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By Herbert A. Pohl

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Extra info for Quantum Mechanics For Science And Engineering (Prentice Hall Series In Materials Science)

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For the nonrelativistic theory that we have been discussing, the primitive ontology is given by particles described by their positions, btu we see no compelling reason to insist upon this ontology for a relativistic extension of Bohmian mechanics. Indeed, the most obvious ontology for a bosonic field theory is a field ontology, suggested by the fact that in standard quantum theory, it is the field configurations of a bosonic field theory that plays the role analogous to that of the particle configurations in the particle theory.

Note that it follows from (29) that W,(x, Y,) = '\jf,(x),(Y,), so that the 40 DETLEF DURR ET AL. effective wave function is unambiguous, and indeed agrees with the conditional wave function up to an irrelevant constant factor. We remark that it is the relative stability of the macroscopic disjointness employed in the definition of the effective wave function, arising from what are nowadays often called mechanisms of decoherence - the destruction of the coherent spreading of the wave function due to dissipation, the effectively irreversible flow of "phase information" into the (macroscopic) environment - which accounts for the fact that the effective wave function of a system obeys SchrOdinger's equation for the system alone whenever this system is isolated.

1992a,b) of (27) is the fundamental conditional probability formula: (30) IP(X, E dx I Y,) = l'lf,(x)l 2 dx, where IP(dQ) = I'P 0 (Q)I 2 dQ. Now suppose that at time t the x-system consists itself of many identical subsystems x 1, ... , xM, each one having effective wave function 'If (with respect to coordinates relative to suitable frames). Then (Diirr et al. 1992a,b) the effective wave function of the x-system is the product wave function (31) '\jf1(X) = '\jf(X 1) ••• '\jf(XM). Note that it follows from (30) and (31) that the configurations of these subsystems are independent identically distributed random variables with respect to the initial universal quantum equilibrium distribution IP conditioned on the environment of these subsystems.

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