Undergraduate Lecture Notes in Physics Masud Chaichian Hugo Perez Rojas Anca Tureanu Basic Concepts in Physics From the Cosmos to Quarks Second Edition Undergraduate Lecture Notes in Physics Series Editors Neil Ashby, University of Colorado, Boulder, CO, USA William Brantley, Department of Physics, Furman University, Greenville, SC, USA Matthew Deady, Physics Program, Bard College, Annandale-on-Hudson, NY, USA Michael Fowler, Department of Physics, University of Virginia, Charlottesville, VA, USA Morten Hjorth-Jensen, Department of Physics, University of Oslo, Oslo, Norway Michael Inglis, Department of Physical Sciences, SUNY Suffolk County Community College, Selden, NY, USA www.com Undergraduate Lecture Notes in Physics (ULNP) publishes authoritative texts covering topics throughout pure and applied physics. Each title in the series is suitable as a basis for undergraduate instruction, typically containing practice problems, worked examples, chapter summaries, and suggestions for further reading. ULNP titles must provide at least one of the following: • An exceptionally clear and concise treatment of a standard undergraduate subject. • A solid undergraduate-level introduction to a graduate, advanced, or non-standard subject.
• A novel perspective or an unusual approach to teaching a subject. ULNP especially encourages new, original, and idiosyncratic approaches to physics teaching at the undergraduate level. The purpose of ULNP is to provide intriguing, absorbing books that will continue to be the reader’s preferred reference throughout their academic career. More information about this series at http://www.com/series/8917 www.com Masud Chaichian Hugo Perez Rojas • • Anca Tureanu Basic Concepts in Physics From the Cosmos to Quarks Second Edition 123 www.com Masud Chaichian Hugo Perez Rojas Department of Physics Department of Theoretical Physics University of Helsinki ICIMAF Helsinki, Finland La Habana, Cuba Anca Tureanu Department of Physics University of Helsinki Helsinki, Finland ISSN 2192-4791 ISSN 2192-4805 (electronic) Undergraduate Lecture Notes in Physics ISBN 978-3-662-62312-1 ISBN 978-3-662-62313-8 (eBook) https://doi.1007/978-3-662-62313-8 1st edition: © Springer-Verlag Berlin Heidelberg 2014 2nd edition: © Springer-Verlag GmbH Germany, part of Springer Nature 2021 This work is subject to copyright.
All rights are reserved by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. The publisher, the authors and the editors are safe to assume that the advice and information in this book are believed to be true and accurate at the date of publication.
Neither the publisher nor the authors or the editors give a warranty, expressed or implied, with respect to the material contained herein or for any errors or omissions that may have been made. The publisher remains neutral with regard to jurisdictional claims in published maps and institutional affiliations. This Springer imprint is published by the registered company Springer-Verlag GmbH, DE part of Springer Nature. The registered company address is: Heidelberger Platz 3, 14197 Berlin, Germany www.com Preface to the Second Edition The praise of the first edition of the book by many readers encouraged us to prepare the present second edition.
We express our deep gratitude to all those readers for their remarks and suggestions – in this edition we have tried to take into account all of them as much as possible, and as well to come up with their wishes to include some problems to be solved, together with their solutions or at least sufficient hints to solve them. As its previous edition, this book is intended for undergraduate students, physics teachers, students in high schools, researchers and general readers interested to know what physics is about together with its latest developments and discoveries. Thinking about the book to be useful also as a textbook, totally or in part, we have added several new topics with the latest findings in those fields. For instance, the recent discovery of gravitational waves, as one of the most important achievements of modern physical sciences, is presented in Chap.
At the end of Chaps. 1–11 some problems are included with their solutions or hints how to solve them given at the end of the book. Those problems are useful for a complementary understanding of the theories and their implication. However, for non-specialized readers it is recommended to bypass, at least in their first-time reading, the problems as well as the mathematical details.
The added new topics also provide connections among the subjects treated in different chapters. For instance, the wobble of some stars interacting with their planets, as explained by the two body Kepler problem, helps to detect invisible companions, by using Doppler spectroscopy of the star light. The Clapeyron– Clausius equation helps to understand the development of life at dark, deep and hot oceanic vents at high pressures, as well as why the hot Earth nucleus is solid. The creation of the magnetosphere is explained as due to the deviation of the solar wind by the Earth magnetic field.
A reference to the former experiments is made in order to resolve the loophole appeared there and to support, thanks to more recent experiments, the occurrence of quantum entanglement, and to show the validity of the violation of Bell inequalities as a genuine quantum phenomenon. Gravitational lensing, as well as the correction of time for GPS satellites, as the v www.com vi Preface to the Second Edition technical applications of special and general relativity, are explained. Some earlier figures have been improved and new ones were added. Our special thanks go to François Englert, Igal Galili, and Markku Oksanen for their valuable comments and advice.
Helsinki, Finland Masud Chaichian La Habana, Cuba Hugo Perez Rojas Helsinki, Finland Anca Tureanu May 2021 www.com Preface to the First Edition This book is the outcome of many lectures, seminars, and colloquia the authors have given on different occasions to different audiences in several countries over a long period of time and the experience and feedback obtained from them. With a wide range of readers in mind, some topics have been presented in twofold form, both descriptively and more formally. This book is intended not only for first to second year undergraduate students, as a complement to specialized textbooks but also for physics teachers and students in high schools. At the same time, it is addressed to researchers and scientists in other fields, including engineers and general readers interested in acquiring an overview of modern physics.
A minimal mathematical background, up to elementary cal- culus, matrix algebra and vector analysis, is required. However, mathematical technicalities have not been stressed, and long calculations have been avoided. The basic and most important ideas have been presented with a view to introducing the physical concepts in a pedagogical way. Since some specific topics of modern physics, particularly those related to quantum theory, are an important ingredient of student courses nowadays, the first five chapters on classical physics are presented keeping in mind their connection to modern physics whenever possible.
In most chapters, historical facts are included. Several themes are discussed which are sometimes omitted in basic courses on physics. For instance, the relation between entropy and information, exchange energy and ferromagnetism, super- conductivity and the relation between phase transitions and spontaneous symmetry breaking, chirality, the fundamental C, P, and T invariances, paradoxes of quantum theory, the problem of measurement in quantum mechanics, quantum statistics and specific heat in solids, quantum Hall effect, graphene, general relativity and cos- mology, CP violation, Casimir and Aharonov–Bohm effects, causality, unitarity, spontaneous symmetry breaking and the Standard Model, inflation, baryogenesis, and nucleosynthesis, ending with a chapter on the relationship between physics and life, including biological chiral symmetry breaking. To non-specialized readers it is recommended to bypass, at least on a first reading, the mathematical content of sections and subsections 1.com viii Preface to the First Edition During the preparation of this book the authors have benefited greatly from discussions with many of their colleagues and students, to whom we are indebted.
It is a pleasure to express our gratitude in particular to Cristian Armendariz-Picon, Alexander D. Dolgov, François Englert, Josef Kluson, Vladimir M. Mostepanenko, Viatcheslav Mukhanov, Markku Oksanen, Roberto Sussmann, and Ruibin Zhang for their stimulating suggestions and comments, while our special thanks go to Tiberiu Harko, Peter Prešnajder and Daniel Radu, to whom we are most grateful for their valuable advice in improving an initial version of the manuscript. Helsinki, Finland Masud Chaichian La Habana, Cuba Hugo Perez Rojas Helsinki, Finland Anca Tureanu March 2013 www.com Contents 1 Gravitation and Newton’s Laws .1 From Pythagoras to the Middle Ages .2 Copernicus, Kepler, and Galileo .3 Newton and Modern Science .1 Newton’s First Law .2 Newton’s Second Law .3 Planetary Motion in Newton’s Theory .4 Newton’s Third Law .1 Conservation of Linear Momentum .2 Conservation of Angular Momentum .3 Conservation of Energy .6 Degrees of Freedom .7 Inertial and Non-inertial Systems .9 The Principle of Least Action .11 Complements on Gravity and Planetary Motion .12 Advice for Solving Problems.
60 2 Entropy, Statistical Physics, and Information .1 First Law of Thermodynamics .2 Second Law of Thermodynamics .3 Third Law of Thermodynamics .3 Entropy and Statistical Physics .4 Temperature and Chemical Potential .3 Grand Canonical Ensemble .6 Entropy and Information .7 Maxwell’s Demon and Perpetuum Mobile .8 First Order Phase Transitions. 99 3 Electromagnetism and Maxwell’s Equations .2 Electrostatic and Gravitational Fields .3 Conductors, Semiconductors, and Insulators .1 Gauss’s Law for Electric Fields .2 Gauss’s Law for Magnetism .4 Ampère–Maxwell Law .8 Fields in a Medium .4 Ferrimagnetism, Antiferromagnetism, and Magnetic Frustration .5 Spin Ices and Monopoles .10 Second Order Phase Transitions .11 Spontaneous Symmetry Breaking .13 Meissner Effect: Type I and II Superconductors .14 Appendix of Formulas .com Contents xi 4 Electromagnetic Waves .1 Waves in a Medium and in Æther .2 Electromagnetic Waves and Maxwell’s Equations .3 Generation of Electromagnetic Waves .2 Mechanisms Generating Electromagnetic Waves .5 Fourier Series and Integrals .6 Reflection and Refraction .7 Dispersion of Light .8 Black Body Radiation. 165 5 Special Theory of Relativity .1 Postulates of Special Relativity .3 Light Cone and Causality .4 Contraction of Lengths .5 Time Dilation: Proper Time .6 Addition of Velocities .7 Relativistic Four-Vectors .8 Electrodynamics in Relativistically Covariant Formalism .9 Energy and Momentum .12 Tachyons and Superluminal Signals .13 The Lagrangian for a Particle in an Electromagnetic Field. 194 6 Atoms and Quantum Theory .1 Motion of a Particle .2 Evolution of the Concept of Atom .5 Schrödinger’s Equation .com xii Contents 6.7 Operators and States in Quantum Mechanics .8 One-Dimensional Systems in Quantum Mechanics .1 The Infinite Potential Well .2 Quantum Harmonic Oscillator .3 Charged Particle in a Constant Magnetic Field .9 Emission and Absorption of Radiation .10 Stimulated Emission and Lasers .12 Indistinguishability and Pauli’s Principle .14 Exchange Energy and Ferromagnetism .15 Distribution of Electrons in the Atom .1 U and R Evolution Procedures .2 On Theory and Observable Quantities .17 Paradoxes in Quantum Mechanics .1 De Broglie’s Paradox .2 Schrödinger’s Cat Paradox .3 Toward the EPR Paradox .4 A Hidden Variable Model and Bell’s Theorem .5 Bell Inequality and Conventional Quantum Mechanics .6 EPR Paradox: Quantum Mechanics Versus Special Relativity .18 Quantum Computation and Teleportation .1 The Spin of the Electron .2 Hydrogen Atom in Dirac’s Theory .3 Hole Theory and Positrons .2 Intermezzo: Natural Units and the Metric Used in Particle Physics .3 Quantized Fields and Particles .1 Unitarity in Quantum Electrodynamics .5 Electron Self-energy and Vacuum Polarization .6 Renormalization and Running Coupling Constant .com Contents xiii 7.5 Quantum Vacuum and Casimir Effect .6 Principle of Gauge Invariance.
286 8 Fermi–Dirac and Bose–Einstein Statistics .1 Fermi–Dirac Statistics .2 Fermi–Dirac and Bose–Einstein Distributions .3 The Ideal Electron Gas .4 Heat Capacity of Metals .5 Metals, Semiconductors, and Insulators .6 Electrons and Holes .7 Applications of the Fermi–Dirac Statistics .