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PLASMA BRAIN DYNAMICS (PBD): II. QUANTUM EFFECTS ON CONSCIOUSNESS.

1. INTRODUCTION

In the mid-1960s, Ricciardi & Umezawa first suggested the Quantum Brain Dynamics (QBD). (2) The model has been developed over the last half century, and significant progress has been made in recent years to account for the neuro-and-cognitive mechanism of human consciousness, (3) a process dominated by the prefrontal cortex in the brain neuronal system to express the brain cognitive ability. (4) Among the achievements stand Penrose's neural "firing and not firing" model (5) and Penrose-Sameroff's neural "microtubule" one. (6) Nevertheless, studies on the neural de-coherence rates indicated that the consciousness should be thought of as a "classical rather than quantum" neural process, both for regular neuron firing and for kink-like polarization excitations in brain microtubules. (7) Consequently, the QBD paradigm have met serious challenges to provide not only convincing physical mechanisms but also qualitative or quantitative data-fit visualizations of holistic neuronal behaviours, particularly after the neuronal activities were found to adhere to long-range extracellular flows, (8) and the collective behaviour of the neuronal network to comply with stochastic movements. (9)

New advances in brain studies exhibit that the axonal actions of the neuronal system are similar to the scaled equivalents of plasma lightning, (10) while the cerebral cortex and its white matter system of the cortico-cortical fibres turn out to be a system somewhat analogous to the earth's ionospheric shell. (11) The research trend inspired us to develop an alternative model, namely, Plasma Brain Dynamics (PBD) which was proposed in the early 1970s (12) to deal with the collective features of the brain consciousness. Our work set up a set of two-fluid, collision-free Vlasov-Maxwell equations to obtain self-similar differential equations which were used to simulate the excitation and propagation of nonlinear brain EEG waves. (13) Results show that the waves can be classified into two groups: Group-I, complex stormlike waves ([alpha], [beta], and [gamma]); Group-2, simple quasilinear waves ([theta] and [delta]). Group-1 packets are composed of three ingredients: high-frequency ion-acoustic (IA) mode, intermediate-frequency lower-hybrid (LH) mode, and, low-frequency ion-cyclotron (IC) mode; by contrast, Group-2 waveforms fall within the IA band, featured by one or a combination of the three envelopes: sinusoidal, sawtooth, and spiky/bipolar.

Though the PBD paradigm offered a more effective tool than the QBD one to expose the excitation and propagation of measurable brain waves, we notice that the human consciousness resides mainly in the outer layer of the cerebrum, cerebral cortex, with a thickness of (2~5)x[10.sup.-]3 m and a surface area of 0.16~0.4 [m.sup.2], (14) giving a volume of (3.2~20)x[10.sup.-4] [m.sub.3]. Because the adult male human brain of an average of 1.5 kg has 86 billion neurons (nerve cells) and 85 billion non-neuronal cells,i5 the average volume density of neurons turns out to be in the order of 10 (14) neurons/[m.sup.3]. (16) These neurons are interconnected with each other with each neuron to link with up to [10.sup.4] other neurons, forming a highly intricate system to pass signals via as many as 1000 trillion synaptic connections. (17) What is more, in both the intracellular and extracellular spaces, the concentration of negative ions (124.0 mM) is far less than that of positive ones (317.5 mM), giving the charge number densities of [n.sub.+] [approximately equal to] 1.9 x [10.sup.26] [m.sub.-3], and [n.sub.-] [approximately equal to] 39% [n.sub.+], (18) with [n.sub.+] ~ 1/1000 of the molecular number density of water or the free electron density in copper, while the excess positive charges are balanced by the abundant electrons coming from the macromolecules such as nucleic acids and proteins in the brain to keep the brain electrically neutral. (19)

Such a high charge density in the order of [10.sup.26] [m.sup.-3] makes the brain plasma distinguishable from the classical low-density fusion or space plasmas which are characterized by the regimes in which the quantum effect can be totally negligible. It may be more appropriately defined as a new kind of so-called "quantum plasma" in which there coexists both the plasma and quantum effects, a state dwelled by some physical or astrophysical processes happening in, for example, the metallic nanostructure-arenas, semiconductors, or white dwarf stars. (20) Such a non-classical system should not still be treated by employing the Vlasov-Maxwell equations. In this case, the Wigner-Poisson or Wigner-Maxwell equations come to the stage by incorporating the quantum term into account in the Vlasov equations under electrostatic or electromagnetic conditions, respectively. This term may exert an ineligible impact on the plasma system if any or both of the following conditions of the two dimension-free parameters, [[chi].sub.1] and [[chi].sub.2], are satisfied: (21)

[[chi].sub.1] = 4/3 [pi]([n.sub.0][[lambda].sup.3.sub.B] [greater than or equal to] 1; [[chi].sub.2] = [T.sub.F]/[T.sub.0] = [(3/8[pi] [[eta].sub.0][[lambda].sup.3.sub.B]).sup.2/3] = 0.09[[chi].sup.2/3.sub.1] [greater than or equal to] 1 (1)

in which [[chi].sub.1] and [[chi].sub.2] are the two dimension-free parameters; [n.sub.0] = [n.sub.+] [approximately equal to] [n.sub.-] is the mean-field plasma density; [[lambda].sub.B] = h/([m.sub.e][v.sub.Te]) is the electron thermal de Broglie wavelength in which h = 6.63 X [10.sup.-34] J*s is the Planck's constant, [m.sub.e] = 9.11 x [10.sup.-31] kg, [v.sub.Te] is the most-probable speed of the thermal-equilibrium electrons which follow the Maxwell-Boltzmann distribution, satisfying 1/2 [m.sub.e][v.sup.2.sub.TE] = [k.sub.B][T.sub.e] where [k.sub.B] = 1.38 x [10.sup.-23] J/K is the Boltzmann constant and [T.sup.e] is the electron temperature; [T.sub.F] is the Fermi temperature; and [T.sub.0] is the plasma thermal temperature with [T.sub.0] [approximately equal to] [T.sub.e] for a locally thermodynamical quasi-equilibrium plasma system. For typical parameters of n ~ [10.sub.26] [m.sup.-3] and [T.sub.0] ~ 300 K, we obtain [[lambda].sub.B] = 7.28 nm, [v.sub.Te] = 100 km/s, [n.sub.0][[lambda].sup.3.sub.B] = 38.55, and [[chi].sub.1] = 161.46 > 1, [[chi].sub.2] = 2.77 >1. As a result, the brain plasma is non-classical and may be influenced by the quantum effect, if there are no additional factors to mitigate or cancel the effect.

Albeit the fact mentioned above, our data-fitting EEG simulations were carried out within the reliable classical regime where the quantum interference was not encountered by the plasma brain dynamics. We therefore postulated that the quantum effect appeared not playing a significant role in brain consciousness. This means that there might exist some kind of mechanism which acts against the quantum uncertainty and damps out or neutralizes the quantum effect. This paper focuses on investigating the role played by the quantum term in the brain consciousness by generalizing PBD's Vlasov-Maxwell equations with the extra quantum term, thus forming the Wigner-Maxwell equations. Its purpose is to give a clear answer to the dilemma of whether the quantum effect has an impact on the mental activities of the human brain.

The layout of the paper is as follows: Section 2 introduces the quantum plasma model. A set of electrostatic Wigner-Poisson equations are given in the absence of an external magnetic field, [B.sub.0], where an additional quantum term comes into being relative to the classical Vlasov-Maxwell equations under electrostatic conditions. Section 3 solves the Wigner-Poisson equations by applying the linearization approach. The perturbation of the quantum term is obtained to show the quantum effect on the unperturbed meanfield property, and the results are extrapolated to a generalized case in the presence of [B.sub.0]. Section 4 gives the conclusions of the study. SI units are used throughout the paper.

2. QUANTUM PLASMA: WIGNER-POISSON EQUATIONS

In classical plasmas at the sites of, such as, fusion, ionosphere or stars, constituent particles obey classical laws of physics, and it is unnecessary to consider their quantum nature. However, as the density increases or the temperature decreases to such a degree that the interparticle distance becomes comparable to the thermal de Broglie wavelength, the quantum effect starts to affect the properties and dynamics of the classical plasmas which are now known as quantum plasmas. With following assumptions, (22)

(1) an ideal plasma;

(2) particle interaction via the classical electrodynamics only;

(3) collision-free;

(4) non-relativistic; and,

(5) spin-free,

the quantum plasmas can be described by either Wigner-Poisson or Wigner-Maxwell equations under the self-consistent collective electrostatic or electromagnetic conditions, respectively. To reduce the complexity of solving the problem while still being able to develop a tenable approach, we consider the simpler electrostatic case in the present study, and take it for granted that the plasma consists of only electrons of mass [m.sub.e], charge -e, and density [n.sub.e] = [n.sub.-], and one-species positively charged ions of mass [m.sub.i], charge +e, and density [n.sub.i] = [n.sub.+] = [n.sub.0], while ions are immobile but constitute the neutralizing background for the active electrons. In addition, as done in the previous work, (12) we suggest that all the test particles of the brain quantum plasma under modeling are well inside the extracellular space thereby being able to neglect all the edge effects.

Under the above simplifications, the set of kinetic Wigner-Poisson equations for electrons is as follows in the absence of an external magnetic field, [B.sub.0]: (23)

[mathematical expression not reproducible] (2)

where the upper and the lower equations are the Wigner and Poission ones, respectively, while f is the distribution function, t is time, V is electron velocity, [phi] is the self-consistent electrostatic potential, h = h/(2[pi]) is the Dirac constant, and [[epsilon].sub.0] = 8.85 x [10.sup.-12] F/m is the permittivity of free space. Relative to the classical Vlasov-Maxwell equations under electrostatic conditions, this set of equations includes an additional quantum term. Note that the acceleration term, dv/dt, is equivalent to e[nabla][phi]/[m.sub.e] in the absence of an external magnetic field. Adopting a slab model with the only spatial variable, X, reduces Eq.(2) to the following, where v is the electron speed along x:

[mathematical expression not reproducible] (3)

In the above, substituting the 3rd-order partial derivative of [phi] in the RHS term of the upper equation with the RHS term of the lower equation yields

[mathematical expression not reproducible] (4)

in which [[omega].sub.pe] = [square root of ([n.sub.e][e.sup.2]/([[epsilon].sub.0][m.sub.e]))] is the electron plasma angular frequency the mean-field value of which is spatially uniform to give a mean-field thermal-equilibrium Maxwell-Boltzmann distribution, [f.sub.0]; it is 5.66 x [10.sup.14] rad/s for a typical value of [n.sub.e]~[10.sup.26] [m.sup.-3]. The electron plasma frequency, [f.sub.pe], and electron quantum energy, [E.sub.qe], can be given as [f.sub.pe] = [[omega].sub.pe]/(2[pi]) = 9 x [10.sup.13] Hz, and [E.sub.qe] = h[[omega].sub.pe] = 6 x [10.sup.-20] J, respectively. Here, [E.sub.qe] is a newly introduced parameter to evaluate the order of the electron quantum energy relative to the electron thermal energy, [E.sub.te] = [k.sub.B][T.sub.e], which turns out be [E.sub.te] = 0.41 x [10.sup.-20] J for a typical value of [T.sub.0]~300 K. Clearly, the ratio, [eta], of the two energies is [eta] = [E.sub.qe]/[E.sub.te]~15. Besides, the electron thermal potential, [[phi].sub.e] = [E.sub.te]/e, is 26 mV, and the electron Debye length, [[lambda].sub.e] = [square root of ([[epsilon].sub.0][E.sub.t]e/([n.sub.e][e.sup.2]))], is 1.2 [Angstrom] (the same order of the radii of isolated neutral atoms; note that the classical electron radius is ~[10.sup.-5][Angstrom]). Note that there exists a relation that [mathematical expression not reproducible]

This equation is a semi-classical quantum Vlasov equation. However, unlike the classical case that Df/Dt [not equal to] 0 owing to the RHS quantum h-term in Eq.(4), the distribution function f is not preserved, except for linear electric fields that leads to a vanishing h-term due to [[partial derivative].sup.3][phi]/[partial derivative][x.sup.3] = 0, along with the classical characteristic equations of the electrons:

dx/dv = v and dv/dt = [e/[m.sub.e]] [partial derivative][phi]/[partial derivative]x [right arrow] [1/2][m.sub.e][v.sup.2] - e[phi] (5)

Using 1/[f.sub.pe], [[lambda].sub.e], [v.sub.Te], [n.sub.o] and [[phi].sub.e] as the units of t, x, v, [n.sub.e] and [phi] respectively, in Eq. (4) produces a dimension-free Wigner-Poisson equation as follows, in which [alpha] = [square root of 2][pi] [[eta].sup.2]/48 is a quantum coefficient:

[mathematical expression not reproducible] (6)

Similarly, Eq.(5) becomes

[v.sup.2.sub.0] = [v.sup.2] - [phi] (7)

In Eq.(6), the contribution of the quantum effect depends not merely on [alpha], but is determined by the product of [alpha], the partial derivative of [[omega].sup.2.sub.pe] over x, and the the 3rd-order partial derivative of f over v. That is, only [epsilon] itself is unable to govern the contribution of the quantum effect on any brain system. More importantly, the presence of the quantum effect makes it impossible to take the too spiky Wigner functions as the solution of the distribution function, f, which would be against the uncertainty principle, [integral][f.sup.2]dxdv [less than or equal to][m.sub.e][N.sup.2.sub.e]/h (where [N.sub.e] is the total electron number); instead, the solution should take the form of f = [f.sub.0] + [f.sub.1], where [f.sub.0] is the exact solution of Eq.(6) in the absence of the RHS quantum term; and, [f.sub.1] is the leading quantum correction. (24) Adopting the previously developed backward-mapping approach (25) to the motion of electrons which follow an initial Maxwellian function, together using Eq.(7), yields the mean-field [f.sub.0] as follows:

[mathematical expression not reproducible] (8)

3. MAGNITUDE OF QUANTUM PERTURBATION

3.1 In the absence of external magnetic field, [B.sub.0]

In the electrostatic brain, the electric potential [phi] comes into being as a perturbation [[phi].sub.1] of the mean-field state at which the electron characteristics of motion is determined by the integrated acceleration dv/dt. In the absence of an external magnetic field, [B.sub.0], replacing f with [f.sub.0] + [f.sub.1] and [phi] = [[phi].sub.1] in the Wigner-Poisson equation, Eq.(6), offers the linearized semi-classical quantum Vlasov equation in which Eq.(5) is kept unchanged:

[mathematical expression not reproducible] (9)

In this equation, there are two RHS terms, one is quantum term, a product of the two 3rd-order derivatives of both [phi] and [f.sub.0]; the other one is the classical term, a product of the two ist-order derivatives of [phi] and [f.sub.0]. Using the above estimated [eta] value, the ratio of the two coefficients of the two terms is [alpha]/([square root of 2[pi]) = [[eta].sup.2]/48 = 4.69. Clearly, it is the competition between the quantum and the classical terms which determines the contribution of the quantum effect.

Using the Fourier transform in time and space and expressing any perturbations to vary with ~[e.sup.i(kx-[omega]t) where k and [omega] are the electrostatic wave number and angular frequency in units of [[lambda].sup.-1.sub.3] and [f.sub.pe], respectively, we have the dimension-free potential perturbation as follows:

[mathematical expression not reproducible] (10)

Here, [[phi].sub.10] is the dimension-free amplitude of the potential normalized by the electron thermal potential, [[phi].sub.e].

Integrating Eq.(9) gives

[mathematical expression not reproducible] (11)

By applying Eqs.(7,8,10) and considering the electron kinetic energy of the unperturbed orbits is a constant of motion for = [[phi].sub.0], Eq.(11) is

[f.sub.1] [f.sub.0] = 2[[phi].sub.10] [[square root of 2[pi]] - 2[alpha][k.sup.2] (3 - 2[v.sup.2])] * I (12)

where the derivation of I is obtained by reducing a generalized 3D case (26) to the present ID case with

I = [[integral].sup.t.sub.-[infinity]] ikv'[e.sup.i(kx'-[omega]t?)]dt' = [e.sup.i(kx-[omega]t)] [kv/kv - [omega]] (13)

Therefore, Eq. (12) becomes

[f.sub.1]/[f.sub.0] = 2[[square root of 2[pi]] - 2[alpha][k.sup.2](3 - 2[v.sup.2])]/1 - [omega]/(kv) [[phi].sub.1](x,t) (14)

In the above, the [omega]-k relation is determined by the dispersion relation obtained from solving the electrostatic wave equations of electrons: (27)

[[omega].sup.2] = [[omega].sup.2.sub.pe] + [[gamma]e/2] [k.sup.2])[v.sup.2.sub.Te] [right arrow] [[omega].sup.2] = 4[[pi].sup.2](1 + [[gamma].sub.e] [k.sup.2]) (dimension-free) (15)

where [[gamma].sub.e] is the ratio of specific heats; here, [[gamma].sub.e] = 3 because the density compressions are one-dimensional in x only. Eq.(i5) is the dispersion relation of the Langmuir waves. It determines the dependence of the wave frequency on the wavenumber. Obviously, the electron thermal motion leads to a dispersion of the electron plasma oscillations by introducing the dependence of the wave frequency on wavenumber. In general, (equivalently, the wavelength) is not stable and able to vary in the range from zero to 1/[square root of [[gamma].sub.e]] = 0.58, resulting in a change in the frequency of the electron plasma waves, roughly speaking, between [omega] and [square root of 2][omega].

Using Eq.(15) in Eq.(14) gives

[f.sub.1]/[f.sub.0] = [2kv[[square root of 2][pi] - 2a[k.sup.2](3 - 2[v.sub.2])]/kv - 2[pi][square root of (1 + [[gamma].sub.e][k.sup.2])]] [[phi].sub.1](x,t) (16)

In this equation, the quantum effect is expressed by the -term, and parameter v is the speed of the electrons which obey the Maxwell-Boltzmann distribution as given in Eq.(8). Although every electron is most likely to have the most-probable speed, [v.sub.Te], which is used for the unit of the speed in this paper, it is always in a random motion and can move at various speeds. Thus, the average speed of all the electrons equals zero since the distribution function, [f.sub.0], is symmetric to v = 0. However, all the electrons have kinetic energies, as expressed by the dimension-free [v.sup.2], which are determined by the internal thermal energy dependent of their temperature, [T.sub.e], irrelevant of the directions the speeds are in. The collective average kinetic energy of [v.sup.2], and the root-mean-square speed of v provided by this energy, are 3/2 and [square root of (3/2)], respectively, for the given electron Maxwell-Boltzmann distribution of Eq. (8) at the normal brain states. Using v = [square root of (3/2)] in Eq. (16) makes the quantum [alpha]-term become zero, that is, the quantum effect does not exist in brain activities in general cases where the brain thermal equilibrium is only disturbed by electrostatic perturbations under normal conscious conditions.

However, the brain temperature is not always stable but fluctuates within, say, a few degrees as measured in laboratory experiments, especially in situations like a sudden head trauma, stroke, headache, mood disorder, etc. (28) For a serious deviation of [+ or -] 5[degrees]C relative [T.sub.o] ~ 300 K, the variation above and below [v.sup.2] = 3/2, [DELTA][v.sup.2], is [+ or -] 1.67%. In this case, the ratio, R, of the quantum a-term to the classical perturbation for k = 1/[square root of [[gamma].sub.e]] is

R [less than or equal to] 2[alpha][k.sup.2](3 - 2[DELTA][v.sup.2])/[square root of 2[pi]] = [+ or -] 10.63% (17)

Thus, in the absence of an external magnetic field, [B.sub.0], the quantum effect contributes no more than 11% of the classical electrostatic perturbation even in the unusual circumstances.

3.2 In the presence of external magnetic field, [B.sub.0]

It is worth to see the influence of [B.sub.0] on the above results. Although [B.sub.0] may contributes to an extra acceleration in dv/dt in Eq.(9) due to a possible Lorentz force, -(e/[m.sub.e])v X [B.sub.0], it does not cause any gains or losses in electron energy but only changes the velocity direction. Neglecting non-electromagnetic components, Eq. (7) is still valid. However, both Eq.(9) and Eq.(5) are generalized in a 3D (x,y,z)-frame, respectively, where [B.sub.0] is assumed along z:

[mathematical expression not reproducible] (18)

and

dx/dt = v and dv/dt = - [e/[m.sub.e]] v x [B.sub.0] (19)

in which [[phi].sub.0] = 0 is also considered. Define subscripts "[perpendicular to]" and "[parallel]" to denote the components perpendicular and parallel to [B.sub.0], respectively. After adopting the backward-mapping technique again to express v = (v[perpendicular to], [v.sub.[parallel]]} (in which v[perpendicular to] = {[v.sub.x], [v.sub.y]}) and x = (x, y, z} at the initial state, t', by those at the final state, t, and, let [[OMEGA].sub.t] = e[B.sub.0]/[m.sub.e], we have

[mathematical expression not reproducible] (20)

and,

[mathematical expression not reproducible] (21)

Writing a 3D wavenumber k = {[k.sub.[perpendicular to]]/[k.sub.[parallel]]}. The generalized 3D expression of the perturbed potential is

([[phi].sub.1](x,t) = ([[phi].sub.10][e.sup.i(k*x-[omega]t)] [right arrow] [nabla][[phi].sub.1] = ik[[phi].sub.1], and, [[nabla].sup.3][[phi].sub.1] = - i[k.sup.3] [[phi].sub.1] (22)

which reduces to Eq.(10) in the 1D case. In addition, the generalized Eq.(11) is

[mathematical expression not reproducible] (23)

where [f.sub.0] in Eq.(8) is in a generalized 3D form:

[mathematical expression not reproducible] (24)

Finally, the I-integration in Eq.(i3) has a generalized form given as (25)

I = [[integral].sup.t-[infinity]] ik * v(t?)[e.sup.i[k*x(t?)-[omega]t?]] dt' = [e.sup.i(k*x(t?)-[omega]t)] X (25)

in which

[mathematical expression not reproducible] (26)

where [phi] is the angle between [k.sub.[perpendicular to]] and [v.sub.[perpendicular to]]; and [J.sub.n] is the Bessel function. Thus, the generalized form of Eq.(i4) is:

[f.sub.1]/[f.sub.0] = 2X * [[square root of 2][pi] - 2[alpha][k.sup.2](3 - 2[v.sup.2])][[phi].sub.1](x, t) (27)

On the one hand, for [B.sub.0] = 0 and n = 0, Eq.(27) recovers the solution given by Eq.(14) after taking into account the reduced expression of X in Eq.(26). On the other hand, because [[OMEGA]~8,800 krad/s [much less than][omega]~[k.sub.[perpendicular to]] [v.sub.[perpendicular to]]~ [k.sub.[parallel]][v.sub. [parallel]]] of the order of [[omega].sub.pe]~[10.sup.11]krad/s, equivalent to [B.sub.0] [right arrow] 0 and n = 0, X in Eq.(26) approach to [[1 - [omega]/(kv)].sup.-1]. Thus,

[f.sub.1]/[f.sub.0] = [2[[square root of 2][pi] - 2[alpha][k.sup.2](3 - 2[v.sup.2])]/1 - [omega]/(kv)] [[phi].sub.1] (x,t) (28)

A comparison between Eq.(28) and Eq.(14) shows that the external magnetic field modulates neither the relative amplitude of the perturbation to the mean-field, nor the quantum effect obtained in the absence of the magnetic field, except that the 1D scalar k and V are substituted by the 3D vector k and V in the quantum a-term.

4. CONCLUSION

The classical PBD theory (11) was proven to provide a useful tool in the data-fit modelling of measured brain EEG signals, regardless of either the highly nonlinear structures featured by a train of storm-like wave packets, or the quasilinear envelops featured by deformed linear waves. (12) However, it is important to make use of the quantum mechanics to explain the neuro-and-cognitive mechanism of human consciousness. (29) This paper takes into account the quantum behaviour of electrons to investigate the quantum role played in brain consciousness.

Unclassical quantum effects arise when particle density is too high or temperature is too low. In human brain, the charge density is in the order of [10.sup.26] [m.sup.-3], so high enough to give two dimension-free parameters, [[chi].sub.1] and [[chi].sub.2] much larger than 1. No doubt, the brain plasma is non-classical and may be influenced by the quantum effect if it is not mitigated or cancelled by some mechanism(s). This paper formulates a quantum plasma model by generalizing PBD's Vlasov-Maxwell equations with the extra quantum term. The obtained electrostatic electron Wigner-Poisson equations are solved in both the absence and presence of an external magnetic field by applying a backward-mapping approach to the motion of Maxwellian electrons. The perturbation of the quantum term is obtained to superimpose on the classical perturbation of the mean-field property. Main results include:

(1) Different from the classical perturbation which is determined by the 1st-order derivatives of both [phi] and [f.sub.0], the quantum perturbation is dependent of the 3rd-order derivatives of the two parameters;

(2) In the absence of an external magnetic field, the quantum perturbation competes with the classical electrostatic perturbation, and is determined by the difference between 3 and the dimensional magnitude of 2[(v/[v.sub.Te]).sup.2];

(3) Under the same condition, the quantum perturbation has no effects at the normal brain states where the collective speed of all the Maxwell-Boltzmann electrons takes the dimensional root-mean-square speed, [square root of (3/2)][v.sub.Te];

(4) Under the same condition, if brain temperature fluctuates, a serious deviation of [+ or -] 5 K relative to ~300 K causes the quantum effect to contribute no more than 11% of the classical perturbation;

(5) In the presence of the external magnetic field, the above results are not influenced, except the 1D scalar parameters substituted by corresponding 3D vectors in the quantum [alpha]-term.

ACKNOWLEDGMENT

This paper is the text version of the remote PPT presentation (Part 3) at the meeting of Foundations of Mind V: The New AI Scare, on November 3-4, 2017, Room 304, CIIS, 1453 Mission St, San Francisco, CA 94103.

zma@mymail. ciis.edu

Philosophy, Cosmology and Consciousness

California Institute of Integral Studies

1453 Mission St., San Francisco, CA 94103

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Author:Ma, John Z.G.
Publication:Cosmos and History: The Journal of Natural and Social Philosophy
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Date:Jan 1, 2018
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