
On
the End of a Quantum Mechanical Romance
vedi
1  2
 3  4


Gregory R. Mulhauser/Department
of Philosophy/University of Glasgow/ http://psyche.cs.monash.edu.au/v2/psyche205stapp.html
KEYWORDS: cosmology, interactive decoherence, measurement theory,
objectivity, quantum mechanics, state vector, reduction, superselection.
ABSTRACT: Comparatively recent advances in quantum measurement theory suggest
that the decadesold flirtation between quantum mechanics and the philosophy
of mind is about to end. Various approaches to what I have elsewhere dubbed
'interactive decoherence' promise to remove the conscious observer from the
phenomenon of state vector reduction. The mechanisms whereby decoherence occurs
suggest, on the one hand, that consciousness per se has no role in explaining
the outcomes of quantum events and, on the other, that perhaps apart from
questions about the very lowest level properties of minds' instantiating hardware
or wetware, the unique features of quantum mechanics are utterly irrelevant
to the philosophy of mind. Here we explore a better account of interactive
decoherence than I have offered elsewhere, make explicit the argument for
irrelevance, and address some unanswered questions and an interesting objection
against the formulation of decoherence on which our discussion is based.
1. Introduction
1.1 Quantum mechanics
excites the imagination unlike any classical theory of physics, probably at
least in part because peculiarities of the quantum world conflict so spectacularly
with the intuitions most of us develop in the course of interacting with our
macroscopic, quasiclassical world. Since its earliest days, philosophers trying
to understand similarly peculiar and perhaps counterintuitive properties of
minds and of consciousness have turned to the quantum theory as a possible source
of explanation. Often philosophers appeal to the apparent indeterminacies of
quantum mechanics to supply a foothold for free will in our otherwise seemingly
deterministic world, although there are good reasons to think this a red herring.
(Grunbaum, 1972; see also the specifically quantum mechanical objection of Fine,
1993, who nonetheless favours Grunbaum's conclusion.) Here, this subtle question
does not occupy us; instead, we consider the relationship between physics and
philosopy of mind from the perspective of quantum linear superposition and state
vector reduction.
1.2 For our purposes, we understand quantum theories of mind or consciousness
which do not especially appeal to indeterminacy to fall under two headings.
First are those which point to minds as causal factors or determinants in reducing
state vector descriptions of material substrates such as brains, while second
are those which appeal to linear superposition, nonlocality, or some such to
endow material structures with unique information transforming (but not necessarily
computational, in the recursion theoretic sensesee Section 4) abilities
meant to subserve correspondingly unique abilities of minds. I take the psychon
theory of Sir John Eccles (1986, 1990; also Popper & Eccles, 1977) as a
paradigm example of the former and something like the approach of Roger Penrose
(1989) as an example of the latter, with Marcer (1992) combining elements of
each. Recently (Mulhauser, 1995, in press) I have tried to apply a new development
in quantum measurement theory to questions in philosophy and cognitive science,
a development which suggests theories of both these types are misguided. Our
task here is to clarify that development and its significance for the philosophy
of mind.
1.3 We begin with a look at the standard account of state vector reduction and
the theory of interactive decoherence which promises to supplant it. The new
theory leads us on to the position that quantum mechanics has little, if any,
bearing on philosophy of mind. Finally, we take a moment to defend decoherence
theory against an objection raised by Brian Josephson before finishing with
some concluding remarks on unsolved problems and broader difficulties in interpreting
quantum mechanics.
2. Traditional
Measurement: The Ghost of Mechanics Past
2.1 On the standard
account of quantum measurement, originally due to John von Neumann (1955/1932),
the act of observation discontinuously projects a quantum system into one of
the basis statesrepresented as a set of eigenvectors spanning Hilbert spacefor
the observable operator in question. We can think of the probability of finding
the system in a state corresponding to a given basis vector as proportional
to the magnitude of the system's original state vectorthe Hilbert space representation
of its wavefunctionprojected along that basis vector. (Alternatively, the
probability is just the square modulus of each basis vector's coefficient in
the linear superposition which makes up the state vector.) The set of probabilities
returned when we apply the observable operator to the state vector of a system
(or 'collapse the wavefunction' or 'reduce the state vector') is that system's
reduced density matrix.
2.2 A crucial fact for our discussion is that it makes no difference
to the statistical predictions of quantum mechanics exactly when in the course
of observation state vector reduction occurs, as long as it happens some time
before the result of a measurement has entered the conscious mind of an observer.
In this sense, the observer is said to terminate the socalled von Neumann
chain, the sequence of interactions from quantum system up through measuring
apparatus(es) and into a mind. But it is on the end of this von Neumann chain
that the philosophers' quantum mechanical romance begins. Some suggest that
we take consciousness as more than just the terminus of this chain, that we
take consciousness itself as the very mechanism which precipitates state
vector reduction. The view that consciousness actually brings about state vector
reduction has very nearly become the standard in mainstream philosophy, and
it has even entered popular folklore, figuring centrally in almost every popular
account of the 'new physics'. (See, for instance, Capra, 1982, 1984; Talbot,
1980; compare Squires, 1990.) Nor is it remotely foreign to the physics literature.
(London & Bauer, 1939; Wheeler, 1977, 1980; Wigner, 1961, 1963, 1967; Jahn,
1981) Since quantum mechanics predicts deterministic unitary evolution for isolated
systems and probabilistic state vector reduction for observed systems, it is
easy to see how this interpretation might appeal: the difference between the
two cases seems to be just the presence of the conscious observer, so we might
think it is exactly that which turns what von Neumann called the type
I process (unitary evolution in accordance with the Schrodinger equation) into
the type II process (state vector reduction).
2.3 In the course of my earlier account of decoherence (Mulhauser 1995), I described
a range of problems which this view of state vector reduction creates for philosophy
of mind and philosophy of science. Without rehearsing those problems here, we
can observe in the current context that this viewthe view that the consciousness
of an observer actually precipitates state vector reductionlends itself congenially
to both types of theories we mentioned above which attempt to apply quantum
mechanics to questions of mind (or vice versa, or both). The notion straightforwardly
encourages approaches like that of Eccles, who maintains that causally prior
mental 'psychons' govern the states of structures at or above the level of cells
in the neocortex by collapsing wavefunction descriptions of presynaptic vesicular
grids. Likewise, the position that state vector reduction doesn't actually take
place until the very end of the von Neumann chain allows the possibility of
gross biological structures existing in states of linear superposition for extended
periods of time (a la Schrodinger's cat) unless or until they are consciously
observed. Appeals to such persisting superposed or wavelike states of gross
computationally relevant structures are at the heart of those quantum theories
of mind which fall under the second heading. (As an aside, note that our arguments
explicitly do not apply to theories which appeal to other apply
to theories which appeal to other kinds of wavelike properties of gross
biological structures, such as that of Zaman (1992), who offers an electromagnetic
theory of brain dynamics governed by Maxwell's equations; this particular theory
is probably untenable for other reasons, however, not the least of which is
that at the relevant EEG and MEG frequencies, electric and magnetic fields are
uncoupled.)
2.4 In the next section, we see that quantum measurement theory has outgrown
the need for any account which explicitly appeals to the consciousness of an
observer. We see how a quasiclassical world may emerge from the laws of quantum
mechanics and how this occurs entirely in the absence of the traditional sorts
of 'observer'.
3. Decoherence:
Traditional Measurement Theory Gives up the Ghost
3.1 The modern description
of decoherence derives from the work of a range of physicists including Murray
GellMann, Jim Hartle, Stephen Hawking, Erich Joos, Dieter Zeh, Wojciech Zurek,
and others. (It is also especially comprehensible within Hugh Everett's 1957
interpretation of quantum mechanics, and it needn't be incompatible with it,
as I incorrectly speculated in Mulhauser (1995). It has grown out of the conviction
of quantum cosmology that quantum mechanics ought to apply to the entire cosmos
throughout all time, with no arbitrary Copenhagenstyle line of demarcation
between the quantum world and a classical one. (Coleman, et al., 1991, makes
an interesting introduction to quantum cosmology.) If this is true, this conviction
that we ought to be able to explain with quantum mechanics (and general and
special relativity) all observable behaviour in the entire cosmos, then somehow
from quantum mechanics we ought to be able to derive laws describing the quasiclassical
behaviour we observe around us most of the time.
3.2 To see how something like this might work, it is helpful first to recall
that contemporary quantum mechanics understands a system's wavefunction to contain
all the information there is about that system. But while the wavefunction
contains answers to all the questions we could ask about a system, not all those
questions can meaningfully be answered simultaneously. More specifically, we
cannot obtain a precise value for the state of a system with respect to one
observable without obliterating information about the state of the system with
respect to all other noncommuting observables. Perhaps the most common illustration
of this point is the observation that we cannot ascertain both a particle's
position and its momentum at the same time. In practice as well as in theory,
explaining or predicting the behaviour a quantum system requires extracting
from a complete wavefunction certain information about that system while ignoring
other information about that system or about other systems with correlated states.
3.3 The significant feature of decoherence is that it turns out when we treat
the entire cosmos as a quantum system with a wavefunction description, we can
ask questions about the behaviour of macroscopic collections of particles and
get answers which very closely approximate the answers offered by classical
physics. Of course in practice it is impossible actually to formulate the wavefunction
description of any but the smallest subsystems of the cosmos, so obviously we
can't begin with the wavefunction of the cosmos and then extract information
about our chosen subsystem. To get at what we will use instead, let's take an
example of some macroscopic object such as a billiard ball. (Such very
coarse graining is probably inadequate for a proper specification of the quasiclassical
domain, but the details do not concern us here.)
3.4 Suppose we'd like to know the physical position of the billiard ball to
within some degree of precision. Significantly, in formulating our question
about the billiard ball's location, we ignore the quantum state of everything
else in the cosmos. We don't ask about the velocity of certain fleas on John
Major's dog or about the state of the Russian economy or even about whether
there is a collection of particles known as planet Earth (although there being
a position for something like a billiard ball might be contingent on there being
a planet Earth). Now, subject to a certain condition we'll specify in a moment,
we can use the possible positions of the billiard ball, together with our hypothetical
wavefunction of the whole cosmos, to partition the set of possible states
for everything elseeverything we're ignoring just nowinto equivalence classes
with respect to each of which the billiard ball is in a different position (to
some rough approximation). There might be myriad possible states in each of
the equivalence classes, but within each class every possible state for everything
else is compatible with just one (approximate) location of the billiard ball
and incompatible with all its other possible locations.
3.5 The proviso which enables this partitioning is that there be a good degree
of correlation between the state of the billiard ball and the state of
everything else. That is, given that the cosmos is in a pure quantum state,
we cannot separate off the billiard ball and be left with a billiard ball in
a pure state and a restofthecosmos in a pure state. Each subsystemthe billiard
ball and the rest of the cosmosis in a mixed state, and there are nonseparable
correlations between the two. In other words, its evironment, the rest of the
cosmos, contains information about the state of the billiard balljust
as the billiard ball contains information about the state of the rest of the
cosmos. At the level of individual particles such as electrons being fired through
a couple of slits at a screen, there might be only very little of this environmental
recordkeeping, but by the time we reach the level of macroscopic collections
of particles like billiard balls being fired through slits (or sat on tables,
or whatever), correlations between those collections and the environment are
widespread and farreaching.
3.6 As extensive numerical analysis of complex quantum systems with a degree
of environmental interaction reveals, the immediate effect of this environmental
recordkeeping is that the coherence of what might otherwise have been
a smooth continuous wavefunction description of the billiard ball is destroyed
extremely rapidly. (For some technical examples illustrating this process through
socalled spontaneous 'dynamical' decoherence or the decoherence functional
of the sum over histories formulation, see Albrecht, 1992; DeWitt, 1993; Dowker
and Halliwell, 1992; Finkelstein, 1993; Joos & Zeh, 1985; Paz, et al., 1993;
Paz and Sinha, 1992; Paz & Zurek, 1992; Zeh, 1993; Zurek, 1991, 1993, 1994.)
That is, the buildup of nonseparable correlations between a system such as a
billiard ball and its environmentwhich, in one famous example, could even
be as little as cosmic background radiationcauses a very rapid decrease in
the possible states of the system which can be distinguished through their
effects on the environment. This is little more than a restatement of the
partitioning process: because of the correlations between the billiard ball
and the rest of the cosmos, asking just about the state of the billiard ball
effectively partitions the space of possible states for the rest of the cosmos
into equivalence classes, and it is only the billiard ball states which pick
out nonempty classes which can be distinguished through their effects on the
environment.
3.7 As Paz, et al (1993) suggest, this process "results in a negative selection
which leads to the emergence of a preferred set of states... which remain least
affected by the 'openness' of the system in question". (p. 488) Conveniently
and unsurprisingly, the states that emerge from this environmentinduced superselection,
which I prefer to call 'interactive decoherence' rather than the 'spontaneous
decoherence' common in the physics literature, correspond closely to those of
the macroscopic observables of the quasiclassical world. (Albrecht, 1992; Paz,
et al., 1993) When we ask the right questions of quantum systems large or small,
as long as there is a suitable degree of environmental interaction (which, generally
speaking, can be extraordinarily minute), the predictions we derive from this
process exactly mimic those of traditional state vector reduction. The most
significant difference is that the consciousness of an observer plays no
role in the decoherence story. The process whereby the billiard ball comes
determinately to be in my hand, or in the corner pocket, or in geosynchronous
orbit around the third planet from the Sun has no need for any supervising consciousness.
Quantum measurement has outgrown the conscious observer, and it is getting by
just fine without us! As Zurek suggests in a popular rendition,
Conscious
observers have lost their monopoly on acquiring and storing information. The
environment can also monitor a system, and...such monitoring causes decoherence,
which allows the familiar approximation known as classical objective realitya
perception of a selected subset of all conceivable quantum states evolving
in a largely predictable mannerto emerge from the quantum substrate. (Zurek,
1991, p. 44)
3.8 Hopefully it
is apparent from this discussion of interactive decoherence that the first category
of quantum theories of mind we mentioned above, those which appeal to minds
as causal factors or determinants in reducing the state vector descriptions
of appropriate hardware or wetware, have lost any support they may have enjoyed
from more traditional quantum measurement theory. On the modern view, interactive
decoherence would occur even if there were not a single conscious observer in
the cosmos. (And, likewise, when a conscious observer is involved, selection
of the basis states takes place because of the nonseparable correlations introduced
by the measurement process and not because of the consciousness itself.)
In the next section we turn the discussion the other way round: if mind is irrelevant
to quantum mechanics, is quantum mechanics also irrelevant to mind? In Mulhauser,
1995, I state this side of the discussion without argumentthat quantum mechanics
simply was utterly irrelevant to philosophy of mindbut here we take up the
argument explicitly.
4. Exorcising
The Ghost in the Machine
4.1 With this new
understanding of interactive decoherence as a process which occurs automatically
and independently, without the influence of any conscious observer, and apparently
for every body in the cosmos which has any significant degree of interaction
with its environment, it is much easier than it might have been before to see
that the relevance of quantum mechanics to questions of mind is analogous to
the relevance of quantum mechanics to questions of digital computation. This
analogy emphatically does not rest on any presupposition of functional
similarity between digital computation and the dynamics of minds' hardware or
wetware; the analogy comes instead from the levels at which we may describe
digital computers on the one hand and things like brains on the other.
4.2 Taking the digital computer example first, the peculiarities of quantum
mechanics are of course relevant to a proper understanding of the very lowest
level behaviour of logic gates in the silicon chips which typically implement
digital computers. But the higher level behaviour of a digital computerand
indeed the theory of digital computation itselfrequires that influences of
quantum deviations from the classical deterministic framework are completely
nonexistent at or above the level of the gate itself. That is, while the mechanisms
which make the gate work the way it does may be quantum in nature, the gate
must play its functional role in the computer in an absolutely deterministic,
quasiclassical way that is utterly independent of quantum fluctuations. Indeed,
the existence of quantum effects at the lowest levels of digital computers is
purely an accident of their micronlevel implementation in silicon, for they
theoretically work just the same way, if more than a little more slowly, implemented
with comparatively huge Babbagestyle gears and cogs.
4.3 The most important point is that while quantum mechanics is relevant to
understanding the very lowest level properties of digital computers, as it is
relevant to understanding the very lowest level properties of any material body
at all, it is utterly irrelevant to the theory of digital computationthe 'philosophy
of digital computation', if you will. Likewise for philosophy of mind. The very
nature of a brain or the hardware substrate of an artificial intelligence as
a high temperature physical object in continual strong interaction with
its environment bodes very unfavourably for the possibility of coherent unitary
evolution of components at all but the smallest scales. Carrying complex information
in the form of correlations between states of physical observables (the preferred
'physicalist' definition of the word 'information'; see Landauer, 1991) appears
straightforwardly incompatible with existing in a coherent state of quantum
linear superposition. And without adopting any especially strong views about
information processing in minds, the incompatibility between being an informationcarrier
and maintaining quantum coherence makes it difficult to see how any specifically
quantum subsystem could play a functionally relevant role in a mind's hardware
or wetware or, alternatively, how any functionally relevant subsystem could
have specifically quantum behaviour.
4.4 This does not of course mean that no specifically quantum events
ever occur in brains, for instance, any more than it means quantum events do
not occur in digital computers. For example, quantum effects may well be relevant,
as Eccles (1986) suggests, at the level of presynaptic vesicular grids. We
needn't dispute events which are quantum in character here, or in the activations
of voltagegated ion channels, or in many other comparatively low energy subcellular
mechanisms. We need only dispute the emergence of any consistent relationships
between such quantum events which could be relevant to understanding
minds. Quantum mechanics may be very important for understanding why extremely
low level structures in brains and the like work as they do, but interactive
decoherence precludes its having anything to say about larger scale properties
of such structures orvery probablyof minds. The phenomenon of interactive
decoherence suggests that relevant kinds of higher level structures cannot exist
in coherent quantum states, and it guarantees that even lower level structure
can exist in coherent quantum states only so long as their interaction with
their environment is kept to an absolute minimum. (Zurek, 1991, notes that a
rough calculation shows coherence of a 1 gm solid mass at room temperature is
destroyed in less than 10^23 seconds. Coherence even for dust grains interacting
with cosmic background radiation is still destroyed in nanoseconds; see Joos
& Zeh, 1985, also DeWitt, 1993.) We might speculate that the entire range
of actual quantum effects in things like brains could simply be treated stochastically,
with nothing relevant to philosophical questions about minds lost by giving
up specifically quantum mechanical descriptions.
4.5 In short, then, the argument against the relevance of quantum mechanics
to philosophy of mind is twofold. On the one hand, consciousness is irrelevant
to the modern formulation of quantum measurement. Theories of the first kind
above, those which appeal to minds as causal factors in collapsing state vector
descriptions of mind hardware or wetware, lose all theoretical grounding in
light of interactive decoherence. On the other hand, interactive decoherence
also reveals that only subsystems either very low in total energy or lacking
any significant degree of environmental interaction can exist in coherent quantum
superpositions. Thus, quantum mechanics cannot comment on any large scale properties
of the material substrates associated with minds, and it certainly does not
permit coherent superposed evolution of gross functionally relevant information
transforming structures. Theories of the second kind, those which appeal to
quantum effects to endow hardware or wetware with unique information transforming
properties meant to subserve unique abilities of minds, thus also lose their
theoretical grounding in light of interactive decoherence. (By 'information
transforming' we denote a far broader class of physical structures than those
merely 'computational' or 'computable' in the recursion theoretic sensesee,
for instance, PourEl & Richards, 1989.)
4.6 As an aside, it is worth noting that those such as Penrose (1989), who would
appeal to quantum mechanics to endow brains with noncomputable (in the recursion
theoretic sense) capabilities, thus moving them into a more powerful class than
algorithmic Turing machines or cellular automata, need look no further than
deterministic chaos. As early as 1992, I predicted on the basis of theoretical
considerations (Mulhauser, 1992; see also Mulhauser, 1993, In Press) that systems
which are both chaotic and analogue may exhibit behaviour which cannot
be effectively simulated by a digital computer (thus contradicting the ChurchTuring
thesis which has rested safely at the centre of theoretical computer science
since the 1930s). Notwithstanding attacks from philosophers such as Peter Smith
(1993a, 1993b and in press), who seems often to maintain essentially that chaotic
systems are covered by exactly the same computational and physical framework
as any other kind of deterministic dynamical system, this position has now been
vindicated by the recent specification of a chaotic analogue neural network
with 'SuperTuring' capabilities. (Siegelmann, 1995; see also Siegelmann &
Sontag, 1994, Sommerer & Ott, 1994; see Blum, et al., 1989, for a more general
treatment of computation over the real numbers as opposed to the rationals and
Vergis, et al., 1986, for an earlier analysis of specifically analogue computation.)
4.7 In the next section, we address a tempting objection to the formulation
of decoherence to which we've been appealing before continuing on to some closing
thoughts about decoherence and broader problems in the interpretation of quantum
mechanics.
5. Interactive
Decoherence: An Afterthought?
5.1 Soon after making
available on the International Philosophical Preprint Exchange a preprint of
my earlier account of decoherence, Brian Josephson offered some interesting
objections which can help us get at one matter at the heart of quantum measurement.
Josephson suggests there often seems to be some sleight of hand at work in the
decoherence literature (B. D. Josephson, personal communication, November 10,
1993), although he concedes the merit of my own account is that it goes through
the argument sufficiently clearly that perhaps we can see where the sleight
of hand occurs. With that thought in mind, let's address the objections and
make sure we've discharged sleight of hand from any important roles in the story
of decoherenceor from any roles at all!
5.2 The objection first emerges in the straightforward question about something
like Schrodinger's cat, "how do we go from the mathematical property of decoherence
to the assertion that 'the cat is already either alive or dead long before anyone
opens the box'?". (B. D. Josephson, personal communication, November 10, 1993,
quoting Mulhauser, 1995) As he indicates,
The
nub of the matter is that ordinary physics implies a determinisitic correlation
between whether the particle decayed and whether the cat is subsequently alive
or dead, plus the fact that owing to the linearity of the Schrodinger equation,
once a superposition always a superposition. ...Decoherence implies [only]
that the two dead/alive components are entangled states [i.e., that the cat
is in a mixed stateG.R.M.] rather than simple product states.
5.3 Josephson wonders
whether we could have "continued superposition" when coherence has been lost
(B. D. Josephson, personal communication, November 11, 1993), and he objects
that "the idea that the system is actually in one of the...[basis]...
states is put in as an ad hoc axiom, justified by its consistency". (B. D. Josephson,
personal communication, November 25, 1993) In other words, decoherence may indicate
a preferred basis, but it doesn't show why a system must actually be in a state
corresponding to an eigenvector in the basis. Is our assumption that a system
actually objectively exists in one of the states used to partition the states
of everything else in the cosmos just an unargued afterthought? That a system
may objectively exist in a superposed state after coherence of the state vector
has been destroyed is a possibility with little more than a subtle background
influence for those physicists on whose work the present view as we have outlined
it is based, but very lately some commentators have begun suggesting the problem
of 'interpreting probabilities'exactly the same problem to which Josephson's
objection pointsis crucial to a proper understanding of the emergence of quasiclassical
eigenstates. (See, for instance, the more philosophically thorough treatment
of Saunders 1995, who seeks an analogy between relational approaches to time
and to quantum measurement.) The difficulty is whether to attribute to the mechanisms
of decoherence the same kind of power to 'actualise' basis vectors as we have
hitherto attributed to state vector reduction. Let's examine the question more
closely and see whether it really is an afterthought to suppose a system is
actually in one of the interactively decohered states.
5.4 The outline of one possible answer to the problem begins with a consideration
of the experimentally verifiable difference between the proposition that a decohered
system has actually 'collapsed' into an eigenstate and the proposition that
it still exists in a superposed state, except that the superposition is, on
account of decoherence, a linear combination of vectors describing only quasiclassical
basis states. The first proposition enables us to tell a story about the system's
evolution which proceeds through interaction with an environment and ends with
a description of the different eigenstates in which the system might be found
upon observation, together with a prediction of the probability of finding the
system in any particular eigenstate. Crucially, the probabilities describe the
chance the system will have already collapsed into one of these states,
although, until the observation is made, we remain ignorant of which state is
objectively real. The second proposition prompts a story of the system which
proceeds through interaction with an environment and ends with a description
of a superposition of eigenstates into one of which the system may be forced
by conscious observation, together with a prediction of the probability of the
system entering any particular eigenstate. Crucially, the probabilities describe
the chance the system will collapse into one of these states, since before
the observation is actually made, the state of the system remains a superposition
and it is not determinately in any one of the eigenstates.
5.5 In both these cases, of course, the probabilities sum to unity, so the prediction
is that the system will be found in precisely one of the eigenstates.
And thousands or millions of experiments have revealed the unparalleled accuracy
of these predictions: in this sense, the enormous body of experimental evidence
tends to confirm both accounts equally well. If there doesn't seem to be any
experimentally verifiable difference between the two accounts, has the advocate
of interactive decoherence succumbed to the afterthought temptation and simply
opted for the new view over the established one for no sound reason?
5.6 The story we've told so far now clearly recommends a negative answer to
this question. If we start from the standpoint of the traditional quantum measurement
theory of more than the last half century, it might seem at first that 'adding
in' the proposition that a decohered system is actually objectively in
an eigenstate before a conscious observation is made is unfairly putting consciousness
on the dole. But recall that under the original projection postulate, consciousness
terminated the von Neumann chain: the observation was merely the latest
time by which a wavepacket could collapse, and the predictions of quantum mechanics
were no different whether it collapsed at this last instant or at some earlier
time in the chain. Interactive decoherence may now offer an account of the actual
mechanisms which precipitate state vector reduction, independently of
any consciousness phenomenon. It is hardly mysterious that we don't actually
know the outcome of a measurement until the von Neumann chain is terminated,
since after all we don't know the outcome of any measurement, quantum
or classical, until we actually complete an observation. Apparently we now have
in decoherence theory an account of the emergence of the basis vectorsas Josephson
concedes but it is perhaps confusingly obvious that we can't expect to know
which eigenstate is actual until we observe it. On the account of interactive
decoherence offered here, we are left with only the question of whether the
system is actually in an eigenstate before observation. But as we have seen
there is no experimentally verifiable difference between the two alternatives,
and on this view it is the proponent of accepted quantum measurement theory
whose "sleight of hand" is adding in a consciousness phenomenon which has no
explanatory value. Consciousness is redundant. (In Mulhauser, 1995, pp.
210, 215, I offer a simple but difficult to perform 'consciousness detector'
experiment which would distinguish between the two accounts of decoherence,
provided that we have some independent means of deciding whether a given observer
is conscious. This experiment also implies that von Neumann's account of the
type II process is wrong that it makes no difference where in the chain state
vector reduction takes place. In our context, we proceed as if von Neumann is
correct; I believe our account remains convincing enough!)
5.7 This is the simple answer, anyway. In the next section we turn to some problems
with this approach and consider broader questions of interpretation in areas
of quantum mechanics which even under decoherence theory still await explanation.
6. Quantum Realities:
How Many and Which Ones?
6.1 This type of
reply to the problem of interpreting probabilities and their reference accepts
state vector reduction as an actual physical process, albeit one which derives
from unitary evolution. This is in the same spirit as Hartle (1993), and
it mirrors Griffiths's (1984) early account of decoherence which explicitly
rejects the notion that a single individual system may exist in a linear superposition
of decohered eigenstates. The problem, of course, is that such an interpretation,
appealing only to the theoretical constructs which have emerged from decoherence
theory to date, on the face of it requires either an ignorance interpretation
or an 'ad hoc' addition (pace Josephson) of the power of decoherence to 'actualise'
eigenstates. Our answer does still permit us to reject consciousness
as a mechanism for precipitating state vector reduction, since along the lines
of the above it performs no experimentally verifiable job over and above the
standard picture of the von Neumann chain together with interactive decoherence.
But it does not answer fully the problem of interpreting probabilities.
6.2 The problem of probabilities and the project of salvaging all of our reply
to Josephson's objection may be approached in at least two different ways. On
the one hand, we might simply take the logic of probability as fundamental
and deny that our account of measurement has to explain anything about
it at all. Griffiths (1984) and Omnes (1990) adopt this approach in their formulation
of the process of decoherence itself if not entirely in the interpretation
of the resultant decohered states (see also Omnes, 1992), while GellMann and
Hartle (1990) and Zurek (1991) are at least sympathetic to it.
6.3 My own preference is to 'bite the bullet' on the ignorance approach to Griffiths's
explicit rejection of superposition after decoherence, except with a different
twist on 'ignorance': I suspect what is hidden might not be some extra set of
variables from which the laws of unitary evolution derive, but instead might
be some features of the interaction of complex quantum subsystems which,
due simply to the computational power required to analyse them, haven't been
discovered yet. Analsyses of only very simple interacting systems have yet to
appear in the literature, and I suspect that with time we may witness the emergence
of certain constraints on the evolution of increasingly complex systems.
6.4 That is, we might expect that given an adequately large repertoire of interacting
subsystems, certain configurations of states and correlations between them simply
become impossible. Indeed, the other outstanding problem in decoherence theory
today, apart from interpreting probabilities, is the closely related problem
of accounting for the uniqueness of the quasiclassical domain which arises
from the processes of decoherence. Could there be more than one nonequivalent
way of partitioning states of subsystems, enabling decoherence into more than
one possible state of basis vectors? If so, how do we (or Nature) choose between
them? GellMann and Hartle (1990) and GellMann (1994) suggest that macroscopic
adaptive systems (such as ourselves) may simply have emerged with only the capacity
to utilise the probabilities of a particular quasiclassical domain, without
denying the possibility of other, equally 'real', nonequivalent domains. Zurek
(1994) and Saunders (1993a, 1993b) make other appeals to evolutionary constraints
on complex systems, while I suggest a more radical version in Mulhauser (in
press).
6.5 This more radical version continues the flirtation with ignorance interpretations
of measurement; it is simply the idea that it may turn out that interactions
between a sufficiently large number of subsystems not only pares down the possible
states in which subsystems may exist (thus yielding the basis vectors), but
it may even determine which of those states are actualised. This amounts
to a more serious 'evolutionary' constraint on the cosmos itself. Hopes like
this have been expressed before in the guise of standard 'hidden variables'
theories, and while it is not those which I am advocating, it is nonetheless
instructive in our context to note some features of those accounts as they might
bear on the project of ultimately fitting all the pieces of a picture of decoherence
into place.
6.6 Most significantly, contrary to popular opinion, quantum mechanics is not
incompatible with hidden variables theories; experimentally verified violation
of Bell's inequalities shows only that quantum mechanics cannot be explained
with specifically local hidden variables. (Bell, 1964, 1966; for what
set it all off, see Einstein, et al., 1935 and Bohr's reply, 1935a, 1935b; on
experimental verification see Aspect, 1976, Freedman & Clauser, 1972, Fry
& Thomson, 1976.) Hidden variables of a nonlocal variety are entirely compatible
with quantum mechanics, and they are the basis of at least one possible deterministic
interpretation of the quantum theory. (Bohm, 1952) Moreover, if Lockwood's (1990/1989;
compare Maudlin, in press) argument against the idea that standard stories of
nonlocality actually permit propagation of signals faster than light is to be
taken at face value, nonlocal hidden variables might not be as bad as they are
commonly supposed. (Faster than light signalling is usually supposed to be the
harbinger of doom, since special relativity suggests spacelike communication
would open up no end of possible assaults on causation.)
6.7 In any case, the speculation I would like to offer is that this general
approach to nonlocality, together with interactive decoherence theory, points
in the direction of a different sort of deterministic interpretation of quantum
mechanics. In particular, I wonder if the kind of nonlocality observed in pure
quantum systems like the EPR experiment might also figure in the interactions
of hidden variables in the socalled 'quantum vacuum', the source of virtual
particles? (See Podolny, 1986 for a charming nontechnical introduction to the
quantum vacuum as well as a romantic history of science in the former Soviet
Union.) If so, I wonder how decoherence theory would bear on questions about
the states of these hidden variables? If decoherence theory could explain fluctuations
in the quantum vacuum, perhaps it could also offer deterministic predictions
about which of several actual states a decohering system might enter. Or, even
more optimistically, perhaps decoherence theorists will eventually discover
that hidden variables are no longer necessary because the environment, considered
in all its complexity, actually determines the state to which a system will
collapse.
6.8 This is the initial speculation I offered above; if this approach bears
fruit, the problems of probability and of the uniqueness of the quasiclassical
domain simply disappear, and the irrelevance of consciousness becomes all the
more convincing. Even success of a weaker version of this speculationone which
would give a single quasiclassical domain without necessarily making it deterministic
would enable the sort of 'softer' approach offered by Saunders (1995, pp. 255256)
wherein decoherence does actualise states, but without actual state vector
reduction. On his speculative account, we would then have unitary evolution
for the entire cosmos, without state vector reduction, and we would have 'actual'
states for macroscopic objects, but we would give up 'actual' states for lowerlevel
subsystems which might be part of decohered macroscopic objects.
6.9 It remains to be seen what will become of such speculations as decoherence
theory becomes more widely accepted and attracts more attention in the theoretical
community. What does seem clear at this early stage, however, is that quantum
measurement truly has outgrown the need for a conscious observer. We've undertaken
these closing considerations of probability and the uniqueness of the quasiclassical
domain only because they remain outstanding problems in decoherence theory;
it should now be clear that our original position that consciousness is irrelevant
to quantum mechanics and vice versa does not depend upon any particular
resolution of these questions. However these questions are ultimately answered,
the fact remains that the story of quantum measurement can now be told without
mention of any specifically conscious observer. This maturation of quantum mechanics
demands similar growth in those areas of philosophy of mind which formerly made
some appeal to the quantum world. Seemingly bizarre things still happen as a
result of quantum mechanics, but for better or worse consciousness does not
appear to be one of those things directly affectedor effectedby it. The
partnership between quantum mechanics and one area of philosophy is ending,
and quantum mechanics grows on without it; philosophy must do the same.
Acknowledgements
I am grateful to
the Gifford Lectureship Committee, who fund my present research at the University
of Glasgow, and to the Marshall Aid Commemoration Commission, who funded my
previous research at the University of Edinburgh on which part of this paper
is based. Thanks also to two anonymous PSYCHE referees, to the staff of the
International Philosophical Preprint Exchange, where Mulhauser (in press; 1995)
have been available, and to many email correspondents and members of seminar
and lecture audiences for insightful comments which have helped distill the
arguments offered here.
References
Albrecht, A. (1992) Investigating Decoherence in a Simple System.
Physical Review D, 46, 55045520.
Aspect, A. (1976) Proposed Experiment to Test the Nonseparability of Quantum
Mechanics. Physical Review D, 14, 19441951.
Bell, J. S. (1964) On the Einstein Podolsky Rosen Paradox. Physics, 1,
195200.
Bell, J. S. (1966) On the Problem of Hidden Variables in Quantum Mechanics.
Reviews of Modern Physics, 38, 447452.
Blum, L., Shub, M., & Smale, S. (1989) On a Theory of Computation and Complexity
Over the Real Numbers: NPCompleteness, Recursive Functions and Universal Machines.
Bulletin (New Series) of the American Mathematical Society, 21, 146.
Bohm, D. (1952) A Suggested Interpretation of the Quantum Theory in Terms of
"Hidden" Variables. Physical Review, 85, 166193.
Bohr, N. (1935a) Quantum Mechanics and Physical Reality. Nature, 136,
65.
Bohr, N. (1935b) Can QuantumMechanical Description of Physical Reality Be Considered
Complete? Physical Review, 48, 696702.
Capra, F. (1982) The Turning Point. New York: Bantam.
Capra, F. (1984) The Tao of Physics (2nd ed.). New York: Bantam.
Coleman, S., Hartle, J., Piran, T., & Weinberg, S. (Eds.) (1991) Quantum
Cosmology and Baby Universes. Proceedings of the 7th Jerusalem Winter School,
Jerusalem, Israel, 1990. Singapore: World Scientific.
DeWitt, B. (1993) How Does the Classical World Emerge from the Wave Function?
In F. Mansouri and J.J. Scanio (Eds.). Topics on Quantum Gravity and Beyond.
Singapore: World Scientific.
Dowker, H.F., & J.J. Halliwell (1992) Quantum Mechanics of History: The
Decoherence Functional in Quantum Mechanics. Physical Review D, 46, 15801609.
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,
411428.
Eccles, J. (1990) A Unitary Hypothesis of MindBrain Interaction in the Cerebral
Cortex. Proceedings of the Royal Society of London B, 240, 433451.
Einstein, A., Podolsky, B & Rosen, N. (1935) Can QuantumMechanical Description
of Physical Reality Be Considered Complete? Physical Review, 47, 777780.
Everett, H. (1957) "Relative State" Formulation of Quantum Mechanics. Reviews
of Modern Physics, 29, 454462.
Fine, A. (1993) Indeterminism and the Freedom of the Will. In J. Earman, Janis,
A. I., Massey, G. J. & Rescher, N (Eds.). Philosophical Problems of the
Internal and External Worlds: Essays on the Philosophy of Adolph Grunbaum.
(pp. 551572). Pittsburgh: University of Pittsburgh Press.
Finkelstein, J. (1993) Definition of Decoherence. Physical Review D, 47,
54305433.
Freedman, S. J., & Clauser, J. F. (1972) Experimental Test of Hidden Variable
Theories. Physical Review Letters, 28, 938941.
Fry, E. S., & Thompson R. C. (1976) Experimental Test of Local HiddenVariable
Theories. Physical Review Letters, 37, 465468.
GellMann, M. (1994) The Quark and the Jaguar. New York: W.H. Freeman.
GellMann, M., & Hartle, J. B. (1990) Quantum Mechanics in the Light of
Quantum Cosmology In W.H. Zurek (Ed.). Complexity, Entropy, and the Physics
of Information. (pp. 425459). Reading, Massachusetts: AddisonWesley.
Griffiths, R. (1984) Consistent Histories and the Interpretation of Quantum
Mechanics. Journal of Statistical Physics, 36, 219272.
Grunbaum, A. (1972) Free Will and the Laws of Human Behavior In H. Feigl, W.
Sellars, and K. Lehrer (Eds.) New Readings in Philosophical Analysis.
New York: AppletonCenturyCrofts, pp. 60527. (Originally published in American
Philosophical Quarterly, 8, 299317.) Hartle, J. B. (1993) Reduction of
the State Vector and Limitations on Measurement in the Quantum Mechanics of
Closed Systems. Unpublished manuscript. (UCSBTH9216.) Jahn, R. G. (Ed.)
(1981) The Role of Consciousness in the Physical World. Boulder, Colorado:
Westview.
Joos, E., & Zeh, H. D. (1985) The Emergence of Classical Properties through
Interaction with the Environment. Zeitschrift fur Physik B, 59, 223.
Landauer, R. (1991) Information is Physical. Physics Today, 44, 2329.
Lockwood, M. (1990/1989) Mind, Brain, and the Quantum. Oxford: Basil
Blackwell.
London, F. & Bauer, E. (1939) La theorie de l'observation en mecanique quantique,
No. 775 of Actualites scientifiques et industrielles. P. Langevin, (Ed.) Paris:
Hermann. Translated in J.A. Wheeler and W.H. Zurek, (Eds.) Quantum Theory
and Measurement. (pp. 217259). Princeton: Princeton University Press.
Marcer, P. J. (1992) The Conscious Machine and the Quantum Revolution in Information
Technology. Kybernetes, 21(1), 1822.
Maudlin, T. (1994) Quantum NonLocality and Relativity. Oxford: Blackwell.
Mulhauser, G. R. (In Press) Mind Out of Matter: Topics in the Physical Foundations
of Consciousness and Cognition. Kluwer Academic Publishers
Mulhauser, G. R. (In Press) Suppose A Wavefunction Collapsed in the Forest...
In P. Pylkkanen and P. Pylkko (Eds.). New Directions in Cognitive Science.
Helsinki: Finnish Artificial Intelligence Society.
Mulhauser, G. R. (1995) Materialism and the "Problem" of Quantum Measurement.
Minds and Machines, 5(2), 207217.
Mulhauser, G. R. (1993). Computability in Chaotic Analogue Systems. Presented
at the International Congress on Computer Systems and Applied Mathematics in
St. Petersburg, Russia.
Mulhauser, G. R. (1992, September). Computability in Neural Networks.
Presented at the meeting of the British Society for the Philosophy of Science
in Durham, England.
Omnes, R. (1990) From Hilbert Space to Common Sense: A Synthesis of Recent Progress
in the Interpretation of Quantum Mechanics. Annals of Physics, 20, 354447.
Omnes, R. (1992) Consistent Interpretations of Quantum Mechanics. Reviews
of Modern Physics, 64, 339382.
Paz, J. P., Habib, S., & Zurek, W. H. (1993) Reduction of the Wave Packet:
Preferred Observable and Decoherence Time Scale. Physical Review D, 47,
488501.
Paz, J. P., & Sinha, S. (1992) Decoherence and Back Reaction in Quantum
CosmologyMultidimensional Minisuperspace Examples. Physical Review D, 45,
28232842.
Paz, J. P., & Zurek, W. H. (1992) Environment Induced Superselection
and the Consistent Histories Approach to Decoherence. (Los Alamos Report
No. LAUR92878).
Penrose, R. (1989) The Emperor's New Mind. Oxford: Oxford University
Press.
Podolny, R. (1986) Something Called Nothing. (Nicholas Weinstein Trans.).
Moscow: Mir Publishers.
Popper, K. R. and Eccles, J. (1977) The Self and Its Brain: An Argument for
Interactionism. Berlin: Springer.
PourEl, M. B. & Richards, J. I. (1989) Computability in Analysis and
Physics. Heidelberg: SpringerVerlag.
Saunders, S. (1993a) Decoherence, Relative States, and Evolutionary Adaptation.
Foundations of Physics, 23, 15531585.
Saunders, S. (1993b) Decoherence and Evolutionary Adaptation. Physics Letters
A, 184, 15.
Saunders, S. (1995) Time, Quantum Mechanics, and Decoherence, Synthese, 102,
235266.
Siegelmann, H. T. (1995) Computation Beyond the Turing Limit. Science, 268,
545548.
Siegelmann, H. T. & Sontag, E. D. (1994) Analog computation via neural networks.
Theoretical Computer Science, 131, 331360.
Smith, P. (1993a) Commentary on G.R. Mulhauser, Chaotic Dynamics and Introspectively
Transparent Brain Processes. Presented at the Second Annual Conference of
the European Society for Philosopy and Psychology.
Smith, P. (1993b) Chaos: Explanation, Prediction & Randomness. Manuscript
of Easter Term 1993 Cambridge lecture series on chaos.
Smith, P. (in press). Explaining Chaos. Cambridge: Cambridge University
Press.
Sommerer, J. C. & Ott, E. (1993) A Physical System with Qualitatively Uncertain
Dynamics. Nature, 365, 138140.
Squires, E. (1990) Conscious Mind in the Physical World. New York: Adam
Hilger.
Talbot, M. (1980) Mysticism and the New Physics. New York: Bantam.
Vergis, A., Steiglitz, K., & Dickinson, B. (1986) The Complexity of Analog
Computation. Mathematics and Computers in Simulation, 28, 91113.
Von Neumann, J. (1955/1932) Mathematical Foundations of Quantum Mechanics.
Princeton, New Jersey: Princeton University Press.
Wheeler, J. A. (1977) Include the Observer in the Wave Function? In J. Leite
Lopes & M. Paty (Eds.). Quantum Mechanics, a Half Century Later.
(pp. 118). Dordrecht: Riedel.
Wheeler, J. A. (1980) Beyond the Black Hole. In H. Woolf (Ed.). Some Strangeness
in the Proportion: A Centennial Symposium to Celebrate the Achievements of Albert
Einstein. (pp. 341375) Reading, Massachusetts: AddisonWesley.
Wigner, E. P. (1961) Remarks on the MindBody Question. In I.J. Good, (Ed.).
The Scientist Speculates: An Anthology of PartlyBaked Ideas. (pp. 284302)
London: Heinemann.
Wigner, E. P. (1963) The Problem of Measurement. American Journal of Physics,
31, 615.
Wigner, E. P. (1967) Symmetries and Reflections. Bloomington, Indiana:
Indiana University Press.
Zaman, L. F. (1992) Brain Electromagnetic Fields. Presented 18 February
1992 at the Pan Pacific Workshop on Brain Electric and Magnetic Topography.
Melbourne, Australia.
Zeh, H. D. (1993) There are No Quantum Jumps, Nor are there Particles. Physics
Letters A, 172, 189192.
Zurek, W. H. (1991) Decoherence and the Transition From Quantum to Classical.
Physics Today, 44, 3644.
Zurek, W. H. (1993) Negotiating the Tricky Border Between Quantum and Classical.
Physics Today, 46, 1315+.
Zurek, W. H. (1994) Preferred States, Predictability, Classicality, and the
EnvironmentInduced Decoherence In J.J. Halliwell, J. PerezMercador, and W.H.
Zurek (Eds.). The Physical Origins of Time Asymmetry. Cambridge: Cambridge
University Press.