- Commutative Probability , and Quantum Entanglement

We construct a rigourous model of quantum measurement. A two-state model of a negative temperature amplifier, such as a laser, is taken to a classical thermodynamic limit. In the limit, it becomes a classical measurement apparatus obeying the stochastic axioms of quantum mechanics. Thus we derive the probabilities from a deterministic Schroedinger's equation by procedures analogous to those of classical statistical mechanics. This requires making precise the notion of 'macroscopic.' Macroscopic entanglement is a fact of life. But the topic of Quantum Measurement has to explain in what sense decoherence between pointer positions of a measurement apparatus can happen, and propose a mechanism to produce it. In this paper we study a simple two-state model of an amplifying apparatus being used as a particle detector. Schroedinger's equation's being exactly valid over laboratory dimensions, including the amplifying apparatus, the states of the particle and the apparatus are entangled, after the measurement process is complete. We take a closed system approach, so we neglect the effect of the environment. If the apparatus is large enough, it is well approximated by a new kind of thermodynamic limit, which we introduce, and the Ming Effect shows that superpositions of pointer positions are practically negligible. No special mechanism is required. Introduction Although Quantum Mechanics, in the form discovered by Heisenberg, Schroedinger, and Dirac in 1925, is the most successful physics theory in history, explaining almost every phenomenon within laboratory dimensions, especially including all of chemistry and biology, there has always been some dissatisfaction with it. Nobel prizewinners such as Einstein, de Broglie, Planck, and Schroedinger himself have all ended up dissenting from the usual interpretation of Quantum Mechanics. At issue is not the formal, mathematical methods of calculating experimentally verifiable quantities, but rather what philosophical interpretation or mental picture of the wave-particle duality can be considered true, or even sensible? Wigner [15] analysed this as the problem of Quantum Measurement. As long as we do not measure anything, all Nature is governed by a deterministic wave equation, Schroedinger's equation, and what the wave will do in the future is completely determined by what it did in the past. All calculations of experimentally verifiable quantities involve calculations involving this wave and using the wave equation. But whenever we measure a system, its wave makes some kind of jump which is a violation of the wave equation, is random and unpredictable, and our measurement always seems to …