Are Fundamental Entities Discrete or Continuous & What Discretization at Fundamental Level Could Mean?

Abstract

Are fundamental physical objects are discrete or continuous? Is it possible to have unique discretization in given measurement resolution? These questions inspired this article trying to provide overall view about number theoretical discretization provided by adelic physics in which reals and extensions of various p-adic number fields induced by given extension of rationals are fused together to form adele. Rationals and their extensions give rise to a unique discretizations of space-time surface (for instance) - cognitive representation - having interpretation in terms of finite measurement resolution. Number theory emerges in TGD also via classical number fields and one has dimensional hierarchy with rationals and their extensions at bottom, and reals, complex numbers, quaternions, and octonions above them.