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Journal of Pure and Applied Mathematics

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Quantum modeling: The real and the mathematical

Author(s): Finley Harris*

The records of mathematical modeling doors physics have been ruled via way of means of using classical mathematical fashions, C-fashions, usually the ones of a probabilistic or statistical nature. More recently, however, quantum mathematical fashions, Q-fashions, primarily based totally withinside the mathematical formalism of quantum principle have grown to be extra outstanding in psychology, economics, and selection technological know-how. The use of Q-fashions in those fields stays controversial, in element as it isn't always totally clear whether or not Q-fashions are important for handling the phenomena in the query or whether or not C-fashions could nonetheless suffice. My aim, however, isn't always to evaluate the need for Q-fashions in those fields, but alternatively to mirror what the feasible applicability of Q-fashions may also inform us approximately the corresponding phenomena there, vis-à-vis quantum phenomena in physics. To do so, I shall first speak about the important thing motives for using Q-fashions in physics. In particular, I shall look at the essential concepts that caused the improvement of quantum mechanics. Then I shall don't forget a likely function of comparable concepts in the use of Q-fashions doors physics. Psychology, economics, and selection technological know-how borrow already to be had Q-fashions from quantum principle, instead of deriving them from their inner concepts, whilst quantum mechanics changed into derived from such concepts, due to the fact there has been no quite simply to be had mathematical version to deal with quantum phenomena, even though the arithmetic at the end utilized in quantum did in truth exist then. I shall argue, however, that the precept angle on mathematical modeling doors physics would possibly assist us to recognize higher the function of Q-fashions in those fields and likely to examine new fashions, conceptually analogous to however mathematically distinct from the ones of quantum principle, that can be useful or may be important there or in physics itself. I shall, in closing, endorse one feasible form of such fashions, singularized probabilistic fashions, SP-fashions, several of which can be time-dependent, TDSP-fashions. The necessity of the use of such fashions may also extrude the character of mathematical modeling in technological know-how and, thus, the character of technological know-how, because it passed off withinside the case of Q-fashions, which now no longer simplest caused an innovative transformation of physics however additionally opened new opportunities for clinical wondering and mathematical modeling past beyond physics.

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