**4. The von Neumann/Stapp Approach**

Von Neumann quantum theory is a formulation in which the entire physical
universe, including the bodies and brains of the conscious human
participant/observers, is represented in the basic quantum state, which
is called the state of the universe. The state of a subsystem, such as a
brain, is formed by averaging (tracing) this basic state over all
variables *other* than those that describe the state of that subsystem.
The dynamics involves *three* processes.

Process **1** is the choice on the part of the experimenter about how he
will act. This choice is sometimes called "The Heisenberg Choice,"
because Heisenberg emphasized strongly its crucial role in quantum
dynamics. At the pragmatic level it is a "free choice," because it is
controlled, at least in practice, by the conscious intentions of the
experimenter/participant, and neither the Copenhagen nor von Neumann
formulations provide any description of the *causal origins* of this
choice, apart from the mental intentions of the human agent. Each
intentional action involves an effort that is intended to result in a
conceived experiential feedback, which can be an immediate confirmation
of the success of the action, or a delayed monitoring the experiential
consequences of the action.

Process **2** is the quantum analog of the equations of motion of
classical physics. As in classical physics, these equations of motion
are local (i.e., all interactions are between immediate neighbors) and
deterministic. They are obtained from the classical equations by a
certain *quantization* procedure, and are reduced to the classical
equations by taking the *classical approximation* of setting to zero the
value of Planck's constant everywhere it appears. Evolution via the
quantum Process **2** normally has the effect of expanding the
microscopic uncertainties demanded by the Heisenberg uncertainty
principle into the macroscopic domain: the *centers* of large objects
tend to become diffused over large regions. The disparity between this
Process-**2**-generated theoretical indefiniteness and the consciously
experienced definiteness of the positions of visible objects is resolved
in quantum theory by invoking Processes **1** and **3**.

Process **3** is sometimes call the "Dirac Choice." Dirac called it a
"choice on the part of Nature." It can be regarded as Nature's answer to
a question effectively posed by the Process **1** choice made by the
experimenter. This posed question might be: Will the Geiger counter be
observed to be in the intended position? Or, Will the Geiger counter be
observed to "fire" in accordance with the experiential conditions that
define a 'Yes' response? The application of quantum theory demands the
formulation/posing/choosing of a definite yes-or-no question -- or a set
of such questions -- in connection with each potential experience for
which a prediction is to be made.

Although Process **1** brings the conscious choices made by the
observer/participant into the dynamics in an essential way, there is a
tendency for this dependence upon the agent's choice to be wiped out by
the subsequent averaging over the two possible answers, 'Yes' and 'No,'
to any question posed by Process **1**. However, Stapp has pointed out
that if willful effort can adequately control the *rate* at which a
sequence of similar Process 1 events occur then willful effort can
become highly causally efficacious: such a sequence of events, if
sufficiently rapid, can hold certain properties of the brain in a
subspace corresponding to a certain conscious intention. This
consciously controllable *arresting of the state of attention* can thus
hold in place, in the brain, a "template for intentional action," and
the prolongation of the activation of this pattern of brain activity can
tend to produce the intended physical action of the body or brain, in
accordance with William James's "ideo-motor" theory of action (James,
1890: 522)

This "holding effect" of a rapid sequence of similar Process **1**
events is an automatic consequence of the von Neumann equations of
motion, and it has been extensively studied, both empirically and
theoretically, by quantum physicists under the title "The Quantum Zeno
Effect."

This quantum account of the origin of the causal efficacy of conscious
will (effort) corresponds closely to the ideas of William James, as is
made evident by the following quotations:

\`\`Thus we find that we reach the heart of

our inquiry into volition when we ask by

what process is it that the thought of any

given action comes to prevail stably in the

mind.\'\' (James, 1890:564)

and later

\`\`The essential achievement of the will,

in short, when it is most \`voluntary,\' is to

attend to a difficult object and hold it fast

before the mind. \... Effort of attention is

thus the essential phenomenon of will.\'\'

Still later, James says:

\`\`Consent to the idea\'s undivided presence,

this is effort\'s sole achievement.\'\'\...

\`\`Everywhere, then, the function of effort is

the same: to keep affirming and adopting the

thought which, if left to itself, would slip away.\'\'

The important conclusion is that the apparent capacity of conscious
effort to influence physical actions, which seems so puzzling and
illusory within the framework of classical physical theory, flows
naturally from the equations of quantum theory.

The question arises: What causes this *causally efficacious* feeling of
effort or will?

The *classical-physics-based* response is to affirm the belief -- or
faith -- that the cause is completely describable in *micro-local*
terms: in terms of essentially mechanical contact interactions between
tiny physical elements. But this faith is not based on science! Science
tells us that the old micro-local classical ideas *cannot* *be correct*.
Consequently, there is no *rational* reason to insist, *on the basis of
science*, that the cause of the feeling of effort must be describable
microlocally. Idea-like qualities are certainly parts of reality, and
there is no evidence from science that they cannot be *irreplaceable*
components of the causal chains that connect our experiences to each
other. Contemporary basic physical theory explicitly introduces into the
dynamical equations the physical effects of our conscious choices about
how to act, and it is counterproductive, at least at the level of
practical science, to eliminate these pertinent, controllable, and
knowable variables in favor of idealized theoretical concepts that are
known to be false, and involve parameters that are unknowable not only
in practice but also in principle.

This tripartite quantum dynamics involving Choice, Causation, and Chance
\[Processes **1**, **2**, & **3**, respectively\] and the implementation
of Will (Volition) via the conscious control of the rapidity of Process
**1** events, provides the foundation of a quantum approach to
neuro-psychology. But how well does this quantum approach work in actual
practice?

*The Pashler Data*

A great deal of experimental work over the past three decades in the
field of The Psychology of Attention is summarized in Harold Pashler's
book of that title \[Pashler, 1998\].

Pashler organizes his discussion by separating perceptual processing
from post-perceptual processing. The former covers processing that,
first of all, identifies such basic physical properties of stimuli as
location, color, loudness, and pitch, and, secondly, identifies stimuli
in terms of categories of meaning. The post-perceptual process covers
the tasks of producing motor actions and cognitive action beyond mere
categorical identification. Pashler emphasizes \[p. 33\] that \`\`the
empirical findings of attention studies specifically argue for a
distinction between perceptual limitations and more central limitations
involved in thought and the planning of action.\'\' The existence of
these two different processes, with different characteristics, is a
principal theme of Pashler\'s book. \[pp. 33, 263, 293, 317, 404.\] He
argues that the former processes are carried out in parallel, but that
the latter processes, which seem to require effortful choosing, operate
in series, and have a capacity that can be enlarged by willful effort,
but is limited.

Pashler's conclusion is based on the analysis of a huge array of recent
experiments. But the central finding is succinctly illustrated in a
result dating from the nineteenth century: mental exertion reduces the
amount of physical force that a person can apply. He notes that:
\`\`This puzzling phenomena remains unexplained.\'\' \[p. 387\].
However, if we take the sequence of Process I events associated with an
agent to have a limited "capacity" in terms of events per second, then
this effect is an automatic consequence of quantum theory: creating a
physical force by muscle contraction requires a *conscious effort* that
prolongs the existence of the neural template for action that opposes
the Process-**2**-generated tendency of the brain to evolve toward a
more relaxed state. This prolongation is produced by the Quantum Zeno
Effect, and its effect is roughly proportional to the number of bits per
second of central processing capacity that is devoted to the task. So if
part of this processing capacity is directed to another task, then the
applied force will diminish.

This example is just one simple case. But it illustrates the general
principle: identification of Pashler's limited central serial "capacity"
with the rate of occurrence of Process **1** events, assumed to be
increasable by willful effort, up to a limit, appears to explain the
general features of all of the many diverse empirical results cited by
Pashler in support of his thesis. ( Stapp, 2001)

This success of von Neumann's psychophysical theory in accounting for
Pashler's data does not mean that classical physics could not be
supplemented in an ad hoc way that would enable it to match that
performance. However, the von Neumann theory allows the data to be
explained directly in terms of *the already existing explicitly
described tripartite process that constitutes the core of contemporary
basic physical theory*, whereas an explanation based on classical
physics is not only predicated on the untenable idea that microlocal
causation can be extended to the realm of the motions of ions within
nerve terminals, but also rests on a theory that, although false, is
dynamically and logically complete without entailing the existence of
consciousness. In contrast, von Neumann's equations, namely those that
specify the effects of Process **1** and **3,** specify definite
dynamical connections between consciousness and brain activity, and they
do so in a theoretical framework that automatically entails all of the
valid predictions of classical physics. So what is the rationale, in
neuro-psychology, for rejecting the fundamental equations of
contemporary physics, which encompass consciousness, and all of the
phenomenally valid classical features, in an empirically satisfactory,
logically coherent, and practically useful way, in favor of classical
concepts that are known to be fundamentally false and that leave
consciousness out?

*The Libet Data*

Probably the best way to understand the essence of the quantum approach
to consciousness is to see, in detail, how it applies to the famous
Libet experiments about willful action. (Libet, 2003)

The "problem" with the Libet data is that when an action is 'willed'--
such as 'willing' a finger to rise-- a readiness potential (RP) appears
*before* the experience of 'willing' appears. Libet explains this by
saying that the conscious choice to perform this action does not occur
until the state of readiness is in place: the conscious choice is simply
a choice either to "Veto" or "Consent To" a specified action, whose
physical 'template for action' is already in place, imbedded in the
structure of a particular pattern of neural activity. \[This is slight
elaboration upon Libet's explanation.\]

In the exposition that follows I shall introduce some symbols and
equations. Non-physicists should regard each of these as just a
pictorial or symbolic representation of the corresponding idea that I
describe in words, together with the promise that this picture, in the
minds of physicists, encodes a definite mathematical procedure.

Quantum theory is based on Heisenberg's discovery that the empirical
facts of physics (many of which are logically incompatible with the
basic precepts of classical physics) can be described by a new theory,
quantum theory, which can be constructed by replacing the "numbers" in
classical physics by "actions" (operators). \[The ordering of the
*numbers* in a product does not matter, but the order in which
*actions/operations* are performed does matter.\]

In vN/S theory the dynamics of a conscious brain depends critically upon
an essential correspondence between certain actions/operators in the
mathematical structure and associated human experiences. Each such
action is represented by a "projection operator" P, which satisfies
PP=P. \[The double action PP of a projection operator P has the same
effect as a single action P.\] If the experience is labeled by 'e' then
the associated projection operator is represented by P(e). In von
Neumann's formulation of quantum theory this operator P(e) acts upon the
state of the brain of the observer/participant/agent and specifies the
neural correlate of the experience 'e.' The mappings P(e) specify a
mind-to-matter correspondence that plays a key role in the dynamics of
the brain of a conscious agent.

Any adequate theory of the connection between the stream of
consciousness and the brain processes of the conscious agent must
involve connections between conscious events and associated patterns of
brain/neural activity. These are the so-called "neural correlates of
consciousness," the NCC's. But technical differences between classical
theory and quantum theory render the dynamical roles of the NCC's very
different in these two theories. In classical theory the conscious
events are either (perhaps "emergent") causally inert by-products of
brain activity that have no influence on physical processes. or they are
certain properties of a person's brain activity that can be described in
terms of the concepts of classical physics, and that also appear in
streams of consciousness as psychologically describable experiences. In
both cases, the person's conscious experiences play no essential causal
role in the determination of his actions, in the sense that the causal
chain can be described in purely physical terms. On the other hand, a
person's conscious choices enter *irreplaceably* into the quantum
dynamics as free input variables, replacing the in-principle-unknowable
classically conceived parameters.

Here, in more detail, is how the theory works!

The (quantum) state S of a system is an action/operator, called "the
statistical operator" \[or "the density matrix."\] It specifies the
statistical weight \[probability\] of every projection operator P
associated with that system. The formula for the statistical weight of P
-- the probability of getting the answer 'Yes' to the question
associated with P -- in the state S is:

\<P\> = Trace PSP/Trace S.

\[If A is an action/operator then Trace A is a *number* that is
generated by performing a certain kind of quantum averaging process on
A. Normally an operator "acts on" the operator that stands to its right.
But the rightmost operator in a chain can also act back around on the
left-most operator of that chain, like a snake biting its own tail. This
produces the "Trace" of that chain of operators, which might be a single
operator. The connection of the mathematical formulas to measurable
numbers is always given by this Trace operation.\]

Quantum dynamics is built upon these operators P(e) and S, and on *two
kinds of choices*. The first kind of choice is made by the
experimenter/observer/participant. It is called "Process **1**" by von
Neumann.

The other kind of choice was called by Dirac "a choice on the part of
nature." I have called it "The Dirac Choice." I also call it "Process
**3**" to distinguish it from von Neumann's Process **1** and Process
**2**. \[Process **2** is the quantum analog of Newton's classical
equation's of motion, and is obtained by replacing classical numbers by
corresponding quantum operators.\]

In classical physics there is just one dynamical process, namely the
classical approximation to the quantum Process **2**. But orthodox
quantum theory has two additional processes, one involving a choice made
by a conscious participant/agent/observer about how he will act, and one
made by Nature about how she will respond to the agent's choice.

Contemporary orthodox quantum theory does not specify what the agents's
choice will be. In atomic physics the agent's choice is treated as a
free variable that is fixed by the aims of the experimenter/participant.
These aims are considered to lie outside the realm of atomic physics.
They are to be covered by neuro-psychology, and are presumably
determined by some combination of the neurological-physical and
psychological-experiential processes that enter into quantum
neurodynamics.

Figuring out exactly what this combination is, from a detailed analysis
of the psycho-neurological data, is the task of neuroscience,
psychology, and physics, working together. Only the general overall
quantum dynamical framework was provided by von Neumann.

To get a preliminary general orientation, I have proposed a simple model
for the agent's choice.

The state S(t) of the participant's body-brain is defined by taking the
"partial trace (over all ***other*** degrees of freedom in the
universe)" of the state of the universe at time t (say, in the rest
frame of the cosmic background radiation, just to be specific.)

Then the projection operator P(t) is defined to be that operator in the
set {P(e)} that maximizes

Trace P(e)S(t)P(e)/Trace S(t).

This special P(t) is the P(e) that has at time t the greatest
statistical weight.

As a first guess, I propose that a Process **1** event associated with
P(T) occurs automatically at any time T=t such that \<P(t)\> = Trace
P(t)S(t)P(t)/Trace S(t) reaches a local (in time) maximum. This Process
**1** puts to Nature the question: Does the quantum jump of S(T) to the
state P(T)S(T)P(T) occur?

Notice that the timing and form of this event is determined jointly by
the physical side, from S(T), and by the psychological side from P(T).
But it is determined, nevertheless, by a mathematical law: it is not
coming from "out of the blue." The Process **1** event changes S(T) to
S'(T) = P(T)S(T)P(T) + P'(T)S(T)P'(T), where P' = (1-P).

Then Nature's choice, Process **3**, occurs. It is a "quantum jump." The
State S'(T) is reduced to P(T)S(T)P(T) with probability Trace
P(T)S(T)P(t)/Trace S(T) or to P'(T)S(T)P'(T) with probability Trace
P'(T)S(T)P'(T)/Trace S(T). If the chosen state is P(T)S(T)P(T), then the
associated experience 'e' occurs: otherwise no experience occurs in
conjunction with this Process **3** event.

This "experience" occurs essentially automatically, if Nature's Process
**3** answer is 'Yes'. The occurrence of the experience is a consequence
of these partly deterministic and partly statistically deterministic
equations. Consciousness enters only indirectly, by virtue of the
limitation on the set {P(e)} of all P(e)'s, which enters into the
definition of P(t).

Conscious Will comes in if the state actualized by the 'Yes' choice on
the part of Nature not only eliminates all components of the brain state
that fail to have the template for an action specified by P(T), but also
puts to the agent the question "shall I exert the effort needed to ask
again of nature, almost immediately, the question specified by P(T)". If
the rapidity of these Process **1** events is sufficiently great then
this sequence of Process **1** events will activate the Quantum Zeno
Effect, which will tend to hold the state S(t) in the subspace defined
by this P(e), and this can, according to James's ideo-motor theory,
produce the physical raising of the finger, which should lead to the
feedback experience 'e' of raising the finger.

This completes the more detailed description of the basic elements of
vN/S theory, which will now be applied to the Libet experiment.

The original commitment by the subject to, say, "raise my finger within
the next minute" will condition his brain to bring forth a succession of
potential RP's, distributed over the next minute. When the probability
for any one of the potential RP's in this sequence peaks (reaches a
local maximum) the associated Process **1** question "shall I initiate
the raising of my finger" is asked. Because the commitment is spread
over a minute the probability that Nature's answer will be 'Yes' will be
very small for each individual RP in the sequence. Hence most of the
possible RP's in the sequence will not be actualized: they will be
tossed out by the "No" answer on the part of Nature. But for some one of
these Process **1** events Nature will say "Yes," and the associated
initiating experience 'e' will occur. If, in the light of the feelings
thus actualized, the agent "chooses to exert the effort needed to raise
the finger", then a sufficiently rapid sequence of Process **1** events
will be actualized, and this will cause the finger to rise.

The conscious choice to exert the needed effort that causes the finger
to rise occurs, therefore, *after* the beginning of the build-up of the
associated readiness potential, just as Libet says. This readiness
potential is actualized by Nature's first 'Yes' answer. None of the
"potential readiness potentials" associated with the 'No' answers to the
earlier Process **1** events will have been actualized. So the physical
situation actualized by the 'Yes' answer at some time T will actualize a
physical situation that includes a readiness potential that has already
begun its build up before time T, and peaked at time T. But the mental
decision to consent, not veto, comes after T, and only if this consent
is given will the Quantum Zeno Effect kick in and hold persistently in
place the "template of action" needed to consciously raise the finger.

It might seem that this occurrence of the build up of the readiness
potential *before* *the conscious choice that triggers the raising of
the finger* might violate causality requirements. But the computations
of orthodox quantum theory show that this kind of precursor activity
*cannot be controlled* in such a way as to, say, send a specified
message backward in time. It is controlled in this case by **Nature's
choice** to say 'Yes' at time T, not before. *Given* this 'Yes" choice
*on the part of Nature* the (human) agent is given the choice to consent
or veto the rapid sequence that will cause the finger actually rise.
This human choice to consent or veto, on the basis of his feelings, is
treated in quantum theory as a free variable. But one must take into
account the fact that if the consent is given then Nature must choose,
*with specified statistical weights*, between the 'Yes' and 'No' answers
to each of the Process **1** questions in the ensuing rapid sequence.
The result is that the granting of the consent can directly and strongly
influence whether or not the finger will rise, but will have no effect,
on the average, on whether or not the precursor readiness potential
appears: the fact that that this RP appears was fixed already by the
'Yes' answer given at time T. Consequently, the occurrence of the RP is
not controlled by the subsequent "free choice of whether or not to exert
the needed effort, and there is no conflict with the stringent causal
requirements of the theory of relativity, which forbids sending
controlled messages except via physical transfers of momentum energy.
There can be no such transfer backward in time (or outside the forward
light cone) and hence no violation of the requirements of the theory of
relativity, even though the readiness potential appears before the
conscious choice that actually *causes* the finger to rise.

The projection operators P(e) are necessarily nonlocal operators: they
grasp in a unified way an informational structure that can extend over a
large part of the body-brain of the participant. This brings into the
dynamics holistic features that are in principle beyond the reach of
systems that operate according to the local principles of classical
physics. These holistic features are in line with our perception and
conception of ourselves as creatures that can consciously grasp complex
informational structures as wholes, and can choose to act efficaciously
on the basis of those graspings.

*Applications in Neuropsychology and Neuropsychiatry*

This theory has been applied in both Neuropsychology and
Neuropsychiatry. In the former case (Oschner, 2002; Schwartz, 2003)
human subjects are first instructed how to alter their mental reactions
to emotionally-charged visual stimuli by adopting certain mental
strategies. Then their reactions to such stimuli are studied using fMRI
under differing choices of mental set. The brain scans reveal profoundly
different patterns of response to the stimuli according to the strategy
chosen by the subject. The key *empirical* input variables here are the
willful choices by the human subject about how he or she will (mentally)
act, and vN/S theory provides a physics-based framework for analyzing
the data in terms of these input parameters, without being limited by
the idea that basic science requires all psychogenic causes to be
explained purely by classically conceived physiological causes. Indeed,
quantum theory says that micro-local expIanations of brain dynamics in
terms of the concepts of classical physics are impossible in principle,
and suggests that willful choices about how to act be treated as the
pertinent causally efficacious psychogenic input parameters, in line
with the treatments of the Libet and Pashler data.

In the psychiatric cases (Schwartz, 2002) the crucial communication
between therapist and patients was enhanced by instructing the patients
that quantum theory allows bona fide psychogenic influences of freely
chosen actions, and interpreting differences in brain scans of patients
as evidence of the therapeutic value of properly directed willful
conscious control of attention. Psychogenically based therapy is given a
foundation in basic physics. (Stapp, 1999)

The key elements of the theory are the NCC's, which are specified by the
projection operators P(e). But how is this mapping between the two
conceptually disparate regimes established. The answer is by trial and
error empirical testing of the correspondence between quality of
conscious effort and quality of experiential feedback. Every healthy
alert infant is incessantly engaged in mapping out the correspondences
between efforts and feedbacks, and he/she builds up over the course of
time a repertoire of correspondences between the feel of the effort and
the feel of the feedback. This is possible because different effortful
choices have, according to the quantum equations, different physical
consequences, which produce different experiential consequences. This
whole process of learning would appear to depend crucially upon the
actual causal efficacy of chosen willful efforts.

The focus here has been on the theoretical foundations of pragmatic
scientific practice. However, vN/S theory lends itself to ontological
interpretation. The essential change from classical theory is that the
classical state of the universe represents a purported *material*
realty, whereas the von Neumann quantum state of the universe represents
a purported *informational* reality. This latter reality has certain
matter-like features: it can be represented in terms of micro-local
entities (local quantum fields) that *usually* evolve by direct
interactions with their neighbors. But the von Neumann quantum state
represents the collective knowledge of all agents, and it changes
whenever the knowledge of any agent changes. The state changes in three
ways: by the mechanical Process **2**; by the injection via Process
**1** choices made by agents; and by the injection via Process **3** of
choices made by Nature. Taken at face value the quantum state of the von
Neumann universe acts like the giant playing board upon which a game of
"choices" is being played between agents and Nature. Quite apart from
the question of "truth," this "game" conception of quantum theory
provides a good understanding of the practical workings of the theory.

It should be mentioned that everything said in this section on the vNS
theory is completely compatible with there being very strong
interactions between the brain and its environment: the state S(t) of
the brain is what is know as the statistical operator (reduced density
matrix) corresponding to the brain. It is formed by averaging (tracing)
over all non-brain degrees of freedom, and incorporates all of the
decoherence effects arising from interactions with the environment.

Von Neumann's theory provides a general physics-based psycho-physical
framework. We now turn to efforts to tie it to the detailed structure of
the brain.

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