Quantum physics can only make statistical predictions about possible
measurement outcomes, and these predictions originate from an operator algebra
that is fundamentally different from the conventional definition of probability
as a subjective lack of information regarding the physical reality of the
system. In the present paper, I explore how the operator formalism accommodates
the vast number of possible states and measurements by characterizing its
essential function as a description of causality relations between initial
conditions and subsequent observations. It is shown that any complete
description of causality must involve non-positive statistical elements that
cannot be associated with any directly observable effects. The necessity of
non-positive elements is demonstrated by the uniquely defined mathematical
description of ideal correlations which explains the physics of maximally
entangled states, quantum teleportation and quantum cloning. The operator
formalism thus modifies the concept of causality by providing a universally
valid description of deterministic relations between initial states and
subsequent observations that cannot be expressed in terms of directly
observable measurement outcomes. Instead, the identifiable elements of
causality are necessarily non-positive and hence unobservable. The validity of
the operator algebra therefore indicates that a consistent explanation of the
various uncertainty limited phenomena associated with physical objects is only
possible if we learn to accept the fact that the elements of causality cannot
be reconciled with a continuation of observable reality in the physical object.Comment: 13 pages, feature article for the special issue of Entropy on Quantum
Probability, Statistics and Control. Improved explanation of the U_SWAP
equivalence in Eq.(11) and added comments and references in the section on
quasi-probabilitie
