Spacetime quantum probabilities II: Relativized descriptions and Popperian propensities

Abstract

In the first part of this work⁽¹⁾ we have explicated the spacetime structure of the probabilistic organization of quantum mechanics. We have shown that each quantum mechanical state, in consequence of the spacetime characteristics of the epistemic operations by which the observer produces the state to be studied and the processes of qualification of these, brings in a tree-like spacetime structure, a “quantum mechanical probability tree,” thattransgresses the theory of probabilities as it now stands. In this second part we develop the general implications of these results.

Starting from the lowest level of cognitive action and creating an appropriate symbolism, we construct a “relativizing epistemic syntax,” a “general method of relativized conceptualization” where—systematically—each description is explicitly referred to the epistemic operations by which the observer produces the entity to be described and obtains qualifications of it. The method generates a typology of increasingly complex relativized descriptions where the question of realism admits of a particularly clear pronouncement. Inside this typology the epistemic processes that lie—UNIVERSALLY—at thebasis ofany conceptualization, reveal a tree-like spacetime structure. It appears in particular that the spacetime structure of the relativized representation of aprobabilistic description, which transgresses the nowadays theory of probabilities,is the general mould of which the quantum mechanical probability trees are only particular realizations. This entails a clear definition of the descriptional status of quantum mechanics. While the recognition of theuniversal cognitive content of the quantum mechanical formalism opens up vistas towardmathematical developments of the relativizing epistemic syntax.

The relativized representation of a probabilistic description leads with inner necessity to a “morphic” interpretation of probabilities thatcan be regarded as a formalized and deepening elaboration of Sir Karl Popper's “propensity” interpretation. A functional is then constructed, the “opacity functional,” that associatesa mathematical expression to the Popperian “propensities”. Furthermore the opacity functional produces adeductive definition of Shannon's “informational entropy.” Thereby there appears an explicitly unified relativized probabilistic-informational approach. This sketches out a second branch of a future mathematical epistemic syntax, to be connected with the branch stemming from quantum mechanics.

The problem of the objectivity of probabilistic descriptions acquires certain precise rephrasings and—in a sense—solution.