Complexified quantum and classical mechanics

TL;DR

This paper introduces anti self-adjoint operators for coordinate and momentum to explore quantum tunneling, black hole horizons, and cosmological expansion, suggesting imaginary variables can explain phenomena without dark energy.

Contribution

It presents a novel approach using imaginary observables to analyze tunneling, black hole singularities, and universe expansion, challenging traditional real-variable frameworks.

Findings

Imaginary momentum unavoidably appears in tunneling through potential barriers.

No singularity exists at the black hole center when considering imaginary variables.

Negative energies in the imaginary domain can explain universe acceleration without dark energy.

Abstract

The anti self-adjoint operators of coordinate and momentum are introduced and applied in discussion of tunneling through the potential barrier where imaginary value of momentum unavoidably appears. Tunneling through temporal barrier is proceeded in a similar way and it is shown that the quantum system can tunnel, while the classical systems are destroyed by such barrier. The imaginary observables of coordinate and momentum are used in a novel treatment of passage through the event horizon. By considering the event horizon as the border of the finite potential barrier, it is found that there is no singularity at the center of a black hole. The imaginary variables of coordinate and momentum are used for the construction of a toy model of the universe. It is shown that the acceleration of the expansion of the universe does not need dark energies to be explained since negative energies are present and characteristic for the imaginary world.