The Relativistic Kepler Problem and Gödel’s Paradox

Abstract

Employing a characteristic functional model that conscripts arrays of operators in terms of energy and momentum adjoined with their conjugate operators of time and position, we have recently derived an extended superposition principle compatible both with quantum mechanics and Einstein’s laws of relativity. We have likewise derived a global, universal superposition principle with the autonomous choice to implement, when required, classical or quantum representations. The present viewpoint amalgamates the microscopic and the macroscopic domains via abstract complex symmetric forms through suitable operator classifications including appropriate boundary conditions. An important case in point comes from the theory of general relativity, i.e. the demand for the proper limiting order at the Schwarzschild radius. In this example, one obtains a surprising relation between Gödel’s incompleteness theorem and the proper limiting behaviour of the present theory at the Schwarzschild singularity. In the present study, we will apply our theoretical formulation to the relativistic Kepler problem, recovering the celebrated result from the theory of general relativity in the calculation of the perihelion movement of Mercury.