Models of the World, Data-models and the Practice of Science: The Semantics of Quantum Theory Mauricio Suarez London School of Economics and Political Science Thesis submitted for the degree of Doctor of Philosophy of London University August 1997 UMI Number: U615429 All rights reserved INFORMATION TO ALL USERS The quality of this reproduction is dependent upon the quality of the copy submitted. In the unlikely event that the author did not send a complete manuscript and there are missing pages, these will be noted. Also, if material had to be removed, a note will indicate the deletion. Dissertation Publishing UMI U615429 Published by ProQuest LLC 2014. Copyright in the Dissertation held by the Author. Microform Edition © ProQuest LLC. All rights reserved. This work is protected against unauthorized copying under Title 17, United States Code. ProQuest LLC 789 East Eisenhower Parkway P.O. Box 1346 Ann Arbor, Ml 48106-1346 I hhz'S ci S F Gl ]5 A bstract The most important problems in the philosophy of quantum mechanics are the problem of measurement and the problem of the ‘acausal’ EPR correlations. It is commonly thought that these problems call for a new interpretation of the quantum theory. I argue that it is possible to construe both problems rather differently, as resulting from a mistaken understanding of scientific theory-application. It then becomes possible to tackle both problems independently of questions of interpretation, by attending carefully to what constitutes a successful application of a scientific theory, and of the quantum theory in particular. In the first part of the Thesis, I argue against a standard conception of scientific theory-application. This standard conception, which is often presupposed in the philosophical discussions of quantum mechanics, takes the applications of a scientific theory to constitute its domain of empirical adequacy. I argue that, on the contrary, a scientific theory can be applied to phenomena that it does not subsume. I present a case study in the history of superconductivity to illustrate and to motivate this claim. In the second part, I argue that the problem of measurement can be construed as the impossibility of applying the quantum theory to measure­ ment interactions. I then argue that Arthur Fine’s proposed solution to the measurement problem implicitly abandons the standard conception of application. Finally I look at quantum correlation phenomena. Bas Van Fraassen has claimed that the EPR correlations fit no causal model. The correctness of this claim depends on what probabilistic constraints a causal model is taken to have to satisfy. I argue, following Nancy Cartwright, that Van Fraassen’s constraints on common-cause models are too strong; and I describe a direct-cause model that, I urge, constitutes a successful applica­ tion of the quantum theory to the EPR correlations. Contents 0.1 Introduction ................................................................................... 4 0.2 Acknowledgements ....................................................................... 6 I Scientific Application and Empirical Adequacy 9 1 Mediating Models, Superconductivity and Realism 10 1.1 Models as M ediators .................................................................... 10 1.1.1 Features of Mediating Models ........................................ 11 1.1.2 Mediating Models in the Philosophy of Science .... 14 1.2 The Idealization Account of Application .................................. 16 1.2.1 Forms of Idealization ....................................................... 16 1.2.2 Idealization and Scientific R ealism .............................. 20 1.3 The Role of Models in Theory-Application ...................................24 1.3.1 Problems with Idealization ........................................... 25 1.3.2 The Problem of Material Abstraction ........................ 29 1.4 How Models Mediate: The Case of Superconductivity .... 34 1.4.1 The Hallmarks of Superconductivity ........................... 36 1.4.2 Applying Electromagnetism ........................................... 38 1.4.3 Enter the M o d e l ............................................................. 40 1.4.4 The Role of the Theoretical C o n tex t ............................... 45 1.5 Application in Practice: Problems for Realism ........................ 52 1.5.1 The Epistemology of Theory-Application ................... 53 1.5.2 Conclusions ...................................................................... 57 1 1.6 Summary ...................................................................................... 58 2 The Semantic View: Empirical Adequacy, Truth and Appli­ cation 59 2.1 To Save the Phenom ena ............................................................. 59 2.2 The Nature of Scientific T heories .............................................. 64 2.2.1 The Syntactic Conception .............................................. 64 2.2.2 Critique of the Syntactic Conception ............................ 66 2.2.3 The Semantic Conception .............................................. 70 2.3 Empirical Adequacy in the Semantic Conception .................... 75 2.3.1 Van Fraassen’s Embedding ........................................... 75 2.3.2 Friedman’s Model-Submodel R ed u ctio n ..................... 80 2.4 The Empirical Basis of S cien ce ................................................. 85 2.4.1 Models of D a ta ................................................................. 86 2.4.2 The Empirical Basis: Data or P henom ena? ............... 88 2.5 The Application of Scientific T h e o rie s ..................................... 95 2.5.1 Revisiting the London A ccount ..................................... 95 2.5.2 Instrumental R eliability ................................................. 99 2.6 S u m m ary ........................................................................................ 103 II Application in the Foundations of Quantum Theory 105 3 Quantum Theory of Measurement 106 3.1 The Problem of Measurement ...................................................... 106 3.1.1 The Measurement Problem for Pure S ta te s ..................107 3.1.2 The Ignorance Interpretation of M ixtures .....................109 3.1.3 Conditions on Measurement Interactions ........................113 3.1.4 The Insolubility P ro o f .......................................................118 3.2 The Modal Interpretation and Its Problems ............................... 120 3.2.1 The Kochen-Heaiey-Dieks Modal Interpretation .... 121 3.2.2 Albert and Loewer’s Criticism .......................................125 3.2.3 Non-ideal Measurements ................................................... 127 2 3.2.4 The Ignorance Interpretation of Reduced States .... 131 3.2.5 Conclusions ......................................................................... 134 3.3 Measurement and Application ........................................................136 3.3.1 Selective Interactions ..........................................................136 3.3.2 Ignorance, and State-descriptions .................................... 140 3.3.3 Equivalence Classes as Physical A spects ........................ 144 3.4 S u m m ary ..........................................................................................148 3.5 Appendix 1: Basic Principles of Quantum Theory ...................... 148 3.6 Appendix 2: Mixed States and Statistical O p erato rs ................ 152 3.7 Appendix 3: The Interaction Formalism ......................................153 3.8 Appendix 4: A Lemma for Reduced States .................................. 155 4 Quantum Causation 157 4.1 Quantum Correlation Phenomena ..................................................157 4.1.1 The Einstein-Podolsky-Rosen Correlations ..................... 158 4.1.2 Bell’s Result ......................................................................161 4.1.3 Factorizability ...................................................................164 4.2 The Principle of the Common Cause ........................................... 166 4.2.1 Reichenbach’s Formal Conditions .................................... 168 4.2.2 Van Fraassen against Causal Realism ........................... 172 4.2.3 Causation in a Probabilistic W o rld ................................. 175 4.2.4 The Empirical Adequacy of Causal Theories .................. 184 4.3 Direct-Cause Models for EPR correlations ..................................186 4.3.1 Peaceful Coexistence ..........................................................187 4.3.2 The Relativistic Argument Rebutted .............................. 189 4.3.3 A Quantum Mechanical M o d e l........................................195 4.4 S u m m ary .........................................................................................200 3 0.1 Introduction It is often assumed that the domain of empirical adequacy of a scientific theory is constituted by all of the theory’s applications. This assumption has its simplicity in its favour, but it also occassionally yields some seem­ ingly counterintuitive results. Quantum theory, for instance, would be in a dramatically much better shape than the general theory of relativity: the ap­ plications of quantum theory are many, diverse and widely accessible; those of general relativity are few, and highly remote. Thus, quantum theory should be much better confirmed than general relativity -and yet, scientists seem generally to think that both theories are just about as equally likely -or as equally unlikely-