Joseph D. Miller Ph.D
Department of Pharmacology
Texas Tech University Health Sciences Center
Lubbock, TX 79430

• Abstract
  

• Introduction
  

• Philosophical History
  

• Interpretations of Quantum Mechanics
  

• A Thought Experiment
  

• Observation of the Superposed State
  

• Potential Application to Neurobiology
  

• Implications for Psychiatry and Neurology
  

• Conclusion
  

• Acknowledgments
  

• Footnotes
  

• Legends
  

• References
  

INTRODUCTION

. Neuroscience has largely committed itself to the paradigms of molecular biology. The Human Genome Project will eventually provide a catalog of the genes that ultimately regulate the production of every human character, including cognitive behavior. With that map and with the new interventionist strategies of gene therapy and genetic engineering, the genome itself will be modifiable, certainly at the somatic level and eventually at the germ cell level.

There must be a point in this reductionist program where molecular biology enters the domain of quantum physics, a point at which classical, Newtonian, deterministic theory (the usually unacknowledged underpinning of modern biology) must give way to quantum mechanical interpretation. Nowhere will this be seen more clearly than in attempts to understand the mechanism and function of the central nervous system and the diseases to which it is prone. Already, quantum mechanical considerations are necessary in the modelling of neurotransmitter receptor structure (Pardo et al., 1996). It is possible that some of the "hard" problems in neurobiology, such as the nature, origin, and development of conscious experience will require a quantum perspective. The inevitable intersection of neurobiology with quantum mechanics may lead to a twin understanding of cognition and the role of the observer in quantum mechanics. That knowledge in turn will have profound implications for psychiatric medicine, the definition of "human", and perhaps the interpretation of physical reality itself. But to evaluate such possibilities it is necessary to briefly consider both philosophical approaches to the nature of consciousness and the essentials of quantum mechanics. The difficulties in the interpretation of quantum mechanics (as opposed to its pragmatic application) may provide unique insight into some of the most difficult problems of neurobiology.

PHILOSOPHICAL HISTORY

Historical conceptions of the nature of consciousness have one extreme pole in the idealism of Bishop Berkeley (Russell, 1967). Berkeley's idealism posited that the only real things are minds and ideas. Being is perceiving. The constancy of the physical world is attributed to a God who continually perceives and never sleeps. The similarity of our perceptions of this world follow from our partial participation in God's perceptions and, presumably, mind. This is a kind of social solipsism. Reality is inherently consensual.

Psychology at its origin still maintained a dualistic outlook. But experimental difficulties in studying the contents of conscious thought, along with the blooming of the logical positivist school, rapidly produced the materialist outlook of Watson and ultimately Skinner in this country. Psychology in this century has been dominated by the behaviorist outlook, which is an essentially materialist tradition. This was not by any means a bad outcome, since the tools necessary to objectively study the cerebral correlates of conscious experience have only recently been developed. Such imaging methodologies as magnetic resonance imaging and positron emission tomography now allow the examination of the physiological substrate of consciousness. In the absence of such tools, the Behaviorists developed useful paradigms for the analysis of what was observable at that time, the behavior of organisms.

INTERPRETATIONS OF QUANTUM MECHANICS

But while the behavioral tradition was just beginning to flower, physics itself went through a paradigm shift, first with the special and general relativity of Einstein, then with the quantum mechanics of Bohr, Heisenberg and others in the twenties and thirties (Baggott, 1994). In particular, the essence of quantum mechanics is that particles of a sufficiently small size, generally of atomic radius or smaller, can simultaneously exist in multiple linearly superposed states, the sum of which is called a wave function. These states can correspond to different positions, momenta, spin etc. Each state evolves over time according to the Schrödinger equation in a completely deterministic fashion. However, if an observation of the system is made, the wave function collapses. That is, somehow the observation "selects" a particular state (on the basis of its relative probability) and that state corresponds to an exclusive classical alternative, i.e., a particularized position, spin or whatever. All other states are excluded. That new state can now evolve deterministically until the next observation. Thus quantum mechanics incorporates an operation, collapse of the wave function (also called reduction of the state vector where the state vector is the linear sum of the complexly weighted possible alternative states) which is inherently probabilistic, rather than deterministic in the classical Newtonian sense. Furthermore, unlike the classical Newtonian picture (or even the relativistic picture) of the universe, an observer is absolutely necessary (see, for instance, Renninger's negative result, 1953 or the delayed choice experiment of Wheeler, 1978, as cited in Cramer, 1986).

Perhaps the most widely accepted attempt to evade the role of the observer is Everett's Many Worlds model (Everett, 1957). In this interpretation, the collapse of the wave function never occurs. Instead, at every possible choice point, a new parallel universe buds off, corresponding to every possible superposed state. Everett required that these universes be non-communicating. Apparently communicating universes are logically equivalent to a megaverse in which mutually exclusive alternatives could co-exist, much like the state(s) of Schrödinger's Cat before the lid of the box is lifted. Furthermore, if communication were allowed, then at least some of the possible allowed states would include visitation of this particular world at this particular time by travelers who would be quite willing to demonstrate their means of transit! Since this has apparently not occurred, it would seem more likely that Everett's Many Worlds are indeed non-communicating. However, this in turn means that the theory is inherently untestable. One caveat here is that if a traveler could attain velocities faster than light or if other means were found for time travel into the past, then it would be possible (and probably required to avert paradox) for the traveler to take a new path through the Many Worlds.

At least two other models posit that wave function collapse does not occur. Bohm's pilot wave theory (Bohm, 1952) suggests that the wave function is as "real" as any other wave and determines the position of particles according to the magnitude of a quantum potential. Unfortunately, this global "hidden variables" theory makes predictions indistinguishable from those of standard quantum theory, making it as difficult to test as Many Worlds. More recently, quantum information theory (Cerf and Adami, 1996) asserts that there are only waves, particles are illusory, and the wave function does not collapse. It is not yet clear whether this theory is falsifiable in the Popperian sense.

Other attempts allow wave function collapse, but avoid observer-induced collapse. Such notions include Penrose's assumption (1991) that a future theory of quantum gravity will provide such collapse without the necessity of an observer, the hypothesis that the probability of wave function collapse increases smoothly as a function of the total number of atoms comprising the system (Ghiradi et al., 1986) and Cramer's interpretation (1986) that requires a kind of virtual tachyon (advanced waves). A major problem for such hypotheses are "delayed choice" experiments. In one cosmological version of such an experiment, the wave function potentially can persist in the superposed state for billions of years, until an observation is made (Wheeler and Zurek, 1983). Thus the most accepted interpretation of quantum mechanics does seem to require the observer. In particular, what is required is a kind of measuring device with the capacity to collapse both the external wave function as well as its own internal wave function (both consciousness of externals and self-consciousness). Von Neumann (1955), Wigner (1961), and most recently, Stapp (1993) have gone so far as to suggest that the apparent collapse of the external wave function actually represents a collapse of internal superposed brain states in the observer. It is argued here that that capacity characterizes self-consciousness and that empirical test of the observer interpretation may be possible.

The observer interpretation is not without difficulties. Strong interpretation along the lines of von Neumann and Wigner suggest that observers lacking in self-consciousness could not collapse the wave function. At this point it is necessary to ask what species are likely to be self-conscious. That in turn requires some empirical test of self-consciousness. One such test actually exists (Oakley, 1985). It consists of dabbing a spot of paint on the forehead of some test species and then placing the subject in front of a mirror. If the subject then wipes the paint spot off his head it may be inferred that he has identified the reflection in the mirror with some sort of internal spatial map of his own body. This ability to externalize the body image, to correlate the internal body image point by point with an external reflection presupposes the concept "my body" and the concept "me". This in turn suggests self-reference and self-consciousness. Now this test is of course crude. One could easily imagine organisms with a sense of self who simply think that the mirror-reversed image is another entity. But this is the best that can currently be done. It is interesting that chimpanzees, gorillas, and apparently porpoises pass this test, but gibbons, orangutans, baboons and other primates do not. The species that do pass the test seem to have some rudimentary protolinguistic ability, as evidenced by the capacity for simple two or three word sentences in sign language or other abstract modes of communication. Perhaps the linguistic capacity makes it easier for a sense of self to develop because it allows the explicit formulation of self-reference, such as the cogito of Descartes (i.e., I think, therefore I am).

A THOUGHT EXPERIMENT

In any case, it may be asked whether a chimp can collapse the wave function, as opposed to a dog. This is actually a doable experiment, without asphyxiating cats or alarming the animal rights people. The dark-adapted retina can detect a single photon, a quantum event (Baylor et al., 1979). Imagine an apparatus that splits a pair of orbital electrons. The spin of the first electron is registered by a device that converts the detection of the electron spin into a single pixel on a monitor screen; red pixel for spin up, blue pixel for spin down. The second electron is transposed to a similar monitor 186,000 miles away. Well-trained chimps are placed in front of both monitors. Each chimp has been conditioned to press either a lever for fruit juice reward if she detects a point of red light, or a button for banana pellet reward if she detects a blue dot on the monitor. If both colored lights are simultaneously observed, the chimp throws a switch, which behavior is rewarded with a sugar cube. Each chimp "simultaneously" observes the remote screen. Now Pauli's Exclusion Principle states that orbital electrons must have opposite spins. But the Schrödinger equation states that the wave function of each electron is a superposition of the two opposite spin states, up and down, before an observation takes place. If chimps can collapse the wave function, then the pixels observed on the two monitors must be of opposite colors to satisfy Pauli's requirement; if the first chimp sees red, the second chimp must see blue and vice versa. What the chimps "see" is inferred from whether they push the fruit juice lever or the banana pellet button. If the chimps cannot collapse the wave function, then they may "see" both colors simultaneously (the superposed spin states) and both will throw the sugar-rewarded switch. That would provide a test of whether both chimps are perceiving the ordinarily mutually exclusive superposed uncollapsed states simultaneously. This procedure could be used to determine whether any trainable species can collapse the wave function.

Another point is that the entire evaluation of the described experiment would have to be done by a human observer after the fact. There is no difficulty if chimps can indeed collapse the wave function. In that case a human observer would note that if one chimp chooses the fruit juice button, the other chimp chooses the banana pellet button; both chimps never push the same button. But if chimps (or other species) cannot collapse the wave function, there is an interpretational problem. It is instructive to consider that the proposed experiment is an example of the famed Wigner's Friend gedankenexperiment (1961). Here a second observer, Wigner's Friend, actually opens Schrödinger's Box in the absence of Wigner.Wigner evaluates the state of the cat by interrogating his friend. If his Friend is indeed a conscious observer, the wave function collapsed at the time of the Friend's observation, and Wigner's Friend simply tells Wigner whether the cat is alive or dead. But if Wigner's Friend is not a conscious observer, then he is mathematically equivalent to part of the "measuring instrument" that Wigner employs post facto to determine the state of the cat. Wigner's observation of the output of this "measuring instrument" collapses the wave function into either dead cat or alive cat.

OBSERVATION OF THE SUPERPOSED STATE

In the chimp experiment, shouldn't the human observer likewise collapse the wave function, if the chimp is unable to do so? In that event, there should never be an observation of a sugar-rewarded switch throw! Can a failure of wave function collapse be observed even in principle? The answer, at least for beryllium atoms, surprisingly appears to be yes (Monroe et al., 1996). Superposition of states has been observed experimentally at the mesoscopic level; that is, the level of a single isolated atom. So it is necessary to at least provisionally conclude that the switch throw result is possible to observe.

In addition to collapsing the wave function, can the observer in any way influence the final collapsed state? What happens to the wave function if the observer lies? More importantly, what happens if the observer misperceives? It seems such possibilities must be considered if, as Stapp suggests, the collapse is essentially a neural event in the brain of the observer. Future neurophysiologists might well be able to induce a pattern of neural activity corresponding to any desired visual perception in the brain of a given subject. So when Schrödinger's box is opened, whether the cat is observed to be dead or alive is entirely at the discretion of the neurophysiologists. But then who is collapsing the wave function? The neurophysiologists? The federal agency that funds the neurophysiologists? Could the wave function "really" collapse to one result, even if it is perceived to collapse to an opposite result? A positivist interpretation would say this statement is without meaning; we are limited to the entirely operational aspects of observation. But it appears that such an interpretation of quantum mechanics must admit to the same consensuality of perception that characterized Berkelian idealism. And this quandary does not result from some possibly unrealizable advance in neurophysiology. Many experiments in social psychology show that verbal report is very strongly influenced by social factors. One famous experiment (Asch, 1958) involved a group of observers who were asked to estimate the length of a line in a darkened room. All observers but one were confederates of the psychologist who designed the experiment. The confederates were enjoined to consistently over-or underestimate the length of the yardstick. In about one third of the estimates the verbal report of the true experimental subject matched the bogus estimations of the confederates. It is impossible to know whether this particular experiment represented compliancy on the part of the subject or a truly altered perception. But in other experiments the social factor is clear. In a prototypical experiment a confederate rushes into a crowded lecture hall, points a banana at the lecturer and yells bang. The lecturer falls over backwards with a ketchup stain spreading over his white shirt. Students after the fact report that they saw a gunman shoot the professor (such experiments are discussed in Loftus, 1979). Just how many fingers did Winston Smith see in the interrogation scene in Orwell's 1984? So there can be no doubt that the perception of the observer is malleable. This implies that observer-induced collapse of the wave function must be malleable and subject to all the influences of social psychology.

However, a realist interpretation would say that the wave function collapses to a particularized state no matter what the observer may perceive. In this case, the observer institutes collapse, but can have no effect, no matter how small, on the final state to which the wave function collapses. If this were not the case, then in the chimp experiment (see above) the manipulation of one chimp's sensory experience (a bias toward the perception of one spin state or another) would influence the collapsed spin state observed by that chimp, as well as the reciprocal spin state observed by the second chimp. This paradigm could then be employed to send information at a velocity greater than that of light, contradicting the central tenet of special relativity (see above). This contradiction and the lack of any experimental evidence that the observer can influence in any way the final state of the wave function collapse suggests that the realist interpretation (see above) may be correct. But absence of evidence is not evidence of absence! It is not at all clear that the realist view of collapse without observer influence (other than to precipitate the collapse) is any more verifiable than the hidden variable theories which constitute another form of realist interpretation. In fact, yet another variant on Wigner's Friend can be imagined. Assume both a neurally controlled observer and fifty "uncontrolled" observers who all observe a series of openings of Schrödinger cat boxes. The controlled observer's perceptions are manipulated so as to produce an outcome of 50 dead and 50 live cats over a series of 100 observations. The uncontrolled observers should observe the same cumulative percentages. However, the expectation is that all uncontrolled observers will agree on the outcome of any individual box opening. In contrast, the controlled observer will agree with the other observers only 50% of the time. Is this evidence for a realist interpretation, a reality at variance with the controlled perceptions of the individual observer? But what if the 50 observers are actually the ones who are controlled and the single observer is the uncontrolled observer (much like the Asch experiment, see above)? The point is that without prior knowledge of the various factors which influence perception, we cannot know which outcome represents "reality"; all we have is a majority opinion. In general, such prior knowledge is not available. From an operational standpoint, then, a majority opinion might as well represent reality as consensual delusion.

It is still possible to ask the question, "What was the state of the universe before there was a social psychology; that is, let's say two million years ago before the advent of self-conscious primates?" Now one answer to this is that the universe was in an uncollapsed superposition of all possible states. Tipler's Strong Anthropic Principle (Tipler, 1986) suggests that the physical constants of the universe have the values they have because they resulted from an evolutionary process that produced self-conscious observers who in turn collapsed the wave function to just that alternative state associated with those particular physical constants conducive to the existence of self-conscious observers. But even in this "just so" story there is no reason to conclude that higher primates (and perhaps cetaceans) are the only self-conscious organisms in the universe. In fact, this argument may actually be used to infer the existence of extra-terrestrial intelligences capable of collapsing the wave function billions of years before the condensation of the earth from the solar nebula.

POTENTIAL APPLICATION TO NEUROBIOLOGY

So it appears that an observer interpretation of quantum mechanics is plausible (although it does lead to teleological peculiarities). More importantly, and unlike the other interpretations discussed, it is testable. But what does all this have to do with neurobiology?

The greatest evolutionary advance of primates and, to a lesser extent, mammals in general, has been a tremendous increase in cortical surface area in comparison with non-mammalian species. Certain regions of cortex in particular are greatly elaborated in the greater apes and in man. Chief among them are the temporal cortical regions involved in the generation and comprehension of language and the frontal regions, particularly prefrontal cortex, which seem to be essential for such tasks as decision making, and strategic planning. Conscious function appears to be distributed very widely over cortical areas. Localized brain damage rarely affects the sense of self; only in those diseases in which there is massive cortical destruction or loss of cortical activating input (e.g., Alzheimer's, Parkinson's; Perry and Perry, 1995) is there seen an apparent loss of that sense of self (It would be interesting to employ the "mirror test", Oakley, 1985, in such patients). Remarkably, in Parkinson's Disease some reversibility can be observed. In the 1950s when the l-dopa treatment was first employed (Sacks, 1983), institutionalized patients were able to move and speak for the first time in decades, in some cases for the first time in 40 years. One of the biggest difficulties with such patients was making them understand just how much time had passed. These patients were unwilling time travelers into the future. When asked where his mind was for the long period before l-dopa treatment, one patient responded that it was as if he had been inhabiting a black hole. In spite of the vividness of this metaphor, the patient may have experienced a loss of memory for the prior state, rather than a lack of conscious experience at that time (although memory and consciousness have much in common; see below). But there is another reversible loss of consciousness; the slow wave, non-dreaming sleep humans experience every night. Once again, in this state there is a great reduction in cortical electrical activity, and an absence of conscious experience (as opposed to rapid eye movement or dream sleep, in which there is a restoration of cortical activity and at least some, albeit fragmented, cognitive experience). But every morning on awakening the same self is perceived that retired the previous night (although it is not possible to remember the precise moment of sleep). Similarly, occasionally individuals recover from long-lasting coma, experiencing no change in this sense of self.

Such considerations suggest that consciousness is global, stored as some kind of permanent record, and dependent only for activation (booting up?) on some immediate pattern of electrical activity in the brain. Such properties are also characteristic of memory. Long term storage of memory depends on molecular modification in the brain; the reading out of new patterns in messenger RNA and the conversion of that message into newly synthesized protein. The laying down of such records in the course of maturation and learning is often under conscious direction and control, altering the consciousness that is doing the learning. In this sense consciousness is a self-programming program. But if the capacity for laying down memory, consolidation, is lost, consciousness is stuck in whatever state it was in when the consolidation mechanism was damaged. Thus Sachs (1990) reports a patient with such damage whose consciousness is locked in 1945; no possible experience can move his self from that particular temporal frame.

Is it possible to localize sub-programs of consciousness in particular areas? Available evidence suggests that this is so. Various areas of cortex are necessary for conscious auditory, visual, and somatic perception. Other regions are necessary for fine motor control. Wernicke's area in the left temporal lobe is absolutely necessary for language (at least in right-handed males). Undoubtedly such a cortical capacity for language sharpens our sense of self, but it is unlikely that it is essential for self-consciousness. Many aspects of conscious experience appear to be non-verbal. The split-brain experiments of Sperry, Gazzaniga and others (summarized in Gazzaniga et al., 1970) showed that the right hemisphere, the non-speech hemisphere, is conscious even though it lacks access to the speech centers of the left hemisphere because the connecting fibers have been cut as a treatment for intractable epilepsy. In fact, using non-verbal communication procedures, one patient was shown to have motivationally different life goals dependent on which hemisphere was queried (Gazzaniga et al., 1977); this suggests that consciousness can not only persist in a hemisphere disconnected from the speech centers, but actually evolve and change in the way that hemispherically integrated selves seem to do.

Although consciousness appears to be global, is it possible that the neural mechanism responsible for collapsing the wave function is localized? If so, the obvious place to look is prefrontal cortex, the phylogenetically youngest cortical area. One of the earliest documented cases of prefrontal lesion in humans was the case of Phineas Gage. Gage was a miner who managed to propel a blasting rod through his jaw and out the frontal portion of his skull, effectively destroying his prefrontal cortex. From that point onward, Gage lost the capacity for decisiveness, could no longer function as a foreman, and seemed to lack the self-censoring function that Freud referred to as super-ego. Is it possible that Gage lost the capacity to collapse the wave function and from that point on functioned only as a kind of robot on the stage of human affairs? Certainly experimental lesion data in non-human primates suggest strongly that prefrontal cortex is necessary for tasks involving choice, particularly choices that are separated in time (delayed response, delayed alternation; Warren and Akert, 1964). One way of describing this deficit is to call it a deficit in strategic planning; the application of past memory to future choice.

Available genetic data suggest that the uniqueness of the human species in comparison to the chimpanzee boils down to about 600 quintessentially human genes, not present in chimps (this calculation assumes 98% identity between human and chimp genomes (Luke and Verma, 1995) and about 30,000 genes in the human central nervous system (Sutcliffe et al. 1983). The prefrontal cortex (and probably temporal cortex) would seem to be particularly good places to look for the activation of such genes. In fact, new molecular techniques such as differential display will soon be used to define that suite of specifically human genes and, by implication, perhaps humanity itself. It is possible that one such gene could code for a protein rich in the prefrontal cortex that is essential for the observer's ability to collapse the wave function, a function that might very well subjectively feel like conscious choice. In fact an entire cascade of such proteins could be the substrate of wave function collapse. Hypothetical wave function collapsing proteins will be referred to here as collapsins.

But there are more constraints that can be placed on this neural model of wave function collapse. If the conservative assumption is made that neural superposed states will eventually spontaneously collapse, even in the absence of observation, then it is possible to calculate that a sub-neuronal region with a radius of one micron could persist for a period of not more than 50 milliseconds in a superposition of states, before irrevocable collapse of the wave function (Penrose, 1994). The argument reflects the inevitable entanglement of the superposed states with surrounding macroscopic states. So there are two boundaries in the neuronal regime; the spatial one corresponds to sub-neuronal dimensions, the temporal one is in the same domain as many neuronal processes and comparable (within a factor of two) to the latency at which a visual stimulus maximally disrupts visual iconic memory (25 msec; Weisstein and Haber, 1965). Such disruption could reflect the instability of a superposed neural wave function near the point of spontaneous collapse. Furthermore, if iconic memory exemplifies the shortest possible cognitive/perceptual event, such considerations suggest that thought itself could be quantized, as was anticipated over forty years ago (successive sensory stimuli will interfere only if they occur within the same "quantum of psychological time"-Stroud, 1955). It is perhaps no coincidence that the reciprocal of this time interval (40 Hz) is the frequency of a magnetoencephalographic oscillation that has been proposed to bind fragmentary sensation/discrete neuronal activity into unitary conscious experience (Llinas and Ribary, 1993).

What sub-neuronal process could possibly meet the hypothesized spatial and temporal criteria just discussed? Penrose (1994) suggests microtubules, the structural support network of cells. But microtubules are ubiquitous in all cells. Wave function collapse might then be initiated by paramecia, a prospect perhaps acceptable to Heisenberg, but not to most neurobiologists!

Are there specifically neural mechanisms that could operate under these spatio-temporal constraints? There are at least three (Ghosh et al., 1995). The first is the mechanism by which calcium ions enter a terminal bouton and effect the release of a synaptic vesicle, filled with a neurotransmitter, into the synaptic cleft. Stapp (1993) calculates that the effective wave function of a calcium ion is much larger than its classical radius, making this process of transmitter release one in which superposition of many ionic states is possible. The actual release of the contents of a vesicle may require just four calcium ions, probably well within the quantum regime (Heidelberger et al., 1994). A second possibility is the binding of the neurotransmitter with the receptor on the postsynaptic membrane. Although release of transmitter may be a quantum event, the effect of receptor occupation is probably a classical process. Each vesicle discharges about 5000 molecules of transmitter into the synaptic cleft (e.g., Hartzell et al., 1976), and the smallest transmitter has a molecular weight of about 200. So this is the rough quantum equivalent of perhaps a million protons, surely well within the classical regime. Furthermore, to produce any macroscopic response, many receptors may require occupation. So even if transmitter release is a quantum event, the effect of that transmitter can be treated in classical terms, and typically is according to the laws of statistical thermodynamics. However, although an interruption in neurotransmission may disrupt the expression of consciousness (e.g., as in slow wave sleep), the molecular "record" of consciousness somehow persists, even after many years in coma. What is required is a means of altering that record. Thus, a third mechanism, based on the action of intracellular calcium, may have all the characteristics of the quantum regime and in addition be relevant to the process of molecular registration that would seem to underly conscious experience. In fact, this mechanism is very often the effector or final common path for the first two mechanisms considered, largely because intracellular enzymes are generally calcium-dependent. So intracellular calcium is a focal point for all the neuronal events that transpire after the occupation of postsynaptic receptors by neurotransmitter molecules.

Calcium-activated calcium release is an intracellular mechanism that magnifies the activity of as little as one calcium ion. Consider the possible effect of a single calcium ion entering the neuron through a voltage or neurotransmitter-gated calcium channel. If that calcium ion encounters a ryanodine receptor-gated pool of calcium it can facilitate the further release of calcium from that pool in a positive feedback-mediated exponential process within about 50 milliseconds (Monck et al., 1994) [Footnote1]. The result is calcium "hot spots" which are easily visualized in individual neurons (Figure 1A, B). That exponential rise in calcium may easily achieve a classical local concentration and thus constitute the molecular basis of the wave function collapse. The amplification involved may be as much as three to four orders of magnitude, a kind of inflationary "little bang" in the internal spacetime of the neuron [Footnote 2]. Furthermore, at least two immediate sequelae are apparent. Calcium ions bind to certain proteins (calcium binding proteins such as calmodulin) to form molecular complexes which can be translocated to the nucleus to initiate genetic transcription, leaving a molecular record or memory of the event. Secondly, the molecular complex may also activate a calcium/calmodulin-dependent protein kinase which can then phosphorylate the calcium channel which admitted the initial calcium ion which initiated the intracellular wave function collapse. Phosphorylation may alter the opening time or probability of opening of the calcium channel. Thus the amplitudes of the next superposed set of states can be affected by structural changes in the calcium channel, which will alter the probability that a calcium ion can pass through the channel and initiate another round of wave function collapse. Furthermore, still other transcriptional and translational events in the nucleus, touched off by the exponential rise in calcium, may also ultimately alter the amplitudes of certain of the superposed states in the next quantum round, affecting the probability of collapse to a subsequent macroscopic state. In essence, this influence of the prior macroscopic substrate of memory on the next macroscopic state may produce the phenomenon of continuity of consciousness.

Assuming roughly spherical neurons with average diameters of 20 microns and perhaps 10 billion such neurons in the human brain, 10 trillion calcium hot spot "collapses" could occur every 25 msec. If 10 % of these events occur in relevant cortical areas, what mechanism could possibly synchronize the collapse of some trillion such wave functions in the requisite time interval? If uncollapsed superposed wave functions (the U state) alternate in time with collapsed or reduced states (the R state), the alternation can be considered an oscillation with a frequency of perhaps 40 Hz (see above). But very early in cognitive development, the U-R oscillations might vary in phase and period. Still, in a coupled multi-oscillator population, the shortest period oscillator will eventually synchronize and drive the remainder of the oscillator population. If 25 msec is indeed the shortest period of a cognitive event, then a global 40 Hz oscillation should eventually dominate (as seems to be the case in those arousal states (waking and rapid eye movement sleep, but not slow wave sleep) in which some form of cognitive activity is possible; Llinas and Ribary, 1993). It would be most interesting to determine if the appearance of the 40 Hz oscillation is correlated with cognitive development in humans.

But even if the calcium collapses are synchronized throughout cortex, the ultimate R states are random (more properly, determined by the probabilities or squared amplitudes of the states making up the U wave function). The unity of conscious experience suggests that the trillion or so R states occurring each 25 msec must be in some sense compatible. One way to provide such compatibility or global coherence would require that the calcium hot spots behave very much like a Bose-Einstein condensate. Such condensates result when an aggregate (potentially macroscopic) population of atoms are forced into the same quantum mechanical state (Anderson et al., 1995). Similar coherent states may occur in biological systems (Fröhlich, 1975; Pribram,1975; Marshall, 1989; Penrose, 1994).

The 40 Hz oscillation in a globally coherent cortical U-R transition could be the signature of the self-conscious observer. The oscillation is both a product of and modifier of the brain states, produced by collapse of the wave function, which enable conscious experience. The 40 Hz oscillation emerges from, but also synchronizes the coherent U-R transition in an objective fashion (a kind of self-organization). At the same time the identification of the 25 msec collapse with the minimal perceptual event potentially preserves the observer-induced collapse interpretation of quantum mechanics at the neural level. Thus, this interpretation is compatible with the hypothesis of Stapp (1993) and simultaneously similar to the hypothesis of "orchestrated objective reduction" of the wave function (Penrose, 1994; Hameroff and Penrose, 1996)[Footnote 3].

What all this condenses to is the hypothesis that the neural substrate for collapse of the wave function is most likely in the phylogenetically new neocortex, perhaps prefrontal cortex. Furthermore, the various spatio-temporal constraints suggest that calcium-activated calcium release could be the mechanism of wave function collapse. The molecules most likely to influence this collapse, previously referred to as collapsins, are likely to be calcium binding proteins or calcium-dependent kinases specific to the prefrontal cortex in homo sapiens and perhaps one or two other mammalian species. Isoforms of these molecular entities (kinases, calcium binding proteins) are indeed distributed in the frontal and prefrontal cortex in a species-specific fashion, so unique human variants are a strong possibility (Picciotto et al., 1993; Stein et al., 1992). While this model employs a particular neuron-specific mechanism, in contrast to microtubule models (e.g., Penrose, 1994; Hameroff and Penrose, 1996), it is certainly possible that other neural structures could constitute the substrate of wave function collapse.

IMPLICATIONS FOR PSYCHIATRY AND NEUROLOGY

What are the implications of neurally-mediated wave function collapse with regard to neuropathology? First, if there is any truth to this hypothesis, it will force a re-examination of certain cherished observations in neurology. For instance, Penfield and Jasper (1954) observed that electrical stimulation of regions of the human temporal lobe prior to temporal resection for intractable epilepsy caused the activation of vivid memory-like subjective experiences in the patient. Such perceptual experience was superimposed on the environment of the operating theatre and sometimes indistinguishable in terms of salience from that "real" environment. This "doubling" of perceptual experience has also been noted at the initiation of temporal lobe seizures in some patients. Is it possible that such patients are indeed experiencing a superposition of neural states? Is it possible that other vivid perceptual conditions such as hallucinations, waking reverie, and lucid dreaming all reflect linear superposition of what are essentially quantum neural states? Certainly in the epileptic state and perhaps in other conditions the 40 Hz U-R transition frequency may be disrupted by seizure activity. If so, wave function collapse may be disturbed or even prevented. In these cases it is clear that external observers do not perceive the "doubling", perhaps because they are part and parcel of the consensus view that such experiences are necessarily personal.

Today dopamine receptor blockers are administered to reduce functional dopamine hyperactivity in schizophrenia-the net result may be reestablishment of global neural quantum coherence. For MPD, the therapeutic goal is to integrate the various personalities into a single dominant personality-this in turn sounds very much like establishing a maximally probable state (highest squared amplitude) for macroscopic collapse of the neural wave function. It is possible that a detailed theory of quantum neurophysiology would allow the determination and perhaps even modulation of superposed state amplitudes in the normal condition and in pathological conditions such as MPD. Furthermore, such a theory might allow an explanation of the means by which excessive dopamine transmission might lead to a failure of quantum coherence and subsequent schizophrenic symptomatology. Both of these diseases have proved refractory to any kind of classical mechanistic interpretation; perhaps a quantum interpretation would be therapeutically useful.

CONCLUSION

It is clear that neurobiological investigations are approaching the size domain at which quantum effects may be predicted. Certain interpretations of quantum mechanics are now proving testable. Already, some of the simplest models of spontaneous wave function collapse have apparently been falsified (Monroe et al., 1996). Observer interpretations of wave function collapse are likewise testable. If such interpretations prove correct, the neural substrate of wave function collapse will require investigation. It has been suggested here that the substrate of collapse may well be calcium-activated calcium release in cortical regions. Such a mechanism could well constitute the substrate of collapse even if such collapse is spontaneous and purely objective, rather than observer-induced.

ACKNOWLEDGMENTS

This work was supported in part by NIA grant PO1 AG11084. The author is indebted to Howard Strahlendorf, Thomas Tenner and Louis Chiodo for helpful suggestions.

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