What is it about?
Probability in quantum mechanics is different from normal probability, and where there is interference it behaves like the variance of the sum of correlated random variables, not a probability. The article sets out to find a pair of hidden variables where the mean of one equals the variance of the other, and where they have the properties needed to be consistent with the formulation of quantum mechanics. While Bell's famous equation rules out reproducing quantum probabilities from classic probability theory the possibility nevertheless remains that hidden variables may exist that would bypass this limitation. Two such variables are found that satisfy quantum mechanics, including nonlocality such as measurements relating to two entangled particles that are too far apart in space and too close together in time for them to be connected even by signals moving at the speed of light. The results suggest that quantum probability itself could originate from a generic universal variable that triggers a process-specific variable where there is quantum activity which continues as a stochastic process while the activity continues. When normalized, this variable would be a stochastic analogue of quantum probability.
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Why is it important?
Although quantum mechanics works perfectly well without a mathematical reconciliation between quantum probability and the axioms of probability, the results provide insight that quantum probability itself could originate from a variable that is its stochastic analogue and whose normalized mean equals the probability as formulated by quantum mechanics. This prospect not only raises intriguing and potentially important questions about the nature of the underlying physics that could be described by such a process, but the deeper variability implied by the results might also inform or otherwise prove useful in quantum technology.
Perspectives
The acclaimed physicist and philosopher Carl Friedrich von Weizsacker concluded his 1973 paper on probability and quantum mechanics by expressing the belief that “there is a quantum theory behind quantum theory, precisely because probabilities can only be defined with the help of probabilities”. In a similar vein this current article sets out to explain why there is an unexplained coincidence in quantum mechanics, namely that mathematically 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, not a pre-normalized probability. This is not necessarily a popular endeavour because quantum mechanics works perfectly well without it. However, the coincidence is an untidy loose end that deserves attention, and the article seeks to give it attention in a way that is consistent with quantum mechanics. A central feature of the mathematics is that a generic variable is uncovered that is not linked to any point in space or time, and that seems to describe a regular phenomenon throughout the universe in which the intensity of the phenomenon varies randomly from instant to instant, with the intensity of each occurrence corresponding to a point on the support of the probability density of this variable, and with each realization of the variable being present everywhere in the universe in the same instant. In each instant this generic variable is formulated to be simultaneously transformed across the universal set of active quantum processes, wherever and for as long as a process is active, into a corresponding universal set of process-specific squared amplitude variables and their stochastic processes. This transformation involves the generic universal variable becoming a set of independent and identically distributed variables, spanning each spatial point and time at which a quantum process is active (but remaining generic and universal elsewhere), with the realization of the variable at a point being scaled by a factor that equals the deterministic squared amplitude of the specific quantum process that is active there. Please note that the reference in Appendix C to a bin ranging from SF to 1.25SF means the bin from 1 to 1.25 for the relevant SF and likewise the cdf interval that follows means the cdf at 1.25 for the relevant SF minus the cdf at 1for that SF.
Mr Tim C Jenkins
Independent Researcher
Read the Original
This page is a summary of: A Search for A Stochastic Archetype of Quantum Probability, Advances in Theoretical & Computational Physics, October 2022, Opast Group LLC,
DOI: 10.33140/atcp.04.04.08.
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