Quantum Approaches Review to
Quantum Brain
(Quantum Science and Technology)
Quantum Physicist and Brain Scientist
Visiting Professor of Quantum Physics, California Institute of Technology
IEEE-USA Fellow
Ph.D. & Dr. Kazusho Kamuro
AERI：Artificial EvolutionResearch Institute
Pasadena, California
HP: https://www.aeri-japan.com/
・In this section, some popular approaches for applying quantum theory to brain states will be surveyed and compared, most of them speculative, with varying degrees of elaboration and viability. Section1: Neurophysiological Levels of Description addresses three different neurophysiological levels of description, to which particular quantum approaches refer. Subsequently, the individual approaches themselves will be discussed — Section2: Stapp, Section3: Vitiello and Freeman, Section 3.4: Beck and Eccles, Section 3.5: Penrose and Hameroff.
・In the following, (some of) the better known and partly worked out approaches that use concepts of quantum theory for inquiries into the nature of consciousness will be presented and discussed. For this purpose, the philosophical distinctions A/B (Section2) and the neurophysiological distinctions addressed in Section1 will serve as guidelines to classify the respective quantum approaches in a systematic way. However, some preliminary qualifications concerning different ways to use quantum theory are in order.
・There are quite a number of accounts discussing quantum theory in relation to consciousness that adopt basic ideas of quantum theory in a purely metaphorical manner. Quantum theoretical terms such as entanglement, superposition, collapse, complementarity, and others are used without specific reference to how they are defined precisely and how they are applicable to specific situations. For instance, conscious acts are just postulated to be interpretable somehow analogously to physical acts of measurement, or correlations in psychological systems are just postulated to be interpretable somehow analogously to physical entanglement. Such accounts may provide fascinating science fiction, and they may even be important to inspire nuclei of ideas to be worked out in detail. But unless such detailed work leads beyond vague metaphors and analogies, they do not yet represent scientific progress. Approaches falling into this category will not be discussed in this contribution.
・A second category includes approaches that use the status quo of present-day quantum theory to describe neurophysiological and/or neuropsychological processes. Among these approaches, the one with the longest history was initiated by von Neumann in the 1930s, later taken up by Wigner, and currently championed by Stapp. It can be roughly characterized as the proposal to consider intentional conscious acts as intrinsically correlated with physical state reductions. Another fairly early idea dating back to Ricciardi and Umezawa in the 1960s is to treat mental states, particularly memory states, in terms of vacuum states of quantum fields. A prominent proponent of this approach at present is Vitiello. Finally, there is the idea suggested by Beck and Eccles in the 1990s, according to which quantum mechanical processes, relevant for the description of exocytosis at the synaptic cleft, can be influenced by mental intentions.
・The third category refers to further developments or generalizations of present-day quantum theory. An obvious candidate in this respect is the proposal by Penrose to relate elementary conscious acts to gravitation-induced reductions of quantum states. Ultimately, this requires the framework of a future theory of quantum gravity which is far from having been developed. Together with Penrose, Hameroff has argued that microtubuli might be the right place to look for such state reductions.
Section1： Neurophysiological Levels of Description
・A mental system can be in many different conscious, intentional, phenomenal mental states. In a hypothetical state space, a sequence of such states forms a trajectory representing what is often called the stream of consciousness. Since different subsets of the state space are typically associated with different stability properties, a mental state can be assumed to be more or less stable, depending on its position in the state space. Stable states are distinguished by a residence time at that position longer than that of metastable or unstable states. If a mental state is stable with respect to perturbations, it “activates” a mental representation encoding a content that is consciously perceived.
1．1 Neural Assemblies
・Moving from this purely psychological, or cognitive, description to its neurophysiological counterpart leads us to the question: What is the neural correlate of a mental representation? According to standard accounts (cf. Noë and Thompson (2004) for discussion), mental representations are correlated with the activity of neuronal assemblies, i.e., ensembles of several thousands of coupled neurons. The neural correlate of a mental representation can be characterized by the fact that the connectivities, or couplings, among those neurons form an assembly confined with respect to its environment, to which connectivities are weaker than within the assembly. The neural correlate of a mental representation is activated if the neurons forming the assembly operate more actively, e.g., produce higher firing rates, than in their default mode.
Figure 1. Balance between inhibitory and excitatory connections among neurons.
・In order to achieve a stable operation of an activated neuronal assembly, there must be a subtle balance between inhibitory and excitatory connections among neurons (cf. Figure 1). If the transfer function of individual neurons is strictly monotonic, i.e., increasing input leads to increasing output, assemblies are difficult to stabilize. For this reason, results establishing a non-monotonic transfer function with a maximal output at intermediate input are of high significance for the modeling of neuronal assemblies (Kuhn et al. 2004). For instance, network models using lattices of coupled maps with quadratic maximum (Kaneko and Tsuda 2000) are paradigmatic examples of such behavior. These and other familiar models of neuronal assemblies (for an overview see Anderson and Rosenfeld 1988) are mostly formulated in a way not invoking well-defined elements of quantum theory. An explicit exception is the approach by Umezawa, Vitiello and others (see Section 3).
1．2 Single Neurons and Synapses
・The fact that neuronal assemblies are mostly described in terms of classical behavior does not rule out that classically undescribable quantum effects may be significant if one focuses on individual constituents of assemblies, i.e., single neurons or interfaces between them. These interfaces, through which the signals between neurons propagate, are called synapses. There are electrical and chemical synapses, depending on whether they transmit a signal electrically or chemically.
・At electrical synapses, the current generated by the action potential at the presynaptic neuron flows directly into the postsynaptic cell, which is physically connected to the presynaptic terminal by a so-called gap junction. At chemical synapses, there is a cleft between pre- and postsynaptic cell. In order to propagate a signal, a chemical transmitter (glutamate) is released at the presynaptic terminal. This release process is called exocytosis. The transmitter diffuses across the synaptic cleft and binds to receptors at the postsynaptic membrane, thus opening an ion channel (see Figure 2). Chemical transmission is slower than electric transmission.
Figure 2. Release of neurotransmitters at the synaptic cleft (exocytosis).
・A model developed by Beck and Eccles applies concrete quantum mechanical features to describe details of the process of exocytosis. Their model proposes that quantum processes are relevant for exocytosis and, moreover, are tightly related to states of consciousness. This will be discussed in more detail in Section 4.
・At this point, another approach developed by Flohr (2000) should be mentioned, for which chemical synapses with a specific type of receptors, so-called NMDA receptors are of paramount significance. Briefly, Flohr observes that the specific plasticity of NMDA receptors is a necessary condition for the formation of extended stable neuronal assemblies correlated to (higher-order) mental representations which he identifies with conscious states. Moreover, he indicates a number of mechanisms caused by anaesthetic agents, which block NMDA receptors and consequently lead to a loss of consciousness. Flohr’s approach is physicalistic and reductive, and it is entirely independent of any specific quantum ideas.
1．3 Microtubuli
・The lowest neurophysiological level, at which quantum processes have been proposed as a correlate to consciousness, is the level at which the interior of single neurons is considered: their cytoskeleton. It consists of protein networks essentially made up of two kinds of structures, neurofilaments and microtubuli (Figure 3, left), which are essential for various transport processes within neurons (as well as other cells). Microtubuli are long polymers usually constructed of 13 longitudinal α and β-tubulin dimers arranged in a tubular array with an outside diameter of about 25 nm (Figure 3, right). For more details see Kandel et al. (2000), Chap. II.4.
Figure 3. (left) microtubuli and neurofilaments, the width of the figure corresponds to approximately 700nm; (right) tubulin dimers, consisting of α- and β-monomers, constituting a microtubule.
・The tubulins in microtubuli are the substrate which, in Hameroff’s proposal, is used to embed Penrose’s theoretical framework neurophysiologically. As will be discussed in more detail in Section 5, tubulin states are assumed to depend on quantum events, so that quantum coherence among different tubulins is possible. Further, a crucial thesis in the scenario of Penrose and Hameroff is that the (gravitation-induced) collapse of such coherent tubulin states corresponds to elementary acts of consciousness.
Section 2： Stapp （Quantum State Reductions and Conscious Acts）
・The act of measurement is a crucial aspect in the framework of quantum theory, that has been the subject of controversy for more than eight decades now. In his monograph on the mathematical foundations of quantum mechanics, von Neumann (1955, Chap. V.1) introduced, in an ad hoc manner, the projection postulate as a mathematical tool for describing measurement in terms of a discontinuous, non-causal, instantaneous (irreversible) act given by (1) the transition of a quantum state to an eigenstate bj of the measured observable B (with a certain probability). This transition is often called the collapse or reduction of the wavefunction, as opposed to (2) the continuous, unitary (reversible) evolution of a system according to the Schrödinger equation.
・In Chapter VI, von Neumann (1955) discussed the conceptual distinction between observed and observing system. In this context, he applied (1) and (2) to the general situation of a measured object system (I), a measuring instrument (II), and (the brain of) a human observer (III). His conclusion was that it makes no difference for the result of measurements on (I) whether the boundary between observed and observing system is posited between I and (II & III) or between (I & II) and III. As a consequence, it is inessential whether a detector or the human brain is ultimately referred to as the “observer”.
・By contrast to von Neumann’s fairly cautious stance, London and Bauer (1939) went further and proposed that it is indeed human consciousness which completes the quantum measurement process (see Jammer (1974, Sec. 11.3 or Shimony (1963) for a detailed account). In this way, they attributed a crucial role to consciousness in understanding quantum measurement in terms of an update of the observer’s knowledge. In the 1960s, Wigner (1967) radicalized this proposal, by suggesting an impact of consciousness on the physical state of the measured system, not only an impact on observer knowledge. In order to describe measurement as a real dynamical process generating irreversible facts, Wigner called for some nonlinear modification of (2) to replace von Neumann’s projection (1).
・Since the 1980s, Stapp has developed his own point of view on the background of von Neumann and Wigner. In particular, he tries to understand specific features of consciousness in relation to quantum theory. Inspired by von Neumann, Stapp uses the freedom to place the interface between observed and observing system and locates it in the observer’s brain. He does not suggest any formal modifications to present-day quantum theory (in particular, he stays essentially within the “orthodox” Hilbert space representation), but adds major interpretational extensions, in particular with respect to a detailed ontological framework.
・In his earlier work, Stapp (1993) started with Heisenberg’s distinction between the potential and the actual (Heisenberg 1958), thereby taking a decisive step beyond the operational Copenhagen interpretation of quantum mechanics. While Heisenberg’s notion of the actual is related to a measured event in the sense of the Copenhagen interpretation, his notion of the potential, of a tendency, relates to the situation before measurement, which expresses the idea of a reality independent of measurement.
・Immediately after its actualization, each event holds the tendency for the impending actualization of another, subsequent actual event. Therefore, events are by definition ambiguous. With respect to their actualized aspect, Stapp’s essential move is to “attach to each Heisenberg actual event an experiential aspect. The latter is called the feel of this event, and it can be considered to be the aspect of the actual event that gives it its status as an intrinsic actuality” (Stapp 1993, p. 149).
・With respect to their tendency aspect, it is tempting to understand events in terms of scheme (B) of Section 2. This is related to Whitehead’s ontology, in which mental and physical poles of so-called “actual occasions” are considered as psychological and physical aspects of reality. The potential antecedents of actual occasions are psychophysically neutral and refer to a mode of existence at which mind and matter are unseparated. This is expressed, for instance, by Stapp’s notion of a “hybrid ontology” with “both idea-like and matter-like qualities” (Stapp 1999, 159). Similarities with a dual-aspect approach (B) are evident.
・In an interview of 2006, Stapp (2006) specifies some ontological features of his approach with respect to Whitehead’s process thinking, where actual occasions rather than matter or mind are fundamental elements of reality. They are conceived as based on a processual rather than a substantial ontology (see the entry on process philosophy). Stapp relates the fundamentally processual nature of actual occasions to both the physical act of state reduction and the correlated psychological intentional act.
・Another significant aspect of his approach is the possibility that “conscious intentions of a human being can influence the activities of his brain” (Stapp 1999, p. 153). Different from the possibly misleading notion of a direct interaction, suggesting an interpretation in terms of scheme (A) of Section 2, he describes this feature in a more subtle manner. The requirement that the mental and material outcomes of an actual occasion must match, i.e. be correlated, acts as a constraint on the way in which these outcomes are formed within the actual occasion (cf. Stapp 2006). The notion of interaction is thus replaced by the notion of a constraint set by mind-matter correlations (see also Stapp 2007).
・At a level at which conscious mental states and material brain states are distinguished, each conscious experience, according to Stapp (1999, p. 153), has as its physical counterpart a quantum state reduction actualizing “the pattern of activity that is sometimes called the neural correlate of that conscious experience”. This pattern of activity may encode an intention and, thus, represent a “template for action”. An intentional decision for an action, preceding the action itself, is then the key for anything like free will in this picture.
・Stapp argues that the mental effort, i.e. attention devoted to such intentional acts, can protract the lifetime of the neuronal assemblies that represent the templates for action due to quantum Zeno-type effects. Concerning the neurophysiological implementation of this idea, intentional mental states are assumed to correspond to reductions of superposition states of neuronal assemblies. Additional commentary concerning the concepts of attention and intention in relation to James’ idea of a holistic stream of consciousness (James 1950 [1890]) was given by Stapp (1999).
・For further progress, it will be mandatory to develop a coherent formal framework for this approach and elaborate on concrete details. For instance, it is not yet worked out precisely how quantum superpositions and their collapses are supposed to occur in neural correlates of conscious events. Some indications are outlined by Schwartz et al. (2005). With these desiderata for future work, the overall conception is conservative insofar as the physical formalism remains unchanged.
・This is why Stapp insisted for years that his approach does not change what he calls “orthodox” quantum mechanics, which is essentially encoded in the statistical formulation by von Neumann (1955). From the point of view of standard present-day quantum physics, however, it is certainly unorthodox to include the mental state of observers in the theory. Although it is true that quantum measurement is not yet finally understood in terms of physical theory, introducing mental states as the essential missing link is highly speculative from a contemporary perspective.
・This link is a radical conceptual move. In what Stapp now denotes as a “semi-orthodox” approach (Stapp 2015), he proposes that the blind-chance kind of randomness of individual quantum events (“nature’s choices”) be reconceived as “not actually random but positively or negatively biased by the positive or negative values in the minds of the observers that are actualized by its (nature’s) choices” (p. 187). This hypothesis leads into mental influences on quantum physical processes which are widely unknown territory at present.
Section 3：Vitiello and Freeman: Quantum Field Theory of Brain States
・In the 1960s, Ricciardi and Umezawa (1967) suggested to utilize the formalism of quantum field theory to describe brain states, with particular emphasis on memory. The basic idea is to conceive of memory states in terms of states of many-particle systems, as inequivalent representations of vacuum states of quantum fields. This proposal has gone through several refinements (e.g., Stuart et al. 1978, 1979; Jibu and Yasue 1995). Major recent progress has been achieved by including effects of dissipation, chaos, fractals and quantum noise (Vitiello 1995; Pessa and Vitiello 2003; Vitiello 2012). For readable nontechnical accounts of the approach in its present form, embedded in quantum field theory as of today, see Vitiello (2001, 2002).
・Quantum field theory (see the entry on quantum field theory) deals with systems with infinitely many degrees of freedom. For such systems, the algebra of observables that results from imposing canonical commutation relations admits of multiple Hilbert-space representations that are not unitarily equivalent to each other. This differs from the case of standard quantum mechanics, which deals with systems with finitely many degrees of freedom. For such systems, the corresponding algebra of observables admits of unitarily equivalent Hilbert-space representations.
・The inequivalent representations of quantum field theory can be generated by spontaneous symmetry breaking (see the entry on symmetry and symmetry breaking), occurring when the ground state (or the vacuum state) of a system is not invariant under the full group of transformations providing the conservation laws for the system. If symmetry breaks down, collective modes are generated (so-called Nambu-Goldstone boson modes), which propagate over the system and introduce long-range correlations in it.
・These correlations are responsible for the emergence of ordered patterns. Unlike in standard thermal systems, a large number of bosons can be condensed in an ordered state in a highly stable fashion. Roughly speaking, this provides a quantum field theoretical derivation of ordered states in many-body systems described in terms of statistical physics. In the proposal by Umezawa these dynamically ordered states represent coherent activity in neuronal assemblies.
・The activation of a neuronal assembly is necessary to make the encoded content consciously accessible. This activation is considered to be initiated by external stimuli. Unless the assembly is activated, its content remains unconscious, unaccessed memory. According to Umezawa, coherent neuronal assemblies correlated to such memory states are regarded as vacuum states; their activation leads to excited states and enables a conscious recollection of the content encoded in the vacuum (ground) state. The stability of such states and the role of external stimuli have been investigated in detail by Stuart et al. (1978, 1979).
・A decisive further step in developing the approach has been achieved by taking dissipation into account. Dissipation is possible when the interaction of a system with its environment is considered. Vitiello (1995) describes how the system-environment interaction causes a doubling of the collective modes of the system in its environment. This yields infinitely many differently coded vacuum states, offering the possibility of many memory contents without overprinting. Moreover, dissipation leads to finite lifetimes of the vacuum states, thus representing temporally limited rather than unlimited memory (Alfinito and Vitiello 2000; Alfinito et al. 2001). Finally, dissipation generates a genuine arrow of time for the system, and its interaction with the environment induces entanglement. Pessa and Vitiello (2003) have addressed additional effects of chaos and quantum noise.
・Umezawa’s proposal addresses the brain as a many-particle system as a whole, where the “particles” are more or less neurons. In the language of Section 1, this refers to the level of neuronal assemblies, which correlate directly with mental activity. Another merit of the quantum field theory approach is that it avoids the restrictions of standard quantum mechanics in a formally sound way. Conceptually speaking, many of the pioneering presentations of the proposal nevertheless confused mental and material states (and their properties). This has been clarified by Freeman and Vitiello (2008): the model “describes the brain, not mental states.”
・For a corresponding description of brain states, Freeman and Vitiello 2006, 2008, 2010) studied neurobiologically relevant observables such as electric and magnetic field amplitudes and neurotransmitter concentration. They found evidence for non-equilibrium analogs of phase transitions (Vitiello 2015) and power-law distributions of spectral energy densities of electrocorticograms (Freeman and Vitiello 2010, Freeman and Quian Quiroga 2013). All these observables are classical, so that neurons, glia cells, “and other physiological units are not quantum objects in the many-body model of brain” (Freeman and Vitiello 2008). However, Vitiello (2012) also points out that the emergence of (self-similar, fractal) power-law distributions in general is intimately related to dissipative quantum coherent states (see also recent developments of the Penrose-Hameroff scenario, Section 5).
・The overall conclusion is that the application of quantum field theory describes why and how classical behavior emerges at the level of brain activity considered. The relevant brain states themselves are viewed as classical states. Similar to a classical thermodynamical description arising from quantum statistical mechanics, the idea is to identify different regimes of stable behavior (phases, attractors) and transitions between them. This way, quantum field theory provides formal elements from which a standard classical description of brain activity can be inferred, and this is its main role in large parts of the model. Only in their last joint paper, Freeman and Vitiello (2016) envision a way in which the mental can be explicitly included. For a recent review including technical background see Sabbadini and Vitiello (2019).
Section 4： Beck and Eccles: Quantum Mechanics at the Synaptic Cleft
・Probably the most concrete suggestion of how quantum mechanics in its present-day appearance can play a role in brain processes is due to Beck and Eccles (1992), later refined by Beck (2001). It refers to particular mechanisms of information transfer at the synaptic cleft. However, ways in which these quantum processes might be relevant for mental activity, and in which their interactions with mental states are conceived, remain unclarified to the present day.
・As presented in Section 1, the information flow between neurons in chemical synapses is initiated by the release of transmitters in the presynaptic terminal. This process is called exocytosis, and it is triggered by an arriving nerve impulse with some small probability. In order to describe the trigger mechanism in a statistical way, thermodynamics or quantum mechanics can be invoked. A look at the corresponding energy regimes shows (Beck and Eccles 1992) that quantum processes are distinguishable from thermal processes for energies higher than 10-2 eV (at room temperature). Assuming a typical length scale for biological microsites of the order of several nanometers, an effective mass below 10 electron masses is sufficient to ensure that quantum processes prevail over thermal processes.
・The upper limit of the time scale of such processes in the quantum regime is of the order of 10-12 sec. This is significantly shorter than the time scale of cellular processes, which is 10-9 sec and longer. The sensible difference between the two time scales makes it possible to treat the corresponding processes as decoupled from one another.
・The detailed trigger mechanism proposed by Beck and Eccles (1992) is based on the quantum concept of quasi-particles, reflecting the particle aspect of a collective mode. Skipping the details of the picture, the proposed trigger mechanism refers to tunneling processes of two-state quasi-particles, resulting in state collapses. It yields a probability of exocytosis in the range between 0 and 0.7, in agreement with empirical observations. Using a theoretical framework developed earlier (Marcus 1956; Jortner 1976), the quantum trigger can be concretely understood in terms of electron transfer between biomolecules. However, the question remains how the trigger may be relevant for conscious mental states. There are two aspects to this question.
・The first one refers to Eccles’ intention to utilize quantum processes in the brain as an entry point for mental causation. The idea, as indicated in Section 1, is that the fundamentally indeterministic nature of individual quantum state collapses offers room for the influence of mental powers on brain states. In the present picture, this is conceived in such a way that “mental intention (volition) becomes neurally effective by momentarily increasing the probability of exocytosis” (Beck and Eccles 1992, 11360). Further justification of this assumption is not given.
・The second aspect refers to the problem that processes at single synapses cannot be simply correlated to mental activity, whose neural correlates are coherent assemblies of neurons. Most plausibly, prima facie uncorrelated random processes at individual synapses would result in a stochastic network of neurons (Hepp 1999). Although Beck (2001) has indicated possibilities (such as quantum stochastic resonance) for achieving ordered patterns at the level of assemblies from fundamentally random synaptic processes, this remains an unsolved problem.
・With the exception of Eccles’ idea of mental causation, the approach by Beck and Eccles essentially focuses on brain states and brain dynamics. In this respect, Beck (2001, 109f) states explicitly that “science cannot, by its very nature, present any answer to […] questions related to the mind”. Nevertheless, their biophysical approach may open the door to controlled speculation about mind-matter relations.
・A more recent proposal targeting exocytosis processes at the synaptic cleft is due Fisher (2015, 2017). Similar to the quasi-particles by Beck and Eccles, Fisher refers to so-called Posner molecules, in particular to calcium phosphate, Ca9(PO4)6. The nuclear spins of phosphate ions serve as entangled qubits within the molecules, which protect their coherent states against fast decoherence (resulting in extreme decoherence times in the range of hours or even days). If the Posner molecules are transported into presynaptic glutamatergic neurons, they will stimulate further glutamate release and amplify postsynaptic activity. Due to nonlocal quantum correlations this activity may be enhanced over multiple neurons (which would respond to Hepp’s concern).
・This is a sophisticated mechanism that calls for empirical tests. One of them would be to modify the phosphorus spin dynamics within the Posner molecules. For instance, replacing Ca by different Li isotopes with different nuclear spins gives rise to different decoherence times, affecting postsynaptic activity. Corresponding evidence has been shown in animals (Sechzer et al. 1986, Krug et al. 2019). In fact, lithium is known to be efficacious in tempering manic phases in patients with bipolar disorder.
Section 5： Penrose and Hameroff: Quantum Gravity and Microtubuli
・In the scenario developed by Penrose and neurophysiologically augmented by Hameroff, quantum theory is claimed to be effective for consciousness, but the way this happens is quite sophisticated. It is argued that elementary acts of consciousness are non-algorithmic, i.e., non-computable, and they are neurophysiologically realized as gravitation-induced reductions of coherent superposition states in microtubuli.
・Unlike the approaches discussed so far, which are essentially based on (different features of) status quo quantum theory, the physical part of the scenario, proposed by Penrose, refers to future developments of quantum theory for a proper understanding of the physical process underlying quantum state reduction. The grander picture is that a full-blown theory of quantum gravity is required to ultimately understand quantum measurement (see the entry on quantum gravity).
・This is a far-reaching assumption. Penrose’s rationale for invoking state reduction is not that the corresponding randomness offers room for mental causation to become efficacious (although this is not excluded). His conceptual starting point, at length developed in two books (Penrose 1989, 1994), is that elementary conscious acts cannot be described algorithmically, hence cannot be computed. His background in this respect has a lot to do with the nature of creativity, mathematical insight, Gödel’s incompleteness theorems, and the idea of a Platonic reality beyond mind and matter.
・Penrose argues that a valid formulation of quantum state reduction replacing von Neumann’s projection postulate must faithfully describe an objective physical process that he calls objective reduction. As such a physical process remains empirically unconfirmed so far, Penrose proposes that effects not currently covered by quantum theory could play a role in state reduction. Ideal candidates for him are gravitational effects since gravitation is the only fundamental interaction which is not integrated into quantum theory so far. Rather than modifying elements of the theory of gravitation (i.e., general relativity) to achieve such an integration, Penrose discusses the reverse: that novel features have to be incorporated in quantum theory for this purpose. In this way, he arrives at the proposal of gravitation-induced objective state reduction.
・Why is such a version of state reduction non-computable? Initially one might think of objective state reduction in terms of a stochastic process, as most current proposals for such mechanisms indeed do (see the entry on collapse theories). This would certainly be indeterministic, but probabilistic and stochastic processes can be standardly implemented on a computer, hence they are definitely computable. Penrose (1994, Secs 7.8 and 7.10) sketches some ideas concerning genuinely non-computable, not only random, features of quantum gravity. In order for them to become viable candidates for explaining the non-computability of gravitation-induced state reduction, a long way still has to be gone.
・With respect to the neurophysiological implementation of Penrose’s proposal, his collaboration with Hameroff has been instrumental. With his background as an anaesthesiologist, Hameroff suggested to consider microtubules as an option for where reductions of quantum states can take place in an effective way, see e.g., Hameroff and Penrose (1996). The respective quantum states are assumed to be coherent superpositions of tubulin states, ultimately extending over many neurons. Their simultaneous gravitation-induced collapse is interpreted as an individual elementary act of consciousness. The proposed mechanism by which such superpositions are established includes a number of involved details that remain to be confirmed or disproven.
・The idea of focusing on microtubuli is partly motivated by the argument that special locations are required to ensure that quantum states can live long enough to become reduced by gravitational influence rather than by interactions with the warm and wet environment within the brain. Speculative remarks about how the non-computable aspects of the expected new physics mentioned above could be significant in this scenario are given in Penrose (1994, Sec. 7.7).
・Influential criticism of the possibility that quantum states can in fact survive long enough in the thermal environment of the brain has been raised by Tegmark (2000). He estimates the decoherence time of tubulin superpositions due to interactions in the brain to be less than 10-12 sec. Compared to typical time scales of microtubular processes of the order of milliseconds and more, he concludes that the lifetime of tubulin superpositions is much too short to be significant for neurophysiological processes in the microtubuli. In a response to this criticism, Hagan et al. (2002) showed that a corrected version of Tegmark’s model provides decoherence times up to 10 to 100 μsec（10－6sec), and it has been argued that this can be extended up to the neurophysiologically relevant range of 10 to 100 msec（10－3sec) under particular assumptions of the scenario by Penrose and Hameroff.
・More recently, a novel idea has entered this debate. Theoretical studies of interacting spins have shown that entangled states can be maintained in noisy open quantum systems at high temperature and far from thermal equilibrium. In these studies the effect of decoherence is counterbalanced by a simple “recoherence” mechanism (Hartmann et al. 2006, Li and Paraoanu 2009). This indicates that, under particular circumstances, entanglement may persist even in hot and noisy environments such as the brain.
・However, decoherence is just one piece in the debate about the overall picture suggested by Penrose and Hameroff. From another perspective, their proposal of microtubules as quantum computing devices has recently received support from work of Bandyopadhyay’s lab at Japan, showing evidence for vibrational resonances and conductivity features in microtubules that should be expected if they are macroscopic quantum systems (Sahu et al. 2013). Bandyopadhyay’s results initiated considerable attention and commentary (see Hameroff and Penrose 2014). In a well-informed in-depth analysis, Pitkänen (2014) raised concerns to the effect that the reported results alone may not be sufficient to confirm the approach proposed by Hameroff and Penrose with all its ramifications.
・In a different vein, Craddock et al. (2015, 2017) discussed in detail how microtubular processes (rather than, or in addition to, synaptic processes, see Flohr 2000) may be affected by anesthetics, and may also be responsible for neurodegenerative memory disorders. As the correlation between anesthetics and consciousness seems obvious at the phenomenological level, it is interesting to know the intricate mechanisms by which anesthetic drugs act on the cytoskeleton of neuronal cells, and what role quantum mechanics plays in these mechanisms. Craddock et al. (2015, 2017) point out a number of possible quantum effects (including the power-law behavior addressed by Vitiello, cf. Section 3) which can be investigated using presently available technologies. Recent empirical results about quantum interactions of anesthetics are due to Li et al. (2018) and Burdick et al. (2019).
・From a philosophical perspective, the scenario of Penrose and Hameroff has occasionally received outspoken rejection, see e.g., Grush and Churchland (1995) and the reply by Penrose and Hameroff (1995). Indeed, their approach collects several top level mysteries, among them the relation between mind and matter itself, the ultimate unification of all physical interactions, the origin of mathematical truth, and the understanding of brain dynamics across hierarchical levels. Combining such deep and fascinating issues certainly needs further work to be substantiated, and should neither be too quickly celebrated nor offhandedly dismissed. After more than two decades since its inception one thing can be safely asserted: the approach has fruitfully inspired important innovative research on quantum effects on consciousness, both theoretical and empirical.
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Prof. PhD.Dr. Kamuro
Quantum Physicist and Brain Scientist involved in Caltech & AERI Assosiate Professor and Brain Scientistficial Evolution Research Institute（AERI: https://www.aeri-japan.com/）
IEEE-USA Fellow
Ph.D. & Dr. Kazuto Kamuro
https://www.aeri-japan.com
email: info@aeri-japan.com
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Keywords Artificial EvolutionResearch Institute：AERI
HP： https://www.aeri-japan.com/
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