Penrose-Hameroff Quantum Tubulin Electrons, Chiao Gravity Antennas, and Mead Resonance

Frank D. (Tony) Smith, Jr., Cartersville - August 2002 [[ January 2003 ]]

( contributed to Quantum Mind 2003 - Consciousness, Quantum Physics and the Brain,March 15-19, 2003, University of Arizona, Tucson, Arizona )

For pdf format (178k), Click Here. My attempt to put it on the gen-ph archive was rejected by in August 2002 and an update was rejected in February 2004.

[[ In this html version, material added after August 2002 has been enclosed by [[ ]] double brackets. ]]

[[ My talk at Quantum Mind 2003 had been scheduled for a concurrent session on the afternoon of Saturday, 15 March 2003, but, due to circumstances including my law suit against Cornell et al, I did not go to Tucson and give the talk, although I had registered and reserved a hotel room and purchased an ATL-TUS round-trip Delta airline ticket. ]]


Penrose and Hameroff have proposed that consciousness in the human brain may be based on gravitational interactions and quantum superposition states of electrons in tubulin cages in microtubules.

Chiao has proposed experimental construction of a gravity antenna that might be analogous to tubulin caged electrons.

Tegmark has criticized Penrose-Hameroff quantum consciousness, based on thermal decoherence of any such quantum superposition states.

This paper briefly describes some experimental results and theoretical ideas that indicate to me that Tegmark's criticism may be invalid.

Such theoretical ideas include Mead's quantum physics of resonance.

This paper closes with brief summaries of

Quantum Consciousness

Roger Penrose and Stuart Hameroff propose that Consciousness involves a Planck scale Decoherence of Quantum Superpositions that they call Orch OR in their paper entitled Orchestrated Objective Reduction of Quantum Coherence in Brain Microtubules: The "Orch OR" Model for Consciousness. Figure 1

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 Centrosome, in most animal cells, acts as a Microtubule Organizing Center. Most Centrosomes contain a pair of Centrioles arrranged at right angles to each other in an L-shaped configuration. A Centriole

is about 200 nm wide and 400 nm long. Its wall is made up of 9 groups of 3 microtubles. You can regard the A microtubule of a triplet as being a complete microtubule, with the B and C microtubules being incomplete microtubules fused to A and B respectively. Each triplet is tilted in toward the central axis at an angle of about 45 degrees.

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.

( The two preceding illustrations are from Molecular Biology of the Cell, 2nd ed, by Alberts, Bray, Lewis, Raff, Roberts, and Watson (Garland 1989) )

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.

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.

The human brain contains about 10^11 neurons.

Therefore, the human brain contains about 10^18 tubulins, about 10^17 of which are involved in the consciousness process.

The Tubulins in a Microtubule can represent Information, and act as Cellular Automata to process it.

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 ...".

This is the decoherence time T = h / E.

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. ...".

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

E = G m^2 / a

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. ...".

The superposition energy E_N of N Tubulin Electrons and the corresponding decoherence time T_N can be calculated from the equations E = G m^2 / a and T = h / E.

Therefore for a single Electron (ignoring for simplicity some factors like 2 and pi, etc.):

T = h / ( G m^2 / a ) = ( h / m c ) ( c^2 / G m ) ( a / c ) =

= ( Compton / Schwarzschild ) ( a / c )


2 G m / c^2 = Schwarzschild Radius of a classical black hole of mass m and

h / m c = Compton Radius of an elementary particle of mass m.

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. If the single Tubulin 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

T_electron = h / E_electron =

= ( 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 [Tubulin] 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.". Jack Sarfatti defines the Superposition Energy E_N of N superposed Tubulin Electrons in N Tubulins as

E_N = G M^2 / L

where L is the mesoscopic quantum phase coherence length for the collective mode of N Tubulin Electrons of total mass M = N m with each electron having mass m and with L = a N^(1/3) where a is the separation of individual electrons and the cube root of N is the linear scale of of the whole collection of N Tubulin Electrons in the N Tubulins.

As Jack Sarfatti says (here I have substituted some of my numerical values for his): "... Note the volume ... is the sum of the volumes of all [ 10^17 Tubulins involved in the process of consciousness ] even though they are separated in physical space from each other over the whole cortex of volume 10^3 cc - they are like one super-particle entangled in configuration space of [ about 3 x 10^17 dimensions ]! That is, this sentient post-quantum computing "enchanted web" is [ 10^17 little Tubulin nanoboxes ] ... . Each box has a little arrow in Hilbert space and all the arrows are phase-locked over a time of order [ 0.5 milliseconds ]. The actual physical distance between the boxes is irrelevant to this Einstein-Podolsky-Rosen network that is one coherent conscious system. The mesoscopic quantum coherence length L is what you would get if you lined up all these nanoboxes in a row - ... It is really not a metrical property in ordinary space. ...".

Therefore, we have:

E_N = N^2 G m^2 / a N^(1/3) =

= 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

T_N = h / E_N = h / N^(5/3) E_electron =

= N^(-5/3) T_electron =

= N^(-5/3) 10^26 sec


N = (10^26 / (T_N) )^(3/5) =

= 4 x 10^15 / (T_N)^(3/5)


From the above formulas get the following rough approximate Decoherence Tim T_N for various Numbers of Tubulin Dimers or Neurons, if 10% of the Tubulins in each Neuron are involved in the process of consciousness:

            Time                       Number of       Number of
             T_N                        Tubulins        Neurons   
      10^(-43) sec (Planck)         2.5 x 10^41           
  5 x 10^(-4)  sec (2 kHz)                10^17           10^11   
      10^26    sec = 3 x 10^18 years       1                   

The 10^17 tubulin Electron ( 10^11 Neuron ) line of the table corresponds to the number of neurons in the human brain.

Here is a rough outline of what happens during the 0.5 milliseconds of a single conscious thought involving 10^17 Tubulin Electrons:


During that 0.5 milliseconds of the process of a single conscious thought, the 10^17 Tubulin Electrons are linked in a coherent state by gravity.

For such a gravity linkage to take place, two things are necessary:

First, does there exist a realistic mechanism of gravitational connection between all pairs of the 10^17 Tubulin Electrons?

A positive result in an experiment proposed by Raymond Chiao and described in gr-qc/0204012 [ which is an "... abbreviated writeup of ...[his]... March 23, 2002 Wheeler Symposium lecture, and book chapter for Wheeler Festschrift ..." which book chapter is at gr-qc/0208024 and, in its final version, at gr-qc/0303100 ] might provide an affirmative answer. In that paper, Chiao says:

"... Superconductors will be considered as macroscopic quantum gravitational antennas and transducers, which can directly convert upon reflection a beam of quadrupolar electromagnetic radiation into gravitational radiation, and vice versa, and thus serve as practical laboratory sources and receivers of microwave and other radio-frequency gravitational waves. ... a superconductor can by itself be a direct transducer from electromagnetic to gravitational radiation upon reflection of the wave from a vacuum superconductor interface, with a surprisingly good conversion efficiency. By reciprocity, this conversion process can be reversed, so that gravitational radiation can also be converted upon reflection into electromagnetic radiation from the same interface, with equal efficiency. ... under certain circumstances involving "natural impedance matching" between quadrupolar EM and GR plane waves upon a mirror-like reflection at the planar surface of extreme type II, dissipationless superconductors, the efficiency of such superconductors used as simultaneous transducers and antennas for gravitational radiation, might in fact become of the order of unity, so that a gravitational analog of Hertz's experiment might then become possible. ... These developments suggest the possibility of a simple, Hertz-like experiment, in which the emission and the reception of gravitational radiation at microwave frequencies can be implemented by means of a pair of superconductors used as transducers. ... The schematic of this experiment is ...

... we did not detect any observable signal inside the second Faraday cage, down to a limit of more than 70 dB below the microwave power source of around 10 dBm at 12 GHz. ... Note, however, that since the transition temperature of YBCO is 90 K, there may have been a substantial ohmic dissipation of the microwaves due to the remaining normal electrons at our operating temperature of 77 K, so that the EM wave was absorbed before it could reach the impedance-matching depth at z0. It may therefore be necessary to cool the superconductor down very low temperatures before the normal electron component freezes out sufficiently to achieve such impedance matching. [see gr-qc/0304026 ] ... An improved Hertz-like experiment using extreme type II superconductors with extremely low losses, perhaps at millikelvin temperatures, is a much more difficult, but worthwhile, experiment to perform. Such an improved experiment, if successful, would allow us to communicate through the Earth and its oceans, which, like all classical matter, are transparent to GR waves. ... I would especially like to thank my father-in-law, the late Yi-Fan Chiao, for his financial and moral support of this work. This work was partly supported also by the ONR. ...".

Note that the Faraday cages of Chiao's schematic correspond to the Tubulin Cages of the Tubulin Electrons in the Quantum Tubulin Electron model of Quantum Consciousness, and that if Chiao's gravity antenna can receive gravity signals by graviton links, then Tubulin Electrons in their cages should be able to receive gravity signals establishing graviton links, as needed for the Penrose-Hameroff model of Quantum Tubulin Electron Quantum Consciousness.

Note also that the negative result of the preliminary experiment was probably due to failure of the impedance-matching mechanism for converting EM waves to gravity waves [see gr-qc/0304026 ], and therefore not a failure of the gravity antenna concept, which is the important concept with respect to the Quantum Tubulin Electron model of Quanum Consciousness.

Second, is the superposition state of Tubulin Electrons stable with respect to decoherence during to the 0.5 millisecond duration of the single conscious thought?

Max Tegmark, in quant-ph/9907009, says:

"... Penrose has ... suggested that the dynamics of such excitations can make a microtubule act like a quantum computer, and that microtubules are the site of of human consciousness ... This idea has been further elaborated ... with the conclusion that quantum superpositions of coherent excitations can persist for as long as a second before being destroyed by decoherence ... This was hailed as a success for the model, the interpretation being that the quantum gravity effect on microtubules was identified with the human though process on this same timescale. This decoherence rate T = 1 s was computed assuming that quantum gravity is the main decoherence source. Since this quantum gravity model is somewhat controversial ... and its effect has been found to be more than 20 orders of magnitude weaker than other decoherence sources in some cases ... We will now ... evaluate ... decoherence sources for the microtubule case as well, to see whether they are in fact dominant ... we will ignore collisions between polarized tubulin dimers and nearby water molecules, since it has been argued that these may be in some sense ordered and part of the quantum system ... Let us instead apply ... the decoherence timescale
T = ( a^3 sqrt( m k t ) ) / N g q^2 | r' - r |

caused by a single ion a distance a away. ...[ where k is Boltzmann's constant and g = 1 4 pi e0 is the Coulomb constant, m is ion mass, N is number of ions, q is ion charge, and t is temperature ]... with N = Q / qe = 10^3. The distance to the nearest ion will generally be less than ...[ about ] ... 26 nm ... Superpositions spanning many tubuline dimers ... therefore decohere on a timescale ...[about]... 10^(-13) s. due to the nearest ion alone. This is quite a conservative estimate, since the other ... 10^3 ions that are merely a small fraction further away will also contribute to the decoherence rate ... ... We neglected screening effects because the decoherence rates were dominated by the particles closest to the system, i.e., the very same particles that are responsible for screening the charge from more distant ones. ... We find that the decoherence timescales ...[ about 10^(-13) ]... seconds are typically much shorter than the relevant dynamical timescales ...[ about 0.001 to 0.1 seconds ]... both for regular neuron firing and for kink-like polarization excitations in microtubules. This conclusion disagrees with suggestions by Penrose and others that the brain acts as a quantum computer, and that quantum coherence is related to consciousness in a fundamental way. ...".

I disagree with Tegmark, on both experimental and theoretical grounds. I think that Tegmark has ignored significant phenomena related to maintaining coherence during the 0.5 millisecond duration of a single conscious thought involving 10^17 Tubulin Electrons.


On the experimental side, there are some results that indicate that coherence is maintained much longer than would be expected from analyses such as Tegmark's. For example:


On the theoretical side, there are also some reasons that I disagree with Tegmark. For example:

[ To see how Carver Mead's resonance might be applied to the Penrose-Hameroff tubulin electron model of consciousness, consider the maximal case of N tubulin electrons with N = 10^18, each electron having thermal energy E = kT, where k = 10^(-23) Joules Kelvin^(-1) and T = 300 Kelvin, so that Total Thermal Energy = N^2 kT = 10^(36-23) x 300 = 3 x 10^15 Joules. ( Due to the nonlinear square-scaling, it would take less if the collapse took place gradually, a few electrons at a time. ) Note that decoherence by external thermal energy, with square-scaling, is different from the self-decoherence of the superposition state, based on the energy-time uncertainty principle Energy x Time = h, by which a conscious thought quantum state decoheres to form a completed thought. If N tubulin electrons are in a collective superpostion state of conscious thought, then the total energy needed to decohere them by external thermal energy ( decoherence due to the heat of the brain ) is much greater than the classical kinetic heat energy in the brain, so that Quantum Consciousness in the brain is stable against thermal decoherence due to the heat of the brain. ]
... an N-turn closely coupled coil has an inductance L = N^2 Lo. Once again, we see the collective interaction scaling as the square of the number of interacting charges. ... When two classical massive bodies ... are bolted together, the inertia of the resuting composite body is simply the sum of the two individual inertias. The inertia of a collective system, however, is a manifestation of the interaction, and cannot be assigned to the elements separately. ... Thus, it is clear that collective quantum systems do not have a classical correspondence limit. ... It is instructive to work out the magnitude of the electron inertia in a concrete case. A small superconducting magnet has 10^4 turns of NbTi wire approximately 0.1 mm in diameter. The magent is 7 cm long, and just under 5 cm in diameter, and produces a peak field of 7 tesla at a currrent of 40 amperes. The magnet weighs 0.5 kilograms, and has a measured inductance of approximately 0.5 henry. There are of the order of 10^28 electrons per cubic meter in the wire, or 10^20 electrons per meter length of wire, corresponding to approximately 10 coulombs of electronic charge per meter of wire. At 40 amperes, these electrons move at a velcoity v = 4 m / sec. the total length l of wire is about 10^3 meters, so the total electronic charge in the magnet is about 10^4 coulombs. Using these values, A = PHI / l = L I / l = 0.02 V sec / meter. The electromagnetic momentum p of an electron is just this vector potential multiplied by the electronic charge; from this, we can infer an electromagnetic mass m for each electron: q A = 3.2 x 10^(-21) coulomb V sec / meter = m v m = 10^(-21) kg For comparison, the mass of a free electron is approximately 10^(-30) kg, and the rest mass of a proton is a factor 1800 larger than that of an electron. The electromagnetic mass of an electron in our magnet is thus a factor of 10^9 larger than the rest mass of a free electron. ...[ The electromagnetic mass of all the electrons in the magnet is 10^20 electrons / meter x 10^3 meters x 10^(-21) kg / electron = 100 kg ]... The total inertia of the electron system in the magnet is much larger than the actual mass of all the atoms making up the magnet [ 0.5 kg ]. ...".
[ The above material from Carver Mead is directly applicable to the superposition state of tubulin electrons [[ and is related to the idea of a Quantum Protectorate ]]. The following material shows how the same viewpoint applies to understanding quantum state transitions. ]
... We have developed a detailed description of the energy-transfer process between macroscopic quantum resonators ... We are now in a position to understand the radiative transfer between two identical atomic systems. ... The two atoms act like two small dipole resonators, and energy is radiatively transferred ... Once the coupled mixed state starts to develop, it becomes self-reinforcing. ... This self-reinforcing behavior gives the transition its initial exponential character. Once the transition is fully under way, the two states are nearly equally represented in the superposition, and the coupled system closely resembles the coupled resonators ... Once the transition has run its course, each atom settles into its final eigenstate. ...

... there are quantum jumps, but they are not discontinuities. They may look discontinuous because of the nonlinear, self-reinforcing nature of a quantum transition; but at the fundamental level, everything can be followed in a smooth and continuous way .... to arrive at this picture, we had to give up the one-way direction of time, and allow coupling to everything on the light cone ... the Green's function for collective systems is totally free of singularities, and cannot, by its very nature, generate infinities ... There is no action of an elementary charge [ which is fundamentally an amplitude to transmit or absorb energy by radiative transfer ] upon itself ...".


I close this paper with brief summaries of relevant experiments of Grinberg-Zylberbaum, the quantum cosmology of Paula Zizzi, and 26-dimensional closed unoriented bosonic string theory interpreted as a many-worlds quantum theory in which strings correspond to world lines, with massless spin-2 gravitons in 26-dimensions corresponding to gravitational interaction among tubulin electrons in states with Penrose-Hameroff superposition separation.


Grinberg-Zylberbaum Experiments

Some interesting experimental results relevant to Chiao gravity antennas and to Mead resonant coupling were obtained by neurophysiologist Grinberg-Zylberbaum. According a 1997 Science Within Consciousness web article by Henry Swift:

"... The experiment conducted by neurophysiologist Grinberg-Zylberbaum ... The Einstein- Podolsky-Rosen Paradox in the Brain; The Transferred Potential, Physics Essays 7,(4), 1994. ... demonstrate[s] the existence of a macroscopic quantum system in the human brain through the demonstration of ... non-local correlation between brains ... In this experiment two subjects ... meditated together for twenty minutes. A total of seven pairs of subjects of both sexes, with ages from 20-44 years participated in the study. After meditation and while maintaining their "direct communication" (without speech), they were placed in semi-silent, electro-magnetically shielded chambers separated by 45 feet. ... Both subjects were connected to EEG instruments and 100 random flashes of light were presented to subject A, while both remained reclined with semi-closed eyes. Subject B was not told when the light was flashed for subject A, and control correlation checks were also made at random times with no light flashes. The results indicated that, "after a meditative interaction between two people who were instructed to maintain direct communication (i.e. to feel each other's presence even at a distance), in about one out of four cases when one of the subjects was stimulated in such a way that his/her brain responded clearly (with a distinct evoked potential), the brain of the nonstimulated subject also reacted and showed a transferred potential of a similar morphology....

... The striking similarity of the transferred and evoked potentials and the total absence of transferred potentials in the control experiments leave no room for doubt about the existence of an unusual phenomenon, namely, propagation of influence without local signals. ... It is also extremely significant that the occurrence of transferred potential is always associated with the participants' feeling that their interaction is successfully completed (in contrast to the lack of transferred potential, when there is no such feeling). The interaction that correlates the subjects under study is entirely an interaction via non-local consciousness. ... none of the subjects B ever reported realizing any type of conscious experience related to the appearance of the transferred potential ...". According to a 1996 DynaPsych article by Ervin Laszlo: "... A particularly poignant example was furnished by a young couple, deeply in love. Their EEG patterns remained closely synchronized throughout the experiment, testifying to their report of feeling a deep oneness. ... In a limited way, Grinberg-Zylberbaum could also replicate his results. When a subject exhibited the transferred potentials in one experiment, he or she usually exhibited them in subsequent experiments as well. ...".

What has Grinberg-Zylberbaum done since 1994? That is unknown. According to an article by Sam Quinones, in the July/August 1997 New Age Journal, as shown on a Sustained Action web page:

"... In 1977 Grinberg returned to Mexico City ... A deeply spiritual man, Grinberg had moved from houses where he felt bad energy, believed he once had flown, and kept a meditation room lined with books and pictures of gurus. A semi-observant Jew, he sought out great thinkers on the Kabbalah. ... at UNAM ... he ... met the person who, he wrote later, would influence him more than any other: Barbara Guerrero, a former cabaret singer and lottery ticket seller who had fought with Pancho Villa as a young girl. Doña Pachita, as Guerrero was known, was a curandera. ... Pachita could go into a trance state during which the spirit of Cuauhtémoc, the nephew of the great Aztec ruler Moctezuma, occupied her consciousness. ... Grinberg ... believed that experience and perception were created as a result of this interaction, and that the curative powers of shamans and *curanderas* like Pachita came from their ability to gain access to the informational matrix and change it, thereby affecting reality. ... Grinberg designed an experiment . . . using two people instead of one. Both subjects, with electrodes attached to their skulls, were put in a dark room and told to try to achieve a sort of meditative union. After twenty minutes, one was sent to a separate room. The remaining person was stimulated with a series of light flashes or sounds while his or her brain waves were measured. The brain waves of the isolated person were also measured. In 1987 Grinberg recorded for the first time a simultaneous reaction to the stimuli on the part of the isolated, non-stimulated person, a phenomenon he called 'transferred potential.' Over the years, with increasingly sophisticated equipment, he documented transferred potential 25 percent of the time, he wrote. It was a remarkable finding, totally contrary to the tenets of mainstream science. Grinberg believed it supported his theory of a neuronal field connecting all human minds. ... In 1991, Grinberg, his wife, and Tony Karam visited Castaneda at the latter's invitation in Los Angeles. There, Karam says, Castaneda proposed that Grinberg leave his UNAM lab to live in his community. Grinberg declined. Their relationship disintegrated during a trip Castaneda took to Mexico City two years later. Grinberg's friends and family remember him frequently calling Castaneda an egomaniac, more interested in power than truth. They also recall that Tere [Grinberg's wife] remained enamored with Castaneda and his group. ... For Jacobo Grinberg Zylberbaum, 1994 was a pretty good year. ... At his laboratory in the psychology department of the National Autonomous University of Mexico (UNAM) in Mexico City, he recorded the brain waves of a shaman, Don Rodolfo from Veracruz, in a trance state. ... Grinberg's book on his seminal influence, Barbara Guerrero, the blind witch doctor known as Dona Pachita, was finally about to be published in English. ... Then in December, Grinberg missed some appointments with students. Two days before his long-awaited trip to Nepal on December 14, he failed to attend his own birthday party. ... When Grinberg did not return from Nepal as planned, still no one thought much of it. ... But the weeks became months. Calls were made ... Nothing. No record of Grinberg or his wife ... Tere ... even leaving Mexico. ... In the two-and-a-half years since he disappeared, no trace of him, dead or alive, has been found. All that remain are his books, his theories ... The theory for which Grinberg came to be known reflected his personality. Relying on physics and his experiences with witch doctors, or *curanderos*--a bit of Einstein, a bit of Dona Pachita--its essential message was warm and hopeful: All humankind is interconnected. ...".


Zizzi Quantum Cosmology

In gr-qc/0007006, Paola Zizzi says, ( with some editing by me denoted by [ ] ):

"... the vacuum-dominated early inflationary universe ... is a superposed quantum state of qubits. ... the early universe had a conscious experience at the end of inflation, when the superposed quantum state of ... [ 10^18 = N quantum qubits ] ... underwent Objective Reduction. The striking point is that this value of [ N ] equals the number of superposed tubulins-qubits in our brain ... [ in the inflationary phase of our universe ] ... the quantum register grows with time. In fact, at each time step ... [ Tn = (n+1) Tplanck (where Tplanck = 5.3 x 10^(-44) sec) ] ... a Planckian black hole, ( the n=1 qubit state 1 which acts as a creation operator , supplies the quantum register with extra qubits. ... At time Tn = (n+1) Tplanck the quantum gravity register will consist of (n+1)^2 qubits. [ Let N = (n+1)^2 ] ... By the quantum holographic principle, we associate N qubits to the nth de Sitter horizon ... remember that |1> = Had|0> where Had is the Hadamard gate ... the state ... [ of N qubits ] ... can be expressed as ... [ |N> = ( Had|0> )^N ] ... As the time evolution is discrete, the quantum gravity register resembles more a quantum cellular automata than a quantum computer. Moreover, the quantum gravity register has the peculiarity to grow at each time step ( it is self-producing ). If we adopt an atemporal picture, then the early inflationary universe can be interpreted as an ensemble of quantum gravity registers in parallel ... which reminds us of the many-worlds interpretation. ... The superposed state of quantum gravity registers represents the early inflationary universe which is a closed system. Obviously then, the superposed quantum state cannot undergo environmental decoherence. However, we know that at the end of the inflationary epoch, the universe reheated by getting energy from the vacuum, and started to be radiation-dominated becoming a Friedmann universe. This phase transition should correspond to decoherence of the superposed quantum state. The only possible reduction model in this case is self-reduction ... during inflation, gravitational entropy and quantum entropy are mostly equivalent ... Moreover ... The value of the cosmological constant now is ... /\N = 10^(-56) cm^(-2) ... in agreement with inflationary theories. If decoherence of N qubits occurred now, at Tnow = 10^60 Tplanck ( that is, n = 10^60, N = 10^120 ) there would be a maximum gravitational entropy ... [ maximum entropy Smax = N ln2 = 10^120 ] ... In fact, the actual entropy is about ... [ entropy now Snow = 10^101 ] ... [Therefore] decoherence should have occurred for ... [ Ndecoh = 10^(120-101) = 10^19 = 2^64 ] ... which corresponds to ... [ n = 9 and to ] ... the decoherence time ... [ Tdecoh = 10^9 Tplanck = 10(-34) sec ] ...".
Is there a fundamental reason that the number of qubits at which our inflationary universe experiences self-decoherence is Ndecoh = 10^19 = 2^64 ?

From the point of view of the D4-D5-E6-E7-E8 Vodou Physics model, the fundamental structure is the 2^8 = 256-dimensional Cl(8) Clifford algebra, which can be described by 2^8 qubits. Our inflationary universe decoheres when it has Ndecoh = 2^64 qubits. What is special about 2^64 qubits ? 2^64 qubits corresponds to the Clifford algebra Cl(64) = Cl(8x8). By the periodicity-8 theorem of real Clifford algebras that Cl(K8) = Cl(8) x ... tensor product K times ... x Cl(8), we have: Cl(64) = Cl(8x8) = Cl(8) x Cl(8) x Cl(8) x Cl(8) x Cl(8) x Cl(8) x Cl(8) x Cl(8) Therefore, Cl(64) is the first ( lowest dimension ) Clifford algebra at which we can reflexively identify each component Cl(8) with a vector in the Cl(8) vector space. This reflexive identification/reduction causes decoherence. In my opinion, it is the reason that our universe decoheres at N = 2^64 = 10^19, so that inflation ends at age 10^(-34) sec.

Note that Ndecoh = 2^64 = 10^19 qubits is just an order of magnitude larger than the number of tubulins Ntub = 10^18 of the human brain. In my opinion, conscious thought is due to superposition states of those 10^18 tubulins. Since a brain with Ndecoh = 10^19 tubulins would undergo self-decoherence and would therefore not be able to maintain the superposition necessary for thought, it seems that the human brain is about as big as an individual brain can be.


26-dimensional closed unoriented bosonic string theory interpreted as a Many-Worlds Quantum Theory in which strings correspond to World Lines, with massless spin-2 Gravitons in 26-dimensions corresponding to gravitational interaction among Tubulin Electrons in states with Penrose-Hameroff Superposition Separation  
[[ In the D4-D5-E6-E7-E8 VoDou Physics model, closed strings represent the world-lines of fermion particle-antiparticle pairs ( the pair of fermions acting as a boson so that the entire string is bosonic ) from the time of their creation to their eventual mutual annihilation,
  / \   ...
 /   \ /
/     |         (The illustrated closed string is red.
\     |          It interacts with a partially shown gray string.)
 \   / \...
  \ / 
perhaps with lots of interactions with lots of other particles/antiparticles of other world-lines in the meantime, so that part of each string might represent a photon or other particle of any type formed by interaction of one of the particle/antiparticle pair.

Note that since our Universe began with a Big Bang, all its particles originate from pair creation since then. For pairs that do not appear to reconnect for mutual annihilation within the volume of 26-dimensional spacetime being considered in working with the String Theory,

  \    ...   /
   \      \ /
    \      |         (The illustrated string is red.
     \     |          It interacts with a partially shown gray string.
      \   / \...      A perfect absorber in the future  
       \ /            is indicated by ******* ).
the string is closed by considering the 26-dimensional spacetime to be a compactified 25+1 dimensional Minkowski spacetime due to considering the Universe to "... be a perfect absorber in the future ...[as in]... the Wheeler-Feynman ... absorber theory of radiation ..." described by Narlikar in his book Introduction to Cosmology (Cambridge 1997) (Section 8.8.1) and related to the Collective Electrodynamics of Carver Mead. For most of the matter in our Galactic Cluster, such an absorber could be a Black Hole of the Black Hole Era. Such a compactification is also similar to the conformally compactified 3+1 dimensional Minkowski spacetime M# used by Penrose and Rindler in their book Spinors and Space-Time, Volume 2 (Cambridge 1986) (particularly Chapter 9). ]]


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 ...".
This is the decoherence time T = h / E.

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. ...".

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

E = G m^2 / a

In the Osaka paper, 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. ...".

If 26-dimensional closed unoriented bosonic string theory is interpreted as a Many-Worlds Quantum Theory in which strings correspond to World Lines

( see my paper at )

then massless spin-2 Gravitons in 26 dimensions correspond to gravitational interaction among States with Penrose-Hameroff Superposition Separation.


Such massless spin-2 Gravitons in 26 dimensions are described by Joseph Polchinski in his books String Theory vols. I and II( Cambridge 1998) where he says:

"... [In] the simplest case of 26 flat dimensions ... the closed bosonic string ... theory has the maximal 26-dimensional Poincare invariance ... [and] ... is the unique theory with this symmetry ... It is possible to have a consistent theory with only closed strings ... with Guv representing the graviton ...", as to which Green, Schwartz, and Witten, in their book Superstring Theory, vol. 1, p. 181 (Cambridge 1986) say "... the long-wavelength limit of the interactions of the massless modes of the bosonic closed string ... [which] ... can be put in the form
INTEGRAL d^26 x sqrt(g) R

...[of 26-dimensional general relativistic Einstein Gravitation]...".


A nice description of how such Gravitons propagate in the 26 dimensions is given by Stephen Hawking in his book The Universe in a Nutshell (Bantam 2001). To see how Hawking's description of gravity in 26 dimensions might be applied to the Penrose-Hameroff tubulin electron model of consciousness, first assume the validity of the interpretation of 26-dimensional bosonic string theory as a Many-Worlds Quantum Theory in which strings correspond to World Lines. However, Hawking speaks of branes rather than individual particle world lines. From the viewpoint of this paper, such branes should be regarded as 4-dimensional physical spacetime neighborhoods of individual particles. Timelike parts of such branes should be described in terms of 27-dimensional M-theory, and spacelike parts of such branes should be described in terms of 28-dimensional F-theory ( for more about such M-theory and F-theory, see my paper at ). In his book, Hawking says:

"... Large extra dimensions ... would imply that we live in a brane world, a four-dimensional surface or brane in a higher-dimensional spacetime. Matter and nongravitational forces would be confined to the brane. ... On the other hand, gravity ... would permeate the whole bulk of the higher-dimensional spacetime ... because gravity would spread out in the extra dimensions, it ... would fall off faster with distance than it would in four dimensions. ... If this more rapid falloff of the gravitational force extended to astronomical distances, we would have noticed its effect ... However, this would not happen if the extra dimensions ended on another brane not far away from the brane on which we live. ...

[ Note that in the Penrose-Hameroff model the superposition separation of two individual states in the superposition states of a single tubulin electron is of the order of a nanometer. ]

... A second brane near our brane would prevent gravity from spreading far into the extra dimensions and would mean that at distances greater than the brane separation, gravity would fall off at the rate one would expect for four dimensions. ...

... On the other hand, for distances less than the separation of the branes, gravity would vary more rapidly. The very small gravitational force between heavy objects has been measured accurately in the lab but the experiments so far would not have detected the effects of branes separated by less than a few millimeters. ...".

 Note added 18 July 2005:

Lubos Motl said in his blog post Deviations from Newton's law seen? at dated 6 June 2005:

"... Eric Adelberger et al. ... University of Washington ... seems to have detected deviations from Newton's gravitational law at distances slightly below 100 microns at the "4 sigma" confidence level. ... Their measured force at these multimicron distances is weaker than expected from Newton's formula. ... Note that 100 microns is also the scale of the vacuum energy - the cosmological constant. In other words, "1/(100 microns)^4" equals the energy density of the observed vacuum energy. ...". I commented: "... If gravitational attraction does appear to decrease at distances closer than 100 microns = 10^(-2) cm = 10^31 Planck Lengths (Lp) and if that distance to the 4th power, or 10^124 Lp^4, is taken to be equivalent to the cosmological constant energy density and if the cosmological constant is seen as dark energy that causes large-scale expansion of our universe then could it be that when your experimental system is within a volume corresponding to ... the cosmological constant energy density the dark energy "force" becomes effectively a repulsive force that cancels some of the ordinary gravitational attraction and therefore makes gravity appear to be weaker at distances less than 10^31 Lp ? In other words, the dark energy "force" may be something that manifests itself only on large scales (expansion of the universe) and on small scales (at or below the scale of its energy density). ...".