%REPORTMASTER (revised 8/24/88)
\documentstyle[12pt]{article}
\input math_macros.tex
\def\baselinestretch{1.2}
\def\thefootnote{\fnsymbol{footnote}}
\begin{document}
\begin{titlepage}
\begin{center}
May 29, 1997 \hfill LBNL- 40369 \\
\vskip .5in
{\large \bf On Quantum Theories of the Mind}
\footnote{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.}
\vskip .50in
Henry P. Stapp\\
{\em Lawrence Berkeley National Laboratory\\
University of California\\
Berkeley, California 94720}
\end{center}
\vskip .5in
\begin{abstract}
Replies are given to arguments advanced in this journal that claim to show
that it is to nonlinear classical mechanics rather than quantum mechanics
that one must look for the physical underpinnings of consciousness.
\end{abstract}
\end{titlepage}
%THIS PAGE (PAGE ii) CONTAINS THE LBL DISCLAIMER
%TEXT SHOULD BEGIN ON NEXT PAGE (PAGE 1)
\renewcommand{\thepage}{\roman{page}}
\setcounter{page}{2}
\mbox{ }
\vskip 1in
\begin{center}
{\bf Disclaimer}
\end{center}
\vskip .2in
\begin{scriptsize}
\begin{quotation}
This document was prepared as an account of work sponsored by the United
States Government. While this document is believed to contain correct
information, neither the United States Government nor any agency
thereof, nor The Regents of the University of California, nor any of their
employees, makes any warranty, express or implied, or assumes any legal
liability or responsibility for the accuracy, completeness, or usefulness
of any information, apparatus, product, or process disclosed, or represents
that its use would not infringe privately owned rights. Reference herein
to any specific commercial products process, or service by its trade name,
trademark, manufacturer, or otherwise, does not necessarily constitute or
imply its endorsement, recommendation, or favoring by the United States
Government or any agency thereof, or The Regents of the University of
California. The views and opinions of authors expressed herein do not
necessarily state or reflect those of the United States Government or any
agency thereof or The Regents of the University of California and shall
not be used for advertising or product endorsement purposes.
\end{quotation}
\end{scriptsize}
\vskip 2in
\begin{center}
\begin{small}
{\it Lawrence Berkeley Laboratory is an equal opportunity employer.}
\end{small}
\end{center}
\newpage
\renewcommand{\thepage}{\arabic{page}}
\setcounter{page}{1}
In a paper with the same title as this one Alwyn Scott (1996) has
given reasons for rejecting the idea that quantum theory will play an
important role in understanding the connection between brains and
consciousness. He suggests that it is to nonlinear classical mechanics, not
quantum mechanics, that we should look for the physical underpinnings of
consciousness. I shall examine here all of his arguments, and show why each
one fails.
He first contrasts the linearity of quantum theory with the nonlinearity
of certain classical theories, and notes the complexities induced by the
latter. Thus he asks: "Is not liquid water essentially different from gaseous
hydrogen and oxygen?" Of course it is! And this difference is generated,
according to quantum field theory, by certain nonlinearities in that theory,
namely the nonlinearities in the coupled {\it field equations}. These field
equations (or, more generally, Heisenberg equations) are the direct analogs
of the coupled nonlinear equations of the corresponding classical theory, and
they bring into quantum theory the analogs of the classical nonlinearities:
these nonlinearities are in no way obstructed by the linearity of the
{\it wave equation}.
To understand this point it is helpful to think of the equation of motion
for a classical statistical ensemble. It is linear: the sum of two
classical statistical statistical ensembles evolves into the sum of the two
evolved ensembles. This linearity property is a trivial consequence of the
fact that the elements of the ensembles are imaginary copies of one single
physical system, in different contemplated states, and hence they do not
interact with one another. Thus in classical statistical mechanics we have
both the (generally) nonlinear equations for coupled {\it fields}, and also
the (always) linear equation for a certain statistical quantity.
Similarly, in quantum field theory we have both the (generally) nonlinear field
equations for the coupled {\it fields}, and also the (always) linear wave
equation for a certain statistical quantity, the {\it wave function}. The
fact that a group of several atoms can behave very differently from how they
would behave if each one were alone is a consequence of the nonlinearity of the
field equations: this nonlinearity is not blocked by the linearity of the
wave equation.
This blurring of the important distinction between the completely
compatible linear and nonlinear aspects of quantum theory is carried over
into Scott's discussion of solitons. The nonlinear field equations make the
parts of this configuration of fields hang together indefinitely, and never
spread out like a wave, as could be verified by doing experiments that
probe its `togetherness' by making several measurements simultaneously at
slightly separated points: the various simultaneously existing parts of
the soliton never move far apart. There is no conflict between this
stability of the soliton and the linearity of the quantum mechanical
wave equation. The wave function for the {\it center-of-mass of the
soliton} does eventually spread out in exactly the way that a
{\it a statistical ensemble} consisting of the {\it centers of the solitons}
in an ensemble of freely moving solitons (of fixed finite extension) would do:
the spreading out of the {\it wave function} of the center-of-mass of a
soliton just gives the diffusion analogous to the spreading out of a
statistical ensemble of superposed {\it centers of mass}, due to the
distribution in this ensemble of velocities of these centers of mass:
the extended object itself, the soliton, does not spread out; its parts are
held together by a nonlinear effect that can be attributed to the nonlinearity
of the field equations.
This blurring by Scott of the important conceptual distinctions between the
two very different aspects of the soliton associated with the linear and
nonlinear aspects of quantum theory creates, I think, a very false impression
some significant deficiency of quantum theory with regard to the manifestation
of the analogs in quantum theory of nonlinear classical effects. No such
deficiency exists: the atoms of hydrogen and oxygen do combine, according to
quantum theory, to form water.
Failure carefully to follow through this conceptual distinction is
the root of the failures of all of Scott's arguments.
Scott emphasizes the smallness of the spreading of the wave function of
the center-of-mass of Steffi Graf's tennis ball. That situation involves
the motion of a large massive object, the tennis ball, relative to, say,
a baseline on a large tennis court.
The pertinent analogous situation in the brain involves the motion of a calcium
ion from the exit of a microchannel of diameter 1 nanometer to a target trigger
site for the release of a vesicle of neuro-transmitter 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. So 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 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".
Thus, if there is a situation in which a certain particular {\it set of
vesicles} are released, due to the relevant calcium ions having been
captured at the appropriate sites, then there will be other nearby parts of
the wave function of the brain in which some or all of the relevant captures
do not take place---because, for this part of the wave function, the
calcium ion misses the target---and hence the corresponding vesicles
are not released.
This means, more generally, in a situation that corresponds to a very large
number N of synaptc 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 very different macroscopic behaviours of the body
that is being controlled by the this brain, via the {\it highly nonlinear}
neurodynamics of the brain. This nonlinear dynamics, which can probably be
approximated reasonably well by a classical model, is, roughly speaking,
what is controlling the evolution of the various individual classically
describable possibilities. These various individual classically described
evolutions will lead to various different classically described attractors.
But the important thing, here, is that there is, {\it on top of this
nonlinear and extremely important classically described neuro-dynamics},
a quantum mechanical {statistical effect} analogous to the spreading out
of the wave function of the center of Steffi Graf's tennis ball, relative
to the target base line, but arising in the case of the brain, from the
spreading out of the wave functions of the centers of the various presynaptic
calcium ions relative to their target trigger sites. In this latter case
the spreading is very significant, and it will surely cause the wave function
of the whole brain to disperse into a shower of superposed possibilities.
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, into to different possible macroscopic
behaviors, unless a reduction occurs.
So, although the magnitude of the effect of the spreading of the wave
function of the center of Steffi Graf's tennis ball is virtually nil, the
magnitude of 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 of the wave packet 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 reduction of the wave packet is, in
this latter case, in contrast to the case of Steffi Graf's tennis ball, a
decisive controlling factor: it selects from among all of the very different
possible large-scale bodily actions generated by the nonlinear (and, let us even
suppose, classically describable) neurodynamics.
In this circumstance, the question of how, and in what manner, the reduction
occurs becomes crucial: this reduction plays an absolutely decisive role in the
determination of what bodily behaviour we will observe to be occurring at
the macroscopic scale!
The situation is just opposite, in this respect, to the one involving
the position of the center of Steffi Graf's tennis ball relative to the target
baseline.
In this discussion I have generated the superposed macroscopically differet
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 to increase
the quantum uncertainty, not diminish it.
The situation, therefore, is this: elementary considerations show that
the Heisenberg uncertainty principle {\it forces} the wave packet that
represents body/brain to evolve, in the absence of any reduction, into a
shower of possibilities that includes {\it all} of the different macroscopic
behaviours that are at all likely to occur in the physical situation at hand.
The dispersing of the wave packet in this way is in no way disrupted by
thermal noise: it occurs quite independently of the thermal noise and of
all other classical uncertainties. Nor is it dependent upon any long-range
quantum coherence in the brain. In any individual situation it is therefore
the reduction of the wave packet that controls which of the macroscopic
behaviours will manifest. But in the pragmatic Copenhagen interpretation
of quantum theory, which is the mainstream interprtation, and also in
the von Neumann-Wigner interpretation, described by Wigner (1967) as the
"orthodox" interpretation, the reduction of the wave packet represents a projection
of the conscious knowings of the human observer onto the physicists'
objective mathematical representation of reality. The consciousness of the
observer is thus forced into the dynamical picture by the Heisenberg
uncertainty principle, both at the pragmatic level that is the focus of
the Copenhagen interpretation and at the ontological level that is described
by the von Neumann-Wigner interpretation. This intrusion of consciousness
into the dynamics is a macroscopic consequence of quantum theory that has
nothing at all to do with the fact that quantum theory is needed also if
one wants to get a precise description of the chemical reactions that are
important to the small-scale dynamics: accuracy in the theoretical treatment
of chemical reactions is a matter completely different from what is involved
here!
Scott now lists a number of reasons for believing that quantum theory
is not important in brain dynamics in a way that would relate to consciousness.
However, as I shall now explain, none of these arguments has any relevance to
the issue, which is this: the Heisenberg uncertainty principle forces the
reduction of the wave packet that represents the body/brain to be, in any
given situation, the controlling factor that specifies which macroscopic
behaviour will become manifest, and this collapse is closely tied in quantum
theory to our conscious experience.
Scott's first set of reasons have to do with the Born-Oppenheimer approximation
in the study of the properties of molecules. The brain is, of course,
far more complex than a molecule. But my argument does not depend on any
approximation: I am considering, basically, general exact features of the
evolution of the wave functions of the entire body/brain and its environment.
He then considers a subject he has worked on: polarons. He says the the effect
of the quantum corrections is to degrade the global coherence of the classical
polaron. But this "degrading" is not just some fuzzying-up of the situation:
it is the very thing that is of interest and importance here. In our more
complicated case of a body/brain this "degrading" becomes the separation of
the wave function into branches representing various classical describable
possibilities, only one of which, however, is experienced in the mind
associated with this body/brain. And quantum theory itself in its present form
is mute on the question of which of these possibilities is experienced. But
then what is it that {\it undoes} this huge (in our case) degrading that
the linear wave equation forces on us. It is not the classical nonlinearities,
for the quantum analogs of these are already built into the quantum
description, and they play there the very crucial role of creating the various
classically describable possibilities that we are talking about.
His next two points concern the difficulty of maintaining "quantum coherence"
in a warm wet brain. But I consider, in principle, the wave function of the
entire body/brain and its relevant environment (really the whole universe)
and never appeal to, require, or in any way tacitly assume or depend upon,
any large-scale coherence properties.
Scott's next item is the theory for the propagation of an action potential
along a nerve fiber. He points out that this propagation is well described
by the classical Hodgkin-Huxley equation. But, as I have emphasized above,
I assume in my model (Stapp, 1993) the adequacy of a classical description
of this propagation: I consider, explicitly, only those quantum effects
arising from the motions of the calcium ions in the presynaptic nerve
terminals. (Fogelson and Zucker, 1985; Zucker and Fogelson, 1986). Other
quantum effects can increase the effect I am considering, but are not
required. A more detailed account is given in Stapp (1998a).
Scott's final point is about Schroedinger's cat. He says the Schroedinger
equation cannot be constructed because the cat does not conserve energy.
But I am considering, in principle, the wave function of all the particle
in the universe, in the manner pursued by von Neumann (1950). Within that
theoretical framework there is no problem with the energy of a cat,
or of a human brain.
A discussion of the practical and conceptual advantages of using quantum
theory as the theoretical framework for the scientific study of the connection
between brain/body and our consciously experienced feelings and ideas can be
found in Stapp (1998b)
{\bf References}
Fogelson, A.L. \& Zucker, R.S. (1995),`Presynaptic calcium diffusion
from various arrays of single channels: Implications for transmitter
release and synaptic facilitation', {\it Biophys. J.}, {\bf 48},
pp. 1003-1017.
Scott, A. (1996), `On quantum theories of the mind', {\it Journal of
Consciousness Studies}, {\bf 6}, No. 5-6, pp.484-91.
Stapp, H. (1993), {\it Mind, Matter, and Quantum Mechanics},
(Berlin: Springer), Chapter 6.
Stapp, H. (1998a), `Pragmatic approach to consciousness'
in Brain and Values, ed. Karl Pribram, (Lawrence Erlbaum, Mahwah NJ)
\newline http://www-physics.lbl.gov/$\sim$stappfiles.html
Stapp, H. (1998b), `Whiteheadian Process and Quantum Theory of Mind'
\newline http://www-physics.lbl.gov/$\sim$stappfiles.html
von Neumann, J. (1950), {\it The mathematical principles of quantum
mechanics}, (Princeton: Princeton University Press).
Wigner, E. (1967), {\it Symmetries and Reflections}, (Bloomington:
Indiana University Press), Chapters 12 and 13.
Zucker, R.S. \& Fogelson, A.L. (1996), `Relationship between transmitter
release and presynaptic calcium influx when calcium enters through disrete
channels', {\it Proc. Nat. Acad. Sci. USA}, {\bf 83}, pp. 3032-3036.
\end{document}