Some physicists believe that superselection rules should be implemented to get rid of inconsistencies when a theory is framed in terms of a new mathematical formulation, whilst others think that this new formulation should be modified instead of implementing those rules, at the expense of introducing additional mathematical structure. The outcome, however, is that we are still uncertain whether these rules should be implemented and how they should be interpreted and assessed from the philosophical point of view. Based on a detailed examination of the group-theoretic reformulation of (relativistic and non-relativistic) quantum mechanics that prompts physicists to impose superselection rules, I shall argue that the implementation of these rules involves serious heuristic and epistemological concerns. Considering this argument, I shall conclude that there are suitable philosophical reasons to claim that the implementation of superselection rules should be rejected and that there are certain circumstances when the formulation of a theory should be modified.
Some physicists believe that superselection rules should be implemented to get rid of inconsistencies when a theory is framed in terms of a new mathematical formulation, whilst others think that this new formulation should be modified instead of implementing those rules, at the expense of introducing additional mathematical structure. The outcome, however, is that we are still uncertain whether these rules should be implemented and how they should be interpreted and assessed from the philosophical point of view. Based on a detailed examination of the group-theoretic reformulation of (relativistic and non-relativistic) quantum mechanics that prompts physicists to impose superselection rules, I shall argue that the implementation of these rules involves serious heuristic and epistemological concerns. Considering this argument, I shall conclude that there are suitable philosophical reasons to claim that the implementation of superselection rules should be rejected and that there are certain circumstances when the formulation of a theory should be modified.
The superposition principle is a very basic ingredient of quantum theory. What may come as a surprise to many students, and even to many practitioners of the quantum craft, is tha superposition has limitations imposed by certain requirements of the theory. The discussion of such limitations arising from the so-called superselection rules is the main purpose of this paper. Some of their principal consequences are also discussed. The univalence, mass and particle number superselection rules of non-relativistic quantum mechanics are also derived using rather simple methods.
Surely, after 62 years, we should have an exact formulation of some serious part of quantum mechanics? By ‘exact’ I do not of course mean ‘exactly true’. I mean only that the theory should be fully formulated in mathematical terms, with nothing left to the discretion of the theoretical physicist … until workable approximations are needed in applications. By ‘serious’ I mean that some substantial fragment of physics should be covered. Non-relativistic ‘particle’ quantum mechanics, perhaps with the inclusion of the electromagnetic field and a cut-off interaction, is serious enough. For it covers ‘a large part of physics and the whole of chemistry’. I mean too, by ‘serious’, that ‘apparatus’ should not be separated off from the rest of the world into black boxes, as if it were not made of atoms and not ruled by quantum mechanics. The question, ‘… should we not have an exact formulation …?’, is often answered by one or both of two others. I will try to reply to them: Why bother? Why not look it up in a good book ? Why bother? Perhaps the most distinguished of ‘why bother?’ers has been Dirac. He divided the difficulties of quantum mechanics into two classes, those of the first class and those of the second. The second-class difficulties were essentially the infinities of relativistic quantum field theory. Dirac was very disturbed by these, and was not impressed by the ‘renormalisation’ procedures by which they are circumvented. Dirac tried hard to eliminate these second-class difficulties, and urged others to do likewise.
Mainly due to the EPR trio having declared quantum mechanics as ‘not complete’ and given the acid criticisms of Schrödinger, including his famous cat paradox , many physicists felt encouraged to introduce new interpretations to confront a vaguely assembled orthodox interpretation . Indeed, there are numerous interpretations of quantum mechanics, so numerous that we have decided not to even enter into the interpretational arena, leaving that to the professionals and citing their encyclopedic works instead. In this regard, we are compelled to quote Dyson: ‘We still have passionate arguments between believers of various interpretations… The reason for these arguments is that various interpreters are trying to describe the quantum world in words… and the language is inappropriate for the purpose.’ Here, a humble approach to this subject is taken whilst opting for pragmatism.
Many scientific theories purport to describe empirically inaccessible aspects of the world. The agenda of foundational physics is more ambitious still: to characterize the world at the level of 'primitive ontology'. In this pursuit it often posits new and peculiar physical features, a proclivity aided by the abstract, mathematical way in which foundational theories are framed. But how do we decipher their physical content, and in particular the accounts of primitive ontology they offer, and why think that content is true? This dissertation explores the relationship between these questions -- between the problem of ontological interpretation in foundational physics and the nature of scientific realism. I do not argue for a unified account. Rather, I examine three contexts in which their interactions are particularly interesting and philosophically significant. First, I consider the role scientific methodology plays in a prominent naturalistic defense of scientific realism: the no-miracles argument. The most sophisticated form of this argument rests on the broad claim that successful scientific methodology is irredeemably theory dependent. I examine the nature of this theory dependence within the context of Maxwell's development of electromagnetism, and argue that the presence of competing ontological interpretations undermines the realist's attempt to draw sweeping epistemic conclusions from methodological success. I next consider the concept of theoretical reformulation and how it applies to the claim that Lagrangian dynamics is a reformulation of (part of) Newtonian dynamics. How should this claim be understood in light of the fact that the world is non-classical? What can this tell us about the concept of theory reformulation itself, which plays a central role in arguments against scientific realism? I provide an analysis of theory reformulation in terms of counterfactual interpretative judgments, and then cast doubt on its justification in the classical case by developing a non-Newtonian interpretation of Lagrangian dynamics. Finally, I consider whether competing ontological interpretations raise underdetermination problems for realism about foundational physics. After first re-formulating the underdetermination argument to avoid recent objections that it fails to pose any distinctive threat, I suggest a formulation of realism that vitiates the underdetermination threats posed by competing ontological interpretations.
INTRODUCTION In 1965 Hilary Putnam published the standard work on the interpretation of quantum mechanics, a piece that all philosophers of quantum mechanics of the time had to come to terms with. He laid out one-by-one in a clear non-technical way each of the available approaches to the problem and explained, again non-technically but very exactly, what is wrong with them. In his own final words Putnam took ‘the modest but essential step of becoming clear on the nature and magnitude of the difficulties’ (1965, 158). In the almost forty years since there have been a variety of advances, technical developments and new points of view. But none of these is uncontroversial. In fact each suffers from some one or another of the very difficulties that Putnam summarised. Many of the newer approaches explain why the problem is not a problem after all; a few bury the problems in technical detail; and some make heroic assumptions, often metaphysical, that cause the problems to disappear. My conclusion surveying the contemporary literature is the same as Putnam's in 1965: ‘no satisfactory interpretation of quantum mechanics exists today’ (1965, 157). The time scale is amazing. Putnam's important piece was written forty years after the first formulations and successes of quantum mechanics. I am writing forty years later, and about a theory that has transformed our technology and our way of thinking about the world. Why does this theory still have ‘no satisfactory interpretation’?
A superselection rule advanced in the course of a quantum-mechanical treatment of some phenomenon is an assertion to the effect that the superposition principle of quantum mechanics is to be restricted in the application at hand. Superselection accounts of measurement all have in common a decision to represent the indicator states of detectors by eigenspaces of superselection operators named in a superselection rule, on the grounds that the states in question are states of a so-called classical quantity and therefore not subject to quantum interference effects. By this strategy superselectionists of measurement expect to dispense with use of projection postulates in treatments of measurement. I shall argue that superselection accounts of measurement are self-contradictory, and that treatments of infinite systems, if they can avoid the contradiction, are not true superselection accounts.