1. Decoherence in the Brain Faculty of Physics University of Vienna, Austria Institute for Quantum Optics and Quantum Information Austrian Academy of Sciences Seminar “Quantum Physics and Biology” University of Vienna June 16 th, 2008 Johannes Kofler

2. Motivation Mainstream biophysics Brain is modeled as a neural network obeying classical physics Conjecture Sufficiently complex network can explain consciousness Consciousness as a quantum effect? Wigner, Stapp, Penrose, … Arguments that decoherence destroys superpositions in the brain Zeh, Zurek, Hawking, Hepp, … Settle the issue by detailed calculations Tegmark [Refs.]M. Tegmark, Phys. Rev. E 61, 4194 (2000) M. Tegmark, Inf. Sci. 128, 155 (2000)

3. 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 energy exchange 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 decoherence  diss   coll M/m   dec many collisions are necessary for dissipation

4. 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 /  dec

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

6. Superpositions of neuron states? 1.Brain consists of  10 11 neurons 2.Nonlinear coupling via synapses (in average  10 3 per neuron) 3.Linked to subjective perceptions 4.If H s or H so 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”: U 0  –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 U 1  +0.03 V  the neuron recovers quickly (it can fire over 1000 times per second)

7. Neuron, myelinated axon, axon membrane h thickness of axon membrane  surface charge density L,d length and diameter of axon ffraction of bare area A active surface area  10 6 Number of Na + ions migrating in:

8. Neuron decoherence mechanisms In superposition of firing and not firing we have N  10 6 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 r 1 = x of a single Na + ion evolves to where f depends only on H int.

9. 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.

10. For N  10 6 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.

11. 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 x 0 ):

12. Total charge around the kink: Thus, (18 Ca 2+ ions in each filament contributing to p 0 ) 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)

13. 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

14. HoHo H oe H so

15. H se Reducing object decoherence would not help, since decoherence takes place before the input through sensory nerves is completed. HsHs  dec   dyn

16. 1.Assumption: Consciousness is synonymous to brain processes (Hobbes, 17 th century). 2.Subject degrees of freedom constitute a “world model”. 3.H so 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