Introduction

Hans Jürgen Borchers, Rathindra Nath Sen

Research output: Chapter in Book/Report/Conference proceedingForeword/postscript

Abstract

In every textbook on the theory of relativity it is assumed, without any discussion, that space-time is a differentiable manifold, possibly with singularities. Between a point-set and a differentiable manifold there is an enormous gap, and we felt that physics itself could contribute to narrowing this gap. In experimental physics, one can make only a finite number of well-separated measurements, and therefore it is natural to start with a discrete set of points as a candidate for space-time. As one cannot put an upper bound on the number of measurements, this set cannot be finite; it must, at least, be countable. Next, as one cannot place a quantitative limit on experimental accuracy, one has to admit the "density" property that between any two points on a scale lies a third. Finally, one has to ask how one arrives at the continuum. In short, we felt that it should be possible to start from point-sets and find conditions (axioms) -motivated by physics -which would allow us to construct a topological manifold from the point-set. If this turned out to be true, one could become more ambitious and look for conditions which would imply the differentiability of the manifold.

Original languageEnglish
Title of host publicationMathematical Implications of Einstein-Weyl Causality
Pages1-6
Number of pages6
DOIs
StatePublished - 1 Dec 2006

Publication series

NameLecture Notes in Physics
Volume709
ISSN (Print)0075-8450

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