Some Historical and Philosophical Aspects of Quantum Probability Theory and its Interpretation

Peter Mittelstaedt

Markus Ehberger

Abstract This chapter focuses on Paul Dirac’s introduction of a verbally explicit description of scattering in terms of two successive emission and absorption processes, each coupled to a transition of the atom, not obeying energy conservation and located on the level of probability amplitudes. Historical actors called these energy non-conserving transitions “virtual transition” later on. I will contextualize Dirac’s introduction of this verbal model in reference to his research at the time, his interpretation of quantum theory and his rather pragmatic to flexible approach to mostly philosophical aspects of the interpretation of quantum theory. According to my argument, one of the most important reasons for Dirac to come up with this description was its usefulness in the practice of theory. A comparison between Dirac’s concepts and the concepts of the old quantum theory shows that neither the “intermediate states” of the light quantum point of view nor the “virtual” entities of the BKS theory had an important influence on Dirac.

Luigi Accardi

Hongfang Li

The problem of quantum measurement is an important epistemological problem in philosophical researches of quantum mechanics.Aim at von Neumann's wave packet collapse hypothesis and Bohr's quantum-classical dichotomy,physicists had put forward some alternative solutions that are different from the standard interpretation since 1950s.As historical outcomes in endless flow of development of scientific theory,these alternative solutions indicate that the development of scientific theory always tends to aspects of consistency,apprehensible and testability.

Vasil Dinev Penchev

A historical review and philosophical look at the introduction of “negative probability” as well as “complex probability” is suggested. The generalization of “probability” is forced by mathematical models in physical or technical disciplines. Initially, they are involved only as an auxiliary tool to complement mathematical models to the completeness to corresponding operations. Rewards, they acquire ontological status, especially in quantum mechanics and its formulation as a natural information theory as “quantum information” after the experimental confirmation the phenomena of “entanglement”. Philosophical interpretations appear. A generalization of them is suggested: ontologically, they correspond to a relevant generalization to the relation of a part and its whole where the whole is a subset of the part rather than vice versa. The structure of “vector space” is involved necessarily in order to differ the part “by itself” from it in relation to the whole as a projection within it. That difference is reflected in the new dimension of vector space both mathematically and conceptually. Then, “negative or complex probability” are interpreted as a quantity corresponding the generalized case where the part can be “bigger” than the whole, and it is represented only partly in general within the whole.

Ronnie Hermens