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Empty Waves in Bohmian Quantum Mechanics Peter J. Lewis [email protected] Abstract There is a recurring line of argument in the literature to the effect that Bohm’s theory fails to solve the measurement problem. I show that this argument fails in all its variants. Hence Bohm’s theory, whatever its drawbacks, at least succeeds in solving the measurement problem. I briefly discuss a similar argument that has been raised against the GRW theory 1. Introduction The orthodox account of the import of the measurement problem in quantum mechanics goes something like this: The measurement problem shows that the standard theory of quantum mechanics is inadequate. Several strategies have been proposed to solve the measurement problem, and these yield various alternative theories of quantum mechanics, including hidden variable theories like Bohm’s theory, spontaneous collapse theories like the GRW theory, and many-worlds theories like Everett’s theory. These theories embody very different pictures of the world, so at most one of them can be true. The job of philosophy of physics, then is to assess the virtues and vices of the various solutions to the measurement problem, to determine which of them is the best solution (Albert 1992, ix). Against this orthodoxy, however, there is also a recurring heresy, according to which there has only ever been one adequate line of response to the measurement problem, and that is 1
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the many-worlds strategy. The other strategies—including the hidden variable strategy and the spontaneous collapse strategy—either fail to solve the measurement problem, or reduce to the many-worlds strategy, depending on how you look at them. According to this account, there is no work to be done in comparing the various solutions to the measurement problem, because there is only one solution (Deutsch 1996, 225–226). My goal in this paper is to defend orthodoxy against this heresy. Hidden variable theories and spontaneous collapse theories, I shall argue, do constitute genuine solutions to the measurement problem, and hence the many-worlds approach is not the only option. Most of the literature is directed against Bohmian theories, and so I focus on these arguments. But analogous arguments have been raised against the GRW theory, and I address these briefly. 2. Three Theories This paper compares the three most popular ways of addressing the measurement problem, so let me begin by outlining each of them briefly. The material is familiar, but it will be useful to introduce a uniform terminology for describing the three theories, and to make explicit various assumptions I make for the sake of argument. For example, a realist attitude towards quantum mechanics is a presupposition of this paper. That is, the quantum state | is to be regarded as a description of the objective state of the world, in terms of the distribution of wavefunction-stuff over configuration space. The wavefunction itself can be regarded as something like an objective field. This position is not without its problems—most notably because the wavefunction for an
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  • Fall '17
  • Bohm, measurement problem

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