Online research in philosophy

In other words, classically, probabilities add; quantum mechanically, the probability amplitudes add, leading to the presence of the extra product terms in the quantum case. What this means is that in quantum theory, even though always only one of the various outcomes is obtained in any given observation, some aspect of the non -occurring events, represented by the corresponding complex-valued quantum amplitudes, plays a role in determining the overall probabilities. Indeed, the observed quantum interference effects are correctly captured by the quantum statistical description only because of the presence of these product terms. Therefore, in a realistic construal of quantum theory, if we treat the superposed Ψ function as representing the real state of an individual quantum system, these quantum amplitudes need to be given an ontological status.

In this paper I expand Eric Scerri’s notion of Popper’s naturalised approach to reduction in chemistry and investigate what its consequences might be. I will argue that Popper’s naturalised approach to reduction has a number of interesting consequences when applied to the reduction of chemistry to physics. One of them is that it prompts us to look at a ‘bootstrap’ approach to quantum chemistry, which is based on specific quantum theoretical theorems and practical considerations that turn quantum ‘theory’ into quantum ‘chemistry’ proper. This approach allows us to investigate some of the principles that drive theory formation in quantum chemistry. These ‘enabling theorems’ place certain limits on the explanatory latitude enjoyed by quantum chemists, and form a first step into establishing the relationship between chemistry and physics in more detail.

This paper expands on, and provides a qualified defence of, Arthur Fine's selective interactions solution to the measurement problem. Fine's approach must be understood against the background of the insolubility proof of the quantum measurement. I first defend the proof as an appropriate formal representation of the quantum measurement problem. The nature of selective interactions, and more generally selections, is then clarified, and three arguments in their favour are offered. First, selections provide the only known solution to the measurement problem that does not relinquish any of the explicit premises of the insolubility proofs. Second, unlike some no-collapse interpretations of quantum mechanics, selections suffer no difficulties with non-ideal measurements. Third, unlike most collapse interpretations, selections can be independently motivated by an appeal to quantum propensities. Introduction The problem of quantum measurement 2.1 The ignorance interpretation of mixtures 2.2 The eigenstate–eigenvalue link 2.3 The quantum theory of measurement The insolubility proof of the quantum measurement 3.1 Some notation 3.2 The transfer of probability condition (TPC) 3.3 The occurrence of outcomes condition (OOC) A defence of the insolubility proof 4.1 Stein's critique 4.2 Ignorance is not required 4.3 The problem of quantum measurement is an idealisation Selections 5.1 Representing dispositional properties 5.2 Selections solve the measurement problem 5.3 Selections and ignorance Non-ideal selections 6.1 No-collapse interpretations and non-ideal measurements 6.2 Exact and approximate measurements 6.3 Selections for non-ideal interactions 6.4 Approximate selections 6.5 Implications for ignorance Selective interactions test quantum propensities 7.1 Equivalence classes as physical ‘aspects’: a critique 7.2 Quantum dispositions 7.3 Selections as a propensity modal interpretation 7.4 A comparison with Popper's propensity interpretation.

The basic theme of Popper's philosophy--that something can come from nothing--is related to the present situation in physical theory. Popper carries his investigation right to the center of current debate in quantum physics. He proposes an interpretation of physics--and indeed an entire cosmology--which is realist, conjectural, deductivist and objectivist, anti-positivist, and anti-instrumentalist. He stresses understanding, reminding us that our ignorance grows faster than our conjectural knowledge.

Peter Milne and Neal Grossman have argued against Popper's propensity interpretation of quantum mechanics, by appeal to the two-slit experiment and to the distinction between mixtures and superpositions, respectively. In this paper I show that a different propensity interpretation successfully meets their objections. According to this interpretation, the possession of a quantum propensity by a quantum system is independent of the experimental set-ups designed to test it, even though its manifestations are not.

Popper’s introduction of ‘‘propensity’’ was intended to provide a solid conceptual foundation for objective single-case probabilities. By considering the partly opposed contributions of Humphreys and Miller and Salmon, it is argued that when properly understood, propensities can in fact be understood as objective single-case causal probabilities of transitions between concrete events. The chief claim is that propensities are well-explicated by describing how they fit into the existing formal theory of branching space-times, which is simultaneously indeterministic and causal. Several problematic examples, some commonsense and some quantum-mechanical, are used to make clear the advantages of invoking branching space-times theory in coming to understand propensities. r 2007 Elsevier Ltd. All rights reserved.

This paper reviews four attempts throughout the history of quantum mechanics to explicitly employ dispositional notions in order to solve the quantum paradoxes, namely: Margenau’s latencies, Heisenberg’s potentialities, Maxwell’s propensitons, and the recent selective propensities interpretation of quantum mechanics. Difficulties and challenges are raised for all of them, and it is concluded that the selective propensities approach nicely encompasses the virtues of its predecessors. Finally, some strategies are discussed for reading dispositional notions into two other well-known interpretations of quantum mechanics, namely the GRW interpretation and Bohmian mechanics.

GRW Theory postulates a stochastic mechanism assuring that every so often the wave function of a quantum system is `hit', which leaves it in a localised state. How are we to interpret the probabilities built into this mechanism? GRW theory is a firmly realist proposal and it is therefore clear that these probabilities are objective probabilities (i.e. chances). A discussion of the major theories of chance leads us to the conclusion that GRW probabilities can be understood only as either single case propensities or Humean objective chances. Although single case propensities have some intuitive appeal in the context of GRW theory, on balance it seems that Humean objective chances are preferable on conceptual grounds because single case propensities suffer from various well know problems such as unlimited frequency tolerance and lack of a rationalisation of the principal principle.