Determination of classical behaviour of the Earth for large quantum numbers using quantum guiding equation

TL;DR

This paper uses Bohmian mechanics to demonstrate that Earth's classical orbit around the Sun emerges naturally from quantum principles at large quantum numbers, bridging quantum and classical physics.

Contribution

It applies the Bohmian guiding equation to model Earth's orbit, showing classical Keplerian motion as a limit of quantum behavior, which is a novel approach.

Findings

Earth trajectories converge to Kepler orbit

Classical behavior emerges at large quantum numbers

Bohmian trajectories differ from Newtonian in general

Abstract

For quantum systems, we expect to see the classical behaviour at the limit of large quantum numbers. Hence, we apply Bohmian approach for describing the evolution of Earth around the Sun. We obtain possible trajectories of the Earth system with different initial conditions which converge to a certain stable orbit, known as the Kepler orbit, after a given time. The trajectories are resulted from the guiding equation $p=\nabla S$ in the Bohmian mechanics, which relates the momentum of the system to the phase part of the wave function. Except at some special situations, Bohmian trajectories are not Newtonian in character. We show that the classic behaviour of the Earth can be interpreted as the consequence of the guiding equation at the limit of large quantum numbers.