paper 150111134255

Published: 2015-07-09

Geometry and Its Physical Meaning

Sara Liyuba Vesely,

Sara Liyuba Vesely

I.T.B. --- C.N.R., Italy

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Alessandro Alberto Vesely

Via L. Anelli 13, Italy

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Proceedings of 2015 Photonics & Electromagnetics Research Symposium, Prague, July 6 - 9，Page(s)45-50

Abstract

Until the end of 1800s, the graphical aspect of geometry used to be compared to the external world, called “physical space”, and justified on the basis of mechanics. As a con- sequence of the foundational crisis of mathematics, geometry switched to axiomatic programs and disengaged from the physical intuition of space. Its logical structure was formalized and further developed, neglecting geometrical constructions. Endorser of formalist programs, physics evolved toward more and more sophisticated interpretations of the world, also supported by advancements of surveying and measurement techniques. Physical laws are regarded as interpre- tative algorithms tied to recurring process patterns, no longer as interpretations of a code that Nature is written in the language of. What got lost during that transition, in our opinion, is the ability to avail of both experience and deduction in geometrical models of field theories, so as to provide a logical foundation for interpreting the extent in a physically meaningful way. In particular, (1) irrespectively of whatever code, the optical channel does convey a huge amount of the data, which our experience consists of, and (2) geometry allows to model non-optical elec- tromagnetic signals consistently with the optical ones, so as to analyze them uniformly. In this paper, we stem from models entailed by geometrical optics and discuss the relationships among them, imaging based on projective geometry, and mathematical analysis.

Citation

Sara Liyuba Vesely, and Alessandro Alberto Vesely, "Geometry and Its Physical Meaning," Proceedings of 2015 Photonics & Electromagnetics Research Symposium, Prague, July 6 - 9，Page(s)45-50

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