Donald M.J. - Quantum theory and the brain, Books, Books eng, books NON FICTION, cognitive
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Quantum Theory and the Brain.
Matthew J. Donald
The Cavendish Laboratory, Madingley Road, Cambridge CB3 0HE,
Great Britain.
e-mail: matthew.donald@phy.cam.ac.uk
˜
mjd1014
May 1988
Revised: May 1989
Appears: Proc. Roy. Soc. Lond. A 427, 43-93 (1990)
Abstract. A human brain operates as a pattern of switching. An abstract defini-
tion of a quantum mechanical switch is given which allows for the continual random
fluctuations in the warm wet environment of the brain. Among several switch-like
entities in the brain, we choose to focus on the sodium channel proteins. After explain-
ing what these are, we analyse the ways in which our definition of a quantum switch
can be satisfied by portions of such proteins. We calculate the perturbing eects of
normal variations in temperature and electric field on the quantum state of such a
portion. These are shown to be acceptable within the fluctuations allowed for by our
definition. Information processing and unpredictability in the brain are discussed.
The ultimate goal underlying the paper is an analysis of quantum measurement the-
ory based on an abstract definition of the physical manifestations of consciousness.
The paper is written for physicists with no prior knowledge of neurophysiology, but
enough introductory material has also been included to allow neurophysiologists with
no prior knowledge of quantum mechanics to follow the central arguments.
CONTENTS
1.
Introduction.
2.
The Problems of Quantum Mechanics and the Relevance of the Brain.
3.
Quantum Mechanical Assumptions.
4.
Information Processing in the Brain.
5.
The Quantum Theory of Switches.
6.
Unpredictability in the Brain.
7.
Is the Sodium Channel really a Switch?
8.
Mathematical Models of Warm Wet Switches.
9.
Towards a More Complete Theory.
References
1. Introduction.
A functioning human brain is a lump of warm wet matter of inordinate complex-
ity. As matter, a physicist would like to be able to describe it in quantum mechanical
terms. However, trying to give such a description, even in a very general way, is by no
means straightforward, because the brain is neither thermally isolated, nor in thermal
equilibrium. Instead, it is warm and wet — which is to say, in contact with a heat
bath — and yet it carries very complex patterns of information. This raises inter-
esting and specific questions for all interpretations of quantum mechanics. We shall
give a quantum mechanical description of the brain considered as a family of ther-
mally metastable switches, and shall suggest that the provision of such a description
could play an important part in developing a successful interpretation of quantum
mechanics.
Our essential assumption is that, when conscious, one is directly aware of definite
physical properties of one’s brain. We shall try both to identify suitable properties
and to give a general abstract mathematical characterization of them. We shall look
for properties with simple quantum mechanical descriptions which are directly related
to the functioning of the brain. The point is that, if we can identify the sort of physical
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substrate on which a consciousness constructs his world, then we shall have a definition
of an observer (as something which has that sort of substrate). This could well be a
major step towards providing a complete interpretation of quantum mechanics, since
the analysis of observers and observation is the central problem in that task. We shall
discuss the remaining steps in
§9
. Leaving aside this highly ambitious goal, however,
the paper has three aspects. First, it is a comment, with particular reference to
neurophysiology, on the diculties of giving a fully quantum mechanical treatment
of information-carrying warm wet matter. Second, it is a discussion of mathematical
models of “switches” in quantum theory. Third, it analyses the question of whether
there are examples of such switches in a human brain. Since, ultimately, we would
wish to interpret such examples as those essential correlates of computation of which
the mind is aware, this third aspect can be seen, from another point of view, as asking
whether humans satisfy our prospective definition of “observer”.
The brain will be viewed as a finite-state information processor operating through
the switchings of a finite set of two-state elements. Various physical descriptions of
the brain which support this view will be provided and analysed in
§4
and
§6
. Unlike
most physicists currently involved in brain research (for example, neural network the-
orists), we shall not be concerned here with modelling at the computational level the
mechanisms by which the brain processes information. Instead, we ask how the brain
can possibly function as an information processor under a global quantum mechanical
dynamics. At this level, even the existence of definite information is problematical.
Our central technical problem will be that of characterizing, in quantum me-
chanical terms, what it means for an object to be a “two-state element” or “switch”.
A solution to this problem will be given in
§5
, where we shall argue for the natural-
ness of a specific definition of a switch. Given the environmental perturbations under
which the human brain continues to operate normally, we shall show in
§7
and
§8
that
any such switches in the brain must be of roughly nanometre dimension or smaller.
This suggests that individual molecules or parts of molecules would be appropriate
candidates for such switches. In
§6
and
§7
we shall analyse, from the point of view
of quantum mechanics, the behaviour of a particular class of suitable molecules: the
sodium channel proteins.
§2
and
§3
will be devoted to an exposition of the quantum
mechanical framework used in the rest of the paper.
One of the most interesting conclusions to be drawn from this entire paper is that
the brain can be viewed as functioning by abstractly definable quantum mechanical
switches, but only if the sets of quantum states between which those switches move,
are chosen to be as large as possible compatible with the following definition, which
is given a mathematical translation in
§5
:
Definition A switch is something spatially localized, the quantum state of which
moves between a set of open states and a set of closed states, such that every open
state diers from every closed state by more than the maximum dierence within any
pair of open states or any pair of closed states.
I have written the paper with two types of reader in mind. The first is a neu-
rophysiologist with no knowledge of quantum mechanics who is curious as to why a
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quantum theorist should write about the brain. My hope is that I can persuade this
type of reader to tell us more about randomness in the brain, about the magnitude of
environmental perturbations at neuronal surfaces, and about the detailed behaviour
of sodium channel proteins. He or she can find a self-contained summary of the paper
in
§2
,
§4
,
§6
, and
§7
. The other type of reader is the physicist with no knowledge of
neurophysiology. This reader should read the entire paper. The physicist should ben-
efit from the fact that, by starting from first principles, I have at least tried to make
explicit my understanding of those principles. He or she may well also benefit from
the fact that there is no mathematics in the sections which aim to be comprehensible
to biologists.
2. The Problems of Quantum Mechanics and the Relevance of the Brain.
(This section is designed to be comprehensible to neurophysiologists.)
Quantum theory is the generally accepted physical theory believed to describe
possibly all, and certainly most, forms of matter. For over sixty years, its domain of
application has been steadily extended. Yet the theory remains somewhat mysterious.
At some initial time, one can assign to a given physical object, for example, an
electron or a cricket ball, an appropriate quantum mechanical description (referred
to as the “quantum state” or, simply, “state” of that object). “Appropriate” in this
context means that the description implies that, in as far as is physically possible, the
object is both at a fairly definite place and moving at a fairly definite velocity. Such
descriptions are referred to by physicists as “quasi-classical states”. The assignment
of quasi-classical states at a particular time is one of the best understood and most
successful aspects of the theory. The “laws” of quantum mechanics then tell us
how these states are supposed to change in time. Often the implied dynamics is in
precise agreement with observation. However, there are also circumstances in which
the laws of quantum mechanics tell us that a quasi-classical state develops in time
into a state which is apparently contrary to observation. For example, an electron,
hitting a photographic plate at the end of a cathode ray tube, may, under suitable
circumstances, be predicted to be in a state which describes the electron position as
spread out uniformly over the plate. Yet, when the plate is developed, the electron is
always found to have hit it at one well-localized spot. Physicists say that the electron
state has “collapsed” to a new localized state in the course of hitting the plate. There
is no widely accepted explanation of this process of “collapse”. One object of this
paper is to emphasize that “collapse” occurs with surprising frequency during the
operation of the brain.
The signature of “collapse” is unpredictability. According to quantum theory
there was no conceivable way of determining where the electron was eventually going
to cause a spot to form on the photograph. The most that could be known, even in
principle, was the a priori probability for the electron to arrive at any given part of
the plate. In such situations, it is the quantum state before “collapse” from which one
can calculate these a priori probabilities. That quantum state is believed to provide,
before the plate is developed, the most complete possible description of the physical
situation. Another goal for this paper is to delineate classes of appropriate quantum
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states for the brain at each moment. This requires deciding exactly what information
is necessary for a quasi-classical description of a brain.
Now the brain has surely evolved over the ages in order to process information in
a predictable manner. The trout cannot aord to hesitate as it rises for the mayfly.
Without disputing this fact, however, it is possible to question whether the precise
sequence of events in the fish’s brain are predictable. Even in those invertebrates
in which the wiring diagrams of neurons are conserved across a species, there is no
suggestion that a precise and predictable sequence of neural firings will follow a given
input. Biologically useful information is modulated by a background of noise. I claim
that some of that noise can be interpreted as being of quantum mechanical origin.
Although average behaviour is predictable, the details of behaviour can never be
predicted. A brain is a highly sensitive device, full of amplifiers and feedback loops.
Since such devices are inevitably sensitive to initial noise, quantum mechanical noise
in the brain will be important in “determining” the details of behaviour.
Consider once more the electron hitting the photographic plate. The deepest
mystery of quantum mechanics lies in the suggestion that, perhaps, even after hitting
the plate, the electron is still not really in one definite spot. Perhaps there is merely
a quantum state describing the whole plate, as well as the electron, and perhaps
that state does not describe the spot as being in one definite place, but only gives
probabilities for it being in various positions. Quantum theorists refer in this case
to the quantum state of the plate as being a “mixture” of the quantum states in
which the position of the spot is definite. The experimental evidence tells us that
when we look at the photograph, we only see one definite spot; one element of the
mixture. “Collapse” must happen by the time we become aware of the spot, but
perhaps, carrying the suggestion to its logical conclusion, it does not happen before
that moment.
This astonishing idea has been suggested and commented on by
von Neumann
(1932
, §VI.1),
London and Bauer (1939
, §11), and
Wigner (1961)
. The relevant
parts of these references are translated into English and reprinted in (
Wheeler and
Zureck 1983
). The idea is a straightforward extension of the idea that the central
problem of the interpretation of quantum mechanics is a problem in describing the
interface between measuring device and measured object. Any objective physical
entity can be described by quantum mechanics. In principle, there is no diculty
with assigning a quantum state to a photographic plate, or to the photographic plate
and the electron and the entire camera and the developing machine and so on. These
extended states need not be “collapsed”. There is only one special case in the class of
physical measuring devices. Only at the level of the human brain do we have direct
subjective evidence that we can only see the spot in one place on the plate. The only
special interface is that between mind and brain.
It is not just this idea which necessitates a quantum mechanical analysis of the
normal operation of the brain. It is too widely assumed that the problems of quantum
mechanics are only relevant to exceptional situations involving elementary particles.
It may well be that it is only in such simple situations that we have suciently
complete understanding that the problems are unignorable, but, if we accept quantum
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