Erlangen 2026 – scientific programme

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MP: Fachverband Theoretische und Mathematische Grundlagen der Physik

MP 11: Various Topics in Relativity

MP 11.2: Talk

Thursday, March 19, 2026, 16:30–16:45, KH 00.015

Velocity dependent potential — •Lars Callenbach — Frankfurt am Main, Germany

The four-dimensional wave equation can be transformed to Laplace's equation applying a change of coordinates. In these four-dimensional Laplace coordinates a velocity dependent potential is derived from first principles for relative coordinates and velocities and its properties are analyzed. Especially this potential is the classical three-dimensional potential when the particles are at rest with respect to each other and in general this potential represents a central force interaction. Applying the Lagrange and Hamilton formalism the solutions of the dynamics are derived - with a simple structure: a bounded periodic motion on a circle in four dimensions. The explicit formulas for gravitational (and electrodynamical) equations underlying the motion are presented and the theoretical results are applied to data of our solar system showing that the bounded motion on a circle in four dimensions has many scalar constants of motion.

Keywords: wave equation; gravitation