We propose a novel interpretation of quantum mechanics in which microscopic particles possess definite positions, momenta, and spins at every moment, independent of measurement. These physical quantities are not determined by hidden variables but are randomly realized according to the wave function’s probability distribution. Measurement outcomes reflect the particle’s actual state rather than a wave-function collapse. By treating the measured and measuring systems as a single composite system, we introduce a conditional probability decomposition of the wave function that preserves interference without invoking instantaneous collapse. Potential experimental tests of the conditional probability decomposition are discussed. This framework provides a coherent understanding of quantum measurement, nonlocal correlations, and the EPR paradox, while remaining consistent with all standard quantum predictions including Bell inequality violations and GHZ state.
We discuss the definition of quantum probability in the context of ``timeless'' general-relativistic quantum mechanics. In particular, we study the probability of sequences of events, or multievent probability. In conventional quantum mechanics this can be obtained by means of the ``wave function collapse'' algorithm. We first point out certain difficulties of some natural definitions of multievent probability, including the conditional probability widely considered in the literature. We then observe that multievent probability can be reduced to single-event probability, by taking into account the quantum nature of the measuring apparatus. In fact, by exploiting the von-Neumann freedom of moving the quantum/classical boundary, one can always trade a sequence of noncommuting quantum measurements at different times, with an ensemble of simultaneous commuting measurements on the joint system+apparatus system. This observation permits a formulation of quantum theory based only on single-event probability, where the results of the wave function collapse algorithm can nevertheless be recovered. The discussion also bears on the nature of the quantum collapse.
GAP measures (also known as Scrooge measures) are a natural class of probability distributions on the unit sphere of a Hilbert space that come up in quantum statistical mechanics; for each density matrix
ρ there is a unique measure GAP
ρ. We describe and prove a property of these measures that was not recognized so far: If a wave function
Ψ is GAP
ρ distributed and a collapse occurs, then the collapsed wave function
Ψ′ is again GAP distributed (relative to the appropriate
ρ′). This fact applies to collapses due to a quantum measurement carried out by an observer, as well as to spontaneous collapse theories such as CSL or GRW. More precisely, it is the conditional distribution of
Ψ′, given the measurement outcome (respectively, the noise in CSL or the collapse history in GRW), that is GAP
ρ′.