July 21, 1998 LBNL-40722
Quantum Ontology and Mind-Matter Synthesis
Henry P. Stapp
Lawrence Berkeley National Laboratory
University of California
Berkeley, California 94720
\begin{abstract}
The Solvay conference of 1927 marked the birth of quantum theory. This
theory constitutes a radical break with prior tradition in physics, because
it avers, if taken seriously, that nature is built not out of matter but out
of knowings. However, the founders of the theory stipulated, cautiously,
that the theory was not to be taken seriously, in this sense, as a
description of nature herself, but was to be construed as merely a way of
computing expectations about future knowings on the basis of information
provided by past knowings. There have been many efforts over the intervening
seventy years to rid physics of this contamination of matter by mind. But I
use the reports at this Symposium to support the claim that these
decontamination efforts have failed, and that, because of recent
developments pertaining to causality, the time has come to take quantum
theory seriously: to take it as the basis for a conception of the universe
built on knowings, and other things of the same kind. Quantum theory ensures
that this conception will yield all the empirical regularities that had
formerly been thought to arise from the properties of matter, together
with all of those more recently discovered regularities that cannot
be understood in that mechanical way. Thus I propose to break away from the
cautious stance of the founders of quantum theory, and build a theory of
reality by taking seriously what the incredible accuracy of the predictions
of the formalism seems to proclaim, namely that nature is best understood as
being built around knowings that enjoy the mathematical properties ascribed
to them by quantum theory. I explain why this idea had formerly been
incorrectly regarded as untenable, due to a failure to distinguish signals
from influences: relativistic quantum field theory ensures both that signals
cannot travel faster than light, but that influences, broadly conceived,
cannot be imagined to enjoy that property. Failure to recognize this fact
had made a realistic interpretation of quantum theory seem impossible. I
then explain how our conscious knowings can play a causally efficacious and
binding role in brain dynamics without violating the statistical rules of
quantum theory, and describe how these features provide a foundation for
understanding how consciousness could have evolved by natural selection from
primitive beginnings.
\end{abstract}
Invited Paper: The X-th Max Born Symposium ``Quantum Future''.
1. Introduction.
The modern era was created probably as much by Descartes' conceptual
separation of mind from matter as by any other event. This move freed
science from the religious dogmas and constraints of earlier times, and
allowed scientists to delve into the important mathematical regularities of
the observed physical world. Descartes himself allowed interaction between
mind and matter to occur within the confines of a human brain, but the
deterministic character of the physical world specified later by Newtonian
mechanics seemed to rule out completely, even within our brains, any
interference of mind with the workings of matter. Thus the notion of a
completely mechanical universe, controlled by universal physical laws,
became the new dogma of science.
It can readily be imagined that within the milieu dominated by such thinking
there would be stout opposition to the radical claims of the founders of
quantum theory that our conscious human knowings should be taken as the
basis of our fundamental theory of nature. Yet the opposition to this
profound shift in scientific thinking was less fierce than one might
suppose. For, in the end, no one could dispute that science rests on what we
can know, and quantum theory was formulated in practical human terms that
rested squarely on that fact. Hence the momentous philosophical shift was
achieved by some subtle linguistic reformulations that were inculcated into
the minds of the students and practitioners of quantum theory. The new
thought patterns, and the calculations they engendered, worked beautifully,
insofar as one kept to the specified practical issues, and refrained, as one
was instructed to do, from asking certain ``meaningless'' metaphysical
questions.
Of course, there are a few physicists who are dissatisfied with purely
practical success, and want to understand what the practical success of
these computational rules is telling us about ourselves and the nature of
the world in which we live. Efforts to achieve such an understanding are
proliferating, and the present work is of that genre. Historically, efforts
to achieve increasingly coherent and comprehensive understandings of the
clues we extract from Nature have occasionally led to scientific progress.
The outline of the present work is as follows. In section 2, I document the
claim made above that the orthodox Copenhagen interpretation of quantum
theory is based squarely and explicitly on human knowings. The aim of the
paper is to imbed this orthodox pragmatic epistemological theory in a
rationally coherent naturalistic ontology in a minimalistic way that causes
no disruption of anything that orthodox quantum theory says, but merely
supplies a natural ontological underpinning. In the special case of
processes occurring in human body/brains this ontological structure involves
human conscious knowings that enter into the brain dynamics in a manner that
accounts for the way that these knowings enter into the orthodox
interpretation of quantum theory.
In section 3 I discuss another interpretation, which is probably the common
contemporary interpretation of the Copenhagen interpretation. It is coarse
in that it is imprecise on essential theoretical points. Because it is
common and coarse I call it the Vulgar Copenhagen Interpretation.
In section 4 the unusual causal structure of quantum theory is discussed,
and is used to justify, in the context of trying to understand the role of
mind in nature: 1) the rejection of the classical ontology, 2) the
reasonableness of attempting to ontologicalize the orthodox interpretation
of quantum theory, and 3) the expectation that our knowings involve
non-local aspects.
Section 5 is entitled ``All roads lead to Solvay 1927''. The 1927
Solvay conference, seventy years ago, marked the birth of the orthodox
Copenhagen interpretation of quantum theory. In this section I review
this Symposium from a certain point of view, namely the viewpoint that
many of the highlights of the Symposium confirm the basic message of
the orthodox interpretation, namely that the only reasonable way to
make rational sense out of the empirical data is to regard nature as
being built out of knowings. I argue that the experience of the last
seventy years suggests the reasonableness of taking this
interpretation seriously: more seriously than the founders of quantum
theory took it. Basically, they said, cautiously, that the
mathematical formalism is a useful tool for forming expectations about
our future knowings on the basis of our past ones. That claim has been
now been abundantly confirmed, also in fields far beyond the narrow
confines of atomic physics. But the founders scrupulously avoided any
suggestion that this mathematical formalism corresponded to
reality. They either discouraged us from asking questions about what
is really happening, or, if pressed, looked for reality not in their
own knowledge-based formalism, but in terms of more conventional
physical terms. This reluctance to take their own formalism seriously
was, I think, the result partly of an inertial carry-over from
classical physics, which shunned and excluded any serious
consideration of mind in physics, and partly of a carry-over of an
idea from the special theory of relativity. This is the idea that no
influence or signal could propagate faster than light. However, in
quantum theory there is a sharp distinction between signal and
influence, because it can be proved both that no signal can be
transmitted faster than light, and that this property cannot be
imagined to hold for influences. The distinction between signal and
influence has to do with the difference between the causal structure
of the deterministic evolution of the {\it statistical predictions of
the theory} and the causal structure of something that has no analog
in classical mechanics, namely the {\it selection process} that acts
within the deterministic structure that is the analog of the classical
deterministic structure, but that is not fully determined by that
structure.
In cosmological solutions in general relativity there is usually a preferred
set of advancing spacelike surfaces that provide a natural definition of
instantaneousness. Also, there is the empirical cosmological preferred frame
defined by the background black-body radiation. So the idea of special
relativity that there is no preferred frame for the universe, although it
may indeed hold for the formulation of the general local-deterministic
laws, is not as compelling now as it was in 1905, or even 1927: that idea
could very well break down in our particular universe at the level of the
selection of particular individual results (knowings). Indeed, I believe it
{\it must} break down at that level. (Stapp, 1997)
So I propose to take seriously the message of Solvay 1927, that nature be
understood as built out of knowings. But we must then learn how better to
understand knowings, within the mathematical framework provided by the
quantum formalism.
In section 6 I distinguish the two different components of the quantum
mechanical evolutionary process, the unitary/local part and the nonunitary/
nonlocal part, and note that our conscious knowings, as they occur in the
quantum description, enter only into the latter part. But that part is
eliminated when one takes the classical approximation to the quantum
dynamics. Thus from the perspective of quantum mechanics it would be
irrational to try to find consciousness in a classical conception of
nature, because that conception corresponds to an approximation to the basic
dynamics from which the process associated with consciousness has been
eradicated.
I note there also that the ontologicalization of the quantum mechanical
description dissolves, or at least radically transforms the mind-matter
dualism. The reason is this: in the classical theory one specifies at the
outset that the mathematical quantities of the theory represent the physical
configuration of matter, and hence one needs to explain later how something
so seemingly different from matter as our conscious knowings fit in. But in
the quantum case one specifies from the outset that the mathematical
quantities of the theory describe properties of knowings, so there is no
duality that needs explaining: no reality resembling the substantive matter
of classical physics ever enters at all. One has, instead, a sequence of
events that are associated from the outset with experiences, and that
evolve within a mathematically specified framework.
Section 7 lays out more explicitly the two kinds of processes by showing how
they can be considered to be evolutions in two different time variables,
called process time and mathematical time.
Section 8 goes into the question of the ontological nature of the ``quantum
stuff'' of the universe.
In the sections 9 and 10 I describe the proposed ontology. It brings
conscious knowings efficaciously into quantum brain dynamics. The basic
point is that in a theory with objectively real quantum jumps, some of which
are identifiable with the quantum jumps that occur in the orthodox
epistemological interpretation, one needs three things that lie beyond what
orthodox quantum theory provides:
\noindent 1. A process that defines the conditions under which these jumps
occur, and the possibilities for what that jump might be.
\noindent 2. A process that selects which one of the possibilities actually
occurs.
\noindent 3. A process that brings the entire universe into concordance with
the selected outcome.
Nothing in the normal quantum description of nature in terms of vectors in
Hilbert space accomplishes either 1 or 2. And 3 is simply put in by hand. So
there is a huge logical gap in the orthodox quantum description, if
considered from an ontological point of view. {\it Some extra process, or
set of processes, not described in the orthodox physical theory, is needed.}
I take a minimalistic and naturalistic stance, admitting only the least
needed to account for the structure of the orthodox quantum mechanical
rules.
In appendix A I show why the quantum character of certain synaptic processes
make it virtually certain that the quantum collapse process will exercise
dominant control over the course of a conscious mind/brain processes.
\vskip .1in
\noindent {\bf 2. The subjective character of the orthodox interpretation of
quantum mechanics.}
In the introduction to his book ``Quantum theory and reality'' the
philosopher of science Mario Bunge (1967) said: ``The physicist of the
latest generation is operationalist all right, but usually he does not
know, and refuses to believe, that the original Copenhagen interpretation
--- which he thinks he supports --- was squarely subjectivist, i.e.,
nonphysical.''
Let there be no doubt about this.
Heisenberg (1958a): ``The conception of objective reality of the elementary
particles has thus evaporated not into the cloud of some obscure new reality
concept but into the transparent clarity of a mathematics that represents no
longer the behavior of particles but rather our knowledge of this
behaviour.''
Heisenberg (1958b): ``...the act of registration of the result in the mind
of the observer. The discontinuous change in the probablitity function...
takes place with the act of registration, because it is the discontinuous
change in our knowledge in the instant of registration that has its image
in the discontinuous change of the probability function.''
Heisenberg (1958b:) ``When old adage `Natura non facit saltus' is used as a
basis of a criticism of quantum theory, we can reply that certainly our
knowledge can change suddenly, and that this fact justifies the use of the
term `quantum jump'. ''
Wigner (1961): ``the laws of quantum mechanics cannot be formulated...without
recourse to the concept of consciousness.''
Bohr (1934): ``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.''
In his book ``The creation of quantum mechanics and the Bohr-Pauli
dialogue'' (Hendry, 1984) the historian John Hendry gives a detailed account
of the fierce struggles by such eminent thinkers as Hilbert, Jordan, Weyl,
von Neumann, Born, Einstein, Sommerfeld, Pauli, Heisenberg, Schroedinger,
Dirac, Bohr and others, to come up with a rational way of comprehending the
data from atomic experiments. Each man had his own bias and intuitions, but
in spite of intense effort no rational comprehension was forthcoming.
Finally, at the 1927 Solvay conference a group including Bohr, Heisenberg,
Pauli, Dirac, and Born come into concordance on a solution that came to be
called ``The Copenhagen Interpretation''. Hendry says: ``Dirac, in
discussion, insisted on the restriction of the theory's application to our
knowledge of a system, and on its lack of ontological content.'' Hendry
summarized the concordance by saying: ``On this interpretation it was
agreed that, as Dirac explained, the wave function represented our
knowledge of the system, and the reduced wave packets our more precise
knowledge after measurement.''
Certainly this profound shift in physicists' conception of the basic nature
of their endeavour, and the meanings of their formulas, was not a frivolous
move: it was a last resort. The very idea that in order to comprehend atomic
phenomena one must abandon physical ontology, and construe the mathematical
formulas to be directly about the knowledge of human observers, rather than
about the external real events themselves, is so seemingly preposterous that
no group of eminent and renowned scientists would ever embrace it except as
an extreme last measure. Consequently, it would be frivolous of us simply to
ignore a conclusion so hard won and profound, and of such apparent direct
bearing on our effort to understand the connection of our knowings to our
bodies.
Einstein never accepted the Copenhagen interpretation. He said: ``What does
not satisfy me, from the standpoint of principle, is its attitude toward
what seems to me to be the programmatic aim of all physics: the complete
description of any (individual) real situation (as it supposedly exists
irrespective of any act of observation of substantiation).'' (Einstein,
1951, p.667) and ``What I dislike in this kind of argumentation is the
basic positivistic attitude, which from my view is untenable, and which
seems to me to come to the same thing as Berkeley's principle, {\it esse est
percipi}. (Einstein, 1951, p. 669). Einstein struggled until the end of his
life to get the observer's knowledge back out of physics. But he did not
succeed! Rather he admitted that: ``It is my opinion that the contemporary
quantum theory...constitutes an optimum formulation of the [statistical]
connections.'' (ibid. p. 87). He referred to: ``the most successful physical
theory of our period, viz., the statistical quantum theory which, about
twenty-five years ago took on a logically consistent form. ... This is the
only theory at present which permits a unitary grasp of experiences
concerning the quantum character of micro-mechanical events.'' (ibid p. 81).
One can adopt the cavalier attitude that these profound difficulties with
the classical conception of nature are just some temporary retrograde
aberration in the forward march of science. Or one can imagine that there is
simply some strange confusion that has confounded our best minds for seven
decades, and that their absurd findings should be ignored because they do
not fit our intuitions. Or one can try to say that these problems concern only
atoms and molecules, and not things built out of them. In this connection
Einstein said: ``But the `macroscopic' and `microscopic' are so
inter-related that it appears impracticable to give up this program [of
basing physics on the `real'] in the `microscopic' alone.'' (ibid, p.674).
The examination of the ``locality'' properties entailed by the validity of
the predictions of quantum theory that was begun by Einstein, Podolsky, and
Rosen, and was pursued by J.S. Bell, has led to a strong conclusion (Stapp,
1997) that bears out this insight that the profound deficiencies the
classical conception of nature are not confinable to the micro-level. This
key result will be discussed in section 4. But first I discuss the reason
why, as Mario Bunge said: ``The physicist of the latest generation is
operationalist all right, but usually he does not know, and refuses to
believe, that the original Copenhagen interpretation --- which he thinks he
supports --- was squarely subjectivist, i.e., nonphysical.''
\vskip .1in
\noindent{\bf 3. The Vulgar Copenhagen Interpretation.}
Let me call the original subjectivist, knowledge-based Copenhagen
interpretation the ``strict'' Copenhagen interpretation. It is pragmatic in
the sense that it is a practical viewpoint based on human experience,
including sensations, thoughts, and ideas. These encompass both the
empirical foundation of our physical theories and the carrier of these
theories, and perhaps all that really matters to us, since anything that
will never influence any human experience is, at least from an
anthropocentric viewpoint, of no value to us, and of uncertain realness.
Nevertheless, the prejudice of many physicists, including Einstein, is that
the proper task of scientists is to try to construct a rational theory of
nature that is not centered on such a small part of the natural world as
human experience.
The stalwarts of the Copenhagen interpretation were not unaware of the
appeal of that idea to some of their colleagues, and they had to deal with
it in some way. Thus one finds Bohr(1949) saying, in his contribution
`Discussion with Einstein' to the Schilpp(1951) volume on Einstein:
\noindent ``In particular, it must be realized that---besides in the account
of the placing and timing on the instruments forming the experimental
arrangement---all unambiguous use of space-time concepts in the description
of atomic phenomena is confined to the recording of observations which
refer to marks on a photographic plate or similar practically irreversible
amplification effects like the building of a water drop around an ion in a
cloud-chamber.''
\noindent and,
\noindent ``On the lines of objective description, it is indeed more
appropriate to use the word phenomenon to refer only to observations
obtained under circumstances whose description includes an account of the
whole experimental arrangement. In such terminology, the observational
problem in quantum physics is deprived of any special intricacy and we are,
moreover, directly reminded that every atomic phenomena is closed in the
sense that its observation is based on registrations obtained by
means of suitable amplification devices with irreversible functioning such
as, for example, permanent marks on a photographic plate, caused by the
penetration of electrons into the emulsion. In this connection, it is
important to realize that the quantum mechanical formalism permits
well-defined applications referring only to such closed phenomena.''
These are carefully crafted statements. If read carefully they do not
contradict the basic thesis of the strict Copenhagen interpretation that the
quantum formalism is about our observations described in plain language that
allows us to ``tell others what we have done and what we have learned.''
On the other hand, it seems also to be admitting that there really are
events occurring `out there', which are we are observing, but which do not
derive their realness from our observations of them.
Heisenberg (1958) says something quite similar:
\noindent ``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.''
\noindent "Since through the observation our knowledge of the system has
changed discontinuously, its mathematical representation also has undergone
the quantum jump, and we speak of a `quantum jump' .''
\noindent ``A real difficulty in understanding the interpretation occurs
when one asks the famous question: But what happens `really' in an atomic
event?''
\noindent ``If we want to describe what happens in an atomic event, we have
to realize that the word `happens' can apply only to the observation, not to
the state of affairs between the two observations. It [ the word `happens' ]
applies to the physical, not the psychical act of observation, and we may
say that the transition from the `possible' to the `actual' takes place as
soon as the interaction of the object with the measuring device, and
therefore with the rest of the world, has come into play; it is not
connected with the act of registration of the result in the mind of the
observer. The discontinuous change in the probability function, however,
occurs with the act of registration, because it is the discontinuous change
in our knowledge in the instant of recognition that has its image in the
discontinuous change in the probability function.''
All of this is very reasonable. But it draws a sharp distinction between the
quantum formalism, which is about knowledge, and a world of real events that
are actually occurring `out there', and that can be understood as
transitions from the `possible' to the `actual', closed by irreversible
processes when the interaction between the object and the measuring device,
and hence the rest of the world, comes into play.
Yet the extreme accuracy of detailed theoretical calculations [one part in a
hundred million in one case] seems to make it clear that the mathematical
formalism must be closely connected not merely to our knowledge but also to
what is really happening `out there': it must be much more than a mere
representation of our human knowledge and expectations.
I call this natural idea---that the events in the formalism correspond
closely to real ``physical'' events out there at the devices---the Vulgar
Copenhagen Interpretation: vulgar in the sense of common and coarse.
This vulgar interpretation is I think the common interpretation among
practicing quantum physicists: at this symposium some important
experimentalists were, as Mario Bunge suggested, unwilling to believe that
the quantum mechanical formalism was about `our knowledge'. And it is
coarse: the idea of what constitutes an `irreversible' process is not
carefully specified, nor is the precise meaning of `as soon as the
interaction with the object with the measuring device comes into play'.
My aim in this paper is to reconcile the strict and vulgar interpretations:
i.e., to reconcile the insight of the founders of quantum theory that the
mathematical formalism of quantum is about knowledge with the demand of
Einstein that our basic physical theory be a theory of nature herself.
The main obstacle to a rational understanding of these matters is the
faster-than-light action that the quantum formalism seems to entail, if
interpreted at a physical level. If one takes literally the idea that the
quantum event at the device constitutes a real transition from some physical
state of `possibility' or `propensity' to a state of `actuality' then---in
the `entangled states' of the kind studied by Schroedinger, by Einstein,
Podolsky, and Rosen, and by Bell and others---it would seem that the mere
act of making a measurement in one region would, in certain cases, instantly
produce a change in the physical propensities in some far-away region. This
apparent faster-than-light effect is dealt with in the strict Copenhagen
interpretation by denying that the probability function in the formalism
represents anything physical: the formalism is asserted to represent only
our knowledge, and our knowledge of far-away situations can be instantly
changed---in systems with correlations---by merely acquiring information
locally.
This fact that the strict Copenhagen interpretation ``explains away'' the
apparent violations of the prohibition [suggested by the theory of
relativity] of faster-than-light actions is a main prop of that
interpretation.
So the essential first question in any attempt to describe nature herself is
the logical status of the claimed incompatibility of quantum theory with the
idea---from the theory of relativity in classical physics---that no
influence can act backward in time in any frame of reference.
It is of utmost importance to progress in this field that we get this matter
straight.
\vskip .1in
\noindent {\bf 4. Causality, Locality, and Ontology.}
David Hume cast the notion of causality into disrepute. However, when
one is considering the character of a putative law of evolution of a
physical system it is possible to formulate in a mathematically clean way a
concept of causality that is important in contemporary physical theory.
In relativistic physics, both classical and quantum mechanical,
the idea of causality is introduced in the following way:
We begin with some putative law of evolution of a physical system.
This law is specified by picking a certain function called the Lagragian.
A key feature of the possible Lagrangians is that one can modify them by
adding a term that corresponds to putting in an extra-force that acts only
in some small spacetime region R.
The evolution is specified by the ``law'' specified by the chosen
Lagrangian, plus boundary conditions. Let us suppose that boundary
condition is specified as the complete description of ``everything'' before
some ``initial time'' $T_{in}$. The laws then determine, in principle,
``everything'' for all later times.
In classical mechanics ``everything'' means the values of all of the
physical variables that are supposed to describe the physical system
that is being considered, which might be the entire physical universe.
In quantum mechanics ``everything'' means all of the ``expectation values''
of all of the conceivable possible physical observables, where
``expectation value'' means a predicted average value over an
(in principle) infinite set of instances.
To bring in the notion of causality one proceeds as follows. It is possible,
both in classical and quantum theory, to imagine changing incrementally the
Lagrangian that specifies the law of evolution. The change might correspond
to adding extra terms to the forces acting on certain kinds of particles if
they are in some small spacetime region R that lies later than time
$T_{in}$. Such a change might be regarded as being introduced whimsically by
some outside agent. But, in any case, one can compare the values of
``everything'' at times later than time $T_{in}$ in the new modified world
(i.e., the world controlled by the new modified Lagrangian) to the values
generated from the laws specified by the original Lagrangian. If one is
dealing with an idealized world without gravity, or at least without any
distortion of the `flat' Minkowsky spacetime, then it is a mathematical
property of relativistic field theories, both classical and quantum
mechanical, that ``nothing'' will be changed outside the forward light cone
of the region R in which the Lagrangian was changed!
In other word, ``everything'' will be exactly the same in the two cases
at all points that cannot be reached from the spacetime region R without
moving faster than the speed of light.
This property of relativistic field theories is called a causality property.
The intuition is that this change in the Lagrangian can be regarded, or
identified, as a ``cause'', because it can be imposed whimsically from
outside the physical system. The mathematical property just described says
that the effects of this ``cause'' are confined to its forward light cone;
i.e., to spacetime points that can be reached from the spacetime region R of
the cause without ever traveling at a speed greater than the speed of
light.
Relativistic field theories are formulated mathematically in such a way
that this causality property holds. This means that insofar as it is
legitimate to imagine that human beings can ``freely choose'' [i.e., can
act or not act upon a physical system without there being any
cause {\it from within that physical system} of this act] to do one thing
or another in a region $R$ [e.g., to exert or not exert a force on some
physical particles of the system in region $R$] then ``everything'' outside
the forward light cone of $R$ will be independent of this choice: i.e.,
``everything'' outside this forward light cone will be left unaltered
by any change in this choice.
This relativistic causality property is a key feature of relativistic
field theories in flat Minkowsky spacetime: it is all the causality that
the orthodox pragmatic quantum philosophy calls for.
But notice that by ``everything'' one means, in the quantum case,
merely the ``expectation values'', which are averages over an (in
principle) infinite ensemble of instances.
Now, one might think that since this relativistic causality property
holds for these averages it ought to be {\it at least conceivably
possible} that it could hold also for the individual instances.
But the amazing thing is that this is not true! It is not logically
possible to impose the no-faster-than-light condition in the individual
instances, and maintain also the validity of certain simple predictions of
quantum theory.
The point is this. Suppose one considers an experimental situation involving
two experimental regions that are spacelike separated from each other. This
means that no point in either region can be reached from any point in the
other without traveling faster than the speed of light. In the first region
there is an experimenter who can freely choose to do one experiment or
another. Each of these two alternative possible experiments has two
alternative possible outcomes. There is a similar set up in the second
region. Each possible outcome is confined to the associated experimental
region, so that no outcome of an experiment in one region should be
able to be influenced by the free choice made by the experimenter in the
other region.
One single instance is considered, but with the two free choices of the two
experimenters being treated as two free variables. Thus the one single
instance under consideration, uniquely fixed at all times earlier than the
earliest time in either of the two experimental regions, will go into one or
another of altogether $(2\times 2)=$ four alternative possible evolutions of
this system, depending on which of the two alternative possible choices is
made by each of the two experimenters. There can then be further branchings
that are specified by which of the possible outcomes nature selects for
whichever experiments are performed.
The particular experimental details can be arranged so that the assumed
validity of the predictions of quantum theory for that particular
arrangement entails the {\it nonvalidity} of at least one of the three
following locality conditions:
{\bf LOC1:} It is possible to impose the following condition: If in each of
the two regions the first of the two possible experiments were to be
performed, and a certain result $r$ appeared in the first region then
if this very same experiment were to be performed in the first region
then this same result $r$ would appear there even if the experimenter in
the second region were to elect at the last moment to do the other
measurement.
The rationale for this locality condition is that a free choice of what to
do in one place cannot---relativity theory leads us to believe--- affect, at
a speed faster than the speed of light, what occurs elsewhere: making a
different choice in one region should not be able to force what appears (at
the macroscopic, observable level) in the other region to be different.
Indeed, in some frame of reference the outcome in the first region has
already occurred before the experimenter in the second region makes his free
choice of which experiment he will perform. But, according to ideas from
relativity theory, what someone has already seen and recorded here at some
earlier time cannot be disturbed by what a faraway experimenter freely
chooses to do at some later time.
Notice that LOC1 requires only that it be possible to impose this condition.
The point is that only one of the two possible experiments can actually be
performed in the second region, and hence nature herself will make only one
choice. So what would actually appear in the first region if the
experimenter in the other (far away) region were (at some future time) to
make a different choice in not physically well defined. Thus this is a
theoretical investigation: the question is whether the predictions of QT
are compatible with the notion that nature evolves in such a way that what
one observer sees and records in the past can be imagined to be fixed
independently of what another person will freely choose to do in the future.
{\bf LOC2:} Suppose, under the condition that the first of the two possible
measurements were to be performed in the first region (with no condition
imposed on what the outcome there is) that one can prove from LOC1 and the
predictions of quantum theory, the truth of a statement $S$ that pertains
exclusively to what experimenters can observe under various possible
conditions of their own making in the second region. Then this locality
condition asserts that it is logically possible to demand that $S$ remain
true under the condition that the experimenter in the first region freely
chooses (say in the future) to perform there, instead, the second possible
measurement.
The rationale is that, according to certain ideas from the theory of
relativity, the truth of a statement that pertains to macroscopic conditions
that refer exclusively to one space-time region should not depend on what
someone far away freely chooses to do later.
{\bf LOC3} This is another form of LOC1: Altering the free choice in R
leaves any outcome in L undisturbed. [See Stapp, 1997]
The validity of the predictions of quantum theory in correlation situations
like this are being regularly borne out. (...Most recently in a highly
publicized experiment using the Swiss telephone company optical fibers to
connect experimental regions that were 14 km apart, with the intent of
making important practical applications.) Thus it can, I believe, be
confidently assumed that the pertinent quantum predictions are valid. But in
that case one of the ``locality conditions'' described above {\it must} fail.
Before drawing any conclusions one must consider the impact or significance
of the assumption that the experimenters' choices can be treated as ``free
variables''.
It is part of the orthodox quantum philosophy that the experimenters'
choices can and should be considered to stand outside the physical system
that is being examined. Bohr and Heisenberg argued that biological systems
in general lie outside the domain covered by the pragmatic framework. But
in any case, one thing is certain: the beautiful and elegant quantum
formalism is naturally suited to the idea that it represents a system that
is part of a bigger system that can extract information from it, where the
nature of the information being extracted from the subsystem is controlled
by things outside that subsystem, namely the observer and his instruments of
observation.
But even at a more intuititive level it seems that the decision-making
process of human experimenters are so complex and delicate, and so
insulate-able in principle, prior to the time of the examination,
from the system that they are about to examine, as to render their choices
as to what to look for effectively free, under appropriate conditions of
isolation, from any influence upon them {\it by the system they are about to
examine}. So it would seem to be safe, under appropriate conditions of
prior isolation, to treat these choices {\it as if they were free from such
influences} even in a strictly deterministic universe.
In a quantum universe this move is even more reasonable, because the
choices could be governed by a quantum process, such as the decay of a
radio-active nucleus. Within the quantum theoretical framework each
such decay appears as a spontaneous random event. It is free of any
``physical'' cause, where ``physical'' means something that is part of
the physical world as that world is described by the physical theory.
Thus within both the deterministic and stochastic contexts it seems
reasonable to treat the choices to be made by the experimenters as if
they were free, in the sense of not being influenced by the physical
properties of the system that is about to be examined.
One caveat. The arguments require that meaning be given to
a condition such as: ``If the experimenter in region one performs
experiment one, and the outcome that occurs there is outcome one''.
This condition is nonsensical in the Everett many-minds interpretation,
because {\it every} outcome occurs. I have excluded that interpretation
from consideration on other grounds, which are described in section 5.
The apparent failure of the locality condition has three important
consequences:
1. It gives a solid basis for the conclusion of the founders of quantum
theory that no return to the notions of classical mechanics
(relativistic field theory) is possible: the invalid locality property
certainly holds in relativistic classical mechanics.
2. It makes reasonable the attempt to ontologicalize the orthodox
interpretation. It had formerly been believed that this was a nonsensical
thing to try, because ontologicalization immediately entails
faster-than-light transfer of information on the individual-instance
level. Such transfers had seemed unacceptable, but are now seen to be
unavoidable even in a very general framework that maintains merely the
validity of the {\it predictions} of quantum theory, and the idea that
the experimenters' choices can be considered to be ``free'', in the weak
sense discussed above.
3. Because the nonlocal effects enter into orthodox quantum theory
specifically in connection with the entry of our knowings into the
dynamics there is prima facie evidence that our knowings may be
associated with the nonlocal aspect of nature. It is worth noting that
these effects are not confined to a microscopic scale: in the Swiss
experiment the effect in question extended over a separation of 14km.
And, according to quantum theory, the effect does not fall off at all
with distance. In my proposal each of our knowings is associated with a
brain event that involves, as a unit, a pattern of brain (e.g., neuronal)
activity that may extend over a large part of the brain. The collapse
actualizes this whole pattern, and the associated knowing is an
expression of the functional properties of this pattern.
Once the reality is recognized to be knowledge, rather than substantive
matter, the nonlocal connections seem less problemmatic: nothing but
knowledge about far-away knowings is changed by nearby knowings.
\vskip .1in
\noindent {\bf 5. All Roads Lead to Solvay 1927.}
The Solvay conference of 1927 marks the birth of (coherently formulated)
quantum theory. Two of the many important papers delivered there stand out.
Born and Heisenberg presented a paper on the mathematical formalism and
proclaimed that the essential features of the formalism were complete and
not subject to further revision.
Dirac gave a paper on the interpretation, and claimed
that ``the wave function represents our knowledge of the system, and the
reduced wave packets our more precise knowledge after measurement.''
These two parts, the mathematical formalism and its interpretation
in terms of knowledge, meshed perfectly: that was the logical basis of the
Copenhagen interpretation.
This was an epic event in the history of human thought. Since the time of
the ancient Greeks the central problem in understanding the nature of
reality, and our role in it, had been the puzzling separation of nature into
two seemingly very different parts, mind and matter. This had led to the
divergent approaches of idealism and materialism. According to the precepts
of idealism our ideas, thought, sensations, and other experiential realities
should be taken as basic. But then the mathematical structure carried by
matter was difficult to fathom in any natural way. Materialism, on the other
hand, claimed that matter was basic. But, if one started with matter then
it was difficult to understand how something like your experience of the
redness of a red apple could be constructed out of it, or why the
experiential aspect of reality should exist at all if, as classical
mechanics avers, the material aspect is dynamically complete by itself.
There seemed to be no rationally coherent way to comprehend the relationship
between our experiences of the reality that exists outside our thoughts, and
the nonexperiential-type material substance that the external reality was
claimed to be made of.
Yet at the Solvay meeting, physicists, of all people, had come up with a
perfect blending, based on empirical evidence, in which the mathematical
structure needed to account for all of the empirical regularities formerly
ascribed to substantive matter, was present without there being anything
like substantive matter: the mathematical structure was a property of
knowings!
What an exhilerating moment it must have been. Driven simply by the need to
understand in a rational way the empirical facts that nature had presented
to us, scientists had been led to a marvelous resolution of this most
fundamental of all philosophical problems. It was a tremendous achievement.
Now, seventy years later, we are able to gather here at the X-th Max Born
Symposium to celebrate the unbroken record of successes of that profound
discovery, and to hear about its important new triumphs.
So now, the end of our Symposium, I take this opportunity to review briefly
some of its highlights from the perspective of the Solvay breakthough.
Probably the most exciting reports were from experimentalists who are now
performing experiments that could only be imagined seventy years ago. Yet
the thinking of the founders of quantum theory did involve ``gedanken''
experiments designed to confirm the rational coherency of the framework.
Today these ``thought'' experiments involving preparations and measurements
on small numbers of individual atoms are being carried out, and the results
invariably confirm all of the ``quantum weirdness'' that the Copenhagen
interpretation predicted.
But do these successes really confirm the radical ideas of Solvay 1927? Time
has eroded the message of Solvay to the extent that the scientist performing
the experiments hardly recognize the Solvay insights in the interpretation
of their work, though they give lip service to it. One must probe into the
rational foundations of the subject to see the import of their results on
this deep question.
I cite first the report of Omnes. There had been hope that some way around
the Copenhagen interpretation would emerge from the studies of decoherence
and consistent histories that have been so vigorously pursued of late. No
one has pursued these ideas more deeply than Omnes. His verdict is that
these methods amount to ``the Copenhagen interpretation `done right' ''. He
said similar things in his book (Omnes, 1994). And such prominent proponents
of ``decoherence'' as Zurek(1986) and Joos(1986) have said similar things:
Zurek concluded that the study of decoherence ``constitutes a useful
addition to the Copenhagen ...a clue pointing at a still more satisfactory
resolution of the measurement problem...a hint about how to proceed rather
than the means to settle the matter quickly.'' Joos asks at the beginning
of his article ``Is there some way, at least a hint, how to understand... ''
and at the end says ``one may hope that these superselection rules can be
helpful in developing new ideas ..[about].. measurement processes.'' So they
both stressed that decoherence effects do not resolve the deep problems.
Indeed, decoherence is rather the {\it cause} of the problem: decoherence
effects make it virtually impossible to empirically determine whether
quantum collapses are occurring outside our brains or not. It is precisely
{\it because} of decoherence effects that we cannot tell, empirically,
whether or not collapses actually do occur ``when the interaction of the
object with the measuring device, and hence the rest of the world, comes
into play''.
The decoherence-consistent-histories approach had originally been pursued
within the Everett framework, and indeed was sometimes called the
`post-Everett' approach to stress that it was being pursued within that
framework, rather than the Copenhagen framework, which it sought to unseat.
But Omnes put his finger on the fatal flaw in the Everett approach when he
said that it did not explain the transition from ``and'' to ``or''. In the
evolving wave function of Everett the various branches do evolve
independently, and hence might naturally be imagined to have different
``minds'' associated with them, as Everett suggests. But these branches, and
the minds that are imagined to be properties of these branches, are all
simultaneously present. Hence there is no way to give meaning to the notion
that one mind is far more likely to be present at some finite time than the
others. It is like waves on a pond: the big waves and the small ones are all
present simultaneously. So one needs something else, perhaps like a surfer
that will be pushed into one branch or the other, to define the ``or'' that
is logically needed to define the notion of the probabilities of the
different ``alternatives''. Yet the Everett interpretation allows nothing
else besides the wave function and its properties. So all the minds are
simultaneously present because all the corresponding properties of the
various branches are simultaneously present.
The idea of the surfer being pushed by the wave is exactly the idea behind
the model of David Bohm that was so ably expounded here by D. Duerr and by
F. Faisal. But the model has not been consistently extended to the
relativistic case of quantum electrodynamics, or to quantum chromodynamics,
which are our premiere quantum theories.
The model has other unpleasant features. One is the problem of the empty
branches. Each time a ``good measurement'' is performed the wave function
must separate into different ``branches''. These branches are parts of the
wave function such that the full wave function is a sum (i.e.,
superposition) of these branches, and each branch is nonzero only in a
region (of the 3n-dimensional space in which these wave functions live) that
overlaps none of the other regions. Here n is the number of particles in the
universe.
If two branches separate then the `surfer' (which in the Bohm model would be
the entire classically described physical world) must end up in just one of
these branches. But all the other branches (which are regarded as physically
real) must continue to evolve for all eternity without ever having any
effect upon the `surfer', which is the only part of reality that is directly
connected to human experience, according to the model. This seems wildly
extravagant! If the surfer is the important thing then the effort of nature
to continue to evolve these ineffectual branches for all eternity seems to
be a gigantic waste of effort. But if the surfer is not important then why
is this tiny part of reality there at all? It does nothing but get pushed
around.
There is a perhaps bigger problem with the initial conditions. The model is
predicated on the premise that the single real classical world is a random
element in a statistical ensemble of possibilities. The idea of a
statistical ensemble makes good sense when we have the possibility of
repeated preparations of similar situations. But when we are speaking about
the entire universe it does not seem to make sense to speak of a particular
statistical ensemble of universes with some particular density (weight)
function if only one of them is ever created. Or are we supposed to think
that a whole ensemble of real classical worlds is created, and that ``our''
real world is just one of them? That would seem to be the more natural
interpretation. But I asked David Bohm about that, many years ago, and he
insisted that there was, according to his thinking, only one universe.
Bohm was stimulated to construct his model by conversations with Einstein.
Yet Einstein rejected the model, calling it ``too cheap''.
I asked Bohm what he thought about Einstein's evaluation, and he said he
completely agreed.
Indeed, at the end of his book with Hiley about his model, after finishing
the part describing the model, he added two chapters about going beyond the
model. He motivated those chapters by references to the efforts that I was
making, and that Gell-mann and Hartle were making, to go beyond the
Copenhagen interpretation. Gell-mann and Hartle were pursuing the
decoherence-consistent-histories approach mentioned above, which has led
back to Solvay, and I had proposed a theory of events. The events were real
collapses of a wave function that was considered to be ontologically real.
This brings me to the talk of Rudolf Haag. Haag described his theory of
events, and mentioned that it still needed twenty years of work. In his
written account Haag(1996) mentions that I had proposed essentially the same
theory in the seventies, some twenty years ago (Stapp, 1975, 1977, 1979).
{\it My} twenty years of work on this idea has lead back to Solvay 1927. The
problem is always the same: if one wants to make natural use of what nature
has told us, namely that the beautiful mathematical formalism works to high
precision, then one is led to ascribe to that formalism some ontological
reality. But then the condition for the collapses must be spelled out in
detail.
It is natural for physicists to try to find {\it purely physical}
conditions. But in the end there are no adequate natural conditions of this
kind: the possibilities are all unnatural and ad hoc. Von Neumann said it
all when he showed, back in the thirties, that one could push the boundary
between the world described by the quantum formalism and the world
described in terms our classical concepts all the way to the boundary
between brain and mind without disrupting the predictions of quantum
theory, and noted that there is no other natural place to put the boundary,
without disrupting the integrity of the theory. In fact, it is, in
principle, {\it only} if one pushes the boundary all way to the brain-mind
interface that one obtains, strictly, the prediction of orthodox quantum
theory: otherwise there are rogue collapses that are not associated with
knowings.
Of course, pushing the boundary all the way to mind brings mind into our
theory of nature. But why on earth should we try to keep mind out--- bottled
up, ignored, and isolated from the physical world---when we know it is
present, and seemingly efficacious, particularly when the intense struggle
of physicists to find a rational way of accounting for the observed
phenomena led them to the conclusion that the theory of physical reality has
the form of a theory about knowings, not the form of a theory about matter.
Our aim should be not to bring back moribund matter, which we are well rid
of, but to learn how better to understand knowings, within the mathmatical
framework provided for them by the quantum formalism.
\vskip .1in
\noindent {\bf 6. The Two Quantum Processes.}
There have been many attempts by physicists to `get mind back out of
physics': i.e., to reverse the contamination of physics brought in by Bohr,
Heisenberg, Dirac, Pauli and company in 1927. I believe those
decontamination efforts have failed, even though I myself have worked hard
to achieve it. So I am taking here the other tack, and trying to build a
coherent ontology around the orthodox ideas. In particular, I am accepting
as basic the idea that there are knowings, and that each such knowing occurs
in conjunction with a collapse of the wave function that reduces it to a
form concordant with that knowing. I assume that knowings are not associated
exclusively with human body/brains. But I shall focus here on these
particular kinds of knowings because these are the ones we know most about.
A fundamental fact of orthodox quantum theory is that the evolution of the
state of the physical system between the collapse events is mathematically
very different from the evolution of this state associated with the
collapses: the former are ``unitary'' and ``local'', whereas the latter are
neither.
The ``unitarity'' property means several things. On the one hand, it means
that the evolution is in some sense no change at all: the internal or
intrinsic structure of the state is unaltered. One can imagine that only the
`mode of description' of the state is changed, not the state itself. Indeed,
that point of view is very often adopted in quantum theory, and is the one I
shall adopt here. (See the next section.)
The ``unitarity'' property also means that the transformation operator that
changes the state at an earlier time to the state at a later time does not
depend on that initial (or final) state: there is, in this sense,
in connection with the unitary part of the process of evolution,
{\it no self reference!}
According to the orthodox interpretation, there is no experiential reality
associated with the unitary part of the evolution, which is the part between
the observations: there is no essential change, and no self reference, and
hence, reasonably enough, no experience.
Experiences are associated only with the nonunitary parts of the evolution:
the part associated with observations. For that part there {\it is}
essential change, and the transformation operator analogous to the one
defined for the unitary case would depend on the state upon which it acts.
Thus there would be, in this sense, self-reference. This self reference
(nonlinearity) plays a key role in the dynamics associated with observation.
It is a special kind of self reference that has no counterpart in classical
mechanics.
In the classical approximation to the quantum dynamics only the unitary
part of the dynamical evolution survives. So from a quantum mechanical
point of view it would be nonsensical to look for mind in a system
described by classical physics. For classical physics is the result of an
approximation to the full dynamical process of nature that eliminates the
part of that process that orthodox quantum theory says is associated with
our experiences.
\vskip .1in
\noindent {\bf 7. The Two Times: Process Time and Mathematical Time}
The distinctions between the two processes described above is central to
this work. It can be clarified, and made more vivid, by explaining how
these two processes can be considered to take place in two different times.
In quantum theory there are two very different kinds of mathematical
objects: vectors and operators. Operators operate on vectors:
the action of an operator on a vector changes it to another (generally
different) vector.
Given an operator, and a vector that represents a state of a physical
system (perhaps the entire universe), a number is formed by first letting
the operator act on the vector, and then multipling the resulting vector
by the (complex conjugate of the) original vector. This number is called
the ``expectation value of the operator in the state represented by that
vector''.
Modern field theories are generally expressed in the so-called Heisenberg
picture (rather than the so-called Schroedinger picture). I shall follow
that practice.
In ordinary relativistic quantum field theory each spacetime point has a
collection of associated operators. (I gloss over some technicalities
that are not important in the present context.)
Consider the collection of operators $C(t)$ formed by taking all of the
operator associated with all of the spacetime points that lie at
fixed time $t$.
This set $C(t)$ is ``complete'' in the sense that the expectation values of
all the operators of $C(t)$ in a state $S$ determine all the expectation
values of the all the operators in $C(t')$ in the state $S$, for every time
$t'$. The operators in $C(t)$ are related to those in $C(t')$ by a {\it
unitary} transformation. Whether one represents the state $S$ by giving the
expectation values in this state of all the operators in $C(t)$, or of all
the operators in $C(t')$, is very much like choosing to use one coordinate
system or another to describe a given situation: it is just a matter of
viewpoint. The unitary transformation that relates the collection of
operators $C(t)$ to the collection of operators $C(t')$ is essentially the
unitary transformation associated with the Schroedinger-directed temporal
evolution. It is in this sense that the unitary transformation that
generates evolution in the ``mathematical time'' $t$ is relatively trivial.
It is deterministic, continuous, invertible, and independent of the state
$S$ of the physical system upon which the operators act.
But giving the complete set of all the operators associated with all the
points in spacetime says nothing at all about the evolution of the state!
Saying everything that can be said about the operators themselves, and about
evolution via the unitary part of the transformation has merely fixed the
mode of description, and the connections between different modes of
description. It has not said anything about the all-important evolution of
the state.
The state undergoes a sequence of abrupt jumps:
$$...S_i \longrightarrow S_{i+1} \longrightarrow S_{i+2}... .$$
The situation can be displayed graphically by imagining that $i$ is the
imaginary part of the complex time $t$: the evolution proceeds at constant
imaginary part of $t$ equal $i$, and at constant $S_i$, with the
real part of $t$ increasing until it reaches a certain `jump time' $t_i$,
whereupon there is an abrupt quantum jump to a new constant state $S_{i+1}$,
and a new constant imaginary part of $t$ equal to $i+1$, and the evolution
then again proceeds with increasing real part of $t$ until the next `jump
value' $t_{i+1}$ is reached, and then there is another jump up to a new
value, $i+2$, of the imaginary part of $t$. Thus the full process is
represented in complex time as a line having the shape of a flight of steps.
The horizontal segments where the real part of time is increasing
represent the trivial unitary parts of the process, which correspond
merely to changing the viewpoint, or mode of description, with the state
remaining fixed, and with no associated experience. The vertical segments
correspond to increases in `process time'. These are the parts associated
with experience. (This identification of the vertical axis with imaginary
time is purely pedagogical)
The present endeavour is to begin to fill in the details of the process
associated with the increases in the vertical coordinate, process time,
which is the time associated with the nontrivial part of the evolutionary
process, and with experience. The final phase of each vertical segment is
the fixing of a new knowing. But some process in Nature must bring about
this particular fixing: this process is represented by motion along the
associated vertical segment.
\vskip .1in
\noindent {\bf 8. Quantum Ontology}
What is the connection between the our experiences and the physicists'
theoretical description of the physical world?
The materialist position is that each experience {\it is} some aspect of the
matter from which the physicists say the world is built.
But the physical world certainly is not built out of the substantive matter
that was postulate to exist by classical mechanics. Such stuff simply does
not exist, hence our experiences cannot be built out of it.
The quantum analog of physical reality, namely the quantum state S of the
universe, is more like information and ideas than like the matter of classical
physics: it consist of accumulated knowledge. It changes when human knowledge
changes, and is tied to intentionality, as I shall explain presently.
Orthodox classical mechanics is naturally complete in itself:
the physical world represented in it is dynamically complete,
and there is no hint within its structure of the existence of anything else.
Orthodox quantum mechanics is just the opposite: the physical world
represented by it is not dynamically complete. There is a manifest need for
a process that is not represented within the orthodox description.
In orthodox quantum mechanics the basic realities are our knowings. The
dynamics of the physical world represented in the orthodox quantum formalism
is not internally complete because there is, in connection with each
knowing, a collapse process that appears in the orthodox theory as a
``random choice'' between alternative possibilities: contemporary quantum
theory provides no description of the process that selects the particular
knowing that actually occurs.
This collapse process, which is implemented by a nonunitary/nonlocal
transformation, must specify two things that the contemporary machinery of
quantum theory does specify:
\noindent 1. It must specify an experience E, associated with a corresponding
projection operator P(E), such that the question is put to Nature:
``Does E occur?''
\noindent 2. It must then select either the answer `yes', and accordingly
change the current state (i.e., density matrix) S to the state PSP, or
select the answer `no', and accordingly replace S by (1-P)S(1-P). The
probability of answering `yes' is Trace PSP/TraceS; the probability of
answering `no' is Trace (1-P)S(1-P)/Trace S.
In the orthodox pragmatic interpretation the step 1 is achieved by a human
experimenter's putting in place a device whose observed response will
determine whether the system that is being examined has a certain property
specified by P(E): the occurrence of experience E will confirm, basically
on the basis of past experience, that future experiences will be likely to
conform to the answer ``Yes, the system has property P(E).''
According to the orthodox viewpoint, the experimenter stands outside the
quantum system being examined, and the device is regarded as an extension
of himself.
Step 2 is then achieved by appeal to a random selection process
that picks the answer `Yes' or `No' in accordance with a statistical
rule. This selection process (also) is not represented within the orthodox
Hilbert space description.
How can these two steps be comprehended in a rational, minimalistic,
naturalistic way?
\vskip .1in
\noindent {\bf 9. Von Neumann's Process I.}
The first step in the nonunitary process is what von Neumann called
Process I, in contrast to his Process II, which is the normal unitary
evolution.
Process I consists of ``posing the next question". We can suppose that the
possible answers are $Yes$ or $No$. Nature will then answer the question.
The crucial requirement is that the answer $Yes$ must be recognizably
different from the answer $No$, which includes no recognizable answer at
all.
In practice a human being creates the conditions for Process I, and it is he
who recognizes the positive response: this recognition is a knowing.
For example, the observer may know that he is seeing the pointer on the
device---that he himself has set in plac---resting definitely between the
numbers 6 and 7 on the dial. This is a complex thing that he knows.
But knowings can be known, at least in part, by later knowings. This is
the sort of knowing that science is built upon. Of course, all one can
really know is that one's experiences are of a certain kind, not that there
really is a pointer out there. So we expect the knowings to correspond in
some way to a brain activity of some sort, which under normal circumstances
would be an effect of something going on outside the brain.
Von Neumann accepts the statistical character of the theory, and his
Process I is statistical in character: his Process I covers merely the
posing of the question, and the assignment of a statistical weight to each
of the recognizably different alternative possible answers. It does not
cover the subsequent process whereby Nature delivers an answer.
My basic commitment here is to accept the quantum principles as they are,
rather than to invent new principles that would allow us to exclude mind
from Nature's dynamics. So I accept here, ontologically as well as
pragmatically, that {\it the possibilities singled out in Process I are
defined by different `possible knowings'}.
Two important features of the von Neumann Process I are:
1) It produces an abrupt increase in entropy. If the state of the universe
prior to the process is well defined, so that the entropy (with no coarse
graining) is zero, then if, for example, the Process I gives a
statistical mixture with $50\%\ Yes$ and $50\%\ No$, the entropy will
jump to $ln 2$.
2) It is quasi-local. There will be nonlocal aspects extending over the size
of the examined system, but no long-range nonlocal effects of the kind
mentioned in section 3. That is, there will be, for the Process I
associated with a human knowings, brain-sized nonlocal effects associated
with defining the question, but no nonlocal effects extending outside the
body/brain. Thus Process I is, for human knowings, a human process, not a
global one. [Technically, the reason that there is no effect on
far-away
systems is that such an effect is computed by performing a `trace' over
the degrees of freedom of the nearby system (e.g., the brain/body), but
von Neumann's Process I is achieved by dropping out interference terms
between the alternative possible answers, and that operation leaves this
trace unaltered.]
Process I lies at the root of measurement and mind-body problems. In
approaches that try to explain Process I in purely physical terms, with
knowings not mentioned, but rather forced to follow from physically
characterized processes, the answers tend to assert either that:\\ 1), the
wave function of a particle occasionally just spontaneously reduces to a
wave function that is essentially zero except over a small region, or that\\
2), what is not measurable in practice (i.e., via some practicable
procedure) does not exist in principle: if it is impractical to detect an
interference term them it does not exist.
This latter sort of rule is certainly justified in a pragmatic approach. But
most physicists have been reluctant to accept such rules at the ontological
level. Hence the pragmatic approach has won by default.
From the present standpoint, however, the basic principle is that Nature
responds only to questions that are first posed, and whose answers are
possible knowings, or are things of the same general ontological type as
possible knowings. [The needed generalization will be discussed later, after
the knowings themselves have been discussed.]
But the important immediate point is that the quantum dynamics is organized
so as to put knowings, and their possible generalizations, into the central
position.
All such knowings contribute to the general self knowledge of the universe,
which is represented by the (Hilbert-space) state $S$ of the universe.
\vskip .1in
\noindent {\bf 10. Origin of the Statisical Rules}
\vskip .1in
Without loss of generality we can suppose that each posed question is a
single question answered with a single reply, {\it Yes} or {\it No}. Then
the usual (density matrix) formalism allows the reduction process to be
formalized in the following way. The state of the universe is represented by
the density matrix (operator) $S$. The question is represented by the
projection operator $P$: $P^2 = P$. Then the von Neumann Process I is
represented by $$ S\equiv [PSP+(1-P)S(1-P)+PS(1-P)+(1-P)SP] \longrightarrow
PSP + (1-P)S(1-P). $$ The subsequent completion of the reduction is then
represented by $$ [PSP + (1-P)S(1-P)] \longrightarrow PSP \mbox{ or
}(1-P)S(1-P) $$ where the fractions of the instances giving the two results
are: $$ (Tr PSP)/(Tr PSP + Tr (1-P)S(1-P)) \mbox{\ for\ } PSP $$ \noindent
and $$ (Tr (1-P)S(1-P))/(Tr PSP + Tr(1-P)S(1-P)) \mbox{\ for\ } (1-P)S(1-P).
$$ Here Tr represents the trace operation, which instructs one to sum up the
diagonal elements $*$ of the matrix $$ that represents the
operator, for some complete orthonormal set of states $|i>$. [The value of
the trace does not depend upon which complete orthonormal set is used, and,
for any two (bounded) operators $A$ and $B$, $Tr AB = Tr BA$. Using this
property, and $P^2 = P$, one sees that the denominator in the two equations
just given reduces to $Tr S$. A partial trace is given by the same formula,
but with the vectors $|i>$ now forming a complete orthonormal basis for
{\ part} of the full system]
I believe it is perfectly acceptable to introduce an unexplained random
choice or selection in a pragmatically formulated theory. But in a rational
ontological approach there must be some sufficient cause or reason for a
selection to pick out $Yes$ rather than $No$, or vice versa. In view of the
manifestly nonlocal character of the reduction process, there is, however,
no reason for this selection to be determined locally.
Quantum theory does not specify what this selection process is, and I do not
try to do so. But given our ignorance of what this process is, it is highly
plausible that it should give statistical results in accord with the
rules specified above. The reason is this.
If the selection process depends in some unknown way on things outside the
system being examined then the fractions ought to be invariant under a huge
class of unitary transformations $U$ of the state $S$ that leave $P$
invariant, for these transformations are essentially the trivial
rearrangements of the distant features of the universe:
$$
S\longrightarrow USU^{-1} \ \ \ \ \ \ \ U^{-1}PU = P.
$$
Since the statistical description after the Process I has occurred
is essentially similar to the classical statistical description one
should expect $S$ and $P$ (or $(1-P)$) to enter linearly. But the trace
formulas are the only possibilities that satisfy these conditions, for all
$U$ that leave $P$ invariant.
The point here is only that if the actual selection process depends in a
complicated and unknown way on distant uncontrolled properties of $S$ then
the long-term averages should not be sensitive to basically trivial
rearrangements made far away.
This assumption is quite analogous to the assumption made in classical
statistical analysis---which has a deterministic underpinning---that in the
absence of information about the full details one should integrate over
phase space {\it without any weighting factor other than precisely one} in
those degrees of freedom about which one has no information. Thus the
quantum statistical rules need not be regarded as some mysterious property
of nature to have unanalysable {\it tendencies} to make sudden random jumps:
it is rational to suppose, within an ontological setting, that there is a
causal, though certainly nonlocal, underpinning to these choices, but that
we do not yet know anything about it, and hence our ignorance must be
expressed by the uniquely appropriate averaging over the degrees of freedom
about which we have no knowledge.
The effective randomness of Nature's answers does not render the our
knowings nonefficacious. Our knowings can enter the dynamics in a strongly
controlling way {\it through the choice of the questions}, even though the
answers to these questions are effectively random. The formation of the
questions, in Process I, is human based, even though the selection of the
{\it answers} is presumably global. This will be discussed presently.
The theory is naturalistic in that, although there are knowings, there are
no soul-like experiencers: each human stream of consciousness belongs to a
human body/brain, which provides the structure that links the experiences of
that stream tightly together.
\vskip .1in
\noindent {\bf 11. Brains and Experiences.}
\vskip .1in
The dynamics of the theory is organized around the collection of operators
P(E) that connect experiences E to their effects on the state S of the
universe. I describe here my conception of this connection, and of the
dynamical differences between the quantum version of this connection
and its classical analog.
Each experience is supposed to be one gestalt that, like a percept,
``comes totally or not at all'', in the words of Wm. James (1987. p. 1061).
This experience is part of a sequence whose elements are, according to James,
linked together in two ways: each consists of a fringe that changes only
very slowly from one experience to the next, and a focal part that changes
more rapidly. The fringe provides the stable contextual framework. It is
the background that provides both the contextual setting, within which
the foreground is set, and the experience of a persisting historical
self that provides both the backdrop for the focal part and the carrier
of longer term motivations. The focal part has a sequence of temporally
displaced components that, like the rows of a marching band that are
currently in front of the viewing stand, consists of some that are just
coming into consciousness, some that are at the center, and some that are
fading out. The occurrence together, in each instantaneous experience,
of this sequence of temporal components is what allows comparisons to be
made within a conscious experience. Judgments about courses of events
can be parts of an experiences. The experiences are organized in the first
instance, around experiences of the person's body in the context of his
environment, and later also around abstractions from those primitive
elements. These matters are discussed in more detail in chapter VI
of my book (Stapp ,1993).
Each experience normally has a feel that includes an experience of a
prolongation of the current sequence of temporal components: this
prolongation will normally be a prolongation that is, on the basis of
past experience, likely to be imbedded in the ``current sequence of temporal
components'' of some later experience in the linked sequence of experiences.
Each experience E induces a change of the state of the universe S--$>$ PSP.
This change will, I believe, for reasons I will describe presently, be a
specification of the classical part (see below) of the electro-magnetic field
within the brain of the person. This specification will fix the activities
of the brain in such a way as to produce a coordinated activity that will
generally produce, via a causal chain in the physical world (i.e., via
the causal evolution specified by the Schroedinger or Heisenberg equations
of motion) the potentialities for the next experience, $E'$.
That causal chain may pass, via the motor cortex, to muscle
action, to effects on the environment, to effects on sensors, to effects
on the brain, and finally to a set of potentialities for various possible
prolongations of the current sequence of temporal components.
Then a selection must be made: one of the potential experiences will become
actual.
But this description glosses over an essential basic problem: How do the
possible experiences E and the associations E--$>$ P(E) get
characterized and created in the first place. There is an infinite continuum
of projection operators P such that S--$>$ PSP would generate a new state.
Why are some particular P's given favored status, and why are these favored
P's associated with ``experiences''?
This favored status is this: some one of these favored P's will
be picked out from the continuum of possibilities, in conjunction with the
next phase of the dynamical process. This next phase is the putting to
Nature of the question: Does the current state S jump to PSP or not?
To provide some basis for getting the universe going in a way that
tends to produce stable or enduring structure, instead of mere chaotic
random activity, I assume that a basic characteristic of the underlying
dynamics is to select only projectors P that impose a certain repetitiveness
on the dynamical structure. These qualities of repetitiveness are assumed
to be fundamental qualities of the projectors. But each such quality is a
characteristic that is more general in its nature than any
particular realization of it. These general qualities I call ``feels'':
they encompass all human experiences, but extend far beyond.
Thus the basic assumption is that certain projectors P have ``feels'', but most
do not, where a ``feel'' is a generalized version of a human experience. Each
feel is characterized by a quality of repetitiveness, and the actualization
of this feel entails the actualization of some particular realization of that
quality or pattern of repetitiveness within the dynamical structure that
constitutes the universe. This actualization is expressed by the
transformation S--$>$ PSP where P = P(E), and E is the feel: it is the
quality of the repetitiveness that is being actualized.
This general tendency to produce repetitive spatio-temporal patterns
carries over to human experience, and will, I believe, be greatly enhanced
by natural selection within the biological sphere. Thus the selection, from
among the proferred potential experiences, of the next $E'$, will be such as
to favor a sequences E--$>$ P(E)--$>$ $E'$ such that $E'$ is either the same
as E, or at least the same as E in some essential way. Thus experiences, and
their more general ontological cousins, feels, are tied to the generation of
self-reproducing structures. This generation of regenerating/reverberating
stable structures underlies quantum dynamics, in the form of the creation by
the dynamics of stable and quasi-stable particles, and extends beyond human
beings, both to biological systems in general, and even to the overall
organization of the universe, according to the ideas being developed here.
As regards this repetitiveness, it is undoubtedly pertinent that classical
mechanics is formulated basically in space-time, with lawfulness expressed
essentially by a static or quasi-static quality of momentum-energy. But
the essence of the transition to quantum theory is precisely that this
static quality of momentum-energy is replaced by a repetitive quality, by
a characteristic oscillatory behavior': quantum theory is basically about
repetitive regeneration.
In line with all this, I assume that the projection operators P act by
specifying the (expectation values of the) quantum elecromagetic field.
There are many reason for believing that this is the way nature operates:
1. The EM fields naturally integrate the effects of the motions of the
billions of ions and electrons that are responsible for our neural processes.
Thus examining the EM fields provide a natural way of examining the state of
the brain, and selecting a state of the EM field of the brain provides a
natural way of controlling the behavior of the brain.
2. The EM field has marvelous properties as regards connections to classical
physics. The bulk of the low-energy EM state automatically organizes
itself into a superposition of ``coherent states'', each of which is
described by a classical electromagnetic field, and which enjoys many
properties of this classical elecromagnetic field. These ``classical''
states are brought into the dynamical structure in a natural way: the
condition that each actually realized state will correspond to essentially
a single one of these classically describable coherent states is what is
needed to deal effectively, in a physically realistic way, with the
infra-red divergence problem in quantum electro-dynamics.
[See Stapp (1983), and Kawai and Stapp (1995)]
3, These ``classical'' states (coherent states) of the quantum EM field
are robust (not easily disrupted by the thermal and random noises in a
warm wet brain): they are ideal for use in generating self-reproducing
effects in a warm, wet, noisy enviroment. [See Stapp (1987), (1993, p.130),
and Zurek (1993)]
4. These classical states are described by giving the ampitudes in each
of the oscillatory modes of the field: spacetime structure arises from
phase relationships among the different oscillatory modes.
Although the theory being developed here maintains a close connection
to classical physics, its logical and ontological structure is very
different. In classical physics the dynamics is governed entirely by
myopic local rules: i.e., by rules that specify the evolution of everything
in the universe by making each local variable respond only to the physical
variables in its immediate neighborhood. Human experiences are thus
epiphenomenal in the sense that they do not need to be recognized as
entities that play any dynamical role: the local microscopic description,
and the local laws, are sufficient to specify completely the evolution of
the state of physical universe. Experiential gestalts can regarded as
mere effects of local dynamical causes, not as essential elements in the
causal progession.
But the most profound lesson about nature learned in the twentieth century
is that the empirically revealed structure of natural phenomena cannot be
comprehended in terms of any local dynamics: natural phenomena are strictly
incompatible with the idea that the underlying dynamics is local.
The second most profound lesson is that the known observed regularities
of natural phenomena can be comprehended in terms of a mathematical
model built on a structure that behaves like representations of knowledge,
rather than representations of matter of the kind postulated to exist in
classical mechanics: the carrier of the structure that accounts for the
regularities in nature that were formerly explained by classical physical
theory is, according to contempory theory, more idealike than matterlike,
although it does exhibit a precise mathematical structure.
The third essential lesson is that this new description, although complete
in important practical or pragmatic ways, is, as an ontological description,
incomplete: there is room for additional specifications, and indeed {\it an
absolute need for additional specifications} if answers are to be given to
questions about how our experiences come to be what they are. The presently
known rules simply do not fix this aspect of the dynamics. The purpose of
work is to make a first stab at filling this lacuna.
One key point, here, is that brains are so highly interconnected that it will
generally be only large macroscopic structures that have a good chance of
initiating a causal sequence that will be self-reproductive. So each
possible experience E should correspond to a P(E) that creates a macroscopic
repetitiveness in the states of a brain.
A second key point is that our knowings/experiences can be efficacious not
only in the sense that they select, in each individual case, what actually
happens in that case, but also in the statistical sense that the rules that
determine which questions are put to Nature, can skew the statistical
properties, even if the answers to the posed questions follow the quantum
statistical rules exactly. I turn now to a discussion of this point and its
important consequences.
\vskip .1in
\noindent {\bf 12. Measurements, Observations, and Experiences.}
\vskip .1in
A key question is whether, in a warm wet brain, collapses
associated with knowings would have any effects that are different from what
would be predicted by classical theory, or more precisely, by a Bohm-type
theory. Bohm's theory yields all the predictions of quantum theory in a way
that, like classical mechanics, makes consciousness epiphenomenal:
the flow of consciousness is governed deterministically (but nonlocally)
by a state of the universe that evolves, without regard to consciousness,
in accordance with local deterministic equations of motion. Bohm's theory,
like classical physics, tacitly assumes a connection between consciousness
and brain activity, but the details of this connection are not specified.
The aim of the present work is to specify this connection, starting from
the premise that the quantum state of the universe is essentially a
compendium of knowledge, of some general sort, which includes all human
knowledge, as contrasted to something that is basically mechanical, and
independent of human knowledge, like the quantum state in Bohmian
mechanics.
I distinguish a ``Heisenberg collapse'', S--$>$ PSP or
S--$>$ (1-P)S(1-P), from a ``von Neumann collapse'' S--$>$[PSP + (1-P)S(1-P)].
The latter can be
regarded as either a precursor to the former, or a representation of
the {\it statistical} effect of the collapse: i.e., the effect if one
averages, with the appropriate weighting, over the possible outcomes.
This latter sort of averaging would be pertinent if one wanted to examine
the observable consequences of assuming that a certain
physical system is, or alternatively is not, the locus of collapses.
This issue is a key question: Are there possible empirical distinctions
between the behaviors of systems that are---or alternatively are not---
controlled by high-level collapses of the kind that this theory associates
with consciousness. Can one empirically
distinguish, on the basis of theoretical principles, whether collapses
of this kind are occurring within some system that is purported to be
conscious. This question is pertinent both to the issue of whether some
computer that we have built could, according to this theory, be conscious,
and also to the issue of whether our own behavior, as viewed from the outside,
has aspects that reveal the presence of the sort of quantum collapses that this
theory associates with consciousness.
This question about differences in behaviour at the statistical level feeds
also into the issue of whether being conscious has survival value. If
behaviour has, on the average, no dependence on whether or not
collapses occur in the system then the naturalistic idea that consciousness
develops within biological systems due to the enhancement of survival
rates that the associated collapses provide would become nonsense.
Indeed, that idea is nonsense within classical physics, for
exactly this reason: whether conscious thoughts occur in association with
certain physical activities makes absolutely no difference
to the microlocally determined physical behavior of the system.
There are certain cases in which a von Neumann collapse,
S--$>$ [PSP + (1-P)S(1-P)], would produce no observable effects on
subsequent behavior. To understand these conditions let us examine the
process of measurement/observation.
If one separates the degrees of freedom of the universe into those of
``the system being measured/observed'', and those of the rest of the
universe, and writes the state of the universe as
$$
S = |\Psi >< \Psi |
$$
with
$$
|\Psi> = \sum_i \phi_i \chi_i,
$$
where the $\phi_i$ are states of ``the system being measured/observed'',
and the $\chi_i$ are states of the rest of the universe, then since we
observers are parts of the rest of the universe it is reasonable to demand
that if someone can have an experience E then there should be a basis of
orthonormal states $\chi_i$ such that the corresponding projector P(E) is
defined by
$$
P(E) \phi_i = \phi_i
$$
for all $i$,
$$
P(E) \chi_i = \chi_i
$$
for $i$ in $I(E)$, but
$$
P(E) \chi_i = 0,
$$
otherwise, where $I(E)$ is the set of indices $i$ that label those states
$\chi_i$ that are compatible with experience E.
A ``good measurement'' is
defined to be an interaction between the system being measured and the
rest of the universe such that the set of states $\phi_i$ defined above
with $i$ in $I(E)$ span a proper subspace of the space corresponding
to the measured system. In this case the knowledge that
$i$ is in the set $I(E)$ ensures that the state of the measured system
lies in the subspace spanned by the set of states $\phi_i$ with $i$ in
$I(E)$. That is, experience E would provide knowledge about the
measured system.
Let P\_ be the projector that projects onto the subspace spanned
by the set of states $\phi_i$ with $i$ in $I(E)$. Then a von Neumann
collapse with P\_ in place of P would be identical to the von Neumann
collapse S--$>$ [PSP + (1-P)S(1-P)]. But then the observer would be unable to
determine whether a collapse associated with P\_ occurred in the system,
unbeknownst to him, or whether, on the contrary, the definiteness of the
observed outcome was brought about by the collapse associated with his
own experience. This is essentially von Neumann's conclusion.
But why should an actual collapse associated with the measured/observed system
correspond in this special way to a subsequent experience of some human
being? Why should an actually occurring P\_ be such as to ensure an
equivalence between P\_ and a P(E)?
Von Neumann's approach to the measurement problem suggests that such a
connection would exist.
In both the von Neumann and Copenhagen approaches the measuring device
plays a central role. Different perceptually distinguishable locations
of some ``pointer'' on the device are supposed to become correlated, during
an interaction between the measured system and the measuring device, to
different orthogonal subspaces of the Hilbert space of the measured system.
This perceptual distinctness of the possible pointer positions means that
there is a correlation between pointer {\it locations} and experiences. That
connection must be explained by the theory of consciousness, which is
what is being developed here. But why, ontologically, as opposed to
epistemologically, should the projector P\_ in the space of the
measured/observed system be to a state that is tied in this way to
something outside self, namely the {\it location} of a pointer on a measuring
device with which it might have briefly interacted at some earlier time.
Von Neumann did not try to answer this question ontologically.
If the real collapse were in the brain, and it corresponded to seeing the
pointer at some one of the distinguishable locations, then from an
epistemological point of view the effect of this collapse would be equivalent
to applying P\_ to the state of the measured/observed system.
If one works out from experiences and brains, in this way. one can formulate
the collapses in terms of collapses out in the world, instead of inside
the brain, and largely circumvent (rather than resolve) the mind-brain
problem. Then the equivalence of the experience to the collapse at the
level of the measured/observed system would become true essentially by
construction: one defines the projectors at the level of the
measured/observed system in a way such that they correspond to the distinct
perceptual possibilities.
But from a non-subjectivist viewpoint, one would like to have a
characterization of the conditions for the external collapse that do
not refer in any way to the observers.
One way to circumvent the observers is to use the fact that the pointer
interacts not only with observers but also with ``the environment'', which
is imagined to be described by degrees freedom that will never be measured
or observed. The representation of S given above will again hold with
the $\phi_i$ now representing the states of the system being measured plus
the measuring device, and the $\chi_i$ corresponding to states of the
environment.
The interaction between the pointer and the environment should quickly
cause all the $\chi_i$ that correspond to different distinct locations of
the pointer to become orthogonal.
All observable projectors P are supposed to act nontrivially only on the
states $\phi_i$: they leave unchanged all of the environmental states $\chi_i$.But then all observable aspects of the state S reside in tr S, where tr
stands for the trace over the environmental degrees of freedom.
Let $P_i$ be a projector onto an eigenstate of tr S. Suppose one postulates
that each of the allowed projectors P\_ is a sum over some subset of the
$P_i$, or, equivalently that each possible P\_ commutes with tr S, and is
unity in the space of the degrees of freedom of the environment.
This rule makes each allowed P project onto a statistical mixture of pointer
locations, in cases where these locations are distinct. So it give the sort of
P's that would correspond to what observers can observe, without mentioning
observers.
The P's defined in this way commute with S. But then the effect of any
von Neumann reduction is to transform S into S: the von Neumann reduction
has no effect at all. The collapse would have no effect at all on the
average over the alternative possible answers to the question of whether or
not the collapse occurs. This nondependence of the average is of course an
automatic feature of classical statistical mechanics.
The theory being described here is a development of von Neumann's
approach in the sense that it gives more ontological reality to the
quantum state than the Copenhagen approach, and also in the sense that it
follows von Neumann's suggestion (or what Wigner describes as von
Neumann's suggestion) of bringing consciousness into the theory as a
real player. But it differs from the models discussed above that are based
on his theory of measurement. For it does not associate collapses with
things like positions of pointers on measuring devices. The projectors
P(E) associated experiences E are in terms of classical aspects of
the electromagnetic fields in brains of observers. That would be in
line with von Neumann's general idea, but he did not go into details
about which aspects of the brain were the pertinent ones. Rather he
circumvented the issue of the mind-brain connection by centering his
attention on the external devices and their pointer-type variables.
The classical aspects of the EM field are technically different from
pointers because their interaction with the environment is mainly their
interaction with the ions and electrons of the brain, and these are
the very interactions that both create these aspects of these fields,
and that are in part responsible for the causal effects of the
experiences E through the action of the projectors P(E). So what was
formerly an uncontrolled and unobservable environment that disturbed
the causal connections is now the very thing that creates the coherent
oscillatory structure through which our experiences control our brains.
The effects of this switch will be examined in the next section.
\vskip .1in
\noindent {\bf 13. Efficacy of Knowings.}
\vskip .1in
A formalism for dealing with the classical part of the the
electro-magnetic field, within quantum electrodynamics (QED), has been
developed in Stapp (1983) and Kawai and Stapp (1995), where it was shown
that this part dominates low-energy aspects, and is exactly expressed
in terms of a unitary operator that contains in a finite way the terms
that, if not treated with sufficient precision, lead to the famous infrared
divergence problem in QED. This classical part is a special kind of
quantum state that has been studied extensively. It is a so-called
coherent state of the photon field. Essentially all of the low-energy
contributions are contained within it, and the effects of emission and
re-absorption are all included. However, different classically conceived
current sources produce different ``classical fields'', and hence the
full low-energy field is a quantum superposition of these classical states.
Each such classical state is a combination (a product) of components each
of which has a definite frequency. All of the electrons and ions in the
brain contribute to each of these fixed frequency components, with
an appropriate weighting determined by that frequency. Thus the
description is naturally in the frequency domain, rather than in spacetime
directly: spatial information is encoded in quantum phases of the various
fixed frequency components. Each value is represented, actually, by
a gaussian wave packet centered at that value, in a certain space, and hence
neighboring values are represented by overlapping gaussian wave packets.
To exhibit a basic feature I consider a system of just three of these states.
Suppose state 2 has all of the correct timings to elicit some coordinated
actions. It represents in this simple model the state singled out by
the projector P = P(E). Suppose it is dynamically linked to some motor
state, represented by state 3: the dynamical evolution carries 2 to 3.
Let state 1 be a neighbor of state 2 such that the dynamical evolution
mixes 1 and 2. (I use here the Schroedinger picture, for convenience.)
The transition from 2 to 3 will tend to depopulate the coupled pair
1 and 2. This depopulation of the system 1 and 2 will occur naturally
whether or not any von Neumann collapse associated with P occurs.
The question is: Can a von Neumann collapse associated with P
affect in a systematic way the rate of depopulation from the coupled
pair 1 and 2. The answer is ``Yes'': it can speed up the emptying of the
amplitude in the system 1 and 2 into the system 3 that represents the
motor action. This means that the effect of repeatedly putting to nature
the question associated with P can have the effect of producing the motor
action more quickly than what the dynamics would do if no question was put:
putting the question repeatedly can effect the probabilities, compared Bohm's
model, in which there are no collapses. The quantum rules regarding the
probability of receiving a `Yes', or alternatively a `No', are stricly
observed.
To implement the dynamical conditions suppose the initial state is
represented, in the basis consisting of our three states 1, 2, and 3,
by the Hermitian matrix S with $S_{1,1} = x$, $S_{2,2} = y$,
$S_{1,2}= z$, $S_{2,1}=z^*$, and all other elements zero. Suppose
the coupling between states 2 and 3 is represented by the unitary
matrix U with elements $U_{1.1} = 1$, and
$$
U_{2,2}=U_{2,3}=U_{3,3}= -U_{3,2}= r = (2)^{-1/2},
$$
with all other elements zero.
The mixing between the states 1 and 2 is represented by the unitary
matrix M with
$$
M_{1,1}=c, M_{1,2}= s, M_{2,1}= -s^*, M_{2,2}=c^*, M_{3,3}=1,
$$
with all other elements zero. Here $c^* c + s^* s$ = 1.
The initial probability to be in the state 2 is given
Trace PS = y, where P projects onto state 2.
The action of U depopulates state 2: $Trace PUSU^{-1}= y/2$.
Then the action of the mixing of 1 and 2 generated by M brings
the probability of state 2 to
$$
Trace PMUSU^{-1}M^{-1} = (xs^* s)+ (yc^* c/2) -zcs^*r -z^*c^*sr,
$$
where r is one divided by the square root of 2
For the case c = s = r this gives for the probability of state
2:
$$
(xs^* s) + (yc^* c/2) -zcs^*r - z^*c^*sr = x/2 + y/4 - zr/2 -z^*r/2
$$
Since states 1 and 2 are supposed to be neighbors the most natural
initial condition would be that the feeding into these two states
would be nearly the same: the initial state would be a super position
of the two states with almost equal amplitudes. This would make x = y =
z = $z^*$.
Then the probability of state 2 becomes
$$
prob = y/2 + y/4 -yr
$$
Then the effect of the mixing M is to decrease from y/2 the
probability in the state 2 that feeds the motor action.
If the question E, with P(E)= P, is put to nature before U acts, then the
effect of the corresponding von Neumann reduction is to set z to zero.
Hence in this case
$$
prob = y/2 + y/4,
$$
and the probability is now increased from y/2.
Thus putting the question to Nature speeds up the motor response, on
the average, relative to what that speed would be if the question were not
asked.
The point of this calculation is to establish that this theory allows
experiences to exercise real control over brain activity, not only by
making the individual choices between possibilities whose probabilities
are fixed by the quantum rules, but also at a deeper level by shaping,
through the choices of which questions are put to nature, those
statistical probabilities themselves. This opens the door both to
possible empirical tests of the presence of collapses of the kind
predicated in this theory, and to a natural-selection-driven co-evolution
of brains and their associated minds.
\vskip .1in
\noindent {\bf 14. Natural Selection and the Evolution of Consciousness.}
\vskip .1in
In a naturalistic theory one would not expect consciousness to be
present in association with a biological system unless it had a function:
nothing as complex and refined as consciousness should be present unless it
enhances the survival prospects of the system in some way.
This requirement poses a problem for a classically described system because
there consciousness is causally non-efficatious: it is epiphenomenal. Its
existence is not, under any boundary conditions, {\it implied} by the
principles of classical physics in the way that what we call ``a tornado''
is , under appropriate boundary conditions, implied by the principles of
classical physics. Consciousness could therefore be stripped away without
affecting the behavior of the system in any way. Hence it could have no
survival value.
Consider two species, generally on a par, but such that in the first the
survival-enhancing templates for action are linked to knowings, in the way
described above, but in the second there is no such linkage. Due to the
enhancement effects described in the preceding section the members of the
first species will actualize their survival-enhancing templates for action
faster and more often than the members of the second species, and hence be
more likely to survive. And over the course of generations one would expect
the organism to evolve in such a way that the possible experiences E
associated with it, and their consequences specified by the associated
projection operators P(E), will become ever better suited to the survival
needs of the organism.
\vskip .1in
\noindent {\bf 15. What is Consciousness?}
\vskip .1in
When scientists who study consciousness are asked to define what
it is they study, they are reduced either to defining it in other words that
mean the same thing, or to defining it ostensively by directing the
listener's attention to what the word stands for in his own life. In some
sense that is all one can do for any word: our language is a web of
connections between our experiences of various kinds, including sensations,
ideas, thoughts, and theories.
If we were to ask a physicist of the last century what an ``electron'' is,
he could tell us about its ``charge'', and its ``mass'', and maybe some
things about its ``size'', and how it is related to ``atoms''. But this
could all be some crazy abstract theoretical idea, unless a tie-in to
experiences is made. However, he could give a lengthy description of this
connection, as it was spelled out by classical physical theory. Thus the
reason that a rational physicist or philosopher of the ninteenth century
could believe that ``electrons'' were real, and perhaps even ``more real''
than our thoughts about them, is that they were understandable as parts of a
well-defined mathematical framework that accounted---perhaps not directly
for our experiences themselves, but at least---for how the contents of
our experiences hang together in the way they do.
Now, however, in the debate between materialists and idealists, the tables
are turned: the concepts of classical physics, including the classical
conception of tiny electrons responding only to aspects of their local
environment, absolutely cannot account for the macroscopic phenomena that we
see before our eyes. On the contrary: the only known theory that does
account for all the empirical phenomena, and that is not burdened with
extravagent needless ontological excesses, is a theory that is neatly
formulated directly in terms of our knowings. So the former reason for being
satisfied with the idea of an electron, namely that it is part of a
parsimonious mathematical framework that accounts quantitatively for the
contents of our experiences, and gives us a mathematical representation of
what persists during the intervals between our experiences, has
dissolved insofar as it applies to the classical idea of an electron: it
applies now, instead, to our knowings, and the stored compendium of all
knowings, the Hilbert space state of the universe.
To elicit intuitions, the classical physicist might have resorted to a
demonstration of tiny ``pith balls'' that attract or repel each other due to
(unseen) electric fields, and then asked the viewer to imagine much smaller
versions of what he sees before his eyes. This would give the viewer a
direct intuitive basis for thinking he understood what an electron is.
This intuitive reason for the viewer's being satisfied with the notion of
an electron as an element of reality is that it was a generalization of
something very familiar: a generalization of the tiny grains of sand that
are so common in our ordinary experience, or of the tiny pith balls.
No things are more familiar to us than our own experiences. Yet they are
elusive: each of them disappears almost as soon as it appears, and leaves
behind only a fading impression, and fallible memories.
However, I shall try in this section to nail down a more solid idea of what
a conscious experience is: it unifies the theoretical and intuitive aspects
described above.
The metaphor is the experienced sound of a musical chord.
We have all experienced how a periodic beat will, when the frequency is
increased, first be heard as a closely spaced sequence of individual pulses,
then as a buzz, then as a low tone, and then as tones of higher and higher
pitch. A tone of high pitch, say a high C, is not experienced by most
listeners as a sequence of finely spaced individual pulses, but as
something experientially unigue.
The same goes for major and minor chords: they are experienced differently,
as a different gestalts. Each chord, as normally experienced, has its own
unique total quality, although an experienced listener can attend to it in
a way that may reveal the component elements.
One can generalize still further to the complex experience of a moment of
sound in a Beethoven symphony.
These examples show that a state that can be described physically as a
particular combination of vibratory motions is experienced as a particular
experiential quality: what we cannot follow in time, due to the rapidity of
the variations, is experienced as a gestalt-type impression that is a quality
of the entire distribution of energy among the sensed frequencies.
According to the theory purposed here, the aspect of brain dynamics that
corresponds to a conscious experience is a complex pattern of reverberating
patterns of EM excitations that has reached a stable steady state and
become a template for immediate further brain action. Its actualization by a
quantum event initiates that action: it selects out of an infinite of
alternative competing and conflicting patterns of neural excitations a
single coherent energetic combination of reverberating patterns that
initiates, quides, and monitors, an ongoing coordinated evolution of neural
activities. The experience that accompanies this suddenly-picked-out
``chord'' of reverberations is, I suggest, the ``quality'' of this complex
pattern of reverberations. Because the sensed combinations of EM
reverberations that constitute the template for action is far more complex
than those that represent auditory sounds, the quality of the former chord
must be far more complex than that of the latter.
But the most important quality of our experiencess is that they have
meanings. These meanings arise from their intentionalities, which
encompass both intentions and attentions. The latter are intentions to attend
to---and thereby to update the brains representation of---what is attended to.
These aspects of the experience arise from their self-reproducing
quality: their quality of re-creating themselves. In the case
of our human thoughts this self-reproductive feature has evolved to the
point such that the present thought contains a representation of what
will be part of a subsequent thought: the present experience E contains
an image of a certain prolongation (projection into the future) of the current
Jamesian sequence of temporal components that is likely, by virtue of
the causal effect of E, namely S--$>$ PSP, with P = P(E), to be the
current Jamesian sequence of a subsequent experience $E'$.
Thus the meaning of the experience, through physically imbedded in the present
state of the brain that it engenders, consists of the image of the future
that it is likely to generate, within the context of its fringe.
\vskip .2in
{\bf Acknowledgements}
This article is essentially a reply to detailed questions about
earlier works of mine raised by Aaron Sloman, Pat Hayes, Stan Klein,
David Chalmers, William Robinson, and Peter Mutnick. I thank them for
communicating to me their dissatisfactions. I also thank Gregg Rosenberg
and John Range for general support.
\vskip .2in
{\bf References.}
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(Cambridge: Cambridge University Press).
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from various arrays of single channels: Implications for transmitter
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Lectures in Physics.} (Vol. III, Chapter 21).(New York: Addison-Wesley).
Haag, R. (1996) {\it Local Quantum Physics} (Berlin: Springer).p 321.
Heisenberg, W. (1958a) `The representation of nature in contemporary
physics', {\it Deadalus} {bf 87}, 95-108.
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Row).
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Dialogue} (Dordrecht: Reidel).
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{\it Annals of the New York Academy of Science} {\bf 480} 6-13.
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Princeton U.P.) p. 498.
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\& http://www-physics.lbl.gov/\~{}stapp/stappfiles.html
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of Consciousness Studies}, {\bf 3} 194-210.
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For commentaries on this paper see:\\
http://www-physics.lbl.gov/\~{}stapp/stappfiles.html\\
The papers quant-ph/yymmnnn cited there can be accessed at\\
quant-ph@xxx.lanl.gov by putting in the subject field the command:\\
get yymmnnn
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{\it J. of Mind and Brain}, vol 18, spring and summer.
Stapp, H.P. (1997b) `The Evolution of Consciousness',\\
http://www-physics.lbl.gov/\~{}stapp/stappfiles.html
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unit', in {\it The Logic of Personal Knowledge} ed. M. Polyani
(London: Routledge \& Paul) pp. 231-238.
Zucker, R.S. \& Fogelson, A.L. (1986), `Relationship between transmitter
release and presynaptic calcium influx when calcium enters through disrete
channels', {\it Proc. Nat. Acad. Sci. USA}, {\bf 83}, 3032-3036.
Zurek, W.H. (1986) `Reduction of the Wave Packet and Environment-Induced
Superselection', {\it Annals of the New York Academy of Science} {\bf 480},
89-97
Zurek, W.H., S. Habib, J.P. Paz, (1993) `Coherent States via Decoherence',
Phys. Rev. Lett. {\bf 70} 1187-90.
\newpage
\noindent {\bf Appendix A. Quantum Effect of Presynaptic Calcium
Ion Diffusion.}
Let me assume here, in order to focus attention on a particular easily
analyzable source of an important quantum effect, that the propagation of
the action potential along nerve fibers is well represented by the classical
Hodgson-Huxley equation, and that indeed all of brain dynamics is well
represented by the classical approximation apart from one aspect, namely the
motions of the pre-synaptic calcium ions from the exit of the micro-channels
(through which they have entered the nerve terminal) to their target sites.
The capture of the ion at the target site releases a vesicle of
neurotransmitter into the synaptic cleft.
The purpose of the brain activity is to process clues about the outside
world coming from the sensors, within the context of a current internal
state representing the individual's state of readiness, in order to produce
an appropriate ``template for action'', which can then direct the ensuing
action (Stapp, 1993). Let it be supposed that the classically described
evolution of the brain, governed by the complex nonlinear equations of
neurodynamics, will cause the brain state move into the vicinity of one
member of a set of attractors. The various attractors represent the various
possible templates for action: starting from this vicinity, the state of
the classically described body/brain will evolve through a sequence of
states that represent the macroscopic course of action specified by that
template for action.
Within this classically described setting there are nerve terminals
containing the presynaptic calcium ions. The centers of mass of these ions
must be treated as quantum mechanical variables. To first approximation
this means that each of these individual calcium ions is represented as if
it were a statistical ensemble of classically conceived calcium ions: each
individual (quantum) calcium ion is represented as a cloud or swarm of
virtual classical calcium ions all existing together, superposed. This cloud
of superposed virtual copies is called the wave packet. Our immediate
interest is in the motion of this wave packet as it moves from the exit of
a microchannel of diameter 1 nanometer to a target trigger site for the
release of a vesicle of neurotransmitter into the synaptic cleft.
The irreducible Heisenberg uncertainty in the velocity of the ion as it
exits the microchannel is about $1.5$ m/sec, which is smaller than its
thermal velocity by a factor of about $4 \times 10^{-3}$. The distance to
the target trigger site is about $50$ nanometers.
(Fogelson,1985;Zucker,1986) Hence the spreading of the wave packet is of the
order of $0.2$ nanometers, which is of the order of the size of the ion
itself, and of the target trigger site. Thus the decision as to whether the
vesicle is released or not, in an individual instance, will have a large
uncertainty due to the large Heisenberg quantum uncertainty in the position
of the calcium ion relative to the trigger site: the ion may hit the trigger
site and release the vesicle, or it may miss it the trigger site and fail to
release the vesicle. These two possibilities, yes or no, for the release of
this vesicle by this ion continue to exist, in a superposed state, until a
``reduction of the wave packet'' occurs.
If there is a situation in which a certain particular {\it set of vesicles}
is released, due to the relevant calcium ions having been captured at the
appropriate sites, then there will be other nearby parts of the
(multi-particle) wave function of the brain in which some or all of the
relevant captures do not take place---simply because, for those nearby parts
of the wave function, the pertinent calcium ions miss their targets---and
hence the corresponding vesicles are not released.
More generally, this means, in a situation that corresponds to a very large
number N of synaptic firings, that, until a reduction occurs, all of the
$2^N$ possible combinations of firings and no firings will be represented
with comparable statistical weight in the wave function of the brain/body
and its environment. Different combinations of these firings and no firings
can lead to different attractors, and thence to very different macroscopic
behaviours of the body that is being controlled by this brain.
The important thing, here, is that there is, {\it on top of the nonlinear
classically described neurodynamics}, a quantum mechanical {\it statistical
effect} arising from the spreading out of the wave functions of the centers
of mass of the various presynaptic calcium ions relative to their target
trigger sites.The spreading out of the wave packet is unavoidable, because
it is a consequence of the Heisenberg uncertainty principle. This spreading
is extremely important, because it entails that every vesicle release will
be accompanied by a superposed alternative situation of comparable
statistical weight in which that vesicle is not released. This means that
wave function of the entire brain must, as a direct consequence of the
Heisenberg uncertainty principle, disperse into a shower of superposed
possibilities arising from all the different possible combinations of
vesicle releases or non-releases. Each possibility can be expected to
evolve into the neighborhood of some one of the many different attractors.
These different attactors will be brain states that will evolve, in turn,
if no reduction occurs, into different possible macroscopic behaviors of
the brain and body.
Thus the effect of the spreadings of the wave functions of the centers of
the presynaptic calcium ions is enormous: it will cause the wave function
of the person's body in its environment to disperse, if no reduction occurs,
into a profusion of branches that represent all of the possible actions that
the person is at all likely to take in the circumstance at hand. The
eventual reduction of the wave packet becomes, then, the decisive
controlling factor: in any given individual situation the reduction
selects---from among all of the possible macroscopically different
large-scale bodily actions generated by the nonlinear (and, we have
supposed, classically describable) neurodynamics---the single action that
actually occurs.
In this discussion I have generated the superposed macroscopically different
possibilities by considering only the spreading out of the wave packets of
the centers-of-mass of the pertinent presynaptic calcium ions relative to
the target trigger sites, imagining the rest of the brain neurodynamics to
be adequately approximated by the nonlinear classically describable
neurodynamics of the brain. Improving upon this approximation would tend
only to increase the quantum effect I have described.
It should be emphasized that this effect is generated simply by the
Heisenberg uncertainty principle, and hence cannot be simply dismissed or
ignored within a rational scientific approach. The effect is in no way
dependent upon macroscopic quantum coherence, and is neither wiped out nor
diminished by thermal noise. The shower of different macroscopic
possibilities created by this effect can be reduced to the single actual
macroscopic reality that we observe only by a reduction of the wave packet.
\newpage
{\bf Appendix B. Knowings, Knowledge, and Causality.}
I shall flesh out here the idea that Nature is built out
of knowings, not matter.
A typical knowing of the kind that quantum theory is built upon
is a knowing that the pointer on the measuring device appears to lie
between the numbers 6 and 7 on the dial. This is the sort of fact
that all (or at least most) of science is built upon. It is quite
complex. The idea that the appearance pertains to a dial on something
that acts as a measuring device has a tremendous amount of education
and training built into it. Yet somehow this knowing has this background
idea built into it: that idea is a part of the experience.
William James says about perceptions:
``Your acquaintance with reality grows literally by buds or drops
of perception. Intellectually and upon reflection you can divide
these into components, but as immediately given they come totally
or not at all.''
This fits perfectly with Copenhagen quantum theory, which takes these
gestalts as the basic elements of the theory. In the von Neumann/
Wigner type ontology adopted here there is, in association
with this knowing, a collapse of the state vector of the universe.
It is specified by acting on this state with a projection operator
that acts on the degrees of freedom associated with the brain of the
perceiver, and that reduces the state of the body/brain of the observer,
and consequently also the state of the whole universe, to the part of
that state that is compatible with this knowing.
So a knowing is a complex experiential type of event that, however,
according to the theory, occurs in conjunction with a correspondingly
complex ``physical'' event that reduces the state of the the brain/body
of the person to whom the experience belongs to the part of that state
that is compatible with the knowing. [I shall use the word ``physical''
to denote the aspect of nature that is represented in the Hilbert-space
description used in quantum theory: this aspect is the quantum analog
of the physical description of classical physics.]
That ``person'' is a system consisting of a sequence of
knowings bound together by a set of tendencies that are specified by
the state of the universe. This state is essentially a compendium of
prior knowings. However, these knowings are not merely human knowings,
but more general events of which human knowings are a special case.
In strict Copenhagen interpretation quantum theory is regarded as merely a
set of rules for making predictions about human knowledge on the basis of
human knowledge: horses and pigs do not make theoretical calculations using
these ideas about operators in Hilbert space, and their ``knowings''
are not included in ``our knowldge.
But in a science-based {\it ontology} it would be unreasonable to posit
that human knowledge plays a singular role: human knowings must be
assumed to be particular examples of a general kind of ``knowings'' that
would include ``horse knowings'' and ``pig knowings''. These could be
degraded in many ways compared to human knowings, and perhaps richer
in some other dimensions, but they should still be of the same general
ontological type. And there should have been some sort of things of this
general ontological kind even before the emergence of life.
[In the section, ``What is Consciousness'', I have tried to provide an
intuition about what a knowing associated with a nonbiological system
might be like.]
Science is an ongoing endeavor that is expected to develop ever more
adequate (for human needs) ideas about the nature of ourselves and of
the world in which we find ourselves. Newton himself seemed to
understand this, although some of his successors did not. But the
present stage of theoretical physics makes it clear that we certainly
do not now know all the answers to even the most basic questions: physics
is still very much in a groping stage when it comes to the details of
the basic underlying structure. So it would be folly, from a scientific
perspective, to say that we must give specific answers now to all
questions, in the way that classical physics once presumed to do.
This lack of certainty is highlighted by the fact that the
Copenhagen school could claim to give practical rules that worked in the
realm of human knowledge without paying any attention to the question
of how nonhuman knowings entered into nature. And no evidence contrary to
Copenhagen quantum theory has been established. This lack of data about
nonhuman knowledge would make it presumptuous, in a science-based approach,
to try to spell out at this time details of the nature of nonhuman knowings,
beyond the reasonable presumption that animals with bodies structurally
similar to the bodies of human beings ought, to the extent they also
behave like human beings, to have similar experiences. But knowings cannot
be assumed to be always exactly the kinds of experiences that we human beings
have, and they could be quite different.
The knowings that I mentioned at the outset were percepts: knowings
that appear to be knowings about things lying outside the person's body.
But, according to the von Neummann/ Wigner interpretation, each such knowing
is actually connected directly to the state of the person's
body/brain, after that event has occurred. This state of the body/brain
will, in the case of percepts of the external world, normally be correlated
to aspects of the state of the universe that are not part of the
body/brain. But experienced feelings, such as the feelings of warmth, joy,
depression, devotion, patriotism, mathematical understandings, etc. are not
essentially different from percepts: all are experiences that are
associated with collapse events that reduce the state of the
body/brain to the part of it that is compatible with the experience..
I have spoken here of a body/brain, and its connection to an experience.
But what is this body/brain? It seems to be something different
from the knowing that it is connected to. And what is the nature of this
connection?
The body/brain is an aspect of the quantum mechanically described state
of the universe. This Hilbert-space state (sometimes called density
matrix) is expressed as a complex-valued function of two vectors, each of
which is defined over a product of spaces, each of which corresponds to
a degree of freedom of the universe. Any system is characterized by a
certain set of degrees of freedom, and the state of that system is
defined by taking the trace of the state of the universe over all
other degrees of freedom, thereby eliminating from this state any
explicit reference to those other degrees of freedom.
In this way the state of each system is separately definable,
and dependent only on its own degrees of freedom, even though the system
itself is basically only an aspect of the whole universe. Each part
(i.e., system) is separately definable, yet basically ontologically
inseparable from the whole: that is the inescapable basic message of
quantum theory. Each system has a state that depends only on its own
degrees of freedom, and this system, as specified by its state, is
causally pertinent, because each knowing is associated with some system,
and the probabilities for its alternative possible knowings are specified
by its own state, in spite of the fact that the system itself is
fundamentally an inseparable part of the entire universe. It is the
properties of the trace operation that reconciles these disparate
requirements
The state of the universe specifies only the probabilities
for knowings to occur, and it generally undergoes an instantaneous
global instantaneous jump when a new knowing occurs. But this
probability, by virtue of the way it jumps when a new knowing occurs,
and suddenly changes in regions far away from the system associated
with the new knowing, and that it is formulated in terms of infinite
sets of pssibilities that may never occur, is more like an idea or a
thought than a material reality. Indeed, these properties of the state
are exactly why the founders of quantum theory were led to the conclusion
that the mathematical formalism that they created was about knowledge.
The state of the universe is the preserved compendium of all knowings.
More precisely, it is an aspect of that compendium that expresses certain
statistical properties pertaining to the next knowing. There is
presumeably some deeper structure, not captured by the properties
expressed in the Hilbert-space mathematical structure, that fixes what
actually happens.
The knowings that constitute our experiences are the comings into being
of bits of knowledge, which join to form the knowledge that is
represented by the state of the universe. This gives an ontology
based on knowings, with nothing resembling matter present. But the
statistical causal structure of the sequence knowings is expressed in
terms of equations that are analogs of the mathematical laws that
governed the matter postulated to exist by the principles of classical
mechanics. This connection to classical mechanics is enough to ensure a
close similarity between the predictions of classical mechanics and those
of quantum mechanics in many cases of interest, even though the two
theories are based on very different mathematical structures.
If one starts from the ontological framework suggested by classical
mechanics the questions naturally arise: Why should experiences exist
at all? And given that they do exist, Why should they be composed of
such qualities as sensations of (experiential) colors and (experiential)
sounds, and feelings of warmth and coldness, and perceptions of
simple geometric forms that correspond more directly to the shapes of
structures outside the body/brain than to structures (such as patterns
of neural excitations that are presumably representing these various
features) inside the body/brain. How do these experiential types of
qualities arise in a world that is composed exclusively of tiny
material particle and waves? The experiential qualities are not
constructible from their physical underpinnings in the way that
all the physical properties of a tornado are, according to classical
mechanics, constructible from its physical constituents.
Quantum theory allows one to get around these questions by eliminating
that entire classical ontology that did not seem to mesh naturally with
experiential realities, and replacing that classical ontology with one
built around experiential realities. These latter realities are embedded in
a specified way, which is fixed by the pragmatic rules, into a mathematical
structure that allows the theory to account for all the successes of
classical mechanics without being burdened with its awkward ontological
baggage.
A discussion of this appendix with cognitive scientist Pat Hayes can
be found on my website: \\
(http://www-physics.lbl.gov/`tilde'stapp/stappfiles.html), \\
where `tilde' stands for the tilde symbol.
\newpage
\noindent {\bf Appendix C. Quantum Wholism and Consciousness.}
One reason touted for the need to use quantum theory in order to accomodate
consciousness in our scientific understanding of brain dynamics is the
seeming pertinence of quantum wholism to the unitary or wholistic character
of the conscious experience.
I shall here spell out that reason within the framework of a computer
simulation of brain dynamics.
Suppose we consider a field theory of the brain, with several kinds of
interacting fields, say, for example, the electric and magnetic fields, and
a field representing some mass- and charge-carrying field. Suppose the
equations of motion are local and deterministic. This means that the
evolution in time of each field value at each spacetime point is completely
determined by the values of the various fields in the immediate neighborhood
of that spacetime point. Suppose we can, with good accuracy, simulate this
evolution with a huge collection of computers, one for each point of a cubic
lattice of finely spaced spatial points, where each computer puts out a new
set of values for each the fields, evaluated at that its own spatial point,
at each of a sequence of finely spaced times. Each computer has inputs only
from the outputs of its nearest few neighbors, over a few earlier times in
the sequence of times. The outputs are digital, and the equations of motion
are presumed to reduce to finite-difference equations that can be readily
solved by the stripped-down computers, which can do only that. Thus, given
some appropriate initial conditions at some early times, this battery of
simple digital computers will grind out the evolution of the simulated
brain.
Merely for definiteness I assume that the spatial lattice has a thousand
points along each edge, so the entire lattice has a billion points. Thus our
simulator has a billion simple computers.
Now suppose after some long time the field values should come to spell out a
gigantic letter ``M'': i.e., the fields all vanish except on a set of
lattice points that have the shape of a letter ``M'' on one of the faces of
the lattice. If the outputs are printed out at the location of the
corresponding grid point then you or I, observing the lattice, would know
that the letter ``M'' had been formed.
But would the battery of dynamically linked but ontologically distinct
computers itself contain that information explicitly? None of the computers
has any information in its memory except information about numbers
pertaining to its immediate neighborhood: each computer ``knows'' nothing
except what its immediate environment is. So nowhere in the battery of
computers, B, has the higher-level information about the global structure
been assessed and recorded: the fact that an ``M'' has been formed is not
``known'' to the battery of computers. Some other computer C, appropriately
constructed, could examine the outputs of the various elements of B, and
issue a correct statement about this global properties of B, but that global
information is not explicity expressed in the numbers that are recorded in B
itself: some extra processing would be needed for that.
Of course, brains examine themselves. So B itself might be able to do the
job that C did above, and issue the statement about its own global property,
and also record that information in some way in the configuration of values
in the various simple computers: the existence of this configuration can be
supposed to have been caused by the presence of the ``M'', and can be
supposed to cause, under appropriate conditions, the battery of computers B
to display on some lattice face the message: ``I did contain an `M' ".
So the information about the global structure is now properly contained in
the structure of B, as far as causal functioning is concerned. But even
though the configuration of values that carries the information about the
``M'' is correctly linked causally to past and future, this configuration
itself {\it is} no more than any such configurations was before, namely a
collection of tiny bits of information about tiny regions in space. There is
nothing in this classical conception that corresponds ontologically to the
entire gestalt, ``M'', as a whole. The structure of classical physics is
such that the present reality is specified by values located within in an
infinitesimal interval centered on the present instant, without any need to
refer to any more distant times. To bring relationships to the past and
future events into the present evolving ontological reality would be alien
to the ideas of classical physics. There is simply no need to expand the
idea of reality in this way: it adds only superfluities to the ontologically
and dynamically closed structure of classical physics.
The situation changes completely when one quantizes the system. To make a
computer simulation of the quantum dynamics one generalizes the spatial
points of the classical theory to super-points. Each possible entire
classical state is a super-point. In our case, each super-point is defined
by specifying at each of the points in the lattice a possible value of each
of the several (in our case three) fields. To each super-point we assign a
super-computer. If the number of discrete allowed values for our original
simple computers was, say, one thousand possible values for each of the
three fields, and hence $10^9$ possible output values in all for each simple
computer, then the number of allowed classical states would be $10^9$ raised
to the power $10^9$: each of the $10^9$ simple computers can have $10^9$
possible values. Thus the number of needed super-computers would be $10^9$
raised to the power $10^9$. In the dynamical evolution each of these
super-computers generates, in succession, one complex number (two real
numbers) at each of the times in the finely spaced sequence of times.
One can imagine that a collapse event at some time might make all of these
complex numbers, except one, equal to zero, and make the remaining one equal
to $1$. Then the state would be precisely one of the $10^9$ to the power
$10^9$ classical states. It would then evolve into a superposition of
possible classical states until the next collapse occurs. But the collapse
takes the state to a ``whole'' classical world. That is, each super-computer
is associated not just with some tiny region, but with the whole system, and
the collapses can be to states in which some whole region of spacetime has a
fixed configuration of values. Thus, for example, there would be a
super-computer such that its output's being unity would mean that ``M''
appeared on one face. And the collapse to that single state would actualize
that gestalt ``M''. The sudden selective creation of this gestalt is more
similar to someone's experiencing this gestalt than any occurrence or
happening in the classical dynamics, because in both the experience and the
quantum event the whole body of information (the whole ``M'') suddenly
appears.
This intuitive similarity of collapse events to conscious events is a
reason why many quantum theorists are attracted to the idea that conscious
events are quantum events. Orthodox quantum theory rests on that idea.
There is in the quantum ontology a tie-in to past and future, because if
one asks what the present reality is, the answer can be either knowledge of
the past, or potentialities for the future: the present is an abrupt
transition from fixed past to open future, not a slice of a self-sufficient
continuous reality.
\newpage
\noindent {\bf Appendix D. The Dilemma of Free Will.}
\vskip 0.1in
The two horns of this dilemma are `determinism' and `chance'. If determinism
holds then a person seems reduced to a mechanical device, no more
responsible for his acts than a clock is responsible for telling the wrong
time. But if determinism fails then his actions are controlled in part by
``chance'', rendering him {\it even less} responsible for his acts.
This argument can powerfully affect on our lives: it allows us to
rationalize our own moral failings, and it influences the way we, and our
institutions, deal with the failings of others.
It might appear that there is no way out: either the world is deterministic
or it's not, and the second possibility involves chance. So we get hung on
one horn or the other.
Quantum ontology evades both horns.
The point is that determinism does not imply mechanism. The reason we say we
are not responsible if determinism holds is that ``determinism'' evokes the
idea of ``mechanism''; it evokes the idea of a clock. And, indeed, that's
exactly what {\it is} entailed by the determinism of classical mechanics.
According to the principles of classical mechanics everything you will do in
your life was fixed and settled before you were born {\it by local `myopic'
mechanical laws}: i.e., by essentially the same sort of local mechanical
linkages that control the workings of a clock. If your thoughts and ideas
enter causally into the physical proceedings at all, it is only to the
extent that they are themselves completely controlled by these local
mechanical processes. Hence the causes of your actions can be reduced to a
huge assembly of thoughtless microscopic processes.
But in quantum dynamics our knowings enter as the central dynamical units.
What we have is a dynamics of knowings that evolve according to the rules of
quantum dynamics. To be sure these dynamical rules do involve elements of
chance, but these are no more problematic than the thermal and environmental
noise that occurred in the classical case: our high-level structures cannot
maintain total fine control over every detail. But there is, in spite of
that important similarity, a huge difference because in the classical case
everything was determined from the bottom up, by thoughtless micro
processes, whereas in the quantum case everything is determined from the top
down, by a dynamics that connects earlier knowings to later knowings.
And these knowings are doing what we feel they are doing: initiating complex
actions, both physical and mental, that pave the way to future knowings.
No reduction to knowingless process is possible because each step in the
dynamical processes is the actualization of a knowing that is represented
mathematically as the grasping, as a whole, of a structural complex that is
equivalent to the structure of the knowing.
\end{document}
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