Geometry as an aspect of dynamics
Contrary to the predominant way of doing physics, we claim that the geometrical structure of a general differentiable space-time manifold can be determined from purely dynamical considerations. Any n-dimensional manifold V/sub n/ has associated with it a symplectic structure given by the 2n numbers p and x of the 2n-dimensional contangent fiber bundle TV/sub n/. Hence, one is led, in a natural way, to the Hamiltonian description of dynamics, constructed in terms of the covariant momentum p (a dynamical quantity) and of the contravariant position vector x (a geometrical quantity). That is, the Hamiltonian description furnishes a natural way of relating dynamics and geometry. Thus, starting from the Hamiltonian state function (for a particle)-taken as the fundamental dynamical entity-we show that general relativistic physics implies a general pseudo-Riemannian geometry, whereas the physics of the special theory of relativity is tied up with Minkowski space-time, and nonrelativistic dynamics is bound up to Newton-Cartan space-time.
- Research Organization:
- Departamento de Fisica, Pontificia Universidade Catolica, Cx.P. 38071, Rio de Janeiro, RJ, Brasil
- OSTI ID:
- 6325007
- Journal Information:
- Found. Phys.; (United States), Journal Name: Found. Phys.; (United States) Vol. 15:12; ISSN FNDPA
- Country of Publication:
- United States
- Language:
- English
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