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

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

It has been averred that invoking quantum theory to understand
consciousness is motivated by the thought that quantum theory and
consciousness are two great mysteries, so perhaps they are related. That
claim betrays a profound misunderstanding of the nature of quantum
mechanics, which consists, above all, in a pragmatic scientific solution
to the problem of the relationship between mind and matter. A key
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 *descriptions* of 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 descriptions of physical states, expressed in terms of
mathematical properties assigned to space-time points. A new conception
of the linkage between these two kinds of description was formulated by
Bohr, Heisenberg, Pauli, and their colleagues, and this conception was
later extended by John von Neumann from the domain of atomic science to
the realm of neuroscience and, in particular, to the problem of the
relationship between the minds and brains of human beings.

This new understanding of the relationship between the psychologically
and physically described components of scientific practice was achieved
by abandoning the classical conception of the physical world that had
ruled science since the time of Newton, Galileo, and Descartes. The
building blocks of science were changed from descriptions of tiny bits
of mindless matter and the interactions between them to descriptions of
separate bits of acquired knowledge and the actions that we take to
acquire such knowledge. Science was transformed from its seventeenth
century form to its twentieth century form by an explicit recognition
that this human activity is basically an attempt to probe nature in ways
that can reveal to us features that can be woven into a conceptual
structure that allows us reliably to foresee the experiential
consequences of our intentional actions.

This new understanding underlies the following pronouncements of
Heisenberg and of Bohr:

"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, 1958)

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

Wheeler calls the observers "participants" to emphasize this essentially
*active role* *of conscious agents* in quantum dynamics.

Comprehending this new conception of the relationship between the
empirical and physical sides of the scientific endeavor requires an
appreciation of a certain novelty in the logical structure of quantum
theory, and this fundamental conceptual shift can be appreciated without
becoming enmeshed in technical mathematical details.

*The Classical-Physics Approach.*

Classical physics arose from the theoretical effort of Isaac Newton to
account of the empirical 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. Then Newton discovered that he could explain
*simultaneously* the celestial findings of Kepler and the terrestrial
findings of Galileo and others by postulating 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, but that make no reference to any conscious acts of
experiencing.

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 far away it is. 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 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 does not depend 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
feature is predicted by classical theory, but the specific form of the
distribution predicted by classical physics differs greatly from what is
empirically observed.

Max Planck discovered in 1900 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 very large number of empirical
effects have been found that depend upon this constant, and that
conflict with the predictions that follow from the basic principles of
classical physical theory.

During the twentieth century a theory was devised that accounts in a
uniform way both for all of the successful predictions of classical
physical theory, and also for 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*. 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
in accordance with a quantum mechanical law of motion called the
Schroedinger equation. This law, like its classical analog, is local and
deterministic: the interactions between different elements act by
contact with neighbors, and this law of motion determines the physical
state of any isolated system at any time from its physical state at any
earlier time.

This 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
determine everything. For example, if the state of the universe were to
develop since the big bang solely under the control of the local
deterministic Schroedinger equation then the state of the moon would
represent a structure spread out over a large part of the sky. But that
is not what we perceive.

The smeared-out character of the quantum state of a macroscopic object
is a consequence of the famous Heisenberg Uncertainty Principle,
combined with the fact that tiny uncertainties at the microscopic level
often get magnified over the course of time to large uncertainties in
macroscopic properties.

This contradiction between a mathematical theory that is wonderfully
coherent, and that yields many predictions of incomparable accuracy,
with the blatant realities of everyday experience is the most basic fact
of quantum theory. Its obdurate mathematical certainty allows it to
serve as the fulcrum upon which rests a seismic shift in science's
concept of science itself, and, in particular, of the relationship
between the empirical and theoretical sides of scientific practice.

*"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 at his institute 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 disjoint
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 is described in a language that allows that human agent 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 the data are* that
he thereby acquires. This description is in terms of the conscious
experiences of the agent. It is a description of his intentional
actions, and of the experiential feedback 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:

> \"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:
> 73}

This freedom 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 both the laws that
govern the evolution in time of this mathematical structure, and also
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 theories rests squarely
on a basic technical difference. This difference can be adequately
illustrated by a simple two-dimension 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,' and it can be modeled in a two-dimensional
space.

Consider your desk-top, and two distinct points on it 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* 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).

In quantum theory these three vectors, *V*, *V1*, and *V2*, when
oriented in certain particular ways, are given specific meanings. 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 outcome of the
measurement were 'Yes.' The vector *V2* represents the state that the
observed system would be known to be in if the 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 crucial, though trivial, logical point can now be stated: The
*orientation* 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 by "free 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 the choices made by the experimenters is
not 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 argued that quantum theory should not be applied to living systems.
He also argued that the classical concepts were inadequate for that
purpose. Indeed, quantum effects are clearly and demonstrably important
in living systems, including, in particular, human brains. So the strict
Copenhagen approach is simply to renounce the applicability of the
available physical theories, both classical and quantum, to
neurobiology.

*Von Neumann's Formulation.*

The great mathematician and logician John Von Neumann rigorized quantum
theory to the point of being able to coherently incorporate 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. 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*. The quantum jump of the state of the brain of
an observer to the 'Yes' basis state becomes the representation, *in the
state of that brain*, of the conscious acquisition of the knowledge
associated with that answer 'Yes.' 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.'

Thus the basic elements of the problem of the connection between a brain
and the associated stream of conscious experiences are precisely the
elements that are connected together by von Neumann's dynamical
equations of motion!

Von Neumann showed that this formulation of the theory is essentially
equivalent, in practice, to the Copenhagen interpretation. But it
circumvents the ad hoc separation of the dynamically unified physical
world into two differently described parts, and allows the psychological
description to be a description exclusively of a stream of conscious
experiences.

The key conceptual point is 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,* in order to tie the theory to ongoing human
experiences, and also to complete the determination of the dynamical
evolution of the physically described system. That is, the orientation
of the basis vectors associated with a quantum jump *is not determined*
by the physical description, even when that description is extended to
include the entire physical world, including the bodies and brains of
the human observers.

That is the central point. In classical physics the incorporation of the
entire physical world into the physically described system leads to *the
complete determination* of the state of the brain of the observer, and
hence to the complete exclusion of the consciousness of the observer
from any dynamically necessary role in the determination of the flow of
physical events. But in quantum theory there remain these free variables
that must be fixed in order to tie the mathematics to human experiences.
These variables are, in general, variables that influence our actions.
And in the context of scientific practice they are the variables that
control the empirical conditions, in accordance with Bohr's dictum. This
freedom to choose actions, and hence to specify experimental conditions,
persists even when the physically-described system includes the body and
brain of the observing agent.

*An Altered Perspective.*

This leap by von Neumann from the realm of atomic physics to the realm
of neuroscience was way ahead of its time: neuroscience was in a
relatively primitive state compared to what it is today; it 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.

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 -- and hence provide no
actual theory of consciousness that can be confronted by empirical
data - whereas consciousness plays an essential dynamical role in
quantum theory. In quantum theory the local-deterministic bottom-up
physical process is *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. This causal gap *not
only opens the door* to the possible existence of a dynamically
compatible top-down process governed by conscious choices, but, at the
practical level, *entails the need for* such a top-down process, in
order to tie the mathematical theory to predictions about human
experiences. The bottom-up process alone is unable to make even
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 needs to be *deduced*
from, or constructed from, the already-dynamically-complete physical
side - to the new status of co-equal dynamical partner. Science, at the
practical level, becomes the endeavor to describe the *two-way*
*interplay* between the psychologically described empirical reality and
a physically described mathematical model, rather than an attempt to
deduce the existence and the properties of our streams of conscious
experiences from a presumed-to-be-dynamically-complete theoretical
mechanical model.

Within the von Neumann framework our conscious choices control the
orientation of the basis vectors, and hence these choices have, by
virtue of this power, the ability to influence our actions. These
influences are not illusions. Rather, according to this model, our
conscious thoughts do exercise a certain degree of top-down influence.

*Pragmatic Neuroscience.*

By restricting itself to pragmatic scientific practice the Copenhagen
approach was able to restrict the class of "observers" to human beings:
"pigs do not do science." Although Bohr often applied his general idea
of "the lessons taught by quantum theory" to other domains of science,
these applications were by way of analogy, not by way of a strict
application of the specific laws of quantum theory.

Von Neumann, in his 1932 book, appeared to follow the Copenhagen idea of
focusing on scientific practice. He did not address ontological
questions. Those questions must be answered before any claim can be made
to have created a satisfactory understanding of the true nature of
reality. But they need not be dealt with in order to have a pragmatic
scientific theory of the neurodynamics of conscious human brains that
relates empirical findings to a mathematical model in a way that allows
useful testable predictions to be made, and that is, philosophically and
mathematically, an extension of orthodox atomic physics to the realm of
neuroscience.

Von Neumann's formulation of quantum theory provides the general outline
of a pragmatic neurodynamics of the conscious human brain that grows
naturally out of contemporary physical theory. All quantum approaches to
consciousness start from this von Neumann formulation of quantum theory
as the pragmatic base that provides the essential link to the empirical
data. But various physicists have proposed augmenting this basic
structure in different ways. We turn now turn to the descriptions of a
number of these proposals.