A canonical quantum formalism for discrete systems subject to a discretization changing dynamics is outlined. This framework enables one to systematically study (non-)unitarity of such dynamics, the role of canonical constraints and the fate of Dirac observables on temporally varying discretizations. It will be illustrated how the formalism can also be employed to generate a vacuum for a scalar field on an evolving lattice. Implications for the dynamics in simplicial quantum gravity models are commented on.A canonical quantum formalism for discrete systems subject to a discretization changing dynamics is outlined. This framework enables one to systematically study (non-)unitarity of such dynamics, the role of canonical constraints and the fate of Dirac observables on temporally varying discretizations. It will be illustrated how the formalism can also be employed to generate a vacuum for a scalar field on an evolving lattice. Implications for the dynamics in simplicial quantum gravity models are commented on.

Proceedings of Frontiers of Fundamental Physics 14 — PoS(FFP14)Sep 15, 20160 citations

Using the Discrete Event System Specification to model Quantum Key Distribution system components

Jeffrey D. Morris, Michael R. Grimaila, Douglas D. Hodson +2 more

In this paper, we present modeling a Quantum Key Distribution (QKD) system with its components using the Discrete Event System Specification (DEVS) formalism. The DEVS formalism assures the developed component models are composable and exhibit well-defined temporal behavior independent of the simulation environment. These attributes enable users to assemble a valid simulation using any collection of compatible components to represent complete QKD system architectures. To illustrate the approach, we introduce a prototypical “prepare and measure” QKD system, decompose one of its subsystems, and present the detailed modeling of the subsystem using the DEVS formalism. The developed models are provably composable and exhibit behavior suitable for the intended analytic purpose, thus improving the validity of the simulation. Finally, we examine issues identified during the verification of the conceptual DEVS model and discuss the impact of these findings on implementing a hybrid QKD simulation framework.In this paper, we present modeling a Quantum Key Distribution (QKD) system with its components using the Discrete Event System Specification (DEVS) formalism. The DEVS formalism assures the developed component models are composable and exhibit well-defined temporal behavior independent of the simulation environment. These attributes enable users to assemble a valid simulation using any collection of compatible components to represent complete QKD system architectures. To illustrate the approach, we introduce a prototypical “prepare and measure” QKD system, decompose one of its subsystems, and present the detailed modeling of the subsystem using the DEVS formalism. The developed models are provably composable and exhibit behavior suitable for the intended analytic purpose, thus improving the validity of the simulation. Finally, we examine issues identified during the verification of the conceptual DEVS model and discuss the impact of these findings on implementing a hybrid QKD simulation framework.

The Journal of Defense Modeling and Simulation Applications Methodology TechnologyOct 17, 20147 citations

Discretization and Quantum Mechanics

Robert W. Carroll

Springer eBooksJan 1, 20020 citations

Discrete Directed Temporality: A Foundational Axiom for Physics

Ferran Cañizares Marín

This essay proposes that the arrow of time — the intrinsic directionality and discreteness of temporal evolution — should be treated as a foundational axiom of physics rather than a phenomenon to be derived from other principles. The argument proceeds in stages: (1) entropy increase is identified as a statistical symptom rather than a fundamental law; (2) causality is shown to presuppose temporal directionality, making directionality logically prior; (3) temporal directionality is argued to function as a Gödelian presupposition of physical formalism — necessary for the system to operate but inexpressible within it; (4) the historical analogy with the ultraviolet catastrophe motivates the addition of discreteness to directionality; (5) the combined axiom of Discrete Directed Temporality (DDT) is argued to dissolve the quantum measurement problem, resolve spacetime singularities, address the cosmological constant discrepancy, force spatial discreteness through Lorentz covariance, and provide a natural framework for unifying quantum mechanics and general relativity. The essay positions DDT relative to existing programs (causal set theory, causal dynamical triangulations, loop quantum gravity, GRW collapse models) and identifies testable predictions that distinguish it from standard physics.This essay proposes that the arrow of time — the intrinsic directionality and discreteness of temporal evolution — should be treated as a foundational axiom of physics rather than a phenomenon to be derived from other principles. The argument proceeds in stages: (1) entropy increase is identified as a statistical symptom rather than a fundamental law; (2) causality is shown to presuppose temporal directionality, making directionality logically prior; (3) temporal directionality is argued to function as a Gödelian presupposition of physical formalism — necessary for the system to operate but inexpressible within it; (4) the historical analogy with the ultraviolet catastrophe motivates the addition of discreteness to directionality; (5) the combined axiom of Discrete Directed Temporality (DDT) is argued to dissolve the quantum measurement problem, resolve spacetime singularities, address the cosmological constant discrepancy, force spatial discreteness through Lorentz covariance, and provide a natural framework for unifying quantum mechanics and general relativity. The essay positions DDT relative to existing programs (causal set theory, causal dynamical triangulations, loop quantum gravity, GRW collapse models) and identifies testable predictions that distinguish it from standard physics.

Mar 31, 20260 citations

The quantum-classical bipartite universe and the logical emergence of $\hbar$ from classical temporalityThe quantum-classical bipartite universe and the logical emergence of $\hbar$ from classical temporality

Vincenzo Chilla

We present a foundational reinterpretation of quantum dynamics based on the standard von Neumann formalism, positing a structural logical bipartition between a classical observational environment and a quantum observed system. Against universalist frameworks, we argue that theoretical consistency requires distinct propositional logics: Boolean logic governs the environment, while non-Boolean logic applies to the observed system. Within this framework, an ideal classical clock is represented as an open system whose energy spectrum is uniformly discretized. The dynamics follow from the Gorini-Kossakowski-Sudarshan-Lindblad (GKSL) master equation under the constraint that the Hamiltonian remains observable. Although the clock's temporal evolution is driven by dissipative coupling to the measurement apparatus, it admits a deterministic solution corresponding to information-preserving cyclic dynamics. This deterministic regime may emerge as a logical attractor, stabilized by the Boolean structure inherent to the measurement interaction. Ultimately, $\hbar$ is derived as a fundamental scaling parameter from the classical clock's action operator, revealing that the quantum of action reflects the discrete logical structure underlying classical temporality. Furthermore, this framework establishes an exact mapping with 't Hooft's cellular automaton formalism, offering an alternative ontological interpretation that not require hidden variables and superdeterministic assumptions. The resulting distinction between quantum dynamics (as potential recontextualization) and classical dynamics (as temporal actualization) provides a novel logical approach to the measurement problem.We present a foundational reinterpretation of quantum dynamics based on the standard von Neumann formalism, positing a structural logical bipartition between a classical observational environment and a quantum observed system. Against universalist frameworks, we argue that theoretical consistency requires distinct propositional logics: Boolean logic governs the environment, while non-Boolean logic applies to the observed system. Within this framework, an ideal classical clock is represented as an open system whose energy spectrum is uniformly discretized. The dynamics follow from the Gorini-Kossakowski-Sudarshan-Lindblad (GKSL) master equation under the constraint that the Hamiltonian remains observable. Although the clock's temporal evolution is driven by dissipative coupling to the measurement apparatus, it admits a deterministic solution corresponding to information-preserving cyclic dynamics. This deterministic regime may emerge as a logical attractor, stabilized by the Boolean structure inherent to the measurement interaction. Ultimately, $\hbar$ is derived as a fundamental scaling parameter from the classical clock's action operator, revealing that the quantum of action reflects the discrete logical structure underlying classical temporality. Furthermore, this framework establishes an exact mapping with 't Hooft's cellular automaton formalism, offering an alternative ontological interpretation that not require hidden variables and superdeterministic assumptions. The resulting distinction between quantum dynamics (as potential recontextualization) and classical dynamics (as temporal actualization) provides a novel logical approach to the measurement problem.

quant-pharXiv:2610.05083Oct 6, 20260 citations

The quantum-classical bipartite universe and the logical emergence of

\hbar

from classical temporality

\hbar

is derived as a fundamental scaling parameter from the classical clock's action operator, revealing that the quantum of action reflects the discrete logical structure underlying classical temporality. Furthermore, this framework establishes an exact mapping with 't Hooft's cellular automaton formalism, offering an alternative ontological interpretation that not require hidden variables and superdeterministic assumptions. The resulting distinction between quantum dynamics (as potential recontextualization) and classical dynamics (as temporal actualization) provides a novel logical approach to the measurement problem.