Hiley: "In a non-commutative structure, we must distinguish between a left and a right translation, so that both momenta, (31) and (32), arise by combinations of the left and right translations of the momentum operator. This implies that the real and imaginary parts of a weak value result from the fact that we have, at the fundamental level, a non-commutative structure and by forcing this into a complex structure we have hidden some aspects of the deeper structure."
https://www.sciencedirect.com/science/article/pii/S0003491622000033
As we will bring out, in this approach there is no collapse of any ‘wave function’ as the formalism concentrates on the flow of energy and accounts for what happens when this flow meets any topological obstructions, such as a series of slits or potential barriers. By concentrating on the flow of energy, the usual quantum paradoxes that face a wave function approach are not present..........
It is important to realise that our description involves what is usually called the algebra of operators. However in our context the ‘operators’ are the dynamical variables of the process; they do not ‘operate’ on anything. They describe the structure of the unfolding process, thus giving meaning to Bohm’s original notion of “structure process” [63].
We saw that the appearance of constraints necessitated the introduction of vector potentials leading us to a mathematics that is commonly used in describing vortex motion in fluids. This is no accident because constraints on all motion, classical or quantum, arise as a consequence of the Gromov non-squeezing theorem [6], [9]. The theorem plays a central role in our approach. Gromov’s theorem concerns all symplectomorphisms. It is a collective feature in the sense that all individual movement in a given situation is subject to the same global constraint. This constraint accounts in a new way for the collective feature usually attributed to the wave function in the standard approach to quantum phenomena. By replacing the wave function with a suitable element of a minimal left ideal, we can remove the puzzling and paradoxical aspects of wave–particle duality.
Bohm and Individuality - book chapter of Hiley
starting p. 226
excerpts on citing the origin of use of Phoronomy
https://arxiv.org/pdf/1602.06077.pdf
"Indeed the mathematics suggest that mass is implicated in both the particle and the field aspect. For mass appears in both the mathematical expression of the kinetic energy of the particle and in the mathematical expression of the quantum potential that represents the [psi] field."
p. 234 Hiley,
"Bohm's Approach and Individuality" chapter 12, 2016 in Individuals Across the Sciences
"the quantum potential depends only on the form or the second spatial derivative of the amplitude R, of the [psi] field. This form, in turn, reflects the form of the environment (such as the presence of slits, but also such features as magnetic flux lines, and differences in gravitational potential.)" p. 241
https://arxiv.org/pdf/1809.06072.pdf
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