Stochastic quantum probability and subatomic particle experiment design

What is it about?

This article is the third of a trilogy of articles on the nature of probability in quantum mechanics. The first article [1] began by noting that superposed wavefunctions in quantum mechanics lead to a squared amplitude that introduces interference into the position probability density of an atomic particle, which happens nowhere else in probability theory. It went on to also note that there is an unexplained coincidence in quantum mechanics in that the interference term in the squared amplitude of superposed wavefunctions gives the squared amplitude the form of a variance of a sum of correlated random variables and went on to examine whether there could be an archetypical variable, in the Platonic sense of true form, behind quantum probability that would reconcile quantum probability with classic probability. This examination found such a variable, which can encompass both local and nonlocal quantum events. The second article [2] provided evidence that quantum probability has such a stochastic nature. This evidence was based on the number of electrons that need to be sent through a two-slit interferometer to gain a clear pattern of self-interference, which when compared with the number that would be expected to be sufficient in order for the position probability distribution of the self-interference wavefunction to take clear shape suggests that there is more variability present than that described by the formulation of quantum mechanics, which implies the presence of an underlying and as yet unrecognized physical process. This final article completes the trilogy by considering how a key aspect of experimental design would be affected by the increased variability that would be present if quantum probability is itself stochastic in the manner suggested in the previous two articles. Keywords: quantum probability, two-slit experiment, self-interference, wavefunction, simulation, stochastic, experiment design

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Why is it important?

This article completes a trilogy of articles devoted to the nature of quantum probability. The first article hypothesized that quantum probability is itself stochastic and uncovered an archetypical hidden variable that could be a suitable candidate for such a variable behind quantum probability if indeed it is itself stochastic. The second article examined evidence provided by the famous Tonomura two-slit electron self-interference experiment that supported the hypothesis of the first article. It claimed that if quantum probability is itself stochastic the resulting variability around the mean would explain the much larger number, than the otherwise sufficient 5000 or so electron emissions, that were necessary for a relatively clear picture to form in the Tonomura experiment, where 140,000 electron emissions were necessary. This third and final article has confirmed the claim in the second article, showing, for example, that if there are 200 points where a particle could be any time, and bearing in mind that the realizations of the unit squared amplitude variable at any time are i.i.d, the mean of an experiment with 5000 trials would only closely approximate the deterministic squared amplitude at each of the points about 60% of the time and be distorted about 40% of the time, while the mean of an experiment with 140,000 trials would closely approximate the deterministic squared amplitude at each point about 100% of the time and be distorted almost none of the time. It has also shown that a similar result applies to the variance, but with more amplified distortion than happens with the mean.