Quantum models of brain


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Department of Behavioral and Brain Sciences
University of Pavia, Italy

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Quantum models of brain

  1. 1. QUANTUM MODELS OF BRAIN ELIANO PESSA Department of Behavioral and Brain Sciences University of Pavia, Italy
  2. 2. SOME FEATURES OF MIND AND BRAIN BEHAVIORSFor the present purpose we will focus our attention on two features of both brain and mind behaviors about which there is a common consensus :1)  Both behaviors are often characterized by COHERENCE phenomena or COHERENT aspects2)  Brain and Mind are interrelated by both BOTTOM-UP and TOP-DOWN influences
  3. 3. MIND TOP-DOWN BOTTOM-UP INFLUENCE INFLUENCE BRAINDespite these influences the mind is to be consideredas a fully AUTONOMOUS entity, allowing a LOGICAL(and not PHYSICAL) description
  4. 4. CLASSICAL PHYSICS DOES NOT ALLOW COHERENCENamely classical statistical physics (and whenceTermodynamics) is ruled by a principle known asCORRELATION WEAKENING PRINCIPLE, stating thatwhatever long range correlation DIES AWAY after along enough evolution time.As coherence results from long range correlations, it isevident how the classical physics cannot be used toexplain coherence phenomena within the brain-mindsystem.
  5. 5. ARE QUANTUM THEORIES USEFUL ?Actually we have two different levels:1) QUANTUM MECHANICS, characterized by a fixednumber of particles, a finite number of degrees offreedom, and unitary equivalence between differentrepresentations of the same physical system2) QUANTUM FIELD THEORY, in which the basicentities are field strengths, the number of degrees offreedom is infinite (and continuous), and the number ofparticles is variable
  6. 6. THE NEW PRINCIPLES INTRODUCED BY QUANTUM THEORIESThey consist of a number of UNCERTAINTY PRINCIPLES which essentially follow from the postulate of the existence of an unavoidable “VACUUM FLUCTUATION” of the world and of the whole Universe. The fluctuations occurring in each space-time point are correlated with the ones occurring in every other space-time point. This circumstance gives rise to NON-LOCAL EFFECTS of typically quantum nature which cannot be predicted by classical Physics.
  7. 7. MOTIVATIONS UNDERLYING THE ATTRACTIVENESS OF QUANTUM THEORIES•  Allow the occurrence of spontaneous (andeven large-scale) COHERENCE phenomenawithout the resort to special design,arrangement, boundary conditions, etc.(Prototype : BOSE-EINSTEIN CONDENSATION)•  In suitable cases (Quantum Field Theory) offera framework for describing, understanding, andforecasting PHASE TRANSITION phenomena
  8. 8. This implies that quantum theories can support some form of TOP-DOWN CAUSATION encompassing the pitfalls of the traditional mechanistic and reductionist framework.If we assume that all phenomena related to life,brain, cognition, consciousness, etc. are based onsome forms of EMERGENT SELF-ORGANIZATIONthen quantum theories are the best candidates foran effective theorizing activity in these domains.
  10. 10. THE REDUCTIONIST POSTULATEA complete study of the whole system of previousorganizational levels has been so far impossible.If, however, we introduce a very rough REDUCTIONISTPOSTULATE according to which all processes occuringat the level N can be fully explained in terms of the onesoccurring at the lower level N – 1, EXCEPT FOR THEONES OCCURRING AT THE LEVEL LYING IMMEDIATELYUP TO THE ONE OF ELEMENTARY COMPONENTS, thenthe whole hierarchy of levels collapses to only twolevels and we can directly apply the quantum theories ofcoherence (just designed for two-level hierarchicalsystems).
  11. 11. THE QUANTUM BRAIN THEORIESThe reductionist hypothesis allows the building ofQUANTUM BRAIN THEORIES (UMEZAWA, JIBU,YASUE, VITIELLO, HAMEROFF, TUSCZINSKY). Theyuse a number of typically quantum effects to accountfor the operation of MEMORY and of other COGNITIVEPROCESSES, including the ones characterizing theCONSCIOUSNESS.These theories gave rise to a number of theoreticaladvances as well as of experimental predictions.
  12. 12. TYPICAL EFFECTS USED IN QUANTUM BRAIN THEORIESTypical examples :-  the DAVYDOV EFFECT, consisting in the generationof a solitary wave propagating lattice deformationsalong a linear polymer chain excited by an externaloscillatory input (here a NON-LOCAL input gives riseto a LOCALIZED phenomenon)-  the FRÖHLICH EFFECT, consisting in the excitationof a collective vibrational mode within a set ofreciprocally interacting electric dipoles, generated bya localized external input (here a LOCALIZED inputgives rise to a NON-LOCAL and COLLECTIVEphenomenon)
  13. 13. THE RANGE OF QUANTUM EFFECTSIt can be approximated by the THERMAL DE BROGLIEWAVELENGTH, that is by the average wavelength of thewave associated to each quantum particle of an idealgas at the temperature T. It is given by :h = Planck constant ≅ 6.63x10-34m = particle massK = Boltzmann constant ≅ 1.38x10-23
  14. 14. When the thermal De Broglie wavelength is greater than or of the same order of the typical distances between the particles then a QUANTUM description is needed. For particles like electrons and room temperatures the thermal De Broglie wavelength is of the order of the atomic distances. This induced to think that quantum theories are useful only to describe MICROSCOPIC phenomena.However this view is incorrect for a number of reasons :•  when the mass tends to zero (like for photons) or thetemperature tends to zero the thermal De Broglie wavelengthdiverges•  when the uncertainty about the number of particles is veryhigh (creation and destruction processes being allowed) theuncertainty about their relative phases becomes very smalland MACROSCOPIC COHERENCE phenomena are possible.
  15. 15. THE BIG PROBLEM FOR QUANTUM BRAIN THEORIES: DECOHERENCEAs it is well known, decoherence due to theinteraction with external environment candestroy the coherence of quantum origin.Two remarks :•  Decoherence is a problem only for quantumcomputers. Biological systems needdecoherence in order to avoid becoming likecrystals•  Decoherence is a smaller problem in QFTowing to the infinite number of degrees offreedom and the infinite volume limit
  16. 16. THE ACTORS PLAYING THE DECOHERENCE GAME•  The kind of environment and its symmetries What models of environment? THERMAL BATH (the simplest one) SPIN CHAIN (endowed with symmetry) ACTIVE MEDIA (feedback on the system)•  the NOISE•  the DISSIPATION•  the DISORDER
  17. 17. These actors interact in a very complex waywhich makes the decoherence game stronglydependent on the detailed nature of theSPECIFIC CONTEXTS.Some elementary examples can illustrate someaspects of this game.In order to understand them we can start from asimple CLASSICAL (NEURAL) NETWORK andtransform it into a QUANTUM (NEURAL)NETWORK.
  18. 18. A CLASSICAL NETWORK MODEL•  Neurons arranged in a plane network with toroidal topology O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O •  Number of input lines for each neuron is always the same (4)•  Stochastic activation law•  Initial state randomly chosen
  19. 19. STOCHASTIC ACTIVATION LAWThis law has the form : Prob(output = 1) = 1/(1 + exp[-S/T])where S is the weighted sum of inputs minus thethreshold while T is a parameter, called‘TEMPERATURE’In practical cases biological neurons show a stochasticdischarge pattern
  20. 20. AN EXAMPLE OF EEG PRODUCED BY THIS MODEL Network of 30x30 neurons, threshold = 2, T = 1
  21. 21. The autocorrelation function of this EEG
  23. 23. A QUANTUM NETWORK MODELLet us now compare the behavior of the previousmodel with the one of a QUANTUM NETWORK MODELwith the same structure and topology.Here the momentarily state vector of each unit is givenby a linear combination of the two basic states “0” and“1”. In general the coefficients ψ0 and ψ1 of thiscombination are complex numbers which vary withtime. At every instant the probability of having anoutput 1 is given by | ψ1 |2 .
  24. 24. The dynamical evolution of this network is given by asuitable HAMILTONIAN OPERATOR, whose diagonalterms are constant, while non-diagonal terms containa contribution coming from the output produced byneighboring neurons, minus a given threshold.In turn, this output is computed in a probabilistic wayaccording to the probabilities of “0” and “1” statesexisting in the previous instant.In principle, the evolution of this network should becharacterized by some kind of long-rangecorrelations. BUT IS THIS PREDICTION CORRECT ?
  25. 25. THE EEG OF THIS NETWORK …The same conditions as in the classical case: 30x30neurons, identical initial probabilities, threshold = 2,diagonal terms = 1, non-diagonal terms = 0.5
  26. 26. …but the autocorrelation function differs in adeep way from the classical case ! Evidence for long-range effects
  28. 28. ANOTHER EXAMPLEAverage activity of a quantum neural networkof 10x10 neurons with threshold = 1, non-diagonal elements of the Hamiltonian = 1,second-order approximation.
  29. 29. WHAT HAPPENS IN PRESENCE OF EXTERNAL NOISE ?Average activity of the previous network inpresence of Gaussian input noise with mean=0and standard deviation=5.
  30. 30. As a comparison between the two plots isdifficult, it is more convenient to compare thetwo autocorrelation functions. Without Noise With Noise A difference appears but it is better to compare the autocorrelation functions of the average variances.
  31. 31. Without noise With Noise Superposition of the two plotsLooking at the variance the effect of noise ismore evident !
  32. 32. A first lesson of the above simulations is thatthe effects of the quantum or classical nature ofa network are difficult to detect when looking atthe macroscopic observation of simple averagequantities, such as mean activity.They are best detected when looking at morecomplex statistical quantities.And, even at the level of biological neuralnetworks, the neurons seem to be moresensitive to higher-order statistical features ofthe neural assemblies in which they areembedded.
  33. 33. CAN THE EFFECT OF NOISE BE COUNTERACTED ?Let us suppose, in this regard, that a noisyquantum neural network be interacting withanother coherent system, like a spin bath or aspin chain.A simple way for implementing this situations isto add within the previous quantum neuralnetwork a spin-spin interaction between thequantum neurons, of quantum nature.
  34. 34. Plot of average activity vs t of a noisy quantumneuron with a moderate spin-spinantiferromagnetic interaction betweenneighboring spins.
  35. 35. Autocorrelation Autocorrelation function of the function of average average activity varianceAs expected, the average variance better helpsto detect weak cues of the re-establishment ofsome long-range order.
  36. 36. Another lesson is that taking into accountonly the destroying influence of theenvironment is not enough: if there is someinteraction with another coherent system, thepossibility of a RECOHERENCE or ofcounteracting decoherence remains open.Perhaps different coherence mechanisms cancooperate, even if each one, taken in isolation,is characterized by a very small decoherencetime.
  37. 37. THE MACROSCOPIC SIGNATURE OF QUANTUM PHENOMENAHow can a quantum coherence present at themicroscopic level survive up to mesoscopicand macroscopic level ?The previous examples suggest that, by usingobservations induced by a mean-field analysis,the detection of quantum coherence becomesvery difficult.
  38. 38. However, the simulations show that, bylooking at higher-order statistical features ofmesoscopic and macroscopic quantities, itshould be possible to detect a ‘signature’ ofquantum phenomena at the microscopic level.Another help comes from the existence of anumber of inequalities regarding themacroscopic observations (Bell, Leggett-Garg)that, when not satisfied, are cues revealing anhidden quantum nature. In some cases theseeffects have been experimentally detected.However, they cannot give any informationabout the lower-level quantum processes.
  39. 39. A (PARTIAL) CONCLUSIONThe actual quantum brain theories are still in avery primitive stage, being unable to takesimultaneously into account all contributors tothe decoherence game.Moreover, they still lack a formalism allowing todescribe the whole hierarchy of organizationallevels characterizing the mind-body system.A number of new technical proposals have beenintroduced (e.g. the DISSIPATIVE QUANTUMFIELD THEORY, the OPEN QUANTUM FIELDTHEORY, etc.) in order to avoid theseshortcomings. Actually, however, it is stilldifficult to assess their usefulness.
  40. 40. IS QUANTUM THEORY USEFUL FOR PSYCHIATRISTS ?So far, quantum theory appears to be useful todescribe mostly low-level phenomena. At thehigher levels it seems to be useful mostly as asort of framework for reasoning aboutphenomena of holistic nature. Nobodyprevents, however, from thinking that, onlyunderstood some principles underlying theprocesses occurring within the wholisticmind-brain system, quantum theory can beused to design suitable forms of top-downactions helping the human beings to reach abetter harmony with the environment.
  41. 41. The ultimate goal of these top-down‘technologies’ would be the one of a world inwhich human beings were able to live in a self-sustaining harmony with the world, without anyintervention of drugs, physicians, hospitals,and like. The hope that this state of affairs can berealized in the future is the basic pushunderlying all applications of quantum theoryto the study of brain, cognition, andconsciousness.