How arithmetic generates the logic of quantum experiments

September 26, 2009

Causeology in Quantum Physics

My work finds that hidden within Nature there is a causeology where there are entities whose existence is CAUSED and other entitiies whose existence is PERMITTED.  The caused entities can be confirmed and witnessed; but the permitted entities can be neither confirmed nor denied.
What is interesting is that unlike the causative processes with which we are accustommed in everyday experience, cause acends through chains:   cause, effect…cause, effect…cause,effect…; these quantum causes derive and materialise, not from caused entities up the chain, but permitted entities that are not caused. To illustrate, in a wave/particle duality, all the various wavelengths that make up a wavepacket are caused entities; but the interfering sums of these waves are permitted.  From these permitted interfernces derive caused probabilities.  The interfernces constitute a break in the causal chain. This claim is born out in the mathematics using Model Theory.
In the mathematics, this regime has its origin in the way numbers add and multiply.  The rules are the Field Axioms. Some numbers are caused by these axioms: the rational numbers exist as theorems; others are permitted. Juxtaposed against this system, are  products between orthogonal vectors which force the existence of certain permitted numbers. These orthogonal vectors are objects that, when multiplied with themselves give one, and, when multiplied with each other give zero.
The results lead to a 3-valued logic of true, false and indeterminate.  This was anticipated by Hans Reichenbach.  His 1944 book details the effects of this logic.  It does indeed resolve the paradoxes in quantum physics.  What Reichenbach had no idea of is where his logic came from…so it has been generally ignored.

My work finds that hidden within Nature there is a causeology where there are entities whose existence is caused and other entities whose existence is permitted.  The caused entities can be confirmed and witnessed; but the permitted entities can be neither confirmed nor denied.

What is interesting is that in contrast to the causative processes in classical physics where cause ascends through chains:   cause, effect…cause, effect…cause, effect…; there are quantum entities that derive, not from caused entities up the chain, but permitted entities that are not caused. To illustrate; in a wave/particle duality, all the various wavelengths that make up a wavepacket are caused entities; but the interfering sums of these waves are permitted.  From these permitted interferences derive caused probabilities.  So the interferences constitute a break in the causal chain. This claim is born out in the mathematics using Model Theory.

In the mathematics, this causal regime has its origin in the way numbers add and multiply.  The rules for this adding and multiplying are the Field Axioms. Some numbers are caused by these axioms: the rational numbers exist as theorems; other numbers with imaginary components, are permitted. Juxtaposed against this axiomatic system, are products between orthogonal vectors which force the existence of imaginary numbers which are merely permitted. The orthogonal vectors are objects that, when multiplied with themselves give one, and, when multiplied with each other give zero

The full causeology is 3-valued: cause, deny, permit.  These go hand in hand with a 3-valued logic of true, false and indeterminate.   This 3-valued logic was anticipated by Hans Reichenbach.  His 1944 book details the effects of this logic.  It does indeed resolve the paradoxes in quantum physics.  What Reichenbach had no idea of was where his logic came from…so it has been generally put to one side; now it has foundation.

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