The Mechanism of Wave Function Collapse
From the variations of quantum probabilities under a slip according to formulas (5a and 5b), an explicit mechanism of wave function collapse results. One will not describe it in detail and one mentions only a few significant points:
Equations (5a and 5b) dealt with slips towards a channel j from other channels j, under govern of the matrix pAB +, but one must take also account of slips going from the channel j towards other channels j.
One must also consider the contributions by the matrix — pAB_. Their combined effect cancels all the average values < 8pj > but they let survive the correlation coefficients < 8pj8pj > and the squares of standard deviations < (8p)2 >.An interesting remark is brought by opposite effects of the matrices (pAB +, — PAB-) and also of opposite transitions, j j, from two channels. Since the two matrices pAB + and pAB_ represented already fluctuations in the external flux and the final outcome, which consists only in correlations and squares of standard deviations, makes theses two matrices fight against each other, this means that the final results (which will include collapse), is due to fluctuations in the mutual compensation of positive and negative fluctuations.
This is a remarkable property, with no analog in physics, as far as I know (at least not in quantum mechanics). It came as a surprise when its character was realized and, presumably, would not have been anticipated under other approaches.
One may go then rapidly to the conclusion of these conclusions. It turns out that the quantities < 8pj8pj > and < (Spj)1 > are proportional to the time interval St, which one considers. This behavior is the signature of a Brownian process. A famous theorem by Pearle (1976) implies then that the random variations in the quantum probabilities must end up necessarily with a situation where one quantum probability, say pj, has become equal to 1 and the other probability vanished.
This conclusion is a prediction of collapse. Pearle's theorem asserts moreover that this Brownian probability is equal to the initial value of pj in the state (3), and this is in perfect agreement with Born's fundamental probability rule. (The proof of Pearle's theorem must be slightly enlarged in the present case, but this is only a matter of mathematics owing to the finiteness of an individual slip). More details, including quantitative matters and the case of separate detectors, can be found elsewhere (arXiv:1601.01214v2).
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