Complementarity and Bistable Perception

Thomas FilkInstitute for Frontier Areas in Psychology, Freiburg

Parmenides Foundation for the Study of Thinking, Munich,Department of Physics, University of Freiburg

Monte Verità – May, 23rd 2007

Can we apply ideas and part of the mathematical formalism of (quantum) physics to describe phenomena of consciousness?

Can we apply ideas and part of the mathematical formalism of (quantum) physics to describe phenomena of consciousness?

Not: consciousness as an immediate quantum phenomenon

Content

• Bistable Perception

• Weak Quantum Theory

• The Necker-Zeno Model for Bistable Perception

• Tests for Non-classicality

Bistable Perception

Bistable perception - cup or faces

Bistable perception – mother or daughter

The Necker cubeLouis Albert Necker (1786-1861)

The mental states

state 1 state 2

Rates of perceptive shifts

1

2

t (sec)0 2 4 6 8 18 20 22 24 26 28 30 32 34 3610 12 14 16

J.W.Brascamp et.al, Journal of Vision (2005) 5, 287-298

T=t

Weak Quantum Theory

“Observation”

• An observation not only changes the state of the observing system but also the state of the observed system. It is an interaction between these two systems.

• The algebraic formalism of quantum mechanics grew out of the necessity that observations may have an influence on the observed system.

“Observation”

• No discussion of

– the role of consciousness

– the relevance of the partition

– the pointer basis problem

– the problem of state reduction

Observables and States

• Measurable quantity (measuring recipe): A detailed prescription for the performance of an experiment yielding a definite result.

• Observable: A mathematical object „representing“ a measurable quantity.

• State: A functional (mapping) which associates to each observable a number (expectation value).

Mathematical formalization of classical and quantum mechanics

• Observables:– Commutative C*-

Algebra

– Distributive proposition calculus

– Boolean lattice

• States: positive, linear functionals on the set of observables (expectation values)

• Observables:– Non-commutative C*-

Algebra

– Non-distributive proposition calculus

– Non-boolean lattice

• States: positive, linear functionals on the set of observables (expectation values)

Classical mechanics Quantum mechanics

Mathematical formalization of classical and quantum mechanics

• Observables:– Commutative C*-

Algebra

– Distributive proposition calculus

– Boolean lattice

• States: positive, linear functionals on the observables (expectation values)

• Observables:– Non-commutative C*-

Algebra

– Non-distributive proposition calculus

– Non-boolean lattice

• States: positive, linear functionals on the observables (expectation values)

Classical mechanics Quantum mechanics

Weak quantum mechanicsH. Atmanspacher, H. Römer, H. Wallach (2001)

• Generalization of the algebraic description of classical and quantum physics

• A framework for a theory of observables (propositions) for any system which “has enough internal structure to be a possible object of a meaningful study”.

• No Hilbert-space of states, no a priori probability interpretation, no Schrödinger equation, no Born rule, ….

Sketch of the axioms of weak QT

• The exist states {z} and observables {A}. Observables act on states (change states).

• Observables can be multiplied (related to successive observations).

• Observables have a “spectrum”, i.e., measurements yield definite results.

• There exists an “identity” observable: the trivial “measurement” giving always the same result.

Complementarity

• Two observables A and B are complementary if they do not commute AB BA .

• Two (sets of) observables A and B are complementary, if they do not commute and if they generate the observable algebra .

• Two (sets of) observables A and B are complementary, if they do not commute on states AB z BA z.

• Two (sets of) observables A and B are complementary, if the eigenstates (dispersion-free states) have a maximal distance.

The Necker-Zeno Model for Bistable Perception

The quantum Zeno effectB. Misra and E.C.G. Sudarshan (1977)

Dynamics:

gtgt

gtgttUgH t

cossini

sinicose)(

01

10 iH

Observation:

10

013

States:

0

1

1

0

Dynamics and observation are complementary

Results of observations

The quantum Zeno effectB. Misra and E.C.G. Sudarshan (1977)

Dynamics:

gtgt

gtgttUgH t

cossini

sinicose)(

01

10 iH

Observation:

10

013

States:

0

1

1

0

Dynamics and observation are complementary

Results of observations

The quantum Zeno effect

The probability that the system is in state |+ at t=0 and still in state |+ at time t is: w(t) = |+|U(t)|+|2 = cos2gt .

t0~1/g is the time-scale of unperturbed time evolution.

The probability that the system is in state |+ at t=0 and is measured to be in state |+ N times in intervals Δt and still in state |+ at time t=N·Δt is given by:

wΔt(t) := w(Δt)N = [cos2gΔt]N

Decay time:

ttgtNg ee 222

t

t

tgtT

20

2

1

Quantum Zeno effect

Δtt0

T

w(t)

Ttt0

The Necker-Zeno modelH. Atmanspacher, T. Filk, H. Römer (2004)

Mental state 2:Mental state 1:

dynamics „decay“ (continuous change) of a mental state

observation „update“ of one of the mental states

Internal dynamics and internal observation are complementary.

Time scales in the Necker Zeno model

• Δt : internal „update“ time. Temporal separability of stimuli 25-70 ms

• t0 : time scale without updates (“P300”) 300 ms

• T : average duration of a mental state 2-3 s.

Prediction of the Necker-Zeno model: Ttt0

A first test of the Necker-Zeno model

Tt0

Assumption: for long off-times t0 off-time

Necker-Zeno model predictions for the distribution functions

J.W.Brascamp et.al, Journal of Vision (2005) 5, 287-298

probability density

Cum. probability

Refined model

Modification of

- g g(t)

the „decay“-parameter is smaller in the beginning:

- t t(t)

the update-intervals are shorter in the beginning

Increased attention?

t

g(t), t(t)

Tests for Non-Classicality

Bell‘s inequalitiesJ. Bell (1964)

Let Q1, Q2, Q3, Q4 be observables with possible results +1 and –1.

Let E(i,j)=QiQj

Then the assumption of “local realism” leads to

–2 E(1,2) + E(2,3) + E(3,4) – E(4,1) +2

Temporal Bell’s inequalitiesA.J. Leggett, A. Garg (1985)

-1

1

Let K(ti,tj)=σ3(ti)σ3(tj) be the 2-point correlation function for a measurement of the state, averaged over a classical ensemble of “histories”. Then the following inequality holds:

|K(t1,t2) + K(t2,t3) + K(t3,t4) – K(t1,t4)| 2 .

This inequality can be violated in quantum mechanics, e.g., in the quantum Zeno model.

t

Caveat

• The derivation of temporal Bell‘s inequalities requires the assumption of „non invasive“ measurements.

(This corresponds to locality in the standard case: the first measurement has no influence on the second measurement.)

Summary and Challenges

• The Necker-Zeno model makes predictions for time scales which can be tested.

• The temporal Bell’s inequalities can be tested.• Complementarity between the dynamics and

observations of mental states is presumably easier to find than complementary observables for mental states.

• If Bell’s inequalities are violated (an non-invasiveness has been checked), what are the „non-classical“ states in the Necker-Zeno model? (acategorical mental states?)