Bohm's Ontological Interpretation and its Relations to Three Formulations of Quantum Mechanics

The standard mathematical formulation of quantum mechanics is specified. Bohm's ontological interpretation of quantum mechanics is then shown to be incapable of providing a suitable interpretation of that formulation. It is also shown that Bohm's interpretation may well be viable for two alternative mathematical formulations of quantum mechanics, meaning that the negative result is a significant though not a devastating criticism of Bohm's interpretation. A preliminary case is made for preferring one alternative formulation over the other. This revised version was published online in June 2006 with corrections to the Cover Date.     

Measurement and the Justification of the Statistical Postulate in Bohm's Causal Interpretation of Quantum Mechanics

I briefly sketch Bohm's causal interpretation (BCI) and its solution to the measurement problem. Crucial to BCI's no-collapse account of both ideal and non-ideal measurement is the existence of particles in addition to wavefunctions. The particles in their role as the producers of the observable experimental outcomes render practical considerations, such as what observables can be reasonably measured or how to get rid of interference terms in non-ideal measurements, secondary to BCI's account of measurement. I then explain why it is not easy for BCI to justify its statistical postulate. To successfully justify the postulate would be to solve the distribution problem. Two proposed deterministic solutions to this problem are only briefly set out and not discussed in detail. BCI can solve the measurement problem whether or not the distribution problem is solved. However, if the distribution problem is not solved, BCI cannot be shown to be empirically adequate. This revised version was published online in June 2006 with corrections to the Cover Date.     

Time,Quantum Mechanics,and Probability

A variety of ideas arising in decoherence theory, and in the ongoing debate over Everett's relative-state theory, can be linked to issues in relativity theory and the philosophy of time, specifically the relational theory of tense and of identity over time. These have been systematically presented in companion papers (Saunders 1995; 1996a); in what follows we shall consider the same circle of ideas, but specifically in relation to the interpretation of probability, and its identification with relations in the Hilbert Space norm. The familiar objection that Everett's approach yields probabilities different from quantum mechanics is easily dealt with. The more fundamental question is how to interpret these probabilities consistent with the relational theory of change, and the relational theory of identity over time. I shall show that the relational theory needs nothing more than the physical, minimal criterion of identity as defined by Everett's theory, and that this can be transparently interpreted in terms of the ordinary notion of the chance occurrence of an event, as witnessed in the present. It is in this sense that the theory has empirical content.     

Elementary Propositions and Essentially Incomplete Knowledge: A Framework for the Interpretation of Quantum Mechanics

A central problem in the interpretation of non‐relativistic quantum mechanics is to relate the conceptual structure of the theory to the classical idea of the state of a physical system. This paper approaches the problem by presenting an analysis of the notion of an elementary physical proposition. The notion is shown to be realized in standard formulations of the theory and to illuminate the significance of proofs of the impossibility of hidden variable extensions. In the interpretation of quantum mechanics that emerges from this analysis, the philosophically distinctive features of the theory derive from the fact that it seeks to represent a reality of which complete knowledge is essentially unattainable.     

Three-valued Logic,Indeterminacy and Quantum Mechanics

The paper consists of two parts. The first part begins with the problem of whether the original three-valued calculus, invented by J. ukasiewicz, really conforms to his philosophical and semantic intuitions. I claim that one of the basic semantic assumptions underlying ukasiewicz's three-valued logic should be that if under any possible circumstances a sentence of the form X will be the case at time t is true (resp. false) at time t, then this sentence must be already true (resp. false) at present. However, it is easy to see that this principle is violated in ukasiewicz's original calculus (as the cases of the law of excluded middle and the law of contradiction show). Nevertheless it is possible to construct (either with the help of the notion of supervaluation, or purely algebraically) a different three-valued, semi-classical sentential calculus, which would properly incorporate ukasiewicz's initial intuitions. Algebraically, this calculus has the ordinary Boolean structure, and therefore it retains all classically valid formulas. Yet because possible valuations are no longer represented by ultrafilters, but by filters (not necessarily maximal), the new calculus displays certain non-classical metalogical features (like, for example, non-extensionality and the lack of the metalogical rule enabling one to derive p is true or q is true from pqq is true).The second part analyses whether the proposed calculus could be useful in formalizing inferences in situations, when for some reason (epistemological or ontological) our knowledge of certain facts is subject to limitation. Special attention should be paid to the possibility of employing this calculus to the case of quantum mechanics. I am going to compare it with standard non-Boolean quantum logic (in the Jauch–Piron approach), and to show that certain shortcomings of the latter can be avoided in the former. For example, I will argue that in order to properly account for quantum features of microphysics, we do not need to drop the law of distributivity. Also the idea of reading off the logical structure of propositions from the structure of Hilbert space leads to some conceptual troubles, which I am going to point out. The thesis of the paper is that all we need to speak about quantum reality can be acquired by dropping the principle of bivalence and extensionality, while accepting all classically valid formulas.     

Quantum Mechanics and the Plight of Physicalism

The literature on physicalism often fails to elucidate, I think, what the word physical in physicalism precisely means. Philosophers speak at times of an ideal set of fundamental physical facts, or they stipulate that physical means non-mental, such that all fundamental physical facts are fundamental facts pertaining to the non-mental. In this article, I will probe physicalism in the very much tangible framework of quantum mechanics. Although this theory, unlike “ideal physics” or some “final theory of non-mentality”, is an incomplete theory of the world, I believe this analysis will be of value, if for nothing else, at least for bringing some taste of physical reality, as it were, back to the debate. First, I will introduce a broad characterization of the physicalist credo. In Sect. 2, I will provide a rather quick review of quantum mechanics and some of its current interpretations. In Sect. 3, the notion of quantum non-separability will be analyzed, which will facilitate a discussion of the wave function ontology in Sect. 4. In Sects. 5 and 6, I will explore competing views on the implications of this ontology. In Sect. 7, I will argue that the prior results, based on a thoroughly realist interpretation of quantum mechanics, support only a weak version of non-reductive physicalism.     

Correspondence Truth and Quantum Mechanics

The logic of a physical theory reflects the structure of the propositions referring to the behaviour of a physical system in the domain of the relevant theory. It is argued in relation to classical mechanics that the propositional structure of the theory allows truth-value assignment in conformity with the traditional conception of a correspondence theory of truth. Every proposition in classical mechanics is assigned a definite truth value, either ‘true’ or ‘false’, describing what is actually the case at a certain moment of time. Truth-value assignment in quantum mechanics, however, differs; it is known, by means of a variety of ‘no go’ theorems, that it is not possible to assign definite truth values to all propositions pertaining to a quantum system without generating a Kochen–Specker contradiction. In this respect, the Bub–Clifton ‘uniqueness theorem’ is utilized for arguing that truth-value definiteness is consistently restored with respect to a determinate sublattice of propositions defined by the state of the quantum system concerned and a particular observable to be measured. An account of truth of contextual correspondence is thereby provided that is appropriate to the quantum domain of discourse. The conceptual implications of the resulting account are traced down and analyzed at length. In this light, the traditional conception of correspondence truth may be viewed as a species or as a limit case of the more generic proposed scheme of contextual correspondence when the non-explicit specification of a context of discourse poses no further consequences.     

Quantum Mechanics and Metaphysical Indeterminacy

There has been recent interest in formulating theories of non-representational indeterminacy. The aim of this paper is to clarify the relevance of quantum mechanics to this project. Quantum-mechanical examples of vague objects have been offered by various authors, displaying indeterminate identity, in the face of the famous Evans argument that such an idea is incoherent. It has also been suggested that the quantum-mechanical treatment of state-dependent properties exhibits metaphysical indeterminacy. In both cases it is important to consider the details of the metaphysical account and the way in which the quantum phenomenon is captured within it. Indeed if we adopt a familiar way of thinking about indeterminacy and apply it in a natural way to quantum mechanics, we run into illuminating difficulties and see that the case is far less straightforward than might be hoped.     

Realism and Objectivism in Quantum Mechanics

The present study attempts to provide a consistent and coherent account of what the world could be like, given the conceptual framework and results of contemporary quantum theory. It is suggested that standard quantum mechanics can, and indeed should, be understood as a realist theory within its domain of application. It is pointed out, however, that a viable realist interpretation of quantum theory requires the abandonment or radical revision of the classical conception of physical reality and its traditional philosophical presuppositions. It is argued, in this direction, that the conceptualization of the nature of reality, as arising out of our most basic physical theory, calls for a kind of contextual realism. Within the domain of quantum mechanics, knowledge of ??reality in itself??, ??the real such as it truly is?? independent of the way it is contextualized, is impossible in principle. In this connection, the meaning of objectivity in quantum mechanics is analyzed, whilst the important question concerning the nature of quantum objects is explored.     

Measurement and Indeterminacy in the Quantum Mechanics of Dirac

The quantum-measurement problem and the Heisenberg indeterminacy principle are presented in the language of the Dirac formulation of the quantum theory. Particularly the relationship between quantum state prior to measurement and the result of the measurement are discussed. The relation between the indeterminacy principle and the analog between quantum and classical systems is presented, showing that this principle may be discussed independently of the wave-particle duality. The importance of statistics in the treatment of many body systems is outlined and the approach to investigating God's interaction with human beings is discussed in this context. The treatment is nonmathematical.     

Williams,Pragmatism, and the Law

Res Publica - This paper views Bernard Williams through the lens of the pragmatist tradition. The central insight of pragmatism is that philosophy must start with human practice, in contrast to...     

Introduction: Phenomenology of Quantum Mechanics

Continental Philosophy Review - The collection of essays in this special issue point toward the rich and diverse themes under which the phenomenologist might analyze quantum mechanics. The authors...     

A New Argument for the Nomological Interpretation of the Wave Function: The Galilean Group and the Classical Limit of Nonrelativistic Quantum Mechanics

In this article I investigate, within the framework of realistic interpretations of the wave function in nonrelativistic quantum mechanics, the mathematical and physical nature of the wave function. I argue against the view that mathematically the wave function is a two-component scalar field on configuration space. First, I review how this view makes quantum mechanics non-Galilei invariant and yields the wrong classical limit. Moreover, I argue that interpreting the wave function as a ray, in agreement with many physicists, ensures that Galilei invariance is preserved. In addition, I discuss how the wave function behaves more similarly to a gauge potential than to a field. Finally, I show how this favours a nomological rather than an ontological view of the wave function.     

Pragmatism, Relativism, and the Critique of Philosophy

The relativist strain in Rorty's work should be distinguished from the Davidsonian strain. The latter may be exploited in support of Rorty's critique of philosophy but it is at odds with his use of "solidarity" and "ethnocentrism"as explanatory concepts. Once this is recognized, there remains in Rorty's work a consistent challenge to the search for general philosophical theories of truth, objectivity, and rationality (of which relativism itself is an example). On this reading, however, Rorty's pragmatism is not a theory that offers answers to questions about the authority of beliefs and practices but rather a critical tool used to open detailed, concrete, and critical investigation into particular questions about the establishment and viability of the beliefs and practices we have.     

Pragmatism, Naturalism, and Phenomenology

Pragmatism’s naturalism is inconsistent with the phenomenological tradition’s anti-naturalism. This poses a problem for the methodological consistency of phenomenological work in the pragmatist tradition. Solutions such as phenomenologizing naturalism or naturalizing phenomenology have been proposed, but they fail. As a consequence, pragmatists and other naturalists must answer the phenomenological tradition’s criticisms of naturalism.