**Whiteheadian Quantum Ontology**

Henry P. Stapp

Lawrence Berkeley National Laboratory

University of California

Berkeley, CA 94720

**Introduction**

Upon completing my article "The Copenhagen Interpretation" (Stapp,
1972), which stressed the pragmatic character of that interpretation, I
sent the manuscript to Heisenberg for his approval or reaction. He
expressed general approval, but raised one point:

> There is one problem I would like to mention, not in order to
> criticize the wording of your paper, but for inducing you to more
> investigation of this special point, which however is a very deep and
> old philosophical problem. When you speak about the ideas (especially
> in \[section 3.4\]) you always speak of 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 the time
> when no human mind existed in the world?

He continued:

> I am enclosing the English translation of a passage in one of my
> lectures in which I have tried to describe the philosophy of Plato
> with regard to this point. The English translation was done by an
> American philosopher who, as I think, uses the philosophical
> nomenclature correctly. Perhaps we could connect this Platonic idea
> with pragmatism by saying: It is "convenient" to consider the ideas as
> existing outside the human mind because otherwise it would be
> difficult to speak about the world before human minds have existed.

These remarks highlight the fact that standard quantum philosophy
adheres to the Copenhagen pragmatic stance of erecting science upon
human knowledge. Yet science encompasses cosmology, and also our
attempts to understand the evolutionary process that created our
species. If we want to address the basic question of the nature of human
beings then we need more than merely a framework of practical rules that
work for us. We need to be able to see the pragmatic anthropocentric
theory as a useful distillation of an underlying non-anthropocentric
ontological structure that places the evolution of our conscious species
within the broader context of the structure of nature herself. We need a
fundamentally non-anthropocentric ontology within which the
anthropocentric pragmatic theory is naturally imbedded.

That is a big order! Fortunately, however, there already exists an
ontology that provides a good starting point. It is the ontology
proposed by Alfred North Whitehead. I shall describe here the fusion, as
I conceive it, of relativistic quantum field theory with what I take to
be the key ideas of Whitehead.

\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\--

*"Nature and Nature's Laws lay hid at night*

*God said 'Let Newton be!' and all was light"* Alexander Pope

*"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."* Niels Bohr

These two quotations highlight the question: What is the proper task of
science? Is it to describe Nature herself, and her laws, as Alexander
Pope proclaimed was already achieved by Isaac Newton? Or should the goal
of science be curtailed in the way recommended by Niels Bohr?

Bohr (1958, p. 71) asserted that

> ...the formalism does not allow pictorial representation along
> accustomed lines, but aims directly at establishing relations between
> observations obtained under well-defined conditions."

However, the impossibility of representing reality along accustomed
lines does not automatically preclude every kind of rational
conceptualization. Perhaps an uncustomary idea will work. Even Newton's
mechanical conception was not customary when he proposed it. Hence if
advances in science reveal the incompatibility of the empirical evidence
with customary pictorial representations then perhaps the construction
of a new vision of reality is needed, instead of meek resignation to the
construction of mere practically useful rules. Of course, direct
empirical validation may become elusive insofar as the needed
conceptions carry us beyond the realm of human experience. Hence
increased reliance upon rational coherency will presumably be required.

To operate most effectively in the physical world one needs an adequate
conception\-\--compatible with science\-\--of oneself operating within
that world and upon it. Optimal functioning is impaired if you are armed
only with blind computational rules, severed from a rationally coherent
conception of yourself applying those rules.

There is, of course, no guarantee that our species can come up with an
adequate conceptualization of our mindful selves acting in and upon the
world. And even if such a conceptualization were uncovered, there is no
assurance that it is unique. However, neither the fear of failure nor
the specter of non-uniqueness constitutes a sufficient reason to refrain
from at least trying to find some rationally coherent way of
understanding our conscious selves imbedded in the reality that
surrounds and sustains us.

Due undoubtedly, at least in part, to the impact of Bohr' advice, most
quantum physicists have been reluctant even to try to construct an
ontology\-\--a conception of what really exists\-\--compatible with the
validity of the massively validated pragmatic quantum rules pertaining
to the structure of human experience. However, due to this reticence on
the part of quantum physicists we are faced today with the spectacle of
our society being built increasingly upon a conception of reality
erected upon a mechanical conception of nature now known to be
fundamentally false. Specifically, the quintessential role of our
conscious choices in contemporary physical theory and practice is being
systematically ignored and even denied. Influential philosophers,
pretending to speak for science, claim, on the basis of a grotesquely
inadequate old scientific theory, that the (empirically manifest)
influence of our conscious efforts upon our bodily actions, which
constitutes both the rational and the intuitive basis of our functioning
in this world, is an illusion. As a consequence of this widely
disseminated misinformation the "well informed" officials,
administrators, legislators, judges, educators, and medical
professionals who guide the development of our society are encouraged to
shape our lives in ways predicated on known-to-be-false premises about
"nature and nature's laws".

Bohr's pragmatic quantum philosophy emphasizes the active role that we
human beings play in the development of our scientific knowledge. But
pursuing this approach can easily lead to an overly anthropocentric
conception of reality.

A rational escape from this parochialism is provided by work of the
eminent philosopher, physicist, and logician Alfred North Whitehead. He
created a conception of natural process that captures the essential
innovations wrought by quantum theory in a way that allows the human
involvement specified by quantum theory to be understood within a
fundamentally non-anthropocentric conception of nature as a whole.

Whitehead struggled to reconcile the findings of early twentieth century
physics with the insights and arguments of the giants of Western
philosophy, including, most prominently, Plato, Aristotle, Descartes,
Leibniz, Locke, Hume, Kant, and William James. But although Whitehead
had the hints about "abrupt quantum jumps" and "objective tendencies for
these jumps to occur" that came from early quantum theory, and was
familiar with Einstein's special and general theories of relativity, he
was not acquainted with the important and sophisticated developments in
relativistic quantum field theory represented by the mid-century works
of Tomonaga (1946) and Schwinger (1962).

I shall describe here a conception of reality that stems primarily from
the ontological ideas of Werner Heisenberg, the principal founder of
quantum theory, expressed within an ontological construal of von
Neumann's formulation, as revised by Tomonaga and Schwinger, to bring it
into accord with the physical requirements of the theory of relativity.
This relativistic quantum ontology is in close accord with many key
ideas used by Whitehead, and emphasizing these connections will flesh
out this rational ontological construal of relativistic quantum field
theory.

It will, therefore, both clarify this quantum ontology and bring it into
a certain correspondence with the Whiteheadian framework to begin by
quoting Whitehead's clear enunciations of those key ideas. On the other
hand, I make no claim to encompass every pronouncement of Whitehead, who
wrote long before the work of Tomonaga and Schwinger. Indeed, I shall
always take the quantum theoretical findings as preeminent, and use only
those assertions of Whitehead that mesh nicely with, and flesh out, the
ontological construal of the quantum formalism that springs naturally
from the formulation of John von Neumann, as brought into accord with
the precepts of the special theory of relativity by the works of
Tomonaga and of Schwinger.

The core issue for both Whiteheadian Process and Quantum Process is the
emergence of the discrete from the continuous. This problem is
illustrated by the decay of a radioactive isotope located at the center
of a spherical array of a finite set of detectors, arranged so that they
cover the entire spherical surface. The quantum state of the positron
emitted from the radioactive decay will be a continuous spherical wave,
which will spread out continuously from the center and eventually reach
the spherical array of detectors. But only one of these detectors will
fire. The total space of possibilities (the entire sphere) has been
partitioned into a discrete set of subsets (defined by the part of the
sphere covered by the various individual detectors) and the prior
continuum of potentialities is suddenly reduced to some one particular
part of the whole specified by the prescribed partition.

But what fixes, or determines, this particular partitioning of the
continuous whole into these particular discrete parts?

The orthodox answer is that "the experimenter decides".

Yet if the experimenter himself is made wholly out of physical particles
and fields then his quantum representation by a wave function must also
be a continuous function. But how can a smeared out continuum of
classically conceivable possibilities be partitioned into a set of
discrete components by an agent who is himself a continuous smear of
possibilities. How can the definite fixed boundaries between the
discrete elements of the partition emerge rapidly from a continuous
quantum smear?

None of the founders of quantum theory could figure out how this could
happen in a way compatible with the successful rules of quantum
mechanics, nor has anyone since. Von Neumann, in his rigorous
formulation of the mathematics of quantum theory, calls this
partitioning action an "intervention": it is an intervention into the
continuous deterministic Schroedinger-equation-controlled evolution of
the physically described aspects of the universe.

This "discreteness" problem is resolved in orthodox quantum theory*,
and* *in actual scientific practice*, by what Heisenberg and Bohr call
"a choice on the part of the experimenter". Von Neumann calls by the
name "process 1" the manifestation in the physical world of this choice.
I shall call by the name "process zero", the process that
*selects/chooses* the particular partitioning of the physically
described world specified by von Neumann's process 1.

What seems clear is that this partitioning cannot arise from the
physically described aspects of the world acting alone: continuous
smears acting in accord with the smoothing Schroedinger equation cannot
create a discrete partitioning in a finite time. However, the
experimenter feels that his consciousness is playing a role. So if the
physically described aspects alone cannot do the job, and it feels like
our conscious efforts are helping, then why not try that idea out?
Consciousness is, after all, the only other thing initially in our
ontological arsenal.

But how can we understand, coherently and rationally, how consciousness
can act on the physically described world?

The plan of Part I of the presentation is this:

1\. Specify by using Whitehead's own words what I take to be his key
ideas.

2\. Put them coherently together to form the space-time aspects of
Whiteheadian process.

3\. Describe the basic structure of ontologically conceived
Tomonaga-Schwinger relativistic quantum field theory.

4\. Put these elements coherently together to form the space-time
picture of quantum process.

5\. Note the identity of these two space-time pictures.

6\. Note some further identities, and propose a unified
non-anthropocentric Whiteheadian Quantum Ontology, based on these
connections, and on Whitehead's notion of "feelings".

This ontology is still not completely specified. But it is far more
structured than a general pan-psychism. It specifies distinctive
conditions pertaining to space, time, causation, the notion of the
"now", the physically and psychologically described aspects of nature,
and the nature of conscious agents. The empirically validated
anthropocentric concepts of contemporary orthodox pragmatic quantum
theory become thereby imbedded in a general non-anthropocentric theory
of reality.

**Part I: A Non-Anthropocentric Whiteheadian Quantum Ontology**

[1. Some Key Elements of Whitehead's Process Ontology]{.underline}

I shall now state what I take to be Whitehead's key principles,
expressed in Whitehead's own words, taken from his book "Process and
Reality"

Whitehead's first principle is that the world is built out of actual
entities/occasions.

" *'Actual entities'\-\--also termed 'actual occasions', are the final
real things of which the world is made*." (PR, p.18)

"*The final facts are, all alike, actual entities, and these actual
entities are drops of experience, complex and interdependent*." (PR,
p.18)

Whitehead accepts James's claim about the droplike (atomic/indivisible)
character of experience.

"*Either your experience is of no content, of no change, or it is of a
perceptible amount of content or change. Your acquaintance with reality
grows literally by buds or drops of perception. Intellectually and on
reflection you can divide them into components, but as immediately given
they come totally or not at all*." (Wm. James, 1911)

Whitehead builds also upon James's claim that "*The thought is itself
the thinker*":

"*If the passing thought be the directly verifiable existent, which no
school has hitherto doubted it to be, then that thought is itself the
thinker, and psychology need not look beyond*. (James 1890, p. 401)

Thus the "actual entities" are the "drops of experience" themselves, not
some soul-like entities that know them. Your awareness of your "self"
must be an aspect of your thoughts, and there is no rational need for,
additionally, something besides or beyond the reality that is *that
awareness itself*; except for an understanding of (1), how and why do
these thoughts cling together in "streams of consciousness" that have
the internal structures that they appear to have, and (2), why do these
streams of consciousness have the kinds of relationships to other such
streams of consciousness that our conversations with other persons
suggest that they have. These two kinds of properties need to be
explained, of course, but they are to be understood not as properties of
"matter", as matter was classically conceived, but rather as coordinated
properties of dynamically related collections of "actual
entities/occasions".

Whitehead draws a basic distinction between the two kinds of realities
upon which his ontology is based: "Continuous Potentialities" versus
"Atomic Actualities":

"*Continuity concerns what is potential, whereas actuality is incurably
discrete*." (PR, p. 61)

Another Whiteheadian precept is that actual entities decide things!

"*Actual entities ... make real what was antecedently merely
potential*." (PR, p.72)

"*every decision is referred to one or more actual entities...Actuality
is [decision]{.underline} amid potentiality*." (PR. p. 43).

"*Actual entities are the only reasons*. " (PR, p.24)

Another of Whitehead's key ideas is that each (temporal) actual entity
is associated with a region of space.

"*every actual entity in the temporal world is to be credited with a
spatial volume for its perspective standpoint*\..." (PR, p.68)

A closely associated idea is that these regions "atomize" space-time

"*The actual entities atomize the extensive continuum. This
\[space-time\] continuum is in itself merely potentiality for
division*." (PR, p.67)

"*The contemporary world is in fact divided and atomic, being a
multiplicity of definite actual entities. These contemporary actual
entities are divided from each other, and are not themselves divisible
into other contemporary actual entities*" (PR, p. 62)

A central idea in Whitehead's philosophy is his notion of process

"*The many become one, and are increased by one*." (PR p.21)

Thus in Whiteheadian process the world of fixed and settled facts grows
via a sequence actual occasions. The past actualities generate
potentialities for the next actual occasion, which is tied to a new
space-time standpoint (region) from which the potentialities created by
the past actualities will be prehended (grasped) by the current
occasion. This basic autogenetic process creates the new actual entity,
which, upon the completion of its creation, contributes to the
potentialities for the succeeding actual occasions.

Nature's process assigns a separate space-time region to each actual
entity, and this process fills up, step-by-step, the space-time region
lying in the past of the advancing sequence of space-like surfaces
"now", as indicated by this diagram.

![](media/image1.jpeg){width="6.758333333333334in"
height="3.1555555555555554in"}

Figure 1. A representation of the space-time aspects of the Whiteheadian
process of creation.

*The bottom curvy line represents the (spacelike) three-dimensional
surface "now" that separates\-\--at some stage of the process of
creation\-\--the space-time region corresponding to the fixed and
settled past from the region corresponding to the potential future. Each
new actual occasion has a standpoint space-time region, which gets added
to the past, thereby pushing slightly forward the boundary surface
"now". The small regions with numbers indicate the standpoints of a
succession of actual occasions each representing a step in the creative
process.*

This conception of a growing actual space-time region\-\--filled with
(the standpoints of) the growing set of past actual occasions\-\--that
advances into the potential open future, constitutes a certain
resolution to the famous debate between Newton and Leibniz about the
nature of space. Newton's conception, described in the Scholium in his
main work, "Principia Mathematica", was essentially a *receptacle*
conception, in which space is an empty container into which movable
physical objects can be placed.

Leibniz's argued for the *relational* view that space is naught but
relations among actually existing entities: completely empty space is a
nonsensical idea.

But Whitehead's *actual* space-time is filled by actual atomic
(indivisible) entities. Thus it is not empty. On the other hand, there
is also a yet-to-be-filled space-time future, which, however, is still a
mere potentiality.

This Whiteheadian idea of the growing "Past" can be contrasted with the
corresponding idea in Non-Relativistic Quantum Physics.

In non-relativistic quantum physics the growing "past" lies behind an
advancing (into the future) sequence of constant-time instants "now", as
illustrated below.

![](media/image2.jpeg){width="6.509722222222222in"
height="3.0416666666666665in"}

Figure 2. A representation of the space-time structure in
non-relativistic quantum theory. *At each one of a sequence of
constant-time surfaces an "intervention" occurs in association with an
abrupt jump to a new quantum state Ψ(t).*

In non-relativistic quantum theory (NRQT) the fixed past advances into
the open future in layer-cake fashion, one temporal layer at a time.
Each quantum reduction event occurs at some particular time NOW, *but
over all of space*. In von Neumann's nonrelativistic quantum theory this
event produces the new quantum state ψ(*t*) of the universe at the
instant labeled by the time *t.*

This non-relativistic space-time structure is replaced in
Tomonaga-Schwinger relativistic quantum field theory (RQFT) by a
different structure.

[2. From Von Neumann NRQT to Tomonaga-Schwinger RQFT**.**]{.underline}

In RQFT the NRQT state Ψ(*t*) is replaced by Ψ(σ). Here *t* specifies a
continuous three-dimensional surface in the four-dimensional space-time
continuum, with all spatial points lying at the same time t. But σ
specifies a continuous three-dimensional surface in the four-dimensional
space-time continuum, with every point on that surface
spacelike-separated from every other point (i.e., no point on the
surface can be reached from any other point by moving at the speed of
light or slower.)

*The Whiteheadian space-time structure represented in Figure 1
represents also the space-time structure of a sequence of discrete
actualization events in the Tomonaga-Schwinger formulation of
relativistic quantum field theory. In this case, the sequence of
space-like surfaces "now" represents the relativistic generalizations of
the sequence of fixed-time surfaces upon which, in the non-relativistic
formulation of quantum theory, the quantum state (of the universe) is
(re)defined just after each quantum jump in the sequence of quantum
jumps.*

In the relativistic case the bottom wavy line in Figure 1 represents
some initial surface σ, an initial NOW. In the dynamical evolution of
the quantum state this surface pushes continuously forward first though
the space-time region labeled 1. This unitary evolution, via the
relativistic generalization of the Schroedinger equation, leaves
undisturbed the aspects of the state Ψ(σ) associated with the rest of
the initial surface σ.

Then a new quantum "reduction" event occurs. It acts *directly* (via
projection) only on the new part of the surface, the part represented by
the top boundary of region 1. But this direct change causes *indirect*
changes along the rest of the surface σ, due to quantum entanglements.
These "indirect changes" produce the "faster-than-light" effects called
by Einstein "spooky actions at a distance".

The evolutionary process then advances the surface NOW next through
region 2, then through region 3, etc.. After each successive advance
into the future, a quantum reduction event occurs. It is associated with
a certain mathematical "projection" operator that acts directly only on
the new part of the current surface NOW, but indirectly (via
entanglement) on the entire surface NOW, at least in principle.

[3. Similarities between Whitehead's ontology and ontologically
construed RQFT]{.underline}**.**

Notice the identity, as regards the space-time development indicated
Figure 1, of the RQFT and the Whitehead ontologies.

But there are further correspondences. The first concerns the matching
of the Whiteheadian connections between "Objective Potentia" and
"Subjective Knowledge" with those of the Heisenberg's quantum ontology.

Heisenberg (1958b, p.53):

> *The probability function combines objective and subjective elements.
> It contains statements about possibilities or better tendencies
> ("potentia" in Aristotelian philosophy), and these are completely
> objective,...and it contains statements about our knowledge of the
> system, which of course are subjective in so far as they may be
> different for different observers*.

[4. The Transition from "Potentiality" to "Actuality" in Quantum
Mechanics.]{.underline}

Heisenberg (1958b, p.54):

> *the transition from the 'possible' to the 'actual' takes place during
> the act of observation*.
>
> *The observation itself changes the probability function
> discontinuously; it selects of all possible events the actual one that
> has taken place. Since through the observation our knowledge of the
> system has changed discontinuously, its mathematical representation
> has also undergone the discontinuous change and we may speak of a
> "quantum jump".*

[5. Compatibility with Einstein's (Special) Theory of
Relativity]{.underline}

I have in the foregoing account taken the structure of relativistic
quantum field theory as foundational, and Whitehead's words as
supplemental. Whitehead, of course, took philosophical principles as
foundational, and physics as derivative. However, in regards to the
coordination of his occasions to space-time, and in particular to the
reconciliation of his ontology with the 'Theory of Relativity',
Whitehead repeatedly emphasized that the structure that he was
describing did not follow from his general principles, but appeared to
be features of our particular epoch. That is, his descriptions of the
space-time features of his "actual worlds", "contemporary occasions",
and "durations (the loci of unison in becoming)" were specifically
designed to accord with *his idea* of the demands of "The Theory of
Relativity". However, particularly in connection with the idea of
"unison in becoming (durations)" he brought in ideas from the theory of
relativity associated with mere *conventional* choices of a coordinate
system. In the classical-physics-based developments of the theory of
relativity, the choice of coordinate system\-\--and hence of the locus
of points "now"\-\--is purely conventional, without ontological
significance: "now" is *not* associated with any act of "coming into
being". The notion of "coming into being" has, of course, no meaning in
the deterministic classical-physics "block universe" conception of
physical reality. Consequently, many different surfaces "now" can pass
though a point in deterministic classical physics without conflict. But
an analogous multiplicity of loci of "unision in becoming" would create
conceptual conflicts within the "open future" relativistic quantum
mechanics accommodated by Tomonaga-Schwinger RQFT.

Because of Whitehead's own admitted reliance, in regard to these
space-time features, on his (relatively primitive) conception of the way
that the theory of relativity is to be reconciled with quantum
mechanics, it is reasonable to replace Whitehead's proposals, based on
his quasi-classical ideas about relativity, by proposals concordant with
the way quantum theory was, during the late forties, actually made
compatible with the theory of relativity. In the logically simplest
ontologicalization of the Tomonaga-Schwinger relativistic quantum field
theory, the space-like surface "now" advances always forward into the
open future, and conceptual confusion and conflict is thereby avoided.

Within Tomonaga-Schwinger RQFT all *predictions* are independent of the
sequential ordering of space-like separated events: e.g., switching the
sequential orderings of the occasions labeled 1 and 2 in Figure 1
changes no prediction of the theory.

Furthermore, no "signal" (controlled message) can be transmitted faster
than the speed of light.

Quantum theory is designed to be a theory of predictions, and the
predictions of RQFT conform to the demands of Einstein's (special)
theory of relativity: the *predictions* do not depend upon which one of
any two space-like separated events occurs first in the sequential
unfolding of actuality. Furthermore, by virtue of the detailed structure
of the quantum rules, the indirect effect, via entanglement, of a
quantum event occurring in one region upon predictions/potentialities
pertaining to a faraway (space-like separated) region cannot be used to
transmit a "signal" (a controllable message) faster than the speed of
light. (For details see Stapp 2007, Appendices 5, 6, & 7)

[6. The Psycho-Physical Building Blocks of Reality]{.underline}

In the Whiteheadian ontologicalization of quantum theory, each quantum
reduction event is identified with a Whiteheadian actual
entity/occasion.

*In the quantum version* are two kinds of actual occasions. Each actual
occasion of the first kind is an action that *partitions* a continuum
into a collection of discrete *experientially distinct* possibilities.
Each actual occasion of the second kind selects (actualizes) one of
these discrete possibilities, and obliterates the rest. These two kinds
of actions are represented mathematically in an abstract space called
Hilbert space, and are associated with the feature of discreteness that
Bohr (1962, p. 60) called "The element of wholeness symbolized by the
quantum of action and completely foreign to the classical physical
principles" and that James (1911) called the "buds or drops of
perception". (See appendix)

According to this Whiteheadian Quantum Ontology, objective/absolute
actuality consist of a sequence of psycho-physical quantum reduction
events, each similar to a Whiteheadian actual entity/occasion. This
sequence of happenings creates a growing "past" of "fixed and settled
facts".

Each "fact" is specified by an actual occasion/entity that has both a
physical aspect (pole) and a mental aspect (pole), and a "standpoint"
region in space-time from which it views reality. I take the *physical*
pole or aspect of the actual occasion to consist of a
physically/mathematically described *input* and a
physically/mathematically described *output*. The physical input
(output) is precisely the part of the physically described quantum state
of the universe that is localized\-\--just before (after) the
jump\-\--on the *front* boundary of the standpoint region associated
with the actual occasion.

The mental pole also consists of an input and an output. The mental
inputs and outputs have the ontological character of "feelings". The
mental inputs are drawn largely from the mental outputs of the prior
occasions, and the mental output of the current occasion is the "bud or
drop" of experience created by/at this current event or occasion.

The process by which the mental and physical inputs are combined to
produce mental and physical outputs involves, according to Whitehead,
aspects identified as appetites, evaluations, and satisfactions. Thus
idea-like qualities are asserted to be important in the dynamics of the
basic process that creates the actual occasions, and hence the growing
world of actual facts.

The paradigmatic example of an actual occasion is an event whose mental
output is an addition to a human stream of conscious events, and whose
physical output is the actualization of the neural correlate of that
mental output. Such events are "high-grade" actual occasions. But the
Whitehead allows simpler occasions that have lower-grade outputs also to
exist. Thus the Whitehead Quantum Ontology is essentially an
ontologicalization of the structure of orthodox relativistic quantum
field theory, stripped of any anthropocentric trappings, but supplied
with a dynamical process that makes our thoughts dynamically effective.
This approach takes the physically described and psychologically
described aspects of contemporary orthodox relativistic quantum field
theory to be exemplars of the elements of a general non-anthropocentric
ontology.

This putative understanding of the way nature works is merely an
outline, further details of which can be filled in when additional
pertinent data becomes available. The theory is not *implied* by the
currently available empirical data, but it gives a rationally coherent
way to accommodate the discreteness aspects that Bohr and James
identified.

This program to ontologicalize the anthropocentric, pragmatic, orthodox
quantum mechanics of its founders, and of von Neumann, may seem
misdirected. For how does this explicitly observation-dependent ontology
apply to the formation of a track in a cloud chamber? The physical
happenings in the chamber *seem* to have, fundamentally, very little to
do with any act of observation: our human involvement seems only
incidental. Some physicists want therefore to conclude that the collapse
events in cloud chambers are instigated by purely physically describable
causes alone and that this conclusion holds also for brain events as
well.

Von Neumann's analysis of measurements shows that for all practical
purposes (FAPP) one can indeed assume that an appearing track comes into
being without any dependence upon our human observations of it. Still,
some sort of process 1 type intervention is needed to make the quantum
rules work in this paradigmatic case. If it be granted that the coming
into being of a particular track is a quantum event, which needs to be
described not in terms of classical phase space but in terms of quantum
concepts, namely in terms of vectors in a vector space, and a choice of
basis vectors\-\--see Appendix\-\--then the problem of what chooses the
basis must be dealt with in some way.

The crucial point here is that quantum phenomena appear to require the
entry into reality of the element of discreteness/wholeness associated
with von Neumann's process 1 action, and that this effect cannot be
adequately represented either within the conceptual framework of
classical physics, or within its quantum generalization represented by
the wave function evolving continuously in accordance with the
Schroedinger equation. The proposal here is that each such intervention
is *in its logical form* like the interventions associated with human
observations, which orthodox quantum mathematics describes. This
conceptualization requires the existence of realities that play in a
general context the role played in the orthodox formulation by human
experiences. But what is the ontological nature or character of these
more general realities? A significant achievement of Whitehead's
ontology is a rationally coherent putative identification of the nature
of these realities

Whitehead calls the realities that are described by the
*physical/mathematical formulas of physics* by the name "physical
feelings". Now in classical physics the realities whose properties are
described by the mathematical formulas are conceived to be tiny bits of
mindless matter, or mindless fields of force. In quantum physics, these
mathematically described aspects are converted to features that act like
*potentialities*\-\--like objective tendencies\-\--for psycho-physical
events to occur. Whitehead's move of calling these realities "physical
feelings"\-\--which need to be combined with "conceptual feelings" and
"memory" in order to rise to the level of "conscious
feelings"\-\--provides a uniform basis of "feelings" for the entire
ontology. And this uniform basis is one that allows the conscious
feelings of the kind we know to emerge via a "dynamics of feelings" from
an ontological substrate consisting of realities of one single
ontological type.

Of course, it may not initially be easy to conceive of a "feeling" that
is not a "conscious feeling", for latter is the only kind of feeling
that we actually know, or know of. But if we accept that our conscious
feelings are complex versions of simpler things that can act dynamically
upon other like things, and merge with these other things to form
more-complex things of the same kind, then we have, I think, gained an
important insight into what Whitehead was driving at with his choice of
words; and we will have established a basis for understanding how
consciousness can emerge from realities that are not conscious.

Even in classical physics, physicists sometimes use the phrase "the
electron 'feels' the force exerted by the electric field" to convey the
idea that the electron *responds* to the presence of the electric field,
in a way intuitively akin to the way our thoughts respond to our
feelings. Of course, in the case of the electron, the word "feels" has,
for the physicist, no connotation pertaining to consciousness. The
physicist is completely content to describe the interactions in purely
mathematical language\-\--which is all that he needs or uses\-\--without
any concern pertaining to the ontological character of the stuff whose
mathematical description he employs. Yet non-scientists tend to think of
that stuff as classical "matter", even though the quantum mathematics is
incompatible with that idea. In the quantum description the "stuff"
creates tendencies for the creation of more bits of stuff of the same
kind.

The question "What *is* it that is being described by the mathematics"
is a question that the physicist can properly regard as totally
irrelevant to physics. But if one wants to provide a rational
understanding of how our conscious feelings can emerge from the
activities of our brains then it becomes important to recognize that the
quantum mathematics does not describe motions of bits of classically
conceived matter, but can be understood to describe properties of
"feelings", conceived to be interacting qualities that are dynamically
able to combine with other feelings to form output feelings of the same
ontological kind, which that can, under suitable conditions, be the
complex sort of feelings that populate our streams of conscious
experiences.

Thinking in this way, though based on physics, goes beyond physics: it
is metaphysics. In this connection, William James said, presciently, of
the scientists who would someday illuminate the mind-body problem:

> ...the necessities of the case will make them 'metaphysical'.
> Meanwhile the best way in which we can facilitate their advent is to
> understand how great is the darkness in which we grope, and never
> forget that the natural-science assumptions with which we started are
> provisional and revisable things. (James, 1892, the closing words.)

**Part II: Jamesian Volition in Quantum Theory**

*How our conscious thoughts can affect our physical actions.*

Contemporary science divides our descriptions of the totality of all
things into two categories: descriptions in physical terms; and
descriptions in psychological terms.

Physical properties consist basically of mathematically described
properties localized at points or tiny regions of space-time. More
generally they are the properties dealt with by physicists in physics
courses, or by scientists in the other physical sciences that are
non-problematically reducible to the basic physical properties, whereas,
according to William James, the psychological properties consist of
"thoughts, ideas, and feelings". These psychological elements are
collected into separate "streams of conscious experiences", each
associated, in orthodox psychology, with the subjective inner life of an
individual human person.

**Continuity and Causation in Classical Physics**

Classical physics postulates a continuous process satisfying "causal
closure of the physical". This principle asserts that the physical
description, by itself, provides for a causally complete deterministic
account. The complete physical description over all of space during any
interval of time determines the physical properties over all of
space-time. No effects of mind or consciousness on the physically
described properties need be considered or acknowledged.

This property of classical physics\-\--the causal closure of the
physical\-\--leads to a puzzle expressed by William James as the
observation that consciousness seems to be

> *"an organ, superadded to the other organs which maintain the animal
> in its struggle for existence; and the presumption of course is that
> it helps him in some way in this struggle, just as they do. But it
> cannot help him without being in some way efficacious and influencing
> the course of his bodily history."* (ibid. p. 138)

James goes on to an extensive analysis of the entry of consciousness
into our lives, and ends up by saying:

*"The conclusion that it is useful is, after all this, quite
justifiable. But if it is useful it must be so through its causal
efficaciousness, and the automaton theory must succumb to common
sense."* (ibid. p.144)

**Orthodox Quantum Theory is not Causally Complete: It Has Two Kinds of
Causal Gap.**

In quantum theory there are two kinds of decisions that are *not
determined by the known laws of quantum theory*, yet are needed to make
the theory work!

Gap \# 1

Bohr: "In the great drama of life we are both *actors* and spectators."
\[My highlight\]

Bohr: "free choice of experimental arrangements for which the
mathematical structure of the quantum mechanical formalism offers the
appropriate latitude." (Bohr, 1958, p. 73)

Conscious choices made human agents determine the experimental
conditions, which affect subsequent physical properties. Von Neumann
calls the physical correlates of these conscious choices by the name
"Process 1" *interventions*. These physical actions *intervene* in the
orderly continuous (Schroedinger-equation-controlled) evolution of the
physical state of the universe.

The decisions of the first kind are identified as the "*Free choices*"
made by conscious agents. These are the Process Zero *conscious choices*
that in actual scientific practice determine the physically described
partition, specified by a Process 1 action, of the continuous quantum
mechanically described physical world into discrete experiencible
components. These decisions are choices to act in a particular way, with
an intent to elicit a conceived experiential feedback. *These choices
are made in actual practice by human agents. They are not determined
within orthodox theory either statistically or in any other way*: *This
indeterminateness constitutes the first kind of causal gap!*

Gap #2

Dirac: "Nature's choice of the *outcome* of the experiment."

The intended feedback/outcome may or may not actually occur. However,
the quantum state of the universe just prior to the agent's choice
determines the *probability* for the intended feedback to occur. But it
does not determine whether or not that feedback will actually occur.
This indeterminateness constitutes the second kind of causal gap.

**Significance**

The mainstream neuroscience "materialist" assumption is that "any effect
of mind is causally reducible to the physically describable aspects of
nature". This presumption is in no way a consequence of basic physical
principles: it is neither demanded nor supported by contemporary
orthodox physical theory According to twentieth century physics,
consciousness can *intervene* in brain dynamics in an essential and
non-eliminable way, and thereby select and actualize physical actions
that without this intervention would remain pure quantum potentialities.

It is, however, one thing to notice that the shift from classical
mechanics to quantum mechanics involves in an essential way the
injection of conscious choices into the causal physical structure of the
theory, and to observe that this opens a theoretical door to *possible*
effects of minds upon brains, but it is quite another thing to spell out
in detail how such an effect could actually occur.

**Filling the First Causal Gap.**

**A Simple Example**

Suppose the idea "I shall now raise my arm" pops into your stream of
consciousness, and this experience is colored by a strong feeling of
*the positive value* *to you* of that contemplated action's actually
occurring. It is concordant with normal experience to presume that this
experience will often have a successor in which the core idea "I shall
now raise my arm" is colored now with a feeling of making an "effort to
raise now my arm". The felt connection between "effort" and the
"intensity of experience" makes it natural to suppose that the intensity
of the effort is correlated to the rapidity at which the experiential
events are occurring: that increased effort will be correlated to an
increased rapidity of the sequence of actual occasions associated with
the idea of raising the arm.

The timings of the actual occasions are not specified by the known
quantum mechanical rules. This opens the door to the possibility that
psychologically describable elements, not reducible to physically
described properties, are entering into the causal structure. But even
if that were true, the issue would arise: How can the conscious effort
influence what physically happens. How can a *conscious* *effort* to
raise the arm "cause" in some sense, the physical arm to rise?

What is the neural correlate of the experience of "making an effort to
raise the arm"?. Presumably, it is a pattern of neurological activity
that if sustained over a sufficiently long time will tend to cause, via
the neural machinery, the arm to rise. This correlation will have become
established through trial and error learning involving the comparison of
effortful intentional actions to their experiential feedbacks. I call
such a pattern of neurological activity by the name "template for
action".

Let us suppose, in accord with the earlier remark, that the experience
of "effort to raise the arm" causes an immediate (within a few
milliseconds) repetition of that experience, and that this causes
another immediate repetition, and so on. This rapid sequence of
actualizations of the associated "template for action" will tend\-\--by
virtue of the well known quantum Zeno effect\-\--to hold that template
for action in place for longer than would otherwise be the case. This
persisting excitation of the template for action will, by virtue of its
defining property, tend to cause your arm to rise.

This effect is in exact accord with the observations of William
James(1892, p.227):

> I have spoken as if our attention were wholly determined by neural
> conditions. I believe that the array of things we can attend to is so
> determined. No object can catch our attention except by the neural
> machinery. But the amount of the attention which an object receives
> after it has caught our attention is another question. It often takes
> effort to keep mind upon it. We feel that we can make more or less of
> the effort as we choose. If this feeling be not deceptive, if our
> effort be a spiritual force, and an indeterminate one, then of course
> it contributes coequally with the cerebral conditions to the result.
> Though it introduce no new idea, it will deepen and prolong the stay
> in consciousness of innumerable ideas hich else would fade more
> quickly away. The delay thus gained might not be more than a second in
> duration\-\--but that second may be critical; for in the rising and
> falling considerations in the mind, where two associated systems of
> them are nearly in equilibrium it is often a matter of but a second
> more or less of attention at the outset, whether one system shall gain
> force to occupy the field and develop itself and exclude the other, or
> be excluded itself by the other. When developed it may make us act,
> and that act may seal our doom. When we come to the chapter on the
> Will we shall see that the whole drama of the voluntary life hinges on
> the attention, slightly more or slightly less, which rival motor ideas
> may receive. \...

In the chapter on Will, in the section entitled "Volitional effort is
effort of attention" James (1892. p.417) writes;

> The essential achievement of the will, in short, when it is most
> \`voluntary,\' is to attend to a difficult object and hold it fast
> before the mind. \... Effort of attention is thus the essential
> phenomenon of will.

and

> Consent to the idea\'s undivided presence, this is effort\'s sole
> achievement."\..."Everywhere, then, the function of effort is the
> same: to keep affirming and adopting the thought which, if left to
> itself, would slip away.

**Empirical Support**

Empirical support for this explanation of the way in which our
consciousness affects our brains can be found in Stapp (2001) and
Schwartz, Stapp, and Beauregard (2005).

But beyond the detailed experimental findings described in those works
there is the practical benefit of having a conception of nature, and our
role in nature, that is a harmony with our intuitive feeling that our
intentional thoughts can influence our physical actions, and with the
scientifically validated idea that conscious intentional efforts can
evoke associated brain activities in ways that can, through learning or
training, be correlated to experiential feedbacks. The vast literature
on biofeedback, and the mounting evidence from nerve-activated
prosthetics, attest to the utility of this conception of the mind-brain
connection.

Insofar as one grants that a conscious experience is not simply an
aspect of the activity of a brain that is completely expressible in
terms of the physical concepts of (classical or quantum) physics, but
instead has qualities that cannot be expressed in terms of, or reduce
to, the quantitative properties that occur in the physical description
of the world used by physicists, then one's ontology should specify
whether or not these further properties, which are felt, and which are
parceled into streams of consciousness, are needed to fix the flow of
physically described events, or whether, as in classical physics, the
physically describable flow of events is completely determined in terms
of the physically describable aspects alone.

In that latter case one has difficulty explaining the success of
nerve-activated prosthetics.

Suppose one were to build a computer model of that situation, with
consciousness represented by a higher module that can integrate and
evaluate brain data, and make selections, but that has no causal effect
on the physical machinery that implements or obeys the physical laws
that by themselves determine all physical effects. One would then have
to understand how this module *could be trained* to come into good
alignment with the causal processes upon which it has no causal effect.
There is certainly no automatic uniform concordance between the mental
and physical descriptions, as the numerous examples of mismatches cited
by proponents in mechanistic or materialistic conceptions of reality
attest. But if there is no automatic concordance between conscious
thoughts, ideas, and feelings and physical actions then how can the
empirically occurring correspondences come into being through practice,
if the mental module cannot act upon the physical ones?

Why, I must ask, would anyone ever want to postulate the existence of
such an unnatural and awkward, and seemingly *impossible to comprehend,*
reality, when its only virtue is to conform to ancient laws that are now
known to be false, and to be moreover inapplicable *in principle* to the
causally important motions of the ions in nerve terminals, when
empirically validated laws of physics that are completely applicable to
warm, wet, and noisy brains provide a way of understanding a causal
influence of mental effort upon brain activities that can render
perfectly natural and understandable the empirically manifest phenomena
of effortful guided learning.

**Comments.**

1\. Every aspect of the preceding analysis is in strict accord with the
orthodox laws of quantum physics. No rule has been stretched or altered.
An existing causal gap in the theory has merely been filled in a natural
way, by exploiting effects explicitly assigned by the theory to
conscious free choices, and then applying the known causal laws.

2\. The quantum Zeno effect is itself a decoherence effect, and it is
not diminished by environmental decoherence. *Thus the usual argument
against using quantum mechanics to explain the influence of conscious
thought upon brain activity is nullified.* Environmental decoherence
does reduce pure quantum states to "a mixtures", to a smear of
quasi-classical states, but this does not resolve the problem of the
discreteness of our experiences

3\. The fundamental reason why the effect of conscious thought upon
bodily action is explainable within quantum mechanics, but not within
classical physics, is that orthodox quantum theory *itself* introduces,
as a key innovation (with respect to classical physics), the needed
causal efficacy of our conscious choices. The logically needed Process 1
physical choices have no causal roots in the physically described aspect
of reality specified by the theory, but they are strongly correlated
with sufficient reasons and other motivations describable in
psychological terms. This configuration of causal connections suggests
that the consciousness is the cause, and the correlated Process 1
physically described action is the effect. This is the point of view
that ties quantum theory most naturally and directly both to common
sense and to our deepest intuitions, as well as to actual scientific
practice, where the experimenter chooses on the basis of reasons and
goals which of the options will be pursued. In this connection, Bohr
speaks pertinently of "the free choice of experimental arrangement for
which the mathematical structure of the quantum mechanical formalism
offers the appropriate latitude".(Bohr, 1958,p, 73) What motive could
possibly induce any rational philosopher or scientist interested in the
connection between mind and matter to close his or her .mind to this
hugely pertinent development of physics, and cling instead to
fundamentally false and puzzling nineteenth century materialism, which
has no conceptual place for the streams of conscious thoughts, ideas,
and feelings that constitute our known inner subjective experiential
lives.

**Part III. Contrasts to Whitehead**.

My use of Whitehead's words is intended to flesh out an ontological
construal of relativistic quantum field theory, not to explain
Whitehead's philosophy. Thus I have picked out the aspects of his work
that fit contemporary relativistic quantum theory nicely, and elevate it
from an anthropocentric set of pragmatic rules to a putative partial
description of the reality in which our bodies and our streams of
consciousness are imbedded. But certain departures from Whitehead's
scheme may be worth noting.

I have in section 5 of Part II already discussed the deviations
pertaining to space-time structure that seem required to accommodate
adequately the theory of relativity.

As regards the mental pole of an actual occasion, Whitehead regards it
as primarily associated with the internal dynamics that creates the
occasion. I have taken a key feature of the completed occasion to be the
final whole experience, the bud or drop of experience that James
describes in connection with the human exemplars, and have taken this to
be *part* of the output of the occasion. Whitehead achieves a similar
effect when he speaks of the conceptual reproduction in a later occasion
of conceptual features of the earlier occasions that it prehends. But
since I want to tie the "physically described" aspects of the output of
an occasion with those aspects that are represented in the
mathematically described quantum state, I need to allow that the output
is not confined exclusively to those mathematically described aspects:
there is also a "feeling" aspect that can be picked up by a later
prehending occasion.

I do not see how an electron, for example, traveling through a vacuum,
can be conceived of as a society of occasions, at least insofar as these
occasions have smallish standpoints at which the electron becomes
localized. That would seem to preclude, well established interference
effects, such as the famous double slit experiment. Similar experiments
with neutrons going in two different ways around a football field are
feasible, I am told.

An actual (process-1-associated) occasion, X, should occur, I believe,
only in a situation sufficiently complex so that the actualization of
the physically described possible 'Yes' outcome of the situation created
by X specifies, according to the quantum rules, classically specifiable
quasi-stable tendencies pertaining to future potential "reproductions"
of X. In this case the "conceptual feel" could represent a certain
quasi-stable tendency/intent that is expressed *conceptually* within the
domain of classical notions, but that is implemented *physically* in the
mathematically described quantum world by the process 1 action
associated with X. This arrangement would be completely compatible with
Whitehead, apart from his idea that elementary particles, such as
"electrons", are societies of actual occasions. In quantum theory a
freely propagating elementary particle represents a propagation of
*tendencies* for a happening to occur, say at a measuring device, not a
collection of actual localized happenings. At least that is the way that
this situation is normally understood, and was described by Heisenberg.

**Appendix: Connection between Classical Physics and Quantum Physics**

In connection with the nature of quantum mechanics Bohr speaks of:

> The element of wholeness, symbolized by the quantum of action and
> completely foreign to classical physical principles. (1962, p. 60)

In connection with the nature of experience William James said:

"*Either your experience is of no content, of no change, or it is of a
perceptible amount of content or change. Your acquaintance with reality
grows literally by buds or drops of perception. Intellectually and on
reflection you can divide them into components, but as immediately given
they come totally or not at all*." (Wm. James, 1911)

To understand the connection between classical physics and quantum
physics consider first a classically conceived system consisting of one
single point particle confined to a large cubical box in ordinary
three-dimensional space. Suppose we divide this box into a very large
number N of tiny cubical regions. Then one way to represent some
information about the system at some particular instant of time is to
assign to each tiny cube a number 'one' or 'zero' according to whether
the particle is in, or is not in, that tiny cube at that instant. Thus,
at each instant, all N boxes will be assigned a "zero" except for one
box, which will be assigned a 'one'. (A special rule can be introduced
to cover the case where the particle lies exactly on a boundary.) Over
the course of time this 'one' will, due to the motion of the particle,
occasionally jump from one tiny cubical box to an adjacent one.

Information about the velocity of the particle can be added by
introducing, *for each of the little coordinate-space boxes just
mentioned*, a collection of M little boxes in a space that represents
the velocity of the particle, or better, its *momentum*\-\--which is the
product of its velocity times its mass.

Quantum mechanics is somewhat analogous to classical *statistical*
mechanics. That latter theory covers situations where one wishes to make
statistical predictions about future observations on the basis of the
known equations of motion, when one has only statistical information
about the initial conditions. In this case each little box represents a
tiny region in the combined coordinate-momentum space\-\--which is
called *phase space*\-\--and the initial number assigned to this box
will generally be not 'zero' or 'one', but some number in between. This
number represents the initial probability that the combination of the
location and the momentum of the particle lies in that tiny region.
These numbers will sum to unity (one). One can let the sizes of these
little boxes become increasingly small, and finally go over to a
continuous "probability density". Then the classical equations of motion
can be used to determine how this probability density changes over the
course of time.

A typical "measurement" from the classical physical-description-based
point of view, is an action that answers the question: "Do the position
and momentum of the system at a time t lie in some specified region R in
phase space." Given the initial probability conditions, the probability
that the answer is 'Yes', at the time t is obtained by summing up all of
the contributions to the evolved probability distribution that lie
within the specified region R at the time t of the observation.

The case just described is a very simple case in which the physical
system being observed is just one single point particle. But the same
discussion applies essentially unchanged to any physical system,
including, in particular, the brain of a conscious human being. In that
case, the space in which the little boxes lie is a space each point of
which represents a complete classically conceived brain, and each little
box represents a tiny range of values in this space: each little box can
represent a tiny region in which both the location and the momentum of
every particle in the brain are very close to the values specified by a
classically conceived and described possible state of the brain.
According to the classical conception of nature, the actual state of the
person's brain at any particular instant lies in exactly one of these
little boxes, and all but one box is assigned a zero. In a classically
conceived *statistical* context a set of probability contributions that
sums to unity can be distributed in any chosen (smooth) way among these
small boxes, each of which can in principle be shrunk to an arbitrarily
small size.

In the quantum generalization of classical statistical mechanics the
region R associated with an actual (conscious) observation cannot be
represented by an arbitrarily small (or even sharply defined) region of
the classically conceived phase space. The size of
the\-\--fuzzy-in-principle\-\--region in phase space, defined in a
suitable way, is a multiple of Planck's quantum of action. The intrinsic
wholeness of each conscious thought renders the phase space of classical
physics an inappropriate basis. The physical state of the brain is
represented, rather, as a *vector* in an appropriate *vector space*, and
each permissible conscious observation associated with that brain is
associated with some set of mutually orthogonal (perpendicular) *basis
vectors*. *Thus the basic mathematical structure needed for the
conscious-observation-based quantum theory of phenomena is fundamentally
incompatible with the mathematical structure used in the
physical-measurement-based classical theory of phenomena. An irreducible
element of wholeness is present in the former but absent from the
latter.*

The neural correlates of our conscious thoughts are, according quantum
mechanics, represented in a vector space of a very large number of
dimensions. But the basic idea of a *vector in a vector space* can be
illustrated by the simple example in which that space has just two
dimensions.

Take a flat sheet of paper and put a point on it. (Imagine that your
pencil is infinitely sharp, and can draw a true point, and perfectly
straight lines of zero width.). Draw a straight line that starts at this
point, called "the origin", and that extends out by a certain amount in
a certain direction. That directed line segment, or the displacement
from the origin that it defines, is a *vector* in a two-dimensional
space.

Any pair of unit-length vectors in this space that are perpendicular to
each other constitute a "basis" in this two-dimensional space. (They are
in fact an "orthonormal basis", but that is the only kind of basis that
will be considered here.) Because any pair of perpendicular unit-length
vectors rigidly rotated by any angle between 0 and 360 degrees gives
another perpendicular pair, there is an infinite number of ways to
choose a basis in a two-dimensional space.

Given a basis, there is a unique way of decomposing any vector in the
space into a sum of displacements, one along each of the two
perpendicular basis vectors. The two individual terms in this sum are a
pair of perpendicular vectors called the *components* of the vector in
this basis. One such decomposition is indicated in Figure 3.

![](media/image3.jpeg){width="5.497916666666667in"
height="3.1680555555555556in"}

Figure 3. Decomposition of vector V of length C, in a two-dimensional
space, into components of lengths A and B directed along a pair of basis
vectors that correspond, respectively, to the 'Yes' and 'No' answers to
a possible process 1 question labeled by Ө.

If V has unit length and A and B are the lengths of the components of V
that are directed along these two basis vectors, then, by virtue of the
theorem of Pythagoras, A^2^ + B ^2^ = 1: the sum of the two squares is
unity. This is what a sum of *probabilities* should be. Consequently,
the concept of probability can be naturally linked to the concept of
vectors in a space of vectors. The angle Ө specifies the different
observational process that are possible in principle for vectors in this
space, *and the two corresponding basis vectors correspond to the two
possible distinct outcomes, 'Yes' or 'No', of the observational process
specified by the angle* Ө.

An N-dimensional (vector) space is similar, but has N dimensions instead
of just two. This means that it allows not just two mutually
perpendicular basis vectors, but N of them. As a mathematical idea this
is well defined. There are clearly an infinite number of ways to choose
a basis\-\--a set of mutually perpendicular unit-lenth vectors\-\--in
any space of two or more dimensions, hence an infinite set of elementary
observational processes that are possible in principle. For any N, and
for any basis in the N-dimensional space, there is a unique way of
decomposing any vector in that space into a sum of displacements each
lying along one of the mutually perpendicular basis vectors.

Each possible observational process is, according to the basic
principles of quantum theory, associated with such a choice of basis
vectors. The N-dimensional generalization of the theorem of Pythagoras
says that the sum of the squares of lengths of the mutually
perpendicular components of the unit length vector V that represents the
quantum state of the physical system is unity. Consequently, the
probability interpretation of the lengths of the components of the
vector V carries neatly over to the N-dimensional case. Vectors in a
vector space provide, therefore, a way to represent in an abstract
mathematical space the probabilities associated with the perceptual
realities that form the empirical basis of science.

According to quantum theory, the alternative possible phenomenal
outcomes of any process of observation are associated with a set of
corresponding basis vectors. Each such basis vector is associated with
an\-\--in principle fuzzy\-\--region in the phase space of the system
that is being probed, hence acted upon. This region has a prescribed
size, specified by Planck's quantum of action, and only certain kinds of
shapes are allowed. Thus the mathematical entities correspond possible
*perceptions* in quantum theory are very restrictive as compared to the
completely general sizes and shapes of the phase-space regions that are
allowed to represent measurable properties of physical systems in
classical physics. The transition to quantum theory imposes a severe
restriction on observational realities, in comparison to the
micro-structure that is deemed measurable in classical mechanics.

A quantum state of a system can be represented by a vector in a space an
infinite number of dimensions. Much of von Neumann's book was devoted to
the fine points of how this could be done in a mathematically well
defined way. Although the number of basis vectors is infinite, it is
countably infinite: the basis vectors can be placed in one-to-one
correspondence to the numbers 1, 2, 3, ... That means that, *given a
basis,* there is a unique decomposition of the state of the system into
a *countable* set of elementary components.

The countability of the set of distinct or discrete possibilities is
important.

If you have a countable set of states then you could, for example,
assign probability ½ to the first state, probability ¼ to the second
state, probability ⅛ to the third, and so on, and the total probability
will add to one (unity), as a sum of probabilities should. This kind of
separation into a countable set of discrete elements, each finite, is
not equivalent to the separation of a continuous line into infinitesimal
points: there is an element of discreteness involved with observation in
quantum theory that is essentially different from what occurs in
classical physics, and from what can naturally be generated from the
genuinely continuous process 2 alone. The decomposition into discrete
holistic components associated with a set of mutually perpendicular
basis vectors in a vector space is the foundation of the relationship of
the quantum mathematics to empirical phenomena. This feature blocks the
association of arbitrarily tiny regions R in phase space with
observation.

This discreteness aspect poses a nontrivial, and I believe fatal,
difficulty for many-world theories, which deny the entry of process 1
interventions. Scientific empirical data lies in the final analysis in
our observations. But then what fixes the set of basis vectors that
corresponds to some individual person's observations? How can this
correspondence, which involves discreteness and wholeness be specified
by the continuous micro-causal physically described process 2 alone?
Quantum theory is based on an elaborate mathematical machinery for
introducing the irreducible element of wholeness, and this machinery is
based on von Neumann's process 1 interventions. Leaving them out is
contrary to the main thrust of quantum theory. The present approach
accepts them as essential ingredients of the theory, and seeks to
elucidate them.

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