Quantum leap: From Dirac and Feynman, across the Universe, to human body and mind

856 Pages·2008·5.09 MB·English

by  Ivancevic

Quantum Leap
From Dirac and Feynman,
Across the Universe,
to Human Body and Mind
TThhiiss ppaaggee iinntteennttiioonnaallllyy lleefftt bbllaannkk
Quantum Leap
From Dirac and Feynman,
Across the Universe,
to Human Body and Mind
Vladimir G Ivancevic
Defence Science & Technology Organisation, Australia
Tijana T Ivancevic
University of South Australia, Australia
World Scientific
NEW JERSEY • LONDON • SINGAPORE • BEIJING • SHANGHAI • HONG KONG • TAIPEI • CHENNAI
Published by
World Scientific Publishing Co. Pte. Ltd.
5 Toh Tuck Link, Singapore 596224
USA office: 27 Warren Street, Suite 401-402, Hackensack, NJ 07601
UK office: 57 Shelton Street, Covent Garden, London WC2H 9HE
British Library Cataloguing-in-Publication Data
A catalogue record for this book is available from the British Library.
QUANTUM LEAP
From Dirac and Feynman, Across the Universe, to Human Body and Mind
Copyright © 2008 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-13 978-981-281-927-7
ISBN-10 981-281-927-4
Printed in Singapore.
LaiFun - Quantum Leap.pmd 1 8/15/2008, 9:25 AM
September15,2008 17:19 WSPC/BookTrimSizefor9inx6in IvQuantLeap˙050608
Dedicated to:
Nick, Atma and Kali
v

September15,2008 17:19 WSPC/BookTrimSizefor9inx6in IvQuantLeap˙050608
Preface
Quantum Leap: From Dirac and Feynman, Across the Universe, to Human
Body and Mind is a monographic textbook in the field of quantum physics
and its relations to human mind and body. The book has seven Chapters.
TheintroductoryChaptergivesbothnon–mathematicalandmathematical
preliminaries for understanding the text. The second Chapter presents the
basics of both non–relativistic and relativistic quantum mechanics. The
third Chapter introduces Feynman path integrals and their application to
quantum fields and string theory, as well as some non–quantum applica-
tions. The fourth Chapter presents quantum universe in the form of loop
quantum gravity and quantum cosmology. The fifth Chapter turns to the
humanbody,applyingquantummechanicsandelectrodynamicstoelectro–
muscular stimulation. The sixth Chapter presents modern quantum games
and quantum computers. The seventh Chapter develops quantum theory
of the mind and consciousness.
This book can be used as a textbook of a two–semester course in quan-
tum physics and its modern applications, at the graduate (or, higher un-
dergraduate) level. Some parts of the book can be also used by engineers,
biologists, psychologists and computer scientists, as well as applied math-
ematicians, both in industry and academia. It includes a comprehensive
bibliography on the subject and a detailed index.
Adelaide, V. Ivancevic, Defence Science & Technology Organisation,
Nov, 2007 Australia, e-mail: [email protected]
T. Ivancevic, School of Mathematics, University of South Australia
e-mail: [email protected]
vii
September15,2008 17:19 WSPC/BookTrimSizefor9inx6in IvQuantLeap˙050608
Acknowledgments
The authors wish to thank Land Operations Division, Defence Science
& Technology Organisation, Australia, for the support in developing the
HumanBiodynamicsEngine (HBE)andallHBE–relatedtextinthismono-
graphandKnowledge-BasedIntelligentEngineeringSystemsCentre(KES),
University of South Australia.
We also express our gratitude to the World Scientific Publishing Com-
pany,andespeciallytotheEditors,Ms. ZhangJiandMs. LaiFunKwong.
Finally, the book approval from Dr. K. K. Phua, Chairman and Editor-in-
Chief of World Scientific is gratefully acknowledged.
viii
September15,2008 17:19 WSPC/BookTrimSizefor9inx6in IvQuantLeap˙050608
Contents
Preface vii
1. Introduction 1
1.1 Soft Introduction to Quantum Mechanics . . . . . . . . . . 1
1.2 Hilbert Space . . . . . . . . . . . . . . . . . . . . . . . . . . 7
1.2.1 Quantum Hilbert Space . . . . . . . . . . . . . . . . 7
1.2.2 Formal Hilbert Space . . . . . . . . . . . . . . . . . . 8
1.3 Human Intelligence, Mind and Reason . . . . . . . . . . . . 11
1.3.0.1 Human Reason . . . . . . . . . . . . . . . . 13
2. Elements of Quantum Mechanics 19
2.1 Basics of Non–Relativistic Quantum Mechanics . . . . . . . 19
2.1.1 Canonical Quantization . . . . . . . . . . . . . . . . 23
2.1.2 Quantum States and Operators . . . . . . . . . . . . 24
2.1.3 Quantum Pictures . . . . . . . . . . . . . . . . . . . 30
2.1.4 Spectrum of a Quantum Operator. . . . . . . . . . . 32
2.1.5 General Representation Model . . . . . . . . . . . . . 35
2.1.6 Direct Product Space . . . . . . . . . . . . . . . . . . 36
2.1.7 State–Space for n Quantum Particles . . . . . . . . . 37
2.2 Relativistic Quantum Mechanics and Electrodynamics . . . 40
2.2.1 Difficulties of the Relativistic Quantum Mechanics . 40
2.2.2 Particles of Half–Odd Integral Spin . . . . . . . . . . 43
2.2.3 Particles of Integral Spin . . . . . . . . . . . . . . . . 45
2.2.4 Dirac’s Electrodynamics Action Principle . . . . . . 54
2.2.5 Dirac Equation and Formal QED in Brief . . . . . . 60
2.2.6 Lorentzian Space-Time and Gravity. . . . . . . . . . 62
ix