Bohmian Mechanics and Quantum Theory: An Appraisal by James T. Cushing (auth.), James T. Cushing, Arthur Fine,

By James T. Cushing (auth.), James T. Cushing, Arthur Fine, Sheldon Goldstein (eds.)

We are frequently advised that quantum phenomena call for radical revisions of our medical international view and that no actual conception describing good outlined items, comparable to debris defined by means of their positions, evolving in a good outlined means, not to mention deterministically, can account for such phenomena. the nice majority of physicists proceed to join this view, although simply the sort of deterministic idea, accounting for the entire phe­ nomena of nonrelativistic quantum mechanics, used to be proposed by way of David Bohm greater than 4 a long time in the past and has arguably been round virtually because the inception of quantum mechanics itself. Our goal in asking colleagues to write down the essays for this quantity has no longer been to provide a Festschrift in honor of David Bohm (worthy an venture as that might were) or to assemble jointly a set of papers easily mentioning uncritically Bohm's perspectives on quantum mechanics. The primary subject round which the essays during this quantity are prepared is David Bohm's model of quantum mechanics. It has via now develop into rather general perform to consult his thought as Bohmian mechanics and to the bigger conceptual framework in which this can be positioned because the causal quantum thought software. whereas it really is precise that possible have reservations in regards to the appropriateness of those particular labels, either do elicit distinc­ tive photos attribute of the foremost suggestions of those techniques and such terminology does serve successfully to distinction this classification of theories with extra typical formulations of quantum theory.

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With regard to the third condition, we are aware that it is not at all clear what should be meant by even an orthodox theory of quantum cosmology or gravity, let alone a Bohmian one. Nonetheless, this condition places strong constraints on the form of the guiding equation. Furthermore, we do not wish to suggest here that the ultimate theory is likely to be a Bohmian theory, though we do think it very likely that if the ultimate theory is a quantum theory it will in fact be a Bohmian theory. Understood in this way, a Bohmian theory is merely a quantum theory with a coherent ontology.

6 Much of the preceding sketch of the emergence and role of operators as observables in Bohmian mechanics, including of course the von Neumann-type picture of "measurement" at which we arrive, applies as well to orthodox quantum theory. 7 In fact, it would appear that the argument against naive realism about operators provided by such an analysis has even greater force from an orthodox perspective: Given the initial wave function, at least in Bohmian mechanics the outcome of the particular experiment is determined by the initial configuration of system and apparatus, while for orthodox quantum theory there is nothing in the initial state which completely determines the outcome.

Notice that the composite map defined by this sequence, from wave functions to probability distributions on the value space, is "bilinear" or "quadratic," since the middle map, to the quantum equilibrium distribution, is obviously bilinear, while all the other maps are linear, all but the second trivially so. Now by elementary functional analysis, the notion of such a bilinear map is completely equivalent to that of a POV! Thus the emergence and role of POV's as "generalized observables" in Bohmian mechanics is merely an expression of the bilinearity of quantum equilibrium together with the linearity of Schr6dinger's evolution.

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