######## Whiteheadian Process and Quantum Theory

Henry P. Stapp

Lawrence Berkeley National Laboratory, Berkeley, California

#### **Introduction**

Quantum theory has been formulated in several different ways. The
original version was 'Copenhagen' quantum theory, which was formulated
as a practical set of rules for making predictions about what we human
observers would observe under certain well-defined sets of conditions.
However, the human observers themselves were excluded from the system,
in much the same way that Descartes excluded human beings from the part
of the world governed by the natural physical laws.

This exclusion of human beings from the world governed by the physical
laws is an awkward feature of Copenhagen quantum theory that is fixed by
"Orthodox" quantum theory, which is the form devised by von Neumann and
Wigner. This orthodox form treats the entire world as a quantum system,
including the brains and bodies of human beings. Some more recent
formulation of quantum theory seek to exclude from the theory all
reference to the experiences of human observers, but I do not consider
them, both because of their technical deficiencies, and because they are
constitutionally unequipped to deal adequately with the causal efficacy
of our conscious thoughts.[^1]

The observer plays a central role in both Copenhagen and Orthodox
quantum theory. In this connection, Bohr, describing the 1927 Solvay
conference, noted that:

> "...an interesting discussion arose about how to speak of the
> appearance of phenomena for which only statistical predictions can be
> made. The question was whether, as to the occurrence of such
> individual events, we should adopt the terminology proposed by Dirac,
> that we were concerned with a choice on the part of 'nature,' or as
> suggested by Heisenberg, we should say we have to do with a choice on
> the part of the 'observer' constructing the measuring instruments and
> reading their recording."[^2]

The point here is that two very different kinds of choices enter into
the determination of what happens.

\(1\) First some particular question must be posed.

\(2\) Then nature gives an answer to that particular question.

The second kind of choice is described by Dirac as a choice on the part
of "nature" as to what the outcome of a given observation will be. For
this kind of choice quantum theory gives a statistical prediction: it
specifies, for each possible outcome of the observation, the probability
for that outcome to appear. This is the famous statistical element in
quantum theory.

But that choice of outcome is out of human hands, and it is not the
focus of this study.

The first kind of choice is also essential to the quantum process. It is
the choice by the experimenter of which aspect of nature he is going to
probe. In the context of an experiment being performed by a scientist on
some external physical system, this choice by this experimenter of which
experiment he will perform is decided by some process going on in the
experimenter's mind/brain. In the Copenhagen interpretation that
mind/brain process is placed definitely outside the system being
investigated. But if, following von Neumann, we take the view that
quantum theory ought to cover all physical systems, including human
brains, then the system that is determining which question will be put
to nature becomes part of the system being studied.

#### **Posing the question**

The starting point of this study is the fact that contemporary quantum
theory is ontologically incomplete. Two fundamental questions remain
unanswered. The theory requires that a sequence of specific questions
with 'yes' or 'no' answers be put to nature, whereupon nature promptly
delivers an answer, The relative statistical weights of the two possible
answers, 'Yes' or 'No,' are then specified by quantum theory. But what
is not specified by contemporary quantum theory is:

\(1\) What determines which questions are put to nature, and

\(2\) What determines whether the individual answer to a posed question
is 'yes' or 'no'?

The objective here is to begin to answer these questions, adhering to
the naturalistic principle that the actually occurring experiences
"supervene on" the entire history of the physical universe, which is the
full history of the evolving quantum state of the universe. However,
that condition of supervenience---although it means that given the full
physical history, the full experiential history is fixed---does not
determine whether our experiences enter as causes, or effects; or as
both or neither.

To make the following discussion of these issues clear to physicists I
shall use the language and symbols of quantum theory. However, I shall
try to explain things in a way that others can understand if they merely
regard the symbols I use as pictorial abbreviations of the ideas that I
describe.

The (physical) state (of the universe) is represented by the (density
operator) *S*. A possible experience is labeled by the letter *e*. The
connection of this experience to the mathematical formalism is via the
correspondence;

e → P~e~

where *P~e~* is the projection operator

P~e~ = SUM~e~ \|i\>\<i\|.

Here *SUM~e~* is over the maximal set of basis states *i* that are
compatible with experience *e*.

The basic dynamical connection is this: If *S* is the state of a system
before experience *e* occurs, then the state of the system after this
experience occurs is:

S → P~e~ S P~e~

This change is called the 'reduction of the wave packet': the reduction
is to the unique new form that incorporates the restriction imposed by
the new knowledge supplied by the experience *e*, and that introduces no
other information into the state.

There is a basic difference in philosophy at this point between the
Copenhagen view espoused by Bohr et. al. and the view proposed by von
Neumann. Bohr assumed that the state involved in the quantum description
is the state of some relatively small system that has been prepared in
some specified way by experimenters, and that the projection operator
*P~e~* acts in the space associated with that small system. The
surrounding world was not represented in the theoretical description
except by way of the scientist's specifications, via ordinary language,
of the experimental set up. Thus the whole quantum procedure was
considered to be merely a procedure that allows scientists to make
statistical predictions about what would appear to themselves under
those well defined observationally specified conditions. However, the
great bulk of the physical world was not represented in the quantum
description, except via our descriptions of our experiences. This
radical restriction on the scope of science, and of its description of
nature, was rejected by Einstein and many others.

Von Neumann adopted the view that one ought to assume that, because
measuring devices and human bodies are made up of atoms, the laws of
quantum theory, if universal, ought to work also for these physical
systems, and hence in principle for the entire physical universe, and
that any partial description was artificial. By following through the
mathematics of that more global perspective von Neumann showed that one
could indeed suppose that the laws of quantum theory applied to the
whole physical universe (at least in the non-relativistic approximation,
and for the somewhat primitive idea of the make‑up of the world that
prevailed in the 1930\'s), and that the projection operator *P~e~* could
then be supposed to act on those degrees of freedom of the universe that
correspond to the brain of the observer. This transformation *S → P~e~
S* P~e~ selects out from *S*, and retains, only those states of the
brain that are compatible with the knowledge that constitutes experience
*e*.

This procedure allows one to recover, in principle, all the predictions
of the technically simpler, but ontologically unsatisfactory, Copenhagen
theory. It provides a conception of the universe that is in accord with
all the predictions of quantum theory, and is in general accord with the
classical idea that there is a causal chain in the physical universe
that links the observed event in the external world to the brain of the
observer of that event, and that this connection leads---under
appropriate conditions of alertness and attention, etc.---to a
corresponding mind‑brain event of the kind we know.

The only 'reductions of wave packets' that are needed in the von Neumann
picture, in order to reproduce the predictions of the pragmatic
Copenhagen interpretation, are reductions associated with human
experiences: these give the increments in 'our knowledge.' Of course, it
is unacceptably anthropocentric to single out our particular species in
a general ontological approach. So I assume that this process in human
brains is just a special case of a general natural process. However, I
focus here on that special case, because we have direct access to the
subjective aspects in that case.

Von Neumann builds into his formulation the demand that a specific
question must be posed by invoking his famous "Process 1." To understand
this, note that for any *P*, the following identity follows from simple
algebra:

S= PSP + (1‑P) S (1‑P) + PS (1‑P) + (1‑P) SP.

'Posing of the question' is represented by the von Neumann reduction
(i.e., by the von Neumann Process 1):

For some possible experience *e*,

S → P~e~ S P~e~ + (1‑P~e~) S (1‑P~e~).

The two 'interference' terms, which involve both *P* and *(1‑P)*, are
dropped.

The first term (after the arrow) is the part of the state *S* that
corresponds to the definite outcome 'Yes, experience *e* occurs now!'
The second term corresponds to the definite outcome 'No, experience *e*
does not occur now.' The other two terms are stripped away by the Von
Neumann Process 1.

This action on S defines which question is put to Nature. Nature will
then give the answer 'Yes' with probability

Tr P~e~ S / Tr S = SUM~e~ \<i\| S \|i\>/ SUM \<i\| S \|i\>.

Here *Tr* denotes the trace operation, the sum *SUM~e~* is defined as
before, and *SUM* is the sum over all members of the basis set.

Quantum theory makes this definite statistical prediction about which
outcome will appear, after the definite question is posed. But it does
not specify what the question will be, beyond the requirement that
answer 'Yes' must correspond to some identifiable experience. Which
question is posed is in the hands of "the observer." This freedom places
in the hands of the observer great power to control the course of
physical events in his brain, without in any way conflicting with the
constraints imposed by the known laws of nature. The argument for this
follows.

#### **Light as foundation of being**

There are many theoretical reasons for believing that our experiences
are correlated mainly to the electromagnetic properties of our brains.
Our experiences have a classical character, and the closest connection
of quantum mechanics to classical mechanics is probably via the
so‑called 'coherent states' of the electromagnetic (EM) field.[^3] These
coherent states integrate a vast amount information about the motions of
individual atomic nuclei and electrons; motions that cannot be expected
to affect our thoughts except via their integrated activity.

These coherent states are probably the most robust feature of brain
dynamics, with respect to perturbations caused by thermal and other
noise.[^4] I shall not go into more detail here, except to say that the
coherent low‑frequency part of EM field in the brain can be decomposed
approximately into mesoscopic modes each of which behaves like a simple
harmonic oscillator. The coherent state description is in terms of this
collection of mesoscopic harmonic oscillators. For each such oscillator
the ground state is a certain gaussian state in both of its internal
variables *p* and *q: exp{‑qq/2}* or *exp{‑pp/2},* This gaussian 'cloud
of possibilities' is centered at the origin *q=0* and *p=0* in both *q*
and *p*. If one shifts this state so that it is centered at some other
point *(Q, P)*, then this center point will move around a circle of
fixed radius with constant velocity, which is just the motion in these
variables that a classical particle would follow for the simple harmonic
oscillator case.

I shall assume that the mind‑brain connection is via these coherent
states of the EM field, and will examine the effects on the brain of
mental action by considering the effects of mental action on these
low‑frequency mesoscopic coherent states of the EM field in the brain.

#### **Effects of mental action on brain behavior**

I first show that, within the framework of quantum theory, the mere
choice of which question is asked, can influence the behavior of a
system, even when an average is made over the possible answers to the
question. This demonstration is intended for physicists and is quite
short. Other readers can perhaps get the gist.

The issue is this:

Can X = Tr \[QPSP + Q(1‑P)S(1‑P)\] depend on P ?

Take Q = sz, S=(1 + sz) \[With sx, sy, and sz the Pauli sigma matrices\]

If P = S/2 then X = 2.

If P= (1 + sy)/2 then X=0.

This just confirms, as a matter of principle, that it matters which
question is posed---and answered---even if one averages over the
possible answers. Thus the gross behavior of a system can depend in
principle upon which questions the system is asking, internally, where
the gross behavior is obtained by averaging over the answers that nature
gives to these questions.

I give two examples of how one's behavior could be influenced in this
way, simply by controlling, via one\'s attention, which question is
posed.

The first example is an application of the Quantum Zeno Effect. This
effect is well understood, theoretically, and has, at least in a certain
sense, been confirmed experimentally.[^5] The point is that according to
quantum theory a very rapid sequence of posings of the same question
'freezes' the answer: if the answer to the first question is 'yes', then
the answer 'yes' will, according to the quantum principles, keep on
occurring. Thus the mere fact that the question is asked repeatedly in
rapid succession keeps the system in the subspace where the answer is
'yes', even in the face of strong mechanical forces that would quickly
take it out of that subspace if the questions were not being asked.

This effect might be connected to the psychological experience that
intense concentration on an idea tends to hold that idea in place. For
example, if one is holding up some heavy object then intense mental
'focus of attention' on an experience e of willful effort could produce
a very rapid sequence of such experiences e, each resulting in a
collapse of the wave function associated with the brain to a state
compatible with this experience e. The effect would be to guide the
evolution of the brain state, holding this idea in place, in spite of
strong purely physical forces that would to tend move the brain away
from this state.

A second example is this. Suppose we are representing the brain, insofar
as its interface with consciousness is concerned, by coherent states of
the EM field. This state is a Gaussian state represented by *N
exp{‑\[(q‑Q)(q‑Q)/2\]}*, where *N* is a normalization constant.

Suppose I ask the question: Will I find the state to be *N
exp{‑\[(q‑Q\')(q‑Q\')/2\]}*? The probability that the answer is 'Yes' is
the square of:

N^2^ ∫ dq exp{‑\[(q‑Q)(q‑Q)/2\]} exp{‑\[(q‑Q\')(q‑Q\')/2\]} =
exp{‑\[(Q‑Q\')(Q‑Q\')/2\]}.

For small *Q* the probability is *(1‑(Q‑Q\')(Q‑Q\'))*.

Suppose one has a large distance *L* in *Q* space, but breaks the
distance into *n* small intervals, for which the above approximation is
adequate, and asks the succession of questions: Is the state the
Gaussian centered at the end of each of the succession of intervals?

Then the probability, at the end of this process, of finding the state
to be the Gaussian centered at *L* is *(1‑(L/n)(L/n)n)*. In the limit of
large n this is unity: the mental effort of focusing attention in this
way will, with high probability, according to the statistical rules of
quantum theory, have changed the state of the brain to this other state
in spite of the absence of any tendency for this to happen via action of
the Schrödinger equation.

These effects may seem strange. But the point is that there is a loose
connection in quantum theory: the physical principles themselves do not
specify which question is posed. This opens up the logical possibility
that, strictly within the bounds of orthodox quantum theory, our
conscious thoughts PER SE could be entering into the mind‑brain dynamics
in a way reducible neither to purely mechanical effects governed by the
Schrödinger equation of motion nor to the random effects of Nature\'s
choices of outcomes, nor to any combination of these two effects. There
is a rigorous need for some third process, which I call the 'Heisenberg
process', and which selects which question is put to nature. This
process is not reducible to the 'Schrödinger process' of evolution
between jumps via the Schrödinger equation, or to the 'Dirac process'
that selects an answer once the question is posed. Thus in orthodox
(vN/W) quantum theory there must be these three process entering into
mind‑brain dynamics: mind‑brain dynamics has a "tripartite causal
structure," one component of which is naturally mental or experiential,
since it must choose a question that has an experientially recognizable
answer.

#### **What determines which question is posed?**

What sort of process might one imagine to be filling this logical gap in
contemporary quantum theory?

Once one becomes open to the notion that maybe our conscious thoughts
have a reality in their own right, it becomes apparent that there is a
natural causally efficacious place for them in quantum mind‑brain
dynamics. The point is that, according to the basic quantum precepts,
the occurrence of a conscious thought associated with a quantum system
is supposed to cause a reduction of the state of that system to the
reduced state that is compatible with the increment in knowledge that
constitutes that conscious knowing. In vN/W quantum theory this
reduction will be a reduction in the brain state of the person who has
the thought. This newly actualized brain state must tend to actualize
the functional properties implicit in the conscious thought: it must
initiate the brain activities that the thought feels are being
initiated. Thus the evolution of this brain state must generate messages
going out to various motor centers, if the thought is about generating
actions. But, in any case, the Schrödinger evolution must also be
generating instructions for the creation of a brain state corresponding
to a succeeding thought. However, the natural diffusion caused by the
Heisenberg uncertainty will entail that the quantum state actually
generated by the brain process will be somewhat fuzzy: a host of
possibilities will be created. But this diffusion can be counteracted in
part, and the process kept on a focused and intended track, by
asking---i.e., attending to the right questions.

We know that often, when we have a thought that initiates an action, we
also initiate a monitoring that will test to see whether the action is
proceeding as intended. That command to monitor is an instruction to
"attend" to some question at some later time. I propose that in general
our thoughts issue, as part of their intentional aspect, commands to
"attend" in the future to certain questions, and that these directives
supply the missing component of the quantum dynamics: THEY pose the
particular questions that are put to nature. Then the necessary posings
of the questions become an aspect of quantum mind‑brain dynamics.

Since the question to be posed is supposed to be of the form "is an
experience of such‑and‑such a kind occurring" it would appear that the
question really ought to be part of the mental, rather than physical,
side of the mind‑brain dynamics. The aspect that makes the mental side
essentially different from the physical aspect governed by the
Schrödinger equation is that the latter process is mechanical: it is
governed by LOCAL causal connections. But conscious thoughts correspond
to global properties of brains. They are associated with the action of
the operators *P*, and these operators must be non-local because any
local projection operator *P* would introduce an infinite amount of
energy into the system.

The essential point here is that quantum theory has a lacuna that can
very naturally be filled in such a way as to allow our thoughts to
exercise real, though not absolute, control over the mechanical aspects
of mind‑brain dynamics. This bringing of the experiential aspect of
nature into the causal structure is very much in line with the ideas of
Alfred North Whitehead.

**Whitehead and the quantum mind/brain.**

It may be useful to expand upon this final point concerning Whitehead.
To bring the issue into focus I shall first briefly summarize the main
points described above about the connection of mind to brain within
quantum physics, and then consider the possible relevance of
Whiteheadian thought.

The main point of the above discussion is that the original Copenhagen
interpretation of quantum theory placed the human experimenter outside
the system that was described in the mathematical language of quantum
theory. In that early approach the human experimenter has three roles.
The first is as a receptacle for the experiences that are the database
of science. The second is to pose to nature a sequence of particular
'Yes--No' questions that nature immediately answers by either returning
the experience associated with the answer 'Yes', or by returning no
experience. The third role is as a scientist who communicates to his
colleagues "what he has done and what he has learned," and thus
contributes to the on-going scientific enterprise. Our interest here is
in the second role as "the chooser of what question to ask." This choice
is not fixed by any laws or processes that are contained in or entailed
by Copenhagen quantum theory. This is firstly because Copenhagen quantum
theory places the human observer outside the system governed by the
quantum laws, which are the only known precise laws. And secondly
because in Copenhagen quantum theory the human observer is treated in a
practical way, and in practice the choice of which experiment to perform
is effectively free: it depends on the observer's intentions and a host
of inscrutable and empirically uncontrolled factors.

Von Neumann considered a sequence of different ways of dividing nature
into the two parts: the first part is the observed system, which is
described in terms of the quantum mathematics, and the second part is
the observing system, which is described in terms of human experiences.
Von Neumann showed that it made no practical difference which of the
various placements of the dividing line between the two parts of nature
he used. In each case the choice of which question to put to nature was
represented by his "Process 1", which was outside the control of the
known physical laws, but was ascribed to the mental processes of the
participant/observer. Von Neumann's final placement of the dividing line
put all systems composed of atomic constituents and physical
fields---such as the electromagnetic and gravitational fields---on the
side described in terms of the quantum mathematics, and thus placed only
the consciousness of the participant/observer outside the mathematically
described physical world. However, there must be a dynamical connection
between the mind and the brain: the mind of the observer is obviously
connected to what is going on in his brain, and his choice of which
questions to put to nature influences his brain in ways controlled in
principle by the quantum laws, once the neural correlates of our
conscious experiences are known. This connection is via the quantum Zeno
effect, which shows explicitly how the choice of questions, and their
timings, can influence the course of events in the probed system, which,
in this case, is the brain of the participant/observer.

This description summarizes the quantum mechanics of the mind/brain
system within the von Neumann formulation of quantum mechanics. It opens
the door to the natural incorporation of causally efficacious conscious
thoughts into contemporary basic science. But it only opens the door: it
does not specify how the brain and the conscious thoughts act together
to formulate the necessary questions, and their timings. This is a
problem to whose solution Whiteheadian process theory might contribute.

A scientist with physicalist leanings would be prone to try to create
some sort of "purely physical process" to produce the needed questions.
This would make our conscious thoughts into either redundant side
effects, or redescriptions of processes that can be completely described
in purely physical terms. But either of these options renders mysterious
the fact that experiences exist as the psychological realities that
populate our streams of consciousness. The fact that, at least within
the Copenhagen and von Neumann approaches, the questions posed are
supposed to have experiencable answers means that experiential realities
must play some special sort of role in the dynamical processing. But in
that case, quite independently of the ultimate truth about the basic
nature of these realities, it makes good theoretical sense to take these
realities as they are actually are known to us, namely as constituents
of human streams of conscious experiences, and weave them into the
physical world described by quantum theory in just the way that such
experiences fit into the quantum framework, namely as efficacious
agents. But they must also conform to philosophical requirements of
rational coherence. That establishes the link to Whitehead, whose
central endeavor was to create a rationally coherent scheme that weaves
experiential-type realities into physical reality by making them
integral parts of event-like actual occasions, which are naturally
identifiable with the psycho-physical events that are the basic
realities of von Neumann's formulation of quantum theory.

The brain is of course the carrier of potentialities generated by the
past events. It carries the physical correlates of appetites for various
particular resolutions of the conflicting potentialities. While the
physicalist might seek to explain the process in purely physical terms,
the Whiteheadian approach recognizes the descriptions in terms of
potential experiences as valid and useful descriptions of real aspects
of nature. It makes use of the huge partial understanding of mind/brain
process provided by exploring the structure of human experience itself.
Quantum theory does not encourage the idea of taking the physically
described aspect of brain process as dynamically complete. It calls for
a psycho-physical process of the creation of events that actualize
experiencable potentialities.

A central Whiteheadian-type notion is that each actual event must have
both an aspect that fixes, experientially and physically, what is taken
from the past, and also an aspect that creates experiential and
physically manifested potentialities for the future. Each event has an
intentionality that does not just take randomly from the past, but
rather takes selectively from the past particular potentialities whose
actualizations create potentialities for future events that serve some
purpose. Quantum theory seems to allow mind/brain events of this kind,
and Whiteheadian thought can be viewed as an effort to provide the
beginning of an understanding of the structure of such events.

Whiteheadian thought also provides an approach to the question of how
one extends quantum dynamics to times and regions where consciousness as
we know it is absent. All of nature is composed of actual occasions of
the same genus, and thus even primordial events must have aspects that
have some kinship to our conscious thoughts.

[^1]: H.P. Stapp, "Flagstaff Talks," (1999); available from
    <http://www-physics.lbl.gov/~stapp/stappfiles.html>; Internet.

[^2]: N. Bohr, "Discussions with Einstein," in *Albert Einstein:
    Philosopher-Scientist,* ed. P.A. Schilpp (New York: Tudor, 1951),
    223.

[^3]: J.R. Klauder and E.C.G. Sudarshan, *Quantum Optics* (New York:
    Benjamin, 1968); R.J. Glauber, "Coherence and Quantum Detection," in
    *Quantum Optics,* eds. S.M. Kay and A. Maitland (New York: Academic
    Press, 1970); H.P. Stapp, "Exact Solution of the Infra-Red Problem,"
    *Physical Review* 28D (1983): 1386--1418; T. Kawai and H. Stapp,
    "Quantum Electrodynamics at Large Distances," *Physical Review* 52D
    (1995): 2484--2532.

[^4]: O. Kuebler and H.D. Zeh, "Dynamics of Quantum Correlations,"
    *Annals of Physics* 76 (1973): 405--418; H.P. Stapp, *Mind, Matter
    and Quantum Mechanics* (New York: Springer-Verlag, 1993), 130; W.L
    Zurek, S. Habib, and J.P. Paz, "Coherent States via Decoherence,"
    *Physical Review Letters* 70 (1993): 1187--1190.

[^5]: W. Itano, D. Heinzen, J. Bollinger, and D. Wineland, "Quantum Zeno
    Effect," *Physical Review* 41A (1990): 2295--2300.