13. Tom Etter, H. Pierre Noyes, Process, System, Causality, and Quantum Mechanics: A Psychoanalysis of Animal Faith

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Volume 12: Pages 733-765, 1999

Process, System, Causality, and Quantum Mechanics: A Psychoanalysis of Animal Faith

Tom Etter 1, H. Pierre Noyes 2

1112 Blackburn Avenue, Menlo Park, CA 94025‐2705 U.S.A.

2Stanford Linear Accelerator Center, Stanford University, Stanford, CA 94039 U.S.A.

We shall argue in this paper that a central piece of modern physics does not really belong to physics at all but to elementary probability theory. Given a joint probability distribution J on a set of random variables containing x and y, define a link between x and y to be the condition x = y on J. Define the state D of a link x = y as the joint probability distribution matrix on x and y without the link. The two core laws of quantum mechanics are the Born probability rule and the unitary dynamical law, whose best known form is Schrödinger's equation. Von Neumann formulated these two laws in the language of Hilbert space as prob(P) = trace(PD) and D′T = TD, respectively, where P is a projection, D and D′ are (von Neumann) density matrices, and T is a unitary transformation. We'll see that if we regard link states as density matrices, the algebraic forms of these two core laws are completely general theorems about links. When we extend probability theory by allowing cases to count negatively, we find that the Hilbert space framework of quantum mechanics proper emerges from the assumption that all D's are symmetrical in rows and columns. On the other hand, Markovian systems emerge when we assume that one of every linked variable pair has a uniform probability distribution. By representing quantum and Markovian structure in this way, we see clearly both how they differ and also how they can coexist in natural harmony with each other, as they must in quantum measurement, which we will examine. Looking beyond quantum mechanics, we see how both structures have their special places in a much larger continuum of formal systems that we have yet to look for in nature.

Keywords: core laws of quantum mechanics, foundations of quantum mechanics, measurement theory, laboratory object, link theory, EPR paradox, Markov processes, time reversal, future boundary conditions, negative probabilities

Received: April 24, 1999; Published online: December 15, 2008