From Towards a Science of Consciousness 3         Section 7: Physical Reality and Consciousness       CogNet Proceedings


Quantum Monadology

Kunio Yasue


Penrose's Platonic stance


Roger Penrose has taken unusual and, in some circles, unpopular and disputed positions in relation to the question of consciousness. Within physics the disputes are reminiscent of long-standing arguments regarding the role of the conscious observer taken by John von Neumann and Eugene Wigner, but the current Penrose-generated disagreement seems even more intense.

Reasons for strenuous opposition from computer scientists, philosophers and some mathematicians to Penrose's view seem clear. He claims first of all that our understanding of the characteristic features of natural numbers comes not from computational rules but through contact with a Platonic world. He arrives at this conclusion by complete use of Gödel's theorem to argue for noncomputational effects in human understanding (eliciting strong criticism from many computer scientists investigating artificial intelligence and artificial life). Penrose and some other mathematicians believe that truly beautiful findings come only after a "visit" to the Platonic world of mathematical reality. However it may be that only a select few mathematicians and theoretical physicists are able to have such a highly irregular experience as visiting the Platonic world. A natural consequence of this might be that most mathematicians and physicists cannot understand Penrose's Platonic position (Penrose 1989, 1994). Despite the soundness of his writings, opponents attack him by forcing a conventional materialistic world view of physical reality.

According to Penrose, Gödel's theorem implies that not only mathematical understanding but also human musical, artistic, and aesthetic creativity and appreciation come from contact with the Platonic world of reality. The conventional and common experience of many scientists implies that human creative power emerges from highly sophisticated but certainly materialistic processes taking place in brain tissue. Unable to follow Penrose's experience in mathematical discovery, they disregard his Platonic world view and focus counter arguments against his claim that consciousness is of noncomputational nature as suggested by Gödel's argument. The ghost of the dispute between Turing and Gödel has thus re-emerged.

Of course, Gödel's argument may imply that this dispute cannot be resolved by a sequence of exchanges of seemingly correct discussions. Therefore, it may be hopeless to determine whether consciousness is of noncomputational or computational nature. Therefore I will concentrate my contribution on Penrose's second claim, which irritates not computer scientists, philosophers, and mathematicians, but physicists and neurobiologists.

Quantum Coherence


Penrose's second claim is a potential solution to the "binding problem" of how disparate features are bound into unitary mental objects: "Coordination of sole mind can be realized by a certain quantum coherence extended over the whole brain." This potential solution to the binding problem came secondary to Penrose's claim that certain quantum mechanical systems occur inside and among neurons. His original motivation for proposing quantum coherence was to enable noncomputational phenomena such as objective reduction in the brain, thought necessary to interface to the Platonic world. Penrose concluded that objective reduction, or self-collapse of a superposed quantum state by a quantum gravity mechanism could be the only fundamental process in physics of a noncomputational, nondeterministic nature. This led to further suggestions with Stuart Hameroff that objective reduction may be occurring in microtubules inside the brain's neurons.

For Penrose's objective reduction to occur, a critical amount of mass must maintain an entangled superposition (separation from itself) for a critical time. In the brain the necessary entanglement (which could also support quantum computation) must cover a macroscopic volume and would essentially solve the binding problem as well. A superposed state of a quantum system of many degrees of freedom is known to result in a nonlocal interconnection over a long distance, and it was natural that Penrose and his supporters interpreted this quantum nonlocal interconnection (calling it quantum coherence) as the key to reaching brain-wide objective reduction and solve the binding problem. Furthermore, recent interests in quantum information and quantum computing has increased the potential utility of macroscopic quantum state/quantum coherence in future technological devices.

As long as quantum coherence is maintained, that is, as long as the quantum system in question is kept in a superposed quantum state, time development of the quantum state is given in a deterministic but parallel way, thus providing super-parallel computing called quantum computing. However, there is a delicate point in the use of such a quantum computer in that the final result of quantum computation cannot be read in a deterministic way but only in an indeterministic way thanks to the quantum reduction. Reduction incorporates either randomness (in the case of environmental decoherence) or noncomputability (according to Penrose, if the reduction is a self-collapse owing to his quantum gravity mechanism). Pragmatic scientists have begun to do quantum computation with clever techniques to perform the same quantum computation several times, gathering only the seemingly correct results and putting unexpected results into the trash. By so doing, quantum computing gives an exponentially fast parallel computing architecture with great utility, expected to be the next generation of electronic computers.

Yes, it's a computer. But remember Penrose's first claim: It's a computer because it dumped all the potential noncomputational results realized by the quantum reduction into the trash. Then, where is the potential manifestation of consciousness? Absolutely, it's in the trash. (So if you want to make your billion dollar quantum computer conscious, upset the trash. If not, keep the trash classified. Then, the truth will not be out there.)

Penrose's second claim of brain-wide macroscopic quantum states is very appealing. However use of the concept of quantum coherence-maintenance of the superposed quantum state as a potential solution to the binding problem-is troublesome. Many physicists are uneasy about the stability and maintenance of the superposed quantum state in the highly interactive physical environment of the brain at body temperature. Applying standard quantum statistical mechanics to the microscopic constituents of brain cells, it would seem that superposed quantum states would all disintegrate into mixed quantum states, with no chance for quantum coherence extending over macroscopic regions of brain tissue.

Penrose refers to Fröhlich's theory of coherent quantum vibrations of biomolecules in living cells to provide a possibility of high temperature superconducting phenomena in the brain. At first glance the network of Fröhlich's coherent quantum vibrations may extend the quantum coherence over a considerable number of brain cells or the whole brain, but the chance of realizing such a quantum coherence highly dependent on underlying molecular structures seems extremely small.

Some advocates of a quantum approach claim that so-called Bose-Einstein condensation of some quanta of the material constituents of the brain may take place at body temperature without specifying the constituents and without experimental evidence. This is unacceptable from the point of view of modern physics. The critical temperature Tcis the limiting temperature below which the condensation of the Bose quanta (i.e., boson condensation) can be maintained. The standard calculation gives:

Tc ~ m-1

The critical temperature is inversely proportional to the mass m of the Bose quantum (i.e., boson) taking part in the boson condensation. Typical superconducting phenomena owing to boson condensation of pairs of electrons (i.e., Cooper pairs) in a metal have extremely low critical temperatures. Even for the very small mass of the Cooper pair of electrons, we have a low critical temperature. For other constituent quanta of matter far heavier than the electron, we have even lower critical temperatures, thus eliminating the possibility of body temperature Bose-Einstein condensation in brain tissue.

So referring back to Penrose's "Coordination of sole mind can be realized by a certain quantum coherence extended over the whole brain" we can see two apparent defects: 1) the concept of quantum coherence carried by the superposed quantum state cannot be maintained in brain matter, 2) the concept of quantum coherence carried by the so-called Bose-Einstein condensation of constituent quanta brain tissue cannot be realized at body temperature. Can there be large scale quantum coherence in the brain?

Quantum field theory


For brain-wide quantum states we must progress from quantum mechanics, and go one step further into modern quantum field theory (QFT)-the most fundamental theory of physics at both the microscopic scale and the macroscopic scale. QFT was systematized by a Japanese physicist Umezawa who lived lifelong in Italy, the United States and Canada. Umezawa sowed the seeds of quantum field theoretical methods in Europe and North America after Yukawa received his Nobel prize for the first use of quantum field theory (originally discovered by Heisenberg and Pauli) to predict the existence of a new elementary particle called today a meson. Beginning in the 1960s Umezawa developed the theoretical framework of quantum field theory to describe fundamental processes in macroscopic living matter with Italian colleagues. Thus today there are many brilliant Italian physicists in this field of research including Giuseppe Vitiello and Emilio Del Giudice.

In the 1970s Umezawa developed a standard field theoretical model of memory mechanism in the brain with the help of another Japanese physicist Takahashi, famous for the Ward-Takahashi identity, which is the central fundamental equation of modern quantum field theory (Takahashi and Umezawa 1978, 1979). In the 1990s this Umezawa-Takahashi model has been formalized by Mari Jibu and her colleagues (Jibu et al. 1994, Jibu and Yasue 1995, Jibu, Pribram, and Yasue 1996) into a concrete theory related to consciousness called quantum brain dynamics. Italian colleagues of Umezawa also developed a general quantum field theoretical framework to describe fundamental processes of biological cells called quantum biodynamics (Del Giudice et al. 1983, Del Giudice, Preparata, and Vitiello 1988).

Quantum field theory (QFT) applied to the brain (quantum brain dynamics-QBD) may back up Roger Penrose's second claim of a unitary brain-wide quantum state. A sophisticated but concrete version of quantum brain dynamics has been developed by Charles Enz (1997), the last coworker of Wolfgang Pauli and my supervisor in Switzerland.

Quantum brain dynamics


Let us sketch the quantum field theoretical (QFT) approach to the brain and consciousness (i.e., quantum brain dynamics-QBD) along lines taken by Umezawa, Takahashi, Vitiello, Del Giudice, Enz, and Jibu. From physicists' eyes, the brain confined within the cranium is a coupled matter-radiation system composed of many atomic constituents and their radiation field, specifically the electromagnetic field. Quantum field theory of electromagnetic field tells us that matter made of atomic constituents can be described as the spatial distribution of quantum electric dipoles in a spatial region, that is, a quantum electric dipole field. Then we see the brain as a quantum electric dipole field coupled with electromagnetic field!

Of course biologists see the brain as a structured mass of brain cells manifesting sophisticated but systematized biomolecular architectures. They see membranes, proteins, cytoskeletons, nuclei, organelles, water, ions, glia, and so on. Here I am saying the brain is a quantum electric dipole field and biologists are wondering: Where are biomolecular structures? Do not worry. They are in the quantum electric dipole field, represented by singularities, topological defects, local symmetries and localizations of the field. Biomolecular architecture provides geometric objects emerging in the quantum electric dipole field. Actual brain tissue can be seen as the quantum electric dipole field equipped with the highly systematized geometric objects manifesting various local symmetries and breaking global symmetries, that is, breaking uniformity of the field.

Umezawa and his colleagues incorporated into modern quantum field theory the capability of dealing with quantum electric dipole fields coupled with electromagnetic fields and manifesting various geometric objects (Wadati, Matsumoto and Umezawa 1978a,1978b; Umezawa 1993). The physical interaction of the brain's quantum electric dipole field to the environment through neural processes create or change the geometric objects, thus the physical interaction can be understood to be stored as memory (Jibu and Yasue 1995). In other words, memory is stored in the specific biomolecular architectures of membranes, cytoskeletons, and water of the structured mass of brain cells which have a corresponding asymmetric quantum field.

At this point quantum brain dynamics seems not so radical, giving a very standard understanding of memory storing mechanism (expressed in terms of quantum fields). But what about memory retrieval, and coming to the central question, what about consciousness? I stand on the elegant words of Miguel de Unamuno: "We live in memory and by memory, and our spiritual life is at bottom simply the effort of our memory to persist, to transform itself into hope into our future."

Umezawa and Takahashi provided us with quite an interesting physical process for memory retrieval in terms of general quantum field theoretical concepts (Stuart, Takahashi and Umezawa 1978, 1979): As long as memory is maintained in the form of geometric objects of the quantum electric dipole field, new quanta called Nambu-Goldstone bosons emerge from geometric objects triggered by arbitrarily small incoming energy. Emergence of Nambu-Goldstone bosons is memory retrieval. Then what is consciousness? It should be some kind of physical entity in the brain taking in those Nambu-Goldstone bosons. What could that be?

There is a well known QFT concept called the Higgs mechanism, famous today for its principal role in the standard gauge field theory of elementary particles (Umezawa 1993). It tells us that for a quantum electric dipole field with geometric objects coupled with electromagnetic field (e.g., the case for quantum brain dynamics) Nambu-Goldstone bosons are all taken into the longitudinal mode of the electromagnetic field. It other words, Nambu-Goldstone bosons are transformed into quanta of electromagnetic field: photons. However these are very specialized photons in the sense that they have nonzero mass and do not propagate and remain nearby the geometric objects.

In physics, such a nonpropagating photon of the electromagnetic field is called a tunneling photon or evanescent photon;we may therefore call photons surrounding the geometric objects of biomolecular architecture "biological tunneling photons." A standard calculation shows that the mass of this biological tunneling photon is about 10 electron-volts, which is far smaller than the mass of an electron (Del Giudice et al. 1983).

Extremely smaller than the electron mass?! Remember that the critical temperature for boson condensation is inversely proportional to boson mass. Because of this, the critical temperature for boson condensation of biological tunneling photons of mass about 10 electron-volts turns out to be actually higher than body temperature (Jibu, Pribram and Yasue 1996).

Memory retrieval in terms of Nambu-Goldstone bosons can emerge from the biomolecular architecture of geometric objects of the brain's quantum electric dipole field net. . So modern quantum field theory indicates that boson condensation of biological tunneling photons can occur at body temperature. Thanks to Umezawa and Takahashi, as well as Miguel de Unamuno, it seems plausible that the physical correlate of conscious mind might be this boson condensation of tunneling photons manifesting quantum coherence throughout the entire brain.

The "hard problem" of conscious experience and frontier physics


Thus far I have shown that central concepts in modern condensed matter physics within the realm of quantum field theory can account for Penrose's second claim of "binding" via brain-wide quantum coherence that cannot be accounted for by "simple minded" quantum mechanics. So quantum brain dynamics may solve this "easy problem" of consciousness. Our theoretical framework starting from first principles of modern physics allows QFT to reveal the existence of body temperature macroscopic-scale boson condensation of biological tunneling photons manifesting long distance quantum coherence over the whole brain. We regard the quantum dynamics of this boson condensation of biological tunneling photons as a physical substrate of consciousness; memory retrieval in terms of Nambu-Goldstone bosons is shown in terms of the dynamics of biological tunneling photons. Consciousness can be understood as an emergent property of memory.

However it is also true that such an approach cannot solve the "hard problem" of consciousness (Chalmers 1996). As pointed out by David Chalmers and Mari Jibu (1998), the problem of conscious experience is the conceptual limit of the scientific framework based on modern physics. The fundamental concepts and formulations of physics must be extended to solve the hard problem. Penrose's first claim seems to suggest a possible direction. Indeed, he proposed a new space-time framework of fundamental physics called spin networksin which not only conventional physical and geometric objects but also protoconscious objects such as qualia can be implemented as underlying mathematical objects. In a sense, he developed a universal mathematical framework simultaneously representing the materialistic world of physical reality and the Platonic world of mathematical reality.

Conceptual extension of fundamental physics is not the normal subject of daily physics in which most physicists are involved, but the subject of "frontier physics." People outside physics research like to hear about frontier physics such as superstrings, blackhole evaporation, Schrödinger's cat, quantum teleportation, quantum time tunnel, however most physicists including myself work toward a common understanding of natural phenomena in terms of daily physics. Thus the QFT/QBD approach taken by Umezawa, Takahashi, Vitiello, Del Giudice, Enz, and Jibu and myself remains concrete but not as sensational as Penrose's approach. The former remain in daily physics, but the latter penetrates into frontier physics. Perhaps Chalmers and Jibu are correct in that the hard problem of conscious experience can be solved only through frontier physics such as Penrose's theory of spin networks. Referring back to Penrose's first claim regarding the Platonic world view, I now embrace the theory of quantum monadology (Nakagomi 1992), which may solve not only the easy problem but also the hard problem of conscious experience from frontier physics. The Platonic world view may well be implemented in the conceptual structure of quantum monads more naturally than in spin networks.

Theory of quantum monadology


Monadology is a famous philosophical framework and attractive world view developed by Gottfried Leibniz in the eighteenth century in which fundamental elements of the world are called monads. A monad was proposed to occupy the center of human mind, and Leibniz's monadology was aimed at the underlying harmonic order among men, society, nature, and the existence of the God. Whitehead (1929) described dynamic monads with psychological being: "occasions of experience." In its original form monadology was too naive to account for human nature and consciousness. However the formal structure of monadology can be implemented in modern frontier physics to give a very simple but attractive conceptual foundation called quantum monadology (Nakagomi 1992). Quantum monadology may be capable of unifying quantum theory and relativity theory, solving the measurement problem in quantum mechanics, deriving and understanding the concept of time, understanding" now," solving the problem of free will, and solving the mind-body problem.

I will briefly describe quantum monadology here; those who want to see the complete picture are invited to read the original paper by Teruaki Nakagomi (1992). For simplicity and brevity I will use minimal mathematical formulation.

In quantum monadology the world is made of a finite number, say M, of quantum algebras called monads.There are no other elements making up the world, and so the world itself can be defined as the totality of M monads; W = .,A1,A2,...,AM.". The world Wis not space-time as is generally assumed in the conventional framework of physics; space-time does not exist at the fundamental level, but emerges from mutual relations among monads. This can be seen by regarding each monad Aias a quantum algebra and the world W = .,A1,A2,...,AM.." as an algebraically structured set of the quantum algebras called a tensor product of Mmonads. The mathematical structure of each quantum algebra representing each monad will be understood to represent the inner world of each monad. Correspondingly, the mathematical structure of the tensor product of Mmonads will be understood to represent the world Witself. To make the mathematical representation of the world of monads simpler, we assume each quantum algebra representing each monad to be a C* algebra A identical with each other, that is, Ai = A for all irunning from 1 to M. Then, the world can be seen as a C* algebra W identical with the Mth tensor power of the C* algebra A.

It is interesting to notice that the world itself can be represented as the structured totality of the inner worlds of M monads. A positive linear functional defined on a C* algebra is called a state. The value of the state (i.e., positive linear functional) for an element of the C* algebra is called an expectation value. Any state of the C* algebra of the world W is said to be a world state, and any state of the C* algebra of each monad A is said to be an individual state. As the world state is a state of the worldW, it can be seen as the tensor power of the individual state. In addition to the individual state, each monad has an image of the world state recognized by itself; it is a world state belonging to each monad.

The world states belonging to any two monads are mutually related in such a way that the world state belonging to the i-th monad can be transformed into that belonging to the j-th monad by a unitary representation of the Lorentz group or the Poincaré group. Identifying the world state belonging to each monad with the world recognized by the monad, the conventional representation of the world as a four dimensional space-time manifold can be derived from the above mutual relation in terms of the Lorentz or Poincaré group. Thus the idealistic concept of the unlimited expansion of space-time geometry in conventional physics is shown to be an imaginary common background for overlapping the world image recognized by every monad.

Each monad has a mutually synchronized clock counting a common clock period, and each monad has a freedom (free will) to choose a new group element g of the Lorentz or Poincaré group G independently with the choice of other monads. If a monad in the world happens to choose a new group element g in G after a single clock period, then the world state belonging to this monad changes in accordance with the unitary transformation representing the chosen group element and the jump transformation representing the quantum reduction of the world state. The world states belonging to other monads also suffer from the change in accordance with the unitary transformation representing the mutual relation between the world state belonging to this monad and the world states belonging to other monads.

For each monad, say the j-th monad, the tendency to make a choice of a new group element g in G after a single clock period is proportional to a universal constant c and the expectation value of the jump transformation with respect to the world state belonging to the j-th monad. Such a change of the world states belonging to all the monads induces the actual time flow, and the freedom to choose the group element is understood as the fundamental element of mind; thus the origin of free will can be identified here. Although I cannot here fully explain Nakagomi's theory of quantum monadology, I want to emphasize that quantum monadology may be the only fundamental framework of frontier physics that can visualize not only the materialistic world of physical reality but also the Platonic world of mathematical and philosophical reality.

Conclusion


To develop a science of consciousness we need 1) an understanding of how a Platonic world could actually exist in frontier physics, as well as 2) a concrete formulation in condensed matter physics of how states may occur in the brain and interact with the Platonic world. To approach the Platonic world, one philosophical avenue involves Leibniz "monads," fundamental pockets of reality. Application of quantum field theory to Leibniz (and Whitehead) suggests quantum monadology in which quantum algebras define spacetime volumes with various properties. Such an approach may form a bridge among philosophical explanations for consciousness, the predictions of Roger Penrose, and the brain.

References


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Whitehead (1929)