Decoherence in the Brain

Faculty of PhysicsUniversity of Vienna, Austria

Institute for Quantum Optics and Quantum InformationAustrian Academy of Sciences

Seminar “Quantum Physics and Biology”

University of Vienna

June 16th, 2008

Johannes Kofler

Motivation

Mainstream biophysicsBrain is modeled as a neural network obeying classical physics

ConjectureSufficiently complex network can explain consciousness

Consciousness as a quantum effect?Wigner, Stapp, Penrose, …

Arguments that decoherence destroys superpositions in the brainZeh, Zurek, Hawking, Hepp, …

Settle the issue by detailed calculationsTegmark

[Refs.] M. Tegmark, Phys. Rev. E 61, 4194 (2000)M. Tegmark, Inf. Sci. 128, 155 (2000)

Introduction

System is decomposed into subsystem 1 and subsystem 2

Effects of interactions Hamiltonian:

1.Fluctuation (e.g. Brownian motion)2.Dissipation (e.g. friction)3.Communication (increase of mutual information)4.Decoherence (pure quantum effect)

exchange of energyexchange of information

( )

Example:

Spatial superposition of colloid of mass M (system 1) in water molecules of mass m (system 2)

dec coll single collision leads to decoherencediss coll M/m dec many collisions are necessary for dissipation

Classification of systems

dyn dec quantum system

dyn diss not independent

dec dyn diss familiar classical system

dec ~ diss microsystem (never classical)

dec diss macrosystem (can be quantum)

diss/dec

dyn

/de

c

Subject, object, environment

1. Subject: degrees of freedom of subjective perceptions of the observer; not other degrees of freedom of the brain

2. Object: the degrees of freedom the observer is studying

3. Environment: everything else

Hse causes decoherence directly in the subject system, e.g. finalizing a “quantum decision”

Superpositions of neuron states?

1. Brain consists of 1011 neurons

2. Nonlinear coupling via synapses (in average 103 per neuron)

3. Linked to subjective perceptions

4. If Hs or Hso puts subject into superposition of two mental states, then some neurons are in superposition of firing and not firing

5. How fast does such a superposition of neuron states decohere?

Neuron “resting state”: U0 –0.07 V across axon membrane (pos. outside)

If the potential becomes slightly less negative, sodium channels open: Na+ ions come in and make the potential even less negative chain reaction propagates with up to 100 m/s

changing potential difference to U1 +0.03 V

the neuron recovers quickly (it can fire over 1000 times per second)

Neuron, myelinated axon, axon membrane

h thickness of axon membrane surface charge densityL,d length and diameter of axonf fraction of bare areaA active surface area

106

Number of Na+ ions migrating in:

Neuron decoherence mechanisms

In superposition of firing and not firing we have N 106 ions in superposition of being inside and outside the axon membrane, separated by h 10 nm.

Sources of decoherence:

1.Collisions with other ions

2.Collisions with water molecules

3.Coulomb interaction with distant ions

4.…

If then the density matrix for the position r1 = x of a single Na+ ion evolves to

where f depends only on Hint.

Ion-ion collisions

Environmental particles (Na+ ions) at 37°C have de Broglie wavelength

The density matrix becomes with

Scattering rate

Density of scatterers n, cross section , velocity v (thermal distribution)

Since (i.e. h ) a spatial superposition decays exponentially on the time scale –1.

For N 106 ions a superposition gets destroyed on a time scale

Coulomb scattering between two ions of unit charge has a cross section

with v the relative velocity and

In thermal equilibrium:

Ion density: where

Ion-ion collisions thus destroy the superposition on the time scale

Similar time scales for ion-water collisions and Coulomb interactions with nearby ions.

Microtubules

• Component of the cytoskeleton, hollow cylinders (diameter D = 24 nm), made of 13 filaments out of tubulin dimers

• Dimers can make transitions between two states corresponding to different electric dipole moments along the tube axis.

– Penrose/Hameroff: microtubules are quantum computers

Calculation of decoherence rate:

Coordinate along the tube axis: x

Tubulin dimer x-component of electric dipole moment: p(x)

Propagating kink like excitations (kink location x0):

Total charge around the kink:

Thus, (18 Ca2+ ions in each filament contributing to p0)

Suppose: kink is in superposition of two different places, separated by |r’–r|, where |r’–r| D = 24 nm

Decoherence (due to Coulomb interaction with nearby ions) takes place on a time scale

12 orders of magnitude smaller than reported by Hameroff (screening effects?)

Decoherence summary (conservative estimates)

Classical nature of brain processes

Cognitive processes: dyn ~ 10–2 s – 1 s

Neuron firing: dyn ~ 10–4 s – 10–3 s

Microtuble excitation: dyn ~ 10–6 s

The brain is a (hyper)classical system

(diss ~ dyn)

Subject-object-environment decomposition

Subject states:

Object states:

Joint system:

dec ~ 10–20 s – 10–13 s

Ho

Hoe

Hso

Hse

Reducing object decoherence would not help, since decoherence takes place before the input through sensory nerves is completed.

Hs

dec dyn

1. Assumption: Consciousness is synonymous to brain processes (Hobbes, 17th century).

2. Subject degrees of freedom constitute a “world model”.

3. Hso keeps correlations with outside world; produces mutual information between subject and surrounding.

4. “Binding problem”: Consciousness does not seem to be localized, but feels like a coherent entity (holisitc effect).

5. Can be explained in classical physics: e.g. oscillation in guitar string or water waves (Fourier space).

6. Decoherence calculations indicate that there is nothing fundamentally quantum mechanical about cognitive processes.

7. The brain seems to be a classical (dissipative) computer.

Conclusion