Non-commutativity is an important and well known aspect of rotations of 3 dimensional bodies.
So explains a well-written Ph.D. analysis of Bohmian physics
Esoteric Quantization, The Esoteric Imagination in David Bohm's Interpretation of Quantum Mechanics
We are exploring the possibility of describing this process by some form of non-commutative algebra, an idea that fits into the general ideas of the Implicate Order. In such a structure, the non-locality of quantum theory can be understood
as a specific feature of this more general a-local background
and that locality, and indeed time, will emerge as a special feature of this deeper a-local structure.
Relativity, Quantum Gravity and Space-time Structures, Birkbeck, University of London (downloaded 12 June 2013)
But that was early Hiley on noncommutativity - say from 2006. Hiley's late research was focused on nonlocal time in which there was a 2D process of energy and then time that is noncommutative.
the famous Heisenberg inequality is just a consequence of the non-
commutativity of the algebra of operators. The deeper fundamental aspect
is the non-commutativity
So Hiley went as far to say that noncommutativity has nothing to do with the uncertainty relation!!
the conclusion is that the wholeness of the quantum states is explicated as the Quantum Potential only when the abstract setting is projected from the non-commutative algebraic structure into a space-time frame. This is in line with Bohm’s philosophical approach
in which the wholeness of the situation is primary and the Quantum Po-
tential appears when a Super Implicate Order is unfolded.
This idea has been the guiding principle in Hiley’s research. With the
help of Robert Callaghan he has successfully completed the first stage
of development of a Causal quantum field theory using a similar structure based on Clifford algebras.
So the key here is the "tower" of Clifford algebras has a 2D with nonlocal time foundation
the wholeness of the algebra is of fundamental relevance and the expression of the potential is secondary,......
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