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 show 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 stable, deterministic solution corresponding to information-preserving cyclic dynamics. This deterministic regime emerges 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-angle commutation relation, 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.
The quantum-classical bipartite universe and the logical emergence of ℏ from classical temporality
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 show 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 stable, deterministic solution corresponding to information-preserving cyclic dynamics. This deterministic regime emerges as a logical attractor, stabilized by the Boolean structure inherent to the measurement interaction. Ultimately, ℏ is derived as a fundamental scaling parameter from the classical clock's action-angle commutation relation, 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 develop a derivation of dynamics of Quantum Mechanics and measurement within a fundamentally timeless and scale-invariant framework. Building on a prior reconstruction of quantum kinematics from renormalization consistency, we extend the analysis to dynamical evolution and the measurement process using three minimal principles: a global constraint (timelessness), a variational formulation, and resolution independence. We show that relational time emerges through conditional decomposition of the global state, leading to an effective Schrödinger evolution under suitable conditions on clock subsystems. Renormalization group (RG) transformations, treated as maps on the state space induced by coarse-graining, generate an effective non-unitary dynamics for reduced states. Under standard assumptions of weak coupling and scale separation, this dynamics takes Lindblad form, providing a structural origin for decoherence. A central result of this work is the formulation of a stability selection principle: configurations contributing to observable physics correspond to those that are simultaneously stationary under the action and stable under RG flow. This principle unifies dynamical selection (via the variational structure) and structural selection (via renormalization), and provides a mechanism for the emergence of classical behavior. Measurement is described as an effective sector dynamics arising from decoherence and coarse-grained evolution. The Lindblad equation admits a stochastic representation in which the system evolves between dynamically independent sectors, leading to an effective description of definite outcomes without introducing a fundamental collapse postulate. The Born rule follows from the unique quadratic measure consistent with refinement structure and is realized dynamically within this framework. Together, these results provide a structural account under minimal assumptions of quantum dynamics, decoherence, and measurement as emergent features of a timeless, renormalization-consistent theory governed by stability across scales.
Markovian open quantum theory assumes evolution with respect to an external classical time parameter, yet no preferred notion of time exists fundamentally in relativistic physics. We resolve this tension by formulating relativistic open quantum dynamics relationally through finite-resolution quantum clocks. Using the Schwinger-Tomonaga formalism, we derive a covariant master equation directly on spacetime hypersurfaces and show that the resulting reduced dynamics is generically non-Markovian even for local interactions. Environmental correlations and clock fluctuations jointly generate the memory kernel, while the Gorini-Kossakowski-Lindblad-Sudarshan (GKLS) structure emerges only after relational coarse-graining, implying that exact Markovian evolution is effective rather than fundamental. In the sharp-clock limit, the formalism reduces to the Anastopoulos-Hu gravitational decoherence equation.
We propose a unified ontological and dynamical framework in which quantum,classical, and cosmological phenomena emerge as scale-dependent manifestationsof a single deterministic substrate. In the Temporal Resolution Theory of Real-ity (TRTR), particles, trajectories, probability clouds, and macroscopic bodies arenot distinct ontological entities but effective descriptions of deterministic chaoticdynamics observed under finite temporal resolution.We formalize observation as a temporal coarse-graining operator acting onphase-space flows. Under appropriate resolution regimes, invariant measures (SRBmeasures) emerge and reproduce probabilistic structure without fundamental ran-domness. Measurement is reinterpreted as a convolution between dynamical sys-tems operating at different intrinsic time scales.We discuss implications for quantum measurement, Born’s rule, and scale uni-fication, and outline conditions under which Schr¨odinger dynamics may arise as aneffective linear approximation of Perron–Frobenius evolution.
This paper presents an interpretive framework for understanding quantum phenomena through the lens of process ontology. We propose that reality consists of discrete actualization events—random selections from pre-defined fundamental options—occurring in Hamilton space. By reinterpreting established quantum mechanics, field theory, and thermodynamics, we show how particles, atoms, and simple structures emerge as stable patterns of repeated actualizations. Energy represents capacity for actualization, information records actualization history, and classical objects emerge as high-probability attractors in the actualization sequence. This framework requires no new physics; rather, it organizes existing experimental and theoretical results into a coherent ontological picture. We demonstrate the framework through detailed examples including hydrogen atom formation, quantum measurement, particle decay, and photon emission. Version 2 will extend this foundation to address molecular complexity, biological systems, and consciousness. Keywords: Process ontology, quantum measurement, actualization, Hamilton space, discrete events, fundamental options, information theory, quantum foundations
Abstract The emergence of definite outcomes from quantum dynamics remains a central conceptual challenge in the foundations of quantum mechanics. While decoherence theory and open quantum systems provide widely accepted mechanisms for the suppression of interference, the relationship between unitary evolution, measurement outcomes, classical behavior, and irreversibility is often treated in fragmented ways. In this working paper, we adopt a dynamical-systems perspective, referred to here as attractor dynamics, in which measurement outcomes and classical states are understood as consequences of stability and basin structure in open quantum evolution. Using minimal Lindblad models and quantum trajectory descriptions, we illustrate how pointer states arise as attractors under coarse-grained dynamics without introducing postulates beyond standard open-system quantum mechanics. This work does not propose new fundamental dynamics. Rather, it offers a conservative conceptual synthesis intended to clarify how measurement, decoherence, and the arrow of time can be viewed within a unified dynamical framework.
This paper starts with surveying the evolution of quantum-like models of cognition and decision making, transitioning from static kinematic representations to a robust dynamical framework based on open quantum systems. We provide a comprehensive analysis of the Gorini-Kossakowski-Sudarshan-Lindblad (GKSL) master equation's application in cognitive psychology and decision making, illustrating how it models mental state evolution as a dissipative process influenced by an informational environment. We categorize dynamical regimes into Passive and Active Hamiltonians, demonstrating how non-commutation with projections on decision basis serves as a mathematical signature of cognitive agency and Quantum Escape from classical equilibria. The utility of this framework is further explored through its ability to stabilize non-Nash outcomes in strategic games, such as the Prisoner's Dilemma. Building upon this dynamical foundation, we identify ``cognitive beats'' as a signature of the internal struggle between competing ``flows of mind'' deliberated at approximately equal frequencies. Distinct from the damped oscillations of simple interference, these beats emerge from a structural tension between Liouvillian channels that generates a secondary, slow-scale modulation of conviction. This beat envelope dictates the timing of peak readiness and hesitation, providing a mathematical map of the transition between conflicting cognitive states. By resolving these nested time scales, we provide a new spectral diagnostic for the depth of cognitive agency and the complexity of the underlying deliberation process. This paper develops a theoretical framework linking GKSL dynamics with quantum-like cognition and decision-making (QCDM), highlighting how dissipative quantum models can capture features of human thought and decision processes.