Macromechanics and two-body problems

Abstract

A wave function can be written in the form of ReiS/ℏ . We put this form of wave function into quantum mechanics equations and take hydrodynamic limit, i. e., let Planck constant be zero. Then equations of motion (EOM) describing the movement of macroscopic bodies are retrieved. From Schrödinger equation, we obtain Newtonian mechanics, including Newton’s three laws of motion; from decouple Klein–Gordon equation with positive kinetic energy (PKE), we obtain EOM of special relativity in classical mechanics. These are for PKE systems. From negative kinetic energy (NKE) Schrödinger equation and decoupled Klein–Gordon equation, the EOM describing low momentum and relativistic motions of macroscopic dark bodies are derived. These are for NKE systems, i. e., dark systems. In all cases scalar and vector potentials are also taken into account. The formalism obtained is collectively called macromechanics. For an isolated system containing PKE and NKE bodies, both total momentum and total kinetic energy are conserved. A dark ideal gas produces a negative pressure, and its microscopic mechanism is disclosed. Two-body problems, where at least one is of NKE, are investigated for both macroscopic bodies and microscopic particles. A NKE proton and a PKE electron can compose a stable PKE atom, and its spectral lines have blue shifts compared to a hydrogen atom. The author suggests to seek for these spectral lines in celestial spectra. This provides a way to seek for dark particles in space. Elastic collisions between a body and a dark body are researched.