Date: Sun, 7 Apr 1996 17:35:40 -0700 (PDT) From: Giuseppe Vitiello <vitiello@vaxsa.csied.unisa.it> To: quantum-d@teleport.com Subject: Re: Quantum memory models? (cont.) This is an extended abstract from the paper "Dissipation and memory capacity in the quantum brain model" Int. J. Mod. Phys.B9 (1995) 973 (quant-ph/9502006) by Giuseppe Vitiello Physics Department, University of Salerno 84100 Salerno, Italy e-mail: vitiello@vaxsa.csied.unisa.it fax +39 89 953804 tel. +39 89 965311 By following independent routes, but stimulated by common belief in the powerfulness of Quantum Field Theory (QFT) and fascinated by its elegance, Herbert Frohlich, Hiroomi Umezawa, Karl Pribram and Alexander Davydov have opened a research path, actively followed in recent years, which aimed to study the basic dynamical laws underlying the rich phenomenology of living systems. One of the motivations for such an approach to the study of biological systems comes from the fact that, although great energy and many valuable efforts have been put into play, it remains still open the question of how order and efficiency arise from, and then coexist with random fluctuations in biochemistry: From one side, there is the high level of space and time ordering and the high functional efficiency observed in living systems; on the other side, the randomness of kinematics which rules any chemical reaction, which by itself is not sufficient to account for those high levels of ordering and efficiency. In the QFT approach to living matter one searches for basic dynamical laws which together with statistical mechanics originate ordering and functional efficiency. Here I want to report about a recent application[1] of dissipative QFT to the problem of memory capacity in the quantum model of brain proposed by Ricciardi and Umezawa[2]. In doing this I will also shortly summarize the main features of the QFT approach[3] to living matter. It is a common observation that the brain functioning appears not significantly affected by the functioning of the single neuron. A characterizing feature of the brain activity seems instead related with the existence of simultaneous responses in several regions of the brain to some external stimuli. Storing and recalling information appear as diffuse activities of the brain not lost even after destructive action of local parts of the brain[4-7]. Ricciardi and Umezawa[2] have then suggested that the brain states may be characterized by the existence, among the brain quantum elementary constituents, of long range coherent correlations playing a more fundamental role than the functioning of the single cell in the brain activity. They proposed to model the memory activities as coding of the brain states whose stability emerges as a dynamical feature rather than as a property of specific neural nets (which would be critically damaged by destructive actions).The elementary constituents are not the neurons and the other cells, which are not quantum objects, but some dynamical variables, called corticons. Information printing is achieved under the action of external stimuli producing breakdown of the continuous phase symmetry associated to corticons. General theorems of QFT show [8,9] that in the presence of spontaneous symmetry breakdown the vacuum (zero energy state) is an ordered state and collective modes (called Nambu-Goldstone modes) propagating over the whole system are dynamically generated and are the carrier of the ordering information (long range correlations). Therefore, in QFT order manifests itself as a global property dynamically generated and associated to collective mode condensation. A bridge between the microscopic scale and the macroscopic functional properties of the system is thus made possible. The collective mode is a massless mode and therefore its condensation in the vacuum does not add energy to it. The stability of the ordering is thus insured. Moreover, infinitely many vacua with different degrees of order may exist, corresponding to different densities of the condensate (different values of the order parameter), which may be considered as code numbers[2] specifying the system state. Code numbers may be organized in classes corresponding to different kinds of dynamical symmetries. In the infinite volume limit the vacua are each other orthogonal (unitarily inequivalent, in the QFT language) and thus represent different physical phases of the system, which therefore appears as a complex system equipped with many macroscopic configurations. In the case of open systems trans- itions may occur among vacua (phase transitions), for large but finite volume, due to coupling with external environment. A dissipative system thus appears as "living over many ground states"[10,11]. One may show that even very weak (although above a certain threshold) perturbations may drive the system through its macroscopic configurations[10]. Occasional (random) weak perturbations are thus recognized to play an important role in the complex behavior of living systems. The collective mode in the quantum model of brain has been called symmetron [2] and the information storage function is represented by the coding of the ground state through symmetron condensation, which also insures the memory stability. The memory non-local character is guaranteed by the coherence of the condensate. Motivated by the observation that living matter is made up by water and other biomolecules equipped with electric dipoles, Del Giudice et al. [12] have assumed that the symmetry to be spontaneously broken is the rotational symmetry for electrical dipoles. Also according to Frohlich [13], the (electric) polarization density thus plays the role of order parameter and the associated Goldstone modes have been named dipole wave quanta (dwq). The water molecules undergo a lasering-like coherent process with a phase locking mechanism with the quantized radiation field (super- radiance)[14]. The time scale for the long range interaction is much shorter (10^-14 sec) than the one of short range interactions. Water coherent domains are therefore protected from thermalization. Moreover, electromagnetic disturbances are shown to undergo self-focusing propa- gation in the ordered domains and to induce polymerization effects [3,12] which may be responsible of the formation (assembly) and of the dynamical features of microtubula. Superradiance and self-induced transparency in microtubula are investigated in [15]. Corticons have been identified[15] with the electric dipole field and symmetron modes with dwq of the spontaneous breakdown of electric dipole rotational symmetry. Excitation of dwq modes under external stimuli similar to the ones producing the memory printing describes the recall process. When the dwq modes are excited the brain "consciously feels"[2] the pre-existing ordered pattern in the ground state. Short-term memory is associated to metastable excited states of dwq condensate[2,16]. In the quantum brain model there is only one class of code numbers since only one kind of symmetry is assumed (the dipole rotational symmetry). Once a vacuum of specific code number has been selected by the printing of a specific information, then no other vacuum state is successively accessible for recording another information, unless producing, under the external stimulus carrying the new information, a (phase) transition to the vacuum specified by the new code number. This will destroy the previously stored information (overprinting): the model thus appears too simple to allow the recording of a huge number of informations and a realistic model would require a huge number of symmetries[2]. However, I have shown[1] that, by taking into account the dissipative dynamics of the brain, one may solve the problem of memory capacity without the introduction of a huge number of symmetries. Let me start by observing that once the dipole rotational symmetry has been broken (and information has thus been recorded), then, as a consequence, time- reversal symmetry is also broken: before the information recording process, the brain can in principle be in anyone of the infinitely many inequivalent vacua. After the information has been recorded, the brain state is completely determined and the brain cannot be brought to the state configuration in which it was before the information printing occurred (...NOW you know it!...). Thus, information printing introduces the arrow of time into brain dynamics: Due to memory printing process time evolution of the brain states is intrinsically irreversible. This leads me to investigate the dissipative quantum brain dynamics (DQBD). A central feature of the quantum dissipation formalism[9,11] is the duplication of the field describing the dissipative system: Let a(k) and ~a(k) denote the dwq mode and the doubled mode, respectively. k generically denotes the field degrees of freedom, e.g. spatial momentum. The ~a mode is shown to be the "time-reversed mirror image"[1,11] of the a mode and represents the environment mode. Taking into account dissipativity requires[1] that the memory state, at the initial time t0, say t0 = 0, is a condensate of equal number of a(a) modes and ~a(k) mirror modes, for any k: N(a(k)) = N(~a(k)) for all k The number N(a(k)) - N(~a(k)) for all k is a constant of motion and it is zero for the vacuum state. As a consequence, there exist infinitely many vacuum states |0>(N) which are orthogonal to each other for N does not equal N' (different codes), denoting the memory states. The label N=N(a(k))... N(a(k)) = N(~a(k)) for all k, at t0 = 0 specifies the set of integers defining the "initial value" of the condensate. A huge number of sequentially recorded informations may thus coexist without destructive interference since infinitely many vacua |0>(N), for all N are independently accessible. Recording information of code N' does not produce destruction of previously printed information of code N not equal to N', contrarily to the nondissipative case, where differently coded vacua are accessible only through a sequence of phase transitions. In the dissipative case the "brain (ground) state" is represented by the collection (or the superposition) of the full set of memory states |0>(N) for all N: the brain appears as a complex system with a huge number of macroscopic states (the memory states). In conclusion, the degeneracy among the vacua |0>(N), for all N, plays a crucial role in solving the problem of memory capacity. The orthogonality in the infinite volume limit among differently coded vacua guaranties that the corresponding printed informations are indeed different or distinguishable informations (N is a good code) and that each information printing is also protected against interference from other information printing (absence of confusion} among informations). The effect of finite (realistic) size of the system may however spoil orthogonality and may lead to "association" of memories. After a characteristic time the memory state |0>(N) is found[1] to decay to the "empty" vacuum |0>(0) where N(k) = 0 for all k: the information has been forgotten. In order to not completely forget certain information, one needs to "restore" the N code, which corresponds to "refresh" the memory by brushing up the subject (external stimuli maintained memory). Time evolution of the memory state is controlled by the entropy variations and the stability condition to be satisfied at each time t by the state |0(t)>(N), implies [1,11] minimizing the free energy functional, which in turn leads to the Bose distribution for a(k) and ~a(k) for each k, at time t. The memory state |0(t)>(N) is then recognized[1] to be a finite temperature state equivalent with the thermo field dynamics vacuum state[9]. I also note that a relation exists[1] between the brain memory states and the squeezed coherent states entering quantum optics[17]. The ~a system is a "replication" of the a system and plays a central role in the recalling process: one can show[1] that the creation (excitation) of the a mode is equivalent, up to a factor, to the destruction (from the memory state) of the ~a mode. One can also see that the ~a mode allows self-interaction of the a system, and in this sense it plays a role in "self-recognition" processes. As already observed, the ~a system is the "mirror in time" system. This fact and the role of the ~a modes in the self-recognition processes leads me to conjecture[1], also according to the image of consciousness as a "mirror", that tilde-system and therefore dissipation is actually responsible for consciousness mechanisms. In a forthcoming work I will discuss possible relations between the above scheme and the gravity induced consciousness mechanism proposed by Hameroff and Penrose. [1] G.Vitiello,Int. J. Mod. Phys. B9, 973 (1995) (quant-ph\9502006) [2] L.M. Ricciardi and H.Umezawa, Kibernetik 4, 44 (1967); C.I.J. Stuart, Y. Takahashi and H. Umezawa, J. Theor. Biol. 71, 605 (1978); C.I.J. Stuart, Y. Takahashi and H. Umezawa, Found. Phys. 9, 301 (1979) [3] E. Del Giudice, S. Doglia, M. Milani and G. Vitiello, in Biological coherence and response to external stimuli}, H. Frohlich ed., Springer-Verlag, Berlin 1988, p.49; G.Vitiello, Nanobiology 1, 221 (1992) [4] J.S. Clegg, in Coherent excitations in biological systems, H. Frohlich and F. Kemmer eds. Spriger-Verlag, Berlin 1983, p.189; J. Tabony and D. Job, Nanobiology 1, 131 (1992) [5] K.H. Pribram, in {\it Macromolecules and behavior}, J.Gaito ed., Academic Press, N.Y. 1966; Languages of the brain, Englewood Cliffs, New Jersey, 1971; Brain and perception, Lawrence Erlbaum, New Jersey, 1991 [6] R. Penrose, The Emperor's new mind, Oxford University Press, London 1989; Shadows of the mind, Oxford University Press, London 1993 [7] M. Mezard, G. Parisi and M. Virasoro, Spin glass theory and beyond, World Sci., Singapore 1993; D.J. Amit Modeling brain functions, Cambridge University Press, Cambridge 1989 [8] C. Itzykson and J.B. Zuber, Quantum Field Theory, McGraw-Hill, N.Y. 1980 [9] H. Umezawa, Advanced field theory: micro, macro and thermal concepts, American Institute of Physics, N.Y. 1993 [10] E. Celeghini, E. Graziano and G. Vitiello, Phys. Lett. 145A, 1 (1990) [11] E. Celeghini, M. Rasetti and G. Vitiello, Annals of Physics (N.Y.) 215, 156 (1992) [12] E. Del Giudice, S. Doglia, M. Milani and G. Vitiello, Phys. Lett. 95A, 508 (1983); Nucl. Phys. B251 [FS 13], 375 (1985); Nucl. Phys. B275 [FS 17], 185 (1986) [13] H. Frohlich, J.Quantum Chemistry 2, 641 (1968); Riv. Nuovo Cimento 7, 399 (1977); Adv. Electron. Phys. 53, 85 (1980) [14] E. Del Giudice, G. Preparata and G. Vitiello, Phys. Rev. Lett. 61, 1085 (1988) [15] M. Jibu , S. Hagan, S.R. Hameroff, K. H. Pribram and K. Yasue, BioSystems 32, 195 (1994); M. Jibu , K. H. Pribram and K. Yasue, Int. J. Mod. Phys. 10, June 1996, in print [16] S.Sivakami and V. Srinivasan, J. Theor. Biol. 102, 287 (1983) [17] H.P. Yuen, Phys. Rev. A13, 2226 (1976); D. Stoler, Phys. Rev. D 1, 3217 (1970) On Mon, 25 Mar 1996, Giuseppe Vitiello wrote: > On this memory model (Int.J.Mod.Phys.B9(1995)973) I will present a talk > at Tucson II on Friday, April 22. Maybe I will try to write a short note > (abstract like) for quantum-d for those who will not be there. > > Giuseppe Vitiello > > On Fri, 22 Mar 1996, Donald Tveter wrote: > > > Can anyone explain the quantum memory models? > > > > My background is Computer Science with an interest in AI but I was an > > undergraduate in Math and Physics so I can understand a little (but only > > a little) of what is going on with the microtubles and interpretations > > of quantum theory. If you care to help me with this problem please take > > this into account. > > > > I saw in the preprint archives the theory by Vitiello about how an > > unlimited number of memories can be stored... > > > > [e.g. http://xxx.lanl.gov/abs/quant-ph/9502006] > > > > ...and apparently the newer > > papers by Nanopoulos and his associates have a similar theory. To a > > computer scientist this is pretty impressive but I haven't the foggiest > > idea how this is done. Can anyone explain this? I think it would be > > especially helpful to have an example where the memory stores simple > > data like A = 1, B = 2 and C = 3 and then retrieves the values on demand. > > > > Thanks, > > > > [an example reference for Nanopoulos's recent ideas is > > http://xxx.lanl.gov/abs/quant-ph/9510003 > > - rs] > > --- > this document at: > http://www.teleport.com/~rhett/quantum-d/posts/vitiello_3-25-96.html >

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