Introduction Necker-Zeno Model for Bistable Perception Empirical Confirmation Temporal Nonlocality Selected References The Necker-Zeno Model Harald Atmanspacher, IGPP Freiburg Collaboration with T. Filk, J. Kornmeier, H. R¨ omer Harald Atmanspacher, IGPP Freiburg The Necker-Zeno Model
Introduction Necker-Zeno Model for Bistable Perception Empirical Confirmation Temporal Nonlocality Selected References 1 Introduction 2 Necker-Zeno Model for Bistable Perception 3 Empirical Confirmation 4 Temporal Nonlocality 5 Selected References Harald Atmanspacher, IGPP Freiburg The Necker-Zeno Model
Introduction Necker-Zeno Model for Bistable Perception Mathematical Approaches in Psychology Empirical Confirmation Generalized Quantum Theory Temporal Nonlocality Selected References Some Remarks • psychology is different from neuroscience Harald Atmanspacher, IGPP Freiburg The Necker-Zeno Model
Introduction Necker-Zeno Model for Bistable Perception Mathematical Approaches in Psychology Empirical Confirmation Generalized Quantum Theory Temporal Nonlocality Selected References Some Remarks • psychology is different from neuroscience • mathematics is more than data processing Harald Atmanspacher, IGPP Freiburg The Necker-Zeno Model
Introduction Necker-Zeno Model for Bistable Perception Mathematical Approaches in Psychology Empirical Confirmation Generalized Quantum Theory Temporal Nonlocality Selected References Some Remarks • psychology is different from neuroscience • mathematics is more than data processing • mathematical precision is more than quantitative Harald Atmanspacher, IGPP Freiburg The Necker-Zeno Model
Introduction Necker-Zeno Model for Bistable Perception Mathematical Approaches in Psychology Empirical Confirmation Generalized Quantum Theory Temporal Nonlocality Selected References Some Remarks • psychology is different from neuroscience • mathematics is more than data processing • mathematical precision is more than quantitative Mathematics serves the precise formulation of conceptual questions in terms of abstract structures (algebras, graphs, etc.). Data processing includes the numerical quantification of observables, statistical analysis of measurement results, etc. Harald Atmanspacher, IGPP Freiburg The Necker-Zeno Model
Introduction Necker-Zeno Model for Bistable Perception Mathematical Approaches in Psychology Empirical Confirmation Generalized Quantum Theory Temporal Nonlocality Selected References Observational processes are interactions of an observing system O with an observed system S (state ψ , observables A , B , ...): (i) weak interaction: no significant effect of O on S, (ii) strong interaction: effect of O on S makes a difference. Harald Atmanspacher, IGPP Freiburg The Necker-Zeno Model
Introduction Necker-Zeno Model for Bistable Perception Mathematical Approaches in Psychology Empirical Confirmation Generalized Quantum Theory Temporal Nonlocality Selected References Observational processes are interactions of an observing system O with an observed system S (state ψ , observables A , B , ...): (i) weak interaction: no significant effect of O on S, (ii) strong interaction: effect of O on S makes a difference. Physics: (i) classical case, AB ψ = BA ψ commutative (ii) quantum case, AB ψ � = BA ψ non-commutative Harald Atmanspacher, IGPP Freiburg The Necker-Zeno Model
Introduction Necker-Zeno Model for Bistable Perception Mathematical Approaches in Psychology Empirical Confirmation Generalized Quantum Theory Temporal Nonlocality Selected References Observational processes are interactions of an observing system O with an observed system S (state ψ , observables A , B , ...): (i) weak interaction: no significant effect of O on S, (ii) strong interaction: effect of O on S makes a difference. Physics: (i) classical case, AB ψ = BA ψ commutative (ii) quantum case, AB ψ � = BA ψ non-commutative Psychology: Almost every action of O entails a significant effect on S. Non-commutativity is the rule rather than the exception. → generalized quantum theory details Harald Atmanspacher, IGPP Freiburg The Necker-Zeno Model
Introduction Necker-Zeno Model for Bistable Perception Necker Cube Empirical Confirmation Quantum Zeno Effect Temporal Nonlocality Necker-Zeno Model Selected References Bistable perception of ambiguous stimuli: the Necker cube spontaneous switches between two possible 3–D representations at a time scale of some seconds Harald Atmanspacher, IGPP Freiburg The Necker-Zeno Model
Introduction Necker-Zeno Model for Bistable Perception Necker Cube Empirical Confirmation Quantum Zeno Effect Temporal Nonlocality Necker-Zeno Model Selected References Misra and Sudarshan (1977): Quantum Zeno Effect • Two kinds of processes in an unstable two-state system: � 1 � 0 � � 0 1 “observation”: σ 3 = switching dynamics: σ 1 = 0 − 1 1 0 Harald Atmanspacher, IGPP Freiburg The Necker-Zeno Model
Introduction Necker-Zeno Model for Bistable Perception Necker Cube Empirical Confirmation Quantum Zeno Effect Temporal Nonlocality Necker-Zeno Model Selected References Misra and Sudarshan (1977): Quantum Zeno Effect • Two kinds of processes in an unstable two-state system: � 1 � 0 � � 0 1 “observation”: σ 3 = switching dynamics: σ 1 = 0 − 1 1 0 σ 1 σ 3 � = σ 3 σ 1 Harald Atmanspacher, IGPP Freiburg The Necker-Zeno Model
Introduction Necker-Zeno Model for Bistable Perception Necker Cube Empirical Confirmation Quantum Zeno Effect Temporal Nonlocality Necker-Zeno Model Selected References Misra and Sudarshan (1977): Quantum Zeno Effect • Two kinds of processes in an unstable two-state system: � 1 � 0 � � 0 1 “observation”: σ 3 = switching dynamics: σ 1 = 0 − 1 1 0 σ 1 σ 3 � = σ 3 σ 1 • The switching dynamics is a continuous rotation according to � cos gt i sin gt � U ( t ) = e iHt = , i sin gt cos gt with H = g σ 1 , and t o = 1 / g characterizes the decay time of the system. Harald Atmanspacher, IGPP Freiburg The Necker-Zeno Model
Introduction Necker-Zeno Model for Bistable Perception Necker Cube Empirical Confirmation Quantum Zeno Effect Temporal Nonlocality Necker-Zeno Model Selected References Misra and Sudarshan (1977): Quantum Zeno Effect • Two kinds of processes in an unstable two-state system: � 1 � 0 � � 0 1 “observation”: σ 3 = switching dynamics: σ 1 = 0 − 1 1 0 σ 1 σ 3 � = σ 3 σ 1 • The switching dynamics is a continuous rotation according to � cos gt i sin gt � U ( t ) = e iHt = , i sin gt cos gt with H = g σ 1 , and t o = 1 / g characterizes the decay time of the system. • “Observation” process is a projection P + or P − onto one of the two eigenstates of σ 3 . Harald Atmanspacher, IGPP Freiburg The Necker-Zeno Model
Introduction Necker-Zeno Model for Bistable Perception Necker Cube Empirical Confirmation Quantum Zeno Effect Temporal Nonlocality Necker-Zeno Model Selected References • System dynamics without observations: Probability that the system is in state | + � at time t if it was in | + � at t = 0: w 1 ( t ) = cos 2 ( gt ) Harald Atmanspacher, IGPP Freiburg The Necker-Zeno Model
Introduction Necker-Zeno Model for Bistable Perception Necker Cube Empirical Confirmation Quantum Zeno Effect Temporal Nonlocality Necker-Zeno Model Selected References • System dynamics without observations: Probability that the system is in state | + � at time t if it was in | + � at t = 0: w 1 ( t ) = cos 2 ( gt ) • Successive observations at intervals ∆ T : Probability that the system is in state | + � at time t = N · ∆ T if it was in | + � at t = 0: (cos 2 ( g ∆ T )) N w N ( t ) = exp( − g 2 ∆ T 2 · N ) = exp( − ∆ T ≈ t ) t 2 o Harald Atmanspacher, IGPP Freiburg The Necker-Zeno Model
Introduction Necker-Zeno Model for Bistable Perception Necker Cube Empirical Confirmation Quantum Zeno Effect Temporal Nonlocality Necker-Zeno Model Selected References • System dynamics without observations: Probability that the system is in state | + � at time t if it was in | + � at t = 0: w 1 ( t ) = cos 2 ( gt ) • Successive observations at intervals ∆ T : Probability that the system is in state | + � at time t = N · ∆ T if it was in | + � at t = 0: (cos 2 ( g ∆ T )) N w N ( t ) = exp( − g 2 ∆ T 2 · N ) = exp( − ∆ T ≈ t ) t 2 o • Effect of observations: stabilization of the system in its unstable states, “dwell time” increases from unperturbed t o to an average time � T � : � T � ≈ t 2 o / ∆ T Harald Atmanspacher, IGPP Freiburg The Necker-Zeno Model
Introduction Necker-Zeno Model for Bistable Perception Necker Cube Empirical Confirmation Quantum Zeno Effect Temporal Nonlocality Necker-Zeno Model Selected References From Quantum Zeno to Necker-Zeno • States | + � and |−� correspond to the cognitive states in the two possible representations of the Necker cube. Harald Atmanspacher, IGPP Freiburg The Necker-Zeno Model
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