Why is the Euclidean line the same as the real line?

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Abstract

This paper investigates whether the differential structure of spacetime follows from accepted laws of physics, or is a mathematical invention. In view of the results of [7], it suffices to consider whether the assumed identity of the Euclidean line E - the line of the geometers of ancient Greece - and the real line R of modern analysis, follows from any known law of nature (i.e., one that can be falsified empirically). Since the totality of empirical data is finite, one is forced to conclude that the completeness of R cannot be falsified empirically - and therefore, according to Popper's criterion, the real line must be an invention, and not a discovery. It then becomes difficult to tell whether Newton's second law of motion (expressed as the differential equation f = mẍ) is an invention or a discovery! Finally, some alternatives to the above analysis are briefly analysed.

Original languageEnglish
Pages (from-to)325-345
Number of pages21
JournalFoundations of Physics Letters
Volume12
Issue number4
DOIs
StatePublished - 1 Jan 1999

Keywords

  • Discrete to continuous in physics
  • Invention or discovery
  • Mathematics
  • Structure of the Euclidean line

ASJC Scopus subject areas

  • General Physics and Astronomy

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