Equivalent Circuit Model of Quantum Mechanics

EQUIVALENT CIRCUIT MODEL OF

QUANTUM

MECHANICS

MASAKAZU SHOJI

EQUIVALENT CIRCUIT MODEL OFQUANTUMMECHANICS

Copyright © 2023 Masakazu Shoji.

All rights reserved. No part of this book may be used or reproduced by any means,

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ISBN: 978-1-6632-4894-7 (sc)

ISBN: 978-1-6632-4896-1 (hc)

ISBN: 978-1-6632-4895-4 (e)

Library of Congress Control Number: 2022922975

iUniverse rev. date: 02/02/2023

CONTENTS

Preface

Chapter 1    Probability In The Quantum World

1.01 Introduction

1.02 Probability

1.03 Diffusion of Probability Segments

1.04 Probability Field Collapse

1.05 Probability Signal Transmission

1.06 Probabilistic Quantum System

1.07 Quantum Laws in the Universe’s History

1.08 Substance and Character of Elementary Particles

1.09 Limit of Splitting Material

Chapter 2    Equivalent Circuit Model Of Quantum Phenomena

2.01 Basic Linear Equivalent Circuits

2.02 Solution of the Schrödinger Equation

2.03 CMOS-Based Quantum Equivalent Circuits

2.04 Digital Waveforms and Particles

2.05 Fermions, Bosons, and Spin

2.06 Equivalent Circuit Model of a Fermion

2.07 Fermion Replacement Motion

2.08 Boson Replacement Motion

2.09 Capacitor Jump Mechanism

2.10 Details of the Capacitor Jump Mechanism

2.11 Parameter Calibration including Inductance

Chapter 3    Quantum Phenomena

3.01 Fermion and Boson Launcher

3.02 Fermion Propagation

3.03 Boson Propagation

3.04 Fermion-Boson Interaction

3.05 Wave and Particle Model

3.06 Relation between Linear and Digital Circuit Models

3.07 Spin and Equivalent Circuit Waveforms

3.08 Model of Spin

3.09 Splitting and Joining Fermion’s Path

3.10 How the Character’s Charge Transmits Force

3.11 Entangled Particles

3.12 Afterthought

Conclusion

PREFACE

Physics students have many basic questions in their quantum mechanics class. From my remote physics student days in the 1950s, I had many difficulties in understanding the basic concepts of quantum mechanics. They appeared almost mysteries to me, and many such mysteries have still not been plainly explained. The theory works as if by magic for trained physicists, but for me, working in the physics’ peripheral area, I feel as if the theory seems to have no solid foundation for understanding.

This work summarizes my effort at trying to understand some of such quantum mysteries. I show what I believe is the possible explanation of some of the mysteries, at least, to myself. The interpretation that was convincing to me may not appear acceptable for everyone. Yet I believe that the explanation, of which I struggled to convince myself, has some seed of truth in it. This work is a follow-up of what I published in the two previous books, Dynamics of Digital Excitation, published by Kluwer Academic in 1997, and in the last chapter, Sense of mystery, in Self-Consciousness, Human Brain as Data Processor, published by iUniverse in 2020. The first book was purely on electronics and physics, but the second book dealt with psychology, in which I used quantum phenomena as an example of mysteries of the human mind, and I tried to combat the now popular belief that human self-consciousness is a quantum phenomenon, which I believe is entirely wrong.

I approach the quantum mysteries from viewpoints that differ from those found in the authoritative textbooks. In my work, I am well aware that the boundary between rigorous logical theory and rational analogy is not clear. In spite of that, I try to present as many comprehensible explanations as possible by creating models of quantum phenomena, so that the basic laws of nature do not remain as mysterious as they are now. To do so, I adopt different viewpoints about the origin of quantum mechanical phenomena.

First, I do not repeat the origin of quantum particles and forces to the phase transition of the early universe. Instead, I consider that the present quantum laws retain features that emerged at various developmental phases of the early universe, starting from the point singularity. As the universe’s size increased, some basic features remained, but various new features emerged, added to the older features, and remained to the present. In effect, I introduce a historical viewpoint in the quantum physics laws. As such, what appear to be the simplest and the most mysterious features of quantum mechanics are the most archaic.

The second viewpoint is a search for the models of quantum phenomena that emerged during the various phases of the universe’s early development within the classical and the elementary quantum physics domain. Wave mechanical representation of a particle’s probability and quantization of parameters are the two basic features of quantum mechanics. In the classical domain, there are models that accommodate these two features. They are the equivalent circuit models in modern electronics. The analog and digital equivalent circuit models reflect the various developmental stages of the universe.

So I sought for various equivalent circuit models suitable to explain mysterious quantum phenomena. Following the historical development of the quantum laws, I developed the proper equivalent circuit models representing the development of the universe. Yet I needed to expand the concept of the basic equivalent circuit models including various exotic modes of operations such as self-altering circuits. This is perhaps the most unique feature of my work; this idea emerged from my background as electronic circuit theorist and systems engineer in my active profession.

There is another interesting feature of my model-based approach, which is one basic reason of my present equivalent circuit–based work. Some strange qualitative features of quantum world emerged from the model I introduced in this book, based on the simple assumptions I made. To reach the same conclusion, the standard model-less quantum theory must go through complex or unusual mathematics. This is the reason why I have been fascinated by this work. The first concerns the two kinds of elementary particles, fermion and boson, that are derived in the standard quantum mechanics textbooks from a curious algebra of symmetrized and anti-symmetrized wave functions. The second is that particles’ internal symmetry conversion (fermion versus boson) makes fermions move in space. The third is the explanation of the mechanism of an elementary particle’s spin, that also emerges from the model, without going through relativistic mathematics. The fourth is a simple explanation of the mysterious phenomenon of quantum entanglement. These are the reasons why I have labored to refine the crude original idea of quantum mechanics I published before. I believe that quantum physics can be reformulated on some kind of models, as classical physics has been. Physics must be a model-based science.

The third viewpoint is that I reexamined the original concept of atoms from the Greek philosophers, that elementary particles are the final products of splitting a macroscopic object to the limit. The splitting is not limited to materials but includes information. By splitting the minimum information, one bit, I get probability, whose segments distributed over space and time develop quantum phenomena. The probability segments behave like diffusing particles, and they follow the semiclassical laws of diffusion, subject to proper generalization and reinterpretation.

The effort of trying to make models of quantum effects is not the mainstream activity of quantum research at present. Indeed, I admit that such a work is considered as a heresy in the mainstream of modern physics. I dare to step into this unpopular territory by my own idle yet genuine curiosity. The quantum world is filled with mysteries. Any mystery is a burden, and also is a challenge to the human mind. Explanation by a model of any mysterious phenomenon removes the mind’s stresses. The human mind deals with the world that works basically according to classical physics. Any feature of explanation that appeals to the human mind must satisfy this basic character of the human mind. Then, the model must be understood by human mind in terms of its classical physics features. What are the differences between quantum and classical physics features? Here I need to think over the quantum mysteries from psychological viewpoints. Psychologically, the boundary between the classical and the quantum features is not so clear as has been believed, especially if the difference is observed from the science of human mind, psychology. There are many quantum phenomena in the classical physics domain.

This book primarily deals with the subjects in the boundary region between the quantum physics and the emerging new area of digital electronic circuit theory. I expect that not many readers are familiar to the both areas. I did not have an easy choice in the writing style. I had a choice to explain every basic concept in elementary details, but after excruciating struggle in my mind, I decided to make the text as compact as possible, so that readers can skim the basic idea without going too much into technical details. I must expect that readers have some background in the both areas, especially in electronic circuit theory and in elementary quantum mechanics—for instance, college students majoring in electronics engineering whose minor is physics. I expect that there are many students of this kind. My hope is that readers understand my intention. I hope that they get the basic message, that models of quantum mechanics can actually be built by using the electronic equivalent circuit model. Relying on the model, there are really not so many mysteries in the elementary quantum world. This is the basic message of this book.

This work is a continuation and summary of my two previous works referenced above. I owe a lot to my wife Marika, a psychologist, who helped during the time of this research through encouragement and support to dig into this unpopular yet unexplored boundary region between physics, electronics, and psychology.

1

PROBABILITY IN THE QUANTUM WORLD

1.01 Introduction

In quantum physics, definite physical parameters are displaced by probabilities. Why does this feature emerge? The basic approach of any natural science is reductionism; that is, splitting any complex object into its components, working with the simplified components, and then assembling the gained information to the comprehensible original object’s attributes.

This approach reaches the limit when the object becomes the elementary particle that cannot be physically split anymore. Such an object is characterized by its unique parameters of mass, energy, momentum, and several universal characters, such as charge, spin, color, etc. To study the nature of elementary particles, some of the parameters must be further split, not physically but conceptually, into the components making them up. Here the concept of probability emerges. The physically undividable particle’s parameters are conceptually divided into probabilities distributed over space and time; their relations and development are mathematically analyzed, and then assembled to understand the nature of the object. Here, division of the parameters and their assembly of the physically meaningful form are the two basic processes.

When any physical object is split into the level of elementary particles, the parameters are specified by several binary numbers, by using the actually measured parameter values as the unit. Electron mass is 1 bit, that is physically 9.11x10-31 kg in the conventional unit. Similarly the electronic charge is 1.60x10-19 coulomb, and the spin is 0.53x10-34 joule-sec. When these quantities are actually measured, the magnitude is represented in the theory by the basic unit’s integral multiples. Then, no real fractional mass, spin, or charge is considered. Some such binary parameters are instead distributed probabilistically over space and time. This is what I call splitting of the basic information. The probability is not measurable by a single observation. The theory and experiment become only statistically comparable. What we measure are the statistical expectation values of the parameters.

This feature suggests that the transition from definite classical parameters to probabilities is the