Finite precision measurement nullifies Euclid's postulates

TL;DR

This paper argues that finite precision measurements, which limit directions to rational approximations, challenge Euclid's postulates by replacing the continuum of directions with a dense subset, thus conflicting with classical geometry.

Contribution

It introduces a model where finite measurement precision replaces the continuum of directions, providing a new perspective on Euclidean geometry's assumptions.

Findings

Finite precision measurement replaces the continuum of directions with a dense rational subset.

This replacement conflicts with Euclidean postulates and classical geometry.

The approach offers insights into the foundational assumptions of geometry and measurement.

Abstract

Following Meyer's argument (quant-ph/9905080) the set of all directions in space is replaced by the dense subset of rational directions. The result conflicts with Euclidean geometry.