## LATEX

### الايزوسبين و النكهة و نموذج الكوارك

بالنسبة للقوة النووية القوية فان التفاعل بين البروتون و النوترون يساوى التفاعل بين البروتون و البروتون يساوى التفاعل بين النوترون و النوترون.
هذا يعنى ان البروتون و النوترون هما فى الواقع حالتين مختلفتين من جسيم واحد نسميه النوية nucleon..
وهى فرضية اول من وضعها كان هايزنبرغ..
نميز هاتين الحالتين بعدد كمومى نسميه الايزوسبين isospin..
فالبروتون له ايزوسبين يساوى زائد نصف..
والنوترون له ايزوسبين يساوى ناقص نصف..
والتفاعلات النووية القوية متناظرة تماما تحت تأثير تحويلات الايزوسبين التى تشكل زمرة SU(2)...
والنوية فى الحقيقة تشكل التمثيلة الاساسية fundamental representation للزمرة SU(2)...
اذن من الناحية الرياضية البحتة فى الايزوسبين هو مماثل للسبين اى عزم اللف لكن الفرق الفيزيائى شاسع لان السبين يؤثر فى الفضاء الفيزيائى الخارجى الذى نعيش فيه و تعيش فيه النوية لكن الايزوسبين يؤثر فى فضاء الحالات الداخلى للنوية..
ثم جاء يوكاوا Yukawa -احد انجازات اليابان- فى العام 1935 و اقترح ان التفاعلات النووية بين البروتون و النوترون التى يتحول فيها البروتون الى نوترون و يتجول فيها النوترون الى نوترون و قد يتحول فيها حتى البروتون الى بروتون آخر و النوترون الى نوترون آخر كل هذه التفاعلات بين البروتونات و النوترونات تتوسط فيها جسيمات سماها البيونات pions و يرمز لها ب π التى يمكن ان تكون مشحونة ايجابيا أو سلبيا او منعدمة الشحنة..
واكثر من هذا فان يوكاوا تمكن من حساب كتلة هذه الجسيمات بالضبط (باستخدام مبدأ الارتياب لهايزنبرغ و حل معادلة كلاين Klein و غوردن Gordon التى يخضع لها اى جسيم سلمى مثل البيون) وايضا حدد قيمة السبين او عزم اللف على انه 0 اى ان البيونات جسيمات سلمية و حدد قيمة الايزوسبين على انه يساوى واحد بمعنى ان البيونات تشكل التمثيلة الشعاعية vector representation لزمرة الايزوسبينات SU(2)..
البيون تم اكتشافه بكل هذه المواصفات عام 1947 وتحصل يوكاوا على نوبل فى الفيزياء من اجل توقعه للبيون عام 1949 بعد قصف اليابان بالقنبلة الذرية بعامين..
اذن البيونات تتوسط التفاعل النووى القوى بين البروتونات و النوترونات (وهو تصور تقريبى) مثلما ان الفوتونات تتوسط التفاعلات الكهرومغناطيسية بين الالكترونات (وهو تصور مضبوط)..
و الايزوسبين هو محفوظ فى القوى النووية مثلما ان الشحنة الكهربائية هى محفوظة فى القوى الكهرومغناطيسية..
لكن هناك فرق آخر فان الايزوسبين I3 هو ناجم عن تناظر شامل global symmetry تقريبى اما الشحنة الكهربائية Q فهى ناجمة عن تناظر موضعى local symmetry..
لكن ليس فقط الايزوسبين I3 هو المحفوظ فى القوى النووية الكبرى لكن ايضا ما يسمى الغرابة strangeness وهو عدد آخر كمومى s يميز الجسيمات التى يتم انتاجها عبر القوى النووية القوية لكنها لا يمكن ان تتهافت الا تحت تأثير القوة النووية الضعيفة..
و اذا اضفنا الغرابة s الى الايزوسبين I3 فان هناك ثنائيات اخرى تحت تأثير الايزوسبين ليست فقط النوية منها مثلا ميزونات الكاوون K و باريونات الكساي Ξ التى فى الصورة..
العلاقة بين الشحنة الكهربائية Q التى هى محفوظة فى كل التفاعلات فى الطبيعة و الايزوسبين I3 و الغرابة s اللذان هما محفوظان فقط فى النووية القوية هى معطاة بعلاقة نيشيجيما Nishijima و غال-مان Gell-Mann فى الصورة المكتوبة بدلالة ما يسمى الشحنة-الفائقة hypercharge التى يرمز لها ب Y و التى تساوى مجموع الغرابة s و العدد الباريونى baryon number الذى يرمز له ب B (وهو يساوى واحد بالنسبة للباريونات و صفر من اجل اى جسم آخر)..
لكن باضافة الغرابة فان تناظرات الايزوسبين SU(2) التى تميز القوى النووية القوية يتم تمديدها الى تناظرات النكهة flavor symmetries المعطاة بالزمرة SU(3) و التى تحتوى بداخلها على ثلاثة زمرات SU(2) مختلفة وهى المعطاة بالسبينات ٍS (الذى يمثل الايزوسبين) و V و U فى الصورة الثالثة..
ال 3 فى الزمرة SU(3) تعنى فى الحقيقة الكواركات الاخف u (الكوارك الواقف up) و d (الكوارك الجالس down) و s (الكوارك الغريب strange) كما أن ال 2 فى الزمرة SU(2) كانت تعنى الكواركات u و d...
هذه الكواركات u و d و s تشكل التمثيلة الاساسية لزمرة النكهة SU(3)..
التناظر SU(3) يسمح لنا بترتيب الجسيمات الاولية فى تمثيلات احادية غير قابلة للاختزال unitary irreducible representation لهذه الزمرة..
ولان الجسيمات المتفاعلة عبر القوة النووية القوية يمكن ان تأتى اما على شكل ميزونات (وهى الجسيمات المشكلة من كوارك و كوارك مضاد) او باريونات (وهى الجسيمات المشكلة من ثلاثة كواركات) فان التمثيلات الاحادية للزمرة SU(3) التى تتنظم فيها الجسيمات الاولية نحصل عليها من الجداءات التنسورية tensor products التالية:
-الجداء التنسورى فى الصورة الرابعة الذى يؤدى الى الميزونات التى فى الصورتين الخامسة و السادسة.
الجداء التنسورى فى الصورة السابعة الذى يؤدى الى الباريونات التى فى الصورتين الثامنة و التاسعة.
هذا يؤدى بنا الى النماذج التالية للقوة النووية القوية:
-الطريق الثماني eightfold way التى اقترحها غال-مان و نعيمان Neeman الاسرائيلى عام 1961.
-نموذج الكوارك quark model الذى اقترحه غال-مان و زويغ Zweig عام 1964 والذى تحصل من اجله غال-مان على نوبل فى عام 1969.
-النظرية اللونية الكمومية quantum chromodynamics و هى النظرية النهائية للقوة النووية القوية التى تدخل كواحدة من المركبتين الاساسيتين للنموذج القياسى standard model للجسيمات الاولية.
مستمد من كتابى عن نظرية الحقل.

### Basics of phenomenology

The physical world is constituted of elementary particles.
There are four types of forces governing all known interactions between these elementary particles:
1-The gravitational force which is not relevant to the energy scales of particle physics so we will not discuss it any further.
2-The strong nuclear force which is crucial in the construction of the standard model of elementary particles. It is a short-range interaction with an interaction radius equal $10^{-13}$ cm.
It is also a force of great relevance to star formation, astrophysics and cosmology of the early Universe.
For example, the heat produced in the Sun is due to the strong nuclear force when deuterium nuclei and protons are combined into helium nuclei.
Particles which feel the strong nuclear force are called hadrons.
These are bound states of quarks subjected to color confinement which is one of the most fundamental characteristic signatures of the strong nuclear force.
Those hadrons with integer spins are called mesons (bound states of a quark and anti-quark) whereas those hadrons with half-integer spins are called baryons (bound states of three quarks or three anti-quarks).
Particles which decay by means of the strong force are called resonances.
The strong nuclear force is described by the theory of quantum chromodynamics or QCD for short which is a local gauge theory based on the gauge group $SU(3)_c$. This is to be contrasted with the electromagnetic force described by the theory of quantum electrodynamics or QED which is also a local gauge theory based on the gauge group $U(1)_{em}$.
A local gauge symmetry means a group of local transformations, i.e. they depend on the space-time locations, which leave the theory (action, local Lagrangian, the quantum vacuum, the spectrum, etc) invariant.
The lower index c in $SU(3)_c$ denotes the strong nuclear charges carried by the quarks which are called colors. There are precisely 3 different charges or colors denoted for example by R (red), G (green) and B (blue) and their conjugates, i.e. anti-charges or anti-colors.
The hadrons are however colorless and we say that they are singlet states under the gauge group. This condition is precisely why hadrons can only come as either baryons (three quarks) or mesons (quark and anti-quark).
We stress the fact that these colors have nothing to do with visual colors but they simply denote extra degrees of freedom which characterize the quarks besides their usual quantum numbers.
In a strict sense these extra degrees of freedom are the charges acted upon by the strong nuclear force in the same way that the electric charge $+$ (and its conjugate $-$) is acted upon by the electromagnetic force.
This is why the electromagnetic gauge group^is $U(1)_{em}$ because there is a single type of electromagnetic charge as opposed to the three types of charge of the the strong nuclear force and the gauge group $SU(3)_c$.
Indeed, the color charges are the sources of the strong nuclear gauge field (also called gluon fields) in the same way that the electric charge is the source of the electromagnetic field (also called photon field).
However, the photon field is chargeless whereas the gluon field is NOT colorless since it carries a color and anti-color charges and as a consequence its absorption and emission by a quark will change the color charge on the quark.
There are therefore $3x3=9$ gluon fields a priori but the color trace combination can not change the color charge on the quark and therefore we are left with only $3x3-1=8$ gluon fields.
This is one of the reason why color gauge symmetry is a strongly interacting force and hence highly non-perturbative whereas electric gauge symmetry is largely weak and perturbative.
The $8$ gluons like the photon are neutral and massless vector particles.
Gauge symmetry (both strong nuclear and electromagnetic) are exact symmetries of Nature (which translates to the masslessness of the gluons and photon) which is also, as it turns out, mathematically equivalent to the conditions of unitarity and renormalizability.
Hadrons are however composite objects and the fundamental degrees of freedom which appear in the QCD Lagrangian are the quarks and the gluons and not hadrons. As a consequence the force between color-neutral (singlet) hadrons is a residual nuclear force which arises from the fundamental color force in the same way that Van der Waals forces between neutral atoms arise from electromagnetism between the constituents electrons.
The photons, as we have said, do not carry electric charge and therefore they create no new electromagnetic field around them (the photon gauge field is not self-interacting).
The electromagnetic field is therefore the strongest around the charge which created it and then it becomes weaker as we go further away from the charge.
In contrast, the gluon gauge field is self-interacting and gluons and quarks exhibit another remarkable phenomena (beside color confinement) called asymptotic freedom.
Gluons carry color charges and therefore they create around them a new color field corresponding to new gluons and these will create new gluons and so on and so forth.
Therefore the color field created by a color charge will be enhanced by the new color fields of the generated virtual gluons and the field therefore tend to increase as we move away from the color charge and not decrease as in the case of the electromagnetic field.
The color charge inside is thus masked by vacuum polarization and becomes effectively larger as seen from larger distances. This is the so-called vacuum polarization effect.
This can also be characterized by the running of the coupling constant $\alpha_s$ of QCD with energy $q^2$ (that is why it is running) which is given by the famous perturbative formula in the image.
In this equation $n_f$ is the number of quark flavors and $\Lambda_{QCD}$ is the QCD scale at which the almost free quarks at high energies (where we can use effectively perturbation theory) become confined in bound states of the known hadrons.
Indeed, for $q^2>>\Lambda_{QCD}^2$ the effective coupling constant $\alpha_s(q)$ becomes small indicating that quarks and gluons are almost free and perturbation theory is a valid prescription.
Whereas when $q^2~\Lambda_{QCD}^2$ we see that the effective coupling constant becomes infinite indicating that bound states of hadrons have formed, quarks and any color state are confined, and perturbation theory is no more a valid approximation.
The QCD scale is not a free parameter of the theory (like the gauge coupling constant $\alpha_s=g_s/4\pi$) but it is determined from experiment to be in the range between 100 and 200 Mev.
The renormalization group evolution of the running gauge coupling constant $\alpha_s$ given by the formula in the image is therefore stating that the strength of the strong nuclear force (the color interaction) as measured by $\alpha_s$ becomes negligible at high-energies $q^2>>\Lambda_{QCD}^2$ and therefore quarks and gluons become approximately free in that regime.
This is the so-called asymptotic freedom.

### Neurons-Synapses Neural Networks and Classical Computation in the Brain

Part III

Penrose-Hameroff theory (final part)

Summary of parts I and II

An integrate-and-fire brain neuron is a cell held together by its cytoskeleton which is formed among other things by microtubules.
The cytoskeleton is effectively a cellular nervous system (Sherrington, 1957).
The neurons are cells which do not undergo mitosis (cell division) and therefore their microtubules are very stable.
The dendritic and somatic microtubules in particular are the most suitable for long term information encoding and memory.
A microtubule is a cylindrical skew hexagonal lattice composed from 13 longitudinal protofilaments of tubulins with helical winding pathways (in the A-lattice) repeating according to the Fibonacci sequence (3,5,8,...).
Each tubulin can be in two conformational states (open or closed).
These are supposed to be quantum states analogous to the spin states (up and down).
The quantum forces are either London forces (instantaneous dipole-induced dipole attractions between electron clouds) or magnetic dipoles due to electron spin enabling spin-flip alternating currents in microtubules.
Thus, a tubulin can exist in an infinite number of superposed states and thus it acts as the quantum bit or qbit of microtubules information processing.
There are 10^9 tubulins per neuron which are switching at 10 MHz which gives a 10^16 operations per second per neuron relevant for qualitative consciousness.
In contrast, the brain consists of 10^11 neurons and each neuron contains 10^3 synapses and each synapses performs 10^2 transmission per second. This gives 10^16 operations per second for the entire brain performing classical computations relevant for functional consciousness.
The information processing of microtubules relevant for quantum computations (qualitative consciousness) far exceeds that of neurons relevant for classical computations which is based on axonal firings and synaptic transmissions (functional consciousness).
Thus, microtubule-level quantum information processing and quantum computation lie perhaps at the origin of neuron-level classical information processing and classical computation in the brain.
And perhaps, consciousness resides in microtubules and not neurons. For example, anesthetic are seen to act in microtubules and not in neurons.
The tubulins in microtubules across many neurons should act coherently through quantum entanglement.
In 2009 Bandyopadhyay's group in Japan showed that microtubules at biological temperatures may indeed enjoy quantum properties.

Orch OR:

In the Diósi–Penrose interpretation an objective reduction of the quantum state (collapse of the wave function) occurs objectively, i.e. dynamically, when a threshold is reached of the order of the lifetime of quantum superposed states which is determined by quantum gravity effects on the spacetime geometry.
This should be understood as a proposed solution for the measurement problem (of why we dont see quantum superposed states and the conflict between processes I and II of von Neumann) which runs effectively opposite to the Copenhagen-von Neumann-Wigner interpretation.
Since in the Penrose interpretation the collapse is effectively an instant of conscious experience whereas in the Wigner interpretation it is the conscious experience that causes collapse.
Thus, in the OR interpretation the collapse of the wave function is an actual independent physical effect arising from quantum gravity (which is the strongest proposal of this proposal in our view) and the bridge between the classical and the quantum is quantum gravity and not environment or many-worlds or consciousness.
According to Penrose, if we assume that the quantum superposition contains for simplicity two stationary states, then the objective reduction of this superposition will occur at a random instant with an average lifetime scale (similar to radioactive decay) τ equal \hbar/E_G where \hbar is Planck's constant and E_G is the gravitational self-energy of the difference between the two stationary mass distributions involved in the superposition.
For rigid mass distributions E_G is the energy required to move one of the distributions in the gravitational field of the other.
The quantum superposition corresponds to a superposition of two spacetime geometries caused respectively by the two stationary mass distributions.
In other words, each mass distribution generates a slightly different spacetime metric.
When the spacetime separation (given in terms of symplectic measure on the space of 4-dimensional metrics) between the two spacetime manifolds reaches a critical amount one of the spacetimes decays instantaneously according to OR and the other one emerges as the actual classical spacetime geometry.
The critical spacetime separation is a product of time separation T and a space separation S which is of order 1 in natural units.
Thus, for small S (such as an electron) τ=T is very large. An electron in a superposed state may reach the OR threshold after thousands of years.
But, for small τ=T the space separation S is very large. Thus a Schrodinger's cat which has large S may reach the OR threshold after only 10^{-43}s (Planck's time).
Indeed, for weak gravitational fields E_G is given by the gravitational self-energy of the difference between the mass distributions of the two superposed states. We get E_G=S and T=τ and hence T=τ=\hbar/E_G=\hbar/S.
In most cases E_G gets most of its contributions from the environment and as a consequence OR becomes indistinguishable from the usual R operation (process I) of Copenhagen caused by environmental decoherence.
Thus, the quantum superposition should be kept isolated from the environment (i.e. it should only be allowed to evolve unitarily under the Schrodinger equation or process II also called process U by Penrose) until the time τ of OR if the reduction is to be due to the system and caused by quantum gravity and not due to the random effect of the environment.
The orchestrated (or tuned) objective reduction proposal or Orch OR is OR with the further assumption that each OR event produces an element of consciousness called proto-consciousness.
Thus, it is required in Orch OR that isolation from the non-orchestrated random environment is achieved so that only orchestrated reductions (not fully random as in Copenhagen but depends on the new quantum gravity physics) are allowed which can support quantum computations, integration, cognition and consciousness.
The R and OR effects are fundamentally non-computable (as opposed to U) and therefore they are associated with the non-computatble aspects of the mental such as understanding and qualia and free will, etc.
Indeed, according to Penrose consciousness is a bilogical quantum computation in the brain in microtubules (in the A-lattice) terminating by objective reductions OR when tiny space-time differences reach the Planck level.
Strictly speaking the unitary quantum evolution corresponds to pre-consciousness , unconsciousness, non-consciousness and functional consciousness while the reduction is what corresponds exactly to consciousness proper.
The OR process is non-computable, non-detreminstic, irreversible and random in some sense (the instant when it occurs) but not completely random as in the Copenhagen since it is guided by Planck-scale geometry.
The location for coherent microtubule Orch OR and consciousness is in post-synaptic dendrites and soma during integration phases in integrate-and-fire brain neurons.
Synaptic inputs orchestrate tubulin superposition in vast numbers of microtubules all involved quantum-coherently together in a large-scale quantum state where entanglement and quantum computation take place during integration.
This quantum computation is terminated by OR at the end of integration where appropriate microtubule states are selected which will then control the axons firing, i.e. conscious behavior.
Quantum entanglement of superposed microtubule is what allows unity and binding of conscious content.
And 1) isolation against environment decoherence (using some bilogical mechanisms such as ordered water and and topological quantum error correction) and 2) orchestration via entanglement and tunneling (through gap junctions) between the microtubules are what yields consciousness at the end of this gravitational OR.
Otherwise without orchestration and isolation we have elementary quanta of consciousness without necessarily any meaningful consciousness.
Thus, proto-consciousness is widespread in the Universe as widespread as elementary particles.
And in the same way that particles are governed by U process these proto-conscious occasions/moments are governed by R.
And in the same way that particles sometimes give rise to bodies but not always these proto-concsious moments can give rise to consciousness.
OR acts instantaneously with respect to the physical time but it creates itself the conscious time.
References:
Sherrington CS. Man on his nature. 2nd edition. Cambridge (MA): Cambridge University Press; 1957.
Penrose R. The emperor’s new mind: concerning computers, minds, and the laws of physics. Oxford: Oxford University Press; 1989.
Penrose R. Shadows of the mind: an approach to the missing science of consciousness. Oxford: Oxford University Press; 1994.
Penrose R. On gravity’s role in quantum state reduction. Gen Relativ Gravit 1996;28:581–600.
Penrose R. Wavefunction collapse as a real gravitational effect. In: Fokas A, Kibble TWB, Grigouriou A, Zegarlinski B, editors. Mathematical physics. London: Imperial College Press; 2000. p. 266–82.
Diósi L. A universal master equation for the gravitational violation of quantum mechanics. Phys Lett A 1987;120(8):377–81.
Diósi L. Models for universal reduction of macroscopic quantum fluctuations. Phys Rev A 1989;40:1165–74.
Sahu S, Ghosh S, Ghosh B, Aswani K, Hirata K, Fujita D, et al. Atomic water channel controlling remarkable properties of a single brain microtubule: correlating single protein to its supramolecular assembly. Biosens Bioelectron 2013;47:141–8.

## Part II

The claim of most modern science and philosophy is that consciousness emerges from the classical computation of neural networks in the brain which are composed of neurons (the basic units of information in the brain similar to transistors in computers ) and synapses (which play the role of wires connecting transistors/neurons).
These neurons are effectively integrate-and-fire logic devices in which the synaptic inputs reaching the various dendrites are integrated into a membrane potential which is then compared to the threshold potential at axon initiation segment or AIS.
If the AIS threshold is reached then an all-or-none action potential is triggered as output and we say that the neuron has fired.
This all-or-nothing situation is precisely what happens also in computers where either there is a signal down a wire (true/1) or there is not (false/0).
So the neurons either they fire or they dont and as a consequence all computations that they can perform is classical computations which -on the account of some- can not capture the aspects of qualia or free feell (compatibility to be accurate) of consciousness.
Some claim (Chalmers and Nagel for example) that qualitative subjective consciousness cannot in principle be captured by any function either based on classical structure or quantum structure.
But others (Stapp and Penrose for example) claim that quantum mechanics will be able to capture those aspects of consciousness that resists classical functional description.
However, they contend, that in order to be able to do that we need to go from the larger scales of classical neurons to the nano scales of microtubules which could potentially support quantum effects.
Microtubules play in cytoskeletons the same role that neurons play in the brain.
In fact the cytoskeleton can be thought of as the brain of the neuron. This is the idea originally championed by Hemeroff since the early 1980's.
The cytoskeleton of a neuron (or of any eukaryotic cell for that matter) is a framework which holds the cell in shape and acts as its control system.
It consists of a protein network of microtubules (MT's), microtubule-associated proteins (MAPs), actin, and intermediate filaments.
The micrtotubules in particular are very crucial to us because they are cylindrical lattices composed of the so-called tubulins which act as our quantum bits in the same way that neurons in neural networks act as classical bits.
Description of Microtubules and Tubulins:
Microtubules are hollow cylindrical tubes with an outside diameter equal 25 nm and an inside diamater equal 14 nm with variable lengths from few hundred nm up to meters in long nerve axons.
See first illustration.
The microtubules are in fact protein polymer constructed out of peanut-shaped tubulin proteins.
Each tubulin is a dimer consisting of two separate monomers called α-tubulin and β-tubulin.
And each monomer is composed from a 450 amino acids.
The dimer is about 8nm x 4nm x 4nm in size with an atomic number about 11x10^4.
The microtubule is organized from a 13 columns or protofilaments of tubulin dimers.
The lateral connections of these 13 protofilaments give rise to two types of hexagonal lattices (the A-lattice and the B-lattice).
These are hexagonal lattices because each tubulin has six nearest neighbors since the protofilaments shift in relation to their neighbors by 3 monomers.
The number 13 is one of the Fibonacci numbers:
0,1,1,2,3,5,8,13,21,..
where each number is the sum of the previous two.
The skew hexagonal A-lattice defines a pattern of microtubules made up of 5 right-handed and 8 left-handed helical arrangements.
We remark that both 5 and 8 are Fibonacci numbers and 13=8+5.
Thus, tubulins are arranged vertically in protofilaments but they also follow helical winding patterns with regular repeat intervals according to the Fibonacci series.
See illustrations 2 and 3.
Each of the tubulins is an electric dipole and therefore the microtubules are lattices of oriented dipoles.
The tubulin units are thought of to represent quantum informational bit states.
Indeed, each tubulin dimer can exist in two geometrical configurations (states) called conformations which correspond to two different states of the dimer's electric polarization.
In one of these conformations the tubulins bend to 30 degree to the direction of the microtubule.
See iIlustration 1.
These two different conformational states arise from the displacement of an electron centrally placed in the α-tubulin/β-tubulin juncture.
Aletrnatively, the α-tubulin can be thought of as - while the β-tubulin can be thought of as +.
In the A-lattice the lateral associations of protofilaments occur between adjacent α and β-tubulin subunits in such a way that an α-tubulin subunit from one protofilament interacts with a β-tubulin subunit from an adjacent protofilament.
Thus, in a protofilament one end will have α-tubulin exposed and therefore it is - while the other end will have β-tubulin exposed and therefore it is +.
And since all protofilaments are parallel the resulting microtubule is also polar with one end positive and the other end negative.
The basic unit of information is therefore the tubulin (analogous to spin).
In fact the tubulin function as a quantum bit or qbit.
A model of protein conformational switching is given in the 4th illustration.
We imagine a pair of electrons in the juncture coupled by London forces (which are quantum forces).
The coupled electrons in the tubulin dimer can exist in the open conformational state or in the closed conformational state or in any linear superposition thereof because of quantum coherence.
Quantum computation in the tubulin dimer is therefore possible by allowing the tubulin to exist in the coherent linear superposition, evolving it unitarily in time according to the Schrodinger equation, and then performing a measurement which will collapse the state to one of the two classical conformational configurations (open or closed).
References:
1-Stuart Hameroff, Ultimate Computing: Biomolecular Consciousness and NanoTechnology, 1987.
2-S.Hameroff, R.Penrose, Consciousness in the universe
A review of the ‘Orch OR’ theory, Physics of Life Reviews 11 (2014) 39–78.
3-S.Hameroff , A. Nip, M. Porter, J. Tuszynski, Conduction pathways in microtubules, biological quantum computation, and consciousness, BioSystems 64 (2002) 149–168.
4-R.Penrose, Shadows of the Mind, Oxford University Press, 1994.

Part I

Neurons and synapses in the brain perform classical computations similar to those performed in computers with transistors (neurons) and wires (synapses).
This is the standard picture due originally to McCullogh and Pitts back in 1943.
Therefore the neurons are the fundamental information units and consciousness emerges from complex classical computations in neural networks consisting of neurons and synapses. This is precisely the statement of physicalism and functionalism the dominant forces in science today.
On the other hand, others maintains that neuronal networks can only correspond to functional consciousness, i.e. consciousness without any associated qualia.
This is effectively the hypothesis of the hard problem of consciousness. In other words, the hypothesis that phenomenal consciousness (which is conscious states associated with qualia) lies outside the realm of function and possibly structure (Chalmers).
A neuron can be thought of as a tree with three main parts:
1-A soma or cell body (trunk of the tree): This is the nucleus where the cell resides.
2-A dendrites (branches of the tree): This is where input from axons of other neurons is received via synapses.
The surface of the dendrites are characterized by small protrusions (called spines) which are effectively the post-synaptic contact sites with synapses.
3-An axon (roots of the tree): This is a long thin structure where an electric signal called an action potential is generated signalling that the neuron is active.
The action potential propagates along the axon and causes the release of neurotransmitters into the synapse (more precisely into the synaptic clef) which then allows communication with other neurons.
Of course, the axon normally bifurcate into separate strands each terminating at a different synapse. Hence the action potential signalling that the neuron is active (or that the neuron has fired) is transmitted to all other neurons.
In biological neuronal networks synapses play a crucial role as important as that of neurons.
Some synapses are excitatory (excites the neuron's firing and contributes positively to the synaptic action) whereas others are inhibitory (inhibits the neuron's firing and contributes negatively to the synaptic action) and they add up to obtain an integrated action potential and then compared to a certain threshold at the axon initiation segment (AIS).
If the AIS threshold is reached then an all-or-none action potential firing is triggered as output and the next neuron will fire.
This picture is effectively that of the original Hodgkin and Huxley model (1953) for which the authors won the Nobel prize in medicine in 1963.
This neuron-synapse picture of the brain can be emulated relatively easily in connectionist models of artificial neural networks.
These emulation take also into account the so-called brain plasticity, i.e. the fact that synapses in the brain are continually changing, by giving appropriate computational rules governing synaptic changes such as Hebb's procedure.
However, all this computation, no matter how complex, remains in a very obvious sense classical and therefore very deterministic (no room for free will) and very objective (no room for phenomenal consciousness) according to Chalmers, Penrose and Hameroff and others.
References:
McCulloch W, Pitts W. A logical calculus of the ideas immanent in nervous activity. Bull Math Biophys 2013;5(9943):115–33.
Hodgkin A, Huxley A. A quantitative description of membrane current and its application to conduction and excitation in nerve. J Physiol 1952;117:500–44.
Hebb DO. Organization of behavior: a neuropsychological theory. New York (NY): John Wiley and Sons; 1949.
The Hodgkin-Huxley Model: Its Extensions, Analysis and Numerics, Ryan Siciliano, 2012.