Abstract
The work on, and the understanding of, gravitation greatly influenced not only the physicist’s conception of nature but also the development of all exact sciences. Newton invented the method of fluxions, and thereby laid down the foundations of calculus, in connection with his research on the motion of bodies and on the law of universal attraction.1 The calculus of variations, the theory of differential equations and the perturbation methods of solving them arose directly from the needs of mechanics and astronomy. Through the work of Poincaré2, the consideration of global and stable properties of motions stimulated the birth of topology. The relativistic theory of gravitation of Einstein3, and his search for a unified theory4, enhanced the development of differential geometry. The notion of a superspace introduced recently by J.A.Wheeler5 provides us with a concrete example of an infinite-dimensional manifold and leads to a number of difficult problems in the theory of Banach manifolds.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
Sir Isaac Newton, Mathematical Principles of Natural Philosophy (translated into English by Andrew Motte), Cambridge University Press (1934).
H. Poincaré, Les méthodes nouvelles de la mécanique céleste, 3 vol., Gauthier-Villars, Paris (1892–99).
A. Einstein, ‘Die Grundlage der allgemeinen Relativitätstheorie’, Ann. Physik 49, 769–822 (1916).
A. Einstein, The Meaning of Relativity, 5th ed., Princeton University Press (1955).
J. A. Wheeler, Einstein’s Vision, Springer Verlag, Berlin (1968).
A short review of the recent theoretical and observational work on relativistic gravitation, together with references to literature, may be found in the author’s Summary of the 6th International Conference on GRG (Copenhagen, July 1971), published in the GRG Journal 3,167 (1972).
J. Weber, ‘Evidence for discovery of gravitational radiation’, Phys. Rev. Lett. 22, 1320 (1969) and ‘Anisotropy and polarization in the gravitational radiation experiments’, Phys. Rev. Lett. 25, 180 (1970).
Various relativistic theories of gravitation have been recently reviewed by K. S. Thorne, C. M. Will, and their co-workers, cf. C. M. Will, The Theoretical Tools of Experimental Gravitation, Lectures presented at Course 56 of the International School of Physics ‘Enrico Fermi’, Varenna, July 1972.
A good review of the research on quantization of the gravitational field done prior to 1967, together with new results, and references to the literature of the subject, can be found in: B. S. DeWitt, ‘Quantum theory of gravity’, Phys. Rev. 160, 1113 (1967); 162,1195 (1967); 162, 1239 (1967).
A. Salam and J. Strathdee, ‘Quantum gravity and infinities in quantum electrodynamics’, Lett. Nuovo Cimento 4,101–108 (1970); C. I. Isham, A. Salam and J. Strathdee, ‘Infinity suppression in gravity-modified quantum electrodynamics’, Phys. Rev. D3, 1805 (1971) and Part II (ICTP preprint no. 14/71).
L. Parker, ‘Quantized fields and particle creation in expanding universes’, Phys. Rev. 183, 1057 (1969).
R. U. Sexl and H. K. Urbantke, ‘Production of particles by gravitational fields’, Phys. Rev. 179, 1247 (1969).
Ya. B. Zeldovich, ‘Creation of particles in cosmology’, Pisma v Zh.E.T.F. 12, 443 (1970); Ya. B. Zeldovich and A. A. Starobinsky, ‘Particle creation and vacuum polarization in the anisotropic gravitational field’, a preprint of the Institute of Applied Mathematics, U.S.S.R. Academy of Sciences (in Russian); Ya. B. Zeldovich and I. D. Novikov, Tieoria tiagotienia i evolutsyia zviezd, Moscow (1971).
S. W. Hawking and R. Penrose, ‘The singularities of gravitational collapse and cosmology’, Proc. Roy. Soc. Lond. A 314, 529 (1970).
E. Kretschmann, ‘Über den physikalischen Sinn der Relativitäts-postulate’, Ann. Physik 53, 575 (1917); A. Einstein, ‘Prinzipielles zur allgemeinen Relativitätstheorie’, Ann. Physik 55, 241 (1918).
V. A. Fock, Theory of Space, Timet and Gravitation, Moscow (1955); and ‘Principles of Galilean mechanics and Einstein’s theory’, Uspekhi Fiz. Nauk 83, 577 (1964).
A. Trautman, ‘Comparison of Newtonian and relativistic theories of space-time’, in Perspectives in Geometry and Relativity (Essays in Honor of V. Hlavaty ), Bloomington (1966).
A. Trautman, ‘The General Theory of Relativity’, Uspekhi Fiz. Nauk 89, 3 (1966).
J. L. Anderson, Principles of Relativity Physics, Academic Press, New York (1967).
S. MacLane, ‘Categorical algebra’, Bull. Amer. Math. Soc. 71, 40–106 (1965); I. Bucur and A. Deleanu, Introduction to the Theory of Categories and Functors, J. Wiley, New York (1969) A. Trautman, ‘Relativity, categories, and gauge invariance’, lecture given at the 5th International Conference on GRG, Tbilisi, 1968 (in print in the Proceedings of the Conference).
N. Steenrod, The Topology of Fibre Bundles, Princeton University Press (1951); A. Lichnerowicz, ‘Espaces fibrés et espaces-temps’, GRG Journal 1, 235–245 (1971); R. Hermann, Vector bundles in mathematical Physics, vol. 1, Benjamin, New York (1970); A. Trautman, ‘Fibre bundles associated with space-time’, Reports on Math. Phys. (Torun) 1, 29–62 (1970).
R. Penrose, ‘Structure of Space-Time’, Chapter VIII of the 1967 Lectures in Mathematics and Physics (Battelle Rencontres) (ed. by C. M. DeWitt and J. A. Wheeler ), Benjamin, New York (1968).
R. Palais, Foundations of Global Analysis, Benjamin, New York (1968).
A. Trautman, ‘Invariance of Lagrangian Systems’, article in General Relativity (papers in honour of J. L. Synge), (ed. by L. O’Raifeartaigh ), Clarendon Press, Oxford (1972).
S. Kobayashi and K. Nomizu, Foundations of Differential Geometry, vol. 1, Interscience, New York (1963).
C. N. Yang and R. L. Mills, ‘Conservation of isotopic spin and isotopic gauge invariance’, Phys. Rev. 96, 191 (1954); T. D. Lee and C. N. Yang, ‘Conservation of heavy particles and generalized gauge transformations’, Phys. Rev. 98, 1501 (1955).
R. Utiyama, ‘Invariant theoretical interpretation of interaction’, Phys. Rev. 101, 1597 (1956); T. W. B. Kibble, ‘Lorentz invariance and the gravitational field’, J. Math. Phys. 2, 212 (1961).
P. G. Bergmann, Introduction to the Theory of Relativity, Prentice-Hall, New York (1942).
A. Trautman, ‘Riemannian Bundles’, Bull. Acad. Polon. Sei., sér. sei. math, et phys. 18, 667 (1970).
E. Cartan, ‘Sur une généralisation de la notion de courbure de Riemann et les éspaces à torsion’, Compt. Rend. Acad. Sei. Paris 174, 593 (1922). E. Cartan, ‘Sur les variétés à connection affine et la théorie de la relativité généralisée, I partie’, Ann. Ec. Norm. 40, 325 (1923) and 41, 1 (1924).
W. Kopczyñski, ‘A non-singular universe with torsion’, Phys. Lett. 39A, 219 (1972).
A. Trautman, ‘On the Einstein-Cartan equations III’, Bull. Acad. Polon. Sei., sér. sei. math, astr. et Phys. 20, 895 (1972).
M. Mathisson, ‘Neue Mechanik materieller Systeme’, Acta Phys. Polon. 6. 163 (1937).
A. Papapetrou, ‘Spinning test-particles in general relativity’, Proc. Roy. Soc. (.London) A209, 249 (1951).
F. W. Hehl, ‘Spin und Torsion in der allgemeinen Relativitäts-theorie oder die RiemannCartansche Geometrie der Welt’, Habilitationsschrift (mimeographed), Tech. Univ. Clausthal (1970).
M. A. Melvin, private communication of 27 September 1972.
Th. Kaluza, Sitz. Preuss. Akad., p. 966 (1921).
R. Kerner, Ann. Inst. H. Poincaré, IX, 143 (1968).
W. Thirring, Act. Phys. Austr. Suppl (1972).
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1973 D. Reidel Publishing Company, Dordrecht-Holland
About this chapter
Cite this chapter
Trautman, A. (1973). Theory of Gravitation. In: Mehra, J. (eds) The Physicist’s Conception of Nature. Springer, Dordrecht. https://doi.org/10.1007/978-94-010-2602-4_8
Download citation
DOI: https://doi.org/10.1007/978-94-010-2602-4_8
Publisher Name: Springer, Dordrecht
Print ISBN: 978-94-010-2604-8
Online ISBN: 978-94-010-2602-4
eBook Packages: Springer Book Archive