Non-Commutative Worlds and Classical Constraints

Abstract

This paper reviews results about discrete physics and non-commutative worlds and explores further the structure and consequences of constraints linking classical calculus and discrete calculus formulated via commutators. In particular, we review how the formalism of generalized non-commutative electromagnetism follows from a first order constraint and how, via the Kilmister equation, relationships with general relativity follow from a second order constraint. It is remarkable that a second order constraint, based on interlacing the commutative and non-commutative worlds, leads to an equivalent tensor equation at the pole of geodesic coordinates for general relativity.

Keywords

• discrete calculus
• iterant
• commutator
• diffusion constant
• Levi-Civita connection
• curvature tensor
• constraints
• Kilmister equation
• Bianchi identity