Can the Configuration of the Human Consciousness be Explained by Means of Quantum Oscillation Collective States Inserted in the Skeleton of Neuron Cells?
The first true question we would propose is: can the manifestation of the human anthropology be exclusively explained in terms of brain actions, in extensive sense, or does it require the addition of new ontological essences that imply doubts about (even the destruction of) the monism principle? This complicate question, in my opinion, is one of the issues in the permanent discussion between Philosophy and Theology with the Neuronal Sciences. This question provokes the existence of a way of knowledge that should be run with the perspective that there is neither definite finish in the race nor definite and conclusive responses along the running. But the pleasure of the intermediate cognitive travel deserves to make efforts even if one can suffer certain deceptions because of possible delays in attaining partial advances. If we accept a sole ontological substance in the human being, which is the assertion posed in the monism principle, there is no reason why an analysis of the psychophysical activity should become carried out by the more pristine laws such as the physical laws are, since all material systems are physical and all material systems are composed of physical components. However, we recognize that the huge complexity of the physical systems can imply the emergence of new self-organized new principles that can either hinder or, at least, make difficult the connexion in a simple way between the primitive and elemental components and the holistic treatment of the human actions and reactions that are objective of these emergent complexity laws. The continuous steps from the microscopic systems with possibility of being analyzed with physical methods to the extremely macroscopic ones generated by almost infinite microscopic subsystems constitutes a task which allows us the connexion between the physical single laws and the biological laws. However, the new challenge of this work is to do a prospective for attempting the possibility of explanation not only of physical-biological connexion but to continue our study looking for a logical and systematic relationship between the physical analysis of the brain and its psychological actions. Within the psyche, external sensorial perceptions can be recorded and evolved; emotions and sentiments are developed, and with the psyche, knowledge is acquired. The human being is able to recognize all these functions as belonging to himself in a conscious way. This self-recognition along with the individual sense of its own existence and presence in the sensorial world are the basis of the consciousness, constituting this essential part of manâ€™s psyche an instrument which is simultaneously the object to study and subject with which we can do our own study. At this point one should ask himself new questions: can Physics carry out an explanatory theory of the sensorial brain actions, emotions, sentiments, the acquisition of knowledge? Can Physics give an overview, a review, reasons and descriptions for the existence of the will of the human being? Can the consciousness be included within the explicandum of the Physics? Has Physics sufficient epistemological architecture to be an effective explicans for the main property of the human self which is the most distinctive property of its true different nature from the other mammalians? Although I have many serious doubts about the possibility of obtaining some valid answers to these questions even within a long time, I think we can establish some ideas, pose some valid assertions and above all, we can find correlations between determined, and up to now unknown, physical states with the neuronal pattern which appears in some brain actions. In a way similar to that of the phenomenology giving support to physical science and the clearly existing psyche phenomena giving support to the Psychology as a true science, our objective is the formulation of a nexus and relationship between some physical states and their psychological manifestation.
From a starting point of view, I think that to look for possible mechanisms and to identify physical states that by having its action in the neuronal system allow us to identify ourselves as an ontological being differentiated from our environment and from other similar beings. The identification of these mechanisms and physical states that define them is maybe the most important achievement which I can dream of obtaining and therefore my research in progress goes in this direction. With this analysis, I would try to find cognitive structures which would allow us to establish methodologies for understanding some things about the reality of our consciousness from a physical point of view as well as that these models are supported, if possible, by experimental evidences which validate the starting hypothesis. It is obvious that the phenomenology of the psyche is within the explicandum of science, but in which particular science should both the explanation and the description of the consciousness be found? It is an issue subject to debate. Maybe some short history of the attempts to explain this theme should be undertaken. There are many scientists that have assumed the tasks of analysing the neuron actions from both a physical and a chemical points of view, but there are three tendencies that ought to be considered as pioneers in these issues: Eccles, Penrose-Hammeroff and Bohm.
Eccles (1992) presents an anatomic solution of the neuron cells including the idea that quantum mechanics is necessary for understanding the interrelationship and connexion among the synapses. He expresses his conviction of the existence of an evolutionary condition for the consciousness. His arguments have more biological and topographic neurological aspects than physical treatment, although he expresses an intuitive consideration that the classical physics is unable to give response to the physical relationship among the neuronal subsystem to which he named Dendron. This Dendron neuronal system is the collective assemblage of excitatory synapses, which are able to construct brain actions with a logical sense.
Penrose alerted by the projection of the artificial intelligence which considered that any logical intelligent action was a Touring machineâ€™s logical operation joins his efforts with the director of the anaesthesiology department, Hameroff, and proposed the so-called Penrose-Hameroff model of the consciousness (1996). The existence of quantum coherence in the microtubules of the skeleton of the neuron cells can be made possible by means of the eiselection of an eigenstate of each tubulin by means of the collapse of the wavefunction in one elemental component of the microtubules of a collective state. In a posterior sequence, a simultaneous and orchestrated reduction of many tubulin states should constitute a collective coherent state. The reason of this collapse is, according to this PH model, due to the difference of the gravitational self-energy occurred in the selected pointer state with respect to the superposed quantum state before this eiselection occurs. The selection of an eigenstate is interpreted as a pre-conscious measurement and the consequent recording in an already classical-like state of the results of this measure is the conscious knowledge.
The ideas of Bohm about the human consciousness have a holistic dimension, an universal conception. Bohm proposes the idea of an universal consciousness with a pantheistic flavour in which the human participation of this universal category represents the meaning of the human consciousness. This is a suggestive idea in which the human race has a self-knowledge of itself via the participation in the general consciousness. In a way similar to that of the elemental particles which constitute a macroscopic system, the individual and â€œmicroscopicâ€ consciousness of all and every component of the human race constitutes the â€œmacroscopicâ€ universal consciousness. Bohm also proposes quantum mechanics for understanding this human property, but, we must remember that the idea of Bohm about Quantum Mechanics is, in certain sense, heterodox. Bohm, maybe, influenced by the success of the discovery of the so-called Ahoronov-Bohm effect, proposed that there are definite trajectories of the particles that emit a coherent potential which can interfere with the potentials of the other particles. This vision is in contradiction with the Copenhague quantum mechanics interpretation
A common idea exists in all models, which is the quantum nature of the brain states which should present collective coherence. Maybe, the most debatable part of the PH model is the gravitational reason for the objective reduction in each one-body state into the tubulin and the appearance of the simultaneous collapse of each one-body tubulin state for obtaining a collective coherent state as a preconscious brain action. I recognize that the fact of understanding these last points of the PH model inspired me this research and in this scenario, I will give my proposal.
As it is well known, the transmission of the nervous signals is produced via the neuronal cytoskeleton (Priel et al.) which is based on different building of cellular proteins which are constituted by three types of protein networks: microfilaments, intermediate filaments and microtubules. These last physical structures are the substrate where the quantum states are formed, evolve and are finally transmitted, even teletransported, between successive and connected neuronal cells constituting the nervous signal transmission. Each microtubule is built up by individual peanut-shaped dimmers called tubulins which are electrical dipoles whose dimension is between 4 and 8 nanometres. These microtubules are rigid and have a hexagonal lattice in which there is an internal coaxial hole. Through this hole, chemical environment liquids based on the lipids and other simple molecules circulate modifying the linear response and dielectric functions which can change the individual tubulin and the microtubules many body- states. Each individual tubulin behaves as an one-body state, similar to a computational bit so that if this is considered as a quantum state, due to its quantum nature, it is called qubit. Consequenly, the rigid microtubules can be monitored by means of Heisenberg-like lattices. In these lattices, the interactions among electric and magnetic moments of different tubulins can be analysed as magnetic and dielectric ordered structures within a background of an electron sea which can be, in principle, both an insulating and a conducting system. The electrical signals or exterior interactions influence the electric moment orientation of the tubulins within the lattice in a similar way to the evolution of the low-lying excitations of the strongly correlated systems. This strong correlation is, in the first place, due to the localized nature of the one-body states located and defined in the tubulins and, in the second place, to the short ranged interactions among the states inserted in two nearby tubulins.
COMPONENTS OF THE SYSTEM. SUMMARY
The brain of an adult human being is an organic structure whose weight is around 1500 grams, perfectly adapted to the cranial cavity by means of the brainspinal liquid that prevents the damage by the rubbing with the cranial bones. This human organ which have a most superficial, rough and external part named cortex, is divided in two almost symmetric parts denominated hemispheres. These hemispheres are joined by a hard substance and have five specific areas whose names refer to the corresponding bones that cover them. The central part is the thalamus which is responsible of distributing the intelligence information that is distributed by the cortex. In the basis of the thalamus there is the hypothalamus whose main mission is metabolic. The left hemisphere is responsible for the oral functions and the perceptions are received and recorded in it. The right hemisphere has the control of the emotional dimension of the human being. The frontal lobule realizes functions of the intellective organization. Each topologic part of the brain has determined functions whose specification and description are out of the objectives of this paper since it is a matter of the anatomical and neurological study. This organ is constituted by several kinds of cells amongst which the most important are the neuron cells and glia cells. Mission of the neuron cells are the brain actions while the glia cells are subsidiary since they yield to the neuron system these chemical substances that produce the neurotransmitter molecules.
From a physical point of view, the brain is a physical system constituted of a hundred Spanish trillion (10^26) elemental particles named electrons whose dynamics is fundamentally governed by electromagnetic interaction. These electrons belong to approximately ten trillion atoms (10^25) which are grouped in a hundred thousand million (10^11) neuronal cells. Each of these cells has around ten thousand synapses which are the connections of the neurons where the adjoining cells get the nervous streams. In addition, inside each neuron, the above cited cytoskeleton works as a structure whose function is similar to that of a spine kind. This cytoskeleton is constituted of filaments and microfilaments that provide the adequate environment for the microtubules which are the true elements for the electrical activity inside the neurons i.e. these microtubules are the transmitters of the nervous signals. Therefore, these microtubules are the main elements responsible of the transmission, storage and implementation of the brain actions. On the other hand, it is necessary to take into account that the mental actions imply the existence of physical states that can involve up to one hundred neuron cells connected by synaptic connections.
Each microtubule is a hollow cylinder whose base diameter has twenty five nanometres and its length is around two hundred nanometres (each nanometre is a millionth of millimetre). Inside this cylinder, water, lipids and proteins travel through its hole supplying an appropriate dielectric behaviour that favours the corresponding function in the global physical state. The microtubules of each neuron cell are composed of around ten millions tubulins that are light proteins, polypeptides or even simple amino acids. The geometrical location of the tubulins within the lateral surface of the microtubules is hexagonal and its dimension is between four and eight nanometres. There are two kinds of tubulins according to the sign of its total charge: the positive charge tubulins, henceforth, we will name them alpha-tubulins and those whose charge is negative, beta-tubulins. The gravity centres of two adjacent tubulins are split around four nanometres. These constituent elements of the microtubules and the neuron cells that are mainly responsible for the generation of the physical states can form pairs that are called dimmers. Each tubulin has a nanometric dimension and is the most simple quantum state that presents the features of a qubit (quantum bit of a quantum computer). Consequently, the associated tubulins forming dimmers are biqubits that, in turn, are two particle system quantum states.
QUANTUM MECHANICS OF TUBULINS AND THEIR ENSAMBLAGE
The tubulins form tubulin pairs which constitute dipoles with a well defined module of their dipolar moment. The dipolar moment is a vector whose module is the product of the positive charge with the distance between two contiguous tubulins. The dipole moment vector of each tubulin pair can fluctuate space-temporally in all possible directions. The quantum physical interpretation of each tubulin is a qubit which corresponds to a two dimensional Hilbert space whose basis contains two states corresponding to the classical bit states |1> and |0> of the standard computers. However, the number of states for each tubulin is infinite due to the quantum physics nature of its corresponding state that is defined via the superposition of alpha and beta states, in such a way that an one-body quantum state is defined by |x>=A|alpha>+B|beta>, where A, B are complex numbers where the sum of the squares of their modules is the unity. The meaning of these number within Quantum Mechanics is related to the probability amplitude of that the |x>-state in a given time can collapse in either the state |alpha> (the value |A|^2) or |beta> (the value |B|^2). The collapse of the wavefunctions also named objective reduction of the |x>-state that is converted either |alpha> or |beta> can be due to an external interaction which can come from the dielectric and/or magnetic environment. This collapse is also named einselection (see Zurek 2003). This terminology comes from the quantum theory action whose meaning is the selection of a given eigenstate of a physical variable (magnitude). In quantum mechanics, each eigenstate of a given physical magnitude is determined via a secular equation H|n>=a|n>, where H is the hermitic operator defining the magnitude, |n> is the eigenstate and the a-parameter is the corresponding eigenvalue. As a consequence, as said above, there are infinite possible states for each tubulin and each gstate is defined by its two complex numbers A and B. But in the case of two dimension Hilbert space, only two possible values are possible for each physical magnitude. This can be understood by considering the well-known SchrË†dingerâ€™s cat example which has two possible values (eigenvalues): alive and dead even though this cat can present infinite intermediate states such as the tubulins have. This paradigmatic metaphor that allows the clarification of the different philosophies within the Classical and Quantum Physics of the tubulins is useful to distinguish standard bits from quantum qubits. The collective state is present in a neuron or neuron set, where each tubulin is in a different one-body state, i.e. each tubulin contains different A and B values and thus, the neuron is in an incoherent random state which does not yield nor store any computable information.
Electrical and magnetic streams are produced by excitations and external stimulations that are transmitted through the nervous system to the brain. Then, successive processes start that can be materialized in one body quantum state in the tubulins. Afterwards, a collective assembling of identical states generates a coherent many-body state. In principle, each tubulin yields an individual state that becomes different in each tubulin and then the collective many-tubulin state is incoherent. The brain does not interpret anything in front of this incoherent state. The neuron intelligent system tries to measure and observe the many body state and from this observation a result should be obtained which the incoherence hinders. In opposition to it, if the state presents coherence (I will define quantum coherence later on) as in any measurement process, the measurement of the brain can obtain values of eigenstates. This last process that happens in coherent states is equivalent to the collapse of wavefunction of each one-body state, which implies the selection of an eigenstate of each tubulin corresponding to an eigenvalue. When this selected state simultaneously coheres in the tubulins of a neuron, the global state of this cell oscillates coherently. The obtained coherence allows the storage of information from the external excitations, since a correlation between the nervous streams produced by the external signal and the coherent global state is established. The internal coherent global state can be transmitted to the network of connected neurons by means of a Josephson-like effect similar to that occurring in superconductor-insulating-superconductor devices.
Unfortunately, there are multiple dynamic reasons that are able to undo the coherence and this coherence destruction modifies the quantum superposition of the individual tubulin states and therefore, hinders the election of a given eigenstate, either alpha or beta. As a continuation, we will give some of these reasons that are stated in the section of proposals in this paper. One of the most striking ideas of Quantum Mechanics is that there are two kinds of particles, bosons and fermions, The fermionic particles such as electron, proton, neutron, electronic and muonic neutrinos, etc, are defined as those particles that occupy an individual state (one-body state) and, in addition, each of these states contains only one particle, these particles normally have mass and some of them, electron, proton and muon have also electrical charge. These particles can suffer interactions, the four interactions from nature. On the other hand, the bosonic particles such as photon, phonon, gluon, graviton, exciton, magnon, etc., can share the same state any arbitrary (even infinite) number of these particles. Furthermore, these bosonic particles become the messengers of the interaction between the fermionic particles. Moreover, the fermionic and bosonic particles present another difference: fermions have a half integer spin and the bosons have an integer spin (the spin is the internal angular moment which is the total angular moment in the system in which the particle has zero speed). The property of having a different spin value for each kind of particle is, according to the spin-statistic principle, equivalent to that of the Pauling principle of different state occupation.
The capability of occupying many (even infinite) particles the same one-body state can be obtained with fermions when they form new individual entities constituted of an even number of fermions, in such a way that the resulting entities are bosons. Each two half integer spin particles joined via an attractive interaction generate a new bosonic composite particle. Then, an indefinite number of these new particles can occupy the same state and thus the collective many body state constituted of fermion pairs can be coherent in itself. Two examples of coherent states are, on one hand, the superconducting state based the so-called Cooper pairs (electron pairs), and on the other hand, the cases of some Bose-Einstein condensate whose elemental pair components are excitons formed by electron-positron (hole) pairs. There are many kinds of Bose-Einstein condensates, some whose single components are fermion pairs and others based on genuine bosons such as phonons (quantum lattice oscillations) or magnons (energy quantized spin oscillations). One of the basis of the physical theories about consciousness comes from the idea that mental and brain actions arise from the appearance of global coherent states that evolve in the neuronal lattices. In a certain sense the coherence in brain operations seems to be an image and even a consequence of the physical coherence of the global state that defines the corresponding brain action. We say â€œseemsâ€ since there is not yet a conclusive and apodictic theory that confirms and ratifies this point. The storing and reproduction properties of these coherent many-body states are due to the easy intersynapses transmission of external signals via physical mechanisms similar to the tunnel and Josephson effects. Moreover, these states become perfectly characterized with the internal parameters required in their construction. However, the main problem for these theories is the extreme difficulty of maintaining the coherence property of these states since this is a subtleness of the global system which has a strong tendency to disappear in the absence of the equilibrium conditions. Therefore, the hypothesis that the global coherence implemented within the neuron lattice can be representative of assigned mental/brain actions presents difficulties and therefore some points should be considered in order to establish a possible consolidation of this assertion.
- From a physical point of view, the elemental particles responsible for the dynamics of the brain actions are almost exclusively electrons and these particles are fermions. Therefore, the coherence with global states can be obtained from either fermion pairs (electron-electron pairs and/or electron-hole pairs) or particles coming from collective oscillations (magnetic oscillations named magnons, dielectric oscillations named polaritons and lattice oscillations named phonons). As it is well known, the interactions among electrons are repulsive and those existing between electrons and positrons though are attractive, it is necessary the excitation of an electron from the valence band to the conduction band. The existence of electron pairs is only possible at very low temperatures, since the highest temperature of a superconducting state is lower than â€“ 140Âº C. Therefore the superconducting state is discarded. The remedy for attaining the coherent global state via pair couplings of electron and holes is in the interaction between the tubulin system and the environment. This interaction is mediated by the circulation of water, lipids and polypeptides inside the microtubule hole yielding a dielectric medium in which the coupling of two tubulins (or pair coupling ) is then favoured. These dimmers have a bosonic spin character and then the coherent states can be transmitted among synapses of the neuronal lattice. The theoretical and experimental first problem is to establish how the dimmers are formed and how the density of these dimmers increases until reaching a critical value for obtaining a coherent state.
- A second problem related to the quantum coherence is that this extremely subtle quantum property can easily be broken. The possibility of obtaining coherent states is relatively probable and normal in electronic many-body systems, but these usually are quantum excited states. The half life of these states decreases as a consequence of the increase of their excitation energies. Therefore, their processed implementation and recording even in the appropriate brain zone is not possible. A coherent state requires at least a thousandth of second to attain a mental representation and this time is extraordinarily long for the permanence of a coherent state. This is the reason for the requirement of catalytic activators of the memory which fulfil the task of lengthening the half life of the quantum coherent states in order to facilitate their recording.
- The third problem constitutes the most important objection to the coherence of the many-body state to be the basis for the brain actions. This is, maybe, the strongest criticism and the most substantial discrepancy in the development of Quantum Physics in the issue of coherence and the quantum coherent states within neuron transmission. The coherence in the collective states such as it occurs in both the superconducting states and the Bose- Einstein states constituted by particles with mass (electrons, positrons, muons, holes) is a weak and subtle property which is usually maintained only at very low temperatures: 125Âº C below zero would be the maximum temperature at which this coherence is possible, this being, at least, the opinion of the quantum neurology objectors.
- Although brain actions should be formulated via the dynamics of the electrons, the magnetic moment coming from the spins of the electrons can generate a configuration of many-body coherent states based on collective oscillations of their spins. These collective systems can, in very restrictive conditions, form a Bose-Einstein condensate whose survival temperature can be as high as room temperature, this situation being recently experimentally found. The analysis for obtaining a description of this BEC state presents similarities from a physical point of view with the antiferromagetic dimmers construction via Kondo-Heisenberg exchange interactions. The antiferromagnetic lattices acquire the appropriate conditions via the existence of a determined medium that is equivalent to the cellular environment in the neuronal systems. The tubulins are submerged in a medium containing proteins, lipids, water and peptides such as oxotin, serotonin, noradrenalin, oxicetin, riboflavin, endomorphin, etc., which are responsible for the microtubule bath that favours the evolution of tubulin dynamics. A large biochemical experience has improved the neurological studies in such a way that there is a huge amount of experimental data about which nourishment can aid the development of the performance of the brain and mind actions.
Seven years ago, a lively debate based on whether the coherence is or not possible for temperatures around 309 K was maintained by several groups. The basis of the main discrepancies was that the consciousness actions can not be explained by the existence of quantum coherence in the neuron systems because this quantum property is too weak and can not be held at these high temperatures (Tegmark 2000). On the contrary, those who defended this coherence possibility for explaining the brain actions argued that the environment of both intra and inter-neuron cells interact with tubulin states and then, the coherent states can survive up to higher temperatures than that of the human body (Hameroff 2002). The main objective of my research, as said above, is to present models for obtaining the coherent assemblage of tubulins for making possible the appearance of collective oscillations that can persist even at high temperatures. Some new technics such as the magnetoencephalography are applied to the cerebral diagnostic. This technique is based on the existence of certain magnetic behaviour of the brain, which can imply the appearance of a quantum protectorate that preserves the coherence of magnon-like BEC states up to high temperatures. These BEC states have been experimentally detected in several inorganic materials. In any case, the criticism of Tegmark (Tegmark 2000) who is the leader of the opposition to the quantum neurology presents robust arguments that should induce reflexion in order to dispel the existing doubts about the applicability of Quantum Mechanics to the physical knowledge of consciousness.
DYNAMICS IN STRONGLY CORRELATED TUBULINS
The determination of the low-lying excitations of the strongly correlated (SC) systems has revealed many interesting properties of non-conventional new materials. Using the similarities between the system of tubulin qubit states and the Heisenberg-Kondo lattices (Hewson), we can analyze the dynamical behaviour of the complex systems; some of the conclusions can be applied to the evolution of the many-body microtubules states. These SC systems present peculiar features concerning electrical conductivity and magnetic ordering behaviour in such a way that these physical properties are inextricably mixed, and it is particularly difficult to put forward arguments that can separately explain each of them (19,20,21). The simplest system that presents this relation between conducting and magnetic properties is a magnetic impurity submerged in a sea of extended band electrons(19). The analogy to this impurity model within the tubulin-microtubule systems is the existence of defects within the hexagonal structure of the microtubules in which a lack of hexagonal symmetry can occur. The rich phenomenology that appears in this system becomes the so-called Kondo effect (Mahan). The main consequence of this effect is that the resistivity presents a minimum for a temperature named Kondo temperature (Hewson). This modification of the resistivity can be experimentally detected via the change of the transmission of the neural signal. The cause of this behaviour is found in the existence of a well-defined resonance, appearing close to $E_F$. The width of this resonance is produced by the hybridization of the localized impurity state with the conduction electrons existing in the tubulins and is proportional to the Kondo temperature (21). This Kondo resonance state is foreseen and deduced by the single-site Kondo Hamiltonian and also by the impurity Anderson Hamiltonian in the so-called Kondo regime (Hewson). When this regime is considered in diluted systems of non-interacting magnetic impurities, the result is similar to that of the one impurity model (22,23). For increasing magnetic impurity concentrations, the system can present coherence effects due to the interacting one-body states, and following this, the Kondo lattice phenomena appears. Our proposal establishes that the dynamics of qubit states for constructing a many-body coherent state within the rigid microtubule can, in certain conditions, be similar to that of the strongly correlated insulating heavy-fermion Kondo lattice. Such lattices present similarities to the Hopfield networks and their analysis is within the discipline of the Quantum Field Theory. Therefore, we analyze these physical systems determining the nature of structure of the different many-body coherent states arising from the Kondo-Heisenberg lattices. The existence of these coherent states and the possible permanence of the coherence with increasing temperatures up to the human $T_c$ (309 K) is the main goal of this paper, this objective being inspired by the idea that our conclusions in this physical state can be translated to the brain functions using a similar parallelism to that of the Penrose-Hameroff collapse model for the conscious function.
According to this model when a measurement is made inside the quantum state, the wavefuncion suffers a collapse and this collapse is assumed as a conscious action. In this tubulin Kondo system, there is a characteristic temperature, T^*, below which the material behaves as a coherent lattice, and above which as an incoherent aggregation of independent impurities and the classical circuit networks can work. The thermodynamic regime studied in this paper is for T<T^*. In this regime, we analyze the physical mechanisms of tubulin coupling in a similar way to electron-hole coupling or electron-electron coupling with spin (electric moment) fluctuations. The calculation of the spectra of low-energy excitations is determined via Hopfield-like lattices (Behrman et al.) in a similar way to several other magnetic systems, such as high T$_c$ cuprates (Dagotto et al., Syljuasen et al.) and manganese oxides which can be treated by means of different Kondo Hamiltonian variants (Dagotto et al.). In this paper, we perform an analysis of the low-energy excitations states aimed at understanding certain key features that may shed light on explaining some of these debated issues, and which could be useful in explaining the properties of systems that suffer energy condensates produced by magnetic and electric fluctuation waves.
It is well known that the tendency to the dipole order similar to the antiferromagnetism and local electric-magnetic fluctuations in the tubulin dipoles may be the origin of the great value of electron susceptibility and specific heat such as occurs in heavy-fermion systems. In addition, the interplay between two dipole correlations and the spin fluctuations due to the interactions of the dipole field with the charged liquid can produce band conditions for different states of matter (24). Some of these phases present anomalous electrical-resistance behaviour, which can be exotic superconductors, Bose condensate states such as those appearing in some inorganic materials (Sigrist et al.) and other different coherent states whose origin is due to several fermionic couplings. These behaviours can be analyzed in a way parallel to that of the Heisenberg spin field interactions and the Kondo lattice dynamics. In addition, this allows to connect, in some of these compounds, the existence of different types of energy condensation states with the heavy-fermion properties of the electron states close to $E_F$. On the other hand, another many-body state is possible in these strongly correlated systems: this is the exciton condensed (EC) state. In this many-body state, the same fluctuating electromagnetic waves, which can produce superconductivity in certain systems for certain values of the governing parameters of the Hamiltonian, contribute in others to the binding energy of the excitons in a decisive way. The properties of these states, both the superconductor and insulating EC, can be attained via the intermediate action of the same electromagnetic excitations that allow fermionic pairs to be formed, in some cases electron-electron and/or hole-hole pairs and, in others, electron-hole excitons.
The structural composition of microtubules systems allows us to assume the hypothesis that these system behave as strongly correlated states where the tubulins play the role of the strongly correlated electrons of materials such as the lanthanide, actinide and some metals transition compounds. These tubulins are single one-body states that are governed by a double exchange interactions present in other inorganic compounds. In these systems of tubulins, electric moment fluctuations waves can be produced by the existence of external-neuronal signals. These fluctuations allow the couplings and the formation of dimmers with single qubits coming from two tubulins. For certain conditions, these couplings can, via Kondo plus Heisenberg-like interactions within the localized tubulin field, produce the two different kinds of collective states whose thermodynamic properties are similar to those of the BCS states, but their electromagnetic behaviours are opposed: one of them is a magnetic insulator and the another one has metal or semimetal behaviour where the exciton formation is possible. The analysis of these phases carried out with our model allows us to explain some experimental results obtained in neuronal systems.
MODELS FOR THE NEURON COHERENCE
From a classical physics point of view, the coherence can be summarized saying that when one variable has a coherent evolution in the space-time dimensions and its value is known in one minkowski space point this physical variable is known in all minkowki space. This occurs, for instance, in an electromagnetic wave. It can also be said that two electromagnetic waves coherently interfere if they have the same frequency.
The quantum physics point of view is different because the physical variables are not functions of the space-time but operators that act on the states which evolve in the space-time dimensions. The states are deterministically deduced via either the Dirac or Schrodinger equations but the coherence is defined when the physical variables have known values. However, the values of the physical variables are obtained via measurement operations. In quantum mechanics, the measurement operations imply the modification of the original wavefunctions of the state in which one wants to know the physical variables. This modification will only be null if the state is an eigenstate of the operator defining the concrete variable. In the measurement operations of the state, the variables have more or less uncertainty which is regulated by the HeisenbergÂ´s principle. According to this principle, the canonical conjugate variables have their uncertainties related in such a way that the product of the uncertainties of two canonical conjugate variables is normally larger than the half of reduced Planckâ€™s constant. In this context, the coherent states are defined as those with maximum quantum coherence which is the property of those states in which all pairs of canonical conjugate variables have a minimum product of their uncertainties, i.e. this product equals the half of the reduced Planckâ€™s universal constant. From a heuristic perspective the coherence of a system implies the maximum determination of this system. This feature implies that the coherent quantum system is the one which presents the most similitude with a classical system. In this sense an electromagnetic quantum coherent state (for instance laser radiation) is one which has the most similarity with a classical electromagnetic wave.
Model 1. Magnon Coherent State
In this model, we consider that the dynamics of the tubulins is governed by the magnetic moment (spin) of the charge in each tubulin and the corresponding Heisenberg interactions between the spins of each pair of charges. In addition, we suppose that the environment generates an insulating medium in which the electrical current is zero, i.e. the skeleton of the neuron microtubule is immersed in a dielectric medium that hinders the free movement of charges. These conditions truly exist within determined neuron cells. This implies that the dynamics is exclusively governed via the spin exchange Hamiltonian of Heisenberg. I have determined the ground state wavefunction among all possible spin configurations of the system. I found that according to determined conditions and before the presence of weak magnetic fields produced by the charge movements, external to the microtubule, a superposition of spin configurations is formed that has similar quantum coherence properties to those of the electromagnetic quantum coherent radiation which is the basis of the laser radiation. This ground state is a collective state composed by quantum magnetic oscillations named magnons. A magnon is an oscillation of the magnetic moment caused by the competition between the external magnetic field and the Heisenberg interaction between the different magnetic moments localized in each tubulin of the lattice that constitutes the microtubule. The physical magnitudes that imply the dynamics of both the one-body state and the global magnon state are the dipolar moments whose orientation is quantized in a way similar to the spin of the charge carriers which are sensitive to be manifested in experimental phenomena such as the magnetoencephalography. This neuronal magnetic technique yields a brain pattern of magnetic field stimulations that can reflect the oscillations of the spin of the neuron cell skeleton as well as the possible transmission among the different cell sets.
In a second step, I determined the low-energy excited states that complete the basis of the Hilbert space. All components of this basis are coherent states whose distinction with the ground state is that the linear moments of these excitations are different from zero and, on the contrary, the ground state has zero linear moment.
The third step consists of a thermodynamic analysis via the determination of the free energy of the system generated by the spectra of the coherent states deduced from the first and second steps. This allows us to obtain the entropy and the system as well as the specific heat which has a divergence for a temperature named critical temperature. This T-divergence indicates the existence of a second class phase transition. Below this critical temperature, the system is coherent and it is constituted of the bosons with a great occupation. These conditions allows us to define the system as a Bose-Einstein condensate which has a definite linear moment and the product of the uncertainties of the occupation number (intensity) and the quantum phase is minimum. These states are coherent, collective many body coherent states which can be recorded and reproduced by means of the necessary conditions that generated them. The transmission intersynapses can occur either via chemical neurotransmisors or by coherent spin transfer between molecularly bridged quantum dots (see Ouyang et al. 2003). The advantage of this model versus any other is that the magnons are bosons without mass which form mini Bose-Einstein condensates located in neuron microtubules that can survive above room temperature. Besides, the large collimation of the coherent state, similar to that of laser radiation, allows the transmission of information without it being scattered around the environment. This collimation property implies the easy transmission of the global magnon state through the appropriate neuronal pathways. Our proposition agrees with experimental results given by Schofellen et al. (2005) However, this model have or may have some disadvantage since, although there exists clues for the magnetic intermolecular transmission of the spin states among intersynaptic gaps, at the present time, these theories require more experimental confirmation and ratification. In any case, this conjectural way for the transmission of the coherent states trough the intersynaptic gap can give support to this model of magnon â€œlaserâ€ for explaining the brain actions by means of physical states. Maybe, the consistent theory that explains the generation of coherence in the brain actions and its transmission in appropriate directions in the neuronal system should be investigated with conducting-(magnetic)insulating mixed models. Therefore, we have done a prospective in the conducting excitons procedures which can be mixed in the Kondo-Heisenberg lattices.
Model 2. Exciton Coherent State
Both the insulating and conducting behaviours are possible within the neuron microtubule, and the modification or phase change is possible to be attained according to different conditions of the environment, i. e. the dielectric and magnetic material medium. In the cases with conducting behaviour, the model of alpha and beta tubulins can be treated as an excitonic gas which is inserted within the periodic system that constitutes the assemblage of the tubulins in order to form the microtubule. Each pair of alpha-beta tubulins has a behaviour as a hydrogen atom whose spin is an integer number, either 0 or 1. These excitons have a dynamics similar to that which is present in the photosynthetic conversion of sun light for the green vegetable world (see Engel et al. (2007)). The charge density inside the tubulins is such that a geometrical distribution of positive and negative unity charge appears in the microtubules. This implies the existence of an alpha-beta state lattice in the microtubules within each neuron cells. Each alpha-beta state pair presents a strong attractive binding energy which can be more or less screened by the dielectric media. In any case this allows us to analyze the possibility of considering the exciton system as collectives systems of bosons. The possibility for attaining the condition of the Bose-Einstein condensate depends on the possibility that the occupation number of the low energy state overpasses the critical value for obtaining the phase transition. The occupation of states is governed by the minimal energy principle and therefore, we should evaluate the imbalance between the total attractive (potential negative energy) and the total positive kinetic energy of all boson components.. In other words, the total energy of the microtubule system formed by the alpha-beta dimmers is decreased by the attractive energy of the binding potential of the excitons (here excitons and dimmers are two equivalent words). When the exciton number exceeds the critical value, the microtubule global state is, obviously, coherent because when these excitons are moved by either electric or magnetic fields, all dimmers move with the same linear moment and kinetic energy. Hence, the resulting global many-body state is formed by bosons and therefore, it is a coherent Bose-Einstein condensate.
The procedure for determining this global BEC state is excluding the Heisenberg localized spin-spin interaction of the Kondo Hamiltonian. I consider three terms, the kinetic energy, the attractive electron-positron interaction and the magnetic exchange between the localized magnetic moment and the conducting band electron spins. The interplay of these three energy contributions may yield the critical values for transiting of a semimetal and metal behaviour (conducting) towards the condensate of excitons. In addition, it must be remembered that an external signal can produce electric excitation which can in turn produce a wave of linear moment within the coherent BE condensate. The resulting many-body state presents a new set of quantum numbers. Then, this excitation remains defined by a new BEC state, in such a way that a correlation can exist between an external signal and the physical change of the resulting modified condensate. The advantage of this model with respect to the former magnon BEC state is that the intercommunication across the intersynaptic gaps can be produced via the tunnel effect. In this tunnel effect the tunnelled particles are the excitons, i.e. this specific tunnel effect is a boson transmission among neuron cells. Therefore, this effect is not the normal tunnel crossover of electrons between conductors through an insulating layer, but the transmission of a many-body coherent BEC state that passes through the dielectric medium existing among synapses of different neuron cells. This anomalous tunnel effect is more similar to the superconducting Josephson one than to that arising from the metal-insulating-metal devices.
One of the most significant properties of the Josephson stream is that there is particle current independently of the existence of electric potential between the two sides of Josephson junction. The existence of any electric field between the two poles of the device can imply that the signal is an alternating current that oscillates with a frequency that is related to this potential. All these characteristic features are due to the fact that the tunnelled particles are bosons instead of the fermions that cross the device poles in the normal tunnel effect. These experimental features give support to the Josephson channel for transmitting the exciton coherent state among neuron cells. The oscillating transmissions are perfectly characterized with fixed quantum numbers corresponding to a coherent BE condensate. These quantum numbers remain as a â€œdefinitionâ€ in the mind that corresponds to the external signal that provoked it. This allows us the establishment of a correlation between a conscious mental action described by the BEC state and the corresponding cited signal. This correlation is useful for attributing the recorded BEC to the information arising from the external signal, this attribution being established in an unconscious and automatic way. An example that could shed light at this crucial point, which has analogies with the photosynthetic function of the green vegetable world is the construction of optical images produced by the visible spectrum which falls on the specific cells of the retina. The electromagnetic wave excites these cells producing electron-hole transitions and the corresponding excitons are transmitted by means of nervous streams towards the brain. These streams can yield exciton coherent states which are correlated with the above mentioned exterior elctromagnetic field. This correlation gives us the idea of the exterior optical image. Obviously, a quantitative evaluation of these processes should be carried out for obtaining a true analysis from a physical point of view. In order to satisfy this objective, it is necessary to calculate the energy and linear moment of the ground many-body state formed before and after the presence of the exterior stimuli as well as the possible excitations of the total neuronal system. This requires a quantitative study which can only be analyzed from the quantum field theories, and whose technical details will be published in a specialized journal.
Competition between two order parameters
The electrical behaviour inside the neuronal cell cytoskeleton can have an electric conductor behaviour with interacting magnetic moment in the tubulins. Then there is a mixed and competing exchange interaction between localized and delocalized electron spins (Kondo lattice) and Heisenberg interactions corresponding to the localized spin field. This is the most interesting situation from a theoretical point of view, however, we should obtain experimental tests for determining the possibility and probability of each of the three options. In this mixed case there are two order parameters. One of them corresponds to the occupation ratio of magnon coherent state with respect to the number of lattice sites of the magnetic structure which is related with the quantum number of the â€œmagnon laserâ€ state. The another order parameter is the critical density of excitons. The Kondo exchange normally competes with the exchange Heisenberg interaction and therefore, the equilibrium normally becomes unstable. However, the quantum number of the two BEC states that are generated can maintain a different information because of the duality of packs of quantum numbers that are established in the presence of the two mixed subsystems. The theoretical formulation of this third mixed model is very difficult because there are two components of the thermodynamical free energy and two contributions of the entropy. There is not interference between the two BEC states but the increase of one of them implies the decrease of the another one and this interplay is dynamic and this fact makes the equilibrium unstable. In terms of the quantum language, we can say that the ground state of the mixed system is degenerated. The design of this mixed model should be profoundly studied since the foreseeable electric and magnetic situation of the neuronal sets can be close to the suppositions of this mixed exciton-magnon coherent state.
The dialogue between Theology and Experimental Sciences in Cosmology has items where they can clearly confront their points of view. This debate can be centered on the controversy about creationism versus self-transcendent nature of matter. In the field of Neurology and Neurobiology, at first sight, it seems that there is no element for discussion. The difficulty of this dialogue is due to the almost inexistence of religious texts dealing with issues related to the neuronal system, brain, mind, and very little about the human soul. However, from an anthropological point of view, we would try to propose a double possibility for the essence of the human being that presents parallelism and analogy with the case of the dualism in the Cosmology vision. This double starting point would remain reflected in the following terms: has the human race in its material constitution sufficient elements for developing all its functions, such as to think with freedom, to create artistic, literary and scientific opusses, to have sentiments, to have free will and to want to improve their own qualia and himself, etc.? or on the contrary, do the essence of the human being require for developing these functions a complementary ontological spiritual substance which is the inductor for generating the above mentioned human functions? If the first alternative is rejected, the study of anthropology would be incomplete with the simple scientific method. It should be completed with a theological analysis, because the spiritual components of the human constitution would remain outside of the material universe point of view. In other words, the existence of the human being would be inextricably joined to the existence of a soul whose dimension is outside of an autonomous material Universe. The question above given is, in my opinion, the cornerstone of the dialogue which can be completed with a second question that would continue the line of arguments. This second questions is: can the states of brain matter define and explain the mind actions, the self and its nature considered from philosophical and theological perspectives? If the answer to this new question is yes then any thing different from the neuronal scheme is unnecessary. Because the brain system is composed of physical particles, it is logical to try the explanation for the free will, the sentiments and emotions from a physical point of view. In any case, if this treatment seems to be too close to the reductionism, one should make an effort to include parallelism between the two dichotomies: on the one hand, the metaphysical treatment of the human being versus the possibilities of explaining the brain performance from a physical point of view, and on the other hand, the existence of a prime creator of the universe versus the supposed transcendence of the matter/energy.
The idea of the emergentism or emergence of different laws according to the systems increase in complexity is used for explaining the appearance of new structural and ontological essences starting from the primordial physical elements. Although my ideas about the emergentism can be considered heterodox, I do not relinquish expressing that in front of a lack of understanding of the complex system from the dynamic evolution of its components there exists a tendency to formulate new global laws that hide this lack and allows us to continue the analysis of the global system. (It must be remembered that the dynamic evolution of three interacting particles is mathematically and physically unknown) .
The ignorance of the global analysis of a complex system by means of the evolution of the N interacting (with the four nature forces) elemental particles and the extended ignorance to the consequent and evolutionary appearance of the human being from those initial and pristine components, the antrophic principles were formulated. These anthropic principles were argued as a prerequisite of the primordial components of the cosmic â€œsoupâ€ in such a way that the complexity laws should lead to existence of the human race. These logical implications can give support to the acceptance of the anthropic principles as responsible for the formation of the necessary coupling among these constitutive elements of the primitive Universe. As a consequence, a tendency to believe that the primordial laws are susceptible of evolution is consolidating within the philosophical thinking. However, the reason and motor for the slow, continued and permanent changes of these laws is enveloped in the mysterious universal evolution principle. The reality is that the cooling of the primordial universe leads to the successive formation of subsystems based on the congregations of elemental particles. This leads to the erection of successive intermediate conglomerates of primitive particles that step by step and through the mentioned evolution principle, the present human race was the final consequence. The complexity laws activated their mechanisms for achieving the macromolecules that are formed by atoms and this sets the basis for the genesis of the replicating complex structures: the cells. The association of cells constitutes the organs and after a long evolutionary chain, the human race appears. By continued logical inference rules in the complexity laws a question immediately arose: is there either a correspondence relationship or a causality rule between the simplest primitive physical elements and the final anthropic consequence, the conscious human being? It seems that the most probable and easy answer is to say no, because the interplay of intermediate complexity laws hinders a direct relation between the first and last phases of reality evolution. Then, the question above formulated can be continued as follows: when the mind, the brain and, why not, the soul act, these actions produce determined neuronal states which can be described by physical models? Is the inverse proposition also certain?, Do these physical states condition the acts of human self? Maybe, to end this conclusive part of my work asking similar questions to those proposed in its title could be considered a sign of the fiasco in my reflection and may be so. But intellectual uprightness requires the recognition that the advances in the objective of this work, which is the physical interpretation of the consciousness, are modest. However, my achievement is reduced to the formalization of two models for the collective quantum coherence in the neuron systems. Nevertheless, from a philosophical point of view, I have opened ways to reflection and speculation about many questions already proposed in a previous paper (32).
SUMMARY AND CONCLUDING REMARKS
The main goal of my work is to search for the correlation between clearly determined quantum states located in the neuronal system with conscious brain functions, which allows us to identify the true essence of the human consciousness with these collective states. The state of art of this Quantum Neurology and within it my research in progress in this issue is too primitive and its development is yet initial, but the scanty knowledge of the physical perspective of consciousness is, or should be, stimulating for the physicists and above all it should not be a reason for desisting from further study.
The Penrose-Hameroff model for the physical concept of consciousness is brilliant and fascinating but, in my opinion, intuitive and conjectural and, to my knowledge, is not justified by either any experimental proof or data obtained from any measurement. The gravitational incidence in this point may be a smart argument which can have theoretical internal charm and coherence but has the additional difficulty that it theoretically adjoins the intervention of two theories, General Relativity and Quantum Mechanics which, at least at the present time, seem to be incompatible.
My proposition is that using only Quantum Mechanics one can find sufficient correlation between brain actions and the physical quantum states to establish cognitive structures which allows us to advance in the knowledge of the consciousness from a physical point of view. However I recognize that even in this intermediate objective of the search of these correlations my study is initial. However, I think that experimenting with the coherent state theory deserves continuation in order to improve our physical vision of the consciousness of human beings.
Our proposals have the common idea of the quantum coherence of the many-body (collective) states (this point can be congruent with the PH model). These states have a well determined set of quantum numbers that can be recorded, and reproduced afterwards by soft memories located in the skeletons of the neuron cells. The second idea is to analyze the mechanism for the appearance of these quantum coherent states, which can be generated via the interactions with external signals coming from sensorial windows. The causal formation of these states with the external interactions and their description is another objective of this work. Finally, the possible survival of the coherence of these states beyond room temperature of the human brain in normal conditions is an argument which gives support to these models as solutions for understanding the neuronal functions. In addition, these models clarify certain obscure points about quantum coherence which produced a lively debate between Tegmarkâ€™s group and Hameroffâ€™s group.
The tubulins are the elemental components of the microtubules that, in turn, are the main structures of the skeleton of the neuronal cells. These tubulins are lattices similar to some organic crystals. In these lattices, the existence of magnetic order provoked by the spin orientation of the electronic components can be possible. The oscillations of these magnetic lattices constitute magnon coherent states whose properties are similar to the coherent light radiation. The coherence of these states remains even with high temperatures, therefore, they can survive in the brain, their record can be correlated with a mind action and consequently, they can be reproduced when the external interaction that initially provoked its appearance is repeated. Other coherent states are tested as possible solutions for explaining the conscious actions. One of them is the excitonic model. The charge density inside the tubulins is such that a geometrical distribution of positive and negative unity charges appear in the microtubules. This implies the existence of an alpha-beta state lattice in the microtubules within each neuron cell. Each alpha-beta state pair presents a strong attractive binding energy which allows us to treat these pairs (excitons) with similar dynamics to hydrogen atoms. These positive-negative charges have a clear image within the condensed matter theory and this is the excitonic structure. In a latter section of this work, I comment the possible consistence of each of these models as well as the concurrence and concomitance among all of them for acting altogether. In any case, I consider that my achievements and advances in the physical description of the human consciousness via the formation of coherent states are modest, at least for the moment. However, I think that quantitative analysis of those above cited correspondences between microtubule states and mind actions can allow us to advance in the physical knowledge of the consciousness.
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