dorsal/arxiv
View SchemaCremonian Space-Time(s) as an Emergent Phenomenon
| Authors | Metod Saniga |
|---|---|
| Categories | |
| ArXiv ID | physics/0402097 |
| URL | https://arxiv.org/abs/physics/0402097 |
| DOI | 10.1016/j.chaos.2004.05.018 |
| Journal | Chaos, Solitons and Fractals 23 (2005) 645-650 |
Abstract
It is shown that the notion of fundamental elements can be extended to_any_, i.e. not necessarily homaloidal, web of rational surfaces in a three-dimensional projective space. A Cremonian space-time can then be viewed as an_emergent_ phenomenon when the condition of "homaloidity" of the corresponding web is satisfied. The point is illustrated by a couple of particular types of "almost-homaloidal" webs of quadratic surfaces. In the first case, the quadrics have a line and two distinct points in common and the corresponding pseudo-Cremonian manifold is endowed with just two spatial dimensions. In the second case, the quadrics share six distinct points, no three of them collinear, that lie in quadruples in three different planes, and the corresponding pseudo-Cremonian configuration features three time dimensions. In both the cases, the limiting process of the emergence of generic Cremonian space-times is explicitly demonstrated.
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"abstract": "It is shown that the notion of fundamental elements can be extended to_any_,\ni.e. not necessarily homaloidal, web of rational surfaces in a\nthree-dimensional projective space. A Cremonian space-time can then be viewed\nas an_emergent_ phenomenon when the condition of \"homaloidity\" of the\ncorresponding web is satisfied. The point is illustrated by a couple of\nparticular types of \"almost-homaloidal\" webs of quadratic surfaces. In the\nfirst case, the quadrics have a line and two distinct points in common and the\ncorresponding pseudo-Cremonian manifold is endowed with just two spatial\ndimensions. In the second case, the quadrics share six distinct points, no\nthree of them collinear, that lie in quadruples in three different planes, and\nthe corresponding pseudo-Cremonian configuration features three time\ndimensions. In both the cases, the limiting process of the emergence of generic\nCremonian space-times is explicitly demonstrated.",
"arxiv_id": "physics/0402097",
"authors": [
"Metod Saniga"
],
"categories": [
"physics.gen-ph"
],
"doi": "10.1016/j.chaos.2004.05.018",
"journal_ref": "Chaos, Solitons and Fractals 23 (2005) 645-650",
"title": "Cremonian Space-Time(s) as an Emergent Phenomenon",
"url": "https://arxiv.org/abs/physics/0402097"
},
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