**Philosophy of Mind and the Problem of Free Will in the Light of
Quantum Mechanics.**

*Henry P. Stapp*

*Lawrence Berkeley National Laboratory*

*University of California*

*Berkeley, California 94720*

**Abstract**

Arguments pertaining to the mind-brain connection and to the physical
effectiveness of our conscious choices have been presented in two recent
books, one by John Searle, the other by Jaegwon Kim. These arguments are
examined, and it is explained how the encountered difficulties arise
from a defective understanding and application of a pertinent part of
contemporary science, namely quantum mechanics. The principled quantum
uncertainties entering at the microscopic levels of brain processing
cannot be confined to the micro level, but percolate up to the
macroscopic regime. To cope with the conflict between the resulting
macroscopic indefiniteness and the definiteness of our conscious
experiences, orthodox quantum mechanics introduces the idea of
agent-generated probing actions, each of which specifies a definite set
of alternative possible empirically/experientially distinguishable
outcomes. Quantum theory then introduces the mathematical concept of
randomness to describe the probabilities of the various alternative
possible outcomes of the chosen probing action. But the agent-generated
choice of which probing action to perform is not governed by any known
law or rule, statistical or otherwise. This causal gap provides a
logical opening, and indeed a logical need, for the entry into the
dynamical structure of nature of a process that goes beyond the
currently understood quantum mechanical statistical generalization of
the deterministic laws of classical physics. The well-known quantum Zeno
effect can then be exploited to provide a natural process that
establishes a causal psychophysical link within the complex structure
consisting of a stream of conscious experiences and certain macroscopic
classical features of a quantum mechanically described brain. This
naturally created causal link effectively allows consciously felt
intentions to affect brain activity in a way that tends to produce the
intended feedback. This quantum mechanism provides an eminently
satisfactory alternative to the classical physics conclusion that the
physical present is completely determined by the physical past, and
hence provides a physics-based way out of the dilemma that Searle and
Kim tried to resolve by philosophical analysis.

**1. Introduction.**

The central problem in philosophy of mind is the mind-body problem: the
problem of reconciling our science-based understandings of the causal
structure of the physically described world, including our bodies and
brains, with the apparent capacity of our conscious thoughts and efforts
to cause our bodies to move in consciously intended ways.

The contention of the present work is that the difficulties that
philosophers of mind are encountering in coming to a satisfactory
resolution of this problem arise from a faulty understanding and
application of a relevant part of contemporary science, namely quantum
mechanics. Philosophy of mind is a vast field, so to make my task
manageable I shall limit my remarks to the opinions and arguments
presented in two recent books, John Searle's *Freedom and Neurobiology:
Reflections on Free Will, Language, and Political Power^1^*, and Jaegwon
Kim's *Physicalism, or Something Near Enough^2^*.

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

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

**2. Searle's Approach.**

John Searle begins Section 1 of his book with the assertion: "There is
exactly one overriding question in contemporary philosophy...As a
preliminary succinct formulation we could put it in these terms: How do
we fit in?" He explains that: "We now have a reasonable well-established
conception of the basic structure of the universe." "We understand that
the universe consists entirely of particles (or whatever entities the
ultimately true physics arrives at), and these exist in fields of force
and are typically organized into systems." He observes that: "On our
earth, carbon-based systems made of molecules that also contain a lot of
hydrogen, nitrogen and oxygen have provided the substrate of human,
animal and plant evolution", and says that: "These and other such facts
about the basic structure of the universe, I will call, for short, the
'basic facts' . The most important sets of basic facts, for our present
purposes, are given in the atomic theory of matter and the evolutionary
theory of biology."

These statements identify the foundation and orientation of Searle's
approach: We human beings are biological systems made of atoms and
molecules, and our complete understanding of ourselves should therefore
emerge from an analysis of our understandings of our biological
structures, which rest in turn on the atomic theory of matter.

Searle notes that his approach rests also on an important difference
between what is possible in philosophy today and what was feasible in
the past. He notes that "For three centuries after Descartes, the
epistemological questions, especially the skeptical questions, formed
the center of philosophical interest. (p.26)" That quest can now be
ended because "We simply know too much. We have a prodigious amount of
knowledge that is known with objectivity, certainty, and universality.
... They are known with certainty, in the sense that the evidence is now
so great that it is irrational to doubt them."(p. 27)" Searle thus
escapes the search-for-certainty dead end by accepting the
above-mentioned 'basic facts'.

Searle observes that we have, however, in addition to the 'basic facts'
also a conception of ourselves as conscious, intentionalistic, rational,
...free will possessing agents," and he identifies the question to be
addressed by his book\--which is also the topic of this article\--as:
"How can we square this self-conception of ourselves as mindful,
meaning-creating, free, rational, etc., agents with a universe that
consists entirely of mindless, meaningless, unfree, nonrational, brute
physical particles.(p.5)"

Two key problems facing this endeavor are "consciousness" and "free
will". Searle claims to have solved the *philosophical* problem of
consciousness by asserting that "Conscious states are entirely caused by
neuronal processes in the brain, and are realized in the brain." The
residual problems of consciousness are thereby relegated to
neurobiology: "How exactly does the brain cause conscious experiences,
and how are those experiences realized in the brain." (p.6)

**3. Free Will.**

The free-will problem is "How can there exist genuinely free actions in
a world where all events, at least at the macro level, apparently have
causally sufficient antecedent conditions? Every event at that level
appears to be determined by causes that preceded it. Why should acts
performed during apparent human consciousness of freedom be an
exception? It is true that there is an indeterminacy in nature at the
quantum level, but that indeterminacy is pure randomness and randomness
is not by itself sufficient to give free will." (p. 10-11)

Searle admits that for the problem of free will "we are nowhere remotely
near having a solution." (p.11)

Why is solving the problem of free will so important?

The useful practical purpose of philosophy is to arrive at a coherent
understanding of how we fit in, in order that we may conduct our lives
in accordance with principles not beset with contradictions. Searle
makes a convincing case (p.11) that we must, in order to function
rationally in this world, believe that we are sometimes free to choose
our actions. To deny this would create a self-contradiction. But without
resolving the problem of free will, philosophy loses its rational
coherence, and men will turn to other sources for the foundations of
their beliefs.

The importance of arriving at a solution of the free-will problem is
highlighted also by recent controlled studies^3^ that show that
experimental subjects conditioned by arguments that promote the thesis
that we have no free will, that free will is an illusion, that mind is
epiphenomenal, are more likely to cheat and lie than subjects
conditioned by arguments defending the thesis that the freedom that we
feel is bona fide. Hence, again, achieving a solution of the free-will
problem has important consequences in our lives.. This motivates our
taking a closer look at Searle's arguments and the difficulties that
they create for solving the free-will problem.

Searle, following his neurobiological approach, must explain how free
will can be converted to a problem in neurobiology. He considers two
hypotheses (p.61-73):

Hypothesis 1: The neurobiological state of the brain is causally
sufficient to determine the behavior of the brain, hence the body. In
this case, the *feeling of freedom to choose* some of our actions is an
illusion! Consciousness lacks causal efficacy. It is purely
epiphenomenal. Searle emphasizes that this idea\-\--that nature has
provided us with this fantastic feature, consciousness, that seems to
play an essential role in the successful conduct of our lives, but that
actually does nothing\-\--is "unattractive" (p.70). He emphasizes the
great biological cost of producing the machinery needed to create
consciousness. The suggestion that the output of this costly biological
process has no physical effect is hard to square with evolutionary
theory.

Hypothesis 2: The neurobiological state of the brain is causally
*in*sufficient to determine the behavior of the brain, and this causal
gap allows our conscious choices to influence our conduct in the way
that they seem to do, namely on the basis of *choices based on*
*reasons*. He argues that "reasons" can fulfill the role of sufficient
conditions only by way of influencing our deliberating, choosing, and
physically efficacious conscious "selves".

The demand that neurobiological state of the brain is causally
insufficient to determine the ongoing behavior of the brain entails the
failure of one of the chief properties of classical physical theories,
the causal closure of the physically described aspects of nature. Searle
says:

"It is tempting, indeed irresistible, to think that the explanation of
the conscious experience of free will must be a manifestation of quantum
indeterminism at the level of conscious, rational decision making.
Previously I never could see the point of introducing quantum mechanics
into the discussion of consciousness. But here is at least a strict
argument requiring the introduction of quantum indeterminism.

Premise 1. All indeterminism in nature is quantum indeterminism.

Premise 2. Consciousness is a feature of nature that manifests
indeterminism.

Conclusion: Consciousness manifests quantum indeterminism."

"....This \[conclusion\] is important for contemporary research. The
standard lines of research...make no appeal to quantum mechanics. If
Hypothesis 2 is true these cannot succeed, at least not for volitional
consciousness." (p.75)

He goes on: "If quantum indeterminism amounts to randomness then quantum
indeterminism by itself seems useless in explaining the problem of free
will because free actions are not random." The point here is that we
need an explanation not only of the *failure* of physical determinism,
but an explanation also of the filling of that causal gap by our "free"
choices based on *reasons*.

Summarizing, he says: "Once we sorted out the issues we found two
possibilities, Hypothesis 1 and Hypothesis 2. Neither is very appealing.
If we had to bet, the odds would surely favor Hypothesis 1, because it
is simpler and fits with our overall view of biology. But it gives
results that are literally incredible." (One cannot literally believe
that oneself cannot make choices.) But "Hypothesis 2 is a mess, because
it gives us three mysteries for one. We thought free will was a mystery,
but consciousness and quantum mechanics were two separate and distinct
mysteries. Now we have the result that in order to solve the first we
have to solve the second and invoke one of the most mysterious aspects
of the third to solve the first two."

**4. The Three Mysteries.**

But who could think that these three "mysteries" were separate and
distinct?

With regard to the connection between free will and mind, William James
asserted, near the beginning of *The Principles of Psychology^4^*,

> "*The pursuance of future ends and the choice of means for their
> attainment are thus the mark and criterion of the presence of
> mentality* in a phenomenon". (James, p.8)
>
> "*No actions but such as are done for an end, and show a choice of
> means, can be called indubitable expressions of Mind*". (James, p.10)

Thus, for James, mind is fundamentally tied to *the choice of a means to
an end.* On the other hand, the solution that Searle offered long ago to
the mind-brain problem did not touch on free will. It said simply:
"Conscious states are entirely caused by neuronal processes in the
brain, and are realized in the brain." He notes, as mentioned above,
that this *philosophical* solution relegates to neurobiology the
residual questions: "How exactly does the brain cause conscious
experiences?" "How are those experiences realized in the brain." And he
admits that contemporary mainstream neurobiology is nowhere near solving
these residual questions. Indeed, insofar as neurobiology bases itself
purely on classical mechanics, it lacks any logical or theoretical basis
to link the empirically observed correlations between conscious
experiences and brain behavior to any notion of how this classically
conceived physically described brain could *cause to occur events having
the knowingness and feelingness that characterize our conscious
experiences*. There is nothing in the classical conception of physically
described matter that could *cause* (even) a complex classically
conceived high-level systems property to embellish itself, or endow
itself, with *an experience of knowing or feeling*. Such a causal
capacity is not in the inventory of properties assigned to physically
described systems by classical physics. The physically described aspects
of systems, as conceived of in classical physics\-\--*unlike the
physically described aspects of systems as conceived of in quantum
mechanics*\-\--have been stripped of any necessary causal connection to
knowings or feelings. The physical aspects are both causally and
conceptually complete. Thus, insofar as the neurobiology that Searle
contemplates is based fundamentally on the classical physics of the
seventeenth through nineteenth centuries, it is not true that the 'basic
facts' entail a neurobiological solution of the mind-body problem of the
kind that Searle asserts. There is a logical gap! A true 'basic fact' is
that this classical conception of the physical is inadequate to explain
the atomic properties upon which actual neurobiological structures are
based. Because Searle has not incorporated the logical and causal
structure of quantum mechanics into his conception of neurobiology, his
claim to have solved even the purely philosophical part of the mind-body
problem is not rationally justified: there is no rational reason to
believe that a solution along classical lines is possible in a
fundamentally non-classical universe, particularly since the orthodox
quantum successor to classical physics involves the *necessary*
introduction, into the basic dynamics, of actions by agents; actions
that are not specified by the micro-physical laws, but that, within the
theory, arise from *free choices of means to attain intended ends*.

This flaw is implicit in Searle's open-ended introductory proviso, i.e.
"(or whatever entities the ultimately true physics arrives at)." His
arguments tacitly assume that these entities will be like "quarks" or
other "mindless" entities, not like the mindful elements of our streams
of consciousness. Yet Searle's 'basic facts' include atomic theory,
which was radically transformed during the twentieth century. Searle
uses the new theory, quantum theory, in his analysis of free will.
However, the opening words of Bohr's 1934 book *Atomic Theory and the
Description of Nature^5^* are: "The task of science is both to extend
the range of our experience and reduce it to order." This idea is
restated many times in many ways, for example as: "In our description of
nature the purpose is not to disclose the real essence of phenomena but
only to track down as far as possible relations between the multifold
aspects of our experience. (p.18)" Werner Heisenberg's famous expression
of this point was:

> "The conception of the objective reality of the elementary particles
> has thus evaporated not into the cloud of some obscure new reality
> concept but into the transparent clarity of a mathematics that
> represents no longer the behavior of the particles but rather our
> knowledge of this behavior" (Heisenberg^6^ , p.100)

These statements emphasize that the basic ontological realities of
quantum theory are not physical particles, but rather increments in
knowledge. They are conscious experiences occurring in streams of
conscious experiences. The "physical description" of earlier (classical)
physical theories is *transformed* in quantum mechanics to a
mathematical structure that represents not material particles but rather
"potentia" (objective tendencies) for new knowledge-increasing events to
occur in our streams of consciousness. Each such event is accompanied by
a change in the mathematically described "potentia" for future events.
This change renders the potentialities for future experiences consistent
with the increased knowledge. The theory is therefore useful and
testable because it directly predicts *relationships between our
experiences\-\--between our conscious acts of knowing.*

Searle introduces, in connection with his analysis of free will, the
indeterminacy aspect of quantum mechanics but not the other profoundly
relevant features just mentioned. On page 11 he says "It is true that
there is an indeterminacy in nature at the quantum level, but that
indeterminacy is pure randomness and randomness is not by itself
sufficient to give free will."

While it is absolutely true that randomness is different from, and
insufficient for, free will, which involves reason-based choices of
means to attain intended ends, it is *absolutely untrue* that quantum
indeterminism is pure randomness. Bohr says:

> To my mind there is no alternative than to admit that, in this field
> of experience, we are dealing with individual phenomena and that our
> possibilities of handling the measuring instruments allow us only to
> make a choice between the different complementary types of phenomena
> that we want to study. (Bohr^7^, p.51)
>
> The freedom of experimentation, ... is fully retained and corresponds
> to the free choice of experimental arrangement for which the
> mathematical structure of the quantum mechanical formalism offers the
> appropriate latitude^6^. (Bohr^7^, p. 71)

This "appropriate latitude" "offered by the mathematical structure of
the quantum mechanical formalism" is a key aspect of the indeterminism
of quantum mechanics, but it is quite different from another aspect
which is the "randomness". The quantum mechanical approach rests on a
postulated connection between two aspects of the scientific description
of phenomena. One aspect is described in terms of the mathematical
structure of the quantum mechanical formalism. The other aspect is
described in terms of

appearances:

> ...we must recognize above all that, even when the phenomena transcend
> the scope of classical physics, the account of the experimental
> arrangements must be given in plain language, suitably supplemented by
> technical physical terminology. This is a simple 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^7^, p.72)

Von Neumann^8^ formulated quantum mechanics in a mathematically and
logically rigorous way. He gave the name "process 1" to the *physically
described counterpart* of the "free choice of experimental arrangement"
that is described in terms of appearances/experiences. A key feature of
this choice, and hence of its process 1 physical counterpart, is that it
is "free" in the specific sense that the quantum laws and rules place no
conditions, *statistical or otherwise*, upon it! This choice is free of
any known theoretical constraint! It is indeterminate. The 'random'
aspect comes in, logically, only *after* this process 1 physical action.
The process 1 action specifies some particular *partition* of the prior
physical state into a countable set of distinct possibilities. Orthodox
quantum theory then asserts that some single one of the
*specified-by-process-1 distinct possibilities* will occur, randomly.
The "randomness" condition asserts that these *occurrences of outcomes*
will be in accord with statistical weights that are specified by the
quantum mechanical formalism. But the preceding *partitioning of the
prior collection of possibilities into a (countable) set of distinct
possibilities is an indeterminate processes that according to orthodox
quantum mechanics is not random, but is treated, rather, as a
reason-based choice of means to an end!* The experimenter chooses
between this set-up or that set-up on the basis of reasons! More
generally, a person's most consciously made choices appear to arise from
reasons, and feelings. And within quantum mechanics there is a *logical*
*need* for physically effective choices that are not determined, even
statistically, by the known laws of quantum mechanics. There is,
therefore, a rational opening for the causal roots of the causally
effective choices mandated by quantum theory to lie, in part, in the
realm of our streams of consciousness, and hence for the principle of
the causal closure of the physical to fail.

Von Neumann's work allows our bodies and brains to be described in terms
of the quantum mechanical formalism. This makes the two disparate
descriptions\-\--perceptual-intentional and
quantum-mathematical\-\--that occur in quantum mechanics identifiable
with the two disparate descriptions occurring in the mind-body problem.

What these features of quantum mechanics imply is that Searle's basic
idea that the "basic facts" entail "a universe that consists entirely of
mindless, meaningless, unfree, nonrational, brute physical particles" is
grossly at odds with a universe containing ourselves in the way
specified by quantum mechanics. The reduction to "brute physical
particles" is a feature that emerges only in the classical
approximation.

Searle concludes (p.71) that "It seems to me that there are three
conditions, in ascending order of difficulty, and an account of brain
functioning in accord with Hypothesis 2 would have to explain how the
brain meets these conditions."

1.  "Consciousness, as caused by neuronal processes and realized in
    neuronal systems, functions causally in moving the body."

2.  "The brain causes and sustains the existence of a conscious self
    that is able to make rational decisions and carry them out in
    actions."

3.  "The brain is such that the conscious self is able to make and carry
    out decisions in the gap, where neither decision nor action is
    determined in advance by causally sufficient conditions, yet both
    are rationally explained by the reasons the agent is acting on."

As regards condition 1, Searle claims that he has already explained how
this is possible, by analogy with the Roger Sperry's example of how the
"solidity" (a high-level property) allows the motion of the whole wheel
to cause its molecules to move in a coordinated way, controlled from
top-down by high-level collective properties. But he had already noted
(p. 64) that: "any analogy goes only so far. The analogy, solidity is to
molecular behavior as consciousness is to neuronal behavior, is
inadequate at, at least, two points. First, we take the wheel to be
entirely deterministic, and \... second, the solidity of the wheel
ontologically reducible to the behavior of the molecules", whereas
neither of these conditions carry over to the Hypothesis 2 case. Hence
the basis of his earlier claim to have solved the consciousness
(mind-body) problem disintegrates in the Hypothesis 2 case. There is no
need, on the basis of the *true* 'basic facts', for consciousness to be
(fully) caused by the brain, as the brain is described in quantum
mechanics.

As regards Searle's condition 2, the quantum ontological foundation of a
person's stream of conscious experiences is no longer solely a
classically conceived brain. The quantum mechanically conceived brain
specifies only the potentialities/probabilities for certain
psychophysical events to occur *under the condition that certain
associated described process 1 choices have previously been made*. These
dual-aspect psychophysical events are the basic entities. The
psychological description and the physical description specify two
aspects (sides) of a single event-type entity. The conscious self is a
stream of conscious events. These events are the psychologically
described aspects of a sequence of psychophysical events whose physical
aspects are a sequence of physical events in a single brain. Mental
process is to be understood in terms of this richer dualistic
ontological base, rather than the impoverished purely physical part that
survives contraction to the classical approximation. So it is not
completely evident that the brain "causes" the conscious self, as Searle
avers, as contrasted to the possibility that the detailed structure of
the evolving brain comes to be what it is at any moment in time by
virtue of a process that is more of a collaboration between mind and
brain, dependent in part upon the physical effects of the
conscious-agent-generated process 1 physical process rather than
exclusively upon a one-way bottom-up causal process.

The way that condition 3 is satisfied in quantum mechanics is described
in sections 7 and 8, and relies heavily on the quantum Zeno effect.

I turn next to a discussion of Kim's arguments.

**5. Physicalism.**

The widely held philosophical position called "physicalism" has been
described and defended in a recent book by Jaegwon Kim^2^. The
physicalist 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 contravened 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 the
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 article is to show that the physicalist's
dilemma dissolves when one shifts from the classical notion of the
physical to its quantum mechanical successor. Understanding this shift
involves distinguishing the quantum conception of the mind-brain from
the shadow of itself that survives reduction to the classical
approximation.

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^9-12^. 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 intended 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, and in
the issue of free will, 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
extra ideas about the form of the mind-brain connection.

**6. 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 principles of his (Copenhagen) approach are
insufficient to cover biological systems. But that limitation 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^8^ showed how to preserve the
rules and precepts of quantum mechanics all the way up to the mind-brain
interface, preserving the basic 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 Copenhagen 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 psychophysical 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 collection of potentialities or
possibilities for future events. 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 calls this choice
"the free choice of experimental arrangement for which the quantum
mechanical formalism offers the appropriate latitude." (Bohr^7^, 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 necessarily determined, even
statistically, by the physically described aspects of the theory.

The fact that this choice made by the human observer/agent is not
necessarily determined by the physical state of the universe means that
*the principle of the causal closure of the physical domain is not
necessarily 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 ." (p. 14) Kim indicates that
supervenience is a common element of all *physicalist theories.* But
since this supervenience property is not required by basic (i.e.,
quantum) physics, the easy first step 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 also of this idea of supervenience, do not hold in real
brains, whose activities are influenced heavily by quantum processes
that require (process 1) physical inputs that are not necessarily
*wholly* determined by what happens with our bodily 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?" (Kim, p.7) The problem of consciousness is:
"How can there be such a thing as consciousness 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." (Kim, p. 7)

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 undeniable 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 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 incredibly out of step with the physics of their day.

Kim's "physicalist" solution to the problem of the connection between
mind and brain is essentially to separate a mental reality such as a
"pain", by dividing "being in pain" into "the conscious experience of
being in pain" and the "state of being in pain", and allowing the latter
to be characterized as being caused by certain physically described
causes and as causing some physically described effects/behaviors. The
second part can be physical, and hence mind-body "physicalism" is
achieved, except for the fact that the first part, "the conscious
experience of being in pain", is non-physical and epiphenomenal. Kim
claims that this is the best that can be done by way of saving mind-body
physicalism, but that this is "near enough". However, the epiphenomenal
character of our streams of conscious experiences within
classical-physics-based ontologies has always been the central problem,
and Kim's physicalist "near enough" solution does not really solve it.

Kim tries in his chapter 3 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 on the
mind side with mysterious disconnected "souls" whose "essential nature
is that they are wholly outside the spatial order and lack all spatial
properties". (p. 87). However, the experientially described mental
entities that occur in pragmatic quantum theory are the basic realities
of science. They are the ideas that we are able to 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.
In ontologically construed orthodox quantum mechanics these descriptions
are descriptions of mental idea-like aspects of *real actual events,*
each of which has also a physically described aspect that imposes in the
spatio-temporally-based realm of potentialities for future
psycho-physical events the conditions entailed by the increment in
knowledge that constitutes its mental aspect. Criticizing dualism in the
soul-based (essentially disconnected) form advanced by Descartes during
the seventeenth century instead of in the dual-aspect reduction-event
form implicated by 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 in the role of our conscious
minds that had occurred in basic science during the 1920s.

Kim's chapter 3 is supposed to rule out dualism. But the dualism that he
mainly addresses is a stark Cartesian (substance) dualism involving
"souls" existing "outside physical space". He says "My target will be
the interactionist dualism of Descartes." But Quantum mechanics involves
a particular kind of dualism: it is a dual-aspect theory. In footnote 3
on page 71 Kim suggests that "dual-aspect" theories are "only variants
of property dualism." He says later that "What has become increasingly
evident over the past thirty years is that mental causation poses
insuperable difficulties for all forms of mind-body dualism\-\--for
property dualism no less than substance dualism. ...but I believe that
if we have learned anything from the three decades of debate, it is that
unless we bring the supposed mental causes fully into the physical world
there is no hope of vindicating their status as causes, and that the
reality of mental causation requires reduction of mentality to physical
processes, or of minds to brains." (p.156). He gives on the preceding
page a supposed way of "generating the problem of mental causation for
property dualism" without assuming "the causal closure of the physical".
But his argument includes an assumption "Given that your finger
twitching, a physical event, has a full physical cause." This assumption
is indeed less than an assumption of full causal closure of the
physical. But in the quantum mechanical explanation of the way that mind
causes bodily action the twitching does not have "a fully physical
cause." According to quantum mechanics there needs to be a process 1
action mediating the connection between the psychologically described
cause\-\--a pain in this case\-\--and any physical action caused by the
pain. But the process 1 action has no known or necessary fully physical
cause. A quantum mechanical account of how consciousness, per se,
becomes causally effective is described in sections 7 and 8. It does not
"bring the ...mental causes fully into the physical world" but rather
brings only the *effects* of the mental causes into the physical world.

Searle also has a problem with dualism. He says: "I am rejecting ...any
form of dualism. Dualism is usually defined as the view that we live in
two distinct realms, ...the mental and the physical. The problem with
dualism is that it amounts to giving up on the central enterprise of
philosophy. ...It might turn out, for example, that after our bodies are
destroyed, our souls or conscious states will float about in a
disembodied fashion. But it would be giving up on the philosophical (not
to mention scientific) enterprise of trying to explain what we know to
be real phenomena if we say that they defy explanation because they
inhabit a separate realm." (p. 19).

But is dualism (in any form) usually the view that we live in two
distinct realms?

The Oxford Companion to Philosophy (T. Honderich, ed.) defines:

Dualism: The theory that mind and matter are two distinct things. (p.
206)

The Blackwell "A Companion to Philosophy of Mind" (S. Guttenplan ed,)
says:

...the dualist answer is that each person's mind is at least not
identical with his body, so these are two different things. (p. 256)

Quantum mechanics allows the physical and mental aspects of a
psychophysical event to be non-identical, while not saying that real
phenomena defy explanation because they inhabit a separate realm. Rather
it *explains* how conscious mental intentions can, *by virtue of the
quantum mechanical laws themselves*, have the intended physically
described effects.

Philosophers of mind appear to have arrived, today, at
less-than-satisfactory solutions to the mind-brain and free will
problems, and the difficulties seem, *at least* *prima facie*, very
closely connected to their acceptance of a known-to-be-false
understanding of the basic nature of the physical world, and of the
causal role of our conscious thoughts within it.

In the following two sections I shall explain how these difficulties can
be resolved by accepting an ontological construal of the essentially
orthodox (von Neumann/Heisenberg) quantum mechanical understanding of
the mind-body connection. By "orthodox" I mean an understanding that
accepts the existence of reduction events that coordinate increments of
knowledge to reductions of the physically described potentialities for
future events.

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

7.1 The two basic formulas.

Quantum mechanics is a conceptual structure erected upon a certain kind
of mathematical description of physical states, and a certain kind of
phenomenal description of conscious experiences, and upon two basic
formulas that connect these two kinds of descriptions. The physically
described state of the universe, or of any physically describable
subsystem, is represented by a mathematical structure called a density
matrix or probability operator. It is usually represented in the theory
by the symbol ρ. The first basic formula specifies the action upon the
prior physical state ρ by a *process 1 physical action*. This physically
described action is tied, both conceptually and causally, to an
associated "free choice of probing action described in everyday
language, refined by the concepts of classical physical theory". An
elementary process 1 action partitions the prior state ρ into two
distinct non-interfering parts.

ρ  P ρ P + P' ρ P' (P'= 1-P)

The first part, P ρ P, is associated with the occurrence/appearance of a
pre-specified, possible, perceptually identifiable outcome 'Yes'. The
other part is associated with a failure of that 'Yes' outcome to
occur/appear.

The symbol P represents an operator that satisfies PP=P. Such an
operator is called a *projection operator*.

The quantum game is like "twenty questions": the observer-agent "freely
poses" a question with an experientially identifiable answer 'Yes'. The
physical process 1 probing action corresponding to this question is
represented in the mathematical formalism by a projection operator P.
Nature then returns an answer 'Yes' or 'No'. The probability that the
experienced answer is 'Yes' is given by the basic probability formula of
quantum mechanics:

\< P \> *= Trace* P *ρ* P */Trace ρ.*

The "Trace" operation acting upon an operator X, which is conceived of
as an action that acts on whatever stands on its right, is the
instruction: "Let X act back around upon itself!" The result is always a
number. \[For a detailed explanation of the mathematical meaning and
workings of the above basic formulas see:
http://arXiv.org/abs/0803.1625\]

These two formulas constitute the foundation of the quantum mechanical
rules for predicting certain statistical connections between: (1), the
aspects of our conscious experiences that are described in the language
that we use to describe to ourselves and to others the perceptual
contents of our streams of conscious experiences; and (2), the aspects
that are described in the mathematical formalism of quantum physics.

7.2 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^7^, 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^7^, 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: i.e., of an understanding that goes
beyond merely understanding how to use it in practice. So I will
consider next the problem of reconciling the quantum and classical
concepts, within the context of a quantum theory of the mind-brain
connection.

7.3 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 ρ is the 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~\[Q,P\]~, 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 trjectory of states P~\[Q(t),P(t)\]~, 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 = 10^7^ 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, P~\[Q,.P\]~, and P~\[Q',P'\]~, 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
10^7^ 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 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, P~\[Q,.P\]~, is completely specified by
the corresponding classical state (Q, P): the quantum mechanical spread
away from 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*. In actual practice, what happens 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 would then correspond to the actualization of
strictly quantum states that are both specified by classical states, and
whose behaviors 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.

**8. The Mind-Brain Connection.**

The general features of this quantum mechanical approach to the
mind-brain problem have been described in several prior
publications^9-12^ . In this section I will present a specific model
based on the general ideas described in those publications, but that
adds some specifications pertaining to the quantum-classical
connection..

Mounting empirical evidence^13,14^ 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
felt 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 mental and
physical aspects of events be mechanically established by trial and
error learning. With no such connection the physical action could become
completely disconnected from the associated conscious intent with no
adverse consequences.

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
quantum probability formula, have intended experiential consequences.

In this model, the repetition rate (attention density) of the sequence
of process 1 actions is assumed to be controlled by conscious effort. In
particular, in the model where the projection operators P(*t*~i~) are
projection operators P\[Q(*t*~i~), P(*t*~i~)\]\-\--\[In order to
accommodate subscripts, I have now raised to *on-line* the arguments
that in Chapter 7 I wrote as subscripts\]\-\--the presumption is that
the size of the intervals (*t*~i+1~ ─ *t*~i~) are under the control of
the psychological aspect of the probing action. This is in line with the
general assumption that some of the details of the process 1 probing
actions are at least partly under control of the associated stream of
consciousness. This postulated influence of consciousness upon the
*timings* of the events is the *only* influence granted to mind by this
model. All other features of the events are assumed to be specified in
some way by the physically described conditions.

I describe the quantum properties of the EM field in the formulation of
relativistic quantum field theory developed by Tomonaga and by
Schwinger. It 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 projection operator P corresponding to 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 P\[Q~1~,
P~1~ \] in R~1~ , *and* some quasi-classical state P\[Q~2,~ P~2~\] in
R~2~, *and* some quasi-classical P\[Q~3\ ,~ P~3~ \] in R~3~ , etc.. The
state P of this combination is the *product* of these P\[Q~i~ , P~i~\]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 (via the
quantum Zeno effect) by effort. Learning is achieved by effort, which
increases attention density, and holds the template for action in place
during learning. 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 application 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, if the
initial answer is 'Yes', then the basic probability formula of quantum
mechanics entails 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,* *specified by the
sequence of projection operators P~h~(t~i~) associated with the
previously learned action*. Thus the power merely to influence only the
*intention densities* of a repetitious sequence of the process 1 actions
confers upon conscious effort the power both to instill in the
neuro-plastic brain, by trial and error learning, physical templates for
action associated with felt intentional effort, and, later, to hold in
place by a similar mental effort the physical templates for the
previously learned action. These "attention densities", though causally
efficacious in the brain, are not themselves determined by any known law
or rule. Hence they and their physical consequences *could be*, as they
seem to us to be, influenced by conscious mental effort per se.

**9. Conclusion**.

Large-scale brain dynamics can be largely controlled by macroscopic
brain activities that generate classically describable oscillating
states of the electromagnetic field measured by EEG and MEG procedures.
These states contain huge amounts of energy, on the atomic scale.
Nevertheless, if we accept the principle that the underlying brain
dynamics *must* *in principle* be treated quantum mechanically, then we
must replace these classically conceived brain activities by their
quasi-classical quantum counterparts. These are physically described SHO
projection operators, each of which specifies the potentiality for the
arising in the brain of a particular template for action. *The physical
structure underlying each such template is instantiated in the
neuroplastic brain, in association with a conscious effort, by a natural
quantum process that exploits the quantum Zeno effect. A subsequent
activation of this template can be sustained by a similar later
conscious effort via the same quantum- Zeno-based process.* Thus the
principles of orthodox (von Neumann/Heisenberg) quantum mechanics
provide the dynamical basis for the natural creation causal mind-brain
connections that allows an escape from the horns of the physicalists'
dilemma. It gives each person's effortful conscious intentions the
*direct* power to causally influence the course of events in his or her
quantum mechanically described brain in a way that tends to produce the
intended experiential feedback.

A further development and discussion of the mathematical details can be
found in reference 15.

**Acknowledgement.**

I thank Ed Kelly for useful suggestions pertaining to the form of this
paper.

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