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(image from Scientific American, September 1992, article by Gerald D. Fischbach, Mind and Brain, page 52)
Neurons are on the scale of a micron (or 1,000 nanometers) in size. The micron size scale of a Neuron is in the scale range at which the Casimir effect is measurable and is also about the range of GravitoEM Induction Region Virtual Gravity Waves.
Submillimeter gravity is being studied by experiments under way in 1998 at Stanford and the University of Colorado in Boulder.
Neurons are connected to each other by three types of Communicating Junctions.
Electrons can cross the Gap Junctions by Quantum Tunnelling, thus allowing Quantum Superposition States to extend from Neuron to Neuron across Gap Junctions.
Three types of Communicating Junctions are:
According to Stuart Hameroff, "... A given cortical neuron may have 10,000 chemical synapses, and relatively few gap junctions (15% of the number of chemical synapses [or 1,500 Gap Junctions for a Neuron with 10,000 Chemical Synapses] is sometimes estimated). ... There are special organelles (dendritic lamellar bodies - DLBs) found only on either side of gap junctions in dendrites in the brain. The DLBs are attached by filamentous proteins to the microtubules, and their structure suggests they may be suitable if not ideal for quantum electron tunneling devices. ... What [Hameroff and Penrose have] suggested is that electron tunneling occurs [across Gap Junctions] between micotubules in each of two adjacent neurons. The distance across the gap junction itself is only 3.5 nanometers, though its a bit further to the [microtubules]. ...".
The cytoskeleton of cells, including neurons of the brain, is made up of microtubules:
which are connected to each other by Microtubule Associated Proteins (MAPs). With these structures in mind
in their paper entitled Orchestrated Objective Reduction of Quantum Coherence in Brain Microtubules: The "Orch OR" Model for Consciousness. Figure 1 (shown above) is a "Schematic of central region of neuron (distal axon and dendrites not shown) showing parallel arrayed microtubules interconnected by MAPs [Microtubule Associated Proteins]. Microtubules in axons are lengthy and continuous, whereas in dendrites they are interrupted and of mixed polarity. Linking proteins connect microtubules to membrane proteins including receptors on dendritic spines.".
The human brain contains about 10^18 tubulins.
Each microtubule is a hollow cylindrical tube with about 25 nm outside diameter and 14 nm inside diameter, made up of 13 columns of Tubulin Dimers.
Click HERE for more details about Microtubules.
Each Tubulin Dimer is about 8 nm x 4 nm x 4 nm, consists of two parts, alpha-tubulin and beta-tubulin (each made up of about 450 Amino Acids, each of which contains roughly 20 Atoms), and can exist in (at least) 2 different geometrical configurations, or conformations, involving the position of a single Electron. Call this Electron the Conformation Electron, because in a single Tubulin Dimer its the position at the junction of the alpha-tubulin and the beta-tubulin determines the 2 different conformations of the Tubulin, which correspond to 2 different states of the dimer's electric polarization.
An analogous structure is described in a 6 July 2001 New Scientist article by Willis Knight:
"... Molecular transistors that run on single electrons now work at room temperature. Dutch scientists achieved the feat by buckling carbon nanotubes with an atomic force microscope. ... "The next step will be to think about how to combine these elements into complex circuits," ... lead researcher Cees Dekker of Delft University ... says. Molecular computers would be high speed and low power. ... The transistors inside normal computers control the flow of thousands of electrons at a time. Transistors capable of manipulating individual electrons could potentially do the same work faster and more efficiently. However, functioning at this tiny scale can be difficult as heat can cause electrons to leak in and out of the molecular components. To avoid this, previous molecular transistors were cooled to near absolute zero. The Delft researchers wanted to create a device that worked at more practical temperatures. By buckling a metallic carbon nanotube, they formed a small area from which a single electron cannot escape at room temperature unless a current is applied via an electrode. ... An interesting and unexpected quantum phenomena also came from the experiment. Dekker says that pushing a single electron through the transistor caused it to exhibit quantum coherence. This means that the electron maintains some of the quantum state it obtained whilst inside the transistor when it leaves. The effect is not found within normal electronics. ...".
According to Physics News Update Number 603 #2, September 9, 2002 by Phil Schewe, James Riordon, and Ben Stein:
"... certain highly curved (on a nanoscopic scale) surfaces modify the electromagnetic properties of physical vacuum in their vicinity. This changes the behavior of an atom near nanobodies (quantum dots, nanospheres, nanocylinders, etc.). Generally called the Purcell effect, the phenomenon happens because an excited electron inside the outside atom strongly senses the modified structure of physical vacuum near surfaces in its vicinity. New calculations performed by physicists at the Belarusian State University in Minsk show that due to unique conducting properties of carbon nanotubes the fluorescence rate of an excited atom or molecule in their vicinity should be enhanced by as much as million, a much greater effect than for other geometries studied. The Purcell effect has been observed in many of these other cases, and the Belarusian scientists (contact Prof. Sergei Maksimenko, firstname.lastname@example.org) hope to find collaborators to test their nanotube hypothesis. The hope is to exploit the enhanced spontaneous decay rate to control the behavior of nuclei, atoms, or organic molecules outside or inside nanotubes. (Bondarev et al., Physical Review Letters, 9 September 2002.) ...".
The Tubulins in a Microtubule can represent Information, and act as Cellular Automata to process it.
The human brain contains about 10^11 neurons. There are 10^7 Tubulin Dimers per neuron, with 10% of them, or 10^6, estimated to be involved in the consciousness process, and the remainder doing other things needed to keep the cell alive.
Roger Penrose says, in Shadows of the Mind (Oxford 1994), page 344, "... We can now consider the gravitational self-energy of that mass distribution which is the difference between the mass distributions of the two states that are to be considered in quantum linear superposition. The reciprocal of this self-energy gives ... the reduction timescale ...".
For a given Particle, Stuart Hameroff describes this as a particle being separated from itself, saying that the Superposition Separation a is "... the separation/displacement of a mass separated from its superposed self. ... The picture is spacetime geometry separating from itself, and re-anealing after time T. ...".
In the Osaka paper ( Hameroff, S.R. (1997) Quantum computing in microtubules: an intra-neural correlate of consciousness? Cognitive Studies: Bulletin of the Japanese Cognitive Science Society 4(3):67-92.) ), Hameroff says that Penrose describes Superposition Separation as "... shearing off into separate, multiple spacetime universes as described in the Everett "multi&endash;worlds" view of quantum theory. ...".
Jack Sarfatti proposes that a Quantum Fluctuation in a State of Superposition is not Reduced until the Gravitational Binding Energy of the Difference among the Superposed States exceeds the Bekenstein threshold of One Bit of Shannon Classical Information, that is, the product of Energy E and Time T equals Planck's Constant h, giving the decoherence time formula T = h / E.
.... the experiment ... consists of a Michelson interferometer in which one arm has a tiny moveable mirror. The radiation pressure of a single photon displaces the tiny mirror. The initial superposition of the photon being in either arm causes the system to evolve into a superposition of states corresponding to two distinct locations of the mirror. In the present proposal a high-finesse cavity is used to enhance the interaction between the photon and the mirror. The observed interference of the photon allows one to study the creation of coherent superposition states periodic with the motion of the mirror. ... If the environment of the mirror "remembers" that the mirror has moved, then, even after a full period, the photon will still be entangled with the mirror's environment, and thus the interference for the photon will be reduced. Therefore the setup can be used to measure the decoherence of the mirror. ...".
If the Superposition consists of States involving one Particle of Mass m, but with Superposition Separation a, then the Superposition Separation Energy Difference is the gravitational energy
An essential ingredient in this model is the gravitational interaction between the two different position states of tubulin electrons. Although the position separation between the two states of any single given tubulin electron is about a = 1 nanometer = 10^(-7) cm, which is well within the micron range of strong gravity, what is relevant is the total gravitational interaction among all N tubulin electrons, and the vast majority of them within the 10-cm scale human brain are far more distant from each other than the micron range of strong gravity, so in calculating the superposition energy E_N of N tubulin electrons and the corresponding time T_N, you should use (as do Hameroff and Penrose) ordinary Far Field gravity with ordinary G.
Since the human brain is on the order of 10 cm, its volume is about 10^3 cm^3. Since a micron is 10^(-6) m = 10^(-4) cm, and since the human brain has about 10^18 tubulin electrons, it has about 10^18 / 10^3 = 10^15 tubulin electrons/cm^3, so that the typical linear distance between tubulin electrons is about 1 / (10^15)^(1/3) = 1 / 10^5 = 10^(-5) cm = 0.1 microns. Therefore the micron range of strong gravity is far enough to connect a tubulin electron with its near neighbors (near including nearest neighbors plus up to order 10 near neighbors). These overlapping Near Field Induction/Static region gravitational neighborhoods help the human brain to maintain superposition of its 10^18 tubulin electrons.
In other words, ordinary weak gravity determines E_N and T_N for the human brain as a whole, while micron-range strong Induction/Static Region gravity with overlapping micron-range neighborhoods helps maintain the superpositions during the T_N time of a conscious thought.
Therefore (ignoring for simplicity some factors like 2 and pi, etc.):
2 G m / c^2 = Schwarzschild Radius of a classical black hole of mass m and
h / m c = Compton Radius of the Sidharth Kerr-Newman naked singularity model of an elementary particle of mass m.
Here, ordinary gravity is used, not because it is realistic for a 1-naonometer distance, but because the calculation for a single Electron will be used as the basis for a superpositon of N Electrons over the 10-cm scale human brain, for which ordinary gravity is realistic and should be used. If the single Conformation Electron with mass m_e has a Superposition Displacement a that is of the order of 10^(-7) cm, or one nanometer, then, since Compton = 10^(-11) cm and Schwarzschild = 10^(-55) cm and the speed of light c = 3 x 10^10 cm/sec, and since E_electron = G ( m_e )^2 / a, we have
for a single Electron and ordinary gravity
= ( Compton / Schwarzschild ) ( a / c ) = 10^26 sec = 10^19 years.
Now consider the case of N Tubulin Electrons in Coherent Superposition, in which ordinary gravity is realistic.
As Jack Sarfatti says, "Since all the [Conformation] Electrons are nonlocally connected into a coherent whole we do not want to treat them as fluctuating statistically independent of each other ... .", and Stuart Hameroff agrees, saying "True. That's why we consider them coherently linked or entangled.". As Jack Sarfatti explains, "... this is for a macro-mass M. So change m to M = Nm for a network of N connected pieces forming a coherent whole. Note the pair binding energy is small. But we need the gravity self-energy of this big whole of N entangled pieces since this is some kind of a quantum collective mode! Therefore, the size parameter ... is the whole not the part. We are not looking at the gravity self energy of the part, but the gravity self energy of the whole. Since it also has to be a metric fluctuation, I use Wheeler's "L" for the scale of the metric fluctuation.So, I get ...[ E = G M^2 / L = N^2 G m^2 / L where ]... L is the scale of the metric quantum gravity fluctuation in the sense of John Archibald Wheeler. Clearly L is over the entire region of cortex containing N switching units that coherently participates in the "orch OR" process whatever it may be. So how do we relate L to the microdisplacements of the pieces of the whole? The obvious thing to try is L^3 = N a^3 [where] "a" is the displacement of each piece. Now you can use Hameroff's pictures of what the individual pieces are doing to get a number for "a". Remember we are only doing orders of magnitude so we are not interested in 1% or even 10% corrections. If we get roughly the right power of 10 we are happy. ... the entire model is still very primitive. ...
( c Gravity Self-Collapse Time )^2 ( Classical )^2 = ( Quantum )^2 ( Spatial Coherence Length )^2 = 4D Blister Volume
for quantum gravity self-collapse from [Hameroff-Penrose] space-time geometry separation.
( c T )^2 ( G M / c^2 )^2 = ( h / M c )^2 L^2
( c Coherence Time )( Classical Wormhole Radius ) = ( Quantum Wormhole Radius ) ( Spatial Coherence Length )
c T G M / c^2 = ( h / M c ) L
G M^2 / L = h / T
L = a N^(1/3)
M = N m
a = spatial coherence length of a single q-bit
m = mass of a single q-bit
N q-bits form a single coherent network or collective mode. So
( c Collective Coherence Time ) / (Collective Mode Coherence Length ) = ( Quantum / Classical )
The effective squared space-time interval is ( c Coherence Time ) - ( Spatial Coherence Length ). When is this zero or lightlike? Clearly only when Quantum = Classical [at the Planck scale of] M = 10^(-5) gm. For elementary particles (Quantum/Classical) >> 1, so the effective interval is timelike. For classical black holes the reverse is true so the effective interval is spacelike. ... Note the squares of the lengths are all Bekenstein information measures! So timelike means that in some sense the Bekenstein temporal information is greater than the spatial information since each bit of Bekenstein information has area h G / c^2 [which is the square 10^(-66) cm^2 of the Planck length, which can be compared to the square 10^(-22) cm^2 of the Electron Compton Radius]. So we see that the square of the space-time interval in Einstein's classical theory of relativity has a deeper informational meaning. The hyperbolic signature of spacetime means subtracting two informational measures. In Hawking's imaginary time we add the measures. This also connects with the Christodoulo black hole fusion formula that obeys the Pythagorean theorem ... . Both relativity and quantum theory are really surface forms of an information theory according to Wheeler's "IT FROM BIT". ... In first order perturbation theory in the space-time picture (not the momentum-energy space) use Huyghen's principle for the quantum information waves of the coherent spatially separated q-bit sources
(Gm^2/L)^(1/2) ( e^(i PHI(j+)) + e^(i PHI(j-)) ) / 2
is the Wheeler-Feynman quantum gravity near field Huyghen's wavelet from the jth q-bit, where j = 1 to N, + is the advanced phase and - is the retarded phase from the two poles of the Feynman propagators. Note the coherent absorbers in the nano-boxes protecting the q-bits from environmental decoherence allow for the Libet-Radin-Bierman back-causation from non cancellation of the advanced against the retarded amplitudes! That is the interference between past and future is no longer completely constructive in sentient matter. The total coherent Feynman amplitude is
( G m^2 / L )^(1/2) Pribram Brain Hologram Phase Modulation Pattern
This Phase Modulation Pattern is the coherent sum of the both the advanced (from the future) and the retarded (from the past) phase factors. All alternative histories have equal amplitude hence the common (Gm^2/L)^1/2 factor. In the "ground state" all the phases are zero and we get for the squared coherent amplitude
N^2 G m^2 / L = N^(5/3) G m^2 / a
where T = h / ( N^(5/3) G m^2 / a ) for the objective decay of the Bohm information field in the implicate order. (... in ... ordinary matter where the individual phases are random ... you would get N G m^2 / a for incoherence of individual pieces instead of N^2 G m^2 / L for the coherent mesoscopic collective mode ...) In addition, there is the self-organization time from the self-reaction of the Bohm world line to the action of the Bohm information field on that world line t = Tgrw / N ...".
Jack Sarfatti defines the Superposition Energy E_N of N superposed Conformation Electrons in N Tubulins as
where L is the mesoscopic quantum phase coherence length for the collective mode of N Conformation Electrons of total mass M in the N Tubulins, so that
= N^(5/3) G m^2 / a=
= N^(5/3) E_electron
To get the decoherence time for the system of N Tubulin Electrons, recall that T_electron = h / E_electron = ( Compton / Schwarzschild ) ( a / c ) = 10^26 sec = 10^19 years, so that
= N^(-5/3) T_electron =
= N^(-5/3) 10^26 sec
and (ignoring for simplicity some factors like 2 and pi, or 4 in this case)
= 10^15 / (T_N)^(3/5)
From the above formulas get the following rough approximate Table of Decoherence Times T_N for various phenomena and structures involving various Numbers of Tubulin Dimers or Neurons, assuming that 10% of the Tubulins in each Neuron are involved in the process of consciousness:
Time Number of Number of Scale L =
T_N Tubulins Neurons = N^(1/3) s
10^(-43) sec (Planck) 10^41 10^35 500 km
10^(-14) sec (local protein) 2 x 10^23 2 x 10^17 50 cm
10^(-10) sec (global protein) 10^21 10^15 10 cm
10^(-10) sec (Frohlich) 10^21 10^15 10 cm
10^(-5) sec 10^18 10^12 1 cm
5 x 10^(-4) sec (2 kHz) 10^17 10^11 0.5 cm
25 x 10^(-3) sec (40 Hz) 10^16 10^10 0.2 cm
100 x 10^(-3) sec (EEG alpha) 4 x 10^15 4 x 10^9 0.16 cm
500 x 10^(-3) sec (Radin/Bierman) 1.5 x 10^15 1.5 x 10^9 0.11 cm
1 sec 10^15 10^9 0.1 cm
10^10 sec = 300 years 10^9 10^3 10^(-3) cm
10^15 sec = 3 x 10^7 years 10^6 1 10^(-4) cm
10^26 sec = 3 x 10^18 years 1 10^(-6) cm
the van der Waals interaction; and
Sidharth-Sarfatti Proton GravitoEM Induction Region Virtual Gravitons that have nanometer-scale range, similar to the scale of Tubulins, of the Superposition Separation Distance of the Conformation Electron of a Tubulin, and of gap junctions.
To see that this picture is consistent with the electron picture, start with the case of one Tubulin whose Conformation Electron is in Coherent Superposition with the Atoms of the Tubulin. Since the Tubulin has 2 parts (alpha and beta), each with about 450 amino acids, and each amino acid has about 20 Atoms, the Tubulin consist of about 2x450x20 = 18,000 Atoms, or about 20,000 Atoms. I consider that the entire Tubulin is only displaced by a distance a_tubulin such that the total Superposition Separation Energy of the entire Tubulin is equal to the Superposition Separation Energy of its Conformation Electron by a nanometer. Hameroff and Penrose, in Section 5.1.1 (Protein Spheres) of their Orch OR paper, have calculated the Superposition Separation Energy, saying (changing some of their notation): "... Since the [Superposition Separation] displacement is less than the sphere radius, we need a detailed calculation to obtain the gravitational self-energy E of the difference between the displaced mass distributions for each tubulin monomer, considered as a uniform sphere. Taking the sphere to have a radius R and the distance of displacement to be a, we find, as the result of a double integration:
If the radius R of the Tubulin is taken to be about 2 nanometers as a rough estimate, and the displacement will be much less than R, then, as Hameroff and Penrose say, "... We can ignore the higher-order terms, so we obtain ...
If there are about 5 nucleons per Atom, and about 20,000 Atoms per Tubulin, then there are about 100,000 nucleons per Tubulin. Since the mass of a nucleon is about 2,000 Electron masses, the total mass of the Tubulin is about 2 x 10^8 m_e, where m_e is the Electron mass. If E_e is the Superposition Separation Energy of one Electron by one nanometer and the Tubulin is to be displaced by a distance a so that the Superposition Separation Energy E_tubulin of the Tubulin is equal to E_e, we have (ignoring some factors of 2 for simplicity):
so that the Superposition Separation for the entire single Tubulin is given by
a_tubulin = 2 x 10^(-15) cm
= 10^26 sec = 10^19 years.
Since 10^(-13) cm = 5 GeV^(-1), a_tubulin = 2 x 10(-15) cm = (1/50) x 10^(-13) cm corresponds to an energy scale of about 250 GeV, which is roughly the Higgs Vaccum Expectation Value (possibly related to the Compressibility of the Aether), and is of the order of the masses of the Truth Quark and Weak Force interactions involving W and Z gauge bosons, and probably of the (not yet experimentally observed) Higgs Scalar, all of whose masses are of the order of 100 GeV, or about 200,000 m_e.
Jack Sarfatti has noted the relevance of the fundamental
which sets a threshold for consciousness phenomena at Tgrw_N = Tgrw / N, since GRW Dynamical Decoherence scales as 1 / N. I use the value Tgrw = 3 x 10^14 sec. You can find the intersection point of the Tgrw_N function with the T_N Tubulin Back-Reaction function by setting
so that the number of Tubulins N_BRgrw at the intersection point is
= ( 3 x 10^10 )^(3/2) = 5 x 10^15 Tubulins.
From the above table, N_BRgrw Tubulins roughly corresponds to:
The GRW event at Tgrw_N means that Superposition is Destroyed because of GRW, which is an Individual Process for each Tubulin Site Electron, and not by an Orch OR Orchestration of a Superposition of States of many Tubulin Site Electrons.
The Tubulin event at T_N means that Superposition is Destroyed, not by an Individual GRW Process, but as the Climax of an Orch OR Orchestration of a Superposition of Tubulin States that produces a Superposition (or, from the Penrose point of view, a blister of superposition of spacetimes) that grows so large that it decoheres because it is so big that it violates the uncertainty principle E T = h and thus cannot hold together coherently.
A Superposition of an Orch OR Orchestration Process in progress will be Terminated Without Completion if the GRW event occurs before the Tubulin event of the Orch OR process, or, in other words, if Tgrw_N is less than T_N where N is the number of Tubulins involved in the Orch OR process.
To see more clearly how this works, make the following logT - log N plot of the Tgrw_N GRW function versus the T_N Orch OR Tubulin Back-Reaction function:
In the above logT - logN curves::
Therefore, taking into account both GRW and Orch OR Tubulin Back-Reaction, the purple, green, and gold areas are the only regions for coherent Superposition of States. The purple area is the area of Small Scale Abstract Thought Consciousness due to GRW Superposition of States, while the green and gold areas are the areas for Large Scale Abstract Thought Consciousness.
For N smaller than the intersection of the curves, that is, for N smaller than about 5 x 10^15, which is the purple area, the GRW curve controls, because GRW decoherence occurs before Orch OR Tubulin Back-Reaction decoherence has time to occur. Since for GRW T N = constant, that is a curve that is equivalent to the Hameroff T = h / E curve.
For N larger than the intersection of the curves, which is the green and gold areas, the Tubulin Back-Reaction T N^(5/3) = constant curve that Jack Sarfatti formulated is the one that controls, because Orch OR Tubulin Back-Reaction decoherence occurs before GRW decoherence has time to occur.
The green area is the part of the Orch OR Tubulin Back-Reaction region for which N is at most 10^18, or in other words, for which N is within the size of the human brain at 10^7 Tubulins per Neuron.
The gold area is the part of the Orch OR Tubulin Back-Reaction region for which N exceeds about 10^18, or, at 10^7 Tubulins per Neuron, for which N exceeds the size of the human brain.
Therefore, to make decisions faster, or, in other words, to decohere the coherent superpostion faster, you need more and more Neurons. The fastest that humans can think is the upper limit of the green region, on the order of about 10^(-5) seconds.
Further, for less than about 10^15 Tubulins or so, GRW decoheres the superposition BEFORE the Orch OR Tubulin Back-Reaction decoherence takes place, so that you must have AT LEAST 10^15 Tubulins to have Large Scale Abstract Thought consciousness based on Orch OR Tubulin Back-Reaction. Since 10^15 Tubulins is about 10^9 Neurons or so (assuming that 10 per cent of the 10^7 Tubulins in a Neuron are available for conscious thought rather than doing other things to maintain the cell), a brain 1 per cent the the size (10^11 Neurons) of a human brain is large enough to be Conscious with respect to Large Scale Abstract Thought by the Orch OR Tubulin Back-Action mechanism (of course, other mechanisms could be responsible for different forms of what is sometimes called consciousness, including but not limited to Small Scale Abstract Thought by GRW Superposition of States and simple Neural Network learning).
There should also be an upper limit on the scale of a Tubulin brain, at which the time for light to travel the scale distance is greater than the Orch OR Tubulin Back-Reaction decoherence time. From my table, it seems that is a little over 10^21 Tubulins, for which the scale is about 10 cm, the light travel time is 10 / (3 x 10^10) = 3 x 10^(-10) sec and the Tubulin Back-Reaction decoherence time is 10^(-10) sec.
However, if you want the Orch OR Tubulin Back-Reaction decoherence phenomena to be synchronized with chemical phenomena such as neurotransmitter transfer, then you cannot use the speed of light, and must use a much slower speed and so insist that the minimum timescale be of the order of a fraction of a millisecond at the shortest. For half a millisecond, the number of Tubulins is 10^17, and (assuming that 10 per cent of the 10^7 Tubulins in a Neuron are available for Abstract Thought Consciousness rather than doing other things to maintain the cell) the maximum number of Neurons is about 10^11, the size of the human brain.
Abstract Thought Consciousness is the process of operation by an Abstract Thought on a Superposition of Many Abstract Ideas.
Large Scale Abstract Thought Consciousness is due to Orchestrated Coherence of many Electrons, such as by the Hameroff-Penrose Orch OR process.
Small Scale Abstract Thought Consciousness is due to GRW Superposition of States, and involves single Elementary Particles or Coherent (generally smaller) Groups of Elementary Particles.
If the GRW process is considered to be an expression of the Mind of the Universe, then the GRW termination may allow
small-N things to be more tuned in to the Mind of the Universe at large, while
large-N things would be more self-absorbed by the self-contained orchestration process.
The crossing point where Tgrw = T_N is roughly at the size of the Human Brain, and is also roughly where N is such that it is equally in touch with
the Mind of the Universe (through GRW) and
the self-conscious self (through the self-contained orchestration process).
Since submillimeter gravity of Sidharth-Sarfatti Electron GravitoEM Induction Region physics has a range of only about a micron, which is about the size of a single Neuron,
Consider Two Types of Cycle:
The Biology Cycle is based on Stuart Hameroff's viewpoint, and is very similar to it. Its Stages are:
1 - A Tubulin Site Electron sits within its tubulin cage in one of its 2 Quantum States. The Tubulin Site Electron has one of 2^1 = 2 States, so it contains one qbit of information, representable by the 2^1 = 2-dimensional Cl(1) Clifford Algebra that is isomorphic to the Complex Numbers.
2 - That Tubulin acts on its Microtubule through the Tiling (and possibly through interaction with Superradiant Photons in the Microtubule Core). The sum of such actions by N_mt Tubulins within the Microtubule determines the Conformation State of the Microtubule. The Conformation State is representable by the 2^N_mt dimensional Cl(N_mt) Clifford Algebra.
3 - The Microtubule Conformation State is transmitted by MAP links to affect the Conformation States of other Microtubles in the same Neuron.
4 - The size of the main body of a Neuron is roughly the micron range of submillimeter gravity. To connect between different Neurons, Stuart Hameroff has "... suggested ... that Electron [Quantum] Tunneling [such as that described by Evan Harris Walker] occurs between Micotubules in ... adjacent Neurons. The distance across the Gap Junction itself is only 3.5 nanometers, though it is a bit further to the Microtubules. ... There are special organelles (dendritic lamellar bodies - DLBs) found only on either side of Gap Junctions in dendrites in the brain. The DLBs are attached by filamentous proteins to the Microtubules, and their structure suggests they may be suitable ... for Quantum Electron Tunneling devices ...".
5 - Through the links of Stages 2-4, a total of N Tubulin Site Electrons are connected and brought into a coherent Superposition of States. The Superposition of States is representable by the 2^N dimensional Cl(N) Clifford Algebra.
The QUANTUM STATE CYCLE occurs during the Superposition of States. It is based on Penrose lightcone cycles and on Sarfatti Back-Reaction. Many of the Quantum States of the Superposition are Closed Timelike Loops, some of which intersect with others. If each Closed Timelike Loop represents an Abstract Idea, then the Intersections among the Closed Timelike Loops represent Interactive Abstract Thought operating on the set of Abstract Ideas.
During the time of Superposition, new Abstract Thoughts can be derived from the original ones by reorganizing the corresponding Closed Timelike Loops and their Intersections.
This Thought Process of forming and holding an Abstract Conscious Thought, does not involve a physical flow of a current of Electrons across the Synaptic Junction, but rather involves maintaining a coherent state that extends to both sides of the Synaptic Junction, thus connecting the two Neurons.
Dimi Chakalov has made an important observation about the Quantum State Cycle: "... Talking about what is going on "during" Superposition is like trying to explain how a completely dark room might look like, by showing pictures of it. ...". Even though the Quantum State Cycle is not easy to observe, it is the process of Abstract Conscious Thought.
6 - The Quantum State Cycle ends when the Decoherence/Collapse time T_N is reached. Then, Decoherence/Collapse occurs, and a single Abstract Idea is chosen from the enlarged Set of States in the Superposition.
This is the Execution Process, which involves choosing one Abstract Idea and rejecting/executing the other Ideas of the Superposition.
If T_grw is shorter than T_N, then Decoherence/Collapse occurs by GRW instead of by the OR reduction in the Orchestated Objective Reduction Orch OR process of Penrose-Hameroff, whose Decoherence/Collapse time is T_N. Since GRW Decoherence/Collapse is due to the collapse of any individual one of the N Tubulin Site Electrons in the Superposition, and T_N Decoherence/Collapse is due to the Orchestrated Decoherence/Collapse of all N of them acting together coherently, GRW Decoherence/Collapse destroys the process of Abstract Conscious Thought, so that Abstract Conscious thought does not exist for N less than about 5 x 10^15 Tubulin Site Electrons.
7 - When you Execute the Thought by choosing an Abstract Idea State, the chosen State from the Superposition determines the Positions of all the Gap Junction Electrons of the Quantum Tunnelling connections between Neurons.
8 - The Positions of the Gap Junction Electrons determine the Conformations of the Micrtubules that are adjacent to the Gap Junctions.
9 - The Conformations of those Microtubles determine, through MAP connections, the Conformations of other Microtubules in the same Neuron.
10 - The Conformation of a Microtubule determines the State of its Tubulins.
11 - The State of a Tubulin determines the State of its Tubulin Site Electron, thus COMPLETING THE BIOLOGY CYCLE.
Each Quantum Superposition of States contains MANY Closed Timelike Loops of Bohm-Sarfatti Back-Reaction. Each of the Closed Timelike Loops represents an Abstract Idea, and their Superposition represents an Abstract Thought that operates on and with those Abstract Ideas.
In the Hameroff-Penrose model, Roger Penrose describes the Closed Timelike Loops in terms of Lightcones of Relativity. Penrose describes a quantum gravity theory of David Deutsch in which only a very small fraction of the spacetime geometries in a superposition contain closed timelike loops. Even the very small fraction of closed timelike loops permit non-computable operations to be performed by a human-brain quantum computer, which could feed on its own output, running around the closed timelike loop.
Within the range of about a micron, Sidharth-Sarfatti GravitoEM Induction Region physics gives submillimeter gravity. In the D4-D5-E6-E7 physics model, virtual 4-pair gravitons, which are effectively Planck-mass black holes, could tilt the lightcones of spacetime, resulting in closed timelike loops. For an illustration of tilted lightcones, see the lightcones in Duchamp's The Large Glass. In the D4-D5-E6-E7 physics model, such tilted lightcone spacetimes may be only a very small proportion of any quantum superposition describing physical spacetime.
In The Transactional Interpretation of Quantum Mechanics due to Cramer, Rev. Mod. Phys. 58 (1986) 647-687), the probability of taking a given link in a path among the Many Worlds is the product of amplitude for that link times the amplitude for its complex conjugate. Since the complex conjugate amplitude is the time reversal of the link amplitude, Cramer's picture is that of the present interacting with the future. The present amplitude makes an "offer" that can be accepted by a "handshake" with a complex conjugate amplitude "confirmation" from the future, so that the resulting observation is a "transaction". The offer from the past is Yang, while the confirmation from the future is like Yin. Combined, they form Closed Timelike Loops.
In this connection, it is interesting to note that
In addition to the Human Brain Biology Cycle described above, there are:
Other possible types of Biology Cycles based on Biologies different from that of the Human Brain.
Dimitri Nanopoulos and his collaborators have written a series of papers describing a model of quantum consciousness that is similar to mine in that it involves microtubules, but differs in that it is based on superstring theory. In hep-th/9207103, John Ellis, N.E. Mavromatos and D.V. Nanopoulos say:
"... We argue that the light particles in string theory obey an effective quantum mechanics modified by the inclusion of a quantum-gravitational friction term, induced by unavoidable couplings to unobserved massive string states in the space-time foam. This term is related to the W-symmetries that couple light particles to massive solitonic string states in black hole backgrounds, and has a formal similarity to simple models of environmental quantum friction. It increases apparent entropy, and may induce the wave functions of macroscopic systems to collapse. ... the evolution of quantum-mechanical systems over time-scales that are long compared with the Planck time should be described by a modified Liouville equation ...[that]... is characteristic of open quantum-mechanical systems, and represents in our interpretation the intrinsic coupling of a microscopic system to space-time foam. ... An operationally similar modification of the Liouville equation was proposed independently on completely phenomenological grounds by Ghirardi, Rimini and Weber [GRW], and the required values of their model parameters were entirely consistent with our upper bounds and order-of-magnitude estimates. ...".
In hep-ph/9505374, Nanopoulos says:
"... MicroTubules (MTs), protein polymers constructing the cytoskeleton, participate in ... bioinformation processes such as learning and memory, by possessing a well-known binary error-correcting code with 64 words. In fact, MTs and DNA/RNA are unique cell structures that possess a code system. It seems that the MTs' code system is strongly related to a kind of "Mental Code" in the following sense. The MTs' periodic paracrystalline structure make them able to support a superposition of coherent quantum states, as it has been recently conjectured by Hameroff and Penrose, representing an external or mental order, for suffcient time needed for effcient quantum computing. Then the quantum superposition collapses spontaneously/dynamically through a new, string-derived mechanism for collapse proposed recently by Ellis, Mavromatos, and myself. ... At the moment of collapse, organized quantum exocytosis occurs, i.e., the simultaneous emission of neurotransmitter molecules by the synaptic vesicles, embedded in the "firing zone" of the presynaptic vesicular grids. Since in the superposition of the quantum states only those participate that are related to the "initial signal", when collapse occurs, it only enhances the probability for "firing" of the relevant neurotransmitter molecules. That is how a "mental order" may be translated into a "physiological action". Our equation for quantum collapse, tailored to the MT system, predicts that it takes 10,000 neurons O(1 sec) to dynamically collapse, in other words to process and imprint information. Different observations/experiments and various schools of thought are in agreement with the above numbers concerning "conscious events". If indeed MTs, with their fine structure, vulnerable to our quantum collapse mechanism may be considered as the microsites of consciousness, then several, unexplained (at least to my knowledge) by traditional neuroscience, properties of consciousness/awareness, get easily explained, including "backward masking", "referal backwards in time", etc. Furthermore, it is amusing to notice that the famous puzzle of why the left (right) part of the brain coordinates the right (left) part of the body, i.e., the signals travel maximal distance, is easily explained in our picture. In order to have timely quantum collapse we need to excite as much relevant material as possible, thus signals have to travel the maximal possible distance. The non-locality in the cerebral cortex of neurons related to particular missions, and the related unitary sense of self as well as non-deterministic free will are consequences of the basic principles of quantum mechanics, in sharp contrast to the "sticks and balls" classical approach of conventional neural networks. The proposed approach clearly belongs to the reductionist school since quantum physics is an integrated part of our physical world. ... the quantum collapse becomes a detailed dynamical mechanism instead of being an "external" ad-hoc process, may find some application to some quantum aspects of brain function. It looks like a big universality principle is at work here, because both in the black hole and the brain we are struggling with the way information is processed imprinted, and retrieved. ...".
In quant-ph/0007088, Andreas Mershin, Dimitri V. Nanopoulos and Efthimios M.C. Skoulakis say:
"... We identify quantum-physics derived mechanisms conceivably underlying the integrated yet differentiated aspects of memory encoding/recall as well as the molecular basis of the engram. We treat the tubulin molecule as the fundamental computation unit (qubit) in a quantum-computational network that consists of microtubules (MTs), networks of MTs and ultimately entire neurons and neural networks. ... in our model, a single neuron is upgraded from a relatively simple (yet adjustable) switch to a device capable of information processing. In addition, within the context of our model, (at least some) neurons are capable of launching fast connections to establish correlations with distant neurons using the principles of quantum entanglement and/or photon interactions ... The tubulin system described above could easily serve as a textbook example of how a biological qubit should look like! The two tubulin conformations make for a simple binary qubit with the ability of entanglement with similar neighboring qubits/dimers in the protofilaments giving us a quantum cluster! The timescale for the spontaneous conformational changes in the tubulin dimers is of order 10 11sec Once in an entangled state, a "measurement" or interaction with the environment will collapse the state into one of its basis states ... Yet, the correlations can be communicated instantaneously among the tubulin qubits ... spanning entire MTs or conceivably whole neurons or neural networks. ...
... Damage to neural MTs resulting from hyperphosphorylation of ... a microtubule associated protein (MAP), results in memory loss in Alzheimer's Disease (AD) patients ... Neurofibrillary Tangles (NFTs) are bundles of twisted MTs that are no longer held apart by their MAPs. Post-mortem histological examination of AD patients shows a clear and direct correlation between NFTs and duration and severity of the disease ...
... binding of an anesthetic molecule to the hydrophobic pocket of the tubulin dimer may have the effect of preventing changing the electron orbitals (i.e. the tubulin's ability to flip) thus shutting the whole system down. ... Furthermore, if the general anesthetic concentrations are not too high, complete reversibility of anesthetic effects is possible, indicating that the temporary van der Waals blockage of the crucial tubulin electron(s) has ended and conformational changes are free to occur again. ...
... There is evidence that the hollow interior of MTs may be capable of supporting a very special state of "ordered" water molecules both inside and outside of the MT ... The interaction of the dipole-quanta coherent modes with the protein dimers results in an entanglement which we claim is responsible for the emergence of soliton quantum coherent states, extending over large scales, e.g. the MT or even the entire MT network. ...
... the existence of a quantum-error correcting code is needed to protect the delicate coherent qubits from decoherence. This has been the major problem of quantum computers until the works of Shor and Steane have independently shown that such a code can be implemented. We conjecture that the K-code apparent in the packing of the tubulin dimers and protofilaments is partially responsible for keeping coherence among the tubulin dimers. By simulating the brain as a quantum computer it seems we are capable of obtaining a more accurate picture than if we simulate the brain as a classical, digital computer. ...
... We have been successful in our initial experiments to train flies and test their learning and memory for up to 6hrs. ... However, our initial attempts to localize MAP-2 within the fly brain have been unsuccessful. ... We are currently in the process of trying a number of anti-MAP-2 polyclonal antibodies to select the one that best reveals the MAP-2 distribution in the fly brain. ...".
In quant-ph/0204021, Nick E. Mavromatos, Andreas Mershin, and Dimitri V. Nanopoulos say:
"... We refine a QED-cavity model of microtubules (MTs) ... and suggest mechanisms for the formation of biomolecular mesoscopic coherent and/or entangled quantum states, which may avoid decoherence for times comparable to biological characteristic times. This refined model predicts dissipationless energy transfer along such "shielded" macromolecules at near room temperatures as well as quantum teleportation of states across MTs and perhaps neurons. ... microtubules (MTs) can be treated as quantum-mechanically isolated (QED) cavities, exhibiting properties analogous to those of electromagnetic cavities routinely used in quantum optics. Recently, our speculative model has been supported by some indirect experimental evidence. It has been experimentally shown, that it is possible to maintain partial entanglement of the bulk spin of a macroscopic quantity of Caesium (Cs) atoms (N = 10^12), at room temperature, for a relatively long time (0.5ms). ... In such experiments entanglement is generated via interaction with pules of light. ... A direct consequence of our model for MTs as QED cavities is that virtually every experimentally known QED-cavity-based observation may have an analogue in living MTs and we show this analytically with the specific case of intra- and inter-cellular dissipation-less energy transfer and quantum teleportation of coherent quantum states. ... we present a straight forward calculation of how quantum teleportation of states can occur in MTs, in direct analogy to the suggester experimental quantum teleportation in optical cavities that has been observed recently. We also draw a parallel between certain geometrical features of MTs such as their ordered structure which obeys a potentially information-encoding code and suggest how this can be exploited for (quantum) error-correction and dense coding. ... teleportation of coherent quantum states across and between cells ...[is defined]... the complete transfer of the coherent state of an MT without any direct transfer of mass or energy. This means that the 'receiver' MT finds itself in an identical state to the 'sender' MT. We will demonstrate that given the possibility for entangled states, teleportation between microtubule A and microtubule C can happen ...
... Schematic of a microtubular quantum teleportation of states. MT a sends its state (represented by a cross) to MT c without any transgfer of mass or energy. Both MT a and MT c are entangled with MT b (entanglement represented by presence of connecting MAPs. ...
... Example of a microtubular logic gate:
A XOR logic gate where "0" is represented by absence of soliton and "1" by presence of soliton.(a)Input MT. (b) Output MT. (c)A MAP transmitting a soliton. (d) A "quiet" MAP. MT a has two solitons travelling, encountering two MAPs that transmit both solitons to MT b (b).In this hypothetical scenario, the solitons arrive out of phase at MT b and cancel each other out. The truth table for XOR reads: 0,0 -> 0;0,1 -> 1;1,0 -> 1,1,1 -> 0. and in this case is realized by MTs if the MAPs are arranged such that each can transmit a soliton independently but if they both transmit, the solitons cancel out. ...".
In a Tucson 3 paper described on a cognet.mit.edu web page, Dick J. Bierman and Dean Radin say: "... the experimental results ...[in]... experiments ... by Radin ... to explore physiological indicators of "precognitive information" in which subjects respond prior to presented stimuli ... suggested a true, large and replicable "precognitive" psi effects with a remarkable signal to noise ratio ... DJB ... was skeptical of these results and therefore decided to replicate the experiments using the same general procedure ... After 7.05 seconds ... the foreperiod ... Radin originally used a 5 seconds foreperiod. ... a randomly chosen picture, either calm or highly emotional, is displayed for a specific exposure time ... Before, during and after exposure the skin conductance is sampled by the computer with a sampling rate of 5 samples per second ... The major (and maybe only) source of normal explanations left after Radin's original studies was the hypothesis that subjects developed anticipatory strategies ... The major point in favour of the psi hypothesis is however that there are no indications in the real data that support any of these sequential strategy models so far. ...
... An interpretation of the exposure times findings is difficult because there were 3 different times used. It appears that an exposure time of 600 msec is better than 3000 msec but an exposure time of 400 msecs is inferior. It should be noted that for 400 msec exposures the subjects do not always recognize the (emotional) contents of the pictures. So in that condition they may not always consciously experience an emotion. ...
... It is said that on the path toward complete control of one's consciousness at some point psi-phenomena will appear. It is also said that one should not pay attention to these phenomena because that would only frustrate progress in meditation performance. Within this, admittedly very speculative, framework the expected point of symmetry on the time axis is NOT at stimulus onset but rather at the start of the conscious (emotional) experience, which may be around 500 msec later. Therefore the peak of the presponse is not expected around 3.5 seconds before the stimulus onset (where it would be if it was a mirror image of the response with symmetry point at stimulus onset) but rather about 2.5 seconds before stimulus onset ...".
In the paper itself (revised 12/11/01), Bierman and Radin say: "... Figure 2 shows the mean response for change in skin conductance for all calm and emotional trials. ...
... In Figure 4 the average difference in presponse between emotional and calm is given for long (3000 msec) and short (400 msec) exposures. ...
... it is concluded that these data only seem explicable as a form of "backaction" or retro-causal effect due to conscious experience. Backaction was discussed in the light of the role of time-symmetry in physics. It was speculated that consciousness plays the role of a highly coherent absorber and is therefore responsible for constructive "backaction" rather than destructive retro-causal effects which are thought to arise from non-coherent absorbers. ...".
to use what we used to call in college
SuperNatural Units in which c = G = h = 1 = 2 = pi
(In other words I sometimes ignore factors like 2 and pi, etc., for simplicity.)
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