Cremona transformations and the conundrum of dimensionality and signature of macro-spacetime
type: Item
instance of: scholarly article
title: Cremona transformations and the conundrum of dimensionality and signature of macro-spacetime
zbMATH Open document ID: 1014.53041
DOI: 10.1016/S0960-0779(00)00183-1
author: Metod Saniga
published in: Chaos, Solitons and Fractals
publication date: 2002-06-13T00:00:00Z
review text: The paper under review has a deep philosophical motivation: understanding why (apparently) our universe has four dimensions and a \((-,+,+,+)\) signature, and why the time arrow corresponds to the negatively defined direction. These facts do not seem to derive from the first principles of Physics (they are some ``observationally fixed'' parameters). The author constructs a theory of pencil-generated spacetimes. The spatial coordinates are identified with pencils of lines and the time dimension is identified with a pencil of conics, all arranged in the three-dimensional projective space. The separation of spatial and time-like coordinates is linked with the ``quadro-cubic'' Cremona transformations of the projective space. In the author's opinion, the algebro-geometric classifications of pencils suggest a plausible explanation for the fundamental physical and philosophical problems described above.
reviewed by: Gabriel Teodor Pripoae
Mathematics Subject Classification ID: 53C55
Mathematics Subject Classification ID: 83C99
Mathematics Subject Classification ID: 00A30
Mathematics Subject Classification ID: 14E05
zbMATH DE Number: 1755327
zbMATH Keywords: universe
zbMATH Keywords: principles of physics
zbMATH Keywords: pencil-generated spacetimes
zbMATH Keywords: projective space
zbMATH Keywords: physical and philosophical problem
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1755327