The Relativistic Kepler Problem and Gödel’s Paradox

  • Erkki J. Brändas
Conference paper
Part of the Progress in Theoretical Chemistry and Physics book series (PTCP, volume 26)


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.


Rest Mass Truth Table Jordan Block Conjugate Problem Kepler Problem 
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The current results have been presented at the XVIth International Workshop on Quantum Systems in Chemistry and Physics (QSCP XVI) held at the Ishikawa Prefecture Museum of Art (IPMA), Kanazawa, Japan, 11–17 September 2011. The author thanks the organiser of QSCP XVI, Prof. Kiyoshi Nishikawa, Kanazawa University, for friendly cooperation, an excellent programme and outstanding organisation, as well as generous hospitality. The present research has, over the years, been supported by the Swedish Natural Science Research Council, the Swedish Foundation for Strategic Research, the European Commission and the Nobel Foundation.


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Copyright information

© Springer Science+Business Media Dordrecht 2012

Authors and Affiliations

  1. 1.Department of Chemistry, Ångström Laboratory, Institute of Theoretical ChemistryUppsala UniversityUppsalaSweden

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