Historical Roots of Gauge Invariance
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Gustav Robert Kirchhoff War Der Sohn Eines Landrichters
Akademischer Werdegang *12.03.1824 in Königsberg (heute: Kaliningrad) Besuch des Kneiphöschen Gymnasiums in Königsberg ab 1842 Studium der Mathematik und Physik an der Universität Königsberg 1847 Promotion in Berlin 1850 Berufung zum außerordentlichen Professor nach Breslau (Polen) 1854 Professor für Physik an der Universität Heidelberg 1874 – 1886 Professor für mathematische Physik in Berlin 1876 Cothenius – Medaille der Leopoldina als Auszeichnung für [1] wissenschaftliches Arbeiten † 17.10.1887 in Berlin Gustav Robert Kirchhoff war der Sohn eines Landrichters. Während des Studiums in seiner Heimatstadt wurde er u. a. von den Professoren F.E. Neumann und F. J. Richelot gelehrt. Im Physikseminar von Neumann verfasste Kirchhoff mit 21 Jahren seine erste Arbeit über den Durchgang der Elektrizität durch Platten. Während der Promotions- und Habilitationsphase an der Universität Berlin entwickelte sich eine Freundschaft mit dem Universalgenie H. Helmholtz. Kirchhoff folgte schließlich der Berufung zum außerordentlichen Professor nach Breslau, wo er R. W. Bunsen, den Erfinder des Bunsenbrenners kennen lernte. Dieser wechselte zur Universität nach Heidelberg, worauf ihm Kirchhoff folgte. Gemeinsam veröffentlichten sie zahlreiche Schriften und entdeckten, wie verschiedene chemische Elemente die Flamme eines Gasbrenners färben. Sie prägten die Spektralanalyse als physikalische Analysemethode und konnten mit ihrer Hilfe eine Erklärung der Frauenhoferlinie finden. Außerdem verzeichneten sie die Entdeckung der Elemente Caesium und Rubidium. Des Weiteren entstand bei Experimenten der Spektralanalyse der Kirchhoffsche Strahlungssatz. Kirchhoffs und Bunsens erster Spektralapparat [2] Kirchhoff arbeitete auch an der Plattentheorie. Der Piola-Kirchhoff-Spannungstensor, die Kirchhoff-Love- Hypothese und die sogenannten Kirchhoff-Platten erinnern daran. 1857 heiratete er Clara Richelot, die Tochter seines Professors für Mathematik. Gemeinsam bekamen sie vier Kinder und führten eine glückliche Ehe. -
The Second Physicist on the History of Theoretical Physics in Germany
springer.com Physics : Theoretical, Mathematical and Computational Physics Jungnickel, Christa, McCormmach, Russell The Second Physicist On the History of Theoretical Physics in Germany Explores the rise of theoretical physics in 19th century Germany Shows how physics developed within German universities Characterizes the work of theoretical physics This book explores the rise of theoretical physics in 19th century Germany. The authors show how the junior second physicist in German universities over time became the theoretical physicist, of equal standing to the experimental physicist. Gustav Kirchhoff, Hermann von Helmholtz, and Max Planck are among the great German theoretical physicists whose work and career are examined in this book. Physics was then the only natural science in whichtheoreticalwork developed into a major teaching and research specialty in its own right. Readers will discover how German physicists arrived at a well-defined field of theoretical physics with well understood and generally accepted goals and needs. The authors explain the Springer nature of theworkof theoretical physics with many examples, taking care always to locate the 1st ed. 2017, XXXI, 460 p. research within the workplace. The book is a revised and shortened version ofIntellectual 1st 15 illus. Mastery of Nature: Theoretical Physics from Ohm to Einstein, a two-volume work by the same edition authors. This new edition represents a reformulation of the larger work. It retains what is most important in the original work, while including new material, -
Gauge-Underdetermination and Shades of Locality in the Aharonov-Bohm Effect*
Gauge-underdetermination and shades of locality in the Aharonov-Bohm effect* Ruward A. Mulder Abstract I address the view that the classical electromagnetic potentials are shown by the Aharonov-Bohm effect to be physically real (which I dub: `the potentials view'). I give a historico-philosophical presentation of this view and assess its prospects, more precisely than has so far been done in the literature. Taking the potential as physically real runs prima facie into `gauge-underdetermination': different gauge choices repre- sent different physical states of affairs and hence different theories. This fact is usually not acknowledged in the literature (or in classrooms), neither by proponents nor by opponents of the potentials view. I then illustrate this theme by what I take to be the basic insight of the AB effect for the potentials view, namely that the gauge equivalence class that directly corresponds to the electric and magnetic fields (which I call the Wide Equivalence Class) is too wide, i.e., the Narrow Equivalence Class encodes additional physical degrees of freedom: these only play a distinct role in a multiply-connected space. There is a trade-off between explanatory power and gauge symmetries. On the one hand, this narrower equivalence class gives a local explanation of the AB effect in the sense that the phase is incrementally picked up along the path of the electron. On the other hand, locality is not satisfied in the sense of signal locality, viz. the finite speed of propagation exhibited by electric and magnetic fields. It is therefore intellec- tually mandatory to seek desiderata that will distinguish even within these narrower equivalence classes, i.e. -
Christa Jungnickel Russell Mccormmach on the History
Archimedes 48 New Studies in the History and Philosophy of Science and Technology Christa Jungnickel Russell McCormmach The Second Physicist On the History of Theoretical Physics in Germany The Second Physicist Archimedes NEW STUDIES IN THE HISTORY AND PHILOSOPHY OF SCIENCE AND TECHNOLOGY VOLUME 48 EDITOR JED Z. BUCHWALD, Dreyfuss Professor of History, California Institute of Technology, Pasadena, USA. ASSOCIATE EDITORS FOR MATHEMATICS AND PHYSICAL SCIENCES JEREMY GRAY, The Faculty of Mathematics and Computing, The Open University, UK. TILMAN SAUER, Johannes Gutenberg University Mainz, Germany ASSOCIATE EDITORS FOR BIOLOGICAL SCIENCES SHARON KINGSLAND, Department of History of Science and Technology, Johns Hopkins University, Baltimore, USA. MANFRED LAUBICHLER, Arizona State University, USA ADVISORY BOARD FOR MATHEMATICS, PHYSICAL SCIENCES AND TECHNOLOGY HENK BOS, University of Utrecht, The Netherlands MORDECHAI FEINGOLD, California Institute of Technology, USA ALLAN D. FRANKLIN, University of Colorado at Boulder, USA KOSTAS GAVROGLU, National Technical University of Athens, Greece PAUL HOYNINGEN-HUENE, Leibniz University in Hannover, Germany TREVOR LEVERE, University of Toronto, Canada JESPER LU¨ TZEN, Copenhagen University, Denmark WILLIAM NEWMAN, Indiana University, Bloomington, USA LAWRENCE PRINCIPE, The Johns Hopkins University, USA JU¨ RGEN RENN, Max Planck Institute for the History of Science, Germany ALEX ROLAND, Duke University, USA ALAN SHAPIRO, University of Minnesota, USA NOEL SWERDLOW, California Institute of Technology, USA -
Advantage of Kirchhoff Law in Electrical Circuit
October 2017, Volume 4, Issue 10 JETIR (ISSN-2349-5162) ADVANTAGE OF KIRCHHOFF LAW IN ELECTRICAL CIRCUIT 1Prem Raj , 2Pawan Gupta , 3Deepak Kumar Sharma , 4Neeraj Kumar sharma , 5Bhuvnesh Yadav Department of Physics, Students, B.Sc. Final year, Parishkar College of Global Excellence, Jaipur Abstract: The purpose of this report is to verify Ohm’s law, Kirchoff’s Current Law and Kirchoff’s Voltage Law. Ohm’s law relates voltage to resistance and current; Kirchoff’s laws deal solely with current and voltage. A circuit was built using a given schematic. This circuit was also drawn in P-Spice. The circuit was then analyzed using three separate methods: the three laws, the P-Spice simulation and a digital multi-meter. Ohm’s law and Kirchoff’s laws were found to be valid after comparing the results from all three tests. INTRODUCTION Ohm’s law, Kirchoff’s Voltage Law and Kirchoff’s Current Law are essential in the analysis of linear circuitry. Kirchoff’s laws deal with the voltage and current in the circuit. Ohm’s law relates voltage, current and resistance to one another. These three laws apply to resistive circuits where the only elements are voltage and/or current sources and resistors. Using the three laws any resistance of, current through or voltage across a resistor can be found if any two are already known. The purpose of this paper is to provide verification of these laws. In the year 1845, Gustav Kirchhoff (German physicist) introduces a set of laws which deal with current and voltage in the electrical circuits. -
Robert Bunsen.Indd
Historical profile Blazing a trail Robert Bunsen’s explosive career left an indelible impact – both in advancement of knowledge and the ubiquitous gas burner. Mike Sutton follows in his footsteps CHARLES D. WINTERS/SCIENCE PHOTO LIBRARY PHOTO WINTERS/SCIENCE D. CHARLES 46 | Chemistry World | July 2011 www.chemistryworld.org When Iceland’s Mount Hekla erupted compounds which were both (N≡C–C≡N) – he lost consciousness In short in 1845 there were no airliners for poisonous and inflammable. and was dragged to safety by a it to ground. However, like the ash These were the cacodyl Robert Bunsen is best colleague. His researches showed clouds spewed out of Eyjafjallajökull compounds – a name derived from known as the developer that German charcoal-burning in 2010 and Grímsvötn this year, the the Greek word for ‘stinking’ – of a simple but efficient furnaces wasted almost 50 per cent event aroused considerable scientific and their exact composition was gas burner of their fuel, while a later study interest. The Danish government uncertain until Bunsen tackled them. He was a supreme of British coke-fired furnaces (in commissioned an expedition in 1846 His investigations demonstrated experimentalist and was collaboration with the scientist and which included Robert Bunsen, a that they were all derivatives of called upon to investigate politician Lyon Playfair) indicated German chemist whose experience one parent compound, which we volcanic eruptions, blast a wastage rate of 80 per cent. analysing blast-furnace gases now know as tetramethyldiarsine, furnaces and geysers Ironmasters were reluctant to adopt qualified him for the task. (CH3)2As–As(CH3)2. -
Ludwig Edward Boltzmann
Ludwig Edward Boltzmann S. Rajasekar School of Physics, Bharathidasan University, Tiruchirapalli – 620 024, Tamilnadu, India∗ N.Athavan Department of Physics, H.H. The Rajah’s College, Pudukottai 622 001, Tamilnadu, India Abstract In this manuscript we present a brief life history of Ludwig Edward Boltzmann and his achive- ments. Particularly, we discuss his H-theorem, his work on entropy and statistical interpretation of second-law of thermodynamics. We point out his some other contributions in physics, charac- teristics of his work, his strong support on atomism, character of his personality and relationship with his students and final part of his life. Keywords: Boltzmann; H-theorem; entroy; second-law of thermodynamics arXiv:physics/0609047v1 [physics.hist-ph] 7 Sep 2006 ∗Electronic address: [email protected] 1 I. INTRODUCTION Boltzmann was born on 20 February 1844 in Vienna, Austria. He was born during the night between Shrove Tuesday and Ash Wednesday. Boltzmann used to say that this was the reason for the violent swing of his mood from one of great happiness to one of deep depression. His father Ludwig George Boltzmann was a taxation officer. His mother was Katharina Pauernfeind. After his birth his parents moved to Wels and then to Linz. He attended a high school at Linz. When he was fifteen his father died while his mother died in 1885. He studied physics at the University of Vienna. He was awarded a Ph.D. degree in 1866 for his work on the kinetic theory of gases supervised by Josef Stefan. Like molecules, he never stayed very long in any place. -
The Gibbs Paradox: Early History and Solutions
entropy Article The Gibbs Paradox: Early History and Solutions Olivier Darrigol UMR SPHere, CNRS, Université Denis Diderot, 75013 Paris, France; [email protected] Received: 9 April 2018; Accepted: 28 May 2018; Published: 6 June 2018 Abstract: This article is a detailed history of the Gibbs paradox, with philosophical morals. It purports to explain the origins of the paradox, to describe and criticize solutions of the paradox from the early times to the present, to use the history of statistical mechanics as a reservoir of ideas for clarifying foundations and removing prejudices, and to relate the paradox to broad misunderstandings of the nature of physical theory. Keywords: Gibbs paradox; mixing; entropy; irreversibility; thermochemistry 1. Introduction The history of thermodynamics has three famous “paradoxes”: Josiah Willard Gibbs’s mixing paradox of 1876, Josef Loschmidt reversibility paradox of the same year, and Ernst Zermelo’s recurrence paradox of 1896. The second and third revealed contradictions between the law of entropy increase and the properties of the underlying molecular dynamics. They prompted Ludwig Boltzmann to deepen the statistical understanding of thermodynamic irreversibility. The Gibbs paradox—first called a paradox by Pierre Duhem in 1892—denounced a violation of the continuity principle: the mixing entropy of two gases (to be defined in a moment) has the same finite value no matter how small the difference between the two gases, even though common sense requires the mixing entropy to vanish for identical gases (you do not really mix two identical substances). Although this paradox originally belonged to purely macroscopic thermodynamics, Gibbs perceived kinetic-molecular implications and James Clerk Maxwell promptly followed him in this direction. -
Historical Roots of Gauge Invariance
1 12 March 2001 LBNL - 47066 Historical roots of gauge invariance J. D. Jackson * University of California and Lawrence Berkeley National Laboratory, Berkeley, CA 94720 L. B. Okun Ê ITEP, 117218, Moscow, Russia ABSTRACT Gauge invariance is the basis of the modern theory of electroweak and strong interactions (the so called Standard Model). The roots of gauge invariance go back to the year 1820 when electromagnetism was discovered and the first electrodynamic theory was proposed. Subsequent developments led to the discovery that different forms of the vector potential result in the same observable forces. The partial arbitrariness of the vector potential A ¡ A µ brought forth various restrictions on it. = 0 was proposed by J. C. Maxwell; ǵA = 0 was proposed L. V. Lorenz in the middle of 1860's . In most of the modern texts the latter condition is attributed to H. A. Lorentz, who half a century later was one of the key figures in the final formulation of classical electrodynamics. In 1926 a relativistic quantum-mechanical equation for charged spinless particles was formulated by E. Schríodinger, O. Klein, and V. Fock. The latter discovered that this equation is invariant with respect to multiplication of the wave function by a phase factor exp(ieç/Óc ) with the accompanying additions to the scalar potential of -Çç/cÇt and to the vector potential of ç. In 1929 H. Weyl proclaimed this invariance as a general principle and called it Eichinvarianz in German and gauge invariance in English. The present era of non-abelian gauge theories started in 1954 with the paper by C. -
S8: Covariant Electromagnetism MAXWELL's EQUATIONS 1
S8: Covariant Electromagnetism MAXWELL’S EQUATIONS 1 Maxwell’s equations are: D = ρ ∇· B =0 ∇· ∂B E + =0 ∇ ∧ ∂t ∂D H = J ∇ ∧ − ∂t In these equations: ρ and J are the density and flux of free charge; E and B are the fields that exert forces on charges and currents (f is force per unit volume): f = ρE + J B; or for a point charge F = q(E + v B); ∧ ∧ D and H are related to E and B but include contributions from charges and currents bound within atoms: D = ǫ E + P H = B/µ M; 0 0 − P is the polarization and M the magnetization of the matter. −7 −2 µ0 has a defined value of 4π 10 kgmC . S8: Covariant Electromagnetism MAXWELL’S EQUATIONS 2 Maxwell’s equations in this form apply to spatial averages (over regions of atomic size) of the fundamental charges, currents and fields. This averaging generates a division of the charges and currents into two classes: the free charges, represented by ρ and J, and charges and cur- rents in atoms, whose averaged effects are represented by P and M. We can see what these effects are by substituting for D and H: E =(ρ P) /ǫ ∇· −∇· 0 B =0 ∇· ∂B E + =0 ∇ ∧ ∂t ∂E ∂P B ǫ µ = µ J + + M . ∇ ∧ − 0 0 ∂t 0 ∂t ∇ ∧ We see that the divergence of P generates a charge density: ρb = P −∇ ·∂P and the curl of M and temporal changes in P generate current: J = + M. b ∂t ∇ ∧ Any physical model of the atomic charges and currents will produce these spatially averaged effects (see problems). -
An Introduction to Gauge Theory
An Introduction to Gauge Theory Department of Physics, Drexel University, Philadelphia, PA 19104 Quantum Mechanics II Frank Jones Abstract Gauge theory is a field theory in which the equations of motion do not change under coordinate transformations. In general, this transformation will make a problem easier to solve as long as the transformation produces a result that is physically meaningful. This paper discusses the uses of gauge theory and its applications in physics. Gauge transformations were first introduced in electrodynamics, therefore we will start by deriving a gauge transformation for electromagnetic field in classical mechanics and then move on to a derivation in quantum mechanics. In the conclusion of this paper we will analyze the Yang Mills theory and see how it has played a role in the development of modern gauge theories. 1 Introduction From the beginning of our general physics class we are tought, unknowingly, the ideas of gauge theory and gauge invariance. In this paper we will discuss the uses of gauge theory and the meaning of gauge invariance. We will see that some problems have dimensions of freedom that will allow us to manipulate the problem as long as we apply transformations to the potentials so that the equations of motion remain unchanged. Examples of gauge trans- formations will be discussed including electromagnetism, the Loterntz condition, and phase transformations in quantum mechanics. Finally Yang-Mills gauge theory will be addressed as an anaology to classical electromagnetic gauge transformations. We begin by defining a gauge theory as a field theory in which the equations of motion remain unchanged after a transformation. -
611: Electromagnetic Theory II
611: Electromagnetic Theory II CONTENTS Special relativity; Lorentz covariance of Maxwell equations • Scalar and vector potentials, and gauge invariance • Relativistic motion of charged particles • Action principle for electromagnetism; energy-momentum tensor • Electromagnetic waves; waveguides • Fields due to moving charges • Radiation from accelerating charges • Antennae • Radiation reaction • Magnetic monopoles, duality, Yang-Mills theory • Contents 1 Electrodynamics and Special Relativity 4 1.1 Introduction.................................... 4 1.2 TheLorentzTransformation. ... 7 1.3 An interlude on 3-vectors and suffix notation . ...... 9 1.4 4-vectorsand4-tensors. 15 1.5 Lorentztensors .................................. 21 1.6 Propertimeand4-velocity. 23 2 Electrodynamics and Maxwell’s Equations 25 2.1 Naturalunits ................................... 25 2.2 Gauge potentials and gauge invariance . ...... 26 2.3 Maxwell’s equations in 4-tensor notation . ........ 28 2.4 Lorentz transformation of E~ and B~ ....................... 34 2.5 TheLorentzforce................................. 35 2.6 Action principle for charged particles . ........ 36 2.7 Gauge invariance of the action . 40 2.8 Canonical momentum, and Hamiltonian . 41 3 Particle Motion in Static Electromagnetic Fields 42 3.1 Description in terms of potentials . ...... 42 3.2 Particle motion in static uniform E~ and B~ fields ............... 44 4 Action Principle for Electrodynamics 50 4.1 Invariants of the electromagnetic field . ....... 50 4.2 Actionforelectrodynamics . 53 4.3 Inclusionofsources.............................. 55 4.4 Energydensityandenergyflux . 58 4.5 Energy-momentumtensor . 60 4.6 Energy-momentum tensor for the electromagnetic field . .......... 66 4.7 Inclusion of massive charged particles . ....... 69 5 Coulomb’s Law 71 5.1 Potential of a point charge . 71 5.2 Electrostaticenergy ............................. 73 1 5.3 Fieldofauniformlymovingcharge . 74 5.4 Motion of a charge in a Coulomb potential .