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May 29, 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.

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.


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