**QUANTUM MECHANICAL THEORIES OF CONSCIOUSNESS**

**\[First draft of contribution to 'Blackwell Companion to
Consciousness'\]**

**Abstract**

*Quantum mechanical theories of conscious are contrasted to classical
ones. A key difference is that the quantum laws are fundamentally
psychophysical and hence can provide a dynamical explanation of the
causal effect of conscious effort on neural processes, while the law of
classical physics, being purely physical, cannot. The quantum approach
explains detailed findings in psychology, and impacts on neuroscience.*

**Introduction**

Isaac Newton initiated in the seventeenth century an approach to
understanding nature that, with important contributions from Clerk
Maxwell and Albert Einstein, developed into what is called classical
mechanics. That theory is now known to be fundamentally incorrect. It
was replaced around 1926 by a profoundly different theory called quantum
mechanics. A principal conceptual difference between classical mechanics
and its quantum successor is that the former is exclusively physical
whereas the latter is essentially psychophysical. In particular,
classical mechanics is theory of a material physical world conceived to
be completely specified by numbers assigned to points in space and time,
and to be, moreover, dynamically complete, in the sense that the
behavior of these numbers for all times is completely specified by laws
and initial conditions that involve only these numbers themselves.
Contrastingly, orthodox quantum mechanics brings into the dynamics
certain experiential elements that can have large causal effects in the
physical world yet are not entailed by currently known laws of physics.

This entry of causally efficacious conscious experiences into
contemporary physics has led some quantum physicists to believe that an
adequate scientific theory consciousness must be quantum mechanical.
This view has been challenged by some nonphysicists, who argue that
quantum theory deals with microscopic atomic-level processes whereas
consciousness is associated with macroscopic neuronal processes, and
that the concepts of classical physics provide an adequate understanding
of such macroscopic systems.

That argument is not valid. Quantum mechanics deals with the observed
*macroscopic* behaviors of systems, in cases where those behaviors
depend sensitively upon the properties of the atomic-level constituents
of the physically described aspects of the world. Brains are such
systems: their behaviors depend strongly upon the effects of, for
example, the ions that flow into nerve terminals. Computations show that
the quantum uncertainties in the ion-induced release of neurotransmitter
molecules at the nerve terminals are large (Stapp, 1993, p.133, 152).
These uncertainties propagate in principle up to the macroscopic level.
But then the psychophysical laws of quantum physics can come into play.
and produce dynamical effects of mental effort on brain behavior.

No comparable derivation from the principles of classical physics is
possible because, in the first place, no occurrence of any
psychologically described reality is *entailed* by the dynamically
complete classical laws. Hence there is no possibility of *actually
deducing* anything pertaining to conscious experiences from the laws of
classical physics. In the second place, classical mechanics is an
*approximation* to quantum physics, and in this approximation the domain
of physical uncertainty *within which the quantum causal effects of
mental effort operate* shrinks to zero, rendering conscious effort
necessarily devoid of those causal effects that the unapproximated
theory can entail.

The entry into quantum dynamics of experiential elements, and in
particular of our conscious choices, is rendered possible by the
effective elimination from quantum mechanics of the classical concept of
material substance. Quantum theory retains the core feature of classical
physics, namely a structure of mathematical quantities assigned to
points in space and time. But the dynamical role and behavior of this
structure is greatly altered. The mathematical structure represents no
longer a classically conceived material universe but rather an
*informational structure* that represents the *knowledge* associated
with psychophysical events that have already occurred, and also
*objective tendencies* (propensities) for the occurrence of future
possible psychophysical events This conceptual revision is heralded by
the famous pronouncement of Heisenberg (1958):

The conception of 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 particles but rather our knowledge of this behavior.

The aim of this chapter is to explain briefly, in plain words, how this
enormous change came about, how it works, and how this altered
conception of the role of consciousness in physics impacts on psychology
and neuroscience.

**Copenhagen quantum mechanics**

Quantum mechanics was initiated by a discovery made by Max Planck in
1900. Planck was studying the distribution over frequencies of the
radiant energy emitted from a tiny whole in hollow container. Classical
physics gave clear predictions about the dependence of this energy
distribution upon the temperature of the container, but those
predictions did not match the empirical facts.

Planck found that the empirical data could be accounted for if he
assumed that the radiant energy associated with each given frequency was
concentrated in units, or quanta, with the amount of energy in a unit
being directly proportional to the frequency of the radiation that
carried it. The constant of proportionality was measured by Planck, and
is called Planck's constant.

This discovery was followed by a flood of empirical data that tested
various predictions of classical physics that depended sensitively on
the classical conception of such things as electrons and
electro-magnetic radiation. The data revealed fascinating mathematical
structures, which seemed to involve Planck's constant, but, like
Planck's data, was essentially incompatible with the classical
materialist conception of the world.

Many of the best mathematicians of the generation, men such as as
Hilbert, Jordan, Weyl, von Neumann, Born, Einstein, Sommerfeld, and
Pauli, struggled to unravel this mystery, but it was not until 1925 that
the key step was made. Heisenberg found that correct predictions could
be obtained if one transformed classical mechanics into a new theory by
a certain "quantization" procedure. This procedure replaced the
*numbers* that specified the structure of the classically conceived
material universe by *actions*. Actions differ from numbers in that the
ordering of numerical factors does not matter\-\--2 times 3 is the same
as 3 times 2\-\--whereas the order in which two actions are applied can
matter.

This replacement of numbers by actions is the mathematical foundation of
quantum mechanics. But an adequate physical theory requires more than
just mathematical rules. It requires also a conceptual framework that
allows certain mathematical statements to be tied to human experiences.
In classical mechanics the interpretive framework that ties the
mathematics to experience does not disturb the mathematics. It
*envelopes* the mathematical structure *but does not affect it*. The
basic idea of the classically conceived connection between the
physically and psychologically described aspects of nature is a
carry-over from the planetary dynamics that was the origin of classical
mechanics: the locations of the centers of objects are regarded as being
directly experiencable, without producing any effects on those objects.
But in quantum mechanics the numbers that in classical mechanics
represent, for example, the location of a material object are replaced
by actions. These actions are associated with *the process of acquiring
information* or knowledge pertaining to the location of that object, and
this action normally affects the state that is being probed. Thus the
act of acquiring knowledge about the object becomes enmeshed in a
non-classical way with the state of the object being examined.

This elimination of the numbers that were imagined to specify the
physical state of the material world, and their replacement by actions
associated with the acquisition of knowledge, raises huge philosophical
difficulties. The needed conceptual adjustments were worked out
principally by Bohr, Heisenberg, Pauli, and Born. The center of this
activity was Bohr's institute in Copenhagen, and the conceptual
framework created by these physicists is called The Copenhagen
Interpretation.

A key feature of the new philosophy is described by Bohr:

> 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. (Bohr,
> 1934, p.18)
>
> \...the appropriate physical interpretation of the symbolic quantum
> mechanical formalism amounts only to prediction of determinate or
> statistical character, pertaining to individual phenomena appearing
> under conditions defined by classical physics concepts. (Bohr, 1958,
> p.64).

The references to \`\"classical physics concepts\'\' is explained as
follows:

> \...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, 1958, p.88).
>
> The decisive point is to recognize that the description of the
> experimental arrangement and the recording of observations must be
> given in plain language suitably refined by the usual physical
> terminology. This is a simple logical demand since by the word
> "experiment" we can only mean a procedure regarding which we are able
> to communicate to others what we have done and what we have learnt
> (Bohr, 1958, p 3)

Bohr is saying that scientists do in fact use, and must use, the
concepts of classical physics in communicating to their colleagues the
specifications on how the experiment is to be set up, and what will
constitute a certain type of outcome. He in no way claims or admits that
there is an actual reality out there that conforms to the precepts of
classical physics.

But how can one use jointly and consistently these two mutually
inconsistent mathematical structures? This is the problem that the
Copenhagen Interpretation solves, at least for all practical purposes.

The Copenhagen solution is to divide nature into two parts. One part is
the observing system, including the bodies, brains, and minds of the
human beings that are setting up the experimental situations and
acquiring, via the experiential feedbacks, increments in knowledge. This
observing part includes also the measuring devices. This observing
system is described in ordinary language refined by the concepts of
classical physics. Thus the agent can say "I placed the measuring device
in the center of the room, and one minute later I saw the pointer swing
to the right." The agent's description is a description of what he
does\-\--of what probing actions he takes\-\--and of the experienced
consequences of his actions.

The other part of nature is the system being probed by the classically
conceived and described observing system. This probed system is
described in the symbolic language of quantum mathematics.

In classical physics the classical concepts are asserted to be
applicable in principle right down to the atomic level, but according to
the quantum precepts the quantum mathematical description must be used
where ever the classical approximation is not justified.

The separation between the two parts of nature is called the Heisenberg
cut. Above the cut one uses experience-based classical descriptions,
while below the cut one uses the quantum mathematical description.

The cut can be moved from below a measuring device to above it. This
generates two *parallel descriptions* of this device, one classical and
the other quantum mechanical. The quantum description is roughly a
continuous smear of classical-type states. The postulated theoretical
correspondence, roughly, is that the smeared out mathematical quantum
state specifies the *statistical weights* of the various alternative
possible classically described experiencable states. The predictions of
the theory thereby become, in general, statistical predictions about
possible experiences described in the conceptual framework of classical
physics.

There is, however, a fly in the ointment. In order to extract
statistical predictions pertaining to possible experiences, a specific
kind of question must be physically posed. The question must have a
*countable* set of experientially distinct alternative possible answers.
"Countable" means that the answers can be placed in one-to-one
correspondence with the whole numbers 1, 2, 3, ....or with some finite
subset of these numbers. But the number of possible classically
describable possibilities is not countable: there is a continuous
infinity of such possibilities. Yet before any statistical consequence
can be drawn from the theory, some definite question with a countable
set of empirically distinct alternative possible answers must be
physically posed.

The mathematical structure of the theory does not specify what this
question is, or even put statistical constraints on what it might be.
Thus the mathematical theory is dynamically incomplete on three counts:
it fails to specify which question will be posed, when it will be posed,
and which answer will then appear. The theory does assign a statistical
weight (probability) to each of the alternative possible answers to the
physically posed question.

Von Neumann emphasized the need for the process of posing a particular
question by calling it Process 1, and distinguishing it from the very
different Process 2, which is the mathematically specified evolution of
the quantum state in accordance with the rules specified by the
quantization procedure.

How does orthodox Copenhagen quantum theory resolve this basis problem?

It resolves it by adopting a pragmatic stance. Copenhagen quantum theory
is regarded as a procedure that provides predictions about the likely
classically describable experiential consequences of the alternative
possible probing actions that experimenters can choose to institute.
Within that pragmatic framework the human agent is free to choose which
experiment (probing action) he or she will perform. Thus it is normally
a consciously chosen action by an experimenter/agent that resolves the
basis problem.

This resolution of the basis problem has the effect of allowing our
conscious choices to be causally efficacious in the physically described
world Our conscious choice of how we will act\-\--which question we will
pose\-\--determines *the set of possible experiential feedbacks*. Under
certain circumstances, which will be described later, a person's
conscious choices about which questions to pose, and when to pose them,
can, *by virtue of the quantum laws themselves,* strongly influence the
behavior of the system being probed!

Bohr often emphasized this crucial element of freedom:

> The freedom of experimentation, presupposed in classical physics, is
> of course retained and corresponds to the free choice of experimental
> arrangement for which the mathematical structure of the quantum
> mechanical formalism offers the appropriate latitude. (Bohr, 1958,
> p.73).
>
> "To my mind there is no other alternative than to admit in this field
> of experience, we are dealing with individual phenomena and that our
> possibilities of handling the measuring instruments allow us to make a
> choice between the different complementary types of phenomena that we
> want to study. (Bohr, 1958, p. 51).

These quotes highlight the fact that Process 1 is determined within the
framework of contemporary physics not by the known mathematical laws but
rather by a free choice made by a conscious agent.

**Von Neumann's Extension**

Von Neumann first expressed Copenhagen quantum mechanics in a
mathematically rigorous form, and then showed that the Heisenberg cut
could be pushed all the way up, so that the bodies and brains of the
agents are treated quantum mechanically. This placement of the cut does
not eliminate the need for Process1. It merely places the physical
aspect of the Process 1 psychophysical event in the brain of the
conscious agent. The psychologically described aspect, identified as the
conscious choice, is still needed to specify Process 1. The carrier of
this psychological element is called by von Neumann (1955, p. 421) the
"abstract ego".

Bohr emphasized that the laws of quantum theory should continue to be
valid in biological systems, but that the latitude introduced by the
severe constraints upon observation imposed by the demands of sustaining
life could permit such concepts such as "teleology" and "volition" to
come *consistently* into play. (Bohr, 1958, p.10, p.22)

It should be noted that quantum theory does not *explain why conscious
exists*. It accepts that we human beings are conscious, and then creates
a conceptual framework that links our conscious thoughts in a
scientifically useful way to a mathematical generalization of classical
physics.

.

**Psychophysical events**

In classical physics the universe, and every subsystem of it, evolves
continuously. In quantum theory the analogous evolutions are *usually*
continuous, and specified by Process 2, which is the "quantized" version
of the laws of motion of classical physics. But according to orthodox
von Neumann quantum theory this continuous mechanically controlled
evolution is occasionally interrupted by a Process 1 event. Each Process
1 event has two coordinated aspects. One describes a conscious
experience, the other describes an associated change in a physical
state. The conscious experience is a choice to act in a way that is
intended to bring into being intended experiential feedbacks. For
example, an experimenter may choose to first set a polaroid lens at a
certain angle and then attend to the visual sensation that results from
looking through the lens at the source of a photon that will soon be
emitted. If he experiences the expected confirmation about the setting,
then whether he experiences or not a visual sensation as he looks at the
source through the lens will give him a new bit of knowledge about the
photon, about his brain, and about the content of his stream of
consciousness. Von Neumann showed how it is

> ...possible to describe the extra-physical process of subjective
> perception as if it were in reality in the physical world\-\--i.e., to
> assign to its parts equivalent physical processes in the physical
> world. (von Neumann, 1955, p.419)

For example, choosing to set the lens in a certain way, and then to
attend to the visual sensation, will probably be followed by an
experience of the lens being set in place, and then, perhaps, by the
visual sensation of "seeing the photon". Within this context the visual
sensation is *equivalent*, for the purposes of computing probabilities,
to a certain mathematical *action* on the quantum state of the photon,
or, equivalently, on the quantum state of the agent's brain. A
theoretical equivalence is thereby established, *within the quantum
theoretical framework*, between the visual sensation of seeing the
photon and an associated physical action that brings into existence a
certain state of the photon or, equivalently, that brings into being
*the neural correlate of the visual experience of seeing the photon*.
The empirical predictions of the pragmatic theory are based squarely on
these psychophysical events.

The main differences between the quantum treatment and the analogous
classical treatments are, first, that the "extra-physical process of
subjective perception", with its image in the mathematical/physical
description, are core parts of quantum theoretical structure; and,
second, that the quantum dynamics features a process, Process 1, that
enters importantly into the dynamics, but is not selected or caused by
any yet-known law.

In contemporary quantum physics the choices of which probing actions to
make, and when to make them, are, as just emphasized, not specified by
the known laws of nature. They are treated as "free variables",
controlled by conscious choices made by agents. Although these choices
are not determined by the quantum laws, they do exert upon the brain of
the agent effects that are determined by the quantum laws. The situation
is thus just the reverse of the one in classical physics, where it is
generally assumed that the psychological happening is somehow determined
by the brain state\-\--presumably by some extra psychophysical law that
supplements the usual physical ones\-\--but that this psychological
reality exerts no influence back upon the brain, whose behavior is
already completely determined by the physically described variables
acting in accordance with the usual physical laws

The fact that the conscious choices are not determined by the known laws
yet can influence neural processing opens the way to an understanding of
the apparent power of mental volitional effort to control brain, hence
bodily processes. If one postulates that the rapidity with which probing
actions take place can be increased by conscious effort then the
dynamical effect of conscious effort will, if sufficiently strong, be to
*hold in place, against the mechanical effects of Process 2*, the neural
correlate of the idea of the intended feedback.

This quantum effect is an application at the level of the brain of the
well known quantum Zeno effect, which is a theoretically well understood
and well verified consequence of quantum theory. (Misra, 1977:Itano,
!990) Quantum theory is able, therefore, to give to conscious choices
both freedom from mechanical coercion and yet a capacity to influence
neural behavior in a way that tends to bring intended experiences into
the stream of consciousness. The details are described in Stapp (1999,
2001) and in Schwartz, Stapp, and Beauregard (2003, 2004).

**Comparison to psychological findings**

The dynamical effect of the volition-induced high rapidity of the
Process 1 probing actions is exactly in line with the description of the
effects of volition described by William James (1892). In the section
entitled *Volitional effort is effort of attention* he writes:

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. (p, 417)

The essential achievement of will, in short, when it is most

'voluntary,' is to attend to a difficult object and hold it fast

before the mind. (p.417).

Everywhere, then, the function of effort is the same: to keep

affirming and adopting the thought which, if left to itself, would slip
away.

(p.421)

James apparently foresaw, on the basis of his efforts to understand the
mind-brain connection, the implied eventual downfall of classical
mechanics. He closed his book with the prophetic words

> ...and never forget that the natural-science assumptions with which we
> started are provisional and revisable things. (p.433)

A lot has happened in psychology since the time of William James, but
these developments support James's idea of the
holding-attention-in-place action of volition. Much of the recent
empirical and theoretical work pertaining to attention is summarized in
Harold Pashler's book *The Psychology of Attention* (Pashler, 1998).
Pashler concluded that the evidence indicates the existence of two
distinct kinds of mental processes, one that appears not to involve
volition, and that allows several perceptual processes to proceed in
parallel without significant interference, and one that does involve
volition and that includes planning and memory storage. This latter
process seems to involve a linear queuing effect with limited total
capacity. The properties of the volition-driven process appear to be
completely in line with the idea that volition is associated with a
linear sequence of Process 1 events that can hold in place, by means of
the quantum Zeno effect, the pattern of neural activity that will tend
to bring into being the intended effects. This details of how this works
are spelled out in the references cited at the end of the preceding
section.

**Impact on Neuroscience**

An application in neuroscience is to the work of Ochsner et.al. (2001)
on the cognitive control of emotion. Subjects are trained how to
cognitively re-evalute emotional scenes. When they then consciously
choose to cognitively re-evaluate emotion-laden visual scenes that they
are viewing the activity of their brains as determined by fMRI
measurements shifts from limbic to prefrontal. The influence of
volitional conscious choices on brain activity is thus empirically
exhibited.

How does a shift to a quantum mechanical theory of consciousness impact
upon scientific practice pertaining to experiments of this kind?

Within a classical approach the conscious choices are incidental to the
causal chain. Hence a causal description would involve a causal
connection between *the physical* *causes of the feeling* of conscious
effort and the seeming effect of that effort. But quantum considerations
suggest that when difficult choices are involved the quantum
uncertainties will block *in principle* any causal explanation of that
kind. It suggests an alternative approach in which the conscious choices
to apply effort are treated as free variables, the only allowed effect
of which is to hold in place the neural correlate of the effort, which
is the pattern of neural activity that if held in place long enough will
tend to bring into being, eventually, the intended experiential
feedback.

The classical and quantum approaches thus involve fundamentally
different understandings of the causal underpinnings of mind-brain
behavior, and hence lead to different research programs to test and fill
in the details of the competing models.

The only objections to this quantum approach to mind-brain dynamics that
I know of are the claims of some nonphysicists that the principles of
classical physics are completely adequate for an understanding of the
mind-brain connection, in spite of their being fundamentally false, and
independent of mind, and the somewhat similar contention of some
physicist that the pragmatic approach should be replaced by an
ontological one in which consciousness plays no causative role. Neither
of these objections claim an actual *error* in the pragmatic quantum
approach. Both claim, rather, the superiority of an alternative approach
in which our thoughts have no influence on physical activity, and purely
physical determinism prevails. Orthodox contemporary quantum theory
provides a rational physics-based foundation for the opposing view that
mind really matters.

There are several alternative quantum theories of consciousness, but all
of them start with von Neumann's work. The considerations described
above rest completely on the basic von Neumann framework. I describe
next some proposals that introduce some more controversial and
unconventional ideas.

**The Penrose-Hameroff Theory**

Roger Penrose and Stuart Hameroff (Hameroff & Penrose, 1996) have
proposed a quantum theory of consciousness that brings together three
exciting but controversial ideas. The first pertains to the
still-to-be-worked-out quantum theory of gravity. The second involves
the famous incompleteness theorem of Gödel. The third rests upon the
fairly recently discovered microtubular structure of neurons.

Penrose proposes that the abrupt changes of the quantum state that are
associated with conscious experiences are generated by the qravitational
effects of particles of the brain upon the structure of space-time in
the vicinity of the brain. Ordinarily one would think that the effects
of gravity *within the brain* would be too minuscule to have any
significant effect on the functioning of the brain. But Penrose and
Hameroff come up with an estimate of typical times associated with the
gravitational effects that are in the tenth of a second range associated
with conscious experiences. This fuels the speculation that the abrupt
changes in the quantum state that occur in quantum theory are caused not
by the entry of thoughts into brain dynamics, but by quantum effects of
gravity.

But then why should thoughts or consciousness be involved at all?

Two reasons are given. Penrose uses Gödel's incompleteness theorem to
argue that mental processing cannot be wholly mechanical or algorithmic.
The argument takes hundreds of pages (Penrose, 1986, 1994) and has been
attacked by many qualified critics. (e.g., Putnam, 1994). It is fair to
say that it has not passed the usual demands made upon mathematical and
logical arguments. But the argument claims that both mental processing
and the gravitational effects are non-algorithmic, and that the latter
could therefore provide in a natural way the non-algorithmic element
needed for the former

The second connection of the proposed gravitational effect with
consciousness is that the estimated time associated with the
gravitational effect was based on the presumption that the components of
the brain critical to consciousness were functioning microtubules. Data
pertaining to loss of consciousness under the influence of various
anesthetic agents indicate that the proper functioning of microtubules
is necessary for consciousness. But many things are *necessary* for
consciousness, so this argument that the gravitational effect is
connected consciousness via microtubules is not compelling. *.*

A serious objection to the Penrose-Hameroff theory has been raised by
Max Tegmark (2000) The Penrose-Hameroff theory requires that the
critical microtubular state be a *coherent* quantum state that extends
over a macroscopic region in the brain. Normally one expects any
macroscopic coherence of a quantum state in a warm wet brain to be
destroyed almost immediately. Tegmark estimates the duration of
coherence to be on the order of 10^-13^ seconds, which is far smaller
than the one tenth of a second associated with consciouness. Hagen,
Hameroff, and Tuszynski (2002). have claimed that Tegmark's assumptions
should be amended, so that the decohence time becomes 10^-4^ seconds,
and they suggest that the needed factor of a thousand can be made up by
biological factors. In any case, the need to maintain macroscopic
quantum cohererence in a warm wet brain is certainly a serious problem
for the Penrose-Hameroff model.

It might be mentioned here here that in the von Neumann model described
in the preceding sections quantum decoherence is an important *asset,*
because it allows the quantum state of the brain to be understood as
essentially a smeared out statistical ensemble (i.e., collection) of
essentially classically conceived states, which, however, can interact
with neighboring members of the ensemble in a way that preserves the
quantum Zeno effect. This quasi-classical conceptualization of the
quantum state of the brain allows non-physicists to have a relatively
simple understanding of the mind-brain system..

**The Eccles-Beck approach**

An early quantum approach to the mind-brain problem was made by John
Eccles (1990) who emphasized the entry of quantum effects into brain
dynamics in connection with effects at nerve terminals. However, instead
of building directly on the quantum rules and the profound conceptual
relationships between quantum and classical mechanics he introduced a
conscious biasing of the quantum statistical rules. This actually
contradicts the quantum rules, thereby upsetting the logical coherency
of the whole scheme. In a later work with Beck (2003) he retained the
quantum rules, while introducing quantum uncertainties at the nerve
terminals that can play the same role that they do in the standard
approach described earlier. This brings the model into accord with the
standard model described above, in regard to this technical point.
However, Eccles added a superstructure involving conscious "souls" that
can exist apart from physical brains. That suggestion goes beyond the
ideas described here..

**Other Theories**

Several quantum theories of consciousness have been proposed. All are
outgrowths of von Neumann's formulation. The differences in these
proposals are mainly at the level of technical physics. I have focused
here on the over-riding general issues of why quantum theory should be
relevant to consciousness in the first place, and how the switch to
quantum physics impacts upon the question\-\--important in neuroscience,
psychology, and philosophy\-\--of the neural effects of volitional
effort.

HENRY P. STAPP

**Further Reading**

The Emperor's New Mind, Roger Penrose

Mind, Matter, and Quantum Mechanics, Henry Stapp

The Large, the Small, and the human Mind, Roger Penrose (with

Abner Shimony, Nancy Cartwright, and Stephen Hawking)

The Mind and the Brain: Neuroplasticity and the power of mental force,
Jeffrey Schwartz and Sharon Begley

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Bohr, N. 1958. *Atomic Physics and Human Knowledge.* New York: Wiley.

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Eccles, J.C. 1994: *How the Self Controls its Brain.* Berlin,
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