Materialism and the "Problem" of Quantum Measurement

Gregory R. Mulhauser

Department of Philosophy, University of Glasgow

Glasgow, Scotland G12 8QQ

scarab@udcf.gla.ac.uk

**Abstract.** For nearly six decades, the conscious observer

has played a central and essential role in quantum

measurement theory. I outline some difficulties which

the traditional account of measurement presents for

material theories of mind before introducing a new

development which promises to exorcise the ghost of con

sciousness from physics and relieve the cognitive

scientist of the burden of explaining why certain

material structures reduce wavefunctions by virtue of

being conscious while others do not. The interactive

decoherence of complex quantum systems reveals that the

oddities and complexities of linear superposition and

state vector reduction are irrelevant to computational

aspects of the philosophy of mind and that many con

clusions in related fields are ill founded.

Key words. Artificial intelligence, cognitive science,

consciousness, cosmology, decoherence, materialism,

measurement theory, objectivity, physics, pointer basis,

preferred basis, quantum mechanics, state vector

reduction, subjectivity, superselection.

1. Quantum Measurement: The Ghost in the Mechanics

Consider how different life would be if we found

ourselves in a world where macroscopic objects like bats,

cats, lumps of wax, and even people evolved in time the

way sub-microscopic objects like electrons and pi-mesons

do under the Schrdinger equation of quantum mechanics.

My friend might admonish me, "Hey, I saw one of your

state vector components out with that Maclean woman last

Saturday-I thought you had better eigenvalues than that!"

I might justifiably retort that I was also in my flat

doing work, and he should localise his wavepacket

elsewhere and stop interfering with my superpositions.

The standard account of why we never see objects in

states of linear superposition is that the very act of

observing a quantum system precipitates a discontinuous

jump in the system's state from what might have been a

superposition into a single determinate state. In the

Hilbert space framework of quantum mechanics,

wavefunctions are represented as vectors, and maximal

quantum observables correspond to operators. For each of

these operators, there is an associated basis, a set of

orthonormal vectors which spans Hilbert space and

represents the eigenvalues of that operator. For our

purposes, these eigenvectors can be thought of simply as

the real states in which it is possible for an observed

system to exist. According to the projection postulate,

originally due to von Neumann (1932), when a quantum

system is observed the system's wavefunction, its state

vector in Hilbert space, is projected discontinuously

into an eigenstate of the appropriate observable. The

probability of the system's being found in a state corre

sponding to any given basis vector is simply the square

modulus of that vector's coefficient when the state

vector is expressed as a linear combination of the basis

vectors. The set of probabilities corresponding to the

eigenvectors when a given operator is applied to a

wavefunction is called that state vector's reduced

density matrix. The process of state vector reduction

when a quantum mechanical system is observed-"collapsing

the wavepacket"-has excited the attention of philosophers

both because of the indeterminacy the reduced density

matrix brings to physics and because of the high stature

it is understood to give to the consciousness of the

observer.

Under the projection postulate, it is irrelevant to

the statistical predictions of quantum theory at what

point state vector reduction is taken to have occurred-as

long as it is some time before the outcome of a mea

surement enters the conscious mind of an observer. That

state vector reduction could take place after a quantum

system interacts with a macroscopic measuring apparatus

but before a conscious observer has noted the state of

the apparatus is the basis of the well-worn thought

experiment about Schrdinger's cat. The example includes

some device meant to poison a cat (who is taken, perhaps

wrongly, not to be conscious) if and only if a detector

measures a certain event in a quantum system such as the

decay of a nucleus in a radioactive sample. According to

the laws of unitary evolution (i.e., evolution in

accordance with the Schrdinger equation), a system like

this which is appropriately shielded from the envi

ronment-more on this later-must evolve into a superposed

state representing both the case where the atom decays

and the cat is poisoned and the case where the atom does

not decay and the cat lives. It is supposedly only the

act of observing the system-opening up the box and

peering inside, if you will-which brings it about that

its wavefunction description reduces to a single

eigenstate in which the cat is either determinately alive

or determinately dead. As someone has said of the latter

possibility, "curiosity killed the cat".

Because interaction with a conscious mind bounds the

time by which state vector reduction must occur, and

because physicists have understood to be unverifiable any

prediction that it occurs earlier, some physicists

(perhaps Wigner 1962, 1967 most famously) and many

philosophers have taken consciousness itself to be the

mechanism which brings about wavepacket collapse.

Even in Everett's (1957) many worlds interpretation

of quantum mechanics, in which state vectors are never

reduced, consciousness nonetheless plays a central role.

Under his account, the consciousness of observers remains

responsible for the perspectival nature of experience-the

fact that observers only ever experience one of the many

components of the superposition of states through which

the cosmos is continuously evolving.

However we interpret quantum measurement along the

traditional lines, we seem faced with an unexplained

consciousness phenomenon which somehow makes everything

go. Next I outline some of the problems this ghost in

the mechanism creates for materialist accounts of cogni

tion.

2. Problems for the Materialist

By the term 'materialist', I mean to include all

monists who hold that only physical things exist, that

there is no separate realm of mind things with positive

ontological status, that the world is not instead purely

ideal. I mean also to include dual aspect monists, who

maintain that there are matters of fact about what it is

like to be a given material thing which may not be

expressible purely in terms of the objective physical

properties of that thing.

Regardless of the particular brand of materialism we

are concerned to defend, maintaining that consciousness

is a physical phenomenon while allowing that it plays the

unique role in quantum measurement theory it has hitherto

been accorded means giving an account of how it is that

conscious material arrangements reduce state vectors

while other, perhaps equally complex but nonconscious

ones, do not. For instance, a materialist who is a

functionalist must explain what particular types of

information processing arrangements are capable, all by

themselves, of reducing state vectors. (This might lead

to something as peculiar as: applying function Äc to

datum x brings it about that x has become conscious-and

the state vector thereby has been reduced of the entire

composite system consisting of both that of which x is a

measurement and whatever is doing the calculating-whereas

applying any function Ä1ÉÄn does not.) More to the

point, we must answer the question of why some physical

systems are, by virtue of the functional arrangements

they embody or whatever, prohibited from existing in

states of linear superposition while other similar ones

apparently are not. But the problem is worse.

Indeed, if the source of consciousness is to be

found in functional arrangement, quantum measurement

theory implies that we should be able to pin down the

exact spatio-temporal location in an information

manipulating process where a given piece of data becomes

conscious. The projection postulate does not require

that state vector reduction take place at the terminus of

what has come to be called the von Neumann chain, the

chain of interactions from quantum system to conscious

mind which constitutes an observation. But it does

require that there is a terminus, such that if state

vector reduction takes place after that point, then an

experiment could be devised to show it. If consciousness

can be described in functional terms, then so must be the

location of this terminus.

Aside from the bizarreness of effecting state vector

reduction of quantum systems by applying functions to

data about them, pinning down an exact location where a

piece of data becomes conscious should be unacceptable to

any materialist who wishes to describe consciousness in

terms of processes which are not necessarily functions.1

In this case, there might not be any well defined time at

which a piece of data enters conscious awareness.2 But

we are then left with a clumsy notion difficult to recon

cile with the mathematical elegance of the rest of

quantum theory: an ill defined terminus to the von

Neumann chain itself. Moreover, with an ill defined

terminus to the chain, it is awkward to accommodate the

fact that we are still guaranteed some time such that it

could be experimentally verified if state vector reduc

tion occurred after it but not before it.

A similar line of thought leads to the unappealing

conclusion that consciousness cannot be a vague

phenomenon: it must be an altogether all or nothing

affair. This is because while the predictions of state

vector reduction are probabilistic, that it occurs is

not. Either interaction with a given physical system

forces state vector reduction, or it does not. There can

be no fuzzy area in between. Indeed, we could imagine a

sort of "consciousness detector" which exploits the

familiar behaviour of the double slit experiment. Given

a "sufficiently shielded" system akin to Schrdinger's

cat arrangement, we might fit an electron measuring appa

ratus with a (nonconscious) device to convert information

about electrons before they've passed through the slits

into an appropriate form and pass it on to whatever

possibly conscious system we're wishing to analyse. We

may then simply run the electron gun for awhile, and when

we examine the photographic plate, we'll find an interfer

ence pattern if and only if the subject of the experiment

did not consciously process information about the

electrons. If the pattern corresponds to that predicted

by classical mechanics, then it was because the state

vector descriptions of the electrons were reduced as a

result of information about them becoming conscious.

Finally, accepting that state vector reduction

occurs as a result of interaction with any and only those

material arrangements with some special material property

that makes them conscious even has curious implications

for the way we think about the evolution of conscious

life. If conscious life was not present when the cosmos

began, then the universe could only have evolved (in the

mathematical sense) in a state of quantum linear

superposition until the first conscious organism evolved

(in a biological sense) and observed it, thereby

collapsing the wavefunction of the entire cosmos and

making determinate that single path of history which made

the organism's own existence possible! We might of

course posit a (material?) divine being who frequently

observed the cosmos and prevented its ever evolving into

a superposed state. Since the phenomenon whereby fre

quent observations of a quantum system keep it from evolv

ing into a superposed state is often called the "watchdog

effect", we might name the divine observation hypothesis

the "watchgod effect". But in any case, without such a

"watchgod effect", it would appear that the first

conscious organism was its own efficient cause.

Fortunately, all these strange problems with

including consciousness in quantum measurement theory

apparently never need arise. While it is always danger

ous to speculate on anything's being "an answer" in

physics, it appears that the quest has ended for a theory

of quantum measurement which discharges consciousness

from its central role. The best thing about the new view

of quantum measurement is that it requires no new

premises: it falls out of a careful reexamination of the

problem and numerical analysis of the evolution of

complex systems described under existing theory.

3. Interactive Decoherence: Ghostbusting

The current description of interactive decoherence3

was originally motivated by quantum cosmology and both

benefits and is benefitted by research in the physics of

information. Quantum cosmology (see, for instance,

Coleman, et al 1991) seeks to understand the entire

cosmos as a quantum system. This approach can

accommodate neither an arbitrary Copenhagen-style

distinction between microscopic and macroscopic worlds

nor an unexplained consciousness phenomenon driving state

vector reduction. The quantum cosmologist must

ultimately be able to derive a description of a quasi-

classical world from the laws of quantum mechanics. From

a quantum description of the world, we must be able to

predict the existence of "correlations" between

macroscopic coordinates and momenta which approximately

obey the classical laws of motion, and we must be able to

account for the fact that interference effects between

different classical states are never observed. (Paz and

Sinha 1992) The relevant aspect of information theory is

the growing conviction that information cannot be

abstracted away from a physical substrate (Landauer 1991)

and how that fact bears on what can be said about natural

laws, observers, and the interactions between subsystems

of the cosmos.

The most important step in the development of

decoherence theory was the "re-realisation" that no

system but the entire cosmos is closed, or perfectly

isolated, and that the environment will thus always

contain some amount of information about the state of a

system. The Schrdinger equation is meant to apply just

to closed (or very nearly closed) systems, and for the

sake of computational simplicity absurd degrees of

isolation are often tolerated in examples of the

Schrdinger equation's application. (This is the point

of the extremely well-shielded box in Schrdinger's cat

example: no information about the coherent superposed

state of the system must exist in any external system,

for then observation of this external system would

collapse the wavefunction of the entire composite sys

tem.) But numerical analysis of systems which preserve

some of those complications abstracted away in the

idealised example systems-essentially much greater

internal and external degrees of freedom-reveals that

correlations between the state of a quantum system and

its environment or even correlations within itself are

sufficient to break the coherence of what might otherwise

be an incredibly complex wavefunction.

These correlations are understood as records, or

information, about the system, information which Wojciech

Zurek (1991), a leading researcher in interactive decoher

ence at the Santa Fe Institute, emphasises is entirely

independent of the presence of any conscious observer.

The buildup of nonseparable correlations between the sys

tem and its environment (which could be little more than

cosmic background radiation) causes a very rapid decrease

in the possible superpositions of the system which can be

distinguished through their effect on the environment.

As Paz, et al (1993) put it, "this results in a negative

selection which leads to the emergence of a preferred set

of statesÉwhich remain least affected by the 'openness'

of the system in question." (p. 488) It is these

preferred states, sometimes called the "pointer basis" (a

term coined by Zurek, alluding to the pointer of a garden

variety measurement apparatus), which, conveniently and

unsurprisingly, correspond closely to those of the

observables we encounter in the quasi-classical world.4

(Albrecht 1992b; Paz, et al 1993) The cosmos is

watching! While the dynamics of the system determine the

"options" for a system's evolution, it is the

correlations between the system and its environ

ment-rather than the intervention of any conscious

observer-which determine the probability of the system's

being in a given state.

It is important to stress that while analysis of

interactive decoherence provides the reduced density

matrix, or set of probabilities for each of the possible

states "allowed through" the nonconscious environmental

record-keeping, it is not, as one researcher has called

it, a mere "calculational tool" (Kiefer 1991, p. 379)

with which we duplicate the predictions of consciousness-

driven wavepacket collapse while never essentially

erasing consciousness from the picture. In effect,

decoherence supersedes the wavepacket collapse of

traditional quantum measurement theory by offering an

alternative account of what is mathematically the same

process, free of the superfluous and unexplained

consciousness factor. Indeed, the equivalence of results

provided by the two mechanisms leads some researchers to

apply the older term explicitly in referring to the

replacement process. (Albrecht 1992a; Paz, et al 1993)

To apply the point to Schrdinger's thought experiment,

decoherence tells us that the cat is already either alive

or dead long before anyone opens the box-with a

probability given by the appropriate reduced density

matrix-but not as a result of a von Neumann chain-style

interaction with consciousness at the terminus.

Finally, in the interest of thoroughness, I should

mention that while the description I have given of

decoherence is based purely on existing theory, there is

another formalism known as the "consistent histories"

approach which does rely upon a "decoherence functional"

(Gell-Mann and Hartle 1990) which has not yet been fully

defined. It is related to the sum over histories

formulation of quantum mechanics and is used to determine

whether one can attribute well-defined probabilities to

different possible histories of a given system. (When

this is possible, the histories are called "consistent",

or "decohering".) However, this second approach in its

present form allows through as "consistent" sets of

highly non-classical histories. For this reason, the

environment-induced superselection I have described is

preferable. (See Paz and Zurek 1992 for one comparison

of the two formalisms.)

4. Discussion and Conclusions

We can see from this description of interactive

decoherence that the consciousness of an observer is no

longer essential to the theory of quantum measurement.

As Zurek puts it,

"Conscious observers have lost their monopoly

on acquiring and storing information. The

environment can also monitor a system, andÉsuch

monitoring causes decoherence, which allows the

familiar approximation known as classical objec

tive reality-a perception of a selected subset

of all conceivable quantum states evolving in a

largely predictable manner-to emerge from the

quantum substrate." (Zurek 1991, p. 44)

As it stands, even in the absence of a conscious

observer, the wavefunction of any quantum system with

sufficient complexity and energy will decohere. Thus it

seems that apart, perhaps, from theory concerning very

low energy computation, quantum mechanics is utterly

irrelevant to computational aspects of the philosophy of

mind. None of the problems I outlined for materialism in

general, functionalism in particular, or even the origins

of conscious life arise under this new picture of quantum

measurement.

Likewise, many interesting results in the philosophy

of mind and related fields which have derived from the

assumption that macroscopic objects can exist in

superposition until they are observed have lost their

theoretical underpinnings. For instance, Deutsch's

(1985b) "universal quantum computer", whose capabilities

are a superset of those of the familiar Universal Turing

Machine or Bernoulli-Turing Machine, seems destined to

exist only in the world of theory. The eventual

application of other research in quantum computing (for

instance, Margolus 1986, 1990) inspired by Deutsch or

Feynman's (1986) efforts is unclear; what is clear is

that any quantum computer of even rudimentary complexity

must operate at extremely low temperatures in order to

preserve the coherent wavefunction description on which

such devices rely for their special properties. (Indeed,

the information processing nature of such devices might,

in itself, create such internal correlations that

coherent unitary evolution cannot be sustained.) Because

the operating temperature of the human brain is many

orders of magnitude higher than what is required to

sustain prolonged unitary evolution these special

properties of quantum computers are almost certainly

irrelevant to brain research. Unfortunately, it seems

also that in light of interactive decoherence, Deutsch's

(1985a) description of an experimental test of Everett's

interpretation (a suggestion contradicting the conven

tional wisdom that it is indistinguishable from rival

interpretations) using nonconscious automata is also

unworkable. This should not be too surprising, however,

since Everett's theory stipulated that state vector

reduction never actually took place. While it is cer

tainly no trivial project, we might anticipate that some

or all elements of Everett's view will soon be proven

inconsistent with decoherence theory.

Albert's (1983, 1987, 1990) work showing that a

specifically nonconscious automaton could make privileged

predictions about itself by measuring quantum observables

which for any external observer would be incompatible

appears similarly incompatible with interactive decoher

ence. Although arguments from dual aspect monism

indicate a necessary subjectivity to the point of view of

an observer (Mulhauser 1993), and Mackay (1971, 1980) has

argued for an observer's "logical relativity", Albert's

arguments for subjectivity fail because they require

complex automata fitted with quantum mechanical measuring

devices to themselves exist in states of **linear**

superposition.5

Finally, the new view of quantum measurement does

not mix well with the mind-brain interaction theories of

Sir John Eccles, Nobel prizewinning neuroscientist.

Eccles, a self-avowed dualist with respect to the mind-

body problem, has described a scheme (1986, 1990; see

also Popper and Eccles 1977) in which a nonphysical

consciousness collapses the state vector descriptions of

the pre-synaptic vesicular grids which release neurotrans

mitters at neural junctions. He proposes that states of

columnar bundles in the cerebral cortex thus become

correlated with the causally prior mental "psychons" with

which they are paired. But not only is consciousness

itself superfluous in decoherence theory, the high

operating temperature of the human brain again guarantees

decoherence of the wavefunctions of these structures as a

result of internal and external correlations, inde

pendently of any mysterious causally prior mind entity.

In addition to neutralising all these interesting

results which come from allowing nonconscious macroscopic

objects to exist in superposed states until they are

observed, interactive decoherence appears also to have

solved the preferred basis problem. This is the question

of why Nature has chosen for macroscopic objects a set of

basis vectors which correspond to the eigenstates of

macroscopic observables. (Why not a basis corresponding

to some other set of operators, such that the eigenstates

we observe are actually superpositions of the eigenstates

of the macroscopic observables? Out of the infinity of

ways of decomposing state vectors, what makes the basis

corresponding to the set of macroscopic observables so

special?) The emergence of a preferred basis simply as

that basis which is most immune to the openness of

macroscopic systems is at the heart of decoherence

theory.

Thus Lockwood's (1990) approach to the preferred

basis problem through an unexplained consciousness

phenomenon in a reincarnated relative state view is as

unnecessary as it is implausible. Interactive decoher

ence suggests a similarly dim view of Deutsch's (1985a)

interesting but apparently only partially successful

(Foster and Brown 1988) attempt to solve the preferred

basis problem. Other approaches either to removing con

sciousness from quantum measurement altogether or to

solving the preferred basis problem are now also

unnecessary. These include Davies's (1981) and Penrose's

(1985, 1986, 1989) quantum gravity state vector reduction

and Nicholas Maxwell's (1988) propensition theory

positing state vector reduction in the wake of

sufficiently energetic inelastic collisions between

particles.

Overall, the mechanism of interactive decoherence

appears to solve a host of problems without creating

very many new ones. But the question lingers: is this

really the way it happens (or at least a reasonable

approximation), or is it just a parallel account of the

observed phenomena which offers no particular verifiable

advantage over the standard consciousness-driven

wavepacket collapse? Without entering a prolonged

discussion of the philosophy of physics, there are a few

illuminating things which we can say about this.

Insofar as both decoherence theory and the standard

view yield the same reduced density matrix for the

quantum systems so far studied, the huge body of positive

experimental evidence for the accuracy of quantum

mechanics as a predictive theory tends to confirm both

views equally well. Yet, the mechanisms which

precipitate interactive decoherence come for free as

consequences of other elements of existing theory. The

same cannot be said for the standard view, which relies

upon the superfluous phenomenon of consciousness to

terminate the von Neumann chain. In that sense,

interactive decoherence is a more parsimonious theory.

For that reason alone, independently of possible

experimental verification, the standard view may

eventually be replaced as interactive decoherence theory

becomes more widely understood.

However, at least in theory, it is possible to

distinguish experimentally between the two accounts. I

have said that they give identical predictions for all

quantum systems studied so far, but so far not all

imaginable quantum systems have been studied.

Specifically, the two accounts predict different outcomes

for experiments with the fanciful "consciousness detec

tor" I described in ¤2. If such a system-consisting of a

standard electron gun and diffraction grating setup,

together with an "observer"-could be shielded from the

environment, decoherence theory predicts that the con

sciousness detector simply would not work in the way I

outlined under the standard view: the correlations

between the states of the electrons, the measuring

apparatus, and the "observer" (conscious or not) would

cause decoherence and yield a classical distribution

pattern on the photographic plate every time. The

problem here, of course, is that such an experiment

requires a fantastic degree of isolation far beyond the

technological capabilities of today or the foreseeable

future. Probably well before such isolation becomes

possible (if it ever does), theorists will determine how

better to quantify the amount of information which must

be carried in inter-system correlations to guarantee

interactive decoherence. In that case, a similar test

could be carried out by replacing the "observer" with any

system capable of interacting with the electrons to the

required degree. Until this necessary degree of

interaction is quantified6 (or ridiculously thorough

isolation becomes a reality), experimental discrimination

between the two accounts will remain practically

impossible.

Decoherence theory does not answer all the

interesting questions about quantum mechanics-such as why

linear superposition ever occurs at all or why

experimentally verified nonlocality is an apparent

feature of reality. It also raises at least one

intriguing new question: could the state of the system's

environment, considered in all its detail, influence

which eigenstate a system's state vector jumps to? My

own suspicion is that a new non-local but deterministic

picture of quantum reality, more satisfying than Bohm's

(1952) and incorporating a fuller description of interac

tive decoherence, may be forthcoming. But for now, the

cognitive scientist and philosopher of mind can rest

assured that the burden has been lifted for giving an

account of material consciousness capable of playing the

state vector reducing role hitherto supposed necessary in

explaining the observed quantum mechanical phenomena.

Acknowledgements

For many insightful questions and comments, I am

grateful both to two anonymous referees and to members of

three Scottish universities who attended a presentation

of an early version of this paper at the University of

Edinburgh's work in progress seminar in 1993. I am also

grateful to HM Government's Marshall Aid Commemoration

Commission for financial support of my research during

the time this paper was conceived.

Notes

References

Albert, David Z. (1983), 'On Quantum-Mechanical

Automata', Physics Letters 98A, pp. 249-252.

Albert, David Z. (1987), 'A Quantum-Mechanical

Automaton', Philosophy of Science 54, pp. 577-585.

Albert, David Z. (1990), 'The Quantum Mechanics of Self-

Measurement', in W.H. Zurek, ed., Complexity,

Entropy, and the Physics of Information, SFI Studies

in the Sciences of Complexity VIII, Redwood City,

CA: Addison-Wesley, pp. 471-476.

Albrecht, Andreas. (1992a), 'Following a "Collapsing"

Wavefunction', Fermilab Report (unpublished).

Albrecht, Andreas. (1992b), 'Investigating Decoherence

in a Simple System', Physical Review D 46, pp. 5504-

5520.

Bohm, David. (1952), 'A Suggested Interpretation of the

Quantum Theory in Terms of "Hidden" Variables',

Physical Review 85, pp. 166-193.

Coleman, S.; J. Hartle; T. Piran; and S. Wienberg, eds.

(1991), Quantum Cosmology and Baby Universes,

Proceedings of the 7th Jerusalem Winter School,

Jerusalem, Israel, 1990, Singapore: World

Scientific.

Davies, P.C.Q. (1981), 'Is Thermodynamic Gravity a Route

to Quantum Gravity?', in C.J. Isham, R. Penrose and

D.W. Sciama, eds, Quantum Gravity 2: A Second

Oxford Symposium, Oxford: Clarendon Press, pp. 183-

209.

Deutsch, D. (1985a), 'Quantum Theory as a Universal

Physical Theory', International Journal of

Theoretical Physics 24, pp. 1-41.

Deutsch, D. (1985b), 'Quantum Theory, the Church-Turing

Principle and the Universal Quantum Computer',

Proceedings of the Royal Society of London A400, pp.

97-117.

Eccles, J. (1986), 'Do Mental Events Cause Neural Events

Analogously to the Probability Fields of Quantum

Mechanics?', Proceedings of the Royal Society of

London B227, pp. 411-28.

Eccles, J. (1990), 'A Unitary Hypothesis of Mind-Brain

Interaction in the Cerebral Cortex', Proceedings of

the Royal Society of London B240, pp. 433-51.

Everett, H. (1957), '"Relative State" Formulation of

Quantum Mechanics', Reviews of Modern Physics 29,

pp. 454-462.

Feynman, R. (1986), 'Quantum Mechanical Computers',

Foundations of Physics 16, pp. 507-531.

Foster, Sara and Harvey R. Brown. (1988), 'On a Recent

Attempt to Define the Interpretation Basis in the

Many Worlds Interpretation of Quantum Mechanics',

International Journal of Theoretical Physics 27, pp.

1507-1531.

Gell-Mann, M. and J.B. Hartle. (1990), 'Quantum

Mechanics in the Light of Quantum Cosmology', in

W.H. Zurek, ed., Complexity, Entropy, and the

Physics of Information, SFI Studies in the Sciences

of Complexity VIII, Redwood City, CA: Addison-

Wesley, pp. 425-469.

Kiefer, Claus. (1991), 'Interpretation of the

Decoherence Functional in Quantum Cosmology',

Classical and Quantum Gravity 8, pp. 379-391.

Landauer, Rolf. (1991), 'Information is Physical',

Physics Today 44, pp. 23-29.

Lockwood, Michael. (1990), Mind, Brain, and the Quantum,

Oxford: Basil Blackwell. (First published in

1989.)

Mackay, D.M. (1971), 'Scientific Beliefs About Oneself',

in G.N.A. Vesey, ed., The Proper Study, Royal

Institute of Philosophy Lectures 4, London:

Macmillan, pp. 48-63.

Mackay, D.M. (1980), 'Conscious Agency With Unsplit and

Split Brains', in B.D. Josephson and V.S.

Ramachandran, eds., Consciousness and the Physical

World, Oxford: Pergamon Press, pp. 95-113.

Margolus, Norman. (1986), 'Quantum Computation', Annals

of the New York Academy of Science 480, pp. 487-497.

Margolus, Norman. (1990), 'Parallel Quantum

Computation', in W.H. Zurek, ed., Complexity,

Entropy, and the Physics of Information, SFI Studies

in the Sciences of Complexity VIII, Redwood City,

CA: Addison-Wesley, pp. 273-287.

Maxwell, Nicholas. (1988), 'Quantum Propensition Theory:

A Testable Resolution of the Wave/Particle Dilemma',

British Journal of the Philosophy of Science 39, pp.

1-50.

Mulhauser, Gregory R. (1993), 'What is it Like to be

Nagel?', The Philosopher: Journal of the

Philosophical Society of England April, pp. 19-24.

Paz, J.P.; S. Habib; and W.H. Zurek. (1993), 'Reduction

of the Wave Packet: Preferred Observable and

Decoherence Time Scale', Physical Review D 47, pp.

488-501.

Paz, J.P. and S. Sinha. (1992), 'Decoherence and Back

Reaction in Quantum Cosmology-Multidimensional

Minisuperspace Examples', Physical Review D 45, pp.

2823-2842.

Paz, J.P. and W.H. Zurek. (1992), 'Environment Induced

Superselection and the Consistent Histories Approach

to Decoherence', Los Alamos Report no. LA-UR-92-878

(unpublished).

Penrose, R. (1985), 'Quantum Gravity and State Vector

Reduction', in R. Penrosoe and C.J. Isham, eds.,

Quantum Concepts in Space and Time, Oxford: Oxford

University Press, pp. 129-146.

Penrose, R. (1986), 'Big Bangs, Black Holes, and "Time's

Arrow"', in Raymond Flood and Michael Lockwood,

eds., Mindwaves, Oxford: Basil Blackwell, pp. 259-

276.

Penrose, R. (1989), The Emperor's New Mind, Oxford:

Oxford University Press.

Popper, K.R. and Eccles, J.C. (1977), The Self and Its

Brain, Berlin: Springer.

Von Neumann, J. (1955), Mathematical Foundations of

Quantum Mechanics, Princeton, NJ: Princeton

University Press. (First German edition 1932).

Wigner, E.P. (1962), 'Remarks on the Mind-Body

Question', in I.J. Good, ed., The Scientist

Speculates: An Anthology of Partly-Baked Ideas,

London: Heinemann, pp. 284-302.

Wigner, E.P. (1967), Symmetries and Reflections,

Bloomington, IN: Indiana University Press.

Zurek, Wojciech H. (1991), 'Decoherence and the

Transition From Quantum to Classical', Physics Today

44, pp. 36-44.

_______________________________

1 This might be the spread of an activation pattern

across a network, for instance. While all (recursive)

functions can be thought of as algorithms, not all

algorithms are mathematical functions. Functionalists

are typically concerned with the broader class of all

algorithmic processes. Fortunately, however, something

like the more descriptive but awkward "algorithmism" has

never entered use.

2 As an aside, Lockwood's 1990 relativistic argument for

a precise physical location of mental "events" rests on

the assumption that such events have a precise location

in time-an assumption which is untenable on any sort of

connectionist or distributed view.

3 In the physics literature, this phenomenon is

consistently referred to as "spontaneous decoherence".

However, as will become clear, the phenomenon is not

spontaneous in the strict sense and occurs always as a

result of information carrying interactions between

subsystems. Thus, with apologies to the physics

community, I have opted to use this more accurate term

throughout.

4 Note, incidentally, that this doesn't imply all large

systems decohere: as Paz, et al (1993) and Zurek (1991)

point out, even a very massive-on the order of one

tonne-cryogenic Weber bar, by virtue of its extremely low

temperature, must be treated as a coherent quantum

harmonic oscillator.

5 The failure of Deutsch's and Albert's work as physical

possibilities also casts some doubt on the actual

feasibility of quantum cryptography.

6 Early indications are that the time required for

decoherence, and perhaps the degree of necessary

interaction as well, are very small indeed. Although he

doesn't include the technical details, Zurek says that a

rough calculation reveals that for a room temperature

system with a 1gm solid mass, quantum coherence is

destroyed in less than 10-23 seconds. (Zurek 1991)