Basil J. Hiley proves noncommutativity is key to macroscale nonlocality from quantum physics
The mathematics that is necessary to describe the holomovement is a non-commutative algebra and this way of looking at physical processes has a very profound impact on what we mean by the very notion of ‘existence’.
Quantum phenomena seem to have reintroduced the formal cause—let’s call it the ‘formative cause’. Indeed what Bohr was essentially pointing to is that the form of the equations of motion is changed, if the experimental situation is changed. This change of form does not have a mechanical origin. What do we mean by this? In the context of the holomovement, any change of the experimental conditions will change the overall structure process. But it must happen in a way that cannot be achieved by using the laws of classical mechanics. It turns out that this feature is beautifully captured by the non-commutative geometry.
If we go on and examine the mathematical expression of the quantum potential in different typical quantum situations, for example, the two slit interference experiment, we find the potential depends on the slit-width, how far apart the slits are and the momentum of the particles. In other words the quantum potential contains information concerning the experimental arrangement. Thus if we retain the notion of a localised particle, we can regard this potential as feeding the particle information about the environment. With this assumption we can actually calculate a set of individual trajectories, which when combined into an ensemble, gives rise to the observed interference pattern. Thus it seems that in order to have a description that retains the classical image of a localised particle following a trajectory, we have to feed in information about the
experimental context in a way that does not depend on the notion of a classical-like force.
So this ‘non-commutativity’ is basic in activity, while commutativity of
ordinary numbers is a special case working well in classical physics. Thus if we construct any geometry out of the holomovement, it must contain non-commutative elements. Since we started this work, mathematicians have been developing what they call ‘non-commutative algebraic geometry’ and what one finds is that if we go deeply into this new mathematics, we find that the standard quantum formalism is but a fragment of this new geometry. This is not surprising because
the mathematics was inspired by the standard quantum formalism. Within this structure one can see how the algebraic geometry of the classical world emerges. Thus we do not have two worlds as we seem to have now, a ‘weird' quantum world and a ‘sane’ classical world. These emerge as just two aspects of one world.
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