Quantum Trajectories, State Diffusion and Time Asymmetric Eventum Mechanics

TL;DR

This paper establishes an exact quantum stochastic model for continuous measurements, linking quantum trajectories to wave-particle duality and deriving the time arrow from quantum causality principles.

Contribution

It proves the equivalence of quantum Langevin equations to boundary-value problems and algebra reductions, supporting Eventum Mechanics and the wave-particle duality thesis.

Findings

Quantum Langevin dynamics are equivalent to boundary-value problems.

The model supports the wave-particle duality in quantum mechanics.

The time arrow is derived from quantum causality principles.

Abstract

We show that the quantum stochastic unitary dynamics Langevin model for continuous in time measurements provides an exact formulation of the Heisenberg uncertainty error-disturbance principle. Moreover, as it was shown in the 80's, this Markov model induces all stochastic linear and non-linear equations of the phenomenological "quantum trajectories" such as quantum state diffusion and spontaneous localization by a simple quantum filtering method. Here we prove that the quantum Langevin equation is equivalent to a Dirac type boundary-value problem for the second-quantized input "offer waves from future" in one extra dimension, and to a reduction of the algebra of the consistent histories of past events to an Abelian subalgebra for the "trajectories of the output particles". This result supports the wave-particle duality in the form of the thesis of Eventum Mechanics that everything in the future is constituted by quantized waves, everything in the past by trajectories of the recorded particles. We demonstrate how this time arrow can be derived from the principle of quantum causality for nondemolition continuous in time measurements.