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Quantum-mechanical histories and the uncertainty principle. II. Fluctuations about classical predictability.

This paper is concerned with two questions in the decoherent histories approach to quantum mechanics: the emergence of approximate classical predictability, and the fluctuations about it necessitated by the uncertainty principle. It is in part a continuation of an earlier paper on the uncertainty principle for quantum-mechanical histories. We consider histories characterized by position samplings at n moments of time. This includes the case of position sampling continuous in time in the limit n → ∞. We use this to construct a probability distribution on the value of (discrete approximations to) the field equations, F = mx + V'(x), at n − 2 times. We find that it is peaked around F = 0; thus classical correlations are exhibited. We show that the width of the peak ΔF is largely independent of the initial state