Light and Vacuum Downloaded from by on 11/22/17. For personal use only.

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3 World Scientific

4 Published by World Scientific Publishing Co. Pte. Ltd. 5 Toh Tuck Link, Singapore USA office: 27 Warren Street, Suite , Hackensack, NJ UK office: 57 Shelton Street, Covent Garden, London WC2H 9HE Light and Vacuum Downloaded from British Library Cataloguing-in-Publication Data A catalogue record for this book is available from the British Library. LIGHT AND VACUUM The Wave Particle Nature of the Light and the Quantum Vacuum through the Coupling of Electromagnetic Theory and Quantum Electrodynamics Copyright 2015 by World Scientific Publishing Co. Pte. Ltd. All rights reserved. This book, or parts thereof, may not be reproduced in any form or by any means, electronic or mechanical, including photocopying, recording or any information storage and retrieval system now known or to be invented, without written permission from the publisher. For photocopying of material in this volume, please pay a copying fee through the Copyright Clearance Center, Inc., 222 Rosewood Drive, Danvers, MA 01923, USA. In this case permission to photocopy is not required from the publisher. ISBN In-house Editor: Song Yu Typeset by Stalion Press enquiries@stallionpress.com Printed in Singapore

5 To my mother Aphrodite, to Angelika and Hypatia

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7 The infinite vacuum is the real essence of the cosmos, whatever exists has derived from the intrinsic action of the vacuum resulting to positive and negative entities (Anaximander, BC).

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9 Prologue Light and Vacuum Downloaded from Throughout this book, we give the main principles of the electromagnetic theory and quantum electrodynamics (QED), both developed for the understanding of light s nature and for the explanation of the associated phenomena when interacting with matter. Of course, it is not in the scope of this manuscript to give a full and detailed presentation of these theories. Only selected theoretical topics have been chosen, supported by experimental evidence, which are indispensable for the understanding of the present status of the theories on the nature of light. Furthermore, we discuss the main difficulties encountered by both theories, to ensure a complete and coherent mathematical description of the simultaneous wave-particle nature of light put in evidence by experiments. Finally, we consider the basic aspect of QED related to the quantization of the vector potential amplitude of the electromagnetic field to a single photon state, and we advance elaborations on its relationship with the classical electromagnetic wave theory and the vacuum. The topics are all drawn from many works previously published, and given in the bibliography. The perspectives and elaborations on the photon vector potential and its relationship to the quantum vacuum are of my own, in the aim to raise questions and aspire for further theoretical and experimental investigation, in order to improve our knowledge and understanding on the real essence of light and vacuum. Note: In this book, the word light is not limited to the visible field, but concerns the whole electromagnetic spectrum ranging from zero frequency to infinity. ix

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11 Table of Contents Light and Vacuum Downloaded from Prologue 1. Introduction 1 2. Historical Survey and Experimental Evidence 3 The concepts of light during the last 2500 years: corpuscles, ray optics, wave optics, electromagnetic wave theory and finally quantum particle theory Bibliography Basic Principles of the Electromagnetic Wave Theory Maxwell s Equations Electromagnetic Wave Propagation Dispersion relation Physical quantities involved in the electromagnetic field Propagation equations of electromagnetic waves.. 18 Helmholtz equation Energy flux of electromagnetic waves TEM waves Laplace equation Scalar and Vector Potentials Vector Potential and Electromagnetic Field Polarization Guided Propagation of Electromagnetic Waves Rectangular waveguide of cross section a, b(a >b) ix xi

12 xii Light and Vacuum TE m,n Modes TM m,n Components Circular waveguide of radius r TE m,n Modes TM m,n Modes Case of two parallel plates Density of states Conclusion Remarks Bibliography Light and Vacuum Downloaded from 4. From Electromagnetic Waves to Quantum Electrodynamics Elements of Quantum Mechanics Blackbody radiation and the ultraviolet catastrophe Energy and momentum operators in quantum mechanics Particle in a square potential well correspondence with the waveguides Harmonic Oscillator in Quantum Mechanics From the classical expressions to the quantum mechanical ones Dirac representation, creation and annihilation operators a, a Quantum Electrodynamics (QED) and the Photon Description Brief description of selected experiments that have historically played an important role for the introduction of the photon concept The photoelectric effect and the quantum interpretation Compton scattering Low intensity Young s double-slit interferences

13 Table of Contents xiii Light and Vacuum Downloaded from Second Quantization Quantization process of the electromagnetic field Interaction between Electromagnetic Waves and Charged Particles, Reality of the Vector Potential Interaction Hamiltonian between an electromagnetic wave and a charged particle Reality of the vector potential, Ehrenberg Siday or Aharonov Bohm effect Transition Rates and Vacuum Induced Spontaneous Emission Photoelectric effect and the semi-classical interpretation Spontaneous emission rate Dipole approximation and the spontaneous emission The photon spin Lamb Shift Nonrelativistic calculations: Bethe s approach Conclusion Remarks Bibliography Theory, Experiments and Questions Planck s Constant and the Vacuum Intrinsic Electromagnetic Properties Hamiltonian Issued from the Quantization of the Electromagnetic Field QED Singularities Electron-Vacuum Interactions and the Associated Effects Spontaneous emission Lamb shift Casimir effect Simultaneous Wave-particle Nature of the Photon Revealed by the Experiments Discussions

14 xiv Light and Vacuum Photoelectric effect and Young s double-slit experiment Mizobuchi and Ohtake double-prism experiment Grangier s et al. experiments, photon indivisibility Hunter Wadlinger experiments, the photon spatial expansion Conclusion Remarks Bibliography Light and Vacuum Downloaded from 6. Analysis of the Electromagnetic Field Quantization Process and the Photon Vector Potential. The Non- Local Photon Wave-Particle Representation and the Quantum Vacuum Quantized Vector Potential Amplitude of a Single Photon State Dimension analysis from Maxwell s equations. Vector potential amplitude proportional to the frequency Wave equation for the photon vector potential Photon wavelength dimensions following the experimental evidence Wave-particle formalism Relation between the photon vector potential and the electron charge Quantum Vacuum Representation The Quantum Vacuum Field Effects Spontaneous emission Lamb shift Cosmic vacuum energy density Conclusion Remarks Bibliography Epilogue 111 Index 115

QUANTUM MECHANICS. For Electrical Engineers. Quantum Mechanics Downloaded from

QUANTUM MECHANICS. For Electrical Engineers. Quantum Mechanics Downloaded from Quantum Mechanics Downloaded from www.worldscientific.com QUANTUM MECHANICS For Electrical Engineers Quantum Mechanics Downloaded from www.worldscientific.com This page intentionally left blank Quantum