einstein field equations for g and the Maxwell bundle of the tangent bundle to a five- equations for F (at least, in some dimensional manifold (cf., e.g., [6-8]). approximation). All of the attempts were regarded as failures The suspicion that such a “unified field for one reason or another. One problem with theory” might actually exist was perhaps based upon the fact that Maxwell’s theory itself represented a “unified field theory” of the 1 The author has compiled an anthology [3] of electric and magnetic fields, and that there English translations of many of the early papers existed a well-known analogy between on teleparallelism that is available as a free PDF Coulomb’s law of electrostatics and Newton’s download at his website (neo-classical- law of universal gravitation, although there were physics.info) 2 Pre-metric electromagnetism as a path to unification teleparallelism was that it included unphysical passed over that “classical” problem 1 and started solutions, such as a static distribution of with the exchange-particle concept, combined gravitating, uncharged masses. The main with the scattering approximation for the field problem with the other theories was that they dynamics. That means: Rather than speculate on implied no new consequences of that unification; what might constitute the “field equations of i.e., they were “concatenations” of the field QED” or the nature of the electromagnetic theories, not unifications. What was missing “force” that acts between elementary charges at were any sort of “gravito-electromagnetic the quantum level, quantum physics was going to inductions,” that would suggest an analogue to replace the force of interaction with the exchange the electromagnetic induction in Maxwell’s of an elementary particle that would mediate the theory. Indeed, it is important to note that the interaction; for QED, that particle would be the latter inductions had been established photon. Then, rather than posing “classical” experimentally by Faraday before Maxwell problems, such as boundary-value problems in formulated his theory, while to date, no such statics and the Cauchy problem in dynamics, couplings of electromagnetic and gravitational QED would simply pass to the approximation in fields seem to have materialized in the which the initial time was − ∞ and the final time laboratory. (“Gravitomagnetism” is a different was + ∞, which is equivalent to assuming that matter, and we shall discuss it below.) the interaction of particles takes place inside a However, as quantum physics evolved, the very small “black box” time interval in which the nature of the Einstein-Maxwell unification nonlinear nature of the interaction can be problem changed, as well. Increasingly, Einstein enclosed in such a way that the time evolution suspected that gravitation could only be unified operator that takes incoming fields to outgoing with electromagnetism when one went to ones becomes a linear operator that takes quantum electromagnetism. That possibility incoming scattering states (which are asymptotic seems more reasonable nowadays, since the free fields) to outgoing ones. That allows one to phenomenon of “gravitomagnetism” had not use the methods of Fourier analysis and discuss been observed experimentally until relatively the scattering operator in momentum space recently [9]. The essence of that phenomenon is without having to worry that the perturbation that the analogy between Coulomb’s law and series that one defines (i.e., Feynman diagrams Newton’s law goes beyond the scope of statics, or loop expansions) is unphysical. since there is, in fact, a field that is induced by Of course, it is precisely the fundamental the relative motion of a mass that is analogous to distinction between Einstein’s theory of the magnetic field that is induced by the relative gravitation as a “classical” field theory (i.e., one motion of an electric charge, and which is in which one can pose boundary-value problems commonly called the gravitomagnetic field . As a in statics and the Cauchy problem in dynamics), result, one sees that Maxwell’s equations are while QED is a “quantum” field theory (i.e., one closely analogous to the weak-field equations of that begins in the scattering approximation to gravitation, which suggests that perhaps that Cauchy problem) that is the greatest Einstein’s equations of gravitation, which are the obstruction to the unification of those theories, strong-field equations, should be somehow although that fact is rarely addressed in quantum analogous to some hitherto-unknown “strong- gravity, which takes more of a “play it where it field” equations of electromagnetism. lays” approach. The physical realm in which one would Another common critique of the Einstein- expect to find the strongest electromagnetic Maxwell unification problem is that it is fields is in the atomic to subatomic domain, currently a partial unification problem, in the where one approaches the Schwinger critical sense that since the time of Einstein’s early work field strengths at which photons resolve into on gravitation, two other “quantum” interactions electron-positron field-pairs. However, since the time of Heisenberg and Pauli [10], quantum 1 One might suspect that the quantum use of the electrodynamics has not started with a set of word “classical” in a pejorative way is probably “strong-field equations of electromagnetism” an imitation of the pure-mathematical usage of that might perhaps be analogous to Einstein’s the word “trivial,” which often represents little equations of gravitation. Rather, it has simply more than a lack of personal curiosity about the subject, combined with an acceptance of the fact that the problem in question is hard to pose and even harder to solve. David Delphenich 3 have been added to the fundamental interactions, makes perfect sense in the context of the “pre- namely, the weak and strong interactions. metric” approach to electromagnetism. That Furthermore, once Yang and Mills had revisited approach is based upon the observation that the the gauge-field approach to elementary only place in which the Lorentzian metric on interactions that Weyl, Fock, and Ivanenko had spacetime enters into Maxwell’s equations is in studied in the context of electromagnetism at the Hodge * operator. In order to see that, we about the same time that Einstein was pondering express those equations in terms of the unified field theory and the Copenhagen school Minkowski electromagnetic field-strength 2- was defining their foundations for quantum form F as 1: physics, the unification of electromagnetism with the weak interactions as gauge field theories dF = 0, δF = 4 πJ, δJ = 0, (1) defined an entirely different approach to unification that usually took the form of looking in which d represents the exterior derivative for higher-dimensional
Load more

Recommended publications
  • Unification of Gravity and Quantum Theory Adam Daniels Old Dominion University, [email protected]
    Old Dominion University ODU Digital Commons Faculty-Sponsored Student Research Electrical & Computer Engineering 2017 Unification of Gravity and Quantum Theory Adam Daniels Old Dominion University, [email protected] Follow this and additional works at: https://digitalcommons.odu.edu/engineering_students Part of the Elementary Particles and Fields and String Theory Commons, Engineering Physics Commons, and the Quantum Physics Commons Repository Citation Daniels, Adam, "Unification of Gravity and Quantum Theory" (2017). Faculty-Sponsored Student Research. 1. https://digitalcommons.odu.edu/engineering_students/1 This Report is brought to you for free and open access by the Electrical & Computer Engineering at ODU Digital Commons. It has been accepted for inclusion in Faculty-Sponsored Student Research by an authorized administrator of ODU Digital Commons. For more information, please contact [email protected]. Unification of Gravity and Quantum Theory Adam D. Daniels [email protected] Electrical and Computer Engineering Department, Old Dominion University Norfolk, Virginia, United States Abstract- An overview of the four fundamental forces of objects falling on earth. Newton’s insight was that the force that physics as described by the Standard Model (SM) and prevalent governs matter here on Earth was the same force governing the unifying theories beyond it is provided. Background knowledge matter in space. Another critical step forward in unification was of the particles governing the fundamental forces is provided, accomplished in the 1860s when James C. Maxwell wrote down as it will be useful in understanding the way in which the his famous Maxwell’s Equations, showing that electricity and unification efforts of particle physics has evolved, either from magnetism were just two facets of a more fundamental the SM, or apart from it.
    [Show full text]
  • Unification of Nature's Fundamental Forces
    Unification of Nature’s Geoffrey B. West Fredrick M. Cooper Fundamental Forces Emil Mottola a continuing search Michael P. Mattis it was explicitly recognized at the time that basic research had an im- portant and seminal role to play even in the highly programmatic en- vironment of the Manhattan Project. Not surprisingly this mode of opera- tion evolved into the remarkable and unique admixture of pure, applied, programmatic, and technological re- search that is the hallmark of the present Laboratory structure. No- where in the world today can one find under one roof such diversity of talent dealing with such a broad range of scientific and technological challenges—from questions con- cerning the evolution of the universe and the nature of elementary parti- cles to the structure of new materi- als, the design and control of weapons, the mysteries of the gene, and the nature of AIDS! Many of the original scientists would have, in today’s parlance, identified themselves as nuclear or particle physicists. They explored the most basic laws of physics and continued the search for and under- standing of the “fundamental build- ing blocks of nature’’ and the princi- t is a well-known, and much- grappled with deep questions con- ples that govern their interactions. overworked, adage that the group cerning the consequences of quan- It is therefore fitting that this area of Iof scientists brought to Los tum mechanics, the structure of the science has remained a highly visi- Alamos to work on the Manhattan atom and its nucleus, and the devel- ble and active component of the Project constituted the greatest as- opment of quantum electrodynamics basic research activity at Los Alam- semblage of scientific talent ever (QED, the relativistic quantum field os.
    [Show full text]
  • Aspects of Loop Quantum Gravity
    Aspects of loop quantum gravity Alexander Nagen 23 September 2020 Submitted in partial fulfilment of the requirements for the degree of Master of Science of Imperial College London 1 Contents 1 Introduction 4 2 Classical theory 12 2.1 The ADM / initial-value formulation of GR . 12 2.2 Hamiltonian GR . 14 2.3 Ashtekar variables . 18 2.4 Reality conditions . 22 3 Quantisation 23 3.1 Holonomies . 23 3.2 The connection representation . 25 3.3 The loop representation . 25 3.4 Constraints and Hilbert spaces in canonical quantisation . 27 3.4.1 The kinematical Hilbert space . 27 3.4.2 Imposing the Gauss constraint . 29 3.4.3 Imposing the diffeomorphism constraint . 29 3.4.4 Imposing the Hamiltonian constraint . 31 3.4.5 The master constraint . 32 4 Aspects of canonical loop quantum gravity 35 4.1 Properties of spin networks . 35 4.2 The area operator . 36 4.3 The volume operator . 43 2 4.4 Geometry in loop quantum gravity . 46 5 Spin foams 48 5.1 The nature and origin of spin foams . 48 5.2 Spin foam models . 49 5.3 The BF model . 50 5.4 The Barrett-Crane model . 53 5.5 The EPRL model . 57 5.6 The spin foam - GFT correspondence . 59 6 Applications to black holes 61 6.1 Black hole entropy . 61 6.2 Hawking radiation . 65 7 Current topics 69 7.1 Fractal horizons . 69 7.2 Quantum-corrected black hole . 70 7.3 A model for Hawking radiation . 73 7.4 Effective spin-foam models .
    [Show full text]
  • Introduction to Loop Quantum Gravity
    Introduction to Loop Quantum Gravity Abhay Ashtekar Institute for Gravitation and the Cosmos, Penn State A broad perspective on the challenges, structure and successes of loop quantum gravity. Addressed to Young Researchers: From Beginning Students to Senior Post-docs. Organization: 1. Historical & Conceptual Setting 2. Structure of Loop Quantum Gravity 3. Outlook: Challenges and Opportunities – p. 1. Historical and Conceptual Setting Einstein’s resistance to accept quantum mechanics as a fundamental theory is well known. However, he had a deep respect for quantum mechanics and was the first to raise the problem of unifying general relativity with quantum theory. “Nevertheless, due to the inner-atomic movement of electrons, atoms would have to radiate not only electro-magnetic but also gravitational energy, if only in tiny amounts. As this is hardly true in Nature, it appears that quantum theory would have to modify not only Maxwellian electrodynamics, but also the new theory of gravitation.” (Albert Einstein, Preussische Akademie Sitzungsberichte, 1916) – p. • Physics has advanced tremendously in the last 90 years but the the problem of unification of general relativity and quantum physics still open. Why? ⋆ No experimental data with direct ramifications on the quantum nature of Gravity. – p. • Physics has advanced tremendously in the last nine decades but the the problem of unification of general relativity and quantum physics is still open. Why? ⋆ No experimental data with direct ramifications on the quantum nature of Gravity. ⋆ But then this should be a theorist’s haven! Why isn’t there a plethora of theories? – p. ⋆ No experimental data with direct ramifications on quantum Gravity.
    [Show full text]
  • Fundamental Elements and Interactions of Nature: a Classical Unification Theory
    Volume 2 PROGRESS IN PHYSICS April, 2010 Fundamental Elements and Interactions of Nature: A Classical Unification Theory Tianxi Zhang Department of Physics, Alabama A & M University, Normal, Alabama, USA. E-mail: [email protected] A classical unification theory that completely unifies all the fundamental interactions of nature is developed. First, the nature is suggested to be composed of the following four fundamental elements: mass, radiation, electric charge, and color charge. All known types of matter or particles are a combination of one or more of the four fundamental elements. Photons are radiation; neutrons have only mass; protons have both mass and electric charge; and quarks contain mass, electric charge, and color charge. The nature fundamental interactions are interactions among these nature fundamental elements. Mass and radiation are two forms of real energy. Electric and color charges are con- sidered as two forms of imaginary energy. All the fundamental interactions of nature are therefore unified as a single interaction between complex energies. The interac- tion between real energies is the gravitational force, which has three types: mass-mass, mass-radiation, and radiation-radiation interactions. Calculating the work done by the mass-radiation interaction on a photon derives the Einsteinian gravitational redshift. Calculating the work done on a photon by the radiation-radiation interaction derives a radiation redshift, which is much smaller than the gravitational redshift. The interaction between imaginary energies is the electromagnetic (between electric charges), weak (between electric and color charges), and strong (between color charges) interactions. In addition, we have four imaginary forces between real and imaginary energies, which are mass-electric charge, radiation-electric charge, mass-color charge, and radiation- color charge interactions.
    [Show full text]
  • Electromagnetic Unification 84 - Què És La Ciència? 150Th Anniversary of Maxwell's Equations Written by Augusto Beléndez
    Electromagnetic Unification 13/03/15 10:39 CATALÀ ESPAÑOL search... HOME JOURNAL ANNUAL REVIEW SUBSCRIPTIONS BOOKS NEWS O2C MÈTODE TV Home ARTICLE Issues ( All covers ) Electromagnetic Unification 84 - Què és la ciència? 150th Anniversary of Maxwell's Equations Written by Augusto Beléndez Compartir | 0 What Is Science? A Multidisciplinary Approach to Scientific Thought Winter 2014/15 116 pages PVP: 10.00 € Categories -- Select category -- Authors - Select an autor - By kind permission of the Master and Fellows of Peterhouse (Cambridge, UK) Picture of James Clerk Maxwell (1831-1879), who, together with Newton and Einstein, is considered one of the greats in the history of physics. His theory of the electromagnetic field was fundamental for the comprehension of natural phenomena and for the development of technology, specially for telecommunications. When we use mobile phones, listen to the radio, use the remote control, watch «At the beginning of the TV or heat up food in the microwave, we may not know James Clerk Maxwell is the nineteenth century, one to thank for making these technologies possible. In 1865, Maxwell published electricity, magnetism an article titled «A Dynamical Theory of the Electromagnetic Field», where he and optics were three stated: «it seems we have strong reason to conclude that light itself (including independent radiant heat, and other radiations if any) is an electromagnetic disturbance in the disciplines» form of waves propagated through the electromagnetic field according to electromagnetic laws» (Maxwell, 1865). Now, in 2015, we celebrate the 150th anniversary of Maxwell’s equations and the electromagnetic theory of light, events commemorating the «International Year of Light and Light-Based Technologies», declared by the UN.
    [Show full text]
  • Gravity, Particle Physics and Their Unification 1 Introduction
    Gravity, Particle Physics and Their Unification Juan M. Maldacena Department of Physics Harvard University Cambridge, Massachusetts 02138 1 Introduction Our present world picture is based on two theories: the Standard Model of par- ticle physics and general relativity, the theory of gravity. These two theories have scored astonishing successes. It is therefore quite striking when one learns that this picture of the laws of physics is inconsistent. The inconsistency comes from taking a part of theory, the Standard Model, as a quantum theory and the other, gravity, as a classical theory. At first sight, it seems that all we need to do is to quantize general relativity. But if one performs an expansion in terms of Feynman diagrams, the technique used in the Standard Model, then one finds in- finities that cannot be absorbed in a renormalization of the Newton constant (and the cosmological constant). In fact, as one goes to higher and higher orders in perturbation theory, one would have to include more and more counterterms. In other words, the theory is not renormalizable. So, the principle that is so crucial for constructing the Standard Model fails. It is now more surprising that an inconsistent theory could agree so well with experiment! The reason for this is that quantum gravity effects are usually very small, due to the weakness of gravity relative to other forces. Because the effects of gravity are proportional to the mass, or the energy of the particle, they grow at high energies. At energies of the order of E ∼ 1019 GeV, gravity would have a strength comparable with that of the other Standard Model interactions.1 We should also remember that physics, as we understand it now, cannot ex- plain the most important “experiment” that ever happened: the Big Bang.
    [Show full text]
  • The Philosophy Behind Quantum Gravity
    The Philosophy behind Quantum Gravity Henrik Zinkernagel Department of Philosophy, Campus de Cartuja, 18071, University of Granada, Spain. [email protected] Published in Theoria - An International Journal for Theory, History and Foundations of Science (San Sebastián, Spain), Vol. 21/3, 2006, pp. 295-312. Abstract This paper investigates some of the philosophical and conceptual issues raised by the search for a quantum theory of gravity. It is critically discussed whether such a theory is necessary in the first place, and how much would be accomplished if it is eventually constructed. I argue that the motivations behind, and expectations to, a theory of quantum gravity are entangled with central themes in the philosophy of science, in particular unification, reductionism, and the interpretation of quantum mechanics. I further argue that there are –contrary to claims made on behalf of string theory –no good reasons to think that a quantum theory of gravity, if constructed, will provide a theory of everything, that is, a fundamental theory from which all physics in principle can be derived. 1. Introduction One of the outstanding tasks in fundamental physics, according to many theoretical physicists, is the construction of a quantum theory of gravity. The so far unsuccessful attempt to construct such a theory is an attempt to unify Einstein's general theory of relativity with quantum theory (or quantum field theory). While quantum gravity aims to describe everything in the universe in terms of quantum theory, the purpose of the closely related project of quantum cosmology is to describe even the universe as a whole as a quantum system.
    [Show full text]
  • The Elegant Universe
    The Elegant Universe Teacher’s Guide On the Web It’s the holy grail of physics—the search for the ultimate explanation of how the universe works. And in the past few years, excitement has grown among NOVA has developed a companion scientists in pursuit of a revolutionary approach to unify nature’s four Web site to accompany “The Elegant fundamental forces through a set of ideas known as superstring theory. NOVA Universe.” The site features interviews unravels this intriguing theory in its three-part series “The Elegant Universe,” with string theorists, online activities based on physicist Brian Greene’s best-selling book of the same name. to help clarify the concepts of this revolutionary theory, ways to view the The first episode introduces string theory, traces human understanding of the program online, and more. Find it at universe from Newton’s laws to quantum mechanics, and outlines the quest www.pbs.org/nova/elegant/ for and challenges of unification. The second episode traces the development of string theory and the Standard Model and details string theory’s potential to bridge the gap between quantum mechanics and the general theory of relativity. The final episode explores what the universe might be like if string theory is correct and discusses experimental avenues for testing the theory. Throughout the series, scientists who have made advances in the field share personal stories, enabling viewers to experience the thrills and frustrations of physicists’ search for the “theory of everything.” Program Host Brian Greene, a physicist who has made string theory widely accessible to public audiences, hosts NOVA’s three-part series “The Elegant Universe.” A professor of physics and mathematics at Columbia University in New York, Greene received his undergraduate degree from Harvard University and his doctorate from Oxford University, where he was a Rhodes Scholar.
    [Show full text]
  • Zakopane Lectures on Loop Gravity
    Zakopane lectures on loop gravity Carlo Rovelli∗ Centre de Physique Théorique de Luminy,† Case 907, F-13288 Marseille, EU E-mail: [email protected] These are introductory lectures on loop quantum gravity. The theory is presented in self-contained form, without emphasis on its derivation from classical general relativity. Dynamics is given in the covariant form. Some applications are described. 3rd Quantum Gravity and Quantum Geometry School February 28 - March 13, 2011 Zakopane, Poland ∗Speaker. †Unité mixte de recherche (UMR 6207) du CNRS et des Universités de Provence (Aix-Marseille I), de la Méditer- ranée (Aix-Marseille II) et du Sud (Toulon-Var); affilié à la FRUMAM (FR 2291). c Copyright owned by the author(s) under the terms of the Creative Commons Attribution-NonCommercial-ShareAlike Licence. http://pos.sissa.it/ Loop gravity Carlo Rovelli 1. Where are we in quantum gravity? Our current knowledge on the elementary structure of nature is summed up in three theories: quantum theory, the particle-physics standard model (with neutrino mass) and general relativity (with cosmological constant). With the notable exception of the “dark matter" phenomenology, these theories appear to be in accord with virtually all present observations. But there are physical situations where these theories lack predictive power: We do not know the gravitational scattering amplitude for two particles, if the center-of-mass energy is of the order of the impact parameter in Planck units; we miss a reliable framework for very early cosmology, for predicting what happens at the end of the evaporation of a black hole, or describing the quantum structure of spacetime at very small scale.
    [Show full text]
  • Explaining Unification in Physics Internally
    Explaining Unification in Physics Internally Kian Salimkhani∗y Abstract In this paper I challenge two widespread convictions about unification in physics: (1) unification is an aim of physics and (2) unification is driven by metaphysical or metatheoretical presuppositions. I call these external explanations of why there is unification in physics. Against this, I claim that (a) unification is a by-product of physical research and (b) unification is driven by basic methodological strategies of physics alone (without any appeal to metaphysical or metatheoretical presuppositions). I call this an internal (or methodological) explanation of why there is unification in physics. To support my claims, I will investigate the actual practice undertaken in physics in paradigmatic examples of unification. Keywords: Unification; Methodology; Physics; Metaphysics 1 Introduction In this paper I challenge two common convictions about unification in physics: (1) unification is an aim (or the aim) of physics, and (2) unification is driven by metaphysical or metatheoretical presuppositions. Against this, I claim that (a) unification is a result|or for dialectical effect: a by-product|of physical re- search, and (b) unification is driven by basic methodological strategies of physics alone. In particular, I claim that unification is not driven by any appeal to meta- physical or metatheoretical presuppositions. Accordingly, the main objective of this paper is to answer the following questions: If we take physics as not explic- itly aiming for unification, then how do we explain
    [Show full text]
  • Possible Unification of Quantum Mechanics and General Relativity Theory Based on the Three-Dimensional Quantized Spaces
    Preprints (www.preprints.org) | NOT PEER-REVIEWED | Posted: 5 September 2018 doi:10.20944/preprints201809.0097.v1 Possible Unification of Quantum Mechanics and General Relativity Theory Based on the Three-Dimensional Quantized Spaces Jae - Kwang Hwang JJJ Physics Laboratory, Brentwood, TN 37027, USA [email protected] Abstract Three-dimensional quantized space model is newly introduced. Quantum mechanics and relativity theory are explained in terms of the warped three-dimensional quantized spaces with the quantum time width (t=tq). The energy is newly defined as the 4-dimensional space-time volume of E = ctV in the present work. It is shown that the wave function of the quantum mechanics is closely related to the warped quantized space shape with the space time-volume. The quantum entanglement and quantum wave function collapse are explained additionally. The special relativity theory is separated into the energy transition associated with the space-time shape transition of the matter and the momentum transition associated with the space-time location transition. Then, the quantum mechanics and the general relativity theory are about the 4- dimensional space-time volume and the 4-dimensional space-time distance, respectively. Keywords: Quantum mechanics; General and special relativity theories; Origins of the energy and mass; Space-time volume and distance; Origin of quantum wave function; Three-dimensional quantized spaces; Quantum entanglement; Space-time curvatures and quantum metrics 1. Introduction Space and time are the mathematical concept and the energy is the physical concept of the space and time correlated status. The space with the non-zero energy can be called as the universe in the physics point of view.
    [Show full text]