Spacetime quantum probabilities II: Relativized descriptions and Popperian propensities

Abstract

ReceivedIn the first part of this work t~l we have explicated the spacetime structure of the probabilistic organization of quantum mechanies. 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," that transgresses 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 the basis of any conceptualization, reveal a tree-like spacetime structure. It appears in particular that the spacetime structure of the relativized representation of a probabilistic 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 the universal cognitive content of the quantum mechanical formalism opens up vistas toward mathematical developments of the relativizing epistemic syntax.The relativized representation of a probabilistic description leads with inner necessity to a "morphic" interpretation of probabilities that can be regarded as a formalized and deepening elaboration of Sir Karl Popper's "propensity" interpretation. A functional is then constructed, the "opacity functional," that associates a mathematical expression to the Popperian "propensities". Furthermore the opacity functional produces a deductive definition of Shannon's "in for-235 0015-9018/92/0200-0235506,50/0 ~') 1992 Plenum Publishing Corporation 236Mugur-Sch~chter mational 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.

On the concept of probability

“…The current author has for many years held that this interpretation is both deep and important (Mugur Schächter 1992c;Mugur Schächter 2002b;Mugur Schächter 2006). However, it does not provide any pragmatic guidance for the effective construction of the factual probability law asserted to apply to the experimental situation.…”

“…As a result, this cognitive situation and its consequences have never been characterised explicitly, thoroughly and globally. † For details, see Mugur Schächter (1984;1991;1992b;1992c;1993;1995;1997a;2002a;2002b;2002c;2006; 2011) ‡ Our use of the word 'signify' here and elsewhere in the current paper is similar to its use in semiotics where a signifier (a syntactic element) is used to signify (refer to and communicate) the signified (some concept). § We make a clear distinction here between fundamental quantum mechanics, where no models are explicitly formed, or even permitted in principle, and any preceding or subsequent theories of microscopic physical entities (such as atomic and nuclear physics and elementary particle theories), which quite explicitly introduce models.…”