More Than Impossible: Negative And Complex Probabilities And Their Interpretation

EasyChair Preprint 3321

Abstract

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.

Keyphrases: Hilbert space, complex probability, negative probability, probability, quantum information, vector space

@booklet{EasyChair:3321,
  author    = {Vasil Penchev},
  title     = {More Than Impossible: Negative And Complex Probabilities And Their Interpretation},
  howpublished = {EasyChair Preprint 3321},
  year      = {EasyChair, 2020}}