Intro to Paper 1: Some Elementary Geometric Aspects in Extending the Dimension of the Space of Instants

In April 1996 The SASTPC Sponsored an International Conference at the University of Arizona entitled “Modern Mathematical Models of Time and Their Applications to Physics and Cosmology”.   The conference was organized by W. G. Tifft,  W. J.  Cocke, C. DeVito, and A. Pitucco and the proceedings were published in Astop & Space Science Sci. Journal 1996, edited by W. G. Tifft and W. J.  Cocke.  Several papers were presented in areas focusing on the physical and philosophical nature of time as it relates to the physics and cosmology.
The paper posted in this Blog is titled “Some Elementary Geometric Aspects in Extending the Dimension of the Space of Instants” presented by A. Pitucco during this conference.  The paper is based upon the familiar Hamilton-Jacobi theory from the calculus of variations as applied to the configuration space of a particle in the usual dynamical setting in which a classical particle moves in an underlying Euclidean manifold.   This paper extends this theory and considers observable time to be endowed with a 3-dimensional affine coordinate structure called a τ-space in which no such underlying manifold is assumed.

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