Can Classical Epistemic States Be Entangled?

Entanglement is a well-known and central concept in quantum theory, where it expresses a fundamental nonlocality (holism) of ontic quantum states, regarded as independent of epistemic means of gathering knowledge about them. An alternative, epistemic kind of entanglement is proposed for epistemic states (distributions) of dynamical systems represented in classical phase spaces. We conjecture that epistemic entanglement is to be expected if the states are based on improper phase space partitions. The construction of proper partitions crucially depends on the system dynamics. Although improper partitions have a number of undesirable consequences for the characterization of dynamical systems, they offer the potential to understand some interesting features such as incompatible descriptions, which are typical for complex systems. Epistemic entanglement due to improper partitions may give rise to epistemic classical states analogous to quantum superposition states. In mental systems, interesting candidates for such states have been coined acategorial states, and among their key features are temporally nonlocal correlations. These correlations can be related to the situation of epistemic entanglement.

[1]  Y. Lai,et al.  What symbolic dynamics do we get with a misplaced partition? On the validity of threshold crossings analysis of chaotic time-series , 2001 .

[2]  H. Atmanspacher,et al.  Contextual Emergence of Mental States from Neurodynamics , 2005, q-bio/0512034.

[3]  N. MacDonald.  Noisy chaos , 1980, Nature.

[4]  David Ruelle,et al.  The thermodynamic formalism for expanding maps , 1989 .

[5]  Ya. G. Sinai,et al.  On the Notion of Entropy of a Dynamical System , 2010 .

[6]  Gary Froyland,et al.  Extracting Dynamical Behavior via Markov Models , 2001 .

[7]  C. Moore,et al.  What Is a Macrostate? Subjective Observations and Objective Dynamics , 2003, cond-mat/0303625.

[8]  Harald Atmanspacher,et al.  Extending the Philosophical Significance of the Idea of Complementarity , 2009 .

[9]  R. Spekkens.  Evidence for the epistemic view of quantum states: A toy theory , 2004, quant-ph/0401052.

[10]  José Luis Bermúdez,et al.  Nonconceptual Mental Content , 2003 .

[11]  Harald Atmanspacher,et al.  Acategorial states in a reprsentational theory of mental processes , 2010 .

[12]  Hans Primas,et al.  Non-Boolean Descriptions for Mind-Matter Problems , 2007 .

[13]  Jean Gebser.  The Ever-Present Origin , 1985 .

[14]  H. Atmanspacher,et al.  Complementarity in Classical Dynamical Systems , 2006 .

[15]  Thomas Filk,et al.  Quantum Physics and Consciousness: The Quest for a Common Conceptual Foundation , 2009 .

[16]  Harald Atmanspacher,et al.  Contra Classical Causality Violating Temporal Bell Inequalities in Mental Systems , 2012 .

[17]  Harald Atmanspacher,et al.  Acategoriality as mental instability , 2005 .

[18]  Dawson W. Hedges,et al.  The Placebo Effect and Its Implications , 2005 .

[19]  Harald Atmanspacher,et al.  Epistemic and Ontic Quantum Realities , 2003 .

[20]  Hans Primas,et al.  Mathematical and Philosophical Questions in the Theory of Open and Macroscopic Quantum Systems , 1990 .

[21]  E. Pöppel,et al.  A hierarchical model of temporal perception , 1997, Trends in Cognitive Sciences.

[22]  H. Atmanspacher,et al.  Weak Quantum Theory: Complementarity and Entanglement in Physics and Beyond , 2001 .

[23]  Douglas Lind,et al.  An Introduction to Symbolic Dynamics and Coding , 1995 .

[24]  H. Primas,et al.  Theory reduction and non-Boolean theories , 1977, Journal of mathematical biology.

[25]  A. Shiryayev.  New Metric Invariant of Transitive Dynamical Systems and Automorphisms of Lebesgue Spaces , 1993 .

[26]  E. Sudarshan,et al.  PERCEPTION OF QUANTUM SYSTEMS , 1983 .

[27]  A. E. Allahverdyan.  Brownian entanglement (14 pages) , 2005 .

[28]  Harald Atmanspacher,et al.  Mental states as macrostates emerging from brain electrical dynamics. , 2008, Chaos.

[29]  N. Packard,et al.  Symbolic dynamics of noisy chaos , 1983 .

[30]  T. Durt,et al.  Quantum structures in macroscopical reality , 2001 .

[31]  Otfried Ischebeck,et al.  Time, quantum and information , 2003 .

[32]  Diederik Aerts,et al.  Quantum structures in macroscopic reality , 1993 .

[33]  Robert W. Spekkens,et al.  Einstein, Incompleteness, and the Epistemic View of Quantum States , 2007, 0706.2661.

[34]  Celso Grebogi,et al.  Pseudo-Deterministic Chaotic Systems , 2003, Int. J. Bifurc. Chaos.

[35]  Schumacher,et al.  Non-Boolean derived logics for classical systems. , 1993, Physical review. A, Atomic, molecular, and optical physics.

[36]  James P. Crutchfield,et al.  Computational Mechanics: Pattern and Prediction, Structure and Simplicity , 1999, ArXiv.

[37]  Y. Sinai,et al.  Markov partitions and C-diffeomorphisms , 2020, Hamiltonian Dynamical Systems.

[38]  R. Bowen,et al.  MARKOV PARTITIONS FOR AXIOM A DIFFEOMORPHISMS. , 1970 .

[39]  C. Allen,et al.  Stanford Encyclopedia of Philosophy , 2011 .

[40]  Harald Atmanspacher,et al.  Options for Testing Temporal Bell Inequalities for Mental Systems , 2011, QI.

[41]  Harald Atmanspacher,et al.  A proposed test of temporal nonlocality in bistable perception , 2010 .

[42]  Andrei Khrennivov,et al.  Classical and Quantum Mechanics on Information Spaces with Applications to Cognitive, Psychological, Social, and Anomalous Phenomena , 1999, quant-ph/0003016.

[43]  Alistair I. Mees.  Nonlinear Dynamics and Statistics , 2012 .

[44]  Harald Atmanspacher,et al.  Recasting reality : Wolfgang Pauli's philosophical ideas and contemporary science , 2010 .

[45]  A. E. Allahverdyan,et al.  Brownian Entanglement , 2004 .

[46]  Joseph D Skufca,et al.  A concept of homeomorphic defect for defining mostly conjugate dynamical systems. , 2008, Chaos.

[47]  Andrei Khrennikov.  Classical and quantum mechanics on information spaces with applications to cognitive, psychological, social and anomalous phenomena , 2000 .