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:
x~i~,
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.
References
Aspect, A., Grangier, P. & Roger, G. (1982) Experimental
Tests of Bell's Inequalities using Time-varying Analysers. Physical Review
Letters, 49, 1804-1807.
Churchland, P. S. (1992) Neurophilosophy: Toward a Unified Theory of the
Mind/Brain. MIT Press: Cambridge, MA.
Haldane, J. B. S. (1934) Quantum Mechanics as a Basis for Philosophy. Philosphical
Sciences, 1, 78-98.
Kosslyn, S. M. (1994) Image and Brain. MIT Press: Cambridge, MA.
Searle, J. R. (1992) The Rediscovery of the Mind. MIT Press: Cambridge,
MA.
Stapp, H. P. (1972) The Copenhagen Interpretation. American Journal of Physics,
40, 1098-1116. [Reprinted in Stapp (1993).]
Stapp, H. P. (1991) Symposium on the Foundations of Modern Physics. P.
Lahti and P. Mittelsteadt (Eds). World Scientific: Singapore.
Stapp, H. P. (1992) Physics Review, 46A, 6860-6868, Sec. VII
Stapp, H. P. (1993) Mind, Matter, and Quantum Mechanics. Springer-Verlag:
Berlin.
Stapp, H. P. (1994) Phys.Rev., 49A, 4257-4260.
Stapp, H. P. (1995a) Synthese, 102, 139-164.
Stapp, H. P. (1995b) Quantum Mechanical Coherence, Resonance, and Mind. In P.
R. Masini and A. Mandrekar (Eds.), Norbert Wiener Centenary Congress,
to be published by the American Mathematical Society, New York. (Lawrence Berkeley
Laboratory Report LBL-36915). See also PSYCHE (in press).
von Neumann, J. (1955) The Mathematematical Foundations of Quantum Mechanics.
Princeton University Press: Princeton, NJ, Ch VI, Sec. 1. (Translated from the
original (1932) German edition).
Weiner, N. (1932) Back to Leibniz. In Tech. Rev., 34 , 201-203, 222,
224
Weiner, N. (1934) Quantum Mechanics, Haldane, and Leibniz. Philosphical Sciences,
1, 479-482.
Weiner, N. (1936) The Role of the Observer. Philosphical Sciences 3,
307-319.
Wigner, E. (1962) In I. J. Good (Ed.) The Scientist Speculates. Basic
Books: New York, NY.
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.
