January 5,1996 LBL-36915mod.txt
Quantum Mechanical Coherence, Resonance, and Mind.
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%\footnote{This work was supported in part by the Director, Office of
%Energy Research, Office of High Energy and Nuclear Physics, Division of
%High Energy Physics of the U.S. Department of Energy under Contract
%DE-AC03-76SF00098 and in part by the National Science Foundation under
%grant PHY-90-21139.}
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Henry P. Stapp
{\em Theoretical Physics Group\\
Lawrence Berkeley Laboratory\\
University of California\\
Berkeley, California 94720}
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\begin{quotation} Invited Contribution to the Norbert Wiener Centenary
Congress, held at Michigan State University, Nov. 27 - Dec. 3, 1994.
\end{quotation}
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\begin{abstract}
Norbert Wiener and J.B.S. Haldane suggested during the early thirties that
the profound changes in our conception of matter entailed by
quantum theory opens the way for our thoughts, and other experiential or
mind-like qualities, to play a role in nature that is causally interactive and
effective, rather than purely epiphenomenal, as required by classical
mechanics. The mathematical basis of this suggestion is described here, and it
is then shown how, by giving mind this efficacious role in natural process,
the classical character of our perceptions of the quantum universe can be
seen to be a consequence of evolutionary pressures for the survival of the
species.
\end{abstract}
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\noindent{\bf I. Introduction}
\medskip
This session of the congress is entitled ``Leibniz, Haldane, and Wiener on
Mind''. Accordingly, my talk will deal with issues that are often
considered to be more philosophical than mathematical. However, the logical
basis of my remarks is the Hilbert space formalism of quantum mechanics.
I introduce the subject by giving some quotations from Haldane's article
``Quantum mechanics as a Basis for Philosophy''[9], from Wiener's article ``The
Role of the Observer''[36g], and from Bohm's Commentary [1, p.97] in the
Collected Works of Norbert Wiener.
\noindent{\bf Haldane:}
\begin{enumerate}
\item Biologists have as yet taken but little cognizance of the revolution in
human thought which has been inaugurated by physicists in the last five years,
and philosophers have stressed its negative rather than its positive side.
\item If mind is to be regarded as expressive of the wholeness of the body, or
even of the brain, it should probably be thought of as a resonance phenomenon,
in fact part of the wave-like aspect of things.
\item If mind is a resonance phenomenon it is at once clear why it cannot be
definitely located, either in space or time, though it is obviously enough
connected with definite events in a definite material structure.
\item But it is, I think, of importance that philosophers, and even ordinary
persons, should realize that a thorough-going materialism is compatible with the
view that mind has many of the essential properties attributed to it by
metaphysicians.
The theory here presented does not reduce it to an epiphenomenon of matter, but
exhibits it as a reality interacting with ordinary material systems.
\item It has been my object to suggest that the progress of modern physics has
made such a unified view more readily attainable than appeared likely ten years
ago.
\end{enumerate}
\newpage
\noindent{\bf Wiener:}
\begin{enumerate}
\item The Platonist believes in a world of essence, of cleanly defined ideas and
cleanly defined propositions concerning these ideas, into which we may enter as
spectators, but never as participants.
They are out of time, and time is irrelevant to them.
This is pure dogma, and does not check with what we should naively expect.
Of course, our experiences must have some reference outside themselves, in the
sense that they cannot be considered as completely closed and isolated.
Otherwise there could be no knowledge at all.
This by no means asserts that the experience has a reference entirely unaltered
by our participation.
\item Thus physics, the most exact of all sciences, has had to have a thorough
logical housecleaning.
We no longer conceive the laws of physics to apply to some mystical world of
reality behind our observations and instruments: they merely constitute an
intelligible statement of the manner in which our observations and the readings
of our instruments hang together.
\item The philosophy of Hume furnishes the dreadful example of what happens to
an empiricism which seeks its fundamental reality in the fugitive sense-data of
immediate experience.
If the raw stuff of our experience does not contain something of a universal
nature, no manipulation can ever evoke anything which might even be mistaken for
a universal.
\item Science is the explanation of process.
It is neither possible under a rationalism, which does not recognize the
reality of process, nor under an empiricism, which does not recognize the
reality of explanation.
\end{enumerate}
\newpage
\noindent{\bf Bohm:}
\begin{enumerate}
\item In [36G] Wiener goes into the role of the observer, which has been
emphasized in the quantum theory.
He points out that in art, drama, psychology, and medicine we are all familiar
with areas of experience in which the observer is not merely a passive receiver
of perceptions but, on the contrary, plays an active and essential role in all
that is seen.
Wiener proposes that in physics and mathematics a similar approach is now called
for.
We do not ask for a mystical world of reality behind our observations.
Physics is a coherent way of describing the results of our observations and what
is done with them.
\item .... in all his thinking Wiener has consistently and coherently sought to
achieve what he already indicated in the earliest of his papers on the quantum
theory, i.e. something that ``possesses more of an intrinsic logical necessity''
than is possessed by already existing modes of thoughts.
\end{enumerate}
These quotations highlight the fact that the discovery of quantum mechanics has
opened up the possibility that mind - - - i.e., the realm of {\it experiential
things}, such as our thoughts, ideas, and perceptions - - - may not be
epiphenomenal after all: mind may be something quite different from the
causally inert by-product of the {\it microscopically specified and determined}
mechanical processes in our brains (or bodies) that the principles of classical
mechanics require it to be.
This possibility that mind is an interactive and dynamically efficacious aspect
of nature, not reducible to the locally determined mechanical features that
characterize the ``matter'' of classical physics, arises from the circumstance
that quantum dynamics has an element of wholeness that is not reducible
to those local aspects of nature, but that rather complements
them, and interacts with them. This added element is directly tied to
our thoughts by the basic rules of quantum mechanics.
During the twenties and thirties our detailed scientific understanding of brain
processes, and their connection to our thoughts, was too rudimentary to allow
this possibility offered by quantum mechanics to be related to empirical
findings. Now, however, we are entering a period of intensive empirical
scrutiny of brain processes and their connections to thoughts. In this new
climate the fact that quantum mechanics provides a scientifically based
mathematical setting that allows mind to complement and interact with the
aspect of nature that characterizes the ``matter'' of classical mechanics has
become the basis of a line of research that is being aggressively pursued. This
paper presents some recent results in this area, but begins by describing the
situation as it was understood in the thirties.
The most orthodox interpretation of quantum theory is the one formulated by
Niels Bohr. It was radical in its time because it rejected the prevailing idea
that the ultimate task of science was to develop a mathematical model of the
universe. Quantum philosophy asserted that the proper task of science was
merely to formulate rules that allow us to calculate all of the verifiable
relationships among our experiences. According to Bohr:
\noindent ``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.''[3, p.18]
\noindent and
\noindent ``Strictly speaking,
the mathematical formalism of quantum mechanics merely offers rules of
calculation for the deduction of expectations about observations obtained under
well defined experimental conditions specified by classical physical
concepts.''[5, p.60; 17, p.62]
The format for using quantum theory is as follows:
Let A be a classical description of an experimental set up.
Let B be a classical description of a possible outcome of this experiment.
By a ``classical description'' Bohr means a description in terms of ordinary
language, elaborated by the concepts of classical physics.
It is a description of what the technicians who set up the experiment should
{\it do}, and what the observers who observe the results of the experiment
might {\it see}, or otherwise experience.
A mapping from these ``classical descriptions'' to quantum operators is defined,
essentially by calibrations of the devices:
\newpage
$$
A \Longrightarrow \rho_A\eqno(1.1a)
$$
$$
B\Longrightarrow P_B.\eqno(1.1b)
$$
Here $\rho_A$ is the density operator (or statistical operator) that corresponds
to the classical description A,
and $P_B$ is the projection operator (i.e., $P^2_B = P_B$) that is the Hilbert
space representation of the outcome specified by the classical description $B$.
The basic quantum postulate is that the probability $P(B; A)$ that an outcome
that satisfies the specifications $B$ will occur under conditions that satisfy
the specifications A is given by
$$
P(B; A) = Tr P_B \rho_A,\eqno(1.2)
$$
where $Tr$ is the trace operator in Hilbert space:
$$
Tr X = \sum_i < i|X|i>,\eqno(1.3)
$$
Here the index $i$ labels the vectors of a complete orthonormal basis:
$$
* = \delta_{ij} =\Bigg\{
\matrix{ 1 & {\hbox{for}} \ i = j\cr
0 &{\hbox{for}} \ i\neq j}\eqno(1.4a)
$$
and
$$
\sum_i |i>**=|X>$ for all
$ |X>$.
(If the detectors are not 100\% efficient then the operator $P_B$ must be
replaced by an efficiency operator, $e_B$, but I shall ignore here this possible
complication, in order to focus on the central points.)
Notice that there is no mention here of any ``collapse of the wave function'' or
``reduction of the wave packet'' or ``quantum jump''. (See below.)
Notice also that the formulation is pragmatic:
it is a description of how to {\it use } the theory; and the basic
realities in the description are the experiences of the human beings who set up
experiments and observe their outcomes.
The objectivity of the theory is secured by formulating the specifications on
the preparations and observations in terms of the ``objective'' language of
classical description: there is no greater dependence here on individual human
beings than there is in classical physics.
A principal feature of a classical description is that objects and properties
are assigned to locations that are definite, at least at the level of our
perceptions: the center of an observable ``pointer'' that indicates the outcome
specified by a measuring device does not lie simultaneously at two locations
that can be perceived to be different. The whole idea of a measurement, or of
an experiment, refers here to things that can be perceived.
Einstein, and many other scientists, objected to this introduction of human
observers into the formulation of the basic physical theory.
According to Einstein:
\noindent ``Physics is an attempt to conceptually grasp reality as
it is thought independently of its being observed.''[13, p.81]
\noindent and
\noindent ``It is my opinion that contemporary quantum mechanics constitutes an
optimum formulation of [certain] connections but forms no useful point of
departure for future developments.''[13, p.87]
As regards ``future developments'' one may mention biological systems. Quantum
theoretical ideas are important in describing and understanding the properties
of the tissues of biological systems. However, living systems cannot be
isolated from their environment. Yet the orthodox formulation of quantum theory
demands that the observed system, which is the one represented in Hilbert
space, be isolated from the observing system, which consists of the observers,
their devices, and all systems coupled to them, between the time of preparation
of the observed system and the time of its observation. Bohr himself
stressed that this idealization cannot be achieved for biological systems,
and that the scope of quantum theory, as he interpreted it, was
correspondingly limited. [4, p.20]
This isolation requirement fails also for cosmological system, because in this
context the observers are {\it inside} the quantum system that is the object of
study, and hence cannot be isolated from it.
John von Neumann, in his book [19] ``Mathematical Foundations of Quantum
Mechanics'' examined the measurement problem, which is precisely the problem of
specifying the connection between an observed system and the observing one. He
started from the assumption, quite contrary to that of Bohr, that the entire
system of observed and observer should be treated within the quantum formalism.
His main result is easy to state.
Suppose we have a sequence of systems such that the first system is some atomic
system that might be in a state $\psi_{11}$; that might be in a state
$\psi_{12}$; or that might be in a superposed state $a\psi_{11} + b\psi_{12}$,
with $\abs{a}^2 + \abs{b}^2 = 1$. Suppose the second system is a measuring
device that measures whether the first system is in state $\psi_{11}$ or
$\psi_{12}$, in the sense that if the first system is originally in state
$\psi_{11}$ and the second system is originally in some state $\psi_{20}$ then
the combined system, originally $\psi_{11} \otimes \psi_{20}$, will evolve, due
to the interaction between the two systems, into a state $\psi_{11}'\otimes
\psi_{21}$; whereas if the first system is originally in the state $\psi_{12}$,
instead of $\psi_{11}$, then the combined original system $\psi_{12}\otimes
\psi_{20}$ will evolve into the state $\psi_{12}'\otimes \psi_{22}$, where
$\psi_{22}$ represents a state of the device that is perceptually different
from the state represented by $\psi_{21}$, so that an observer, by seeing
whether the second system (the measuring device) is in state $\psi_{21}$ or
$\psi_{22}$, can unambiguously infer whether the atomic system was originally
in the state $\psi_{11}$ or $\psi_{12}$.
The linear nature of the law of evolution of the full quantum system
consisting of the first and second systems ensures that if the first system had originally been in
the state $(a \psi_{11} + b \psi_{12})$, and the combined system had originally
been in the state $(a \psi_{11} + b \psi_{12}) \otimes \psi_{20}$, then this
original state would evolve into the state
$$
\psi = a \psi_{11}' \otimes
\psi_{21} + b \psi_{12}'\otimes \psi_{22}.
$$
But this state has a part
corresponding to each of the two macroscopically distinguishable configurations
of the device: e.g., it has a part, $\psi_{21}$, that corresponds, for example,
to the pointer's having swung to the left, and it has a part, $\psi_{22}$,
that corresponds, for example, to the pointer's having swung to the right. The
general possibility (in principle) of exhibiting interference effects involving
both terms of any superposition of states means that the two terms in the
superposition $\psi$ must be combined as a {\it conjunction} (both parts must
be present in nature) rather than as a {\it disjunction} (only one part or the
other is present in nature). Yet only one or the other position of the pointer
is ever observed, not both simultaneously. But then how does the ``and''
combination become transformed to an ``or'' combination?
To examine this problem von Neumann introduces a sequence of measuring
devices, with each one set up to distinguish the two outcome states of the
immediately preceding one in the sequence.
The previous argument now generalizes:
the original state
$$
\Psi_{10} = \psi_{11} \otimes \psi_{20} \otimes \psi_{30} \otimes ... \otimes
\psi_{N0}\eqno(1.5a)
$$
will evolve into
$$
\Psi_{1} = \psi_{11}'\otimes \psi_{21}\otimes\psi_{31}\otimes ... \otimes
\psi_{N1},\eqno(1.5b)
$$
whereas the original state
$$
\Psi_{20} = \psi_{12} \otimes \psi_{20} \otimes ... \otimes \psi_{N0}.\eqno(1.
5c)
$$
will evolve into
$$
\Psi_{2} = \psi_{12}'\otimes \psi_{22}\otimes \psi_{32}\otimes ... \otimes
\psi_{N2}.\eqno(1.5d)
$$
But then the linearity of the equation of motion ensures that the original state
$$
\Psi_0 =(a\psi_{11} + b\psi_{12})\otimes \psi_{20}\otimes \psi_{30}\otimes ...
\otimes \psi_{N0}\eqno(1.5e)
$$
will evolve into
$$
\eqalignno{
\Psi &= a \psi_{11}' \otimes \psi_{21} \otimes \psi_{31}\otimes ... \otimes
\psi_{N1}\cr
&+ b \psi_{12}' \otimes \psi_{22} \otimes \psi_{32} \otimes ... \otimes
\psi_{N2}.&(1.5f)\cr}
$$
The wave functions $\psi_{N1}$ and $\psi_{N2}$ are taken to be the wave
functions of the parts of the brain that are the {\it brain correlates of the
experiences of the human observer}, in the two alternative possible cases
defined by $\Psi_1$ and $\Psi_2$. Thus $\psi_{N1}$ would represent the brain
correlate of the experience of seeing a device outcome that indicates that the
original state of the atom was $\psi_{11}$, whereas $\psi_{N2}$ would represent
the brain correlate of the experience of seeing a device outcome that indicates
that the original state of the atom was $\psi_{12}$. But then if the original
state of the atom were $(a \psi_{11} + b\psi_{12})$, with $a\neq 0\neq b$, the
final state of the brain would have one component, $\psi_{N1}$, that
corresponds to the experience of seeing a device in a configuration that
indicates that the original wave function of the atom was $\psi_{11}$, and
another component, $\psi_{N2}$, that corresponds to the experience of seeing a
devices in a configuration that indicates that the original wave function of
the atom was $\psi_{12}$. But how do we reconcile the fact that the final
state $\Psi$ has two components corresponding to two different experiences,
namely $\psi_{N1}$, which corresponds to seeing a pointer swung to the left,
{\it and } $\psi_{N2}$, which corresponds to seeing that pointer swung to the
right, with the empirical fact that only one {\it or} the other of the two
possible experiences will actually occur? How has the ``{\it and~}'' at the
level of the device changed over to an ``{\it or~}'' at the level of our
experience.
The answer, if we apply the words of Bohr, arises from the assertion
that
\noindent ``In fact, wave
mechanics, just as the matrix theory, represents on this view a symbolic
transcription of the problem of motion in classical mechanics adapted to the
requirements of quantum theory and {\it only to be interpreted by an explicit
use of the quantum postulate}.''[3, p.75]. (Italics mine.)
The mathematical core of the quantum postulate is the probability rule (1.2):
$$
P(B; A) = Tr P_B \rho_A.
$$
In our example the projection operator $P_B$ associated with the observation of
system $n $ ($1 \leq n \leq N$) in state $j (j=1$ or 2) is (in Dirac's bra-ket
notation)
$$
P_{nj} = |\psi_{nj}> <\psi_{nj}| \times \prod_{s\neq n} I_s,\eqno(1.6)
$$
where $I_s$ is the unit or identity operator in the Hilbert space
associated with system $s$.
The $|\psi_{nj} >$ are normalized so that
$$
<\psi_{nj}|\psi_{m\ell}> = \delta_{nm} \delta_{j\ell}.\eqno(1.7)
$$
The density operator for the final state, under the condition that the original
state of the atom is
$a|\psi_{11}> + b|\psi_{12}>$,
is
$$
\rho_A = |\Psi ><\Psi|,\eqno(1.8a)
$$
where [(1.5f) transcribed into Dirac's notation]
$$\eqalignno{
|\Psi > &= a|\psi_{11}'>\otimes |\psi_{21}>\otimes ... \otimes |\psi_{N1}>\cr
&+ b|\psi_{12}' > \otimes |\psi_{22} > \otimes ... \otimes |\psi_{N2}>.
&(1.8b)\cr}
$$
Then, in the case that the measurement outcome $B$ corresponds to finding
the system $n$ $(1 \leq n \leq N)$ in state $j$ ($j=1$ or $2$), one obtains
$$\eqalignno{
P(B; A) &= Tr P_{nj} \rho_A\cr
&= \abs{a}^2 \delta_{1j} + \abs{b}^2 \delta_{2j}.&(1.9)\cr}
$$
That is, the probability of the outcome $j$ is either $\abs{a}^2$ or
$\abs{b}^2$ according to whether the value of $j$ is 1 or 2, and this result is
independent of which of the $N$ possible systems is specified by $n$: i.e., the
probability for the outcome $j$ is independent of which one of the $N$ systems
is considered to be the ``measured'' or ``observed'' one. Carrying the analysis
up to the level of the brain correlate of the experience does not change the
computed probability.
By combining the ideas of von Neumann and Bohr in this way we have resolved, in
a certain sense, the measurement problem in a way that does not automatically
exclude biological or cosmological systems. In this development
the final system, system $N$, plays a special role: it provides the
Hilbert space in which is represented of the immediate objects of our
experiences. These experiences are the basis of Bohr's approach. However,
Bohr did not recommend considering the brain correlate of the
experience to be the directly experienced system, as,
following the approach of von Neumann, has been done here.
According to the ideas of Bohr, the Hilbert-space state should not be
considered to characterize the objectively existing external reality itself; it
is merely a symbolic form that is to be used only to compute expectations that
pertain to classically describable experiences. Each of the two states
$\psi_{N1}$ and $\psi_{N2}$ is the brain correlate of a classically describable
experience in which, for example, a ``pointer'' of an observable device is
located at a well defined position. But a more general state such as
$a\psi_{N1} + b\psi_{N2}$, with $a \neq 0 \neq b$, would evidently not be the
brain correlate of any single classically describable experience. Hence its
probability would not be something that it would be useful to compute: the
``occurrence'' of such an event would have no empirical meaning. The special
role of classical concepts in the formalism therefore arises, according to this
viewpoint, fundamentally from the circumstance that our perceptual experiences
of the external world have, as a matter of empirical fact, aspects that can be
described in classical terms.
In this Bohr-type way of viewing the theory the Hilbert space quantities are
merely computational devices: the only accepted realities are the experiences
of the observers. Thus the approach is fundamentally idealistic.
We can retain these basic experiential realities yet expand our mathematical
representation of nature to include also a representation of the ``physical''
reality by adopting (with Heisenberg) the Aristotelian notion of ``potentia'':
i.e., by conceiving the Hilbert-space state to be (or to faithfully represent)
a reality that constitutes not the ``actual'' realities in nature, which are
{\it events}, but merely the ``potentia'' for such actual events to occur. Then
the Bohr-type experiential realities can be retained as the ``actual'' things
of nature, while the Hilbert-space state becomes a representation of
``objective tendencies'' (in the words of Heisenberg) for such actual events to
occur.
The notion that the real actual things in nature should occur {\it only} in
conjunction with human brains is an idea that is too anthropocentric to be
taken seriously. Indeed, Heisenberg proposes that actual events should occur
already at the level of the first measuring device. However,
as suggested already by our simple example, there is no empirical evidence
to support the intuitively appealing notion that there are events at that
purely mechanical level. That conclusion is the basic message that comes from
the numerous detailed elaborations of von Neumann's analysis that have been
carried out over the years: the simple example already exhibits the essential
result.
In the present realistic approach the probability rule $P(B; A) = Tr P_B \rho_A$
is interpreted as the probability that an event corresponding to $B$
actually {\it occurs} under the condition that the state of the universe is
specified by $\rho_A$.
If we were adhering to the pragmatic Bohr-type philosophy then it might
be useful, for reasons of computational convenience, to push the level at
which the event is supposed to occur down to a level such that any shift to a
higher level will not change the computed probability significantly. But in a
realistic context the placement of the actual events ought to be be governed
by a general principle, not by reason of its practical convenience.
Putting aside, temporarily, this question of where to place any actual events
that might occur {\it outside} the brain, let us focus on processes occurring
inside human brains. Let us suppose, in line with our attempt to extend Bohr's
pragmatic/idealistic interpretation to a realistic one, that the actual events
in the brain occur only at the top level, i.e., at the level of the brain
correlates of our conscious experiences; at the level of the states $\psi_{N1}$
and $\psi_{N2}$ of our earlier discussion. Then we arrive at the situation
referred to by Haldane, Wiener, and Bohm. In this conception of nature we have,
on the one hand, the ``potentia'', which is represented by the evolving
Hilbert-space state. It constitutes the matter-like aspect of nature, in the
sense that it is represented in terms of local quantities that normally evolve
deterministically in accordance with local laws that are direct generalizations
of the local laws of classical mechanics. But this is not the whole story.
There are, on the other hand, also the ``actual'' events that we experience.
These events are represented in Hilbert space by sudden changes in the state
vector. These two aspects of nature are complementary: it makes no sense to
have ``tendencies'' without having the events that these tendencies are the
tendencies for; and it makes no sense to have separate experiential events with
no reality connecting them. These two complementary aspects of nature interact:
each actual event {\it selects} certain possibilities from among the ones
generated by the evolving ``potentia''. Thus mind is no longer a causally inert
epiphenomenon that can be reduced to the locally specified and determined
matter-like aspects of nature: mind is rather an integral nonlocal aspect of
reality that acts as a unit upon the local deterministic matter-like aspect of
nature, which conditions this mental aspect but does not completely control it.
This completes my skeletal description of the mathematical basis of the idea of
Haldane and Wiener. I now go on to consider two basic issues: 1), Why in a
quantum universe having no events occurring outside human minds would different
observers agree on what they see? and 2), Why in such a quantum universe would
what they see be describable in classical terms?
\newpage
\noindent{\bf 2. Intersubjective Agreement}
\medskip
Within the framework of the quantum mechanical picture of the universe
described above, let us consider the possibility that the events occur only in
conjunction with projection operators $P$ that act nontrivially (i.e., as
something other than a unit operator) only on systems confined to human brains,
or similar organs. In particular, let us suppose that no collapse of a wave
function occurs in connection with a mechanical measuring device. In this
situation the question arises: why do different observers normally agree on
what they see; e.g., why do they all agree that the pointer on a measuring
device that they all are observing has swing, say, to the left, and not to the
right?
To discuss this question it is enough to consider just two such observers, and
to relace the state $|\Psi >$ discussed earlier by a state of the form
$$
\eqalignno{
|\Psi > &= a|\psi_{11}> \otimes |\psi_{21}>\otimes |\psi_{3a1}>\cr
&\otimes [e|\psi_{4a1x}>+f|\psi_{4a1y}>]\cr
&\otimes |\psi_{3b1}>\cr
&\otimes [g|\psi_{4b1z}>+ h|\psi_{4b1w}>]\cr
&+ b|\psi_{12}>\otimes |\psi_{22}>\otimes |\psi_{3a2}> \cr
&\otimes [p|\psi_{4a2u}>+ q|\psi_{4a2v}>]\cr
&\otimes |\psi_{3b2}>\cr
&\otimes [r|\psi_{4b2c}>+s|\psi_{4b2d}>].&(2.1)\cr}
$$
Here $|\psi_{11}>$ and $|\psi_{12}>$ are, as before, the two pertinent states of
the atom; $|\psi_{21}>$ and $|\psi_{22}>$ are the two corresponding states of
the measuring device (e.g., $|\psi_{21}> \sim$ the pointer has swung to the
left: $|\psi_{22} >\sim$ the pointer has swung to the right);
$|\psi_{3aj}>$ and $|\psi_{3bj}>$ are the states associated with the early
(unconscious) processing parts of the nervous systems of the observers ``a'' and
``b'' having registered $\psi_{2j}$, for $j = 1$ or $2$.
The states $|\psi_{4a1x}>$ and $|\psi_{4a1y}>$ are two alternative possible
brain correlates that have arisen in the brain of observer ``a'' from the
lower-level state $|\psi_{3a1}>$.
The doubling of the possibilities arises from the indeterminacy associated with
quantum processes occurring in the brain of observer ``a''.
Such an indeterminacy arises, for example, from quantum processes in the
synapses in his brain [16].
Actually, there will be many more than just two such possibilities, but two is
enough to illustrate the point.
The other states $|\psi_{4ajk}>$ and $|\psi_{4bj\ell}>$ are analogous brain
correlates of thoughts for observers ``a'' and ``b'', respectively.
Suppose observer ``a'' has the experience correlated to the brain state
$|\psi_{4a1x}>$.
This experience corresponds to the jump of the state $|\Psi>$ to the state
$$
|\Psi'> = N P_{4a1x}|\Psi >,\eqno(2.2)
$$
where $N$ is the normalization factor that makes
$$
<\Psi'|\Psi'> =1,\eqno(2.3)
$$
and
$$
\eqalignno{
P_{4a1x} &= |\psi_{4a1x}><\psi_{4a1x}|\cr
&\otimes \prod_{s\neq 4a} I_s,&(2.4)\cr}
$$
where $s$ runs over the set of systems $\{1, 2, 3, 4a, 4b)\}$, and $I_s$ is the unit
operator in the Hilbert space corresponding to system $s$.
The states $\psi_{4ajk}$ for $(j,k)\neq (1, x)$ should be orthogonal to
$\psi_{4a1x}$, because under this condition $\psi_{4ajk}$ and $\psi_{4a1x}$
are the brain correlates of definitely distinguishable experiences:
$$
<\psi_{4ajk}|\psi_{4a1x}> = \delta_{j1}\delta_{kx}.\eqno(2.5)
$$
More generally,
$$
<\psi_{mcik}|\psi_{ndj\ell}> = \delta_{mn} \delta_{cd}\delta_{ij}
\delta_{k\ell}.\eqno(2.6)
$$
But then the conditions (2.1) through (2.6) imply that the state $|\Psi'>$,
which is the state that exists just after the occurrence of the experiential
event of observer ``a'' that is correlated to $|\psi_{4ax1}>$,
is
$$
\eqalignno{
|\Psi'> &= |\psi_{11}>\otimes |\psi_{21}> \otimes |\psi_{3a1}>\otimes
|\psi_{4a1x}>\cr
&\otimes |\psi_{3b1}>\cr
&\otimes [g|\psi_{4b1z}> + h|\psi_{4b1w}>].&(2.7))\cr}
$$
At this stage of the sequential process of actualization no selection has yet
been made between the two states $|\psi_{4b1z}>$ and $|\psi_{4b1w}>$:
i.e., observer ``b''
has not yet had his experience pertaining to the position of the pointer.
But both of the possibilities available to him, namely $|\psi_{4b1z}>$ and
$|\psi_{4b1w}>$, have $j=1$, and hence correspond to his seeing the pointer in
the position specified by $j=1$: both possibilities correspond to his seeing the
pointer swung to the {\it left}.
Thus both observers will agree that the pointer has swung to the left:
intersubjective agreement is automatically assured by the quantum formalism.
According to the basic postulate (1.2), the probability for this event
correlated to $|\psi_{4a1x}>$ to occur is $|a|^2|e|^2$.
If, contrary to the supposition made at the beginning of this section, there
had been a prior event associated with the action of the device (i.e., a
projection onto $P_{21}|\Psi >)$) then, according to (1.2), the probability
for this prior event to occur would have been $|a|^2$.
Under the condition that this prior event did occur, the probability for the
occurrence of the subsequent experiential event correlated to $|\psi_{4a1x}>$
would be $|e|^2$.
Thus the probability for this final event to occur is $|a|^2 |e|^2$ in both
cases: {\it the probability for the occurrence of the experiential event does
not depend upon whether the prior event at the level of the device occurred or
not}~!
Thus there is, in this example, (as in general) no empirical evidence to
support the idea that an event occurs at
the level of the device.
If we assume, in spite of this complete lack of any supporting evidence, that
an event at the level of the device does in fact occur then the question
arises: why does the jump take the device either to the state $|\psi_{21}>$ or
to the state $|\psi_{22}>$, rather than to some linear combination of them? Why
should the classically describable states $|\psi_{21}>$ and $|\psi_{22}>$ be
singled out at the level of the quantum mechanical device itself, before any
involvement or interaction with a potential human observer has occurred.
Of course, one {\it can permit} this prior event to occur without altering the
probabilities associated with our experiences.
Hence at some practical level one may wish to assume, or pretend, that this
event at the level the device does occur.
But in a realistic context, as opposed to a pragmatic one, this fact that
this extra jump {\it could occur} without altering the propensities
pertaining to our human experiences does not seem to be a sufficient reason for
Nature to make this jump.
If Nature should, nevertheless, choose to make a jump at the level of
the device then why should she choose to actualize just a single one of the
classically describable states, $|\psi_{21}>$ or $|\psi_{22}>$, rather than some
linear superposition of them? Jumps to such superpositions would, to be
sure, alter the empirically validated predictions of quantum theory.
Hence we know empirically that jumps to such linear combinations do not occur.
But in a realistic setting there should be a general physical principle that
dictates which kind of states are actualized by the quantum jumps, and the
fact that we cannot, in practice, detect the occurrence of certain kinds
events is not a satisfactory general principle: it is based practical
considerations rather than basic structure, and is too anthropocentric.
Because events occurring at the level of the devices must have a classical
character that is hard to explain within a naturalistic framework, and because
there is absolutely no empirical evidence to support the idea that events occur
at this level, we are led to examine the more parsimonious assumption that the
quantum events or jumps (i.e., the abrupt reductions of the quantum states) are
associated primarily {\it only } with more complex systems, such as brains and
similar organs: such jumps, by themselves, are sufficient to explain all of the
scientifically accepted empirical evidence available to us today. But then a
similar question arises: why, in a realistic framework, should the brain events
associated with the perceptions of external objects correspond to experiences
of objects that are classically describable if these objects themselves, before
they are perceived, are represented by superpositions of such states? That is,
although we know, {\it on empirical grounds}, within the framework of our
theory, and to the extent that the structure of each experience mirrors [17, Ch.
6] the structure of its brain correlate, that the events at the level of brain
correlates of perceptions must actualize brain states that have classically
describable aspects, nevertheless the question arises: {\it why} should
classical conditions be singled out in this way within a quantum universe? Is
there something intrinsically classical about the character of possible
perceptions; something that then forces any brain correlate that mirrors one of
these perceptions to have corresponding classical aspects? That is, must we
resort at this stage to some essentially metaphysical reason? Or, on the
contrary, can the classical character of the brain events, and hence of
mirroring thoughts, be deduced from strictly physical consideration alone?
\newpage
\noindent{\bf 3. Consciousness and Survival}
\medskip
William James observed that ``the study of the phenomena of consciousness which
we shall make throughout this book shows us that consciousness is at all times
primarily a selecting agency''[10, p.139, p.284].
Note that this conclusion is based on a survey of phenomena, rather than on our
immediate subjective feelings.
Our most important and rudimentary choices, such as fight or flight, have to do
with our survival.
Thus from a naturalistic, or purely physical, point of view the character of
consciousness ought to be a consequence of evolutionary pressures.
Within the framework of classical mechanics no such connection is possible, for
in that framework the entire course of natural history is completely fixed by
microscopic considerations involving only particles and local fields.
Any additional structures that we might care to identify, as ``realities'' are,
insofar as they are efficacious, completely reducible to these microscopic ones,
and hence are, as far as the dynamical development of any system is concerned,
completely gratuitous: how they are constructed from, or are related to, the
elementary microscopic realities, or whether they exist at all, has no bearing
on the survival of any organism.
But within the framework of quantum mechanics developed here consciousness does
have a causally efficacious role that is tied directly to the selections of
courses of action: consciousness is a bone fide selecting agency.
Thus it becomes at least logically possible within the quantum framework to link
the character of human consciousness to the evolutionary pressures for human
survival.
Considerations of wholeness led Haldane to suggest that mind is linked to
resonance phenomenoma.
This intuition has been revived by Crick and Koch [6], who suggest that the
empirically observed [7] 40 Hertz frequencies that lock together electrical
activities in widely separated parts of the brain is associated with
consciousness.
I shall accept this general idea of a resonance type of
activity involving widely separated parts of the brain as a characteristic of
the brain correlate of a conscious thought, although the idea of an
``attractor'' would do just as well.
Since energy is available in the brain, the feed-back resonance of a public
address system is a suitable metaphor. [18]
Generally a superposition several alternative possible ``resonant'' or
``attractor'' states will emerge from the quantum dynamics [16, 17, Ch. 6.4].
This is illustrated by the different states $\psi_{4a1x}$ and $\psi_{4a1y}$ in
(2.1). These alternative possible states have certain ``classical'' aspects:
riding on a chaotic ocean of microscopic activity there will be certain
collective variables that are relatively stable and slowly changing, and that
can be called the macroscopic variables of the system. They will be the
variables of classical electromagnetism: charge densities, electric field
strengths, etc., and they are defined by averaging over regions that are small
compared to the brain, but large compared to atoms. The states $\psi_{4a1x}$
and $\psi_{4a1y}$, or, more accurately, the projection operators $P_{[4a1x]}$
and $P_{[4a1y]}$ corresponding to {\it collections} of many micro states
subsumed under the macroscopic characteristics identified by the symbols
$[4a1x]$ and $[4a1y]$, will be characterized in terms of these macroscopic
(classical) variables. These macro-variables will contain both the information
pertaining to the location of the pointer on the external device (specified
here by $j=1)$, and also the additional macroscopic specifications labelled by
the indices $x$ and $y$. Notice that a sum $P$ of orthogonal projection
operators $P_i$,
$$
P =\sum_i P_i \ \ \ \ \ \ P_iP_j = \delta_{ij} P_i,
$$
is a projection operator: $P^2=P$. Hence the quantum rules described above
apply to these operators $P_{[4a1x]}$ and $P_{[4a2y]}$ that are formed as sums
over sets of orthogonal operators $P_i$ that meet the indicated specifications.
Two questions now arise.
The first is this: why should evolutionary pressures tend to force the events in
brains to correspond to projection operators $P$ that project onto
``resonance'' or ``attractor'' states that involve large parts of the brain,
and many neurons, rather than, say, to projection operators that project onto
macroscopically specified states of individual neurons?
The second question is this: why, if the evolutionary pressures do tend to
force the brain events to correspond to large structures, such as large-scale
resonances or attractors, do they not tend to force the events even further in
the direction of largeness, and allow them to correspond to {\it superpositions
} of classically describable macroscopically specified states, instead of
individual ones.
These two questions are addressed in the following two sections.
\newpage
\noindent{\bf 4. Survival Advantage of Having Only Top-Level Events.}
\medskip
A principal task of the brain is to form templates for possible impending
actions. Each such template is conceived here to be resonance or attractor
state that involves activity that is spread out over a large part of the brain.
The evolutionary pressure for survival should tend to promote the emergence of
a brain dynamics that will produce the rapid formation of such top-level
states. However, as will be discussed in this section, the occurrence of
quantum events at lower levels (e.g., at the levels of individual neurons, or
smaller structures) will act as a source of noise that will tend to {\it
inhibit} the maximally efficient formation of these top-level states. Thus the
evolutionary pressure for survival will tend to force the events in brains to
occur preferentially at the higher level, i.e., to actualize mainly the
top-level states. Each of our conscious thoughts seems to have only the
information that is present in the part of the brain state that is actualized
by one of these top-level events [17, Ch. 6]. Hence it is natural to
postulate that the top-level states actualized by quantum events are
precisely the brain correlates of our conscious thoughts.
In the simple example examined earlier there was a separation at each of the
$N-1$ macroscopic levels into two macroscopically distinct branches, labelled
by $j= 1$ or $2$, and there was consequently a natural way to define the
projection operators $P_{n1}$ and $P_{n2}$ at the lower levels that were
effectively equivalent, within that measurement context, to the two
final projection operators $P_{N1}$ and $P_{N2}$ that were
directly associated with the two distinct classically describable experiences.
However, if we try to trace back through the brain dynamics to find
the lower-level projection operators that are
equivalent to the ones associated with top-level events then we would find
operators that are neither simple nor natural.
Moreover, there would be no rationale for projecting at some lower level onto
precisely the low-level brain states that would eventually lead to the
various distinct top-level states.
There is, on the other hand, a widely held notion that brain activity is
basically classical at the level of neuron firings, so that there never is a
superposition of, for example, a state in which some neuron is firing and a
state in which it is not firing.
To reconcile this intuitive idea with our realistically formulated quantum
mechanics we would need to have low-level events that would prevent quantum
superpositions of distinct classically describable states of individual neurons
from developing, or persisting.
There is, however, a problem in implementating this idea.
The processes occurring in brains depend upon the probability densities for
various atoms and ions to be in various places at various times.
These densities are essentially continuous in quantum theory, and this makes
the brain dynamics essentially continuous: a neuron can fire a little sooner,
or a little later, or a little more strongly or weakly, etc.
The quantum propensities define, therefore, only an amorphous structure, insofar
as no events occur. But then the question is: how, in this initially amorphous
situation, does one introduce a set of events (quantum jumps or collapses) that
will keep the lower level (i.e., neuronal) situation essentially classical?
How does one characterize the appropriate low-level projection operators $P_i$
onto classical states in cases where the quantum dynamics itself does not
separate the state into classically distinct and non overlapping low-level
branches? The ``measurement'' situation discussed earlier is essentially
misleading, if applied to the present case,
because it did not involve this problem of reducing an {\it amorphous}
quantum state that is not already decomposed into well separated ``classical''
parts into a description that is essentially classical.
A way of dealing with this problem was proposed in [15].
It is based on coherent states [11, 12].
For any complex number $z = (q+ip)/\sqrt{2}~$
let $|z>$ define a state whose wave function in (a one-dimensional) coordinate
space is
$$
\psi_z(x) = = \pi^{-1/4} e^{ipx} e^{-\half (x-q)^2}.\eqno(4.1)
$$
This state is normalized,
$$
=\sum_x =1,\eqno(4.2)
$$
and it satisfies the important property ,
$$
\eqalignno{
\int {dz\over\pi} |z>$
is
$$
\rho\to \rho'=\sum_zP_z\rho P_z.\eqno(4.4)
$$
This mixture $\rho'$ is ``equivalent'' to $\rho$ in the sense that if
$$ is a slowly varying function of its two variables $x$ and $x'$, on
the scale of the unit interval that characterizes the width of the ``classical''
states $|z>$, then, for any $z'$, one has
$$
\approx.\eqno(4.5)
$$
Proof:
$$
\eqalignno{
&\cr
&=\sum_z \cr
&\approx\sum_z\cr
&=,
\cr}
$$
where the fact that $$ is strongly peaked at $z'=z$ is used.
Thus the transformation from $\rho$ to $\rho'$ leaves the diagonal (and the
nearly diagonal) elements of
$$ approximately unchanged, but changes $\rho$ to a classically
interpretable mixture of states that are localized in coordinate space, on a
certain (unit) scale.
The relationship
$$
Tr\rho'=Tr \rho\eqno(4.6)
$$
also hold.
Proof:
$$
\eqalignno{
& \ \sum_x \cr
&= \sum_x\sum_z \cr
&=\sum_z \sum_x\cr
&= \sum_z\sum_x\sum_{x'} \cr
&=\sum_x\sum_{x'} \cr
&=\sum_x.\cr}
$$
Suppose the dynamics is such as to generate and sustain a state
$|0> $ (i.e., $|z=0>)$ that is a component of a top-level
resonant state. The property of the dynamics to sustain the state $|0>$, but
to cause states orthogonal to it to dissipate, is expressed by the conditions
$$
U(t) |0> = |0>,\eqno(4.7)
$$
for all $t>0$, where $U(t)$ is the unitary operator that generates the evolution
from time zero to time $t$, and for each pair $(z', z)$
$$
\Longrightarrow 0,\eqno(4.8)
$$
where
$P_0 = |0><0|$, and the double arrow signifies the large-time limit.
Then for any pair $(z', z'')$ we have, by virtue of (4.8) and (4.7), (and
assuming that $$ tend to zero for large $|z|$),
$$
\eqalignno{
&,\cr
\Longrightarrow &\cr
=&<0|\rho|0><0|z''>&(4.9)\cr}
$$
Similarly, for any pair $(z', z'')$ and slowly varying $\rho$,
$$
\eqalignno{
&\cr
=\sum_z&\cr
\Longrightarrow \sum_z &<0|z><0|z''>\cr
\approx \sum_z &<0|z><0|\rho|0><0|z''>\cr
= &<0|\rho|0><0|z''>.&(4.10)\cr}
$$
Thus the change from $\rho$ to $\rho'$ makes little difference in these matrix
elements: the statistical mixture of classical states $\rho'$ have approximately
the same matrix elements as the original $\rho$.
After some finite time, however, an originally smooth $\rho$ will, by
virtue of (4.7) and (4.8), develop a classical component proportional to
$|0><0|=P_0$ that will stand out from the smooth background.
Consider, therefore, the effect of the dynamics on $\rho$ and $\rho'$ for this
part of $\rho$ proportional to $\rho_0=P_0$:
$$
\eqalignno{
&\cr
\Longrightarrow &<0|z''>,&(4.11)\cr}
$$
whereas
$$
\eqalignno{
&\cr
= \sum_z &\cr
\times &<0|z>&(4.12)\cr}
$$
$$
\eqalignno{
\Longrightarrow \sum_z &<0|z><0|z><0|z''>\cr
= &<0|z''>\times\sum_z(<0|z>)^2.&(4.13)\cr}
$$
But
$$
0< \ (<0|z>)\ <1\ \ \hbox{for all} \ z\neq 0\eqno(4.14)
$$
and
$$
\sum_z <0|z>=1.\eqno(4.15)
$$
Hence
$$
\sum_z (<0|z>)^2 <1.\eqno(4.16)
$$
Thus the effect of introducing the events that convert $\rho$
to the classical approximation $\rho'$ has the effect of disrupting the
preservation of the state $|0>$:
the probability of staying in this ``preferred'' state is diminished by the
effects of introducing the low-level events.
Although this result was obtained under simplifying assumptions that allowed us
easily to compute the effect, the conclusion is certainly quite general.
It arises essentially from the fact that the transformation $\rho\to\rho'$
``flattens out'' a bump in $\rho$ that is already of a classical size, and hence
inhibits the emergence of a single classical state from an amorphous background.
The problem, in the general context, is this: the quantum dynamics is likely to
be such that certain resonance states (preferred for their survival
advantages) will emerge from an amorphous backgrounds of quantum probabilities.
(See [18]). Each of these resonance states will be a collective phenomena
involving many neurons. The emerging resonant state will be characterized by
specific relationships in the timing of the firings of the various neurons. The
incipient resonances can generate bumps, but it is not known to the system {\it
beforehand} which specific combinations of firing timings will eventually
emerge from the smooth quantum soup via the complex feed-back mechanisms.
The quantum dynamics allows the `optimal' self-generating resonant states to
emerge from the amorphous quantum soup with a certain maximal efficiency,
because all of the possible overlapping configurations of classical
possibilities are simultaneously present, and their consequences are
simultaneously explored by the quantum dynamics. {\it After} the dynamics has
generated an output consisting of a superposition of distinct classical
top-level resonating states {\it then} an event can occur that will select one
of these top-level possibilities without interfering with the dynamics that has
just generated the various top-level possibilities. But if events are required
to occur at a lower level, in order to impose the condition of classical
describability there, then, in order to maintain the maximal efficiencies for
the production of the top-level states, these events would have to project upon
states that have optimal relationships among the timings of the firings of the
neurons. But these timings are not yet known to the system. Thus the
introduction of a statistically distributed set of low-level (e.g.,
neuron-level) events can achieve the demanded reduction to a classical
description at the low level, as in our example, but this disruption of the
quantum dynamics will normally, just as it did in our example, inject into the
evolution of the system an element of noise that will tend to reduce the
efficiency of generating and sustaining the top-level states that resolve in an
optimal way all of the physical constraints on the system (these contraints
being just the brain's representation of the considerations and weightings that
limit and guide the person's response to the situation in which he finds
himself)
The presently known, or empirically tested, principles of quantum theory do not
determines the level at which the ``events'' associated with system such as a
human brain occur. But within a naturalistic setting this level should be
determined by some internal property of that system itself, not by external
fiat. In this case the arguments given above would lead to the conclusion that
evolutionary process should cause brains to evolve in such a way as to create
the properties that cause the events occurring in alert brains to shift to the
top level, thus leaving the dynamics at the neuronal level and below controlled
by the local deterministic quantum law of evolution, namely the Schroedinger
equation. For the creation of these properties will permit the quantum process
to efficiently generate the optimal solutions to the problems that face the
organism without being hindered or blocked by the disruptive effect of the
noise generated by low-level events.
This is the central point, and so a more detailed statement may be in order.
A main defect of the Heisenberg ontology is that no detailed rule is given that
specifies where (at what level) the actual events occur. One possible way to
complete the theory is just to give some system-independent universal rule
(such as the rule proposed by Ghirardi, Rimini, and Weber). But another
possibility is that the place, or level, where the events occur is determined
by properties of the system in which they occur.
Biological systems should have a tendency to evolve into systems that generate
energetic resonating modes that lead to beneficial behaviour. This is because
such modes would be an effective way to store the energy needed to drive an
ordered sequence of actions. Each such mode is essentially a simple harmonic
oscillator mode of the kind that naturally gives rise to a decomposition into
coherent states of the kind used in this section.
If there were a possible physical property P of the biological system that
would have a tendency to cause the events to occur predominantly in an
oscillating mode that carries a large amount of energy, or in a chord of
resonating states that carry a large amount of energy, then it would increase
the chances of survival for members of the species if the organisms were to
develop P, for, as the mathematical arguments in this section have shown,
lower-level events tend to introduce a noise that prevents the best solution
from emerging, or emerging as rapidly. Thus the occurrence of P in the system
would have the effect of reducing the noise in the process of generating the
oscillating modes that embody the templates for action: the optimal modes would
be able to emerge, and emerge more rapidly. Thus the evolutionary pressure
would tend to encourage the occurrence of the property P that causes the
actualization events to be high-level, insofar as these high-level events
create optimal solutions to the dynamical conditions.
If this property P were , in fact, just the presence of these high-energy modes
themselves then the evolutionary advantage of the organism's developing these
modes would be doubly enhanced, because these modes would be then both a
natural carrier of templates for action and also the cause of the suppression
the disruptive noise of low-level events that tend to block the emergence
of the optimal states in these modes.
Actualization events presumeably occur also outside biological systems.
However, it may be profitable to study biological systems first. This is
because, as Bohr stressed, the Copenhagen interpretation is inadequate for
biological systems, and extra ideas are required to deal with them, while, on
the other hand, it seems virtually impossible to extract from experiments on
inanimate laboratory systems any information beyond what the non-ontological
Copenhagen interpretation provides. Cosmological systems might likewise be
source of useful information.
\newpage
\noindent{\bf 5. Classical Description}
\medskip
Classical concepts have entered in an important way into the above description
of the process of actualization of the quantum states: the projection operators
associated with the events have been characterized by classically describable
conditions on certain macroscopic variables. The question thus arises: why
should classical concepts enter at all into the evolution of the quantum
universe? Why should the quantum events project onto states in which the values
of macroscopic field variables at spacetime points are confined to small
domains, instead of projecting onto {\it superpositions} of such classically
describable states?
Here again an answer based on the survival of the species can be given. It is
tied to the local character of the interaction and the concept of symbol.
A {\it symbol} is a physical structure that can be ``interpreted'' by a
mechanism: the mechanism gives a characteristic response to the symbol. In our
model the various actualized states in the brain, the brain correlates of
thoughts, act as symbols. These states are characterized by definite values of
macroscopic classical-type variables, and the motor responses are determined in
large measure by classically describable reactions to the classically
describable inputs provided by these symbols. But then the question is: why
should the quantum events actualize states having this special classical
character instead of superpositions of such states?
To find the answer suppose that the brain has evolved to a point where the
brain correlates have been generated, and that for simplicity, these states are
just two in number. Let these two brain correlates be denoted by $|\varphi_1>$
and $|\varphi_2>$. These two states are supposed to be characterized by
macroscopic variables that are significantly different. Consequently, these two
states will, because of the local character of the interaction, very quickly
generate greatly differing (orthogonal) states in the embedding ocean of
microscopic variables: the brain will, to a very good approximation, evolve to
a state of the form
$$
|\psi> = a|\varphi_1>|\chi_1>+b|\varphi_2>|\chi_2>,\eqno(5.1)
$$
where the states $|\chi_1>$ and $|\chi_2>$ are orthogonal states in the
imbedding space of microscopic degrees of freedom.
The importance of states such as (5.1) is that the significant information is
concentrated into the classical level of description, i.e., in the states
$|\varphi_1>$ and $|\varphi_2>$, and this macroscopically represented
information can control, in large measure, the ongoing evolution via the laws
of classical physics. This provides the evident evolutionary advantage in
having the events correspond to projection operators that act at the level of
the macrovariables, for then the consequences of the selection associated with
an event can be largely governed by deterministic classical laws. But the
question before us now is whether there could be any additional advantage in
having the events correspond to operators that project onto {\it
superpositions} of such macrostates.
In the present simple example the question is whether it could be advantageous
to have events that correspond to projection operator such as
$$
P=(c|\varphi_1>+d|\varphi_2>)(c^*<\varphi_1|+d^*<\varphi_2|) \times
I_\chi\eqno(5.2)
$$
with $cd\neq 0$.
The density operator in our example is
$$
\rho = |\psi><\psi|,\eqno(5.3)
$$
with $|\psi>$ defined in (5.1).
Our first observation is that
$$
Tr P\rho = Tr P\rho',\eqno(5.4)
$$
where
$$
\eqalignno{
\rho' &= |a|^2 |\varphi_1 > |\chi_1><\chi_1|<\varphi_1|\cr
&+|b|^2 |\varphi_2>|\chi_2><\chi_2|<\varphi_2|.&(5.5)\cr}
$$
\noindent Proof:
$$
\eqalignno{&\ Tr P\rho\cr
&= \sum_x + d|\varphi_2>)(c^*<\varphi_1|+d^*<\varphi_2|)\cr
& \hskip .5in \times (a|\varphi_1>|\chi_1>+ b|\varphi_2>|\chi_2>)\cr
&\hskip .5in \times (a^*<\varphi_1|<\chi_1|+b^*<\varphi_2|<\chi_2|)|x>\cr
&= (c^* < \varphi_1| +d^* <\varphi_2|)\cr
&\hskip .5in \times (a|\varphi_1>|\chi_1> + b|\varphi_2> |\chi_2>)\cr
&\hskip .5in \times (a^*<\varphi_1|<\chi_1| + b^*<\varphi_2|<\chi_2|)\cr
&\hskip .5in \times (c |\varphi_1> + d |\varphi_2>)\cr
&= c^* aa^* c + d^* bb^*d\cr
&= |a|^2 |c|^2 + |b|^2 |d|^2\cr
&= Tr P\rho'.&(5.6)\cr}
$$
This means that the probability for the occurrence of the event associated with
$P$ is the same for the density operator $\rho'$ as it is for $\rho$.
Given the fact the information available for determining the subsequent
(macroscopically controlled) dynamics is contained in $\rho'$, what is the form
of $P$ that least degrades this information?
The answer is $P$ with $cd =0$: the $P$ should be either
$|\varphi_1><\varphi_1|$ or $|\varphi_2><\varphi_2|$.
For example, if $|\varphi_1>$ corresponds to a very good choice for the
organism, and $|\varphi_2>$ a very poor one, so that a well conditioned brain
will give a $\rho$ with $|a|^2\simeq 1$ and $|b|^2\simeq 0$, and if the $P$ is
given by (5.2) with $|c|^2 = |d|^2=1/2$ then (5.6) shows that all the
information about $|a|^2$ and $|b|^2$ will be lost: the result is
$1/2(|a|^2+|b|^2)=1/2$ independently of $|a|^2$ and $|b|^2$. This special
example already suggests the answer: $P$ should be either
$|\varphi_1><\varphi_1|$ or $|\varphi_2><\varphi_2|$, in order to retain all
the information. Any other choice causes a degradation of the information
generated by the brain dynamics. In general, the optimal choice for the $P$ is
that it should be one of a set of $P$'s each of which projects onto a single
one of the classically described states generated by the brain dynamics:
otherwise some information generated by the brain will be lost, and the
likelihood that the organism will survive will be diminished.
\newpage
\noindent {\bf 6. Inequivalence of Other Ontological Interpretations}
\medskip
There is an alternative interpretation of quantum theory that can be construed
as an ontology --- i.e., as a putative description of nature herslf --- but in
which there are no collapse events. This is Everett's ``many-minds''
interpretation [8,14]. In this interpretation there is no natural place to
introduce the mental events because nothing ever ``happens'': the entire course
of history is continuously laid out on a spacetime plot, with no clear notion
of any `` actual happenings'' or events.
It is difficult, and I think impossible, to give any rational meaning to
``probability'' in an Everett world where there are no definite happenings or
events. Indeed, because the components of a superposition must be combined
conjunctively --- since in principle they can interfere with each other ---
each of the possibilities present in the evolving state of the universe must
exist together with every other one. Hence they cannot have the independent
probabilities for coming into existence that is allowed for the elements of a
{\it disjunctive} combination of possibilities. Indeed, all of the branches of
the state vector are supposed to exist in unison. The mere fact that that this
physical state can be separated into a superposition of components that
correspond to noncommunicating realms of experience, or to distinct recorded
histories, does not, by itself, make the probabilities for the coming into
existence of these various physical components any different from the single
probability of the whole of which they are the simultaneously existing parts,
or from the probabilities that these parts would have if the associated
experiential realms were not completely noncommunicating. Yet, for empirical
reasons, tiny probabilities must often be assigned to some branches and large
probabilities to others, even though all of them exist in unison, according to
the Everett view.
The only apparent rational way to reconcile these requirement is to introduce
into the ontology some entities, besides the quantum state itself, for the
probabilities to refer to. To make the necessary tie-in to empirical data these
must correspond in some way to growing historical experiencable records that
are allowed to prolong themselves into the future in alternative possible ways,
with the alternative possibilities populating the different branches of the
state vector of the evolving universe. Then the model becomes endowed with
`happenings', namely the selections or choices of the prolongations of each of
these histories into the future, and, correspondingly, with choices between the
simultaneously existing branches of the state vector.
The probabilities for these events are supposed to be governed by the quantum
rules. However, in the Everett framework these events do not influence the
evolution of the quantum state: the influence or control is unidirectional,
from the quantum state to the events. Thus everything is controlled by the
Schroedinger equation except for individual choices, which, however, are buried
in a population whose statistical properties are controlled by the locally
deterministic Schroedinger equation. Thus, within this framework, no arguments
based on survival of organisms can be used to determine just where to locate
the particular physical activities in our brains that correspond to our
thoughts. Any placement would be equivalent, as far as survival is concerned,
to any other one, because the placement is not connected to any difference in
the dynamical evolution of the statistical ensemble that constitutes the full
system: just as in classical mechanics, the evolution of the full system is
completely deterministic, and is independent of where, in the dynamical
unfolding, nature chooses to place the physical correlate of the epiphenomenal
consciousness.
Likewise in Bohm's nonlocal deterministic ontological model [2] the
placement of the nonefficacious consciousness within the deterministically
evolving universe has no effect upon the course of nature, and hence none upon
the suvival of the species. Hence the mechanisms for the evolution of
consciousness discussed here cannot be operative in either of these alternative
frameworks, essentially because consciousness is not efficacious in these
models
\newpage
\noindent{\bf 7. Conclusions }
\medskip
It was suggested by Haldane and Wiener, shortly after the birth of quantum
mechanics, that this profoundly deepened understanding of the nature of matter
allows mind to be liberated from the epiphenomenal status assigned to it by
classical mechanics, and to become, instead, an aspect of nature that is {\it
interactive with}, rather than {\it subservient to}, the local deterministic
matter-like aspect of nature that was mistakenly identified as the entire
physical universe by classical mechanics. This suggestion of Haldane and Weiner
remains viable today and, indeed, is being vigorously pursued. Haldane's
further suggestion that mind is associated with a resonance phenomena has been
revived by Crick and Koch, without its quantum foundation, and is the basis one
of today's premier research programs on the mind-brain problem.
If the level of brain dynamics at which the quantum event occurs is determined
by the physical characteristics of that organ itself, then there should exist
effective evolutionary pressures that will tend to raise this level to the top
level, which is characterized as the formation of macroscopic templates for
possible impending action in which classically describable aspects, expressed
in terms of the macroscopic variables of classical electrodynamics, form
symbols for the activation of processes that, at least in the case of motor
processes, remain largely controlled by macroscopic variables acting in
accordance with classical laws. The general brain process will remain
essentially quantum mechanical. On the other hand, due to the local character
of the interaction, there will also be evolutionary pressure for the top-level
event not to go beyond the classically describable level to the level of {\it
superpositions} of classically describable states. Thus the classical character
of our thoughts, if assumed to mirror the relational structures
specified by the projection operators $P$ associated with the corresponding
brain events [17 Ch. 6], can be naturally explained within the mathematical
framework of quantum mechanics.
This evolution-based explanation of the classical character of our thoughts,
and hence of the observed physical world itself, is independent of whether or
not classically describable events occur at the level of mechanical measuring
devices.
Although the argument given above was specialized to the human organism, it
applies equally well to all organisms whose structure is governed by
evolutionary pressures for survival: the general conclusion would be that in
all such organisms the freedom that inheres in each of its component subsystems
to make quantum choices should be suppressed to the extent that such choices
interfere with the quantum process of the organism as a whole to create
top-level templates for possible actions, and that there should be in all such
organisms top-level events each of which actualizes one of the
templates for possible action generated by the local-deterministic part of the
quantum dynamical process. The way in which the selected event is singled out
from all the other possibilities generated by the quantum dynamics is not yet a
part of what science has revealed to us.
References
1. D. Bohm, Comments on [32c], [34c], [36g] in {\it Norbert Wiener:
Collected Works, Vol.III,} ed. P. Masani, MIT Press, 1985.
2. D. Bohm and B. Hiley, {\it The Undivided Universe: An Ontological
Interpretation of Quantum Theory}, Routledge, London and New York, 1993.
3. N. Bohr, {\it Atomic Theory and the Description of Nature},
Cambridge University Press, Cambridge, 1934.
4. N. Bohr, {\it Atomic Physics and Human Knowledge}, Wiley,
New York, 1958.
5. N. Bohr, {\it Essays 1958/1962 on Atomic Physics and Human
Knowledge}, Wiley, New York, 1963.
6. F. Crick, {\it The Astonishing Hypothesis: The Scientific Search
for the Soul}, Scribner, New York, 1994.
7. A.K. Engle, A.K. Kreiter, P. Koenig, and W. Singer, Synchronization
of oscillatory neuronal responses between striate and extrastriate
visual cortical areas of the cat, {\it Proc. Nat. Acad. Sci.} {\bf 88}(1991),
6048-6052; Interhemispheric synchronization of oscillatory neuronal responses
in cat visual cortex, {\it Science} {\bf 252}(1991), 1177-1179.
8. Hugh Everett III, Relative State Formulation of Quantum Mechanics,{\it
Rev. Mod. Phys.} {\bf 29}(1957), 454-62.
9. J.B.S. Haldane, Quantum Mechanics as a Basis for Philosophy,
{\it Philos. Sci.} {\bf 1}(1934), 78-98.
10. W. James, {\it The Principles of Psychology}, Vol I,
Dover, New York, (1890).
11. J.R. Klauder and B. Skagerstam, {\it Coherent States}, World
Scientific, Singapore, (1985).
12. J.R. Klauder and E.C.G. Sudarshan, {\it Fundamentals of Quantum
Optics}, W.A. Benjamin, New York, 1968.
13. P.A. Schilpp, {\it Albert Einstein: Philosopher-Scientist},
Tudor, New York, 1949.
14. H.P. Stapp, {\it Locality and Reality},
Found. Phys. {\bf 10}(1980), 767-795.
15. H.P. Stapp, in {\it Quantum Implications: Essays in Honor of David Bohm},
Routledge and Paul Kegan, London and New York, (1987) pp. 255-266.
16. H.P. Stapp, {\it Quantum Propensities and the Mind-Brain Connection},
Found. Phys. {\bf 21}(1991), 1451-1477.
17. H.P. Stapp {\it Mind, Matter, and Quantum Mechanics}, Springer
Verlag, Berlin, Heidelberg, New York, London, Paris, Tokyo, Hong Kong,
Barcelona, Budapest, 1993.
18. H.P. Stapp, The Integration of Mind into Physics, {\it Fundamental
Problems in Quantum Theory}, Annals of the
New York Academy of Science Vol. {\bf 755}(1995), 822-833.
19. J. von Neumann, {\it Mathematical Foundations of Quantum Mechanics}
(1932), (English translation) Princeton University Press, Princeton, 1955.
Norbert Wiener References
To assist the reader, the numbering used for the Wiener references is that
adopted in his {\it Collected Works, IV} , MIT Press, Cambridge, MA, 1985.
[32c] N. Wiener, Back to Leibniz! (Physics reoccupies an abandoned
position), {\it Tech. Rev.} {\bf 34}(1932), 201-203, 222, 224.
[34c] N. Wiener, Quantum Mechanics, Haldane, and Leibniz,
{\it Philos. Sci.} {\bf 1}(1934), 479-482.
[36g] N. Wiener, The Role of the Observer, {\it Philos. Sci.}
{\bf 3}(1936), 307-319.
This work was supported by the Director, Office of Energy
Research, Office of High Energy and Nuclear Physics, Division of High
Energy Physics of the U.S. Department of Energy under Contract
DE-AC03-76SF00098.
\end{document}
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