Complementarity in classical dynamical systems
arXiv:nlin/0407046 · doi:10.1007/s10701-005-9013-0
Abstract
The concept of complementarity, originally defined for non-commuting observables of quantum systems with states of non-vanishing dispersion, is extended to classical dynamical systems with a partitioned phase space. Interpreting partitions in terms of ensembles of epistemic states (symbols) with corresponding classical observables, it is shown that such observables are complementary to each other with respect to particular partitions unless those partitions are generating. This explains why symbolic descriptions based on an \emph{ad hoc} partition of an underlying phase space description should generally be expected to be incompatible. Related approaches with different background and different objectives are discussed.
18 pages, no figures
References in corpus (5)
- In defense of the epistemic view of quantum states: a toy theory
- Estimating good discrete partitions from observed data: symbolic false nearest neighbors
- On computational irreducibility and the predictability of complex physical systems
- What Is a Macrostate? Subjective Observations and Objective Dynamics
- Brownian Entanglement
Cited by in corpus (12)
- Contextual Emergence of Mental States from Neurodynamics
- Generalized Quantum Theory: Overview and Latest Developments
- The Invariant Set Postulate: A New Geometric Framework for the Foundations of Quantum Theory and the Role Played by Gravity
- Epistemic Entanglement due to Non-Generating Partitions of Classical Dynamical Systems
- The Backwards Arrow of Time of the Coherently Bayesian Statistical Mechanic
- Why Do We See a Classical World?
- Invariant Set Theory and the Symbolism of Quantum Measurement
- Descriptive and Foundational Aspects of Quantum Cognition
- Quantum Theory and The Symbolic Dynamics of Invariant Sets: Towards a Gravitational Theory of the Quantum
- Hilbert Space Multi-dimensional Modeling
- Complementary Observables and Non-Boolean Logic Outside Quantum Physics
- Generalized Quantum Theory, Contextual Emergence and Non-Hierarchic Alternatives