# «Title of Document: QUANTUM MECHANICS AND QUANTUM INFORMATION THEORY Wesley William Van Camp, Doctor of Philosophy, 2009 Directed By: Distinguished ...»

## ABSTRACT

Title of Document: QUANTUM MECHANICS AND QUANTUM

## INFORMATION THEORY

Wesley William Van Camp, Doctor of

Philosophy, 2009

Directed By: Distinguished University Professor and Chair of

the Committee for Philosophy and the Sciences,

Jeffrey Bub, Department of Philosophy

The principle aim of this dissertation is to investigate the philosophical application of quantum information theory to interpretational issues regarding the theory of quantum mechanics. Recently, quantum information theory has emerged as a potential source for such an interpretation. The main question with which this dissertation will be concerned is whether or not an information-theoretic interpretation can serve as a conceptually acceptable interpretation of quantum mechanics. It will be argued that some of the more obvious approaches – that quantum information theory shows us that ultimately the world is made of information, and quantum Bayesianism – fail as philosophical interpretations of quantum mechanics. However, the informationtheoretic approach of Clifton, Bub, and Halvorson introduces Einstein’s distinction between principle theories and constructive theories, arguing that quantum mechanics is best understood as an information-theoretic principle theory. While I argue that this particular approach fails, it does offer a viable new philosophical role for information theory. Specifically, an investigation of interpretationally successful principle theories such as Newtonian mechanics, special relativity, and general relativity, shows that the particular principles employed are necessary as constitutive elements of a framework which partially defines the basic explanatory concepts of space, time, and motion. Without such constitutive principles as preconditions for empirical meaning, scientific progress is hampered. It is argued that the philosophical issues in quantum mechanics stem from an analogous conceptual crisis. On the basis of this comparison, the best strategy for resolving these problems is to apply a similar sort of conceptual analysis to quantum mechanics so as to provide an appropriate set of constitutive principles clarifying the conceptual issues at stake. It is further argued that quantum information theory is ideally placed as a novel conceptual framework from which to conduct this analysis.

## QUANTUM MECHANICS AND QUANTUM INFORMATION THEORY

By Wesley William Van Camp Dissertation submitted to the Faculty of the Graduate School of the University of Maryland, College Park**Advisory Committee:**

Distinguished University Professor Jeffrey Bub, Chair Associate Professor Allen Stairs Associate Professor Mathias Frisch Associate Professor Michael D. Silberstein Professor Don Perlis © Copyright by Wesley William Van Camp Preface To a very large extent, this manuscript mirrors the course of my actual thinking on these matters. When I first arrived in graduate school I was not familiar with the subject of information theory, let alone quantum information theory.

Therefore, not knowing the subject my dissertation, this seemed an intriguing area of research – new, exiting, promising. Quantum information theory seemed to me to be philosophically promising because much of its successes draw from those aspects of quantum mechanics which had been puzzled over by physicists and philosophers since day one. It did not question these oddities; it embraced them, and got results. It was exiting because the approach in the foundations of physics, seemed to make the claim that physics, at least quantum physics, was “about information”. I did not know what this meant, I am not sure I do still, but it is enticing. It lends itself to at least two obvious interpretations. One, classical mechanics is about particles, waves, and motion, and this seemed to have real ontological significance. Classical mechanics is about describing the things out there in the world. So if quantum mechanics was about information, then by analogy, information must have some sort of ontological significance. Rather than a world made up of particles and waves, it is a world made up of information. Very sci-fi. Two, if quantum mechanics is about information, then it is about our knowledge. So the theory of quantum mechanics tells us simply about what we know and that some of our most fundamental physics is inherently reflexive in some way.

Neither of these approaches felt particularly satisfactory to me. The first hardly coherent, the second just a refrain on instrumental interpretations of quantum

make it any more realist. So I spent some time analyzing why these approaches are not promising. But then the question becomes, what good does quantum information do us regarding the fundamentals? Is it simply an alternate mathematical structure which does not shed any new light on interpretational issues?

Here, Clifton, Bub, and Halvorson (CBH, 2003) provide a third way, though it was only discussed briefly. The idea was that information-theoretic principles could be provided from which the general features of quantum mechanics could be derived.

This, in turn, could mean that there is a principle theory of quantum mechanics, just as there is for relativity theory. But for me, this also raises questions: is, in fact, a principle theory, ipso facto, interpretationally preferable, and if so, why, and why does this now make quantum information theory important (there could be principle theories without quantum information-theoretic principles)? This is where most of my investigation lies. What makes a principle theory valuable? And does that apply in the case of quantum mechanics? And is quantum information theory the right approach?

I was skeptical that in virtue being a principle theory, there was automatically, so to speak, some interpretational groundwork done or swept aside. Einstein did formulate relativity theory as a principle theory, but he also took thermodynamics to be a paradigm example of a principle theory. The final verdict is perhaps not yet in, but it seems to be far from obvious that thermodynamics is a more fundamental theory than statistical mechanics, which many take to underlie thermodynamic phenomena. The lesson is that being a principle theory is not, in itself, enough.

better able to understand the role principle theories play in foundational physics and be more precise about what qualities make them foundational via historical examples.

There are times and instances where principle theories can play this role, indeed, must play this role. The next question then is: is now such a time and is quantum mechanics such an instance? I conclude that yes, it is. So is quantum information theory the place to get such principle from? Perhaps. There is nothing prima facie intrinsically special about quantum information theory; however, it is perhaps the only place which is in fact offering plausible constitutive principles. Other avenues in quantum mechanics, I contend, unless drastically reformulated, cannot play the role which is necessary. So I see myself as pursuing the quantum information-theoretic approach to see how it could work. In the end, I think that it can if applied in the right manner. In particular, the CBH approach hit on something important regarding quantum mechanics and the potential for approaching it as a principle theory using information theory. But more work needs to be done.

First of all I would like to acknowledge the role played by my dissertation advisor Jeff Bub, having first sparked my interest in quantum information theory and for all of the help with the document and clearing up some of my own confusions. I would also like to thank all of the members of my committee Allen Stairs, Mathias Frisch, Michael Silberstein, and Don Perlis.

I would also like to acknowledge and express my gratitude for the support over the years from my family – my father, my brother, and sister, and my mother.

And of course I need to thank my wife Debbie for her love, encouragement, and partnership in this journey.

Preface

Dedication

Acknowledgements

Table of Contents

Chapter 1: Introduction

Chapter 2: Quantum Information

2.1. Introduction

2.2. There’s Information, and then there’s Information

2.3. “All things physical are information-theoretic in origin.”

2.4. Quantum Bayesianism

2.4.1. The View

2.4.2. Critique

2.4.3. Walks Like, Swims Like, Quacks Like

Chapter 3: Principle Theories and Constructive Theories

3.1. Introduction

3.2. Informational Constraints as Principles of Quantum Mechanics

3.3. Principle and Constructive Theories

3.3.1. Introduction

3.3.2. Laying Some Groundwork

3.3.3. Einstein’s Use of the Distinction

3.3.4. Framework vs. Interaction

3.3.5. Theoretical Pluralism

3.3.6. The Role of Explanation

3.4. Some Words on Constructive Quantum Mechanics

3.5. Conclusions

Chapter 4: Constitutive Principles

4.1. Introduction

4.2. Historical Development

4.2.1. The Kantian Origin of the Constitutive Role of Principles in Science..... 94 4.2.2. Logical Positivism and Constitutivity

4.2.2. Summary

4.3. Conceptual Foundations

4.3.1. Galileo

4.3.2. Newton

4.3.3. Einstein

4.4. Analysis

4.4.1. Holism

4.4.2. Unification and Explanation

4.5. Conclusion

Chapter 5: Bub and Pitowsky

5.1. Introduction

5.2. Bub and Pitowsky’s Overall Picture

vii 5.2.1. Layout: Two Dogmas; Two Problems

5.2.2. Treatment

5.3. Understanding Special Relativity

5.3.2. Janssen’s Argument

5.3.3. Critique

5.4. Return to Quantum Mechanics

5.4.1. On the Issue of Realism

5.4.2. Principles and Kinematics

5.4.3. Unification and the Nature of the Problem

5.5. Conclusions

Chapter 6: Where do we go from here?

Appendix: The holographic principle - briefly

Bibliography

The principle aim of this dissertation is to investigate the philosophical application of quantum information theory to interpretational issues regarding the theory of quantum mechanics. Recently, quantum information theory has emerged as a potential source for such an interpretation. The main question with which this dissertation will be concerned is whether or not an information-theoretic interpretation can serve as a conceptually acceptable interpretation of quantum mechanics.

Since its formalization in the 1920’s, quantum mechanics has been resistant to any sort of universally accepted “interpretation”. One need only look to the current philosophical literature on quantum mechanics to verify this. Moreover, such an interpretation has seemed necessary due to the particular nature of quantum mechanics and its results, which seem to contradict both classical physical theories and commonsense physical experience. As a result, throughout the years, many interpretations of quantum mechanics have been formulated, all of which try to make sense of these quantum puzzles in various ways. Part of the project is to analyze what counts as a successful interpretation of a physical theory.

Apart from quantum mechanics, the 20th century saw the advent of another successful theory, the theory of relativity. While this theory brings with it startling results from the standpoint of previous physical theories, it is generally acknowledged that it does not necessitate the kind of further interpretation for which quantum mechanics begs. Quantum mechanics is at least as successful as relativity theory in terms of making accurate predictions about the physical world to which it applies.