More than impossible: negative and complex probabilities and their
philosophical interpretations
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.