The Quantum Nature of Things

How Counting Leads to the Quantum World

T R Robinson

• Publisher: CRC Press
• Year: 2023
• Print ISBN: 9781032455464
• eBook ISBN: 9781000861648
• Edition: 1
• Topic: Technology & Engineering
• Subtopic: Applied Mathematics
• Index: Technology & Engineering

This book offers readers an entirely original and unconventional view of quantum mechanics. It is a view that accepts quantum mechanics as the natural way to think about the way nature works, rather than the view commonly expressed, especially in books on quantum physics, that quantum theory is weird and counterintuitive. It is based on the concept of itemization.

From this simple premise, quantities like energy and momentum, both linear and angular emerge naturally, as do configuration space, potentials, the electromagnetic field, many-body dynamics, special relativity and relativistic wave mechanics. The many-body dynamics, because it is not tied to physics from the outset, can be applied to population dynamics outside physics as well as the usual physical situations.

From this emerges much of the basic physics that describes, mathematically, how the natural world behaves.

This accessible introduction does not require exotic maths, and is aimed at inquisitive physics students and professionals who are interested in exploring unconventional approaches to physics. It may also be of interest to anyone studying quantum information theory or quantum computing.

Key Features

• Provides a unique, new approach to understanding quantum mechanics.

• Uses basic concepts and mathematical methods accessible at the undergraduate level.

• Presents applications outside physics, including a newly devised and original model of cell division that shows how cancer-cell population explosions occur.

"What [the author] has done is changed the way of thinking about how to organize the foundations of quantum mechanics and the approach is a very natural one. This is a book that has the potential to be quite an important one in how we understand the origins of the quantum theory.
This is not an ordinary quantum textbook. It is not trying to teach the full curriculum. It is instead focused on showing the origins of quantum mechanics and how it fits into the relativistic and quantum field theory worlds. It is more in line with foundations of quantum mechanics books, but in my opinion, way better than the whole lot of the rest of them. There is no comparison."
— Professor James Freericks, Georgetown University.

Table of contents

• Cover Page
• Half-Title Page
• Title Page
• Copyright Page
• Dedication Page
• Contents
• Preface
• Acknowledgments
• Prologue
• Chapter 1 The universal quantum hypothesis: Just items
• Chapter 2 An introduction to operators
• Chapter 3 Natural number dynamics I: The basic formulation
• Chapter 4 Multi-category systems: Bosons and fermions
• Chapter 5 The single-category system: The emergence of quantum mechanics
• Chapter 6 Two-category systems
• Chapter 7 Degenerate Two-category Systems
• Chapter 8 Degenerate three-category systems
• Chapter 9 Interactions in multi-category systems
• Chapter 10 Field itemization
• Chapter 11 Phase invariance: The emergence of space-time and wave mechanics
• Chapter 12 Natural number dynamics II: Time-dependent population models
• Chapter 13 Epilogue
• Appendix A Peano axioms
• Appendix B Virial theorem and discrete energy levels
• Appendix C Wave kinematics
• Appendix D Lie groups
• Appendix E Differential operators
• Appendix F Calculus without limits
• Appendix G Mean-field approximation
• Appendix H Legendre transformation
• Bibliography
• Index