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

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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

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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

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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,

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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

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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?

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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

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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.

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[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,

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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

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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

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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.

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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)

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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

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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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conscious will in voluntary action. Behavioural & Brain Sciences, 8,

529-566.

Libet, B. (2003). Cerebral physiology of conscious experience:

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Amsterdam & New York: John Benjamins.

Ochsner, K.N. & Silvia A. Bunge, James J. Gross, and John

D.Gabrieli (2002). Rethinking feelings: An fMRI study of the cognitive

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Pashler, H. (1998). The psychology of attention. Cambridge, MA: MIT

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Schwartz, J. & Begley, S. (2002). The mind and the brain:

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Collins.

Schwartz, J., Stapp, H. & Beauregard, M (2003). The volitional

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Stapp, H. (2001). Quiantum theory and he role of mind in nature.

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