Why Classical Mechanics Cannot Naturally Accommodate Consciousness but Quantum Mechanics Can

Henry P. Stapp
Theoretical Physics Group
Lawrence Berkeley Laboratory
University of California
Berkeley, California 94720

Copyright (c) Henry P. Stapp 1995

PSYCHE, 2(5), May 1995

KEYWORDS: consciousness, mind/brain, physics, and quantum theory.

ABSTRACT: It is argued on the basis of certain mathematical characteristics that classical mechanics is not constitutionally suited to accommodate consciousness, whereas quantum mechanics is. These mathematical characteristics pertain to the nature of the information represented in the state of the brain, and the way this information enters into the dynamics.

1. Introduction

1.1 Classical mechanics arose from the banishment of consciousness from our conception of the physical universe. Hence it should not be surprising to find that the readmission of consciousness requires going beyond that theory.

1.2 The exclusion of consciousness from the material universe was a hallmark of science for over two centuries. However, the shift, in the 1920's, from classical mechanics to quantum mechanics marked a break with that long tradition: it appeared that the only coherent way to incorporate quantum phenomena into the existing science was to admit also the human observer (Stapp, 1972). Although the orthodox approach of Bohr and the Copenhagen school was epistemological rather than ontological, focusing upon "our knowledge" rather than on any effort to introduce consciousness directly into the dynamics, other thinkers such as John von Neumann (1955), Norbert Weiner (1932), and J.B.S. Haldane (1934) were quick to point out that the quantum mechanical aspects of nature seemed tailor-made for bringing consciousness back into our conception of matter.

1.3 This suggestion lay fallow for half a century. But the recent resurgence of interest in the foundations of quantum theory has led increasingly to a focus on the crux of the problem, namely the need to understand the role of consciousness in the unfolding of physical reality. It has become clear that the revolution in our conception of matter wrought by quantum theory has completely altered the complexion of problem of the relationship between mind and matter. Some aspects of this change were discussed already in my recent book (Stapp, 1993). Here I intend to describe in more detail the basic differences between classical mechanics and quantum mechanics in the context of the problem of integrating consciousness into our scientific conception of matter, and to argue that certain logical deficiencies in classical mechanics, as a foundation for a coherent theory of the mind/brain, are overcome in a natural and satisfactory way by replacing the classical conception of matter by a quantum conception. Instead of reconciling the disparities between mind and matter by replacing contemporary (folk) psychology by some yet-to-be- discovered future psychology, as has been suggested by the Churchlands, it seems enough to replace classical (folk) mechanics, which is known to be unable to account for the basic physical and chemical process that underlie brain processes, by quantum mechanics, which does adequately describe these processes.

2. Thoughts Within The Classical Framework

2.1 Thoughts are fleeting things, and our introspections concerning them are certainly fallible. Yet each one seems to have several components bound together by certain relationships. These components appear, on the basis of psycho-neurological data (Kosslyn, 1994), to be associated with neurological activities occurring in different locations in the brain. Hence the question arises: How can neural activities in different locations in the brain be components of a single psychological entity?

2.2 The fundamental principle in classical mechanics is that any physical system can be decomposed into a collection of simple independent local elements each of which interacts only with its immediate neighbors. To formalize this idea let us consider a computer model of the brain. According to the ideas of classical physics it should be possible to simulate brain processes by a massive system of parallel computers, one for each point in a fine grid of spacetime points that cover the brain over some period of time. Each individual computer would compute and record the values of the components of the electromagnetic and matter fields at the associated grid point. Each of these computers receives information only from the computers associated with neighboring grid points in its nearly immediate past, and forms the linear combinations of values that are the digital analogs of, say, the first and second derivatives of various field values in its neighborhood, and hence is able to calculate the values corresponding to its own grid point. The complete computation starts at an early time and moves progressively forward in time.

2.3 On the basis of this computer model of the evolving brain I shall distinguish the intrinsic description of this computer/brain from an extrinsic description of it.

2.4 The intrinsic description consists of the collection of facts represented by the aggregate of the numbers in the various registers of this massive system of parallel computers: each individual fact represented within the intrinsic description is specified by the numbers in the registers in one of these computers, and the full description is simply the conglomeration of these individual facts. This intrinsic description corresponds to the fact that in classical mechanics a complete description of any physical system is supposed to be specified by giving the values of the various fields (e.g., the electric field, the magnetic field, etc.) at each of the relevant spacetime points. Similarly, an intrinsic description of the contents of a television screen might be specified by giving the color and intensity values for each of the individual points (pixels) on the screen, without any interpretive information (Its a picture of Winston Churchill!), or any explicit representation of any relationship that might exist among elements of the intrinsic description (Pixel 1000 has the same values as pixel 1256!). The analogous basic classical-physics description of a steam engine would, similarly, give just the values of the basic fields at each of these relevant spacetime points, with no notice, or explicit representation, of the fact that the system can also be conceived of as composed of various functional entities, such as pistons and drive shafts etc.: the basic or intrinsic description is the description of what the system is, in terms of its logically independent (according to classical mechanics) local components, not the description of how it might be conceived of by an interpreter, or how it might be described in terms of large functional entities constructed out of the ontologically basic local components.

2.5 I distinguish this intrinsic description from an extrinsic description.

2.6 An extrinsic description is a description that could be formed in the mind of an external observer that is free to survey in unison, and act upon together, all of the numbers that constitute the intrinsic description, unfettered by the local rules of operation and storage that limit the activities of the computer/brain. This external observer is given not only the capacity to "know", separately, each of the individual numbers in the intrinsic description; he is given also the ability to know this collection of numbers as a whole, in the sense that he can have a single register that specifies the entire collection of numbers that constitutes the intrinsic description. The entire collection of logically and ontologically independent elements that constitutes the intrinsic description can be represented by a single basic entity in the extrinsic description, and be part of the body of information that this external observer can access directly, without the need for some compositional process in the computer/brain to bring the information together from far-apart locations. In general, collections of independent entities at the level of the intrinsic description can become single entities at the level of an extrinsic description.

2.7 The information that is stored in any one of the simple logically independent computers, of which the computer/brain is the simple aggregate, is supposed to be minimal: it is no more than what is needed to compute the local evolution. This is the analog of the condition that holds in classical physics. As the size of the regions into which one divides a physical system tends to zero the dynamically effective information stored in each individual region tends to something small, namely the values of a few fields and their first few derivatives. And these few values are treated in a very simple way. Thus if we take the regions of the computer simulation of the brain that are represented by the individual local computers to be sufficiently small then the information that resides in any one of these local computers appears to be much less than information needed to specify a complex thought, such as the perception of a visual scene: entries from many logically independent (according to classical physics) computers must be combined together to give the information contained in an individual thought, which, however, is a single experiential entity. Thus the thought, considered as a single whole entity, rather than as a collection of independent entities, belongs to the extrinsic level of description, not to the intrinsic level of description.

2.8 According to classical mechanics, the description of both the state of a physical system and its dynamics can be expressed at the intrinsic level. But then how does one understand the occurrence of experientially whole thoughts? How do extrinsic-level actual entities arise from a dynamics that is completely reducible to an intrinsic-level description?

2.9 One possibility is that the intrinsic-level components of a thought are bound together by some integrative process in the mind of a spirit being, i.e., in the mind of a "ghost behind the machine", of an homunculus. This approach shifts the question to an entirely new realm: in place of the physical brain, about which we know a great deal, and our thoughts, about which we have some direct information, one has a new "spirit realm" about which science has little to say. This approach takes us immediately outside the realm of science, as we know it today.

2.10 Alternatively, there is the functional approach. The brain can probably be conceived of, in some approximation, in terms of large-scale functional entities that, from a certain global perspective, might seem to be controlling the activity of this brain. However, in the framework of classical mechanics such "entities" play no actual role in determining of the course of action taken by the computer/brain: this course of action is completely controlled by local entities and local effects. The apparent efficacy of the large-scale "functional entities" is basically an illusion, according to the precepts of classical mechanics, or the dynamics of the computer/brain that simulates it: the dynamical evolution is completely fixed by local considerations without any reference to such global entities.

2.11 As an example take a belief. Beliefs certainly influence, in some sense, the activities of the human mind/brain. Hilary Putnam characterized the approach of modern functionalism as the idea that, for example, a belief can be regarded as an entry in a "belief register", or a "belief box", that feeds control information into the computer program that represents the brain process. Such a belief would presumably correspond, physically, to correlations in brain activities that extend over a large part of the brain. Thus it would be an example of a functional entity that a human being might, as a short-hand, imagine to exist as a single whole entity, but that, according to the precepts of classical mechanics, is completely analyzable, fundamentally, into a simple aggregate of elementary and ontologically independent local elements. The notion that such an extrinsic-level functional entity actually is, fundamentally, anything more than a simple aggregate of logically independent local elements is contrary to the precepts of classical mechanics. The grafting of such an actual entity onto classical mechanics amounts to importing into the theory an appendage that is unnecessary, non- efficacious, and fundamentally illusory from the perspective of the dynamical workings of that theory itself.

2.12 Since this appendage is causally non-efficacious it has no signature, or sign of existence, within classical physics. The sole reason for adding it to the theory is to account for our direct subjective awareness of it. Logically and rationally it does not fit into the classical theory both because it has no dynamical effects, beyond those due to its local components alone, and because its existence and character contravenes the locality principle that constitutes the foundation of the theory, namely the principle that any physical system is to be conceived of as fundamentally a conglomerate of simple microscopic elements each of which interacts only with its immediate neighbors. Neither the character of the basic description of the brain, within classical mechanics, nor the character of the classical dynamical laws that supposedly govern the brain, provides any basis for considering the brain correlate of a thought to be, at the fundamental as distinguished from functional level, a single whole entity. One may, of course, postulate some extra notion of "emergence". But nature must be able to confer some kind of beingness beyond what is entailed by the precepts of classical mechanics in order to elevate the brain correlate of a belief to the status of an ontological whole.

2.13 This problem with 'beliefs', and other thoughts, arises from the attempt to understand the connection of thoughts to brains within the framework of classical physics. This problem becomes radically transformed, however, once one accepts that the brain is a physical system. For then, according to the precepts of modern physics, the brain must in principle be treated as a quantum system. The classical concepts are known to be grossly inadequate at the fundamental level, and this fundamental inadequacy of the classical concepts is not confined to the molecular level: it certainly extends to large (e.g., brain-sized) systems. Moreover, quantum theory cannot be coherently understood without dealing in some detail with the problem of the relationship between thoughtlike things and brainlike things: some sort of non-trivial considerations involving our thoughts seems essential to a coherent understanding of quantum theory.

2.14 In this respect quantum theory is wholly unlike classical physics, in which a human consciousness is necessarily idealized as a non-participatory observer --- as an entity that can know aspects of the brain without influencing it in any way. This restriction arises because classical physics is dynamically complete in itself: it has no capacity to accommodate any efficacious entities not already completely fixed and specified within its own structure. In quantum theory the situation is more subtle because our perceptions of physical systems are described in a classical language that is unable to express, even in a gross or approximate way, the structural complexity of physical systems, as they are represented within the theory: there is a fundamental structural mismatch between the quantum mechanical description of a physical system and our description of our perceptions of that system. The existence of this structural mismatch is a basic feature of quantum theory, and it opens up the interesting possibility of representing the mind/brain, within contemporary physical theory, as a combination of the thoughtlike and matterlike aspects of a neutral reality.

2.15 One could imagine modifying classical mechanics by appending to it the concept of another kind of reality; a reality that would be thought like, in the sense of being an eventlike grasping of functional entities as wholes. In order to preserve the laws of classical mechanics this added reality could have no effect on the evolution of any physical system, and hence would not be (publicly) observable. Because this new kind of reality could have no physical consequences it could confer no evolutionary advantage, and hence would have, within the scientific framework, no reason to exist. This sort of addition to classical mechanics would convert it from a mechanics with a monistic ontology to a mechanics with a dualistic ontology. Yet this profound shift would have no roots at all in the classical mechanics onto which it is grafted: it would be a completely ad hoc move from a monistic mechanics to a dualistic one.

2.16 In view of this apparent logical need to move from monistic classical mechanics to a dualistic generalization, in order to accommodate mind, it is a striking fact that physicists have already established that classical mechanics cannot adequately describe the physical and chemical processes that underlie brain action: quantum mechanics is needed, and this newer theory, interpreted realistically, in line with the ideas of Heisenberg, already is dualistic. Moreover, the two aspects of this quantum mechanical reality accord in a perfectly natural way with the matterlike and thoughtlike aspects of the mind/brain. This realistic interpretation of quantum mechanics was introduced by Heisenberg not to accommodate mind, but rather to to keep mind out of physics; i.e., to provide a thoroughly objective account of what is happening in nature, outside human beings, without referring to human observers and their thoughts. Yet when this dualistic mechanics is applied to a human brain it can account naturally for the thoughtlike and matterlike aspects of the mind/brain system. The quantum mechanical description of the state of the brain is automatically (see below) an extrinsic-level description, which is the appropriate level for describing brain correlates of thoughts. Moreover, thoughts can be identified with events that constitute efficacious choices. They are integral parts of the quantum mechanical process, rather than appendages introduced ad hoc to accommodate the empirical fact that thoughts exist. These features are discussed in the following sections.

3. Thoughts Within The Quantum Framework

3.1 Let us consider now how the brain would be simulated by a set of parallel computers when the brain is treated as a quantum system. To make this description clear to every reader, particularly those with no familiarity with quantum theory, I shall start again from the classical description, but spell it out in more detail by using some symbols and numbers.

3.2 We introduced a grid of points in the brain. Let these points be represented by a set of vectors:


where i ranges over the integers from 1 to N. At each point x~i~ there was a set of fields:

F~j~ (x~i~),

where j ranges from 1 to M, and M is relatively small, say ten. For each of the allowed values of the pair (i,j) the quantity F~j~ (x~i~) will have (at each fixed time) some value taken from the set of integers that range from -L to +L, where L is a very large number. There is also a grid of temporal values t~n~, with n ranging from 1 to T.

3.3 The description of the classical system at any time t~n~ is given, therefore, by specifying for each pair of value (i,j) with i in the set {1,2,...,N} and j in the set {1,2,..., M} some value of F~j~ (x~i~) in the set {-L, ..., +L}. We would consequently need, in order to specify this classical system at one time t~n~, N x M "registers", each of which is able to hold an integer in the range {-L, ..., +L}.

3.4 We now go over to the quantum mechanical description of this same system. It is helpful to make the transition in two steps. First we pass to the classical statistical description of the classical system. This is done by assigning a probability to each of the possible states of the classical system. The number of possible states of the classical system (at one time) is (2L+1)^(M x N)^. If the probability assigned to each of the possible classical systems is one of K possible values then the statistical description of the classical system at one time requires (2L+1)^(M x N)^ registers, each with the capacity to distinguish K different values. This can be compared to the number of registers that was needed to describe the classical system at one time, which was M x N registers, each with a capacity to distinguish (2L +1) different values.

3.5 If the index m runs over the (2L+1)^(M x N)^ possible classical systems then a probability P~m~ is assigned to each value of m, where P~m~ > or = 0, and the sum over m of P~m~ equals 1.

3.6 The quantum-mechanical description is now obtained by replacing each P~m~ by a complex number:

P~m~ --> r~m~ (cos (a~m~) + i sin (a~m~)),

where r~m~ is the square root of P~m~, a~m~ is an angle, cos (a) and sin (a) are the cosine and sine functions, and i is the square root of -1.

3.7 This replacement might seem an odd thing to do, but one sees that this description does somehow combine the particle-like aspect of things with a wavelike aspect: the probability associated with any specific classical state m is r^2^~m~ = P~m~, and an increase of a~m~ gives a wave-like oscillation.

3.8 I am not trying to explain here how quantum theory works: I am merely describing the way in which the description of the computer/brain system changes when one passes from the classical description of it to the quantum description.

3.9 For the classical description we needed just M x N registers, but for the quantum description we need 2 x (2L +1)^(M x N)^ registers. Thus the information contained in the quantum mechanical description is enormously larger: we need, simultaneously, a value of r~m~ and of a~m~ for each possible state m of the classical system. That is, each of the possible states of the classical system is specified by giving, simultaneously, some value of F~j~ (x~i~) in the range (-L,..., L) for each of the MxN allowed pairs of indices (i,j), but to describe the quantum state on needs, simultaneously for each of the possible classical states m of the entire system, a pair of numbers (r~m,a~m~).

3.10 Consider again a belief. As before, a belief would correspond physically to some combination of values of the fields at many well-separated field points x~i~. In the classical computer model of the brain there was no register that represented, or could represent, such a combination of values, and hence we were led to bring in an "external knower" to provide an adequate ontological substrate for the existence of the belief. But in the quantum-mechanical description there is such a register. Indeed, each of the 2 x (2L+1)^(M x N)^ registers in the quantum mechanical description of the computer/brain corresponds to a possible correlated state of activity of the entire classically-conceived computer/brain. Consequently, there is no longer any need to bring in an "external observer": the quantum system itself has the requisite structural complexity. Moreover, if we accept von Neumann's (and Wigner's (1962)) suggestion that the Heisenberg quantum jumps occur precisely at the high level of brain activity that corresponds to conscious events then there is an "actual happening" (in a particular register, m) that corresponds to the occurrence of the conscious experience of having an awareness of this belief. This "happening" is the quantum jump that shifts the value of r~m~ associated with this register m from some value less than unity to the value unity. This jump constitutes the Heisenberg "actualization" of the particular brain state that corresponds to this belief. Jumps of this general kind are not introduced merely to accommodate the empirical fact that thoughts exist. Instead, they are already an essential feature of the Heisenberg description of nature, which is the most orthodox of the existing quantum mechanical descriptions of the physical world. Thus in the quantum mechanical description of the brain no reference is needed to any "ghost behind the machine": the quantum description already has within itself a register that corresponds to the particular state of the entire brain that corresponds to the belief. Moreover, it already has a dynamical process for representing the "occurrence" of this belief. This dynamical process, namely the occurrence of the quantum jump (reduction of wave packet), associates the thought with a choice between alternative classically describable possibilities, any one of which is allowed to occur, according to the laws of quantum dynamics. Thus the dynamical correlates of thoughts are natural parts of the quantum-mechanical description of the brain, and they play a dynamically efficacious role in the evolution of that physical system.

3.11 The essential point, here, is that the quantum description is automatically holistic, in the sense that its individual registers refer to states of the entire brain, whereas the individual registers in the classically conceived computer/brain represent only local entities. Moreover, the quantum jump associated with the thought is also a holistic entity: it actualizes as a unit the state of the entire brain that is associated with the thought.

3.12 The fundamentally holistic character of the quantum mechanical description nature is perhaps its most basic and pervasive feature. It has been demonstrated to extend to the macroscopic (hundred centimeter) scale in, for example, the experiments of Aspect, Grangier, and Roger (1982). In view of the fact that the holistic character of our thoughts is so antithetical to the principles of classical physics, it would seem imprudent to ignore the holistic aspect of matter that lies at the heart of contemporary physics when trying to grapple with the problem of the connection of matter to consciousness.

4. On The Thesis That 'Mind Is Matter'

4.1 Faced with the centuries-old problem of reconciling the thoughtlike and matterlike aspects of nature many scientists and philosophers are turning to the formula: 'mind is matter' (Churchland, 1992). However, this solution has no content until one specifies what matter is. This need to define 'matter' is highlighted by the extreme disparity in the conceptions of matter in classical mechanics and quantum mechanics.

4.2 One might try to interpret the 'matter' occurring in this formula as the 'matter' that occurs in classical physics. But this kind of matter does not exist in nature. Hence the thesis 'mind is matter', with matter defined in this way, would seem to entail that thoughts do not exist.

4.3 The thesis that 'mind is matter' has been attacked on the ground that matter is conceptually unsuited to be identified with mind. The main rebuttal to this criticism given in Churchland (1992) is that one does not know what the psychological theory of the future will be like. Hence it is conceivable that the future theory of mind may not involve the things such as 'belief', 'desire' and 'awareness' that we now associate with mind. Consequently, some future theory of mind could conceivably allow us to understand how two such apparently disparate things as mind and matter could be the same.

4.4 An alternative way to reconcile a theory of mind with the theory of matter is not through some future conception of our mental life that differs so profoundly from the present-day one, but rather through the introduction the already existing modern theory of matter. Let me elaborate.

4.5 The main objection to the thesis that mind is matter --- as contrasted to the view that mind and matter are different aspects of a single neutral reality --- is based on the fact that each mind is known to only one brain, whereas each brain is knowable to many minds. These two aspects of the mind/brain are different in kind: a mind consists of a sequence of private happenings, whereas a brain consists of a persisting public structure. A mind/brain has both a private inner aspect, mind, and a public outer aspect, brain, and these two aspects have distinctive characteristics.

4.6 In the quantum description of nature proposed by Heisenberg reality has, similarly, two different aspects. The first consists of a set of 'actual events': these events form a sequence of 'happenings', each of which actualizes one of the possibilities offered by the quantum dynamics. The second consists of a set of 'objective tendencies' for these events to occur: these tendencies are represented as persisting structures in space and time. If we correlate thoughts with high-level quantum events in brains, as suggested by von Neumann, Wigner, and others, then we can construct a theory that is a dual-aspect theory of the mind/brain, in the sense that it correlates the inner, or mental, aspects of the mind/brain system with 'actual events' in Heisenberg's picture of nature, and it identifies the outer, or material, aspects of the mind/brain with the 'objective tendencies' of Heisenberg's picture of nature.

4.7 This theory might, on the other hand, equally well be construed as a theory in which 'mind is matter', if we accept the criteria for inter-theoretic reduction proposed in Churchland (1992). For this quantum theory of the brain is built directly upon the concepts of the contemporary theory of matter, and it appears (Stapp, 1993) to be able to explain in terms of the laws of physics the causal connections underlying human behavior that are usually explained in psychological terms. Yet in this theory there is no abandonment of the normal psychological conception of our mental life. It is rather the classical theory of matter that is abandoned. In the terminology used by Churchland folk psychology is retained, but folk physics is replaced by contemporary physics.

5. Final Remarks

5.1 It will be objected that the argument given above is too philosophical; that the simple empirical fact of the matter is that brains are made out of neurons and other cells that are well described by classical physics, and hence that there is simply no need to bring in quantum mechanics.

5.2 The same argument could be made for electrical devices by an electrical engineer, who could argue that wires and generators and antennae etc. can be well described by classical physics. But this would strip him of an adequate theoretical understanding of the properties of the materials that he is dealing with: e.g., with a coherent and adequate theory of the properties of transistors and conducting media, etc. Of course, one can do a vast amount of electrical engineering without paying any attention to its quantum theoretical underpinnings. Yet the frontier developments in engineering today lean heavily on our quantum theoretical understanding of the way electrons behave in different sorts of environments.

5.3 In an even much more important way the processes that make brains work the way they do depend upon the intricate physical and chemical properties of the materials out of which they are made: brain processes depend in an exquisite way on atomic and molecular processes that can be adequately understood only through quantum theory. Of course, it would seem easy to assert that small-scale processes will be described quantum mechanically, and large-scale processes will be described classically. But large-scale processes are built up in some sense from small-scale processes, so there is a problem in showing how to reconcile the large-scale classical behaviour with the small-scale quantum behaviour. There's the rub! For quantum mechanics at the small scale simply does not lead to classical mechanics at the large scale. That is exactly the problem that has perplexed quantum physicists from the very beginning. One can introduce, by hand, some arbitrary dividing line between small scale and large scale, and decree that, in our preferred theory, the quantum laws will hold for small things and the classical laws will hold for large things. But this partition is completely ad hoc: there is no natural way to make this division between small and large in the brain, which is a tight-knit physical system of interacting levels, and there is no empirical evidence that supports the notion that any such separation exists at any level below that at which consciousness appears: all phenomena so far investigated can be understood by assuming that quantum theory (and in particular the Schrouml;dinger equation) holds universally below the level where consciousness enters.

5.4 Bohr resolved this problem of reconciling the quantum and classical aspect of nature by exploiting the fact that the only thing that is known to be classical is our description of our perceptions of physical objects. Von Neumann and Wigner cast this key insight into dynamical form by proposing that the quantum/classical divide be made not on the basis of size, but rather on the basis of the qualitative differences in those aspects of nature that we call mind and matter. The main thrust of Stapp (1993) is to show, in greater detail, how this idea can lead, on the basis of a completely quantum mechanical treatment of our brains, to a satisfactory understanding of why our perceptions of brains, and of all other physical objects, can be described in classical terms, even though the brains with which these perceptions are associated are described in completely quantum mechanical terms. Any alternative theoretical description of the mind/brain system that is consistent and coherent must likewise provide a resolution to the basic theoretical problem of reconciling the underlying quantum-mechanical character of our brains with the classical character of our perceptions of them.

6. Conclusions

6.1 Classical mechanics and quantum mechanics, considered as conceivable descriptions of nature, are structurally very different. According to classical mechanics, the world is to be conceived of as a simple aggregate of logically independent local entities, each of which interacts only with its very close neighbors. By virtue of these interactions large objects and systems can be formed, and we can identify various 'functional entities' such as pistons and drive shafts, and vortices and waves. But the precepts of classical physics tell us that whereas these functional units can be identified by us, and can be helpful in our attempts to comprehend the behaviour of systems, these units do not thereby acquire any special or added ontological character: they continue to be simple aggregates of local entities. No extra quality of beingness is appended to them by virtue of the fact that they have some special functional quality in some context, or by virtue of the fact that they define a spacetime region in which certain quantities such as 'energy density' are greater than in surrounding regions. All such 'functional entities' are, according to the principles of classical physics, to be regarded as simply consequences of particular configurations of the local entities: their functional properties are just 'consequences' of the local dynamics; functional properties do not generate, or cause to come into existence, any extra quality or kind of beingness not inherent in the concept of a simple aggregate of logically independent local entities. There is no extra quality of 'beingness as a whole', or 'coming into beingness as a whole' within the framework of classical physics. There is, therefore, no place within the conceptual framework provided by classical physics for the idea that certain patterns of neuronal activity that cover large parts of the brain, and that have important functional properties, have any special or added quality of beingness that goes beyond their beingness as a simple aggregate of local entities. Yet an experienced thought is experienced as a whole thing. From the point of view of classical physics this requires either some 'knower' that is not part of what is described within classical physics, but that can 'know' as one thing that which is represented within classical physics as a simple aggregation of simple local entities; or it requires some addition to the theory that would confer upon certain functional entities some new quality not specified or represented within classical mechanics. This new quality would be a quality whereby an aggregate of simple independent local entities that acts as a whole (functional) entity, by virtue of the various local interactions described in the theory, becomes a whole (experiential) entity. There is nothing within classical physics that provides for two such levels or qualities of existence or beingness, one pertaining to persisting local entities that evolve according to local mathematical laws, and one pertaining to sudden comings-into-beingness, at a different level or quality of existence, of entities that are bonded wholes whose components are the local entities of the lower-level reality. Yet this is exactly what is provided by quantum mechanics, which thereby provides a logical framework that is perfectly suited to describe the two intertwined aspects of the mind/brain system.

Appendix A. Salient Features Of The Quantum Theory Of The Mind/Brain Described In Stapp (1993)

A.1. FACILITATION: The excitation of a pattern of neural firings produces changes in the neurons that have the effect of facilitating subsequent excitations of that pattern.

A.2. ASSOCIATIVE RECALL: The facilitations mentioned above have the feature that the excitation of a part of the pattern tends to spread to the whole pattern: the sight of Harry's ear brings Harry to mind.

A.3. BODY-WORLD SCHEMA: The physical body of the person and the surrounding world are represented by patterns of neural firings in the brain: these patterns contain the information about the positioning of the body in its environment. They are represented in the context of neural templates for impending action.

A.4. BODY-WORLD-BELIEF SCHEMA: The body-world schema has an extension that represents beliefs and other idea-like structures.

A.5. RECORDS: The B-W-B Schema are representations that have the properties required for records: they endure, are copiable, and are combinable (Stapp, 1991). These requirements entail that these representations are engraved in degrees of freedom that can be characterized as "classical". Superpositions of such classically describable states are generally not classical. This characterization of "classical" (in terms of durability, copiability, and combinability) does not take one outside quantum theory: it merely distinguishes certain functionally important kinds of quantum states.

A.6. EVOLUTION VIA THE SCHROEDINGER EQUATION: The alert brain evolves under the quantum dynamical laws from a state in which one B-W-B schema is excited to a state in which a quantum superposition of several such states are excited. That is, the brain evolves from a state in which one neural template for action is actualized into a quantum state that is a superposition of several alternative possible neural templates for the next action of the organism.

A.7. THE QUANTUM JUMP: The Heisenberg actual event occurs at the high-level of brain activity where different classically describable alternative possible neural templates have come into being: this event actualizes one template and eradicates the others. This process is in exact accord with Heisenberg's idea of what happens in a measuring device. The brain is, in effect, treated as a Heisenberg-type quantum measuring device.

A.8. THOUGHTS: The occurrence of the Heisenberg event at this high level, rather than at some lower level (e.g., when some individual neuron fires) is in line with Wigner's suggestion that the reduction of the wave packet occurs in the brain only at the highest level of processing, where conscious thoughts enter. The state of the brain collapses to a classically describable branch that records, in the form of a facilitated template for action, the template that was just actualized. It is postulated that this actualizing event at the level of the wave function is associated with a conscious event that is the experiential feel of the act of initiating the action initiated by the neural template: the experiential and physical events are concordant. The physical and mental events can be regarded as two aspects of the same event-like reality. The physical event is the image in the physicist's representation of reality of some reality that has also an experiential 'feel'.

A.9. LIMITATIONS: The theory covers only those collapses that occur in the parts of the physical world associated with the organs that control the actions of organisms: e.g., in systems that act in some ways like human brains. Whether similar events occur in man-made devices is not specified, and need not be specified. There is no empirical evidence to support the notion that similar events occur in devices, and the connection to the evolutionary pressure for the survival of the organism that will be mentioned below would not carry over to such devices.

Appendix B. Survival Advantage

B.1 Contemporary quantum theory does not have any definite rule that specifies where the collapses occur. The proposal adopted here is designed to produce a simultaneous resolution of the quantum measurement problem and the mind-matter problem. Thus the proposal is justified by the fact that it produces a coherent model of reality that accords with our actual experience. Yet the deeper question arises: Why should the world be this way, and not some other way? Why should the collapses be to single high-level classical branches, rather than to either lower-level states, such as firings of individual neurons, or to still higher-level states that might include, for example, many classical branches.

B.2 If we suppose that the determination of where the collapses occur is fixed not by some a priori principle but by habits that become ingrained into nature, or by some yet-to-be-discovered characteristic of matter that does not single out the classical branches ab initio, then the question arises: Is the placement of the collapses at high-level classical branches, as specified in our model, favorable to survival of the organism? If so, then there would be an evolutionary pressure for the collapse location to migrate, in our species, to this high-level placement. The fact that the collapses, and hence the accompanying experiences, are classical and high-level would then be consequences of underlying causes, rather than being simply an unexplained fact of nature: it would be advantageous to its survival for the organism to be organized so that whatever fundamental property induces collapses occurs in conjunction with the top-level templates for action.

B.3 In fact, it is evident that placement of the collapses at a lower level would introduce a disruptive stochastic element into the dynamical development of the system. Any sort of dynamical process designed to allow the organism to respond in an optimal way to its environmental situation would have a tendency to be disrupted by the introduction of stochastically instituted low-level collapses, which will not always be to states that are strictly orthogonal. Thus there would be an evolutionary pressure that would tend to push the collapses to higher levels. On the other hand, this pressure would cease once the highest possible level of classically specified branches is reached. The reason is that in order for the organism to learn there must be records of what it has done, and these records must be able to control future actions. But these properties are essentially the properties by which we have defined "classical". Superpositions of such classical states have, because of the local character of the interaction terms in the quantum mechanical laws, no ability to reproduce themselves, or to control future actions of the organism (Stapp, 1991). Thus there should be no migration of the location of the collapse to levels higher than those specified in our model.

B.4 This evolutionary advantage of the classically describable consciousness within the quantum framework is described in more detail in Stapp (1995b). It is of course widely believed that consciousness should confer a survival advantage. But within the deterministic framework of classical physics, where the course of events is the same whether or not consciousness is appended to the local variables specified in classical-physics description, consciousness is non-efficacious, and hence of no relevance to the survival of the species.

Appendix C. Many-Worlds Theories

C.1 I have accepted here Heisenberg's idea that there are real events, that each one represents a transition from "the possible" to "the actual", and that the quantum state can be regarded as a representation of "objective tendencies" for such events to occur. In fact, it is difficult to ascribe any coherent meaning to the quantum state in the absence of such events. For there is then nothing in the theory for the probabilities represented by the wave function to be probabilities of: What does it mean to say that something happens with probability P if nothing actually 'happens', or if everything happens together?

C.2 In our model, if we say that there is no collapse then all the branches continue to exist: there is no singling out and actualization of one single branch. Each of the several branches will evolve independently of the others, and hence it is certainly plausible to say that the different realms of experience that we would like to associate with the different branches should be independent and non-communicating: the records formed in one branch will control only that one branch, and have no effect upon the others. But if there is no collapse then, insofar as the world is represented by the wave function alone, all of the various branches, though dynamically independent, occur in unison, together, and with probability unity. Yet that does not give a match with experience. In order to get a match with experience we must be able to effectively discard in the limit of an infinite number of repetitions of an experiment those branches that have a quantum weight that tends to zero in this limit. That is, quantum states with tiny quantum weights should occur almost never: they should not occur with probability unity! Hence without some added ontological or theoretical structure a theory with no collapse of the wave function cannot give a sensible account of the statistical predictions of quantum theory.

C.3 Of course, the key question is not whether a certain experience X occurs, but rather whether my experience will be experience X. However, the idea that many experiences occur, but that my experience will be only one of them involves some new sort of structure involving a "me" that separates into alternative "me's", even though the wave function is separating into branches that exist conjunctively, in unison. It involves introducing or admitting some structure that takes one beyond the idea that the world is represented simply by a quantum state evolving in accordance with the Schrouml;dinger equation. At that level the various classically describable branches are components that are combined conjunctively: the universe consists of branch 1 and branch 2 and branch 3 and ...; not branch 1 or branch 2 or branch 3 or ... . Yet the world must be decomposed in terms of alternative possibilities in order to assign different statistical weights to the different components: the and composition given by the basic quantum structure must be supplemented by something that provides for the notion of an or composition. This restructuring requires the introduction of some new sort of beingness: it does not emerge simply from a acceptance of the idea that the Schrouml;dinger equation should not suddenly fail. The idea of a psychological being that splits into alternative branches while the associated physical body, evolving in accord with the Schrouml;dinger equation, is splitting into a conjunction of corresponding branches in a highly non-trivial sort of notion. It is really much more complex and strange, logically, than the idea that the wave function represents an objective tendency (propensity) for something to happen, as Heisenberg suggests, and that this happening imposes on the universe a new condition that changes the propensities pertaining to the next happening.

Appendix D: Locality

D.1 A referee suggested that some further discussion of locality in classical and quantum theory would be helpful: I have stressed the nonlocal character of quantum theory and the local character of classical theory, yet orthodox quantum field theory is local in an important sense, and Newton's classical theory of gravity had instantaneous action at a distance, and hence was nonlocal. Some sorting out of the various meanings of "locality" is needed.

D.2 Orthodox modern classical field theory conforms to the requirements of the theory of relativity. It does not permit any faster-than-light transfer of information: a disturbance introduced in a spacetime region R will not produce any physical change at a point P that cannot be reached from R by a smooth spacetime path that is always directed into the closed forward lightcone. Moreover, in the (covariant) field-theoretic formulation the basic interactions are always among immediate neighbors. In these two senses classical theory is local.

D.3 Orthodox quantum field theory, in its covariant form, is local in an analogous sense: the basic interactions that govern the deterministic evolution of the (Heisenberg picture) operators are always between neighbors, and the theory specifies that certain 'commutation relations' must be such that a disturbance in a region R (e.g., the performing of a 'different' measurement in that region) will have no effect on the predictions made by the theory for any physical quantity located at a point P that cannot be reached from R by a smooth spacetime path that is always directed into the closed forward lightcone.

D.4 On the other hand, there are three senses in which orthodox quantum theory is nonlocal:

a. It is nonlocal in the sense that if Everett-type theories are excluded, say for the reasons mentioned in Appendix C, then for certain highly-correlated systems of two particles the set of correlations predicted by quantum theory between the results of certain possible measurements on these two particles is incompatible with the following 'locality' condition: the result of any possible measurement M must be independent of any free choice---say by a human experimenter---that is to be made (in some corresponding frame of reference) later than the mechanical recording of the result of the measurement M (Stapp, 1992 1993, 1994, 1995a): one cannot assume that there is no faster-than- light influence of any kind.

b. It is nonlocal in the sense that any Heisenberg collapse of the wave function, F~i~ --> F~(i+1)~ = P~i~ F~i~, generally changes expectation values all over the universe.

c. It is nonlocal in the sense that the projection operator P~i~ in the above equation is constructed from operators that act at some given time over an extended region in space, such as a human brain. The operator P~i~ places a restriction on the entire state of the brain all at once: it projects onto a state F~(i+1)~ in which certain classically describable conditions pertaining to an entire brain are satisfied together: e.g., the electric field E(x,t) at t=t~0~ is confined to a domain:

E~i~(x) - D~i~(x) E(x,t~0~) E~i~(x) + D~i~(x) for all x in the brain, where E~i~(x) and D~i~(x) are some functions defined over the whole brain. The effect of the action of P~i~ on F~i~ is to select one of the classically describable top-level patterns of neural activity; i.e., one of the alternative possible neural templates for the impending action of the organism. This neural template is one of the host of superposed templates automatically generated by the local deterministic evolution specified by the Schrouml;dinger (or Heisenberg) equation of motion. The contrast between the local deterministic matter-like evolution that generates of a set of possible neural templates for action, and the nonlocal and brain-wide action of the operator P~i~ that selects and actualizes one of these templates is what this paper is about.

D.5 This nonlocal and brain-wide action of the projection operator P~i~ is closely linked to the description given in section 3 of the computer model of the brain. In the context of that description the action of the operator P~i~ is to set all of the variables r~m~ to zero, except for one, which is set to unity. Note that the effect of this action is to set the probability associated with one single one of the (2L+1)^(N x M) registers to unity, and the probability associated to all the rest of these registers to zero. This "actualization" of the quantum state associated with one single one of these registers is a brain-wide action: this single register specifies a state of the whole brain, within the context of the computer model.

D.6 To carry the computer model over to the brain, one may consider that the values specified in the registers of the model represent the values of the quantities that occur in classical electromagnetism. These latter values are related to physics by means of a coarse-grain averaging over small spacetime regions. The size of these small spacetime regions correspond to the grid size in the model. And the intervals associated with the (2L+1) alternative values that the register can take on can be associated with the intervals appearing in paragraph D.4c. The macroscopic degrees of freedom represented in this way are, of course, only a tiny fraction of the full set of degrees of freedom of the brain: there is the chaotic ocean of microvariables upon which these sluggish macrovariables ride. But the projection operator P~i~ acts on the macrovariables alone, and probably on the macrovariables associated with only some regions of the brain, rather than every part of it. But the key point is that the action of P~i~ is brain-wide because the single register that specifies the actualized quantum state corresponds to a set of simultaneous conditions on physical quantities located all over the brain.

Appendix E. Decoherence

E.1 A second referee indicated that the effect upon the arguments advanced here of the disruptive influences of thermal agitations, and the loss of phase coherence arising from the interactions with environment should be discussed.

E.2 It is important to recognize that although these thermal and environmental factors are important at the practical or pragmatic level, they have no significant impact on the matters of principle described in the present work. Physicists are accustomed to thinking in the pragmatic way recommended by Bohr. That was very useful, and had beneficial effects on science during the period before the mind-brain problem could be profitably attacked. On the other hand, it allowed delicate points to be obscured by the fact that our knowledge of the states of macroscopic systems was extremely limited.

E.3 The present approach is ontological rather than pragmatic. The assumption is that there exists in nature a wave function, or state vector, that represents the matter-like aspect of reality, and that each experienced idea or thought corresponds, within this representation, to a quantum event, i.e., to a collapse of the wave function. In this ontological setting neither a breakdown of the meaning of the wave function nor collapse of the wave function is entailed either by our lack of knowledge of what its actual value is, or by the absence of all effective means for us to determine what its actual value is.

E.4 In both classical mechanics and quantum mechanics a change of variables is allowed, and is often useful. A prime example is the introduction of the center-of-mass of an object as one of the variables. More generally there will be many useful macrovariables: the system can be represented in terms of a collection of sluggish macrovariables, of coordinate type, riding on a chaotic ocean of microvariables. The first-order description is in terms of the macrovariables. A first main effect of the microvariables is to destroy observable interference effects between macrostates that are significantly different: this is a consequence of the local character of the underlying dynamics.

E.5 In spite of the chaotic background of microvariables, the von Neumann analysis of the process of measurement proceeds essentially as usual: because the causal connections between various measuring devices is largely controlled by the macro-variables, the von-Neumann-type correlations between the macro-states of the various devices in the von Neumann chain of devices will be maintained. But within the brain the underlying microscopic activity will cause additional branchings of the macrostates, as discussed in Stapp (1995b). The underlying chaotic microactivity is not ignored or disregarded: it is the microscopic foundation upon which the evolution of the macrovariables rests.

E.6 The periodic collapses to states in which certain macrovariable components of the brain state conform to classically describable conditions, as a consequence of the evolutionary pressure for the survival of the organism, keeps the description in terms of classically describable conditions a good first-order description, even though this brain is connected in a complex way to the surrounding universe. For a more detailed discussion of these points the reader is referred to Stapp (1995b), which, however, is written for readers having some familiarity with Hilbert-space concepts.

Appendix F. Comparison With Searle

F.1 John Searle (1992) has described his views on the mind-brain problem in a recent book "The Rediscovery of the Mind". He does not endorse there the thesis that classical mechanics must be replaced by quantum mechanics in order to reconcile mind and matter, but his arguments lend strong support to that conclusion.

F.2 Searle's theme can be divided into three parts. The first is encapsulated in a sentence appearing in the first paragraph of chapter one: "Mental phenomena are caused by neurological processes in the brain and are themselves features of the brain." The same point is repeated many times: "... the mental state of consciousness is just an ordinary biological, that is, physical, feature of the brain."(p. 13); "The brain causes certain 'mental' phenomena, such as conscious mental states, and these are simply higher-level features of the brain."(p.14);" Consciousness is a mental, and therefore physical, property of the brain in the sense in which liquidity is a property of a system of molecules"(p.14); "...these [mental] properties are ordinary higher-level biological properties of neurophysiological systems such as human brains."(p.28); "... consciousness is just an ordinary biological feature of the world." (p.85); " ...consciousness is a causally emergent property of systems. It is an emergent feature of certain systems of neurons in the same way that solidity and liquidity are emergent features of systems of molecules."(p. 112) F.3 The second sub-theme is this: "Conscious mental states and processes have a special feature not possessed by other natural phenomena, namely, subjectivity."(p.93); "the phenomena itself, the actual pain itself, has a subjective mode of existence, and it is in that sense which I am saying that consciousness is subjective."(p.94); "What more can we say about this subjective mode of existence? Well, first it is essential to see that in consequence of its subjectivity, the pain is not equally accessible to any observer. Its existence, we might say, is a first-person existence." (p.94);"...the ontology of the mental is an irreducibly first-person ontology." (p.95); "No description of third-person, objective, physiological facts would convey the subjective, first-person character of the pain simply because the first-person features are different from the third-person features." (p. 116) F.4 The third sub-theme is that the first two sub-themes are not contradictory: "The facts are that biological processes produce conscious mental phenomena, and these are irreducibly subjective." (p. 98); "What I want to insist upon, ceaselessly, is that one can accept the obvious facts of physics---for example that the world is made up entirely of physical particles in fields of force---without at the same time denying the obvious facts about our own existence---for example that we are all conscious and that our conscious states have quite specific irreducible phenomenological properties."(p.28); "According to atomic theory, the world is made up of particles. These particles are organized into systems. Some of these systems are living, and these types of living systems have evolved over long periods of times. Among these, some have evolved brains that are capable of causing and sustaining consciousness. Consciousness is, thus, a biological feature of certain organisms in exactly the same sense of 'biological' in which photosynthesis, mitosis, digestion, and reproduction are biological features of organisms."(p.93) F.5 Searle's main and central point is precisely that there are in nature two modes of existence: two ontological types of beingness. Although he rejects labels, he is an "ontological dualist". He chides the various kinds of "materialists" for not accepting the obvious idea that consciousness is essentially what it seems to be: a physical feature of brains that is not ontologically reducible to third-person features.

F.6 Of course, the reason why traditional "materialists" try to evade or deny what Searle sees as obvious is this: a dualistic ontology appears to them to be contrary to the scientific conception of the physical world. Indeed, Searle's ontologically dualistic conception of the brain is certainly contrary to the conception of the physical world that characterizes classical mechanics. That conception deals exclusively with third-person realities: it has no natural place for a first-person mode of existence, and no causal laws or logical requirements that would demand any type of beingness that goes beyond the third-person kind that it deals with exclusively.

F.7 Searle's argument is based on the fact that consciousness obviously exists, and hence must be included in our account of nature. But the proper conclusion to be drawn from his arguments is that classical mechanics is fundamentally deficient: a better mechanics is needed to account for the known properties of the mind/brain. Of course, physicists have already reached this same conclusion, or at least a closely related one, on the basis of results stemming from empirical studies of the properties of atoms and materials.

F.8 Several conceivable quantum ontologies are being pursued by physicists, but all are fundamentally dualistic. The Bohm-type ontology has both an objectively existing quantum wave function and also a classical world whose essential property is that it, not the quantum wave function, determines what our experiences will be. The Everett-type interpretations, in which there is a wave function that evolves always in accordance with the Schrouml;dinger equation, but in which there is no singled-out classical world, as there is in Bohm's model, also forces one to introduce some other entities for the probabilities to refer to. This was discussed in Appendix C. These other entities control what our thoughts and experiences will be. In the Heisenberg ontology there are the 'actual events' and also the 'objective tendencies' for these events to occur. The objective tendencies evolve in accordance with local deterministic laws (the Heisenberg equations of motion) that are direct analogs of corresponding laws of classical mechanics, whereas the actual events control what our thoughts and experiences will be. In the Wigner-von- Neumann version of the Heisenberg ontology the actual events are either our thoughts and experiences themselves, or they are the images of these experiences in the physicist's mathematical representation of the physical world. In every case the ontology is dualistic, and one of the two parts of the quantum reality is subject to the local deterministic quantum-mechanical law of motion, which is the quantum analog of the local deterministic law that governs the material aspect of nature in classical mechanics , whereas the second part of the quantum reality controls what our thoughts and experiences will be.

F.9 Searle insists that "consciousness is just an ordinary biological feature of the world"---"a biological feature of certain organisms in exactly the same sense of 'biological' in which photosynthesis, mitosis, digestion and reproduction are biological features of organisms". This claim does not exactly square with the fact that digestion and photosynthesis are, ontologically, third-person features, whereas consciousness is of a different ontological type: it is first-person feature. The generation---by a system of ontological type A---of something of the same type, A, is not exactly the same as the generation of something of a different ontological type, B. Indeed, there is no possibility within the ordinary framework of classical mechanics for causal relationships between neurons of the kinds that occur in classical mechanics, to generate anything that has a mode of being different from the third-person mode, for that is the only kind of beingness that occurs in classical mechanics. Some new kind of mechanics is needed to generate, from the third-person realities that classical mechanics deals with, anything with another mode of existence: classical mechanics is not conceptually constituted to create anything having a mode of existence other than the third-person mode that it deals with exclusively.

F.10 Searle's ontological conclusions are, for the reasons given, not compatible with the ontological underpinnings of classical mechanics: they call for a new kind of mechanics. This new kind of mechanics is ontologically similar to quantum mechanics, if not identical to it.


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This work was supported by the Director, Office of Energy Research, Office of High Energy and Nuclear Physics, Division of High Energy Physics of the U.S. Department of Energy under Contract DE-AC03-76SF00098.