Non-unitary evolution of a pure state into a mixed state in the measurement problem from standard Quantum Mechanics and its impact on complex space-time, no-boundary proposal and information loss paradox of singularity-free Quantum Cosmology

Abstract

In order to resolve the measurement problem of Quantum Mechanics, non-unitary time evolution has been derived from the unitarity of standard quantum formalism. New wave functions of free and non-free quantum systems follow from Schroedinger equation after inserting an ansatz. Quantum systems show up as probability waves before measurement. A pure entangled state of a composite system evolves non-unitarily, only to disentangle itself into a definite state after reduction at the measurement point. A classical space-time point is created momentarily in this event. Unitarity is restored at that point. The non-Hermitian observables defined in the domain of rigged Hilbert space transform into Hermitian ones at the measurement point. The problem of preferred basis is resolved by the requirement of specifying the position of measurement point. Two theorems prove that time is a non-Hermitian operator, thus placing space and time on an equal footing. Bound states are found to need discrete space-time, which supports its use in loop quantum gravity. Non-unitarity in the theory helps buttress the no-boundary proposal; and uncertainty relation makes a leeway to singularity-free Quantum Cosmology. Quantum Mechanics also accommodates complex and negative probabilities.