Geometry of Time and Dimensionality of Space
Abstract
Description
One of the most distinguished features of our algebraic geometrical, pencil concept of space-time is the fact that spatial dimensions and time stand, as far as their intrinsic structure is concerned, on completely different footings: the former being represented by pencils of lines, the latter by a pencil of conics. As a consequence, we argue that even at the classical (macroscopic) level there exists a much more intricate and profound coupling between space and time than that dictated by (general) relativity theory. It is surmised that this coupling can be furnished by so-called Cremona (or birational) transformations between two projective spaces of three dimensions, being fully embodied in the structure of configurations of their fundamental elements. We review properties of some of the simplest Cremona transformations and show that the corresponding "fundamental" space-times exhibit an intimate connection between the extrinsic geometry of time dimension and the dimensionality of space. Moreover, these Cremonian space-times seem to provide us with a promising conceptual basis for the possible reconciliation between two extreme concepts of (space-)time, viz. physical and psychological. Some speculative remarks in this respect are made.
10 pages, 4 figures, to appear in the proceedings of the NATO ARW "The Nature of Time: Geometry, Physics and Perception," edited by R. Buccheri, M. Saniga and W.M. Stuckey, Kluwer Academic Publishers, Dordrecht / Boston / London, 2003, pp. 131-143
10 pages, 4 figures, to appear in the proceedings of the NATO ARW "The Nature of Time: Geometry, Physics and Perception," edited by R. Buccheri, M. Saniga and W.M. Stuckey, Kluwer Academic Publishers, Dordrecht / Boston / London, 2003, pp. 131-143
Keywords
Citation
Consulte el texto completo en el siguiente enlace:
https://arxiv.org/abs/physics/0301003
http://arxiv.org/abs/physics/0301003
The Nature of Time: Geometry, Physics and Peception; edited by Rosolino Buccheri, Metod Saniga and William Mark Stuckey, NATO Science Series II: Volume 95, Kluwer Academic Publishers, Dordrecht - Boston - London, 2003, pp. 131-143; ISBN 1-4020-1200-4 (hardbound) and ISBN 1-4020-1201-2 (paperback)
http://arxiv.org/abs/physics/0301003
The Nature of Time: Geometry, Physics and Peception; edited by Rosolino Buccheri, Metod Saniga and William Mark Stuckey, NATO Science Series II: Volume 95, Kluwer Academic Publishers, Dordrecht - Boston - London, 2003, pp. 131-143; ISBN 1-4020-1200-4 (hardbound) and ISBN 1-4020-1201-2 (paperback)