The Intrinsic Time of Alain Connes and Evolutive Properties in higher-d Algebras

Abstract

Alain Connes described automatic evolution in non-commutative measure spaces in his paper ‘Noncommutative Geometry Year 2000’ summarizing progress in that field, and this was a puzzle or riddle to the author for years. The notion some higher-order algebras have built-in evolutive properties appears central to the arguments of Connes, but the explanation given was so abstract it eluded understanding by me and others.  I read Connes’ words again and again, and later became a champion of this idea to other researchers in papers and conference presentations.  People falsely imagine it has no relevance in the real world, because of our limited perspective as creatures walking the face of the Earth and lacking the quantum-mechanical perspective of space as something dynamic.  But grasping intrinsic time may be crucial to survival for people exploring and working in outer space, and essential for understanding the early universe and quantum gravity.  So this paper examines how the ‘intrinsic time’ of Connes is connected to both abstract Maths and real world Physics.