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WORLD SCIENTIFIC eBooks

Quanta, Logic and Spacetime

Stephen Allan Selesnick

Published Jan 1, 2003• 25 citations
Publisher

Abstract

Preliminaries: - Foundations - Quantum Sets - Group Duality, Coherence and Cyclic Actions - Computational Paradigms: - Natural Deduction - Quantum Logic - The Computational Resources of Quantum Logic - The Plenum: - A Quantum Net - Towards a Correspondence Principle for the Quantum Net - A Correspondence Principle for the Quantum Net - Dynamics I - Dynamics II - Comparisons, Interpretations and Speculations

DOI
10.1142/9789812794932

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In this paper, we establish the foundations of a novel logical framework for the π-calculus, based on the deduction-as-computation paradigm. Following the standard proof-theoretic interpretation of logic programming, we represent processes as formulas, and we interpret proofs as computations. For this purpose, we define a cut-free sequent calculus for an extension of first-order multiplicative and additive linear logic. This extension includes a non-commutative and non-associative connective to faithfully model the prefix operator, and nominal quantifiers to represent name restriction. Finally, we design proof nets providing canonical representatives of derivations up to local rule permutations.
This research package presents a hydrodynamic reformulation of quantum mechanics, treating the vacuum as a physical plenum with finite memory capacity and dynamic viscosity. The package includes multiple complementary documents to ensure maximum accessibility and rigor: Core Paper (Italian & Hindi): "Transizioni di Fase Topologiche nel Plenum Quantistico" / "क्वांटम प्लेनम में टोपोलॉजिकल चरण संक्रमण". Details the mathematical framework, deriving the quantum potential as a pressure gradient, establishing non-local coupling via phase coherence topology, and defining unitary phase translation operators. Visual Companion (English): "Topological Phase Transitions in the Quantum Plenum". A page-by-page intuitive guide to the 8 foundational equations of Memodynamics, bridging advanced math with physical intuition. Divulgative Version (Romanesco Dialect): "La Memodinamica Spiegata a modo de Trastevere". A creative, accessible translation of the core concepts designed to democratize the understanding of quantum vacuum dynamics without oversimplifying the underlying logic. This framework suggests that quantum mysteries (non-locality, wave-particle duality) are artifacts of projecting the dynamics of a deeper hydrodynamic substrate onto perceived metric spacetime. (This work builds upon the foundational Memodynamics framework, DOI: 10.5281/zenodo.21210473).
Introduction. Modern financial science increasingly faces a paradox: classical models based on deterministic assumptions fail to adequately describe the nonlinearity and uncertainty of public decision-making. In this context, the quantum paradigm of thinking, originally developed in physics, is becoming increasingly relevant as it gradually penetrates the fields of economics and finance. Problem Statement. In contemporary academic discourse, growing attention is being paid to the integration of the principles of quantum logic into socio-economic systems. Traditional financial science rests upon classical macroeconomic determinants that assume linearity, causal determinacy, and parameter stability. However, in the modern world – characterized by high uncertainty, dynamic crises, and global financial fluctuations – such logic proves insufficient. Therefore, there is a pressing need to employ quantum logic as a modern cognitive and analytical paradigm that enables the comprehension of the essence and structure of public finance through the prism of nonlinear, stochastic, and interrelated phenomena and processes. Purpose is to establish a theoretical and methodological foundation for applying quantum principles in the domain of public finance and to identify directions for their practical implementation. Methods. To obtain the scientific results presented in the article, the following methods were employed: methods of quantum logic, synthesis and analysis, deduction and induction, an abstract-logical method of “negation of negations” in financial decision-making, and theoretical generalization to define the nature of quantum finance. Results. The article reveals the potential for interpreting key principles of quantum physics within the system of public finance. A dual-level research framework is proposed, combining methodological analogies between quantum and financial processes with the practical application of quantum models in state financial management. It is demonstrated that the concepts of uncertainty, superposition, and coherence allow for a deeper understanding of the nature of budgetary decisions, tax expectations, debt imbalances, and behavioral effects in the public sphere. Conclusions. Quantum logic crystallizes a methodological framework for modern public finance capable of accounting for the complexity, uncertainty, and interconnectivity of global transformations, hybrid wars, and the contemporary economy. The application of quantum paradigms makes it possible to construct dynamic, probabilistic models of financial policy that significantly surpass the capacities of classical deterministic methods and open new perspectives for scientifically grounded public governance in the field of public finance.
Introduction. Operational quantum logic: An overview B. Coecke, et al. I: Algebras. Algebraic aspects of orthomodular lattices G. Bruns, J. Harding. Observables in the logico-algebraic approach P. Ptak. Test spaces and orthoalgebras A. Wilce. Representations on unigroups D.J. Foulis. Free extensions of group actions, induced representations, and the foundations of physics D.J. Foulis, A. Wilce. II: Categories. Short introduction to enriched categories F. Borceux, I. Stubbe. Operational Galois adjunctions B. Coecke, D. Moore. Operational axiomatics and compound systems F. Valckenborgh. Quantales J. Paseka, J. Rosicky. III: Languages. Quantales and observational semantics P. Resende. Quantum languages S. Gudder. Indices. Concept index. Citation index.