Test-theory Methodology in Physics A dissertation sublnitted in fulfllnlent of the requirenlents for the Degree of Doctor of Philosophy in Philosophy by David Gunn University of Canterbury 1997 I' ~lEAL PMVS'CAl. S(,IE',ICE!:I SCIE~'ICE'! t.II3RA~' !:I~RA~'!! Contents Abstract v Preface Vll 1 Introduction 1 1.1 Test theories general: character and function 1 1.2 Origins of the test-theory idea 4 1.3 A simple test theory 5 1.4 Precis of following chapters 8 2 Newton's test theory and his experimental philosophy 11 2.1 Newton used a theory? 12 2.2 Defining and auxiliary assumptions 14 2.3 Newton's Phenomena 15 2.4 Newton's application of his test theory 17 2.5 The argument for universal gravitation 21 2.6 Newton's test theory and his concept of force 23 2.7 Newton's test theory and his experimental philosophy 27 2.8 The priority dispute with Hooke 30 3 Modern test theories and Einsteinian physics 34 3.1 Field theory and neo-Cartesian mechanical philosophy 35 3.2 Aside: A test theory for the Newtonian gravitational field 38 3.3 Relativity theory and Einstein's neo-Newtonianisl1l 41 3.4 A test theory for relativistic kinematics 45 3.5 Robertson's test theory 48 3.6 A test theory for relativistic gravity 52 3.7 The Parametrized Post-Newtonian (PPN) Formalism 55 3.8 Searching for gravitomagnetism with the PPN Formalism 58 3.9 Modern test theories and the future of physics 61 3.10 Conclusions 62 4 Spacetime, causation and limits of test-theory methodology 65 4.1 The nature and scope of test-theory methodology 66 4.2 Interpreting physical theory 67 4.3 Distant simultaneity in relativistic kinematics. 68 iii a 1 rlOV {JOO iv Contents 4.4 Test theories for distant simultaneity? 73 4.5 Arguments for curved spacetime 76 4.6 Test theories for geometry? 80 4.7 Efficient versus final cause? 84 4.8 Test theories and quantum physics 88 4.9 \iVhat test theories cannot do 91 5 Test-theory methodology and the philosophy of science 95 5.1 'What's right with reductionism 96 5.2 The hypothetical character of physical theories 99 5.3 What's wrong with meaning holism 101 5.4 The overdetermination of theory by evidence 103 5.5 How crucial falsifying experiments are possible 104 5.6 Normal science, theory change, and commensurability 107 5.7 How physical theories compete with one another 110 5.8 Test theories and bootstrap methodology 111 5.9 Are test-theory arguments eliminative inductions? 114 5.10 The empirical basis of test-theory methodology 118 6 Conclusion 122 6.1 The philosophical significance of test theories 122 6.2 Test theories and the unification programme in physics 125 References 129 Abstract theories are mathematical constructions with a methodological purpose. They enable experimental or other observational evidence ,-<'-'"LUe tively to select a physical theory from out of a of alternatives-a formal deductive method of testing which is (as I will show) distinct from the tional hypothetico-deductive one. I believe that study here of test-theory methodology is important for philosophers of science if they are properly to understand (i) methods of theory appraisal in physics, (ii) certain key concep­ tual issues in the foundations of physics, and (iii) more generally, the growth and structure of physical theory (history). I believe that this study is portant also for physicists who desire a clearer understanding of the power, limitations, and conceptual presuppositions of the test-theory method. (i) Methods. I show how test theories establish relations between ical theory and phenomena which are at once stronger and more systematic relations established by the hypothetico-deductive method. I use this result to defend some positivist methodological doctrines which philosophers today generally reject. I also use the result to criticise certain post-positivist doctrines which are meant to replace the very positivist doctrines I aim to defend. I compare some philosophical accounts of empirical confirmation with test-theory methodology in order to illuminate some features of the test-theory method and criticise standard philosophical accounts of confir­ mation. In this discussion I explore limitations of the test-theory method and identify general conditions which both knowledge and the world must satisfy if the method is to work. (U) Foundations. I address some key issues in foundations of physics, concerning the nature of space, time and causation. I discllss how test-theory methodology reveals the extent to which the very foundations of physics are empirically determinable. This extent is limited I argue: my discussion points to the furthest application but also to some notable tations of the test-theory approach. (iii) History. I argue Newton pioneered use of test-theory con- structions in theoretical physics, and I show how twentieth century physicists have brought the test-theory method to a high level of sophistication. I ar­ gue both that the test-theory idea makes possible a coherent view of the history of physics, and that the history of physics deepens our appreciation of power of the test-theory idea. There is unity, I argue, at the level of test-theory methodology across the seemingly disparate historical phases of physical inquiry (classical versus modern). is power, I maintain, in a method which can fruitfully be applied in seemingly diverse conceptual (Newtonian versus Einsteinian). Preface Test-theory constructions allow empirical evidence to select a physical theory by displaying that theory as falling within a mathematically defined, "parameterised", family of alternatives. The parameter in question is ap­ propriately chosen so that (granting some background assumptions which have been clearly delimited and are typically unproblematic) its value may be definitively "measured" by specific experimental or other observational evidence. The empirical selection of physical theories from a class of al­ ternatives is one very important function of test-theory constructions. In this dissertation I will also draw attention to other key functions, including (1) the way in which test theories provide a means of classifying physical theories, and thereby a measure of the "closeness" of one physical theory to another, and (2) the use of test theories as tools for discovery in theoretical physics. Test-theory methodology is the invention of physicists not philosophers. Even the name 'test theory' has been coined by physicists. The development of test-theory methodology illustrates how methods of empirical discovery in science are themselves discovered empirically. theories have delivered to theoretical physicists the kind of theories they seek-theories of great explanatory power. Physicists themselves endorse test-theory method on the quasi-empirical cum pragmatic basis that it works, that it furthers science's aim to provide explanations of natural phenomena. These facts about theoretical physics make clear how methodologically reflective physi­ cists really are. Thus, physicists challenge philosophers of science to attend not only to tacit, or implicit, aspects of the practice of physics, but also to patterns in that practice which physicists themselves have made explicit. As far as I am aware I am first philosopher of science to respond to this challenge by adopting the terminology that physicists themselves use. Physicists have been test theories for some time now. l:tecent studies in the history and philosophy of science have championed accounts of empirical confirmation involving "demonstrative" and "eliminative" in­ duction, "deduction from phenomena", and "bootstrap" inferences. I will show how these accounts support the same kind of relations between theory and evidence that are established by means of test theories. I will argue that both test-theory methodology and bootstrap methodology, in particu­ lar, make credible certain methodological tenets of logical positivism which many philosophers today reject. Besides demonstrating the importance of test for philosophers of science I wish also in dissertation to help physicists better appreciate the test-theory method. I have stated already my belief physicists today understand well the test-theory method which they have developed. Yet I also believe that a historically informed philosophical study of this method, viii PrE'face such as I undertake in this dissertation, can lead to even greater under­ standing, and possibly even to more significant application, of it. Physicists today emphasise the method's use in testing physical theories-hence the name 'test theory'. But one use of the test-theory method which its con­ temporary practitioners do not stress is its potential as a tool for theoretical discovery. I will argue, on the basis of its empirical credentials, its appli­ cability in a wide range of conceptual contexts, and also on the basis of its unifying power, that the test-theory method is an appropriate method to discover theories which further unify the fundamental physical interac­ tions. I will endeavour to show physicists, in other words, that the label 'test theory' desperately understates the significance and worth of this method. As far as I am aware, there have been no studies of test theories quite like the study that I undertake in this dissertation. In his excellent physics text Theory and Experiment in Gravitational Physics Clifford Will pro­ vides theoretical analyses of test theories for relativistic gravitation, and surveys the experimental results used to determine test-theory parameters. In more l~ecent articles Will also discusses test-theory constructions for rel­ ativistic kinematics. vVnat \iVill does not clo--being a physicist rather than a philosopher-is discuss the test-theory method in a general way. He does not compare the method with other approaches to confirmation, nor does he analyse the conceptual presuppositions of the method. By not investigating these matters Will fails to provide physicists with a clear sense of just how powerful the method is and how important it could be for the future uni­ fication of the fundamental physical interactions.