Underlining some mathematical and physical aspects about the concept of motion in general relativity
The Einstein initial foundations of general relativity have to do with his great intuition and they are not clear as it is for special relativity. As has been widely emphasized, for example, in the book of Ohanian and Ruffini, the very name of the theory indicates a misconception. Despite this, the high school textbooks (at least the Italian ones) and books of scientific divulgation introduce the Einstein gravitational theory still following the initial approach leading, in our opinion, to misinterpretations. A careful student, for example, immediately asks: it is not true that the Earth rotates because I can consider it at rest thanks to general relativity theory. The relativity of motion is trivial in mathematics while it has deep meaning in physics and it is not sufficiently analyzed. Similarly, the arbitrary choice of the origin and the perfect equivalence between all coordinate systems are mathematical properties satisfied by general relativity and students can confuse it with physical equivalence between reference systems that have a deeper meaning and the Einstein theory does not verify it. Gravitational force does not exist and this is the real core of Einsteinian revolution. As happens in Newtonian physics and Special Relativity, also in general relativity the relative motions are the geodesic motions with the difference that spacetime can be curved and geodesics may not be a straight line. Similarly, in general relativity forces cause non-geodesic motion. Geodesic and non-geodesic are tensorial properties and for this reason they are absolute.
KeywordsMach principle Relativity principle General relativity
Mathematics Subject Classification00A35 00A79
The authors wish to thank Prof. Antonio Feoli for comments and discussions. Thanks to the authors of [6, 12]. Their books are clear and very interesting and are also a useful source of references on this subject. This research was partially supported by FAR fund of the University of Sannio.
- 1.Galilei, G.: Discorsi e dimostrazioni matematiche intorno a due nuove scienze attenenti alla mecanica & i movimenti locali. Edizione Nazionale delle Opere di Galilei, Barbera Ristampa del 1968, Dialogues Concerning Two New Sciences, Firenze, vol. VIII, pp. 153–160. Dover, New York (1954)Google Scholar
- 2.Mach, E.: Die Mechanik in ihrer Entwicklung Historisch-Kritisch Dargerstellt. Leipzig, Brockhaus (1883)Google Scholar
- 4.Einstein, A., Infeld, L.: The evolution of Physics Cambridge. Cambridge University Press, Cambridge (1938)Google Scholar
- 7.Gasperini, M.: Manuale di Relatività Ristretta. Springer, Milan (2010)Google Scholar
- 8.Angel, R.B.: Relativity: The Theory and Its Philosophy. Pergamon Press, Oxford (2014)Google Scholar
- 11.Benedetto, E., Feoli, A.: Underlining some aspects of the equivalence principle. Eur. J. Phys. 38(5) (2017)Google Scholar
- 12.Capozziello, S., Funaro, M.: 2006 Introduzione alla Relatività Generale. Liguori Editore, Napoli (2006)Google Scholar
- 13.Eddington, A.S.: Space Time and Gravitation. University Press, Cambridge (1920)Google Scholar
- 15.Weinberg, S.: Gravitation and Cosmology. Wiley, New York (1972)Google Scholar
- 20.Hoyle, F.: Astronomy and Cosmology: a Modern Course. W.H. Freeman & Company, London (1975)Google Scholar