QUANTUM THEORIES OF MIND-BRAIN : WHAT FUTURE ? ELIANO PESSA Department of Psychology University of Pavia, Italy
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
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.
WHAT COULD WE MEAN BY SPEAKING OF ‘QUANTUM THEORIES’ ?TWO ALTERNATIVES :• A set of known physical theories(semiclassical, quantum mechanics, quantumfield theory) associated with a specific value ofPlanck’s constant• A general theoretical framework for describingspecific kinds of fluctuating systems (eventuallyallowing different kinds of ‘effective’ Planck’sconstants)
The second alternative gained popularity in thelast times, owing to a number of circumstances :• some kinds of ‘noisy’ field theories aremathematically equivalent to QM or QFT,provided we allow the introduction of suitable‘effective’ Planck’s constants (see, e.g, Fogedbyet al.)• a number of phenomena in psychology andeconomics, like decision making and conceptformation, can be better described by modelsmathematically equivalent to quantum ones, inwhich, however, Planck’s constant has a valuedifferent from the traditional one (see e.g. Aertset al., Busemeyer et al.)
THE BIG PROBLEM: 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
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
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.
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
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
AN EXAMPLE OF EEG PRODUCED BY THIS MODEL Network of 30x30 neurons, threshold = 2, T = 1
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 ψ 0 and ψ 1 of thiscombination are complex numbers which vary withtime. At every instant the probability of having anoutput 1 is given by | ψ 1 |2 .
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 ?
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
…but the autocorrelation function differs in adeep way from the classical case ! Evidence for long-range effects
EVEN PERIODOGRAM IS DIFFERENT …AND POWER SPECTRUM
ANOTHER EXAMPLEAverage activity of a quantum neural networkof 10x10 neurons with threshold = 1, non-diagonal elements of the Hamiltonian = 1,second-order approximation.
WHAT HAPPENS IN PRESENCE OF EXTERNAL NOISE ?Average activity of the previous network inpresence of Gaussian input noise with mean=0and standard deviation=5.
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.
Without noise With Noise Superposition of the two plotsLooking at the variance the effect of noise ismore evident !
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.
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 situationsis to add within the previous quantum neuralnetwork a spin-spin interaction between thequantum neurons, of quantum nature.
Plot of average activity vs t of a noisy quantumneuron with a moderate spin-spinantiferromagnetic interaction betweenneighboring spins.
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.
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.
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.
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.
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.
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.