DOCSLIB.ORG

Electromagnetism and Magnetic Monopoles

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
Electromagnetism and Magnetic Monopoles Physics & Astronomy Institute for theoretical physics Electromagnetism and magnetic monopoles Author Supervisor F. Carere Dr. T. W. Grimm June 13, 2018 Image: Daniel Dominguez/ CERN Abstract Starting with the highly symmetric form of electromagnetism in tensor notation, the consideration of magnetic monopoles comes very natural. Following then the paper of J. M. Figueroa-OFarrill [1] we encounter the Dirac monopole and the 't Hooft-Polyakov monopole. The former, simpler { at the cost of a singular Dirac string { monopole already leading to the very important Dirac quantization condition, implying the quantization electric charge if magnetic monopoles exist. In particular the latter monopole, which is everywhere smooth and which has a purely topological charge, is found as a finite-energy, static solution of the dynamical equations in an SO(3) gauge invariant Yang-Mills-Higgs system using a spherically symmetric ansatz of the fields. This monopole is equivalent to the Dirac monopole from far away but locally behaves differently because of massive fields, leading to a slightly different quantization condition of the charges. Then the mass of general finite-energy solutions of the Yang-Mills-Higgs system is considered. In particular a lower bound for the mass is found and in the previous ansatz a solution saturating the bound is shown to exist: The (very heavy) BPS monopole. Meanwhile particles with both electric and magnetic charge (dyons) are considered, leading to a relation between the quantization of the magnetic and electric charges of both dyons and, when assuming CP invariance, to an explicit quantization of electric charge. Finally, the Z2 duality of Maxwell's equations is extended. When P SL(2; Z) duality is assumed for electric and magnetic monopoles satisfying the Bogomol'nyi mass bound a dyonic spectrum is found in the orbit of the electron. Contents Preface 1 I Electromagnetism and relativity 2 1 Electromagnetism and electromagnetic duality 2 1.1 Electromagnetism in vector calculus notation . .2 1.2 Electromagnetism in tensor notation . .4 2 A magnetic monopole 6 3 Relativity 7 3.1 The structure of flat spacetime: Minkowski space . .7 3.2 Lorentz transformations . .8 3.3 Proper time . .9 4 Electromagnetism and relativity 11 5 Lagrangian mechanics and actions 13 5.1 Classical mechanics in integral form . 13 5.2 The relativistic Lagrangian . 14 5.3 The classical electromagnetic Lagrangian . 14 5.4 The relativistic electromagnetic Lagrangian . 15 5.5 The Hamiltonian . 16 II Symmetries, fields, gauge theories and the Higgs mechanism 17 1 Symmetry 18 1.1 Classification of symmetries . 18 1.2 Symmetry breaking . 20 1.2.1 Explicit symmetry breaking . 21 1.2.2 Spontaneous symmetry breaking . 22 2 Some classical field theory 23 2.1 General forms of the Lagrangian density . 23 2.2 Noethers theorem . 24 2.3 The Hamiltonian density . 25 3 Gauge theory 26 3.1 Classical abelian gauge theory . 26 3.2 Gauge invariance of the relativistic electromagnetic Lagrangian . 28 3.3 Gauge theory for the Dirac Lagrangian . 29 3.4 The general strategy for U(1) . 29 3.5 Yang-Mills theory . 30 3.6 Again Yang-Mills . 32 3.7 The case of SO(3) ..................................... 33 3.8 Yang-Mills in general . 34 4 The Higgs mechanism 36 4.1 The Higgs field and its potential . 36 4.2 Massless gauge bosons from a broken global symmetry . 37 4.3 The Higgs mechanism . 38 III Magnetic monopoles 39 1 The Dirac monopole 40 1.1 The search for a global vector potential . 40 1.2 The Dirac quantization condition . 41 2 Dirac monopole: Dyons and the Zwanziger-Schwinger quantization condition 44 3 The bosonic part of the Georgi-Glashow model 48 4 Static, finite-energy solutions in the 't Hooft-Polyakov ansatz 52 4.1 The solution of H and K in the 't Hooft-Polyakov ansatz . 53 4.2 The topological origin of the magnetic charge . 56 5 The difference between the Dirac and the 't Hooft-Polyakov monopole 61 6 Mass and the BPS monopoles 62 6.1 The Bogomol'nyi bound . 62 6.2 The BPS monopole . 63 6.2.1 The BPS monopole in the 't Hooft-Polyakov ansatz . 64 7 Electromagnetic duality revisited 67 7.1 The Montonen-Olive conjecture . 67 7.2 Quantization of dyons . 68 7.3 The Witten effect . 69 7.4 P SL(2; Z) Duality . 70 7.5 The modular group . 70 7.6 Orbifolds and the dyonic spectrum . 72 IV Discussion 75 A Tensors 77 A.1 Basistransformations: Co- and contravariant objects . 77 A.1.1 Co- and contravariant indices, raising and lowering indices . 77 A.2 Transformation properties of tensors . 77 B The Hamiltonian density in the 't Hooft-Polyakov ansatz 78 C The fundamental group of maps between circles 80 C.1 The structure of loops . 81 C.2 Homotopy equivalent spaces . 82 C.3 The fundamental group of maps between circles . 82 D Lie groups and Lie algebras 85 D.1 A note on SO(3)...................................... 85 Preface: Discussing magnetic monopoles Around 600 B.C. the Greek philosopher Thales of Miletus described the peculiar phenomena of attractive forces between two substances: Fur and amber [2]. He was likely the first to make a written description of electrical forces. Indeed it is due to the ancient Greeks (and Gilbert) that the term ηλκτρoν (meaning amber) is now used for one of the most fundamental objects in electrostatics: the electron. Furthermore, the Greeks were aware that there existed stones which seemed to attract iron when held close. The magnetic force was found, named after the Turkish city of Magnesia (now Manisa), where the stones were found. These two magical forces turned out to behave very similar. Electric poles were introduced in the theory of electrostatics. Due to a large amount of symmetry in the theories magnetic poles were introduced, in accordance with electrostatics. The first mentioning of magnetic monopoles could well have been in a letter of Pierre of Maricourt in 1269 [3]. The magnetic monopole, however, was { and to this day still is { unobserved. After the discovery of Oersted in 1820 that current deflects a compass needle, electromagnetism was born [4]. This, later on, led to Amp`eresmodel of the magnet, in which the magnetic fields of a magnet come from `little Amperian currents' [5]. This model did no good to the theory of magnetic monopoles, since in this model magnetic fields were not produced by a stationary magnetic monopole but moving electric charges. The intrinsic connection between electricity and magnetism was clearly there and Amp`ere'smodel was the first step to fathom this duality. It was Maxwell's equations, however, which were able to combine the theory of electrostatics and magnetostatics in a very elegant fashion. The four Maxwell equations, together with the equation for the Lorentz force, are able to fully describe (static and dynamic) classical electromagnetism. One of the four laws of Maxwell, however, is r~ · B~ = 0, sometimes called the `no magnetic monopole law'. This short history of classical electromagnetism might indicate that it is completely nonsensical to search for and describe magnetic monopoles. Indeed to this day they have not been seen in experiments. However one important argument in favour of the existence of magnetic monopoles is certainly the amount of symmetry in Maxwell's equations. Including the fact that over the last century gauge theories have become extremely important and very successful in the description of fundamental particles and forces (for instance in the Standard Model), together with the fact that these gauge theories rely on symmetry being an intrinsic property of nature itself, the search for monopoles might seem a bit less odd. Furthermore, in cosmology [6] and in quantum mechanics [7] reasons have come up why it might be that these monopoles have gone unseen and also are not made and observed in particle accelerators. Nevertheless, a reason why these monopoles have not yet been observed could just be the fact that they do not exist. Indeed in 1931 Dirac brought the theory of magnetic monopoles to life [7]. A magnetic monopole similar to the electric monopole was considered, which was therefore coined the Dirac monopole. In 1974 't Hooft [8] and Polyakov [9] both found inevitable monopole solutions in a Yang-Mills theory of a spontaneously broken non-abelian classical Lagrangian system. From far away, these monopoles behave in a similar manner as the Dirac monopole but close by they contain more information, including the mass of such a monopole. Another reason was found that the monopoles are hard to find: they are very heavy. In this paper properties of these types of (classical) magnetic monopoles will be described. In part I. it will start with the symmetrical formulation of Maxwell's equations in electrodynamics, first in vector calculus notation and then going to tensor notation to make it easy on readers with little experience in the latter kind. In the light of the highly symmetric formulation, magnetic monopoles will then be considered in part III, starting with the Dirac monopole and continuing on to the 't Hooft-Polyakov monopole, though a glimpse of gauge theories and symmetry breaking is given first in part II, which is needed for the discussion of the latter monopole. 1 Part I Electromagnetism and relativity Electromagnetism is a (special) relativistically invariant theory. Moreover, special relativity and electromagnetism have been two theories, which have seen development that was really intertwining [10]. For example, on completion of Maxwell's equations in classical electromagnetism, it quickly became clear that light is an electromagnetic wave. Furthermore, from special relativity it became clear that electric fields and magnetic fields are intrinsically connected via Lorentz transformations.
Load more

Recommended publications
  • Unified Field Theory Quest Synopsis
    Unified Field Theory Quest Synopsis file:///Documents/TheoryOfEverything/quest.html The Unified Field Theory - Synopsis of a Personal Quest John A. Gowan June 2014 Home Page The Charges of Matter are the Symmetry Debts of Light Papers: Symmetry Principles of the Unified Field Theory (a "Theory of Everything") - Part I Symmetry Principles of the Unified Field Theory (a "Theory of Everything") - Part 2 Symmetry Principles of the Unified Field Theory (a "Theory of Everything") - Part 3 (Summary) See also: NY Times article on Emmy Noether 26 Mar 2012 Neuenschwander, D. E. Emmy Noether's Wonderful Theorem. 2011. Johns Hopkins University Press. Part I: History When I turned 40 (in 1977), I started to build my personal version of the Unified Field Theory. I did so as a faithful disciple of Einstein, attempting to help the scientific hero of my youth reach his unfulfilled goal. At that time the strong and weak forces were just becoming understood, gravity remained where Einstein had left it (with some more recent help from Hawking, Wheeler, and Bekenstein concerning black holes), and the electromagnetic force had long been solved by a parade of many geniuses, beginning with Faraday and Maxwell, and culminating with Feynman, Schwinger, and Tomonaga ("quantum electrodynamics"- QED). Because of limitations of time, intellect, and energy, I decided not to work on those parts of the theory that others had already solved - so far as I could tell - satisfactorily. Accordingly, I accepted most of what had been done with the electromagnetic and strong forces (the Gell-Mann/Zweig colored-quark model for the latter: "quantum chromodynamics" - QCD).
    [Show full text]
  • Electroweak Symmetry Breaking in Historical Perspective
    FERMILAB–PUB–15/058–T Electroweak Symmetry Breaking in Historical Perspective Chris Quigg∗ Theoretical Physics Department Fermi National Accelerator Laboratory P.O. Box 500, Batavia, Illinois 60510 USA The discovery of the Higgs boson is a major milestone in our progress toward understanding the natural world. A particular aim of this article is to show how diverse ideas came together in the conception of electroweak symmetry breaking that led up to the discovery. I will also survey what we know that we did not know before, what properties of the Higgs boson remain to be established, and what new questions we may now hope to address. I. INTRODUCTION The first goal of this article is to sketch how a broad range of concepts, drawn mainly from weak-interaction A lively continuing conversation between experiment phenomenology, gauge field theories, and condensed- and theory has brought us to a radically simple con- matter physics, came together in the electroweak the- ception of the material world. Fundamental particles ory. The presentation complements the construction of the electroweak theory given in my pre-discovery article, called quarks and leptons are the stuff of direct expe- 26 rience, and two new laws of nature govern their in- “Unanswered Questions in the Electroweak Theory”. teractions. Pursuing clues from experiment, theorists Presentations similar in spirit may be found in Refs. have constructed the electroweak theory1–3 and quantum 27,28. Next, I will briefly summarize what we now know chromodynamics,4–7 refined them within the framework about the Higgs boson, what the discovery has taught of local gauge symmetries, and elaborated their conse- us, and why the discovery is important to our conception quences.
    [Show full text]
  • Light Cone Gauge Quantization of Strings, Dynamics of D-Brane and String Dualities
    Light Cone Gauge Quantization of Strings, Dynamics of D-brane and String dualities. Muhammad Ilyas1 Department of Physics Government College University Lahore, Pakistan Abstract This review aims to show the Light cone gauge quantization of strings. It is divided up into three parts. The first consists of an introduction to bosonic and superstring theories and a brief discussion of Type II superstring theories. The second part deals with different configurations of D-branes, their charges and tachyon condensation. The third part contains the compactification of an extra dimension, the dual picture of D-branes having electric as well as magnetic field and the different dualities in string theories. In ten dimensions, there exist five consistent string theories and in eleven dimensions there is a unique M-Theory under these dualities, the different superstring theoies are the same underlying M-Theory. 1ilyas [email protected] M.Phill thesis in Mathematics and Physics Dec 27, 2013 Author: Muhammad Ilyas Supervisor: Dr. Asim Ali Malik i Contents Abstract i INTRODUCTION 1 BOSONIC STRING THEORY 6 2.1 The relativistic string action . 6 2.1.1 The Nambu-Goto string action . 7 2.1.2 Equation of motions, boundary conditions and D-branes . 7 2.2 Constraints and wave equations . 9 2.3 Open string Mode expansions . 10 2.4 Closed string Mode expansions . 12 2.5 Light cone solution and Transverse Virasoro Modes . 14 2.6 Quantization and Commutations relations . 18 2.7 Transverse Verasoro operators . 22 2.8 Lorentz generators and critical dimensions . 27 2.9 State space and mass spectrum . 29 SUPERSTRINGS 32 3.1 The super string Action .
    [Show full text]
  • Xerox University Microfilms 300 North Zeeb Road Ann Arbor, Michigan 48106 74-17,764
    INFORMATION TO USERS This material was produced from a microfilm copy of the original document. While the most advanced technological means to photograph and reproduce this document have been used, the quality is heavily dependent upon the quality of the original submitted. The following explanation of techniques is provided to help you understand markings or patterns which may appear on this reproduction. 1. The sign or "target" for pages apparently lacking from the document photographed is "Missing Page(s)". If it was possible to obtain the missing page(s) or section, they are spliced into the film along with adjacent pages. This may have necessitated cutting thru an image and duplicating adjacent pages to insure you complete continuity. 2. When an image on the film is obliterated with a large round black mark, it is an indication that the photographer suspected that the copy may have moved during exposure and thus cause a blurred image. You will find a good image of the page in the adjacent frame. 3. When a map, drawing or chart, etc., was part of the material being photographed the photographer followed a definite method in "sectioning" the material. It is customary to begin photoing at the upper left hand corner of a large sheet and to continue photoing from left to right in equal sections with a small overlap. If necessary, sectioning is continued again — beginning below the first row and continuing on until complete. 4. The majority of users indicate that the textual content is of greatest value, however, a somewhat higher quality reproduction could be made from "photographs" if essential to the understanding of the dissertation.
    [Show full text]
  • Strong Interactions, Lattice and HQET
    Strong interactions, Lattice and HQET Vicent Gimenez´ Gomez´ Introduction Strong interactions, Lattice and HQET Historical background Quark model Vicent Gimenez´ Gomez´ Color The parton Departament de F´ısica Teorica-IFIC` model Universitat de Valencia-CSIC` QCD Lagrangian Feynman rules May 3, 2013 Elementary Calculations + e e− annihilation into hadrons 1 / 153 Renormalization Contents Strong interactions, Lattice and 1 Introduction HQET Vicent 2 Historical background Gimenez´ Gomez´ 3 Quark model Introduction 4 Color Historical background 5 The parton model Quark model Color 6 QCD Lagrangian The parton model 7 Feynman rules QCD Lagrangian 8 Elementary Calculations Feynman rules + Elementary 9 e e− annihilation into hadrons Calculations + e e− 10 Renormalization annihilation into hadrons 2 / 153 Renormalization Introduction Strong interactions, Lattice and HQET Quantum Chromodynamics (QCD), first introduced by Gell-Mann and Vicent Frizsch in 1972, is the theory of strong interactions. It is a renormaliz- Gimenez´ able nonabelian gauge theory based on the color SU(3) group which Gomez´ elementary fields are quarks and gluons. Introduction Why is QCD important for Particle Physics? Historical background Electroweak processes of hadrons necessarily involve strong • Quark model interactions. Color A quantitative understanding of the QCD background in • The parton searches for new physics at present and future accelerators is model crucial. QCD Lagrangian In this lectures we give an introduction to the foundation of perturba- Feynman rules tive and nonperturbative QCD and some important physical applications: Elementary Deep Inelastic Scattering (DIS) and e+ e annihilation into hadrons. Calculations − + e e− annihilation into hadrons 3 / 153 Renormalization History Strong interactions, The history that led to the discovery of QCD is fascinating.
    [Show full text]
  • Introducing Special Relativity
    Introducing Special Relativity W. S. C. Williams ""Oded Contents Preface xi Acknowledgements xii 1 Introduction 1 2 Momentum and energy in special relativity 4 **2.I Introduction 4 **2.2 Momentum and energy 4 **2.3 More useful formulae 6 **2.4 Units 8 **2.5 Rest mass energy 9 **2.6 Nuclear binding energy 10 **2.7 Nuclear decays and reactions 11 **2.8 Gravitation and E = Me2 13 **2.9 Summary 14 Problems 15 3 Relativistic kinematics I 17 **3.1 Introduction 17 **3.2 Elementary particle physics 18 **3.3 Two-body decay of a particle at rest 20 *3.4 Three-body decays 24 *3.5 Two-stage three-body decay 26 **3.6 The decay of a moving particle 28 3.7 Kinematics of formation 30 3.8 Examples of formation 33 **3.9 Photons 35 **3.10 Compton scattering 35 **3.11 The centre-of-mass 37 viii Contents **3.12 The centre-of-mass in two-body collisions 41 *3.13 Reaction thresholds in the laboratory 42 *3.14 Summary 43 Problems 43 4 Electrodynamics 46 **4.1 Introduction 46 **4.2 Making contact with electromagnetism 46 **4.3 Relativistic mass 49 **4.4 Historical interlude 50 *4.5 Bucherer 51 *4.6 Accelerators 54 *4.7 The cyclotron frequency 55 *4.8 The cyclotron 56 *4.9 The limitations of the cyclotron 57 4.10 The synchrocyclotron 58 4.11 The synchrotron 59 4.12 Electron accelerators 60 4.13 Centre-of-mass energy at colliders 60 *4.14 Summary 61 Problems 62 5 The foundations of special relativity 64 **5.1 Introduction 64 **5.2 Some definitions 65 **5.3 Galilean transformations 68 **5.4 Electromagnetism and Galilean relativity 70 **5.5 Einstein's relativity 72
    [Show full text]
  • Unified Field Scientific Format Table
    unified field scientific format table file:///Documents/TheoryOfEverything/science.html METAPHYSICAL REALM - Expanded Form - Rational Mind: (4 Conservation Laws Connected in Triplets) Jaccaci's Terms Transform ---> Gather Repeat Share Emergent New Unit Pair Group or Field Gowan's Terms Unit ---> 4 Forces of Electromagnetism Gravitation Strong Weak Physics ---> Comments on the FORCES Energy State Rows: (virtual) Free Energy: Elementary 3-D Space; massless Particles; Light: E = hv (Planck); Suppression of Time by (virtual) electromagnetic Neutrinos; Invariant Motion "c"; "Velocity c"; Composite and (EM) Leptons; All Charges = 0; Space is Created by Sub-Elementary radiation; space; Leptoquarks; Symmetric Light's Particles; "Ylem"; symmetric forms; Particle Pairs; Free Energy Entropy Drive Fractured Leptons; virtual particles; Higgs, "X" IVBs; ("c" gauges light's (intrinsic motion); Quarks; Gluons; "global" symmetric 3 Families; entropy drive Expansion and "Quark Soup"; energy state Neutral Particles; and "non-local" Cooling of Space; Particle- followed by Symmetry- distributional Conservation/Entropy Antiparticle pairs; symmetry- Breaking: symmetry); Domain of Light; Leptoquarks; T breaking; "Higgs Cascade"; Non-local, A-causal, Light's "Interval" = 0; Neutral Particles; R invariance of the Weak Force A-temporal Energy; The Spatial Metric; 3 Energy "Families"; EM constant "c"'; Asymmetric A virtual particle- Gravitational Negative Particle Symmetry (reprising the Decays; antiparticle pairs Energy and Entropy; Total Charge = 0 N "Big Bang"); Real
    [Show full text]
  • Core Electrodynamics Copyright Sandra C Chapman
    CHAPMAN C SANDRA COPYRIGHT ELECTRODYNAMICS CORE Core Electrodynamics Sandra C. Chapman June 29, 2010 Preface CHAPMAN C This monograph is based on a final year undergraduate course in Electro- dynamics that I introduced at Warwick as part of the new four year physics degree. When I gave this course my intention was to engage the students in the elegance of electrodynamics and special relativity, whilst giving them the tools to begin graduate study. Here, from the basis ofSANDRA experiment we first derive the Maxwell equations, and special relativity. Introducing the mathematical framework of generalized tensors, the laws of mechanics, Lorentz force and the Maxwell equations are then cast in manifestly covari- ant form. This provides the basis for graduate study in field theory, high energy astrophysics, general relativity and quantum electrodynamics. As the title suggests, this book is ”electrodynamics lite”. The journey through electrodynamics is kept as brief as possible, with minimal diversion into details, so that the elegance of the theory can be appreciated in a holistic way. It is written in an informalCOPYRIGHT style and has few prerequisites; the derivation of the Maxwell equations and their consequences is dealt with in the first chapter. Chapter 2 is devoted to conservation equations in tensor formulation, here Cartesian tensors are introduced. Special relativity and its consequences for electrodynamics is introduced in Chapter 3 and cast in four vector form, here we introduce generalized tensors. Finally in Chapter 4 Lorentz frame invariant electrodynamics is developed. Supplementary material and examples are provided by the two sets of problems. The first is revision of undergraduate electromagnetism, to ex- pand on the material in the first chapter.
    [Show full text]
  • General Systems Form 12/4/10 6:16 AM
    General Systems Form 12/4/10 6:16 AM Table of Forces (Columns) and Energy States (Rows) (Simple Table #1) 4 Forces of Physics ---> Electromagnetism Gravitation Strong Weak Below: Comments on the FORCES Energy State Rows: Light: E = hv (Planck); (virtual) (virtual) Free Energy, Light: Intrinsic Motion "c"; Space; Composite and Elementary Particles; electromagnetic All Charges = 0; Created by Light's Sub-Elementary Neutrinos; Leptons; radiation; space; Symmetric Entropy Drive; Particles; "Ylem"; Leptoquarks; symmetric energy; Free Energy Conservation/Entropy Fractured Leptons; Particle- virtual particles; ("c" gauges Light's Domain of Light; Quarks; Gluons; Antiparticle Pairs; symmetry-breaking; entropy drive Light's "Interval" = 0; Particle- Higgs (Mass Gauge); (reprising the and "non-local" The Spatial Metric; Antiparticle pairs; Intermediate "Big Bang"); distributional Gravitational Negative Leptoquarks; Vector Bosons; (incurring the debt); symmetry); Energy and Entropy; Neutral Particles; Symmetry-Breaking: Spatial Energy Forms; Non-local, Acausal, Total Energy = 0 Particle Symmetry "Higgs Cascade"; (row 1) Atemporal Energy Total Charge = 0 Real Particles Bound Energy: Mass: Gravitational Creation Alternative matter; history; E = mcc; hv = mcc; of Time from Space; Mass Carriers; Charge Carriers; asymmetric energy; (Einstein-deBroglie); Historic Spacetime; Quarks, Leptons, massive real particles Matter, Momentum; Conservation/Entropy Mesons, Neutrinos: (consequences of row 1 Asymmetric Domain of Information; Baryons, Electron Shell; symmetry-breaking);
    [Show full text]
  • An Introduction to Tetryonic Theory
    International Journal of Scientific and Research Publications, Volume 4, Issue 5, May 2014 1 ISSN 2250-3153 An Introduction to Tetryonic Theory Kelvin C. ABRAHAM [Author] [email protected] Abstract- Tetryonics is a new geometric theory of mass- models on which we can discern our known results and ENERGY-Matter and the forces of motion, stemming from a observations thus excluding any false or misleading assumptions geometric re-interpretation of what squared numbers are in (mathematical or philosophical). physics and its application to quantized angular momentum (QAM). It can now be shown through geometry that the QAM In doing so there exists the promise that a simple underlying of Planck’s constant is in fact the result of its quantized foundation can be found to the physics of our Universe, revealing equilateral ‘triangular’ geometry (and not a vector rotation new and exciting advances in Science that will allow us to usher about a point as has been historically assumed to date). in a new age of scientific and technological advancement for the betterment of humanity as a whole. This quantum geometry gives rise to the physical properties . of electrical permittivity, magnetic permeability and charge along with the rigid physical relationships between inertial I. PLANCK MASS-ENERGY MOMENTA QUANTA mass-energy and momenta in physical systems at all scales of physics. And quantum charge in addition to its role as the Energy, in physics, is an indirectly observed quantity of a system geometric source of physical constants, also provides the that imbues it with the ability to exert a Force or to do Work over quantum field mechanics for radiant 2D mass-energies to a distance.
    [Show full text]
  • A Unified Electro-Gravity (UEG) Thery of Nature
    A Unified Electro-Gravity (UEG) Theory of Nature Nirod K. Das New York University Copyright c 2018 by Nirod K. Das. All Rights Reserved. Registration # TXu 2-128-436, December 20, 2018 i Table of Contents Introduction................................................................................................ (Page 1) Part-I: Unified Electro-Gravity (UEG) Theory in the Small Scale: Particle Physics and Quantum Mechanics .................................(Page 3) 1. A New Unified Electro-Gravity Theory for the Electron................(Page 4) 2. A Generalized Unified Electro-Gravity (UEG) Model Applicable to All El- ementary Particles ............................................................................(Page 14) 3. Unified Electro-Gravity (UEG) Theory and Quantum Electrodynamics ..........................................................................................................(Page 31) Part-II: Extension of the Unified Electro-Gravity (UEG) Theory to Physics in the Large Scale: Stellar, Galactic and Cosmology Models ..........................................................................................................(Page 43) 4. Unified Electro-Gravity (UEG) Theory Applied to Stellar Gravitation, and the Mass-Luminosity Relation (MLR)..............................................(Page 44) 5. Unified Electro-Gravity (UEG) Theory Applied to Spiral Galaxies.............. ..........................................................................................................(Page 59) 6. A Unified Electro-Gravity (UEG) Model as
    [Show full text]
  • Arxiv:1902.05799V2 [Physics.Hist-Ph]
    Feynman’s different approach to electromagnetism Roberto De Luca1, Marco Di Mauro1,2,3, Salvatore Esposito2, Adele Naddeo2 1 Dipartimento di Fisica “E.R. Caianiello”, Universit´adi Salerno, Via Giovanni Paolo II, 84084 Fisciano, Italy. 2 INFN Sezione di Napoli, Via Cinthia, 80126 Naples, Italy. 3E-mail: [email protected] July 6, 2021 Abstract We discuss a previously unpublished description of electromagnetism outlined by Richard P. Feyn- man in the 1960s in five handwritten pages, recently uncovered among his papers, and partly developed in later lectures. Though similar to the existing approaches deriving electromagnetism from special relativity, the present one extends a long way towards the derivation of Maxwell’s equations with minimal physical assumptions. In particular, without postulating Coulomb’s law, homogeneous Maxwell’s equations are written down by following a route different from the stan- dard one, i.e. first introducing electromagnetic potentials in order to write down a relativistic invariant action, which is just the inverse approach to the usual one. Also, Feynman’s derivation of the Lorentz force exclusively follows from its linearity in the charge velocity and from relativis- tic invariance. Going further, i.e. adding the inhomogeneous Maxwell’s equations, requires some more physical input, and can be done by just following conventional lines, hence this task was not pursued here. Despite its incompleteness, this way of proceeding is of great historical and episte- mological significance. We also comment about its possible relevance to didactics, as an interesting supplement to usual treatments. One man’s assumption is another man’s conclusion [1] arXiv:1902.05799v2 [physics.hist-ph] 16 Oct 2019 1 Introduction It is a well-known story that Richard P.
    [Show full text]