Bohm-Bell Dynamics in the Modal Interpretation

Jacob A. Barandes, David T. Kagan

Meir Hemmo

Rob Clifton

Abstract Although Bell’s theorem tells us that any interpretation of quantum mechanics must fail to satisfy Bell’s locality condition, the question of Lorentz­invariance is apparently left open by Bell’s theorem. In­ deed, it has been argued by many that nonlocality is compatible with Lorentz­invariance, given certain interpretations of the latter, or of the former. Some give a ‘weak’ interpretation of Lorentz­ invariance, compatible with a ‘strong’ violation of locality. For example, Bohm’s (1952) theory violates locality in a way that requires a preferred frame; but empirical Lorentz­invariance is preserved in the Bohm theory ­ there is no experiment that could determine the preferred frame. (See, for example, Valentini (199la,b), Bohm and Hiley (1993), and Cushing (1994).) On the other hand, ‘orthodox’ interpretations of special relativity maintain a notion of ‘fundamental

Guido Bacciagaluppi

Manuel Bernardo Muñoz Bastias

This condensed version presents BBMT (Bell–Bohm–Modal–Thomistic) as a controlled interpretative bridge between contemporary Scientific Realism and the analogical ontology of Classical Realism. The construction begins from Bell’s requirement of beables as a mind-independent physical referent, specifies that referent through Bohmian particle configuration and guidance, and introduces the Modal Interpretation to distinguish dynamical and value states as the quantum-modal poles of possibility and actuality. Contextual Boolean algebra is retained as a formal control of modal determination rather than as an additional constitutive component. The decisive transition from M to T is semantic and ontological rather than deductive: Frege’s distinction between sense and reference permits preservation of the physical referent under a change of sense; Thomistic formal abstraction legitimizes the consideration of the same reality under different formal objects; participation grounds the restricted physical realization in a more universal ontological structure; and a combined analogy of proper proportionality and intrinsic attribution relates modal possibility/actuality to potency/act without univocal identification or equivocal rupture. BBMT therefore ascends epistemically from quantum physical determination toward ontology while preserving the inverse direction of ontological priority. The model does not derive Thomistic ontology from quantum mechanics; it proposes a disciplined route by which a realist quantum referent may be interpreted under the act–potency structure and thereby reach the threshold of analogical being.

Manuel Bernardo Muñoz Bastias

This article develops a contextual Boolean formalization of the Bell-Bohm-Modal-Thomistic (BBMT) model under the provisional name Contextual Ontological Actualization Framework (COAF). Its central thesis is deliberately limited: Boolean algebra does not prove the Aristotelian-Thomistic metaphysics of potency and actuality, but it can represent, within compatible quantum contexts, a disciplined sequence of determination, modality, actualization, and renewed determination. That is, it aims to show a path to accessing analogical ontology from BBMT. In this case, the idea is to maximize the algebraic route and postpone conceptual interpretation until the last moment. As I will show in subsequent articles, other options exist, but for now we will follow this path. Under this proposal, the global network of quantum propositions is distinguished from Boolean subalgebras associated with compatible observables, while a privileged beable algebra linked to position is examined as the domain in which a defined valuation can be assigned without postulating a prohibited global valuation1. On the other hand, the transition from physical-mathematical structure to ontology is governed neither by univocal identity nor by equivocal separation, but by a composite analogy. At this point, it is necessary to keep in mind two elements of the realist ontological framework that inspire BBMT-COAF: 1) Reality is divided into actual and potential; that is, potency is part of reality, because otherwise it would be impossible for a being to become actual. 2) The entity, as a transcendental concept, is analogous, and this analogy is twofold: it possesses a horizontal dimension expressed in proportionality and a vertical dimension expressed in its attributive predicability. This last element is the position subscribed to by the author in the discussion of specialists, which should be taken beforehand as a hermeneutical prejudice. Horizontally, a proper proportionality analogy compares the relation between physical possibility and physical actuality with that between potentiality and act. Vertically, an analogy of intrinsic attribution orders physical actuality and potentiality to their ontological analogs. Building on Ángel González Álvarez's synthesis of the Thomistic analogy and Santiago Ramírez's proposed correction to the Cayetano-Suárez opposition, this work also clarifies the conception of being that should govern the interpretation: a being is not an abstract logical unity, but rather the inseparable unity of essence and existence, intrinsically realized in diverse ways. Consequently, COAF is presented as a research program and a formal correspondence, not as a deduction of ontology from quantum mechanics. Furthermore, we must not forget that we are attempting to demonstrate that the analogical realist interpretation is not contradictory; that is, we begin with analogy and then demonstrate that this interpretive option of scientific realism does not lead to contradiction. This technique does not imply circularity and is used in various sciences when direct demonstration, whether experimental or deductive, is not possible. It thus proves that a proposition considered true will maintain this condition as long as no derived contradiction is found. Moreover, we must also remember that the BBMT model and its COAF form part of a hermeneutic and, consequently, interpretive thesis.