Timeless Histories: Quantum Measurement and the Maximum Entropy Principle

Abstract

The quantum measurement problem, i.e. the apparent conflict between unitary quantum evolution and non-unitary, stochastic wave-function collapse, remains unresolved a century after the formulation of quantum mechanics. We first review the standard picture, from the Copenhagen prescription with its Heisenberg cut, through von Neumann's movable cut, to environment-induced decoherence, which explains the emergence of stable classical records but still presupposes the Born rule and therefore cannot by itself replace the measurement postulates. We then connect this problem to the Maximum Entropy Principle in two complementary ways. First, decoherence drives the measurement apparatus toward the least biased state compatible with the dynamically protected pointer distribution, so that the emergent collapse may be viewed as a thermodynamic relaxation toward constrained maximum entropy. Second, we propose a Timeless Histories formulation of quantum mechanics in which the primitive objects are ordered sequences of events rather than evolving wave functions. Their conditional probabilities are assigned, relative to specified refinements, by a single Born-Boltzmann rule that combines the quadratic structure of Born's rule with Boltzmann's counting of equally probable microstates. The textbook form of Born's rule, the projection postulate, density operators, and wave functions are then recovered as derived informational constructs, while collapse becomes Bayesian conditioning on recorded events. Time and space enter only subsequently through unitary translation symmetry. Because the probability rule is postulated independently of any physical collapse or classical observer, decoherence is no longer asked to justify the rule used to interpret its own reduced states, and can be invoked to explain the approximate additivity and stability of macroscopic records, i.e. the emergence of classicality.

23 pages, 2 figure, substantially revised