Quantum probability from temporal structure

TL;DR

This paper presents a deterministic, history-based formulation of quantum probabilities using a universal multi-time wavefunction on the Keldysh contour, incorporating causal and retrocausal elements to derive measurement statistics.

Contribution

It introduces a novel framework that replaces initial conditions with fixed points on a contour, unifying causal and retrocausal aspects to derive quantum probabilities.

Findings

Quantum probabilities are derived from a universal multi-time wavefunction.

The framework incorporates both causal and retrocausal temporal parts.

Measurement statistics with pre- and post-selection are successfully obtained.

Abstract

The Born probability measure describes the statistics of measurements in which observers self-locate themselves in some region of reality. In $\psi$-ontic quantum theories, reality is directly represented by the wavefunction. We show that quantum probabilities may be identified with fractions of a universal multiple-time wavefunction containing both causal and retrocausal temporal parts. This wavefunction is defined in an appropriately generalized history space on the Keldysh time contour. Our deterministic formulation of quantum mechanics replaces the initial condition of standard Schr\"odinger dynamics with a network of `fixed points' defining quantum histories on the contour. The Born measure is derived by summing up the wavefunction along these histories. We then apply the same technique to the derivation of the statistics of measurements with pre- and post-selection.