A theory of amplitudes

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Abstract
A stochastic framework for quantum mechanics is presented in which the elements are measurements and amplitudes. The resulting structure provides three stochastic levels. At the bottom level are the sample points. These may be unobservable, in general. At the next level are the outcomes of measurements. The amplitude of an outcome is computed by summing the amplitudes of the sample points resulting in that outcome upon a measurement. At the highest level are the events of a measurement. The probability of an event is computed by summing the moduli squared of the amplitudes for the outcomes comprising that event. Using these guidelines, various probabilities, conditional probabilities, and expectations are defined. Superpositions of amplitude functions are investigated and superselection sectors are shown to occur in a natural way. The framework is illustrated in various mathematical models such as spin‐ (1)/(2) models, the two‐slit experiment, and phase space quantum mechanics. Finally, a theory of discrete Feynman amplitudes is presented

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