  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.
