**Physicalism Versus Quantum Mechanics**

Henry P. Stapp

*Theoretical Physics Group*

*Lawrence Berkeley National Laboratory*

*University of California*

*Berkeley, California 94720*

**Abstract**

In the context of theories of the connection between mind and brain,
physicalism is the demand that all is basically purely physical. But the
conception of "physical" embodied in this demand is characterized
essentially by the properties of the physical that hold in classical
physical theories. Certain of those properties contradict the character
of the physical in quantum mechanics, which provides a better, more
comprehensive, and more fundamental account of phenomena. It is argued
that the difficulties that have plagued physicalists for half a century,
and that continue to do so, dissolve when the classical idea of the
physical is replaced by its quantum successor. The argument is
concretized in way that makes it accessible to non-physicists by
exploiting the recent evidence connecting our conscious experiences to
macroscopic measurable synchronous oscillations occurring in
well-separated parts of the brain. A specific new model of the
mind-brain connection that is fundamentally quantum mechanical but that
ties conscious experiences to these macroscopic synchronous oscillations
is used to illustrate the essential disparities between the classical
and quantum notions of the physical, and in particular to demonstrate
the failure in the quantum world of the principle of the causal closure
of the physical, a failure that goes beyond what is entailed by the
randomness in the outcomes of observations, and that accommodates the
efficacy in the brain of conscious intention.

**\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_**

**This work was supported by the Director, Office of Science, Office of
High Energy and Nucler Physics, of the U.S. Department of Energy under
contract DE-AC02-05CH11231**

**1. Introduction.**

The widely held philosophical position called "physicalism" has been
described and defended in a recent book by Jaegwon Kim^1^. The
physicalist position claims that the world is basically purely physical.
However, "physical" is interpreted in a way predicated, in effect, upon
certain properties of classical physics that are contradicted by the
precepts of orthodox quantum physics. Kim's arguments reveal two horns
of a dilemma that the physicalist is forced to face as a consequence of
accepting this classical notion of "physical". Kim admits that neither
of the two options, "epiphenomenalism" or "reduction", is very
palatable, but he finds a compromise that he deems acceptable.

The central aim of the present paper is to show that the physicalist's
dilemma dissolves when one shifts from the classical notion of the
physical to the quantum mechanical notion. Understanding this shift
involves distinguishing the classical notion of the mind-brain
connection from its quantum successor.

To make clear the essential features of the quantum mechanical
conception of the mind-brain connection, I shall describe here a model
that is a specific realization of a theory I have described in more
general terms before^2-5^. Being specific reduces generality, but having
a concrete model can be helpful in revealing the general lay of the
land. Also, the specific features added here resolve in a natural way
the puzzle of how our descriptions of our observations can be couched in
the language of classical physics when our brains are operating,
fundamentally, in accordance with the principles of quantum theory. The
specific model also shows how the thoroughly quantum mechanical (quantum
Zeno) effect, which underlies the power of a person's conscious thoughts
to influence in useful ways the physically described processes occurring
in that person's brain, is not appreciably disrupted either by
"environmental decoherence" effects or by thermal effects arising from
the "hotness" of the brain.

In order to communicate to the broad spectrum of scientists and
philosophers interested in the connection between mind and brain, I will
review in the following section the historical and conceptual background
of the needed quantum mechanical ideas, and then describe an approach to
the mind-body problem that is based fundamentally on quantum theory, but
that adds several specific new ideas about the form of the mind-brain
connection.

**2. Quantum Mechanics and Physicalism.**

Rather than just plunging ahead and using the concepts and equations of
quantum mechanics, and thereby making this work unintelligible to many
people that I want to reach, I am going to provide first an historical
and conceptual review of the extremely profound changes in the
philosophical and technical foundations that were wrought by the
transition from classical physics to quantum physics. One key technical
change was the shift from the *numbers* used in classical mechanics to
describe properties of physical systems to the associated *operators* or
*matrices* used to describe related actions. This technical shift
emerged, unsought, from a seismic conceptual shift. Following the path
blazed by Einstein's success in creating special relativity, Heisenberg
changed course. Faced with a quarter century of failures to construct a
successful atomic theory based upon the notion of some presumed-to-exist
space-time structure of the atom, Heisenberg attempted to build a theory
based upon our observations and measurements, rather than upon
conjectured microscopic space-time structures that could be *postulated*
to exist, but that were never directly observed or measured. This shift
in orientation led to grave issues concerning exactly what constituted
an "observation" or "measurement". Those issues were resolved by
shifting from an ontological perspective\-\--which tries to describe
what really exists objectively "out there"\-\-- to a practical or
pragmatic perspective, which regards a physical theory as a useful
collective conceptual human endeavor that aims to provide us with
reliable expectations about our future experiences, for each of the
alternative possible courses of action between which we are (seemingly)
free to choose. As a collective endeavor, and in that sense as an
objective theory, quantum mechanics is built on *descriptions* that
allow us to communicate to others what we have done and what we have
learned. Heisenberg strongly emphasized that this change in perspective
converts the quantum mechanics, in a very real sense, into a theory
about "our knowledge": the relationships between experiential elements
in our streams of consciousness become the core realities of a
conceptual construction that aims to allow us to form, on the basis of
what we already know, useful expectations about our future experiences,
under the various alternative possible conditions between which we seem
able to freely choose.

The paradoxical aspect of claiming the "physical state of a system" to
be a representation of "our knowledge" is starkly exhibited by
"Schroedinger's cat", whose quantum state is, according to this
pragmatic approach, not determined until someone looks. Bohr escapes
this dilemma by saying that the current quantum principles are
insufficient to cover biological matter, but that approach leaves
quantum mechanics fundamentally incomplete, and, in particular,
inapplicable to the physical processes occurring in our brains.

In an effort to do better, von Neumann^6^ showed how to preserve the
rules and precepts of quantum mechanics all the way up to the interface
with "experience", thereby preserving the general character of quantum
mechanics as a theory that aims to provide reliable expectations about
future experiences on the basis of present knowledge. Von Neumann's work
brings into sharp focus the central problem of interest here, which is
the connection between the properties specified in the quantum
mechanical description of a person's brain and the experiential
realities that populate that person's stream of consciousness. Bohr was
undoubtedly right in saying that the orthodox precepts would be
insufficient to cover this case. Additional ideas are needed, and the
purpose of this article is to provide them.

The switch from classical mechanics to quantum mechanics preserves the
idea that a physical system has a physically describable state. But the
character of that state is changed drastically. Previously the physical
state was conceived to have a well defined meaning independently of any
"observation". Now the physically described state has essentially the
character of a "potentia" (an "objective tendency") for the occurrence
of each one of a continuum of alternative possible "events". Each of
these alternative possible events has both an experientially described
aspect and also a physically described aspect: each possible "event" is
a psycho-physical happening. The experientially described aspect of an
event is an element in a person's stream of consciousness, and the
physically described aspect is a *reduction* of the set of objective
tendencies represented by the prior state of that person's body-brain to
the *part* of that prior state that is compatible with the increased
knowledge supplied by the new element in that person's stream of
consciousness. Thus the changing psychologically described state of that
person's knowledge is correlated to the changing physically described
state of the person's body-brain, and the changing physically described
state entails, via the fundamental quantum probability formula, a
changing set of weighted possibilities for future psycho-physical
events.

The practical usefulness of quantum theory flows from this lawful
connection between a person's increasing knowledge and the changing
physical state of his body-brain. The latter is linked to the
surrounding physical world by the dynamical laws of quantum physics.
This linkage allows a person to "observe" the world about him by means
of the lawful relationship between the events in his stream of conscious
experiences and the changing state of his body-brain.

It is worth noting that the physically described aspect of the theory
has lost its character of being a "substance", both in the philosophical
sense that it is no longer *self-sufficient,* being intrinsically and
dynamically linked to the mental, and also in the colloquial sense of no
longer being *material*. It is *stripped of materiality* by its
character of being merely a potentiality or possibility for a future
event. This shift in its basic character renders the physical aspect
somewhat idea-like, even though it is conceived to represent objectively
real tendencies.

The key "utility" property of the theory\-\--namely the property of
being useful\-\--makes no sense, of course, unless we have, in some
sense, some freedom to choose. An examination of the structure of
quantum mechanics reveals that the theory has both a logical place for,
and a logical need for, choices that are made in practice by the human
actor/observers, but that are *not determined by the quantum physical
state of the entire world, or by any part of it*. Bohr^7^ calls this
choice "the free choice of experimental arrangement for which the
quantum mechanical formalism offers the appropriate latitude." (Bohr,
p.73). This "free" choice plays a fundamental role in von Neumann's
rigorous formulation of quantum mechanics, and he gives the physical
aspect of this probing action the name "process 1" (von Neumann, p. 351,
418, 421). This process 1 action is not determined, even statistically,
by the physically described aspects of the theory.

The fact that this choice made by the human observer/agent is not
determined by the physical state of the universe means that *the
principle of the causal closure of the physical domain is not maintained
in contemporary basic physical theory.* It means also that Kim's
formulation of *mind-body supervenience is not entailed by contemporary
physical theory*. That formulation asserts that "what happens in our
mental life is wholly dependent on, and determined by, what happens with
our bodily processes." (Kim, p. 14) Kim indicates that supervenience is
a common element of all *physicalist theories.* But since supervenience
is not required by basic (i.e., quantum) physics, the easy way out of
the difficulties that have been plaguing physicalists for half a
century, and that continue to do so, is simply to recognize that the
precepts of classical physics, which are the scientific source of the
notions of the causal closure of the physical, and of supervenience, do
not hold in real brains, whose activities are influenced heavily by
quantum processes.

Before turning to the details of the quantum mechanical treatment of the
relationship between mind and brain I shall make a few comments on Kim's
attempted resolution of the difficulties confronting the classical
physicalist approach. The essential problem is the mind-body problem.
Kim divides this problem into two parts, the problem of mental causation
and the problem of consciousness. The problem of mental causation is:
"How can the mind exert its causal powers in a world that is
fundamentally physical?" The problem of consciousness is: "How can a
thing such as consciousness exist in a physical world, a world
consisting ultimately of nothing but bits of matter distributed over
space-time in accordance with the laws of physics."

From a modern physics perspective the way to resolve these problems is
immediately obvious: Simply recognize that the assumption that the laws
of physics pertain to "bits of matter distributed over space-time in
accordance with the laws of physics" is false. Indeed, that idea has,
for most of the twentieth century, been asserted by orthodox physicists
to be false, along with the assumption that the world is physical in the
classical sense. Quantum mechanics builds upon the obvious real
existence of our streams of conscious experiences, and provides also, as
we shall see, a natural explanation of their causal power to influence
physical properties. Thus the difficulties that have beset physicalists
for five decades, and have led to incessant controversies and
reformulations, stem, according to the perspective achieved by twentieth
century physics, directly from the fact that the physicalist assumptions
not only do not follow from basic precepts of physics, but instead,
directly contradict them. The premises of classical physicalists have
been, from the outset, incredibly out of step with the physics of their
day.

Kim tries at one point to squash the notion that the difficulties with
physicalism can be avoided by accepting some form of dualism. But the
dualism that he considers is a Cartesian dualism, populated with
mysterious souls. However, quantum mechanics is science! The
experientially described realities that occur in quantum theory are the
core realities of science. They are the ideas that we are able
communicate to others pertaining to what we have done and what we have
learned. These descriptions are essentially descriptions of (parts of)
the accessible contents of the streams of consciousness of real living
observer-agents. Criticizing dualism in the form advanced by Descartes
during the seventeenth century instead of in the form employed in
contemporary science is an indication that philosophers of mind have
isolated themselves in a hermetically sealed world, created by
considering only what other philosophers of mind have said, or are
saying, with no opening to the breezes that bring word of the highly
pertinent revolutionary change that had occurred in basic science
decades earlier.

Kim's main argument leads to the conclusion that a physicalist must, for
each conscious experience, choose between two options: either that
experience is causally powerless, or it must be *defined to be* the
causally efficacious brain activity that possesses its causal power. Kim
himself admits that neither option is very palatable. The idea that our
beliefs, desires, and perceptions, including our pains, have no effects
upon our actions is regarded by Kim as unacceptable. Thus he opts for
what he claims to be the only alternative available to the rational
physicalist, namely that each such efficacious experience must be
(defined to be) a causally efficacious brain activity that causes its
effects: "If anything is to exercize causal power in the physical domain
it must be an element in the physical domain or be reducible to it."
(Kim, p, 170-171) "Only physically reducible mental properties can be
causally efficacious." (Kim, p. 174)

That a conscious experience can be defined to be a physical activity,
described in the mathematical language of physics, is certainly a hard
pill to swallow. Fortunately, it is not true in quantum theory, where
the physically described state represents merely an "objective tendency'
for a psych-physical event to occur. However, the mind-brain identity
that Kim describes does have a less-problematic *analog* in quantum
theory. Each actual event has two sides: an experience; and a reduction
of the prior state of the body-brain to one that incorporates into the
physically described world a causal aspect conceptually represented in
the intentional aspect of the experience. This is the essential core of
the orthodox von Neumann/Heisenberg quantum position. It will be
elaborated upon here.

Kim's solution has another apparent defect: different aspects of a
person's apparently highly integrated stream of consciousness have
fundamentally different statuses, in regard to their connections to that
person's brain. Beliefs, desires and percepts are defined to be brain
activities, whereas colors and other "qualia" are not brain activities
and are not causally efficacious. But how can your desire for a
beautiful painting be simply a brain activity, whereas the particular
colors that combine to excite this desire are epiphenomenal qualities
having no effects on your brain?

The physicalist assumption has apparently led, after 50 years of
development, to conclusions that are far from ideal. These conclusions
fail to explain either why our conscious experiences should exist at all
in a world that is dynamically and logically complete at the physical
level of description, or how they can *be* physical properties that do
not entail the existence of the experiential "feel" that characterize
them. These long-standing difficulties arise directly from accepting the
classical conception of the nature and properties of the physically
described aspects of our description of the world. They are resolved in
a natural way by accepting the quantum mechanical conception of the
nature and properties of the aspects of the world that are described in
physical terms: i.e., in terms of properties specified by assigning
mathematically properties to space-time regions.

In the following sections I shall explain how these difficulties are
resolved by accepting the quantum conception of the physical.

3\. **Quantum Mechanics: The Rules of the Game.**

3.1 The basic formula.

Quantum mechanics is a superstructure erected upon a basic formula. This
formula specifies the probability that a probing action that is
describable in everyday language, refined by the concepts of classical
physical theory, will produce a *pre-specified* possible experienced
outcome that is described in the same kind of terms. First a *preparing*
action must be performed. Its outcome is represented by a (quantum)
state of the prepared system. Then a probing action is chosen and
performed. The elementary probing actions are actions that either
produce a pre-specified outcome 'Yes', or that fail to produce that
pre-specified outcome.

To achieve generality I shall adopt the density matrix formulation
described by von Neumann. In this formulation the physical state of a
system is represented by a matrix that is called the density matrix. It
is traditionally represented by the symbol *ρ*. A measurement or
observation on such a system is effected by means of a probing action,
which is represented by a matrix, traditionally designated by the symbol
*P*, or by a *P* with a subscript, that satisfies *PP=P*. Such a
matrix/operator is called a *projection operator*. The quantum game is
like "twenty questions": the observer-agent "freely poses" a question
with an observable answer 'Yes' or 'No', This question, and the probing
action corresponding to it, are represented in the formalism by some
projection operator *P*. Nature then returns an answer 'Yes' or 'No'.
The probability that the answer is 'Yes' is given by the basic
probability equation of quantum mechanics:

*\<P\> = Trace Pρ/Trace ρ.*

In order not to lose non-physicists, but rather to get them into the
quantum swing of things, and allow them to play this wonderful game, I
shall spell out what this equation means in the simple case in which the
matrices involved have just two rows and two columns. In this case each
matrix/operator has four elements, which are specified by the four
numbers *\<1\|M\|1\>, \<1\|M\|2\>, \<2\|M\|1\>,* and *\<2\|M\|2\>*. The
index on the left specifies the horizontal row, and the index on the
left specifies the vertical column of the matrix in which the matrix
element is to be placed. The rule of matrix multiplication says, for any
two matrices M and N, and any pair of two-valued indices *i and j,*

*\<i\|MN\|j\> = \<i\|M\|k\>\<k\|N\|j\>,*

where one is supposed to sum over the two possible values of the
repeated index k. For any M,

*Trace M = \<k\|M\|k\>*,

where one is again supposed to sum over the (two in this case) different
possible values (1 and 2) of the index *k*.

This case of a system represented by two-by-two matrices is physically
very important: it covers the case of the "spin" degree of freedom of an
electron. Once one sees how quantum mechanics works in this simplest
case, the generalization to all other cases is basically pretty obvious.
So in order to keep non-physicists on board I will spend a little time
spelling things out in detail for this simple case.

Pauli introduced for this two-by-two case four particular matrices
defined by

*\<1\\ σ~0~ \|1\>=1, \<1\\ σ~0~ \|1\>=1, \<1\\ σ~1~ \\2\>=1, \<2\\ σ~1~
\\1\>= 1,*

*\<1 \\ σ~2~* \|2\> = *─ i , \<2 \\ σ~2~* \|*1*\> = *i , \<1\| σ~3~
\|1\> = 1,*

*\<2\| σ~3~ \|2\> = ─1;*

with all other elements zero*.* \[ *i* is the imaginary unit\]

They satisfy *σ~j~ σ~j~ = σ~0~ = I, for all j; σ~1~ σ~2~ = i σ~3~ = ─
σ~2~ σ~1~ ; σ~2~ σ~3~ = i σ~1~ = ─ σ~3~ σ~2~ ;* and *σ~3~ σ~1~ = i σ~2~
= ─ σ~1~ σ~3.\ ~*Most calculations can be done using just these products
of the Pauli matrices.

For actions that probe the direction of the spin of the electron the
projection operator *P = ½(I+ σ~3~ )* represents the probing action that
corresponds to the query "Does the spin of the electron point in the
direction of the axis number 3?" It is also the density matrix that
represents the spin state of the electron if the answer to that query is
'Yes'. In the higher dimensional cases, if *ρ* is the density matrix
prior to the probing action then the density matrix after a probing
action *P* that produces the answer 'Yes' is *PρP* (up to a possible
positive multiplicative factor that drops out of the probability
formula.) If the feedback is 'No' then *ρ* is reduced to *P' ρ P', with
P'= (1-P).*

Suppose one has prepared the spin state of the electron by performing
the probing action corresponding to *P = ½(I+ σ~3~)* and has received
the answer 'Yes'. This means that the density matrix for the system is
now (known to be the state represented by) *ρ =* *½(I+ σ~3~).* Suppose
one now performs the probing action corresponding to the query "Does the
spin point in the direction of axis number 1. The corresponding P is
*½(I+ σ~1~).* Thus the probability that the answer is 'Yes' is

*Trace* *½(I+ σ~1~) ½(I+ σ~3~ )/Trace½(I+ σ~3~)=1/2.*

This simplest example beautifully epitomizes the general case. It
illustrates very accurately how the basic probability formula is used in
actual practice.

The basic probability formula and its workings constitute the foundation
of the quantum mechanical conception of the connection between the
aspects of our scientific understanding of nature described in the
language that we use to describe the pertinent perceptual and felt
contents of our streams of conscious experiences and the aspects
described in the mathematical language of physics.

3.2 Classical Description.

"...we must recognize above all that, even when phenomena transcend the
scope of classical physical theories, the account of the experimental
arrangement and the recording of observations must be given in plain
language, suitably supplemented by technical physical terminology. This
is a clear logical demand, since the very word "experiment" refers to a
situation where we can tell others what we have done and what we have
learned." (Bohr, p. 72)

"...it is imperative to realize that in every account of physical
experience one must describe both experimental conditions and
observations by the same means of communication as the one used in
classical physics." (Bohr, p. 88)

This demand that we *must use* the known-to-be-fundamentally-false
concepts of classical physical theories as a fundamental part of quantum
mechanics has often been cited as the logical incongruity that lies at
the root of the difficulties in arriving at a rationally coherent
understanding of quantum mechanics: of an understanding that goes beyond
merely understanding how to use it in practice. So I focus next on the
problem of reconciling the quantum and classical concepts, within the
context of a theory of the mind-brain connection.

3.3 Quasi-Classical States of the Electromagnetic Field

There is one part of quantum theory in which a particularly tight and
beautiful connection is maintained between classical mechanics and
quantum mechanics. This is the simple harmonic operator (SHO). With a
proper choice of units the energy (or Hamiltonian) of the system has the
simple quadratic form E = H= ½ (p^2^ + q ^2^), where q and p are the
coordinate and momentum *variables* in the classical case, and are the
corresponding *operators* in the quantum case. In the classical case the
trajectory of the "particle" is a circle in q-p space of radius r =
(2E)^1/2^. The angular velocity is constant and independent of E, and in
these special units is ω = 1: one radian per unit of time. The
lowest-energy classical state is represented by a point at rest at the
"origin" q = p = 0.

The lowest-energy quantum state is the state\-\--i.e., projection
operator P\-\--corresponding to a Gaussian wave function that in
coordinate space is

ψ(q) = C exp(─ (½)q^2^) and in momentum space is

ψ(p) = C exp(─ (½ )p^2^), where C is 2^1/4^. If this ground state is
shifted in q-p space by a displacement (Q, P) one obtains a
state\-\--i.e., a projection operator P\-\--labeled by \[Q,P\], which
has the following important property: if one allows this quantum state
to evolve in accordance with the quantum mechanical equations of motion
then it will evolve into the set of states labeled by \[Q(t), P(t)\],
where the (center) point (Q(t), P(t)) moves on a circular trajectory
that is identical to the one followed by the classical point particle.

If one puts a macroscopic amount of energy E into this quantum state
then it becomes "essentially the same as" the corresponding classical
state. Thus if the energy E in this one degree of freedom is the energy
per degree of freedom at body temperature then the quantum state,
instead of being confined to an *exact* *point* (Q(t), P(t)) lying on a
circle of (huge) radius r = 10^6^ in q-p space, will be effectively
confined, due to the Gaussian fall-off of the wave functions, to a disc
of unit radius centered at that point (Q(t), P(t)). Given two such
states, \[Q,P\], and \[Q',P'\], their overlap, defined by the Trace of
the product of these two projection operators, is exp(─ (½ )d^2^), where
d is the distance between their center points. On this 10^6^ scale the
unit size of the quantum state becomes effectively zero. And if the
energy of this classical SHO state is large on the thermal scale then
its motion, as defined by the time evolution of the projection operator
\[Q(t), P(t)\] = P~\[P(t),Q(t)\]~, will be virtually independent of the
effects of both environmental decoherence, which arises from subtle
quantum-phase effects, and thermal noise, for reasons essentially the
same as the reasons for the negligibility these effects on the
classically describable motion of the pendulum on a grandfather clock.

Notice that the quantum state \[Q, P\] is completely specified by the
corresponding classical state (Q, P): the quantum mechanical spreading
around this point is not only very tiny on the classical scale; it is
also completely fixed: the width of the Gaussian wave packet associated
with our

Hamiltonian is fixed, and independent of both the energy and phase of
the SHO.

We are interested here in brain dynamics. Everyone admits that at the
most basic dynamical level the brain must be treated as a quantum
system: the classical laws fail at the atomic level. This dynamics rests
upon myriads of microscopic processes, including flows of ions into
nerve terminals. These atomic-scale processes must in principle be
treated quantum mechanically. But the effect of accepting the quantum
description at the microscopic level is to inject quantum
uncertainties/indeterminacies at this level. Yet introducing even small
uncertainties/indeterminacies at microscopic levels into these nonlinear
systems possessing lots of releasable stored chemical energy has a
strong tendency\-\--the butterfly effect\-\--to produce very large
macroscopic effects later on. Massive parallel processing at various
stages may have a tendency to reduce these indeterminacies, but it is
pure wishful thinking to believe that these indeterminacies can be
completely eliminated in all cases, thereby producing brains that are
completely deterministic at the macroscopic level. *Some* of the
microscopic quantum indeterminacy *must* at least occasionally make its
way up to the macroscopic level.

According to the precepts of orthodox quantum mechanics, these
macroscopic quantum uncertainties are resolved by means of process 1
interventions, *whose forms are not specified by the quantum state of
the universe, or any part thereof*. What happens in actual practice is
determined by conscious choices "for which the quantum mechanical
formalism offers the appropriate latitude". No way has yet been
discovered by quantum theorists to circumvent this need for some sort of
intervention that is not determined by the orthodox physical laws of
quantum physics. In particular, environmental decoherence effects
certainly do not, by themselves, resolve this problem of reconciling the
quantum indeterminacy, which irrepressibly bubbles up from the
microscopic levels of brain dynamics, with the essentially classical
character of our descriptions of our experiences of "what we have done
and what we have learned".

The huge importance of the existence and properties of the
quasi-classical quantum states of SHOs is this: If the projection
operators P associated with our experiences are projection operators of
the kind that instantiate these quasi-classical states then we can
rationally reconcile the demand that the dynamics of our brains be
fundamentally quantum mechanical with the demand that our descriptions
of our experiences of "what we have done and what we have learned" be
essentially classical. This arrangement would be a natural upshot of the
fact that our experiences correspond to the actualization of strictly
quantum states that are both specified by classical states, and that
also closely mimic the properties of their classical counterparts,
*apart from the fact that they represent only potentialities*, and hence
will be subject, just like Schroedinger' macroscopic cat, to the actions
of the projection operators associated with our probing actions. This
quantum aspect entails that, by virtue of the quantum Zeno effect, which
follows from the basic quantum formula that connects our conceptually
described observations to physically described quantum jumps, we can
understand *dynamically* how our conscious choices can affect our
subsequent thoughts and actions: we can rationally explain, by using the
basic principles of orthodox contemporary physics, the causal efficacy
of our conscious thoughts in the physical world, and thereby dissolve
the physicalists' dilemma.

I shall now describe in more detail how this works.

**4. The Mind-Brain Connection.**

The general features of this quantum approach to the mind-brain problem
have been described in several prior publications^2-5,8-11^ . In this
section I will present a specific model based on the general ideas
described in those publications.

Mounting empirical evidence^12,13^ suggests that our conscious
experiences are connected to brain states in which measurable components
of the electromagnetic field located in spatially well separated parts
of the brain are oscillating with the same frequency, and in phase
synchronization. The model being proposed here assumes, accordingly,
that the brain correlate of each conscious experience is an EM
(electromagnetic) excitation of this kind. More specifically, each
process 1 probing action is represented quantum mechanically in terms of
a projection operator that is the quasi-classical counterpart of such an
oscillating component of a classical EM field.

The central idea of this quantum approach to the mind-brain problem is
that each process 1 intervention is the physical aspect of a
psycho-physical event whose psychologically described aspect is the
conscious experience of intending to do, or choosing to do, some
physical or mental action. The physical aspect of the 'Yes' answer to
this probing event is the actualization, by means of a quantum reduction
event, of a pattern of brain activity called a "template for action". A
*template for action* for some action X is a pattern of physical (brain)
activity which if held in place for a sufficiently long time will tend
to cause the action X to occur. The psycho-physical linkage between the
conscious intent and the linked template for action is supposed to be
established by trial and error learning.

A prerequisite for trial and error learning of this kind is that mental
effort be causally efficacious in the physically described world. Only
if conscious choices and efforts have consequences in the physically
described world can an appropriate correlation connecting the two be
mechanically established by trial and error learning. With no such
connection the conscious intention could become completely opposed to
the correlated physical action, with no way to activate a corrective
physical measure.

The feature of quantum mechanics that allows a person's conscious
choices to influence that person's physically described brain process in
the needed way is the so-called "Quantum Zeno Effect". This quantum
effect entails that if a sequence of very similar process 1 probing
actions occur in sufficiently rapid succession then the affected
component of the physical state will be forced, with high probability,
to be, at the particular sequence of times t~i~ at which the probing
actions are made, exactly the sequence of states specified by the
sequence of projection operators P~h~(t~i~) that specify the 'Yes'
outcomes of the sequence of process 1 actions. That is, the affected
component of the brain state\-\--for example some template for
action\-\--will be forced, with high probability, *to evolve in lock
step with* *a sequence of 'Yes' outcomes of a sequence of "freely
chosen" process 1 actions, where "freely chosen" means that* *these
process 1 actions are not determined, via any known law, by the
physically described state of the universe!* This coercion of a
physically described aspect of a brain process to evolve in lock step
with the 'Yes' answers to a sequence of process 1 probing actions that
are free of any known physically described coercion, but that seem to us
to be freely chosen by our mental processes, is what will presently be
demonstrated. It allows physically un-coerced conscious choices to
affect a physically described process that will, by virtue of the basic
probability formula, have experiential consequences.

The repetition rate (attention density!) in the sequence of process 1
actions is assumed to be controlled by conscious effort. In particular,
in the model being described here, where the projection operators
P(*t*~i~) are projection operators \[Q(*t*~i~), P(*t*~i~)\] that are
quasi-classical states of SHOs, the size of the intervals (*t*~i+1~ ─
*t*~i~) \-\-- being a feature of the sequence of "freely chosen" process
1 probing action \-\-- is taken to be under the immediate control of the
psychological aspect of the probing action.

I describe the quantum properties of the EM field in the formulation of
relativistic quantum field theory developed by Tomonaga^14^ and
Schwinger^15^ , which generalizes the idea of the Schroedinger equation
to the case of the electromagnetic field. One can imagine space to be
cut up into very tiny regions, in each of which the values of the six
numbers that define the electric and magnetic fields in that region are
defined. In case the field in that region is executing simple harmonic
oscillations we can imagine that each of the six values is moving in a
potential well that produces the motion of a SHO. If the process 1
action is specified by a 'Yes' state that is a coordinated synchronous
oscillation of the EM field in many regions, {R~1~ , R~2~ , R~3~ , ...}
then this state, if represented quantum mechanically, consists of some
quasi-classical state \[Q~1~, P~1~ \] in R~1~ , *and* some
quasi-classical state \[Q~2,~ P~2~\] in R~2~, *and* some quasi-classical
\[Q~3\ ,~ P~3~ \] in R~3~ , etc.. The state P of this combination is the
*product* of these \[Q~i~ , P~i~\]s, each of which acts in its own SHO
space, and acts like the unit operator (i.e., unity or 'one') in all the
other spaces. This product of P~n~ s, all evaluated at time t~i,~ is the
P~h~(*t*~i~ ) that is the brain aspect of the 'Yes' answer to the
process 1 query that occurs at time t~i~ . The *quantum* frequency of
the state represented by this P~h~(*t*~i~ ) is the sum of the *quantum*
frequencies of the individual regions, and is the total number of quanta
in the full set of SHOs. However, the period of the periodic motion of
the classical EM field remains 2π, in the chosen units, independently of
how many regions are involved, or how highly excited the states of the
SHOs in the various regions become. This smaller frequency is the only
one that the classical state knows about: it is the frequency that
characterizes the features of brain dynamics observed in EEG and MEG
measurements.

The sequence of P~h~(t~i~)s that is honed into observer/agent's
structure by trial and error learning is a sequence of P~h~(t~i~)s that
occurs when the SHO template for action is held in place by effort.
Learning is achieved by effort, which increases attention density, and
holds the template for action in place. Thus if H~0~ is the Hamiltonian
that maintains this SHO motion then for the honed sequence

P~h~(*t*~i+1~) = exp (─ iH~0~ (*t*~i+1~ ─ *t*~i~)) P~h~(t~i~) exp
(iH~0~(*t*~i+1~ ─ *t*~i~)).

But in the new situation there may be disturbing physical influences
that tend to cause a deviation from the learned SHO motion. Suppose that
on the time scale of (*t*~i+1~ ─ *t*~i~ ) the disturbance is small, so
that the perturbed evolution starting from P~h~(t~i~) can be expressed
in the form

P(*t*~i+1~) = exp (─iH~i~ (*t*~i+1~ ─ *t*~i~)) exp (─ iH~0~ (*t*~i+1~ ─
*t*~i~)) P~h~(t~i~)

exp (iH~0~(*t*~i+1~ ─ *t*~i~)) exp ( iH~i~ (*t*~i+1~ ─ *t*~i~))

= exp (─iH~i~ (*t*~i+1~ ─ *t*~i~))) P~h~(*t*~i+1~) exp ( iH~i~ (*t*~i+1~
─ *t*~i~))

where H~i~ is bounded.

According to the basic probability formula, the probability that this
state P(*t*~i+1~) will be found, if measured/observed, to be in the
state P~h~(*t*~i+1~) at time *t*~i+1~ is (using Trace P~h~(*t*~i~) = 1)

Trace P~h~(*t*~i+1~) exp (─iH~i~ (*t*~i+1~ ─ *t*~i~))) P~h~(*t*~i+1~)
exp ( iH~i~ (*t*~i+1~ ─ *t*~i~)).

Inserting the leading and first order terms \[ 1± iH~i~ (*t*~i+1~ ─
*t*~i~)\] in the power series expansion of exp ( ± iH~i~ (*t*~i+1~ ─
*t*~i~)) and using PP= P, and the fact that

Trace AB = Trace BA, for all A and B, one finds that the term linear in

(*t*~i+1~ ─ *t*~i~) vanishes identically.

The vanishing of the term linear in (*t*~i+1~ ─ *t*~i~ ) is the basis of
the quantum Zeno effect. If one considers some finite time interval and
divides it into small intervals (*t*~i+1~ ─ *t*~i~ ) and looks at a
product of factors (1 + c(*t*~i+1~ ─*t*~i~ )^n^ ), then if n is bigger
than one the product will tend to unity (one) as the size of the
intervals (*t*~i+1~ ─ *t*~i~ ) tend to zero. But this means that the
basic probability formula of quantum mechanics requires that, as the
step sizes (*t*~i+1~ ─ *t*~i~) tend to zero, the evolving state of the
system being probed by the sequence of probing action will have a
probability that tends to one (unity) *to evolve in lock step with the
set of 'Yes' answer to the sequence of probing actions*, provided the
initial answer was 'Yes'. But the forms of the projection operators
P~h~(*t*~i~) and the timings of the probing actions are not determined
by the laws of orthodox quantum theory: they are "freely chosen". Hence
orthodox quantum theory accommodates in natural way the capacity of a
person's conscious intentional choices to influence the processes
occurring in his or her physically described brain, and to influence
them in a way that will tend to produce intended consequences.

The point of his derivation is that it is expressed in terms of brain
states that are macroscopic, and that correspond to classically
describable states of the electromagnetic field measured by EEG and MEG
procedures. Even though these states contain huge amounts of energy,
nevertheless, if we accept the principle that the underlying brain
dynamics must in principle be treated quantum mechanically, and,
accordingly, replace these classical states by their quasi-classical
counterparts, which represent potentialities that are related to
experience only via the basic equation, then the principles of orthodox
von Neumann quantum mechanics provide a rationally coherent way of
understanding the mind-brain connection in a way that escapes the horns
of the physicalists' dilemma: it gives each person's intentional
conscious choices the power to causally effect the course of events in
his or her quantum mechanically described brain, and to influence it in
a way that serves these intentions.

**Acknowledgement**

I thank Ed Kelly for many useful suggestions pertaining

to the form of this paper.

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