The Local-Nonlocal Dichotomy Is but a Relative and Local View Point

Elemer Elad Rosinger (1)

1 Department of Mathematics and Applied Mathematics [Pretoria]

As argued earlier elsewhere, what is the Geometric Straight Line, or in short, the GSL, we shall never know, and instead, we can only deal with various mathematical models of it. The so called standard model, given by the usual linearly ordered field $\mathbb{R}$ of real numbers is essentially based on the ancient Egyptian assumption of the Archimedean Axiom which has no known reasons to be assumed in modern physics. Setting aside this axiom, a variety of linearly ordered fields $\mathbb{F}_{\cal U}$ becomes available for the mathematical modelling of the GSL. These fields, which are larger than $\mathbb{R}$, have a rich self-similar structure due to the presence of infinitely small and infinitely large numbers. One of the consequences is the obvious relative and local nature of the long ongoing local versus nonlocal dichotomy which still keeps having foundational implications in quantum mechanics.

Mots clés: local nonlocal dichotomy is relative and local

Domaines: Physique mathématique [math-ph]; Mathématiques générales [math.GM]; Physique Quantique [quant-ph]

Elemer Elad Rosinger. The Local-Nonlocal Dichotomy Is but a Relative and Local View Point. 2011. ⟨hal-00590638⟩