In the present work are identified the main features of the algebraic structure with respect to the logical operations, of the set of all the quantum mechanical utterances for which can be specified a factual counterpart and factual rules for truth valuation. This structure is found not to be a lattice. It depends crucially on the spacetime features of the operations by which the observer prepares the studied states and performs measurements on them.

A new integrated view on the probabilistic organization of quantum mechanics is constructed. It is then proved that for superposition state vectors the theoretical quantum mechanical distribution for the momentum observable is devoid of operational definition, and hence cannot be the source of conditions of compatibility to be imposed upon a researched joint probability concept. A compatible joint probability concept is outlined.

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 can 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. “Il pourrait, en effet, être dangereux pour l'avenir de la Physique qu'elle se contente trop facilement de purs formalismes, d'images floues et d'explications toutes verbales s'exprimant par des mots à signification imprécise”—Louis de Broglie,Certitudes et Incertitudes de la Science (Albin Michel, Paris, 1965). (shrink)

Bell's theorem is believed to establish that the quantum mechanical predictions do not generally admit a causal representation compatible with Einsten's principle of separability, thereby proving incompatibility between quantum mechanics and relativity. This interpretation is contested via two convergent approaches which lead to a sharp distinction between quantum nonseparability and violation of Einstein's theory of relativity.In a first approach we explicate from the quantum mechanical formalism a concept of “reflected dependence.” Founded on this concept, we produce a causal representation of (...) the quantum mechanical probability measure involved in Bell's proof, which is clearly separable in Einstein's sense, i.e., it does not involve supraluminal velocities, and nevertheless is “nonlocal” in Bell's sense. So Bell locality and Einstein separability aredistinct qualifications, and Bell nonlocality (or Bell nonseparability) and Einstein separability arenot incompatible. It is then proved explicitly that with respect to the mentioned representation Bell's derivation does not hold. So Bell's derivation does notestablish thatany Einstein-separable representation is incompatible with quantum mechanics. This first—negative—conclusion is asyntactic fact.The characteristics of the representation and of the reasoning involved in the mentioned counterexample to the usual interpretation of Bell's theorem suggest that the representation used—notwithstanding its ability to bring forth the specified syntactic fact—isnot factually true. Factual truth and syntactic properties also have to be radically distinguished in their turn. So, in a second approach, starting from de Broglie's initial relativistic model of a microsystem, a deeper, factually acceptable representation is constructed. The analyses leading to this second representation show that quantum mechanics does indeed involve basically a certain sort of nonseparability, called here de Broglie-Bohr quantum nonseparability. But the de Broglie-Bohr quantum nonseparability is shown to stem directly from the relativistic character of the considerations which led Louis de Broglie to the fundamental relation p = h/λ,thereby being essentially consistent with relativity. As to Einstein separability, it appears to be a still insufficiently specified conceptof which a future, improved specification, will probably be explicitly harmonizable with the de Broglie-Bohr quantum nonseparability.The ensemble of the conclusions obtained here brings forth a new concept of causality, a concept offolded, zigzag, reflexive causality, with respect to which the type of causality conceived of up to now appears as aparticular case of outstretched, one-way causality. The reflexive causality is found compatible with the results of Aspect's experiment, and it suggests new experiments.Considered globally, the conclusions obtained in the present work might convert the conceptual situation created by Bell's proof into a process of unification of quantum mechanics and relativity. (shrink)

A general representation of the processesof conceptualization, founded upon adescriptional mould drawn from fundamentalquantum mechanics, is outlined. The approach iscalled the method of relativizedconceptualization. This stresses that therepresentation is not researched as a ``neutralstatement of facts'' but, from the start on, asa method subjected to definitedescriptional aims, namely an a prioriexclusion of the emergence of false problems orparadoxes and of any gliding into relativism.The method is characterized by an explicit andsystematic relativization of each descriptionalstep, to all the descriptional elementsinvolved in (...) this step, namely: the epistemicaction by which the object-entity is generated,the object-entity itself, and the epistemicaction by which the object-entity is qualified.Successive steps which complexify progressivelya given initial description, form an unlimitedchain of cells of conceptualization wherethe very first cell, necessarily, is rooted in as yet strictly unconceptualizedphysical factuality while the subsequent cellsconsist of increasingly abstract descriptionsthat are connected hierarchically. The chainsinteract at nodes where they branch, thusgenerating an indefinitely evolving,complexifying web of relativizedconceptualization, free of ambiguities, andwhere each element stays under control.The method contains the positedassertion of a realism of which a definite sortof minimality follows then inside themethod. This generates a clear distinctionbetween illusory qualifications of``how-a-physical-entity-is-in-itself'', and models of this physical entity. Thereby aworked out connection with philosophicalthinking is incorporated in the method. (shrink)

The purpose of this book is to initiate a new discipline, namely a formalized epistemological method drawn from the cognitive strategies practised in the most effective among the modern scientific disciplines, as well as from general philosophical thinking. Indeed, what is lacking in order to improve our knowledge and our domination of the modes which nowadays are available for the generation and communication of knowledge, thoroughly and rapidly and with precision and detail? It is a systematic explication of the epistemological (...) essence encrypted in the specialized languages and algorithms of the major modern scientific approaches, a systematic cross-referencing of the explicated results, and a final elaboration of a new coherent whole. Quantum mechanics, like a diver, can take us down to the level of the very first actions of our conceptualization of reality. And starting from there, it can induce an explicit understanding of certain fundamental features of the new scientific thinking. A formalized epistemology should not be mistaken for a crossdisciplinary or a multidisciplinary project. The latter projects are designed to offer to nonspecialists access to information, to results obtained inside specialized disciplines, as well as a certain understanding of these results; whereas a formalized epistemology should equip anyone with a framework for conceptualizing himself in whatever domain and direction he or she might choose. A formalized epistemology should not be mistaken either for an approach belonging to the modern cognitive sciences. These try to establish as neutrally as possible descriptions of how the human body-and-mind work spontaneously when knowledge is generated; whereas a method of conceptualization should establish what conceptual-operational deliberate procedures have to be applied in order to represent and to achieve processes of generation of knowledge optimized accordingly to any definite aims. This book addresses philosophers of science, physicists, mathematicians, logicians, computer scientists, researchers in cognitive sciences, and biologists, as well as any intellectual who is interested in scientific and philosophical thinking. (shrink)

In connection with my previous paper “Locality, Reflection, and Wave-Particle Duality” [Found. Phys. 17, 813 (1987)], in this paper I distinguish explicitly, in the locality problem, between assertions, deductively established results, interpretations, intuitions, and facts. This clarifies the structure of the problem.

An integrated view concerning the probabilistic organization of quantum mechanics is obtained by systematic confrontation of the Kolmogorov formulation of the abstract theory of probabilities, with the quantum mechanical representationand its factual counterparts. Because these factual counterparts possess a peculiar spacetime structure stemming from the operations by which the observer produces the studied states (operations of state preparation) and the qualifications of these (operations of measurement), the approach brings forth “probability trees,” complex constructs with treelike spacetime support.Though it is strictly (...) entailed by confrontation with the abstract theory of probabilities as it now stands, the construct of a quantum mechanical probability treetransgresses this theory. It indicates the possibility of an extended abstract theory of probabilities including explicit representations of the cognitive operations involved in the probabilistic descriptions. So quantum mechanics appears to be neither a “normal” probabilistic theory nor an “abnormal” one, but a pioneering particular realization of afuture extended abstract theory of probabilities.The consequences of the integrated perception of the probabilistic organization of quantum mechanics are developed constructively. The current identifications of spectral decompositions, with superpositions of states, are removed. Then: (a) Inside the frontiers of the purely operational-observational orthodox formalism, operators of state preparation and the calculus with these are defined consistently with the definition and the calculus of quantum mechanical operators representing measurable dynamical quantities. This permits to grasp the physical meaning of superselection rules. Furthermore, a complement to the quantum theory of measurements is obtained. These prolongations of the orthodox formalism bring forth a “probabilistic incompleteness” of the quantum theory. (b) Beyond quantum mechanics as it now stands, a model is outlined that removes this probabilistic incompleteness, “the [particle + medium] individual model,”microscopic by certain aspects andcosmic by others.Globally, the approach draws attention upon the possibility and the interest of a general representation of the descriptions of any kind founded upon the explicit specification of the epistemic operations—with their spacetime features—by which the observer, who always is involved, produces the objects to be qualified and the qualifications of these. (shrink)