**Quantum Collapse and the Emergence of Actuality**

**from Potentiality.**

*Henry P. Stapp*

> Henry P. Stapp is a theoretical physicist at the University of
> California's Lawrence Berkeley Laboratory. He is the author of two
> books and many publications on the role of mind in the quantum
> mechanical description of nature.

***Orthodox quantum theory: The Copenhagen interpretation.***

> Orthodox quantum theory is the theory propounded in the late 1920's,
> principally by Bohr, Heisenberg, and Pauli. It is, in essence, what is
> taught in our university courses in quantum physics. It is
> epistemological and pragmatic: it consists of rules designed to allow
> us to compute expectations pertaining to our future experiences on the
> basis of the knowledge that we have extracted from our past
> experiences. This approach is proclaimed in the opening words of Niels
> Bohr's 1934 book "Atomic theory and the description of nature":
>
> The task of science is both to extend the range our experience and
> reduce it to order. (Bohr, 1934, p.1)

in conjunction with his later assertions:

> ...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 predictions of
> determinate or statistical character pertaining to individual
> phenomena appearing under conditions defined by classical physical
> concepts. (Bohr, 1958, p. 64)

The stipulation that the experienced conditions must be "defined by
classical physical concepts" creates a seeming contradiction, which
leads directly to the diversity of non-orthodox interpretations of
quantum mechanics. The problem is that the classical physical concepts
are logically incompatible with the quantum physical concepts. The
quantum concepts include the "Heisenberg uncertainty principle", which
entails that the quantum state of say a single particle is effectively a
continuously smeared out distribution of classically possible states of
that particle. Of course, a single elementary particle is too small to
be seen, or directly experienced, by human beings, so there is no
immediate empirical contradiction. However, the quantum principles
specify how combinations of the elementary particles are to be
constructed. The resulting quantum states of large objects turn out to
be smeared out "statistical mixtures" of the corresponding classical
states of these objects. Einstein emphasized that if the state of the
universe were to evolve, from the inception of the universe until the
present time, in accordance with the quantum generalization of the
deterministic laws of classical equations of motion\-\--namely in accord
with the Schroedinger equation\-\--then, for example, the quantum state
of the 'moon' would be smeared out over the entire sky. Likewise, the
quantum state of an alert and thinking human brain, even if it were very
similar to a classically described state at some initial time, would
often evolve in seconds into a smear of possibilities corresponding to
different classically describable experiences. Interactions with the
environment would make this smear "a statistical mixture" of these
classically different possibilities, but the neither the interactions
with the environment nor any other yet-known physically-described
process picks out any single one of this continuum of possibilities to
be the one actually experienced by the person to whom the brain belongs.

In orthodox quantum mechanics the selection that is needed to reconcile
the mathematical/physical description of the evolving state with our
empirical observations is effected by an extra process, called a quantum
collapse, which, in association with an observation, suddenly reduces
the quantum state to the part of itself that is compatible with the
classically described increment in knowledge supplied by the
observation.

A partial understanding of this "quantum collapse" is obtained by
considering the close connection between quantum theory and classical
*statistical* mechanics. Suppose, in classical statistical mechanics,
that a particle is known to be in a closed transparent box, and that our
initial knowledge of the position of that particle is represented by a
likelihood that is uniformly distributed over that box. Although the
(center of the) particle is, according to the classical conception,
"really" at some particular point in the box at each instant of time,
*our knowledge* of its position is represented by this uniform
distribution. Now suppose we shine a very intense beam of light that
intersects only the left-hand side of the box, so that if the particle
were in the left-hand side of the box, we would definitely see it. If we
see no particle in the left-hand side then we now know that the particle
is in the right-hand side of the box, and the probability function
(which represents our knowledge) undergoes a sudden collapse to the part
of itself that corresponds to the particle's being in the right-hand
side of the box: the sudden collapse of the physically described
probability function matches our sudden increase in knowledge. This
conception of the relationship between (1), a sudden increment in
knowledge, and (2), a corresponding sudden change in a probability
function that represents our knowledge, is a basic idea in orthodox
quantum mechanics, which instructs us to regard the theory merely as a
set of rules that allow us to form expectations pertaining to future
increments in knowledge under conditions specified by prior knowledge,
without endeavoring to make any speculative conjectures about underlying
essences that are not supported by empirical evidence.

This epistemic/pragmatic approach is what is taught in physics courses
at our universities. These courses aim to equip the students to use
these quantum rules, which have never been known to fail. These students
are being trained to be physicists, not philosophers. Delving into the
questions about essences can derail the student, and he is, accordingly,
encouraged to keep focused on the mathematical procedures and their
applications to experientially observable phenomena.

If one seeks to go beyond the practical procedures, and tries to develop
some understanding to what is actually going on, then one is faced with
an immediate problem. In classical statistical mechanics the various
classical possibilities evolve dynamically in causal independence of
each other: the different possibilities are regarded classically as
being "really" physically independent possibilities that are collected
together only in our imagination. As such, they must, in our
mathematical model, evolve independently. But the simple example of the
double-slit experiment shows that in practice various different
spatially well-separated paths can 'interfere' with each other: they do
not evolve in causal independence. The interference can, in this case,
be computed by using a 'wave picture', but that picture fails to accord
with the observed behaviors at the emission and subsequent absorption of
an entire 'quantum' of energy at microscopic molecular sites.

The great achievement of quantum theory is to provide a rationally
coherent procedure that uses the empirically validated wavelike
properties for computing the *evolution* of the probability function
from the time of an initial preparatory observation until the time of a
later informing observation, but that relates the sudden changes of the
probability function to the changes in our knowledge in the essentially
the same way that this is done in classical statistical mechanics.
Orthodox quantum mechanics achieves this rational coherence only by
strictly adhering to its epistemological and pragmatic orientation.

Heisenberg, in the chapter "The Copenhagen Interpretation" in his book
*Physics and Beyond* describes this epistemological situation and then
says:

> It should be emphasized, however, that the probability function does
> not in itself represent a course of events in the course of time. It
> represents a tendency for events and our knowledge of events. The
> probability function can be connected with reality only if one
> essential condition is fulfilled: if a new measurement is made to
> determine a certain property of the system. Only then does the
> probability function determine the probable result of the new
> measurement. The result of the measurement will again be stated in
> terms of classical physics. ... It is only in the third step that we
> change again over from the "possible" to the "actual." (Heisenberg,
> 1958, p.46)
>
> The observation, on the other hand, enforces the description in space
> and time but breaks the determined continuity of the probability
> function by changing our knowledge of the system. (p. 50)
>
> A real difficulty in the understanding of this interpretation arises,
> however, when one asks the famous question: But what happens "really"
> in an atomic event?
>
> (p. 50)
>
> ... the probability function does not allow a description of what
> happens between two observations. ... the term "happens" is restricted
> to the observation. (p.52)
>
> The probability function....contains statements about ...
> possibilities or better tendencies ("potentia" in Aristotelian
> philosophy), and these statements are completely objective... (p.53)

To speak about what is "really happening" one must depart from the
strictly orthodox position. This step involves speculation, because the
presently available empirical data do not distinguish between different
proposals that reduce to orthodox quantum theory at the
epistemic-pragmatic level. Nevertheless, it is reasonable to identify as
the "most orthodox" of the various approaches that try to address the
question of what is "really happening" as the one that follows
Heisenberg's suggestion, and replaces the notion of 'possibility' by the
Aristotelian notion of "potentia". According to this approach, the
quantum state *represents* 'our knowledge', just as the probability in
classical statistical mechanics does, yet it *acts not* like a
collection of classically understandable 'possibilities' but *rather*
*as a unified field of potentiality* that creates 'objective tendencies'
for the occurrence of future psychophysical events. Each such event is
associated, like a collapse event in classical statistical mechanics,
with an experiential increment in knowledge, and, simultaneously, with a
reduction of the mathematical/physical state to the part of itself that
is compatible with that increment in knowledge. The "collapse event" is
therefore a *psychophysical event.* And the connection of this state to
future events is specified by quantum rules that involve the *entire*
*quantum probability function evolving as a unit*. This evolving state
contains the physically describable mathematical underpinning of the
rules that yield predictions regarding the occurrences of future
psychophysical events. This underpinning is a necessary mathematically
described input to the procedure for making these predictions, but it is
not by itself logically sufficient to determine what we will experience,
or to determine even a probability for what we will experience. To
obtain such a probability the rules of contemporary quantum mechanics
require also an input from outside the physically described features of
nature.

In actual scientific practice this outside input comes from our streams
of consciousness. To learn anything about nature we must, according to
the theory, pose\-\--put to nature\-\-- some specific question. This
question must be one that can be answered by a 'Yes' or a 'No'.
(Multiple choice question can be reduced to a sequence of 'Yes-No'
questions that sequentially separate each 'No' into two parts.) Each
'Yes' answer is supposed to specify an experientially recognizable
possible response. *The content of the query is not specified by any
yet-known law or rule, statistical or otherwise, but the probabilities
of the two alternative possible answers is specified by the theory.*
Nature's choice of the answer 'Yes' corresponds to the appearance of the
recognizable 'Yes' response in the agent/observer's stream of
consciousness.

There are, in a certain sense, two kinds of probing questions. The first
kind specifies an experience that confirms that the agent himself is
acting in some intended classically describable way; the second
specifies an experience that confirms that some aspect of the external
world appears to have some classically describable form. But both are
fundamentally of the same kind: each is a query about a particular
possible aspect of one's own future experience.

The question that an agent asks places conditions upon the character of
the possible answers that nature can return. This capacity to chose, in
actual practice, the questions asked, and the times at which they are
asked, can, under certain conditions pertaining to the structure of the
agent's brain, give whatever it is that makes these choices, a
significant effect upon the course of the agent's bodily movements.

The fact that in quantum mechanics we human beings enter not merely as
passive observers but also as causal agents is emphasized in the closing
words of Bohr's book, which, in connection with the problems of
consciousness and life, assert:

> That a physicist touches upon such questions may perhaps be excused on
> the ground that the new situation in physics has so forcibly reminded
> us of the old truth that we are both onlookers and actors in the great
> drama of existence. (Bohr, 1934, p. 119)

Bohr repeats this many times in his writings, and Heisenberg's
penultimate sentences in his chapter "The Copenhagen Interpretation"
are:

> Our scientific work in physics consists in asking questions about
> nature in the language we possess and trying to get an answer from
> experiment by the means that are at our disposal. In this way quantum
> theory reminds us, as Bohr has put it, of the old wisdom that when
> searching for harmony in life one must never forget that we are
> ourselves both players and spectators. (Heisenberg, 1958, p. 58)

The logic and mathematical structures of the orthodox interpretation
were put into particularly clear form by the great logician and
mathematician John von Neumann. (1932/1955). The key active role of the
human being was formalized by von Neumann as "process 1". Prior to any
feedback from nature a specific question must be posed. The image in the
quantum mathematics of the action of posing the question is called
*process 1* by von Neumann.

The need to pose a specific question is alluded to by Heisenberg when he
says "if a new measurement is made to determine a certain property of
the system." (p. 46). The process of the creation of our streams of
conscious experiences proceeds like the game of "twenty questions": a
human being poses a question that has a Yes-or-No answer, and then
"nature" delivers an answer, 'Yes' or 'No'. Quantum mechanics specifies,
by some very simple but elegant mathematical rules, the probabilities of
the two alternative possible answers.

***The Key Mathematical Idea***

The key mathematical idea in quantum mechanics is simple enough to be
understood by anyone actually interested in how the world works.

In quantum mechanics the state, or probability function, of any physical
system is represented by a matrix, called the density matrix. It is a
square array of numbers. This array is like a cross word puzzle with the
number of rows equal to the number of columns, and with a number,
instead of a letter, in each little box. Such an array is called a
(square) matrix.

Mathematicians had been using matrices long before quantum theory was
created. One key property of matrices is this: if M and N are two
(finite-sized) square matrices then there is a well defined matrix that
is called the product MN. It is a square matrix with the same common
number of rows (hence also of columns) as both M and N. If M and N each
have just one row and one column, and hence both M and N have just one
entry, then MN is also a matrix with just one row and one column, and
hence just one entry, and this one entry is just the product of the one
entry in M with the one entry in N. For larger matrices the rule is
this: If for any matrix M the element in row i and column j is
\<i\|M\|j\> them \<i\|MN\|j\> is the sum over the full set of indices k
of \<i\|M\|k\>\<k\|N\|j\>. For the case in which the number of rows and
columns is three, the product of a set of matrices can represent the
effect of a sequence of rotations. More generally, products of matrices
can represent in mathematical terms the effects of a sequence of
physical transformations/actions of certain simple kinds.

There is an important single number associated with each square matrix.
It is called the "trace" of the matrix. It is simply the sum of the
so-called "diagonal" elements of M. These are the entries in the square
matrix that lie in the linear sequence of locations such that the number
of the row in which the entry lies is the same as the number of the
column in which that entry lies. The trace of a square matrix M is
denoted by Tr M. Although the rule for forming the product MN allows MN
to be different from NM, this rule nevertheless entails that Tr MN=Tr
NM. In quantum mechanics the basic predictions are in terms of
probabilities, which are expressed in terms of traces of matrices.

The key idea of quantum mechanics is that all information that we have
acquired about a system is represented by a square matrix M. The quantum
mechanical process of acquiring information about a system is, as
already mentioned, like the game of twenty questions. Before nature
delivers any information about any system, a specific question must be
posed. This question must be one that can be answered by either a 'Yes'
or a 'No' response. If the quantum probability function of the system
being probed is represented by a square matrix M with n rows (and hence
n columns) then the question will be represented in the mathematics by a
square matrix P with n rows and n columns. Each such P must be a
"projection operator", which is a matrix P that satisfies PP=P: the
product of the matrix P with itself is again P itself. This operator P
represents *within the quantum mathematics* the answer 'Yes" to the
query. The answer 'No' is represented by P^̍^̍ = (I-P), where I is the
unit operator that satisfies for every square matrix N the conditions
IN=NI= N. Hence P^̍^̍ is also a projection operator: P^̍^̍ P^̍^̍ = P^̍^̍
. The fact that empirical questions with just two possible answers are
represented in the mathematics by a (projection) operator that satisfies
PP=P, is closely connected to the fact that there are only two numbers X
that satisfy XX=X: they are one and zero, corresponding to 'Yes' and
'No'. The matrix P is the *image* in the quantum mathematics of an event
that might occur, or that has occurred, in the agent/observer's streams
of consciousness

The process 1 action of *posing* the question is represented in the
mathematics by the simple formula

M(before)M(after) = PM(before)P + P^̍^̍ M(before) P^̍^̍.

The arrow represents the change in the mathematical description of the
state of a system that accompanies asking the question "Will my
experience be the one in which the experiencing of 'Yes' is represented
in the mathematics by the projection operator P?

This process 1 corresponds merely to the human action of posing the
question. Nature then delivers either the increment in knowledge 'Yes',
in which case the density matrix of the system being probed becomes PMP,
or nature chooses *not* to deliver the answer 'Yes', in which case the
density matrix of the system being probed becomes P^̍^̍ M P^̍^̍ . The
predicted probability of experiencing 'Yes' is Tr PMP /Tr M̍ .

These simple rules specify a tight relationship between the abstract
mathematical formulas of quantum mechanics and our human experiences.
This connection is no longer trivial, and causally inert, as it was in
classical mechanics. The human being becomes, by virtue of these
relatively simple rules, not merely a spectator, but also an actor, in
the great drama of existence.

A key point here is that there is in the quantum formalism nothing in
the physical/mathematically described part that determines what the
operator P will be! Our choices *seem to us* to arise from the mental
realm of our thoughts and mental intentions. Bohr quotes Heisenberg's
idea "that we have to do with a choice on the part of the observer
constructing the measuring instruments and reading their recording."
(Bohr, 1958, p.51) Bohr says:

> 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)

This latitude corresponds to the fact that the mathematical formulas do
not determine what the process 1 choice of P will be.

***The Transition from Potentiality to Actuality***

The mystery of quantum mechanics centers on the two kinds of collapse
events. The first kind of collapse event consists of the "process 1"
action described above. "Process 2" is the name given by von Neumann to
the continuous (non-collapse) deterministic evolution between collapse
events. It is governed by the Schroedinger equation. The response to a
given query is again a collapse process. It called by Dirac "a choice on
the part of nature." In keeping with von Neumann's nomenclature I call
the process of choosing and delivering the *response* by the name
"process 3." Thus we have three different processes: Process 1, the
image in the quantum mathematics of the observer/agent's action of
posing a question; Process 2, the continuous (non-collapse)
deterministic evolution, within the mathematical description, between
collapses; and Process 3, the process of generating and delivering to us
some definite response to each well posed question.

If one seeks to go beyond the strictly epistemic/pragmatic (Copenhagen)
stance then the question arises as to exactly where, physically, do the
violations of the physically deterministic process 2 occur. The process
1 aspect *seems* to originate as an effect of one's mind upon the state
of one's brain, which then produces in turn a bodily action. On the
other hand, the response of a measuring device, such as a cloud chamber
or a Geiger counter, *seems* to occur at the macroscopic device.

In connection with this issue of where the division between the
subjectively described "self" and the physically described objectively
conceived world lies Bohr writes:

> One need only remember here the sensation, often cited by
> psychologists, which everyone has experienced when attempting to
> orient himself in a dark room by feeling with a stick. When the stick
> is held loosely, it appears to the sense of touch to be an object.
> When, however, it is held firmly, we lose the sensation that it is a
> foreign body, and the impression of touch becomes immediately
> localized at the point where the stick is touching the body under
> investigation. (Bohr, 1934, p. 99)

This illustration clarifies a point made repeatedly in Bohr's writings
that "even words like 'to be' and 'to know' lose their unambiguous
meaning." (Bohr. 1934, p. 19)

This issue of where to draw the line between oneself, which is described
in terms of one's personally experienced but communicable knowledge, and
the abstract quantum theoretical model of an objectively existing
"reality" is analyzed by von Neumann (1932/1955), in his chapter VI on
the measuring process. Von Neumann considers first a system consisting
of a system I, which is the system being probed, for example one single
electron ; a system II, which is the measuring device, say a bubble
chamber; and a system III, which consists of experiences. System I is
described in the mathematical language of quantum mechanics\-\--in terms
of matrices. Part III is described in the way that we describe to
ourselves, and to others, our experiences. Part II, the measuring
device, such as the bubble chamber\-\--or the cane\-\--can be regarded
either as part of the physically described world or as part of the
psychologically described world. If the device is regarded as part of
the psychologically described world then the "collapse" would appear to
occur at the interface between systems I and II, because system I,
evolving via process 2, would develop "branches" that are, from a
classical point of view, a set of incompatible alternatives\-\--for
example, alternative possible trajectories of the one single electron
through the chamber\-\--but the classically described (experiences of
bubbles in the) bubble chamber would have only one track. On the other
hand, if the device (bubble chamber) of regarded as part of the
physically described world, which in conjunction with the single
electron is evolving in accordance with the Schroedinger equation of the
combined electron/bubble-chamber system, then the physics representation
of that combined system would have components corresponding to the many
alternative possible tracks in the cloud chamber. But the experience
would, none-the-less, be described as the appearance of a single track
of bubbles. Thus the collapse would now appear to be associated with the
interaction between system I+II and system III. So the location of the
cut at which the "collapse" occurs depends upon how we describe the
system II. That might be alright in a strictly pragmatic framework.

Von Neumann goes on to consider a sequence of devices, each of which
probes the state of the preceding system. The final "measuring device"
is the part of the brain whose activities correspond most directly to
our experiences. The sequence of placements of the boundary is such that
in each new placement one more device is moved into the
mathematically/physically described part of the world, until at last,
the physically described part includes the entire physical world,
including all of the brains of all of the observer/agents. But the
process 1 action still is needed to make the quantum mechanical
computational procedure work! And process 1 constitutes a specific
physically described action that is not determined in any known way by
the physically described aspects of nature. Von Neumann calls the part
III at this final stage by the name "abstract ego" (p. 421)

The upshot of this analysis is that at some point in the sequence of
placements of the boundary the measured parts of the device will become
large enough so that the environmental decoherence effects will become
large enough so that it will be, *for all practical purposes*,
impossible to determine empirically whether the collapse occurs at this
level or at some higher level. If the collapse occurs at that stage or
higher then *for* *all practical purposes* one can assume that the
collapse occurs at the level of the interaction between the brain and
the "abstract ego".

At the present time, in the history of science, no robust
repeatable-on-demand experiment has provided any evidence that any
collapse has actually occurred at any level below the level of the
mind-brain interaction. In any case, there is certainly, in contemporary
physics, a very natural place for the entry of mind-like or idea-like
aspects of nature that act upon the physically described world, but are
not causally or conceptually reducible to the quantum mechanical
physically described part: the idea that the mindless, mechanical
aspects of nature are causally complete is certainly not entailed by
contemporary science,

either empirically or theoretically.

If one considers a typical experiment in which an experimenter sets up
an experiment and then observers its outcome, then one realizes that
there are really two separate series of pairs of collapse events, with
each pair consisting of a process 1 choice of a query, attributable to
the local agent, and an immediate process 3 response attributed to
nature. The first series of double events corresponds to the agent's
controlled sequence of actions that lead to the setting up of the
experiment. The agent by means of a controlled rapid sequence of
intentional actions with feedbacks guides the manipulations that produce
the setting up of the experiment. Later on, there will be a rapid
sequence of pairs that correspond to the observer's action of witnessing
the outcome. Each such witnessing action involves, according to this
theory, first a process 1 choice of exactly what aspect of, say, the
visual scene is to be probed, followed by an answer to that specific
query. Thus both the setting up of the experiment and the observing of
the outcome are achieved by means of rapid sequences of process 1
queries followed by process 3 response, with the entries in each
sequence connected by a common thread of attention and intention.

This theory is intrinsically dualistic: the theory involves in causally
interwoven ways, aspects that are described in the language that we use
to express to ourselves and to communicate to others our everyday
experiences, and also aspects that are expressed in terms of the
abstract mathematical concepts of quantum mechanics. The central
realities are psychophysical collapse events, which link the quantum
mathematics to our ordinary experiences in specified causal ways. These
causal links tie the quantum mathematics to our stream's of
consciousness in ways that allow empirical connections to be computed.
These links prevent the sort of causal disjunction of the two Cartesian
realms that Newtonian physics allowed, that classical physics
perpetuated, and that has been the bane of philosophy for more than
three hundred years.

***How Did It All Begin?***

In 1972 I wrote an article entitled "The Copenhagen Interpretation",
which was published in the American Journal of Physics, and was widely
reprinted elsewhere. I had been working with Heisenberg, and sent him a
pre-publication version, and asked him to comment upon it. He said,
among other things:

> There is one problem which I would like to mention, not in order to
> criticize the wording in your paper, but for inducing you to more
> investigation of this special point, which is however a very deep and
> old philosophical problem. When you speak about the ideas (especially
> in \[Section 3.4\]), you always speak about human ideas, and the
> question arises, do these ideas "exist" outside of the human mind or
> only in the human mind? In other words: Have these ideas existed at a
> time when no human mind existed in the world. (Heisenberg, 1972)

To the extent that I was trying, as I was *there*, to describe merely
the purely epistemic and pragmatic Copenhagen interpretation, which
deals only with the conceptual and mathematical structure of the theory,
and how we human beings use the pragmatic theory, I do not have to say
what happened before human beings existed. But insofar as I am striving
to present an ontological extension of quantum theory, as I am *here*, I
should address Heisenberg's question.

The problem was evidently troubling to Heisenberg himself who, as we
have seen, did try to understand what is really happening. One partial
solution is to extend mind-like quantities to all life, but that merely
pushes the problem back the question of whether "ideas" existed before
life.

This brings us to one of the great conundrums of our time, the
anthropic-principle question: why are the laws of nature so finely tuned
as to permit life. Of course, if they were not sufficiently well tuned
to permit life then we would not be here to ponder the question.

A currently popular idea is that according to string-theory estimates
there are ten to the power 500 different possible solutions to the
string-theory constraints, and this huge set of possibilities might be
expected to include at least one with the right fine tuning. Thus, if
every solution to the string theory conditions does "exist
somewhere-sometime" then the solution of the anthropic-principle
question is simply that we live in one of the probably relatively
extremely rare universes that has the fine-tuning required for the life
that we are part of.

Wheeler had a similar pre-string-theory version, connected to his idea
of "delayed choice" experiments. If some primordial universe had a
continuum of possible couplings (laws of nature) then, in some tiny part
of this primordial world, life with rudimentary brains would be
possible. That part could have an associated mind-brain connection. So
quantum theory could generate queries. A process 1 action could occur,
and a 'Yes' response on the part of nature would bring a world with
brains into existence.

It seems that both of these solutions require a pre-existing mental
realm to exist, lying in wait for a suitable physical world with a brain
to come into being. This is because, just as in classical physics, the
physically described properties alone do not seem to demand the
existence of a mental realm: the physically described part could just be
grinding out "physically described potentialities" forever, with no
connection to anything mental. Of course, if "potentiality" means,
intrinsically, potentiality for a psychophysical event to occur, then
the dualistic character, which includes mental aspects, is built in
basically from the start.

If one tries to understand how such a structure could be created in the
first place, one seems to be pushed back to a primordial mental reality,
for it is difficult to understand how a purely physical/mechanical
structure could create its own laws. In the bible-based culture in which
classical physics was born it was natural to assign to a non-physical
God the role of creator and law-giver for the physically described
universe. But even if we discount the god's of various religions, it
seems difficult to imagine how idea-like realities could emerge from a
world completely devoid of any such aspects, and how physical laws could
come to be fixed by a purely physical mindless universe.

Here, I shall not endeavor to say how the psychophysical world came into
being, but shall focus on how to understand in a rationally coherent way
the nature of a reality that can produce the relationships between our
experiences that are so successfully predicted by contemporary orthodox
dual-aspect pragmatic quantum mechanics. I shall pursue the approach of
Heisenberg, according to which the physical/mathematical probability
functions of orthodox quantum mechanics describe potentialities
(Aristotelian potentia) for actual events, which are quantum collapses
that constitute objectively real transitions of potentialities into
actualities.

***Process 1 and Mental Causation***

The major gap in the causal structure of orthodox quantum mechanics is
process 1. There is a causal gap also in the process-3 choice of the
answer to the query associated with process 1, but for process 3 there
is at least a statistical condition, whereas for process 1 there is,
within contemporary orthodox theory, no indication at all of what it is
that picks the particular query out from the continuum of possibilities
that are in principle available. A clue to the origin of the process 1
query is provided by the fact that it seems to us that our choices of
our actions are at least in part determined by *reasons*, which belong
to the mental realm of idea-like qualities. But reasons are normally
associated with earlier experiences, which leave traces in our brains.
Hence brains, which can be affected by alcohol and drugs, are evidently
influencing, at least indirectly, the creation of the process-1-related
queries, and hence the character of the process 3 responses. So we are
led to the idea that each process 1 query has causal inputs from both
the realm of mind, and also from the realm of the physically described
universe. Each process 1 "collapse" is an actual happening that is
generated by a process with both mental and physical *inputs*, and both
mental and physical *outputs*. The mental output is a new experience,
and the physical output is a process 1 action that converts an M(before)
to an M(after), as described above. The M represents potentialities for
later psychophysical events, and these potentialities are changed by the
current actual psychophysical event.

To make things more specific, consider a simple model. Let M be the
density matrix corresponding to some person's brain. Let B={P} be the
set of projection operators available to that person (to that person's
brain) at this time. Let P~max~ be the P in B that maximizes Tr MP/TrM.
Let P~max~ be the only P that can be chosen at this time. But suppose
the choice of whether or not, or when, to pose this question can be
influenced by mental factors. Since the collapses are quantum effects,
this means that effects of our minds could enter the physical world
through the causal gap present in quantum theory.

In order to limit the influence of our streams of consciousness in a way
that permits them to have the causal effects that they appear to have,
while not injecting uncontrolled chaos into the causal structure, it is
useful make the stipulation that the only effect of consciousness is via
conscious intent, and that the only effect of conscious intent is to
cause, as a psychological reaction to the received answer to a query
just posed, a quick re-posing of essentially that earlier query, with
the time delay of the re-posing inversely correlated to the intensity of
the conscious intent: the stronger the conscious intent the sooner the
re-posing happens. It turns out that this very limited intrusion of
conscious intent into the causal structure allows our intentions to
influence our actions in intended ways. The mechanism for this
connection is the quantum Zeno effect.

***The Quantum Zeno Effect***

The quantum Zeno effect is not some incomprehensible mystery. It follows
easily from the simple formulas already given, plus the simple formula
for the Process 2 continuous evolution between collapses. This process 2
evolution is given by the formula

M(T+t)= (exp --iHt) M(T) (exp +iHt)

The operator/matrix (exp--iHt) equals (I --iHt + ...), where the dots
represent terms of order t squared or higher. Thus the rules described
earlier assert that if the M(T) is the result of receiving a 'Yes'
response to the query represented by the projection operator P,

so that M(T)=PM(T-)P, where M(T-) is the density matrix of the system
being probed just before the 'Yes' response is received, then the
probability of getting the 'Yes' response if the same question P is
posed a short time t later is, up to and including terms linear in t,

Tr P (I --iHt)P M(T-) P (I+iHt) P/Tr (exp --iHt)P M( T-) P(exp +iHt)

= 1+ terms of order t squared

The fact that this probability is equal to unity up to terms quadratic
in t follows immediately from the already mentioned facts that (1), PP=P
; (2), for any N and M,

Tr NM= TrMN; and the fact that (3), (exp +iHt)(exp-iHt)= 1.

If one separates any unit interval in time into n intervals of length
t=1/n, then as n increases the sum of the n contributions of order 1/n
*squared* will drop out, leaving the state frozen at the value
M(T)=PM(T-)P. This is the quantum Zeno effect, so-named because of its
loose connection to Zeno's paradoxical arrow in flight, which, according
to the (flawed) argument of Zeno, can never get anywhere because at each
instant it fits exactly into the place where it is. Yet, according to
the rules of orthodox quantum theory, a rapid repetition of the process
1 probing action will tend to slow down the process 2 evolution of the
system that is being observer. Quantum theory gives new truth to the old
adage: "A watched pot never boils."

**The Effect Of The Mind Upon The Brain**

But how does the quantum Zeno effect, which has to do merely with the
rate at which we human beings pose certain questions, which nature
promptly answers in accordance with her fixed (unbiased) statistical
rules, allow our thoughts to influence our brains, and hence our
actions.

Any intentional action must, in order to be successfully executed,
involve a carefully orchestrated sequence of neural firings. Such an
orchestrated sequence must be controlled by some executive pattern of
actual ongoing neurological activity in the brain. I call such an
executive pattern of brain activity a *template for action*.

A carefully psychologically controlled intentional activity involves a
rapid sequences of acts of attentional awareness. One is aware of
repeated instances of both a sustained feeling of an intent to make the
planned sequence happen, and of a checking of the feedback to find out
whether the action is going as anticipated. Successful trial and error
learning in the past have strengthened neural connections, and their
connections to physically efficacious feelings of intent, in such a way
as to allow the process 1 collapses in the brain that are the brain
correlates of the experienced intention to keep the appropriate template
for action in place.

The effect of the quantum uncertainty principle is to inject a certain
amount of random noise into the proceedings. We no longer have the
boring old clockwork universe: new unexpected and unplanned things can
occur. "Advances" might even occur now and then, where "advance" could
be defined as a change that can perpetuate itself, and lead to a
different sort of "society".

However, *we* are not completely at the mercy of this random noise.
Merely by our capacity to control the rate at which we ask the question
generated by the brain, we have the ability to hold in place a template
for action that is causing to happen something that we want to happen.

***Combining Systems***

Quantum mechanics has very simple rules for combining several (or many)
systems into one bigger system that has the original systems as its
component sub-systems. Many crucial features of quantum mechanics depend
on these rules.

Suppose we have three logically independent systems, such that
\<j\|J\|j'\> are the elements of the density matrix of the first system,
considered as a logically independent system, \<k\|K\|k'\> are the
elements of the density matrix of the second system, considered as a
logically independent system, and \<l\|L\|l'\> are the elements of the
density matrix of the third system. Then the combined system is
represented as

\<j, k,l\|JKL\|j',k', l'\> = \<j\|J\|j'\>\<k\|K\|k'\>\<l\|L\|l'\>

Thus if each subsystem has, for example, ten rows, numbered from zero to
nine, and ten similarly numbered columns, then the rows of the density
matrix JKL can be numbered by the one thousand numbers that begin at 000
and end at 999. But the general form of the density matrix M for the
combined system need not have this simple product form. It could, for
example. be a sum of different terms of this product form.

A key property of the density matrix for a system that consists of a
combination of subsystems is this: Any prediction pertaining to this
combined system that is conditioned only by information does not refer
to one of the subsystems is obtained from a "reduced" density matrix
that is obtained from the full density matrix by performing a "partial
trace". This partial trace is formed by setting the two indices that
pertain to the excluded subsystem equal to each other, and then summing
over all possible values of this equated index. For example, if the
prediction makes no use of conditions on the subsystem associate with
the indices l and l' in the above example then the predictions depend
only upon the reduced density matrix

\<j,k\| M~red~ \|j',k'\> = Sum over l of \<j.k, l\| M \|j',k', l\>

Lack of conditions pertaining to any subsystem is represented by taking
a trace over the indices associated with that subsystem. This gives a
reduced density matrix whose indices are connected to the subsystems
associated with the pertinent conditions.

This structure has important immediate consequences in connection with
non-locality

(faster-than-light) properties. There are correlation experiments in
which two particles interact with each other and then travel to two
different experimental space-time regions that are so far apart that
nothing can travel from either region to the other without moving either
faster than light or backward in time. Relativistic quantum field theory
entails, accordingly, in this situation, that no process 1 action *done*
to a system in the faraway region can influence any prediction
pertaining to observations made in the nearby region. This follows from
the fact that if we know that a certain specified experiment was
performed in a faraway region, but do not know what the outcome there
was, then the probability pertaining to a specified local outcome is
specified by taking the trace over the variables of the faraway region.
But, because the process 1 action leaves the trace unaffected, this that
means that the local predictions are the same as they would be if one
had no knowledge about the faraway system: performing or not the faraway
process 1 makes no difference to the local predictions.

However, a process 3 action in the faraway region does changes the trace
over the indices associated with the faraway subsystem. Hence the
predictions about what appears in the nearby region will depend in
general upon the process 3 action occurring in the far away region.

This latter dependence is not at all surprising. The correlation
established during the interaction between the two particles can
absolutely be expected to entail that the outcomes that appear in the
two regions should be correlated. However, if one treats the process 1
binary choices between alternative possible measurements made by the two
experimenters *as two independent free variables*, and requires that
nature be able to deliver a result compatible with the predictions of
quantum theory for each of the four alternative possible combinations of
choices that might be made by the experimenters, then it can be proved
that nature's process of selecting outcomes must be a non-local process
in the sense that at least one of nature's replies in at least one of
the two regions must depend upon the experimenter's free choice made in
the other region, which is space-like separated from the first. (Stapp,
2007, Appendix G). This non-locality result constitutes a major
condition on any proposed understanding of what is actually happening.

***Relativistic Quantum Field Theory***

Classical non-relativistic physics was built on the idea that space and
time were independent variables that specified a background space-time
structure in which, physical properties could be placed.
Non-relativistic quantum theory carried this idea forward by adopting
the notion that the quantum collapses occur at a discrete sequence of
"instants", each specified by a particular value of time, but extended
over all of space.

Tomonaga (1946) and Schwinger (1951) showed how to generalize this
picture of the evolving universe into one that is more in line with the
precepts of Einstein's (special) theory of relativity. In their
formulation, the constant-time "instants", which are flat surfaces in
space-time, are replaced by "spacelike surfaces". These surfaces are
continuous three-dimensional surfaces in four-dimensional space-time
such that every point on the surface is spacelike separated from every
other point. The advancing succession of flat "instants" of the
non-relativistic theory, upon which the collapses occur, are replaced by
an advancing sequence of spacelike surfaces, where "advancing" means
that every point on one spacelike surface either coincides with a point
on the preceding surface or lies both outside the backward light-cone of
every point on that preceding surface but inside the open forward
light-cone of some of the points on that preceding surface: the
succession of space-like surfaces upon which the collapses occur advance
*locally* into the future.

The rules of relativistic quantum field theory entail that if a
spacelike surface σ has two alternative possible
spacelike-surface-successors σ~A~ and σ~B~, that differ from σ by two
distinct non-overlapping advances, each with an associated process 3
collapse, then the probability for the pair of advances to occur/appear
does no depend upon whether the advance to σ~A~ or to σ~B~ occurs first,
or whether the two advances are treated as parts of a single advance.
The two spacelike separated advances act essentially independently. It
is these features that make the theory "relativistic": the order of
"occurrence" of two spacelike separated collapse events makes no
empirical difference.

Although a "Gods-eye" or global conception of what is "really happening"
seems to require a definite idea of the order in which the different
spacelike separated events *occur*, there is no empirical meaning to the
order in such event *appear* to the local witnesses. Each witness can
establish by direct observations and memories only the ordering of
(certain) events in his backward light-cone, and the theory does not
help out, because it makes all empirical prediction independent of the
relative ordering of occurrence of spacelike separated events. This
means that we are free to imagine that nature actually evolves by means
of collapses that occur in some particular order. But the significance
of such an ordering is obscured by its lack of empirical consequences.

***Comments***

The editor has asked me to comment on the articles by Bagci and by
Epperson in this issue. I have no comment of Epperson's paper.

Professor Bagci's article criticizes Epperson's arguments "that
Whiteheadian process is most compatible with the decoherence
interpretation of quantum mechanics" by arguing that the
Ghirardi-Rimini-Weber (GRW) interpretation fits just as well. I agree
with Bagci. Indeed, I would say that the GRW interpretation fits far
better, because it specifically involves "collapses", and, indeed,
specifies the process that produces the collapses, whereas the
decoherence mechanism merely eliminates certain interference terms that
connect certain kinds of observable outcomes, without specifying how one
particular "fact" becomes actualized: i.e., without specifying how
actuality emerges from potentiality. The central endeavor of Whitehead
is to try to explain how actuality emerges from potentiality.

But even the GRW interpretation does not fit Whiteheadian process
philosophy very well. In GRW, the process that fixes what actually
happens is a *random* mechanical process. Whiteheadian process has a
mental pole, and Whitehead's wording certainly was chosen to suggest
that the process of concrescence could encompass happenings such as a
happening whose mental pole was like an event in a stream of conscious
experiences. Mental aspects are, I believe, a quality of each
Whiteheadian concrescence, or, in any case, of at least some
concrescences. The GRW process is devoid of mentality, and hence is not
Whiteheadian.

It is the orthodox interpretation of quantum mechanics, more than any of
its rivals, that incorporates mental aspects into the process of the
creation of reality. Indeed, the aim of all of the attempted
"improvements" upon the orthodox interpretation has been to get the
mental aspects out of the dynamics. That objective appears to be an
anti-scientific philosophical legacy inherited from the two hundred year
reign of classical mechanics.

*Works Cited*

Bohr, Neils. *Atomic Theory and the Description of Nature*. Cambridge:
Cambridge University Press, 1934.

\-\-\-\-\-\--. *Atomic Physics and Human Knowledge*. New York: Wiley,
1958.

Heisenberg, Werner. *Physics and Beyond*. New York: Harper and Rowe.
1958.

\-\-\-\-\-\-\--. quoted in "The Copenhagen Interpretation", Stapp 1972.

Stapp, Henry P. *Amer. J. Phys*. 40, 1098-1116. 1972 .Reprinted in Stapp
1993/2004.

\-\-\-\-\-\-\--. *Mind, Matter, and Quantum Mechanics*. Berlin,
Heidelberg,

New York: Springer, Appendix B. 1993/2004.

\-\-\-\-\-\-\--. *Mindful Universe: Quantum Mechanics and the
Participating*

*Observer.* Berlin, Heidelberg, New York: Springer, 2007.