Study of the Presence Probability Distribution in Autointerference States

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Abstract
An argument by one of us is first reproduced, demonstrating that the bare negation of the consequences imposed by the completeness hypothesis, concerning the particular formal fact that a quantum-mechanical free wave packet can spread out indefinitely, leads necessarily to predictions on the presence probability distribution in interference states that diverge from the corresponding quantum-mechanical predictions. It follows that, contrary to what seemed to be almost generally accepted, it is erroneous to admit systematically that the completeness problems are essentially unconnected to observation. This result is similar to one previously established by Bell and seems to support a suggestion by Ballentine, that any hidden-variable theory might necessarily lead to predictive divergences from quantum mechanics, if internal "pathologies" are not admitted. The above-mentioned argument entails a first minimal definition of a nonorthodox significance of a state vector. In the continuation of this work this definition is tentatively developed in a constructive way. This development is realized by a modification of de Broglie's model of a microsystem. This modification, imposed by an examination of de Broglie's double-solution theory in the light of our conclusion demonstrated before, is in fact rather profound; in particular, it forces the abandonment of the central idea of two solutions with distinct physical meanings, of a unique evolution law. However, the theory called into consideration by this modification may be capable of leading to objective proofs of the specific descriptive power of the essence of de Broglie's conception on the structure of microsystems. Indeed, inside the general nonorthodox framework tentatively outlined, a detailed definition of the presence probability distribution is elaborated that coincides with the quantum-mechanical one outside interference states, but diverges from it in interference states, in an experimentally testable way. This is a verifiable constructive embodiment of the conclusion only critically obtained at the beginning of this work. A final verdict on the value of the specific basic conception of the outlined theory and of the new perspectives it brings forth can be obtained only by a further systematic theoretical elaboration and by the corresponding experimental tests.

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