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Introduction to Dynamical Wave Function Collapse

Realism in Quantum Physics: Volume 1
Philip Pearle(Autor*in)
Oxford University Press
Erschienen am 15. Januar 2024
224 Seiten
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Quantum theory (QT) is the best, most useful physics theory ever invented. For example, ubiquitous are cell phones, laser scanners, medical imagers, all inventions depending on QT. However, there is something deeply wrong with QT. It describes the probabilities of what happens, but it does not give a description of what actually happens. Most (but not all) physicists are not worried about this flaw, the probabilities are good enough for them. Other physicists, the author included, believe that is not good enough. The purpose of physics is to describe reality. To not do so is to abandon 'the great enterprise' (John Bell). This book shows one way to alter QT so that the new theory does describe what actually happens. This theory, created over three decades ago, has been called the 'Continuous Spontaneous Localization' (CSL) theory. Many experiments over this period have tested CSL, and so far it is neither confirmed nor refuted. This book shows how CSL works, and discusses its consequences. Ideal for academic students, graduates and practising scientists and physicists seeking a deeper understanding of the quantum realm, this book provides accessible explanations and sheds light on the interplay between probability and reality in the realm of quantum theory.
Sprache
Englisch
Verlagsort
Oxford
Großbritannien
ISBN-13
978-0-19-890138-9 (9780198901389)
Schlagworte
Schweitzer Klassifikation
DNB DDC Sachgruppen
Dewey Decimal Classfication (DDC)
BISAC Klassifikation
Professor Philip Pearle was born and grew up in New York City. He graduated from the Bronx High School of Science in 1953, and then attended MIT. He studied Electrical Engineering and obtained his BS in 1957 and MS in 1958 in a cooperative program with Bell Labs. He then entered the MIT PhD program in Physics in 1959, and graduated in 1963. He taught at Harvard between 1963 and 1966, at Case Institute of Technology from 1966 to 1969 and at Hamilton College from 1969 until 2002. As an undergraduate, he became interested in the foundations of Quantum Theory when taking his junior quantum physics course using David Bohm's textbook. He delved into particle physics at first but then followed a compulsion to delve into Foundations later. He was encouraged to do so at Harvard by Wendell Furry, at Case by Leslie Foldy, and in his first years at Hamilton College by Fred Belinfante and Roger Penrose.
  • Cover
  • Title
  • Copyrighrt Page
  • Dedication
  • Acknowledgements
  • Preface
  • Contents
  • 1 Introduction
  • 1.1 The abrupt change by measurement . . . is the most interesting point of the entire theory.
  • 1.2 Guessing a Law of Nature
  • 1.3 Four Remarks
  • 1.3.1 Supplement
  • 1.3.2 A Single SchrLodinger Equation
  • 1.3.3 Interpretational Remarks
  • 1.3.4 Constraints on the Theory
  • 1.4 Requirements on State Vector Dynamics
  • 1.5 Gambler's Ruin Game
  • 1.6 Synopsis
  • 2 Continuous Spontaneous Localization (CSL) Theory
  • 2.1 The Two Equations of CSL
  • 2.1.1 How CSL Works
  • 2.2 CSL Density Matrix
  • 2.3 Evolution Equation for the CSL Density Matrix
  • 2.4 True Collapse and False Collapse
  • 3 CSL Theory Re nements
  • 3.1 Collapse Equations with White Noise
  • 3.2 Including the Hamiltonian: Time{Ordering
  • 3.3 The Density Matrix and Its Evolution Equation
  • 3.4 The CSL Modi ed Schr odinger Equation
  • 3.5 Interregnum: Free Particle Example
  • 3.5.1 Free Particle Wave Function
  • 3.6 Adding More Collapse{Generating Operators
  • 3.7 Replacing Ai by A(x)
  • 4 Non--Relativistic CSL
  • 4.1 Choosing A(x)
  • 4.2 The Two Equations De ning Non-Relativistic CSL
  • 4.3 Density Matrix Evolution Equation for Non-Relativistic CSL
  • 4.3.1 Approximate Density Matrix Evolution Equation for Nucleons
  • 4.4 Collapse of a Superposition of an Object in Two Spatially Separated States
  • 4.4.1 Collapse of a Superposition of a Nucleon in Two SpatiallySeparated States
  • 4.4.2 Collapse of a Superposition of an Extended Object in TwoSpatially Separated States
  • 4.4.3 Lindblad Equation in Terms of Position Operators
  • 4.5 Mean Energy Increase
  • 5 Spontaneous Localization (SL) Theory
  • 5.1 General Structure of SL
  • 5.1.1 Two-State Collapse Example
  • 5.2 SL Density Matrix
  • 5.3 Non-Relativistic SL
  • 5.4 Non-Relativistic SL Density Matrix
  • 5.5 Values of and a
  • 6 Some Experiments Testing CSL
  • 6.1 Theoretical Constraint on the Parameters by Collapse of a Superposition
  • 6.2 Mass Dependence of the Collapse Rate
  • 6.2.1 Excitation of Bound States: General Analysis
  • 6.2.2 Electron Excitation: Spontaneous Radiation in Germanium
  • 6.2.3 Nuclear Excitation: Dissociation of Deuterium
  • 6.3 Gravity?
  • 6.4 Special Relativity?
  • 6.5 Motion of an Isolated Object
  • 6.6 Heating
  • 6.6.1 Temperature Increase of a Large (Dimensions && a) Object
  • 6.6.2 Heating of a Bose{Einstein Condensate
  • 6.7 Spontaneous Radiation of a Free Charged Particle
  • 6.8 Interference
  • 6.8.1 Concluding Comment
  • 7 Interpretational Remarks
  • 7.1 Stu
  • 7.2 Particle Number Stu
  • 7.3 Observability
  • 7.4 Stu for a Macroscopic Object
  • 7.5 Observability of a Pointer during a Measurement
  • 7.5.1 Evolution with No Collapse
  • 7.5.2 Evolution with CSL Collapse
  • 7.6 Tail
  • 7.7 Concluding Remarks
  • 8 Supplement to Chapter 1
  • 8.1 Gambler's Ruin Criteria Expressed as Ensemble Averages
  • 8.1.1 Average Statements Lead to Individual Consequences
  • 8.2 Fair Game Considerations
  • 9 Supplement to Chapter 2
  • 9.1 How CSL Works: Collapse to Position Eigenstates
  • 10 Supplement to Chapter 3
  • 10.1 Particle in One Dimension, Position Collapse
  • 10.1.1 Solution for A(t)
  • 10.1.2 Solution for B(t)
  • 10.1.3 Probability Rule
  • 10.1.4 Proof thatRDwP(w) = 1
  • 10.1.5 Introducing a New White Noise v(t)
  • 10.1.6 Free Particle: Mean Position Behavior
  • 10.1.7 Free Particle: Mean Momentum Behavior
  • 10.1.8 Free Particle: Mean Energy Behavior
  • 10.2 Free Particle Density Matrix
  • 10.2.1 Getting Moments from the Lindblad Equation
  • 10.2.2 Free Particle Density Matrix
  • 10.2.3 Density Matrix at Small and Large Times
  • 10.3 Harmonic Oscillator Problem
  • 11 Supplement to Chapter 4
  • 11.1 Mean Energy Increase of an Object
  • 11.1.1 Some Useful Quantum Fields
  • 11.1.2 Mean Energy Increase
  • 11.2 Galilean Invariance of Non{Relativistic CSL
  • 11.2.1 Time{Translation Invariance
  • 11.2.2 Space{Translation Invariance
  • 11.2.3 Boost Invariance
  • 12 Supplement to Chapter 5
  • 13 Supplement to Chapter 6
  • 13.1 Electron Excitation: Spontaneous Radiation in Germanium
  • 13.2 A Relativistic CSL Model
  • 13.3 Random Walk of an Extended Object in CSL
  • 13.4 Decay of Particle Number in a Bose{Einstein Condensate
  • 13.4.1 Lindblad Equation for Identical Atoms
  • 13.4.2 Creation and Annihilation Operators for One Particle EnergyEigenstates
  • 13.4.3 Decay of Atoms from the BEC
  • 14 Supplement to Chapter 7
  • 14.1 Observable Reality for an Electron in the Ground State of Hydrogen
  • 14.2 Observable Reality for a Particle Undergoing Two-Slit Interference
  • 14.3 Photon Number Operator
  • 15 A Stochastic Di erential Equation Cookbook
  • 15.1 SDE Cookbook Ingredients
  • 15.2 Recipe
  • 15.3 Examples
  • 15.3.1 Example 1
  • 15.3.2 Example 2
  • 15.3.3 Example 3: Langevin Equation
  • 15.4 Plan for the rest of this Supplement
  • 15.5 Fokker_Planck Equation
  • 15.6 It^o Chain Rule
  • 15.7 It^o Product Rule
  • 15.8 It^o and Stratonovich Integrals
  • 15.8.1 Riemann Integral
  • 15.8.2 An ^Ito Integral Compared to a Stratonovich Integral
  • 15.8.3 Stratonovich Integral and the It^o Correction Term
  • 15.9 Stratonovich Calculus
  • 15.9.1 Stratonovich Chain Rule
  • 15.9.2 Consequences of the Stratonovich Chain Rule
  • 15.10 Conclusion
  • 15.11 More than One Variable, One Brownian Function
  • 15.12 One Variable, More than One Brownian Function
  • 15.13 More than One Variable, More than One Brownian Function
  • 16 CSL Expressed as a Schr odinger Stochastic DE
  • 16.1 Stratonovich Schr odinger Equation
  • 16.2 It^o Schr odinger Equation
  • 16.3 Density Matrix Evolution Equation
  • 16.4 Non--relativistic CSL
  • 17 Applying the CSL Stratonovich Equation to the Free Particle Undergoing Collapse in Position
  • 18 Applying the CSL Stratonovich Equation to the Harmonic Oscillator Undergoing Collapse in Position
  • Appendix A Gaussians
  • Appendix B Random Walk
  • B.1 Limit of Random Walk
  • Appendix C Brownian Motion/Wiener Process
  • Appendix D White Noise
  • D.1 Frequency Spectrum of the White Noise Function
  • Appendix E White Noise Field
  • Appendix F Density Matrix
  • F.1 The Trace Operation
  • F.2 Properties of the Density Matrix
  • F.3 Partial Trace
  • F.4 The Lindblad Equation
  • Appendix G Theoretical Constraint Calculations
  • References
  • Index

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