Table Of ContentUnderstanding
Quantum Physics
An Advanced Guide for the Perplexed
Shan Gao
© Shan Gao 2011
All rights reserved
Published 2011
by Amazon Kindle Direct Publishing
www.amazon.com
This book is copyright. Subject to statutory exception and to provisions of
relevant collective licensing agreements, no part of this publication may be
reproduced, stored in a retrieval system, or transmitted in any form or by any
means, without the prior written permission of the author.
This book is dedicated to Erwin Schrödinger, who introduced the wave function,
discovered its equation named after him, and argued that quantum mechanics is
incomplete by his famous cat paradox.
It has even been doubted whether what goes on in an atom can be described
within a scheme of space and time. From a philosophical standpoint, I should
consider a conclusive decision in this sense as equivalent to a complete
surrender. For we cannot really avoid our thinking in terms of space and time,
and what we cannot comprehend within it, we cannot comprehend at all.
—Erwin Schrödinger
Someday we'll understand the whole thing as one single marvelous vision that
will seem so overwhelmingly simple and beautiful that we may say to each other;
"Oh, how could we have been so stupid for so long? How could it have been
otherwise!"
—John Archibald Wheeler
Contents
Acknowledgements
A True Story of Quantum Exploration
1. How Can We Understand Quantum Mechanics?
2. Meaning of the Wave Function
2.1 Standard quantum mechanics and conventional measurements
2.2 Weak measurements
2.3 Protective measurements
2.3.1 Measurements with natural protection
2.3.2 Measurements with artificial protection
2.3.3 Further discussions
2.4 How does the mass and charge of a quantum system distribute?
2.4.1 A heuristic argument
2.4.2 The answer of protective measurement
2.4.3 A specific example
2.5 The origin of mass and charge density
2.5.1 The mass and charge density is not real
2.5.2 The ergodic motion of a particle is discontinuous
2.5.3 An argument for random discontinuous motion
2.6 The wave function represents the state of random discontinuous motion of
particles
2.6.1 An analysis of random discontinuous motion
2.6.2 Interpreting the wave function
3. How Come the Schrödinger Equation?
3.1 Spacetime translation and its invariance
3.2 Relativistic invariance
3.3 Derivation of the free Schrödinger equation
3.4 Further discussions
3.5 On the conservation of energy-momentum
4. The Solution to the Measurement Problem
4.1 The reality of wavefunction collapse
4.1.1 Against the de Broglie-Bohm theory
4.1.2 Against the many-worlds interpretation
4.2 The origin of wavefunction collapse
4.2.1 The chooser in discrete time
4.2.2 Energy conservation and the choices
4.2.3 In search of a deeper basis
4.3 A discrete model of energy-conserved wavefunction collapse
4.4 On the consistency of the model and experiments
4.4.1 Maintenance of coherence
4.4.2 Localization in measurement situations
4.4.3 Emergence of the classical world
4.5 Critical comments on other dynamical collapse models
4.5.1 Penrose's gravity-induced wavefunction collapse model
4.5.2 The CSL model
5. On the Unification of Quantum Mechanics and Special Relativity
5.1 The picture of motion distorted by the Lorentz transformation
5.1.1 Single particle picture
5.1.2 Picture of quantum entanglement
5.1.3 Picture of wavefunction collapse
5.2 On the absoluteness of simultaneity
5.3 Collapse dynamics and preferred Lorentz frame
Bibliography
Notes
Acknowledgements
The idea of random discontinuous motion of particles came to my mind when I
was a postgraduate at the Institute of Electronics, Chinese Academy of Sciences
in 1993. I am happy that finally it has a more logical and satisfying formulation
in this book. During the past twenty or so years, I have benefited from
discussions with many physicists and philosophers of physics who care about the
way the world really is. They are: Stephen Adler, Jacob Bekenstein, Samuel
Braunstein, Jeremy Butterfield, Tian Yu Cao, Zexian Cao, Philippe Eberhard,
Bernard d' Espagnat, Shelly Goldstein, Basil Hiley, Gerard 't Hooft, Sabine
Hossenfelder, Chris Isham, Frederick M. Kronz, Gui-Lu Long, Alwyn van der
Merwe, David Miller, Philip Pearle, Roger Penrose, Huw Price, Alastair Rae,
Erasmo Recami, Dean Rickles, Abner Shimony, Henry P. Stapp, George
Svetlichny, Antoine Suarez, Antony Valentini, Hans Westman, Christian
Wüthrich, Heinz-Dieter Zeh, and Anton Zeilinger, among others. I thank them
all deeply.
My deepest gratitude goes to my parents, QingFeng Gao and LiHua Zhao, who
spared no effort to provide the best possible environment for me to grow up in
and their constant support during my extended studies. They have always
allowed me to have the freedom of choice, and for that I am truly grateful.
Finally, I am deeply indebted to my wife, HuiXia, and my daughter, Vicky, for
their unflagging love and support throughout my study and writing; this book
would have been impossible without them. Moreover, they have never let me
forget the true values of life.
This book was support by a University of Sydney International Scholarship and
a Postgraduate Scholarship in Quantum Foundations provided by the Unit for
History and Philosophy of Science and Centre for Time of the University of
Sydney, as well as by two Lucy Firth Scholarships in Philosophy provided by the
Department of Philosophy of the University of Sydney. I would like to thank
them for their kind support.
Shan Gao
Sydney
November 2011
A True Story of Quantum Exploration
—An Excerpt from God Does Play Dice With the Universe
During my childhood, it had been a wonder for me that the twinkling stars
strewed in the night sky don't fall to the Earth. I had a strong desire to know the
whys and wherefores. Later I found the answer in textbooks. It changed my
picture of the universe. When I was an undergraduate, I began to be entranced by
the deep mysteries of the atomic world. I was especially stunned by the fact that
the commonsense planetary picture of atoms turns out to be utterly false; the
electron in an atom cannot rotate round the atomic nucleus as the Earth rotates
round the sun, or else it would soon radiate its energy and fall into the nucleus,
and as a result, my body composed of atoms would collapse in a blink. How
does the electron move then? It must exist in the atom. It must move in some
way there. But more surprisingly, textbooks provided no picture of the motion of
the electron. On 22 August 1987, I wrote in my diary: "Is it really true that we
have no way to describe the atomic processes as processes happening in space
and time?" I could only search for the answer by myself. Then I started on a
lonely journey to "trace" the elusive electron at the age of 16.
In order to find how the electron moves in an atom, I went to the Institute of
Electronics, Chinese Academy of Sciences to pursue my graduate study. But it
was according to expectation that nobody there could give me any tips either. I
then spent nearly every day in musing on the seemingly indescribable motion of
electrons. If a ball indeed moves in a continuous way, then it seems that an
electron or an atom should also move in the same way. The ball is composed of
atoms after all. But, on the other hand, if an electron moves continuously in an
atom, it will soon fall into the nucleus, while the tragedy does not happen in
reality. This is a great dilemma. I found some possible solutions, but they shortly
proved to be wrong.
The puzzle had been plaguing me. Day after day, I gradually doubted the reality
of continuous motion. But I still felt in my bones that the particles must move in
some way. Finally, in the early morning of 12 October 1993, I experienced a
sudden enlightenment. At that moment, I felt that my body permeated the whole
universe and I was united with it. I "disappeared". A clear picture then appeared:
a particle is jumping in a random and discontinuous way. It is not inert but
active; it moves purely by its own "free will". Maybe God does play dice in the
atomic world. I finally broke loose the tightest shackles of continuous motion
with the help of inspiration. After this event, the outcome seems very natural
from a logical point of view. If a particle cannot move continuously, it must
move in a discontinuous way. How deep-rooted the prejudice of the uniqueness
Description:Quantum physics is admittedly the most difficult subject to understand. Physicists, let alone students and laymen, are still puzzled by it today. As Richard Feynman once famously claimed, nobody understood quantum mechanics. The crux of the matter lies in the meaning of the mysterious wave function
