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November 25, 1997 \hfill LBNL- 40369 \\
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{\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.}
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Henry P. Stapp\\
{\em Lawrence Berkeley National Laboratory\\
University of California\\
Berkeley, California 94720}
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\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.
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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.
Scott contrasts, first, 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 {\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 obscuring 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
of 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.
A 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 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 part of the wave function that
represents 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, some of the calcium ions
miss their 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. Thus the collapse effectively chooses between
very different possible macroscopic bodily actions.
I do not suggest that the mechanism just cited, involving the diffusion of the
calcium ions in the nerve terminals is the {\it only} sources of significant
differences between the macroscopic consequences of the quantum and classical
descriptions of brain dynamics, for many other possible effects have been
identified by quantum physicists interested in brain dynamics. But this effect
is directly computable, whereas some of the others depend on complex factors
that are not yet under theoretical control, and hence could be challenged as
questionable. But this effect pertaining to calcium ions in nerve terminals
gives very directly a reason for the the inappropriateness of the example of
Steffi Graf's tennis ball: the relevant scales are enormously different.
Because of this the huge difference in scales, the consequences of the
Heisenberg uncertainty principle, and the subsequent collapses that they
entail, are irrelevant to the outcome of the tennis match, but are critical to
the bodily outcome of a brain activity that depends on the action at synapses.
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 hinges on a putative connection between conscious thoughts and
quantum reduction events.
The point is this. The quantum reduction/collapse events mentioned above are,
according to orthodox Copenhagen quantum theory, closely tied to our conscious
experiences. I believe that all physicists who suggest that consciousness is
basically a quantum aspect of nature hold that our conscious experiences are
tied to quantum collapses. The motivation for this belief is not merely that it
was only by adopting this idea that the founders of quantum theory were able to
construct a rational theory that encompassed in a unified and logically
coherent way the regularities of physical phenomena in both the classical and
quantum domains. The second powerful motivation is that this association seems
provide a natural physical basis for the unitary character of our conscious
experiences. The point is that quantum theory demands that the collapse of the
wave function represent in Dirac's words ``our more precise knowledge after
measurement''. But the representation of the increase in knowledge associated
with say, some perception, would be represented in the brain as the
actualization, as a whole unit, of a complex brain state that extends over a
large part of the brain. Collapse events of some kind are necessary to make
ontological sense out of orthodox-type quantum theory, and these events can
never be pointlike events: they must have finite extension. But once they are
in principle non-pointlike, they need not be tiny, and can quite naturally
extend over an entire physical system. The natural and necessary occurrence in
quantum theory of these extended holistic macroscopic realities that enter as
inseparable and efficacious units into the quantum dynamics---and which,
according to the physical theory itself, are associated with sudden increments
in our knowledge---seems to put the physical and psychological aspects of
nature into a much closer and more natural correspondence with each other in
quantum theory than in classical mechanics, in which every large-scale thing
is, without any loss, completely decomposable, both ontologically and
dynamically, into its tiny parts.
Scott's first reason for claiming quantum theory to be unimportant to mind
pertains to the speading of wave packets in molecular dynamics. That effect was
just considered, and the crucial spreading of the calcium ion wave packets in
nerve terminals was shown to be large compared to the ion size, contrary to
Scott's estimate.
Scott 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 the
case of a body/brain this ``degrading'' is, more precisely, the separation of
the wave function into branches representing various classical describable
possibilities. However, only one of these classical possibilities is
experienced in the mind associated with this body/brain. Quantum theory in its
present form is mute on the question of which of these possibilities is
experienced: only a statistical rule is provided. But then what is it that {\it
undoes} this huge (in our case) degrading that the linear wave equation
generates. It is not the classical nonlinearities, for the quantum analogs of
these nonlinearities are built into the part of the quantum dynamics that {\it
creates} the superposition of the classically describable possibilities: they
are built into the Schroedinger equation. A collapse, which is the putative
physical counterpart of the conscious experience, is a different effect that
does not enter into the Schroedinger equation. Nor does it enter at all into
the classical approximation to quantum theory. In that approximation there are
no Heisenberg uncertainties or indeterminacies, and hence no collapses, and
hence from the persective of the encompassing and more basic quantum theory, no
physical counterparts of our conscious experiences.
His next two points concern the difficulty of maintaining ``quantum coherence''
in a warm, wet brain. The brain is a complex structure with built-in energy
pumps. The question of whether or not long-range quantum coherence could be
maintained is difficult to settle theoretically. Some explorations have been
made (Vitiello, 1995), but the matter is not yet settled. On the other hand, my
theory yields important quantum effects that are not wiped out by decohence
effects and that could lead to the evolution of a dynamically efficacious
consciousness in coordination with evolution of brains without requiring any
long-range quantum coherence (Stapp, 1997a,b).
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 even among neuroscientists who
accept classical mechanics as an adequate foundation for brain dynamics there
is a recognition that although in some situations the parallel processing
structure produces reliable and essentially deterministic behaviors of groups
of neurons, in spite of the essentially stochastic character of the the
distribution of individual pulses on the individual neurons, in other cases
there are long-range correlations in the timings of pulses. One can expect in
cases where thermal and other classical fluctuation effectively cancel, in such
a way as to give reliable and deterministic behaviors, that the quantum effects
associated with collapses will probably have no major macroscopic consequences.
But in cases where long-range correlations of pulse timings arise, the precise
details of these timings must be controlled in part by stochastic variables
even in a completely classical model that generallly conforms to, say, the
Hodgkin-Huxley equation. In these more delicate situations there is ample room
for the large-scale effects associated with quantum collapses of brain-wide
quantum states to play a decisive dynamical role {\it within} the framework of
possibilities compatible with the classical Hodgkin-Huxley equations. Indeed,
the actualization of global brain states would be expected produce fine-tuned
global regularities that classical mechanics could not account for.
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
the usual assumption in these studies of the quantum mind-brain is that quantum
theory is universally valid, in the sense that the Schroedinger equation is the
equation of motion for the entire universe, in absence of collapse events.
Partial systems are defined by integrating over the other degrees of freedom,
and their energies are not conserved.
\newpage
{\bf References}
Fogelson, A.L. \& Zucker, R.S. (1985),`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. (1997a), `Pragmatic Approach to Consciousness'
To be published in {\it The Neural Correlates of Consciousness},
ed., N. Osaka; To be re-published in {\it Brain and Values}, ed.
K. Pribram, Lawrence Erlbaum, Mahwah, NJ.
\newline Availaible at http://www-physics.lbl.gov/$\sim$stapp/stappfiles.html
Stapp, H. (1997b) `Quantum ontology and mind-matter synthesis',
in {\it The X-th Max Born Symposium}, eds., P. Blanchard and A. Jadczyk,
to be published by Springer-Verlag, Berlin.
\newline Availaible at http://www-physics.lbl.gov/$\sim$stapp/stappfiles.html
Vitiello, G (1995), `Dissipation and memory capacity in the quantum brain
model', Int. J. Mod. Phys. {\bf B9}, 973-89.
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}, pp. 3032-3036.
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