dorsal/arxiv
View SchemaGeometry of Time and Dimensionality of Space
| Authors | Metod Saniga |
|---|---|
| Categories | |
| ArXiv ID | physics/0301003 |
| URL | https://arxiv.org/abs/physics/0301003 |
| Journal | 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) |
Abstract
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.
{
"annotation_id": "2086b52a-c782-45c3-bf8e-92186548ef4c",
"date_created": "2026-03-02T18:00:43.083000Z",
"date_modified": "2026-03-02T18:00:43.083000Z",
"file_hash": "e9fe16766470f7d603f4f1b48b0200313afe66cb4200beaee45b73f94f86a2a0",
"private": false,
"record": {
"abstract": "One of the most distinguished features of our algebraic geometrical, pencil\nconcept of space-time is the fact that spatial dimensions and time stand, as\nfar as their intrinsic structure is concerned, on completely different\nfootings: the former being represented by pencils of lines, the latter by a\npencil of conics. As a consequence, we argue that even at the classical\n(macroscopic) level there exists a much more intricate and profound coupling\nbetween space and time than that dictated by (general) relativity theory. It is\nsurmised that this coupling can be furnished by so-called Cremona (or\nbirational) transformations between two projective spaces of three dimensions,\nbeing fully embodied in the structure of configurations of their fundamental\nelements. We review properties of some of the simplest Cremona transformations\nand show that the corresponding \"fundamental\" space-times exhibit an intimate\nconnection between the extrinsic geometry of time dimension and the\ndimensionality of space. Moreover, these Cremonian space-times seem to provide\nus with a promising conceptual basis for the possible reconciliation between\ntwo extreme concepts of (space-)time, viz. physical and psychological. Some\nspeculative remarks in this respect are made.",
"arxiv_id": "physics/0301003",
"authors": [
"Metod Saniga"
],
"categories": [
"physics.gen-ph"
],
"journal_ref": "The Nature of Time: Geometry, Physics and Peception; edited by\n Rosolino Buccheri, Metod Saniga and William Mark Stuckey, NATO Science Series\n II: Volume 95, Kluwer Academic Publishers, Dordrecht - Boston - London, 2003,\n pp. 131-143; ISBN 1-4020-1200-4 (hardbound) and ISBN 1-4020-1201-2\n (paperback)",
"title": "Geometry of Time and Dimensionality of Space",
"url": "https://arxiv.org/abs/physics/0301003"
},
"schema_id": "dorsal/arxiv",
"source": {
"execution_id": "4407e085-6ae9-4077-a507-d2d978e99f54",
"id": "arXiv Dataset IDs",
"type": "Model",
"variant": "snapshot-2026-03-01",
"version": "0.1.0"
},
"user_id": 1000002
}