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Quantum physics can only make statistical predictions about possiblemeasurement outcomes, and these predictions originate from an operator algebrathat is fundamentally different from the conventional definition of probabilityas a subjective lack of information regarding the physical reality of thesystem. In the present paper, I explore how the operator formalism accommodatesthe vast number of possible states and measurements by characterizing itsessential function as a description of causality relations between initialconditions and subsequent observations. It is shown that any completedescription of causality must involve non-positive statistical elements thatcannot be associated with any directly observable effects. The necessity ofnon-positive elements is demonstrated by the uniquely defined mathematicaldescription of ideal correlations which explains the physics of maximallyentangled states, quantum teleportation and quantum cloning. The operatorformalism thus modifies the concept of causality by providing a universallyvalid description of deterministic relations between initial states andsubsequent observations that cannot be expressed in terms of directlyobservable measurement outcomes. Instead, the identifiable elements ofcausality are necessarily non-positive and hence unobservable. The validity ofthe operator algebra therefore indicates that a consistent explanation of thevarious uncertainty limited phenomena associated with physical objects is onlypossible if we learn to accept the fact that the elements of causality cannotbe reconciled with a continuation of observable reality in the physical object.

What does the operator algebra of quantum statistics tell us about the objective causes of observable effects?