**[Quantum Approaches to Consciousness.]{.underline}**

**[1. Introduction.]{.underline}**

Quantum approaches to consciousness are sometimes said to be motivated
simply by the idea that quantum theory is a mystery and consciousness is
a mystery, so perhaps the two are related. That opinion betrays a
profound misunderstanding of the Nature of quantum mechanics, which
consists fundamentally of a pragmatic scientific solution to the problem
of the relationship between mind and matter.

The key philosophical and scientific achievement of the founders of
quantum theory was to forge a rationally coherent and practically useful
linkage between the two kinds of descriptions that jointly comprise the
foundation of science. Descriptions of the first kind are accounts of
psychologically experienced empirical findings, expressed in a language
that allows us to communicate to our colleagues what we have done and
what we have learned. Descriptions of the second kind are specifications
of physical properties, which are expressed by assigning mathematical
properties space-time points, and formulating laws that determine how
these properties evolve over the course of time. Bohr, Heisenberg,
Pauli, and their colleagues discovered a way to connect these two kinds
of descriptions by causal laws, and their seminal discovery was extended
by John von Neumann from the domain of atomic science to the realm of
neuroscience, and in particular to the problem of understanding and
describing the causal connections between the minds and the brains of
human beings.

The magnitude of the difference between the quantum and classical
conceptions of the connection between mind and brain can scarcely be
exaggerated. All approaches to this problem based on the precepts of
classical physics founder first on the problem of the lack of any need
within classical mechanics for consciousness to exist at all, and second
on the seemingly manifest impossibility of ever actually understanding
how the experiential realities that form our streams of consciousness
could ever be produced by, or naturally come to be associated with, the
motions of the things that classical physics claims the physical world
to be made of. The first problem is that, according to precepts of
classical physics, the causal properties of the physical world suffice,
by themselves, to completely specify all physical properties of the
universe, including the activities of our bodies and brains, without
ever acknowledging the existence of consciousness: everything would go
on just the same if nothing but the physical properties were present.
The second problem is that the differences-in-kind between the
experiential and physical sorts of stuff is so great that it seems
beyond the realm of possibility that a tight rational connection could
exist between them. The fact that consciousness does exist thus enforces
an awkward departure of science from a purely naturalistic stance;
nonphysical entities such as conscious thoughts, ideas, and feelings
must be added for no apparent naturalistic or physical reason!

All of this is completely changed by the switch to quantum physics.
According to quantum physics, as it is both practiced and taught, our
human choices play a key dynamical role in our scientific description of
nature. This injection of observer/participants into the basic causal
structure of physics was the radical revision in the conception of
science ushered in by the founder's of quantum theory. The related
problem of the huge disparity in classical physics between the
experiential and physical kinds of stuff is resolved in quantum
mechanics by altering the nature of the physical stuff: the physical
world is transformed from a substance-based structure to a construct
based on "events" that inject information into an information bearing
quantum state. It is extremely important that this radical revamping at
the foundational level is achieved without giving up, at the practical
level, hardly anything from classical physics. Apart from making room
for, and a need for, conscious choices, the profound changes introduced
by quantum theory at the foundational level preserve at the pragmatic
level almost all of classical physics.

I shall in the remainder of this introductory section sketch out the
transition from the classical-physics conception of reality to the von
Neumann application of the principles of quantum physics to our
conscious brains. In succeeding sections I describe the most prominent
of the many efforts being made by physicists to develop and extend von
Neumann's work.

The quantum conception of the relationship between the psychologically
and physically described components of scientific practice was achieved
by abandoning the classical picture of the physical world that had ruled
science since the time of Newton, Galileo, and Descartes. The building
blocks of science were shifted from descriptions of the behaviors of
tiny bits of mindless matter to accounts of *the actions that we take to
acquire knowledge* and of the *knowledge that we thereby acquire*.
Science was transformed from its seventeenth century form, which
effectively excluded our conscious thoughts from any causal role in the
mechanical workings of Nature, to its twentieth century form, which
focuses on our active engagement with Nature, and on what we can learn
by taking appropriate action.

Twentieth century developments have thus highlighted the fact that
*science is a human activity* that involves us not as passive witnesses
of a mechanically controlled universe, but as agents that can choose to
perform causally efficacious actions. The basic laws of Nature, as they
are now understood, not only fail to determine how we will act, but
moreover inject our *choices about how to act* directly into the
dynamical equations. Human choices, which are both empirically
accessible and consciously controllable, become the essential input
parameters, replacing classically conceived microscopic variables, which
are both *empirically inaccessible* and in principle uncontrollable.

The altered role of conscious agents is poetically expressed by Bohr's
famous dictum:

> "In the great drama of existence we ourselves are both actors and
> spectators." (Bohr, 1963, p. 15: 1958, p. 81)

It is more concretely expressed in statements such as:

> \"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}

The fact that quantum theory is formulated in terms of an *interaction*
between the physically described world and conscious agents that are,
within the causal structure defined by the known physical laws, *free to
choose* which aspect of nature they will probe, is perhaps the most
important innovation of quantum theory. It is the crack, or gap, in the
mechanistic world view that opens the way to a radically new conception
of nature and our place within it.

Another chief innovation pertains to the *nature* of the stuff of the
physically/mathematically described universe. The switch is succinctly
summarized in Heisenberg's famous assertion:

> "The conception of the objective reality of the elementary particles
> has thus evaporated not into the cloud of some obscure new reality
> concept, but into the transparent clarity of a mathematics that
> represents no longer the behavior of the particle but rather our
> knowledge of this behavior." (Heisenberg, 1958a)

What the mathematics describes in no longer the locations of tiny bits
of substance, or matter: it describes instead a knowledge-bearing or
information-bearing structure. This structure is abruptly altered by
discrete "events" that inject new information into it. But the structure
is not passive: it has an active quality. It acts in a mathematically
well-defined way as a carrier of "objective tendencies" or "potentia" or
"propensities" for new events. (Heisenberg, 1958b, p. 53). The
surprising fact is that this radical revamping of the foundational
structure preserves most of classical physics, in domains where it works
well, while allowing deviations from classical determinism in situations
influenced by our conscious free choices.

Comprehending this new conception of the relationship between the
psychologically experienced empirical side and the mathematically
described physical side of the scientific endeavor requires an
appreciation of certain novelties in the logical structure of quantum
theory. This conceptual re-organization can be understood without
becoming enmeshed in technical mathematical details.

*The Classical-Physics Approach.*

To grasp the essential change one must know what came before.

Classical physics arose from the theoretical effort of Isaac Newton to
account for the findings of Johannes Kepler and Galileo Galilei. Kepler
discovered that the planets move in orbits that depend on the location
of other physical objects - such as the sun - but not on the manner or
the timings of our observations: minute-by-minute viewings have no more
influence on a planetary orbit than daily, monthly, or annual
observations. The nature and timings of our observational acts have no
effect at all on the orbital motions described by Kepler. Galileo
observed that certain falling terrestrial objects have similar
properties. Newton then discovered that he could explain
*simultaneously* the celestial findings of Kepler and the terrestrial
findings of Galileo by postulating, in effect, that all objects in our
solar system are composed of tiny planet-like particles whose motions
are controlled by *laws* that refer to the relative locations of the
various particles, and make no reference to any conscious acts of
experiencing. These acts are taken to be simply passive witnessings of
macroscopic properties of large conglomerations of the tiny
individually-invisible particles.

Newton's laws involve instantaneous action at a distance: each particle
has an instantaneous effect on the motion of every other particle, no
matter how distant. Newton considered this non-local feature of his
theory to be unsatisfactory, but proposed no alternative. Eventually,
Albert Einstein, building on ideas of James Clerk Maxwell, constructed a
*local* classical theory in which all dynamical effects are generated by
contact interactions between mathematical described properties localized
at space-time points, and in which no effect is transmitted faster than
the speed of light.

All classical-physics models of Nature are *deterministic*: the state of
any isolated system at any time is completely fixed by the state of that
system at any earlier time. The Einstein-Maxwell theory is deterministic
in this sense, and also "local", in the just-mentioned sense that all
interactions are via contact interactions between neighboring localized
mathematically describable properties, and no influence propagates
faster than the speed of light.

By the end of the nineteenth century certain difficulties with the
general principles of classical physical theory had been uncovered. One
such difficulty was with "black-body radiation." If one analyzes the
electromagnetic radiation emitted from a tiny hole in a big hollow
heated sphere then it is found that the manner in which the emitted
energy is distributed over the various frequencies depends on the
temperature of the sphere, but not upon the chemical or physical
character of the interior surface of the sphere: the spectral
distribution depends neither on whether the interior surface is smooth
or rough nor on whether it is metallic or ceramic. This universality is
predicted by classical theory, but the specific form of the predicted
distribution differs greatly from what is empirically observed.

In 1990 Max Planck discovered a universal law of black-body radiation
that matches the empirical facts. This new law is incompatible with the
basic principles of classical physical theory, and involves a new
constant of Nature, which was identified and measured by Planck, and is
called "Planck's Constant." By now a huge number of empirical effects
have been found that depend upon this constant, and that conflict with
the predictions of classical physical theory.

During the twentieth century a theory was devised that accounts for all
of the successful predictions of classical physical theory, and also for
all of the departures of the predictions of classical theory from the
empirical facts. This theory is called quantum theory. No confirmed
violation of its principles has ever been found.

*The Quantum Approach.*

The core idea of the quantum approach is the seminal discovery by Werner
Heisenberg that the classical model of a physical system can be
considered to be an *approximation* to a quantum version of that model.
This quantum version is constructed by replacing each numerical quantity
of the classical model by an *action*: by an entity that acts on other
such entities, and for which the order in which the actions are
performed matters. The effect of this replacement is to convert each
point-like particle of the classical conceptualization---such as an
electron---to a smeared-out cloudlike structure that evolves, almost
always, in accordance with a quantum mechanical law of motion called the
Schroedinger equation. This law, like its classical analog, is local and
deterministic: the evolution in time is controlled by contact
interactions between localized parts, and the physical state of any
isolated system at any time is completely determined from its physical
state at any earlier time by these contact interactions. The cloud-like
structure that represents an individual "particle", such as an electron,
or proton, tends, under the control of the Schroedinger equation, to
spread out over an ever-growing region of space, whereas according to
the ideas of classical physics an electron is always localized in a very
tiny region.

The local deterministic quantum law of motion is, in certain ways,
incredibly accurate: it correctly fixes *to one part in a hundred
million* the values of some measurable properties that classical physics
cannot predict.

However, this local deterministic quantum law of motion does not
correlate directly to human experience. For example, if the state of the
universe were to have developed from the big bang solely under the
control of the local deterministic Schroedinger equation then the
location of the *center* of the moon would be represented in the theory
by a structure spread out over a large part of the sky, in direct
contradiction to normal human experience.

The smeared-out character of the position of (the center-point of) a
macroscopic object, is a consequence of the famous Heisenberg
Uncertainty Principle, combined with the fact that tiny uncertainties at
the microscopic level usually get magnified over the course of time,
*by* *the Schroedinger equation acting alone*, to large uncertainties in
macroscopic properties.

This contradiction between a mathematical theory that is a direct
mathematical generalization of classical physical theory---and that
yields many predictions of incomparable accuracy---with the facts of
everyday experience is the basic problem that an adequate interpretation
of quantum theory must resolve.

In order to place the accurate predictions of the quantum mathematics
into the context of a rationally coherent and practically useful theory
the whole concept of what physical science is, or should be, was
transformed from its nineteenth form, as a theory of the properties of a
mechanical model of Nature in which we ourselves are mere mechanical
parts, to a theory of the relationship between the physically and
psychologically described aspects of actual scientific practice, in
which we act as agents that probe nature in ways of our own choosing. It
is worthwhile to see in slightly more detail what this revised
conception of science means and how it works.

*"The Observer" and "The Observed System" in Copenhagen Quantum Theory.*

The original formulation of quantum theory is called the Copenhagen
Interpretation because it was created by the physicists that Niels Bohr
had gathered around him in Copenhagen. A central precept of this
approach is that, in any particular application of quantum theory,
Nature is to be considered divided into two parts, "The Observer" and
"The Observed System." The Observer consists of the stream of
consciousness of a human agent, together with the brain and body of that
person, and also the measuring devices that he or she uses to probe The
Observed System.

Each Observer describes himself and his knowledge in a language that
allows him to communicate to colleagues two kinds of information: *How
he has acted* in order to prepare himself - his mind, his body, and his
devices - to receive recognizable and reportable data; and *What he
learns* from the data he thereby acquires. This description is in terms
of the conscious experiences of the agent himself. It is a description
of his intentional probing actions, and of the experiential feedbacks
that he subsequently receives.

In actual scientific practice the experimenters are free to choose which
experiments they perform: the empirical procedures are determined by the
protocols and aims of the experimenters. This element of freedom is
emphasized by Bohr in statements such as:

> "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)

The freedom to choose is achieved in the Copenhagen formulation of
quantum theory by placing the empirically/psychologically described
Observer outside The Observed System that is being probed, and then
subjecting only The Observed System to the rigorously enforced
mathematical laws.

The Observed System is, according to both classical theory and quantum
theory, describable in terms of mathematical properties assigned to
points in space-time. However, the detailed forms of the laws that
govern the evolution in time of this mathematical structure, and of the
rules that specify the connection of this mathematical structure to the
empirical facts, are very different in these two theories.

I am endeavoring here to avoid mathematical technicalities. But the
essential conceptual difference between the two approaches rests
squarely on a basic technical difference. This difference can be
illustrated by a simple two-dimensional picture.

*The Paradigmatic Example.*

Consider an experiment in which an experimenter puts a Geiger counter at
some location with the intention of finding out whether or not this
device will "fire" during some specified time interval. The experiment
is designed to give one of two possible answers: 'Yes', the counter will
fire during the specified interval, or 'No', the counter will not fire
during this specified interval. This is the paradigmatic quantum
measurement process.

This experiment has *two* alternative mutually exclusive possible
responses, 'Yes' or 'No.' Consequently, the key mathematical
relationships can be pictured in a *two*-dimensional space, such as the
top of your desk.

Consider two distinct points on the top of your desk called *zero* and
*p*. The displacement that would move a point placed on *zero* to the
point *p* is called a *vector*. Let it be called *V*. Suppose *V* has
unit length in some units, say meters. Consider any two other
displacements *V1* and *V2* on the desk top that start from zero, have
unit length, and are perpendicular to each other. The displacement *V*
can be formed in a unique way by making a (positive or negative)
displacement along *V1* followed by a (positive or negative)
displacement along *V2*. Let the lengths of these two displacements be
called *X1* and *X2*, respectively. The theorem of Pythagoras says that
*X1* squared plus *X2* squared is one (unity).

Quantum theory is based on the idea that the various experiencable
outcomes have "images" in a vector space. The vector V1 mentioned above
is the image, or representation, in the vector space of the possible
outcome 'Yes,' whereas V2 represents 'No.' I will not try to describe
here how this mapping of possible experiencable outcomes into
corresponding vectors is achieved But the basic presumption in quantum
theory is that such a mapping exists.

The vector *V* represents the state of The Observed System, which has
been prepared at some earlier time, and has been evolving in accordance
with the Schroedinger equation. The vector *V1* represents the state
that this observed system would be known to be in if the observed
outcome of the measurement were 'Yes.' The vector *V2* represents the
state that the observed system would be known to be in if the observed
result of the measurement were 'No.' Of course, the directions of the
two perpendicular vectors *V1* and *V2* depend upon the exact details of
the experiment: on exactly where the experimenters have placed the
Geiger counter, and on other details controlled by the experimenters.

The outcome of the probing measurement will be either *V1* (Yes) or *V2*
(No). The predicted probability for the outcome to be 'Yes' is *X1*
squared and the predicted probability for the outcome to be 'No' is *X2*
squared. These two probabilities sum to unity, by virtue of the theorem
of Pythagoras. The sudden jump of the state from *V* to either *V1* or
*V2* is called a "quantum jump." The general theory is express in terms
of a many-dimensional generalization of your desktop. This
generalization is called a Hilbert Space.

The crucial, though trivial, logical point can now be stated: The two
alternative possible outcomes, 'Yes' or 'No' of the
chosen-by-the-experimenter experiment are associated with a pair of
perpendicular unit-length vectors called "basis vectors". The
*orientation* (i.e., directions) of the set of "basis" vectors, *V1* and
*V2,* enters into the dynamics as a *free variable* controlled by the
experimental conditions, which are specified in practice by choices made
by experimenters. The orientation of the set of basis vectors is thus,
from a mathematical standpoint, a variable that can be, and is,
specified *independently* of the state *V* of the system being probed.

This entry into the dynamics of choices made by the experimenters is not
at all surprising. If the experimenters are considered to stand outside,
and apart from, the system being observed, as specified by the
Copenhagen approach, then it is completely reasonable and natural that
the choices made by the experimenters (about how to probe The Observed
System) should be treated as variables that are independent of the
variables that specify the physical state of the system they are
probing.

Bohr (1958: 92, p. 100) argued that quantum theory should not be applied
to living systems. He also argued that the classical concepts were
inadequate for that purpose. So the strict Copenhagen approach is simply
to renounce the applicability of *contemporary* physical theories, both
classical and quantum, to neurobiology.

*Von Neumann's Formulation.*

The great mathematician and logician John von Neumann (1955/1932)
rigorized and extended quantum theory to the point of being able to
corporate the devices, the body, and the brain of the observer into the
physically described part of the theory, leaving, in the psychologically
described part, only the stream of conscious experiences of the agent.
The part of the physically described system being directly acted upon by
the psychologically described "observer" is, according to von Neumann's
formulation, *the brain of that observer*. (von Neumann, 1955, p. 421).
The quantum jump of the state of the brain of an observer to the 'Yes'
basis state then becomes the representation, *in the state of that
brain*, of the conscious acquisition of the knowledge associated with
that answer 'Yes.' Thus the physical features of the brain state
actualized by the quantum jump to the state V1 associated with the
answer 'Yes' constitute the *neural correlate* of that person's
conscious experience of the feedback 'Yes.' This fixes the essential
link between quantum physics and neuroscience.

This is the key point! Quantum physics is built around "events" that
have both physical and phenomenal aspects. The events are physical
because they are represented in the physical/mathematical description by
a "quantum jump" to one or another of the basis state vectors defined by
the agent/observer's choice of what question to ask. If the resulting
event is such that the 'Yes' feedback experience occurs then this event
"collapses" the prior physical state to a new physical state compatible
with that phenomenal experience. Mind and matter thereby become
dynamically linked in a way that is causally tied to the agent's free
choice of how he will act. Thus a connection is dynamically established
between a person's conscious experience and the actualization of set of
physical properties. The form of this connection is determined in part
by a choice that, according to the theory, is made by the person, but is
not fixed by the laws of contemporary physics.

This logical structure is not some wild philosophical speculation. It
rationally yields, when combined with the statistical rule indicated
already above, all the pragmatic results of quantum theory, which
include, as special cases, all the valid predictions of classical
physics!

Von Neumann showed that his formulation of the theory is essentially
equivalent, in practice, to the Copenhagen interpretation. But it evades
the unnatural limitations imposed by Bohr: it by-passes the ad hoc
separation of the dynamically unified physical world into two
differently described parts. This allows the psychological description
to be---as is natural---the description of a stream of conscious
experiences that is closely tied to an associated sequence of physically
described events in the brain.

It is important that von Neumann's enlargement of the physical system to
include the body and brain of the observer *does not disrupt the basic
mathematical structure of the theory.* In particular, it does not alter
*the critical need to specify the orientation of the set of basis
vectors* (e.g., V1 and V2) in order to make the theory work. *The
specification of basis states continues to be undetermined by* *anything
in contemporary physical theory*, *even when the physical description is
extended to include the entire physical world, including the bodies and
brains of the human observers.*

This leap by von Neumann from the realm of atomic physics to the realm
of neuroscience was way ahead of its time: neuroscience was then in a
relatively primitive state compared to what it is today, and had a long
way to go before mainstream interest turned to the question of the
connection between brains and conscious experiences. But seventy years
of brain science has brought the empirical side up to the level where
the details of the mind-brain relationships are being actively probed,
and intricate results are being obtained that can be compared to the
predictions of the psycho-physical theory prepared long ago by John von
Neumann.

It is evident that a scientific approach to brain dynamics must *in
principle* use quantum theory, in order to deal properly with brain
processes that depend heavily on chemical and ionic processes. For
example, the release of neurotransmitter from a nerve terminal is
controlled by the motions of calcium ions, and these ions are small
enough so that the deterministic laws of classical physics necessarily
fail: quantum theory must *in principle* be used to describe the ion
dynamics. But then the state of the brain is in principle a cloud-like
structure that can encompass many conflicting classical possibilities.
The generation, within the quantum state of the brain, of conflicting
classical possibilities should occur particularly when the low-level
essentially mechanical processes cannot come to agreement on the best
course of action. A higher order "executive decision" is needed. It is
probably important in this connection that, unlike the mechanical
evolution generated by the local deterministic Schoedinger equation, the
quantum jumps associated with conscious experiences are intrinsically
nonlocal: they access *together* physical features that are located over
extended portions of the brain. This will be discussed later.

*Summary.*

The chief differences at the basic conceptual level between the quantum
and classical approaches to consciousness is that the classical
principles make no mention of consciousness. The structure is in
principle completely "bottom up." Everything is, in principle, fully
determined by what goes on at the microscopic atomic level, and any
dependence of microscopic properties upon macroscopic properties, or on
consciousness, is, in the end, a round-about consequence of laws
expressible exclusively in terms of properties of atomic particles and
the physical fields that they produce. But in quantum theory the
local-deterministic (i.e., bottom-up) physical process is *in principle*
*causally incomplete*: it fixes, by itself, neither our actions nor our
experiences, nor even any statistical prediction about how we will act
or what we will experience. The bottom-up process *alone* is unable to
make statistical predictions, because the statistical predictions depend
upon the choice of a set of basis vectors, and the bottom-up
local-deterministic quantum process does not fix this choice.

This reorganization of the dynamical structure leads to an altered
perspective on the entire scientific enterprise. The psychologically
described empirical side of scientific practice is elevated from its
formerly subservient status - as something that should be *deduced*
from, or constructed from, the already-dynamically-complete physical
side - to the new status of co-equal dynamical partner. Science becomes
the endeavor to describe the *two-way* *interplay* between the
psychologically and physically described aspects of nature, rather than
an attempt to deduce the existence and properties of our streams of
conscious experiences from a presumed-to-be-dynamically-complete local
mechanical model.

Within the von Neumann framework our conscious choices control the
orientations of the basis vectors. These choices can strongly influence
our actions. Thus these influences need not be illusions. The theory
provides, as we shall see in the section 3, a specific mechanism that
allows our conscious "free" choices to significantly influence our
physical actions.

*Pragmatic Neuroscience.*

Von Neumann, in his 1932 book followed the Copenhagen tack of focusing
on scientific practice rather than ontological issues: those issues need
not be dealt with in order to have a pragmatically useful scientific
theory of atomic phenomena. Indeed, it can be argued that science is
intrinsically pragmatic rather than ontological: the true nature of
things, other than our experiences themselves, can never be found by the
methods of science.

Von Neumann's formulation of quantum theory provides the foundations of
a pragmatic neurodynamics of the conscious human brain that is built on
pertinent contemporary physical theory, rather than inadequate classical
physics. All quantum approaches to consciousness build upon the
foundation laid by von Neumann, but various physicists have advanced
different ways of developing that core structure. We turn now turn to
the descriptions of a number of these proposals.

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

Bohr, N. (1963). *Essays 1958/1962 on* *Atomic Physics and Human
Knowledge.* New York: Wiley.

Heisenberg, W. (1958a). The representation of Nature in contemporary
physics. *Daedalus* 87, 95-108.

Heisenberg, W. (1958b). *Physics and Philosophy*, New York: Harper,

Von Neumann, J. (1955/1932). *Mathematical Foundations of Quantum
Mechanics.* Princeton: Princeton University Press. (Translated by Robert
T. Beyer from the 1932 German original, Mathematiche Grundlagen der
Quantummechanik. Berlin: J. Springer)