Energy and Momentum Conservation in Bohm's Model for Quantum Mechanics

Bryan Hall - Ph.D. Thesis

University of Western Sydney - 2004

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Supervisor & Examiners

I would most sincerely like to thank Dr Rod Sutherland for his continual guidance and suggestions, as well as his careful checking of the text of this thesis.

I would also like to thank the examiners for their work in preparing reports and suggesting various minor amendments to the thesis. The examiners made the following favourable comments:

Dr Sheldon Goldstein:

"This thesis is a very nice piece of work. It is written with exceptional clarity and facility of expression, and marks a significant contribution to the field."

Dr David Miller:

"The problem with Bohmian mechanics addressed by the thesis concerns energy and momentum conservation and is therefore fundamental. It is timely and important that the problem be addressed. The work in the thesis provides a solution to the problem and therefore makes a significant and original contribution to the discipline."

Dr Craig Callender:

"I recommend that the degree be awarded. Any errors I found were unimportant ones. My overall impression is that this dissertation is a very fine work in the foundations of physics."

Bryan Hall

Abstract

Bohm's model for quantum mechanics is examined and a well-known drawback of the model is considered, namely the fact that the model does not conserve energy and momentum. It is shown that the Lagrangian formalism and the use of energy-momentum tensors provide a way of addressing this non-conservation aspect once the model is considered from the point of view of an interacting particle-field system. The full mathematical formulation that is then presented demonstrates that conservation can be reintroduced without disrupting the present agreement of Bohm's model with experiment.

Contents

All these files are in Adobe PDF format

• Title & Abstract
• Chapter 1: Introduction
• Chapter 2: Interpretations of Quantum Mechanics & the Measurement Problem
• Chapter 3: Bohm's Model
• Chapter 4: Lagrangian Formalism
• Chapter 5: A Lagrangian Formulation of Bohms Model
• Chapter 6: Energy-Momentum Tensors
• Chapter 7: Relativistic Treatment
• Chapter 8: Non-Relativistic Limit
• Chapter 9: Discussion and Conclusions
• Appendix 1: Non Locality
• Appendix 2: Velocity Expression corresponding to the Modified Schrodinger Equation
• Appendix 3: Rate of Change of a Particle's Energy in a Scalar Field
• Appendix 4: Schrodinger Energy-Momentum Tensor
• Appendix 5: Conservation Difficulty with the Schrodinger Energy-Momentum Tensor
• Appendix 6: Viability of a Scalar Potential Description with de Broglie's Relativistic Model
• Appendix 7: Relativistic Equation of Motion
• Appendix 8: Modified Klein-Gordon Equation
• Bibliography

This thesis is archived with the Australian Digital Theses Program
http://library.uws.edu.au/adt-NUWS/public/adt-NUWS20040507.155043/index.html