Online research in philosophy

This paper investigates the possibiity of developing a fully micro realistic version of elementary quantum mechanics. I argue that it is highly desirable to develop such a version of quantum mechanics, and that the failure of all current versions and interpretations of quantum mechanics to constitute micro realistic theories is at the root of many of the interpretative problems associated with quantum mechanics, in particular the problem of measurement. I put forward a propensity micro realistic version of quantum mechanics, and suggest how it might be possible to discriminate, on expermental grounds, between this theory and other versions of quantum mechanics.

This paper attempts an interpretation of Everett's relative state formulation of quantum mechanics that avoids the commitment to new metaphysical entities like ‘worlds’ or ‘minds’. Starting from Everett's quantum mechanical model of an observer, it is argued that an observer's belief to be in an eigenstate of the measurement (corresponding to the observation of a well-defined measurement outcome) is consistent with the fact that she objectively is in a superposition of such states. Subjective states corresponding to such beliefs are constructed. From an analysis of these subjective states and their dynamics it is argued that Everett's pure wave mechanics is subjectively consistent with von Neumann's classical formulation of quantum mechanics. It follows from the argument that the objective state of a system is in principle unobservable. Nevertheless, an adequate concept of empirical reality can be constructed.

This paper attempts an interpretation of Everett''s relative state formulation of quantum mechanics that avoids the commitment to new metaphysical entities like worlds or minds. Starting from Everett''s quantum mechanical model of an observer, it is argued that an observer''s belief to be in an eigenstate of the measurement (corresponding to the observation of a well-defined measurement outcome) is consistent with the fact that she objectively is in a superposition of such states. Subjective states corresponding to such beliefs are constructed. From an analysis of these subjective states and their dynamics it is argued that Everett''s pure wave mechanics is subjectively consistent with von Neumann''s classical formulation of quantum mechanics. It follows from the argument that the objective state of a system is in principle unobservable. Nevertheless, an adequate concept of empirical reality can be constructed.

Advocates of the Everett interpretation of quantum mechanics have long claimed that other interpretations needlessly invoke "new physics" to solve the measurement problem. Call the argument fashioned that gives voice to this claim the Redundancy Argument, or ’Redundancy’ for short. Originating right in Everett’s doctoral thesis, Redundancy has recently enjoyed much attention, having been advanced and developed by a number of commentators, as well as criticized by a few others.[1] Although versions of this argument can target collapse theories of quantum mechanics, it is usually conceived with no-collapse "hidden variable" interpretations in mind, e.g., modal and Bohmian interpretations. In particular, the argument is an attack against theories committed to both realism about the quantum state and realism about entities – what Bell 1987 calls "beables" – that supplement this state. Particles, fields, value states, and more have been suggested as possible ontology to supplement the quantum state. Redundancy is the argument that this supplementation is methodologically otiose, the superfluous pomp that Newton scorned.

This paper discusses the problem of finding and defining chaos in quantum mechanics. While chaotic time evolution appears to be ubiquitous in classical mechanics, it is apparently absent in quantum mechanics in part because for a bound, isolated quantum system, the evolution of its state is multiply periodic. This has led a number of investigators

No categories

Reading list   |  Discuss  |  Edit  |  Categorize  |  

 

My bibliography  |

 

Export citation | Scholar | At my library | More options ...

Interpretations that follow Everett's idea that (at some level of description) the universal wave function contains a multiplicity of coexisting realities, usually claim to give a completely local account of quantum mechanics. That is, they claim to give an account that avoids both a non-local collapse of the wave function, and the action at a distance needed in hidden variable theories in order to reproduce the quantum mechanical violation of the Bell inequalities. In this paper, I sketch how these claims can be substantiated in two renderings of Everett's ideas, namely the many-minds interpretation of Albert and <span class='Hi'>Loewer</span>, and versions of many-worlds interpretations that rely on the concepts of the theory of decoherence.

A perspective on Everett's relative state formulation is proposed leading to a relational quantum mechanics. There are inevitably a large number of different versions of the universe in which a specific observer could exist, and in the universe of the unitary wave function they are all existing and coincident. If these different versions of the universe are superposed the result is a universe in which the superposition of all of the identical copies sums to a single observer. The effective universe in the functional frame of reference of this observer would be highly indeterminate but determinate where observed by this observer. This would naturally relativise the universe of the conventional view since each observer would inhabit an effective universe in which different aspects were determinate. Although the identity of the observer as a physical body does not readily fit this concept, it appears to apply inevitably to the functional identity of an observer as depicted by Everett. In this relational quantum mechanics a collapse dynamics applies only to the functional frame of reference of the observer and raises no incompatibility with the linear dynamics.

Everett proposed resolving the quantum measurement problem by dropping the nonlinear collapse dynamics from quantum mechanics and taking what is left as a complete physical theory. If one takes such a proposal seriously, then the question becomes how much of the predictive and explanatory power of the standard theory can one recover without the collapse postulate and without adding anything else. Quantum mechanics without the collapse postulate has several suggestive properties, which we will consider in some detail. While these properties are not enough to make it acceptable given the usual standards for a satisfactory physical theory, one might want to exploit these properties to cook up a satisfactory no-collapse formulation of quantum mechanics. In considering how this might work, we will see why any no-collapse theory must generally fail to satisfy at least one of two plausible-sounding conditions.

Dualistic interpretations attempt to solve the measurement problem of quantum mechanics by postulating the existence of non-physical minds, and by giving a suitable dynamical equation for how these minds evolve. I consider the relative merits of three extant dualistic interpretations (Albert and Loewer’s single-mind and many-minds interpretations, and Squires’ interpretation), and I defend Squires’ interpretation as preferable to the Albert/Loewer interpretations. I also argue that, for all three of these interpretations, the minds evolve independently of the physical universe, and hence render the physical universe otiose; the interpretations are better viewed as supporting not dualism, but mental monism.

Everett's relative-state formulation of quantum mechanics is an attempt to solve the measurement problem by dropping the collapse dynamics from the standard von Neumann-Dirac theory of quantum mechanics. The main problem with Everett's theory is that it is not at all clear how it is supposed to work. In particular, while it is clear that he wanted to explain why we get determinate measurement results in the context of his theory, it is unclear how he intended to do this. There have been many attempts to reconstruct Everett's no-collapse theory in order to account for the apparent determinateness of measurement outcomes. These attempts have led to such formulations of quantum mechanics as the many-worlds, many-minds, many-histories, and relative-fact theories. Each of these captures part of what Everett claimed for his theory, but each also encounters problems.