From quantum mechanics to universal structures of conceptualization and feedback on quantum mechanics

Abstract

In previous works we have established that the spacetime probabilistic organization of the quantum theory is determined by the spacetime characteristics of the operations by which the observer produces the objects to be studied ("states" of microsystems) and obtains qualifications of these. Guided by this' first conclusion, we have then built a "general syntax of relativized conceptualization" where any description is explicitly and systematically referred to the two basic epistemic operations by which the conceptor introduces the object to be qualified and then obtains qualifications of it. Inside this syntax there emerges a general typology of the relativized descriptions. Here we show that with respect to this typology the type of the predictive quantum mechanical descriptions acquires a precise definition. It appears that the quantum mechanical formalism has captured and has expressed directly in a mathematical language the most complex form in which ean occur a first descriptional phase that lies universally at the bottom of any chain of conceptualization. The main features of the Hilbert-Dirac algorithms are decoded in terms of the general syntax of relativized conceptualization. This renders explicit the semantical contents of the quantum mechanical representations relating each one of these to its mathematical quantum mechanical expression. Basic insufficiencies are thus identified and, correlatively, false problems as well as answers to these, or guides toward answers. Globally the results obtained provide a basis for future attempts at a general mathematical representation of the processes of conceptualization."I1 pourrait, en effet, ~tre dangereux pour l'avenir de la Physique qu'elle se contente trop facilement de purs formalismes, d'images floues et d'explications routes verbales s'exprimant par des roots /t signification impr6cise"--Louis de Broglie, Certitudes et Ineertitudes de la Science (Albin Michel, Paris, 1965).

On the concept of probability

“…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.…”

“…Space limitations mean that we will only be able to list the main features of the general method that we will need for the rest of the paper, though references are given for where full details can be found. However, as an introduction to the general method, and to provide motivation for it, we begin Section 3 with a brief sketch of a special case of the method in the form of infra-quantum mechanics (Mugur Schächter 1991;1992a;1992b;1993;2011).…”