Research ArticleOpen AccessGoogle Scholar indexed
Spacetime Geometry and the Laws of Physics
Gatineau, Québec, Canada
- 1 Gatineau, Québec, Canada
Journal of Modern Physics·Volume 08 (2017)·Pages 330–337·Published 28 February 2017·DOI10.4236/jmp.2017.83022
Copy link · social · email
Abstract
The Laws of Classical and Quantum Mechanics are well known. However, their origin remains mysterious and their interpretation controversial. It has been argued that this situation will continue until one manages to derive the Laws of Physics from some very first principles. In this paper, we use basic concepts of Differential Geometry to yield the Klein-Gordon equation and the Lagrange equations of Relativistic Mechanics without using the standard postulates of Quantum Mechanics, Special Relativity or even General Relativity.
KeywordsScalar FieldCurved SpacetimeKlein-Gordon EquationRelativistic TrajectoriesCharged Particles
- Schroedinger, E. (1926) Annals of Physics, 79, 361-376. https://doi.org/10.1002/andp.19263840404
- Schroedinger, E. (1926) Annals of Physics, 79, 489-527. https://doi.org/10.1002/andp.19263840602
- Ward, D. and Volkmer, S. (2006) How to Derive the Schroedinger Equation. arXiv:physics/0610121
- Field, J.H. (2004) European Journal of Physics, 25, 385-397. https://doi.org/10.1088/0143-0807/25/3/006
- Nelson, E. (1966) Physical Review, 150, 1079-1085. https://doi.org/10.1103/PhysRev.150.1079
- Davidson, M.P. (1979) Journal of Mathematical Physics, 20, 1865-1869. https://doi.org/10.1063/1.524304
- Hall, M.J.W. and Reginato, M. (2002) Journal of Physics A, 35, 3239-3303. https://doi.org/10.1088/0305-4470/35/14/310
- Fuchs, C.A. (2003) Journal of Modern Optics, 50, 987-1023. https://doi.org/10.1080/09500340308234548
- Landau, L.D. and Lifschitz, E.M. (1977) Quantum Mechanics: Non-Relativistic Theory. 3rd Edition, Volume 3, Butterworth-Heinemann, Oxford.
- Rovelli, C. (1996) International Journal of Theoretical Physics, 35, 1637-1678. https://doi.org/10.1007/BF02302261
- Wu, L., Salehi, M., Koirala, N., Moon, J., and Armittage, N.P. (2016) Science, 354, 1124-1127. https://doi.org/10.1126/science.aaf5541
- Enriques, F. (1911) Encyclopedie des Sciences Math. Tome 3. 1-71.
- Schutz, B.F. (1990) A First Course in General Relativity. Cambridge University Press, Cambridge.
- Sjostrom, D.-M. (2013) Bosons and Fermions in Curved Spacetimes. PhD Thesis, Norvegian University of Science and Technology, Mai.
- Arminjon, M. (2008) Foundations of Physics, 38, 1020-1045. https://doi.org/10.1007/s10701-008-9249-6
- Arminjon, M. (2010) Brazilian Journal of Physics, 40, 242-255. https://doi.org/10.1590/S0103-97332010000200020