QUANTUM MECHANICS AND CONSCIOUSNESS:\\ FACT AND FICTION
Ulrich Mohrhoff
Sri Aurobindo International Centre of Education
Pondicherry-605002 India
Abstract
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\title{QUANTUM MECHANICS AND CONSCIOUSNESS:\\
FACT AND FICTION}
\author{Ulrich Mohrhoff\\ 
Sri Aurobindo International Centre of Education\\ 
Pondicherry-605002 India\\ 
\normalsize\tt ujm@satyam.net.in} 
\date{}
\maketitle 
\noindent {\bf Abstract}: This article was written in response to a request from an 
editor of {\it 
American Vedantist}. It is shown that the idea that consciousness is essential to 
understanding quantum mechanics arises from logical fallacies. This may be 
welcome news to those who share the author's annoyance at consciousness being dragged
into discussions of physics, but beware: 
The same fallacies may underlie the reader's own way of making sense of 
quantum mechanics. The article ends up embracing a Vedantic world view, for 
two reasons. For one, such a world view seems to the author to be the most 
sensible alternative to a materialistic one. For another, quantum mechanics is 
inconsistent with a materialistic world view but makes perfect sense within a 
Vedantic framework of thought.

\vspace{24pt}\noindent
Ever since its formulation three quarters of a century ago, quantum mechanics 
(QM) stands accused of applying a double standard to measurements: While as 
physical processes measurements are governed by the Schr\"odinger equation, as 
constituents of a ``classical domain'' they exist in an anterior logical relationship 
to QM and are governed instead by the so-called projection postulate. Some 
physicists have taken this to mean that QM is inconsistent. Others have felt that 
QM is incomplete: It does not tell us when a physical system evolves in a 
deterministic fashion as dictated by the Schr\"odinger equation, and when it 
changes unpredictably in conformity with the projection postulate.

Those who have come closer to understanding the real import of QM have 
realized that QM spells  {\it the end of mathematical realism}: The mathematical 
symbols employed by QM cannot be interpreted as mirroring (representing, 
describing) the physical world. The mathematical formalism of QM provides us 
with probability measures; it serves to assign probabilities to the possible 
outcomes of possible measurements. That's all there is to it. The rest is 
metaphysics. This is OK since physics without metaphysics would not be 
physics---it would be pure mathematics, without any connection to the physical 
world. The problem is to find the right metaphysics, which at the very least 
ought to be free from logical fallacies.

Since the mathematical symbol known as the ``state vector'' or the ``wave 
function'' is nothing but a probability measure, the so-called ``measurement 
problem'' is spurious. No unpredictable transition from one physical state of 
affairs to another occurs, so none needs to be explained. What changes 
unpredictably is a probability measure, and this for reasons that are obvious 
rather than mysterious. Probabilities are assigned to possible events on the basis 
of relevant facts. They depend (i)~on the time $t$ of the events to which they are 
assigned and (ii)~on the facts on which they are based. They can therefore 
change in two ways: in a deterministic manner as functions of $t$, and 
unpredictably with every new relevant fact. The successful completion of a 
measurement is the relevant fact  {\it par excellence}. If the outcome of the 
measurement is unpredictable, as it generally is, it has to be included among the 
relevant facts on which probability assignments must subsequently be based. The 
outcome being unpredictable, the basis of relevant facts changes unpredictably 
as a matter of course, and so do the probabilities that we assign on this basis. No 
mystery there.

Unfortunately it is never hard to invent new pseudo-problems. Let $p\,(R,t)$ 
stand for the probability of finding an alpha particle inside a region $R$ at a 
time~$t$. While few would think of this probability as something that exists 
inside the region~$R$, many succumb to the temptation of thinking of it as 
something that exists at the time~$t$. The idea is that the possibility of finding 
the alpha inside $R$ exists at all times, so the probability associated with this 
possibility also exists at all times and changes as a function of 
time.\cite{probaone} Yet the possibility that something happens at the time $t$ is 
not something that exists at the time~$t$, anymore than the possibility of finding 
the alpha in $R$ is something that one can find inside~$R$. And the same holds 
true of the probabilities associated with these possibilities. Probabilities are not 
things that subsist and change; the time on which quantum-mechanical 
probabilities depend is the time of the measurement to the possible results of 
which they are assigned. To think of possibilities or probabilities as if they 
possessed an actuality of their own, different from the actuality of facts, is to 
commit a category mistake. Some physicists commit it rather bluntly; they call 
their reified possibilities ``propensities''\cite{Popper} or 
``potentialities''\cite{Heisenberg,Shimony} and believe what happens during a 
measurement is that one of these acquires the status of a fact while the others 
lose their semi-actuality and cease to exist. Others commit it implicitly as when 
they hope or attempt to ``understand how it is that probabilities become 
facts''.\cite{Treiman}

This too is a pseudo-problem. Saying in common language that a possibility 
becomes a fact is the same as saying that something that is possible---something 
that  {\it can} be a fact---actually  {\it is} a fact. How can that be a problem? This 
non-problem becomes a pseudo-problem if one forgets that there is only one kind 
of actuality and misconstrues the common-language ``existence'' of a possibility 
as a second kind of actuality. It seems hard to believe that there are 
physicists---and quite a few---who still try to explain the transition from this 
pseudo-actuality to bona fide actuality, but there you are.

Another name for this pseudo-problem is the ``emergence of classicality''. QM is 
a tool for assigning probabilities to possibilities. It assigns probabilities on the 
basis of facts, and it assigns them on the assumption that exactly one possibility 
(no matter which) becomes a fact, in the innocuous common-language sense of 
``becoming a fact''. Since QM  {\it presupposes} facts from beginning to end 
(from the ``preparation'' of a physical system to a measurement on the system), 
it cannot possibly account for the existence of facts. So what accounts for the 
existence of facts---the emergence of ``classicality''?

Counter-question: What  {\it could} account for the existence of facts? The 
existence of facts is not something that can be accounted for, any more than we 
can give an answer to the question of why there is anything at all, rather than 
nothing. As integral Vedantists we may hold that Brahman or Maya (the 
creative power of Brahman) accounts for the existence of facts, but then we stand 
before the mystery of the existence of Brahman, and there we are left 
dumbfounded. The fallacy that the existence of facts can and ought to be 
explained, arises when one thinks of the possibilities to which QM refers, and of 
the probabilities it assigns to them, as if they constituted a self-existent matrix 
from which facts arise. A silly category mistake, but there you are.

To recap, by mistaking the wave function---a probability measure---for an actual 
state of affairs one creates one pseudo-problem (How is it that this actual state of 
affairs changes unpredictably during a measurement?) and by mistaking 
possibilities for actualities one creates another pseudo-problem (How is it that 
certain possibilities acquire the extra actuality that turns them into facts?). Since 
the early days of QM consciousness has been invoked as a filler for either or both 
of these alleged explanatory gaps~\cite{LonBau,vNeu,Wigner,Page,Stapp,Squires,Lockwood,Albert}, for two reasons. The first is that quantum 
physicists habitually speak of ``observations'' when they mean measurements 
and of ``observables'' when they mean measurable quantities. This has created 
the impression, and promptly called forth the claim, that consciousness is 
essential to understanding QM.

The second reason is that QM concerns probability assignments, and in the 
deterministic world of classical physics probabilities are always  {\it subjective}: 
We resort to probability assignments as and when we are  {\it ignorant} of the 
precise initial conditions that determine the subsequent behavior of a physical 
system. Quantum-mechanical probabilities, however, come in two varieties: 
subjective  {\it and objective}: The latter variety has nothing to do with 
ignorance; there is nothing for us to be ignorant of. The probability associated 
with a particular result of a measurement is subjective if it is assigned on the 
basis of an incomplete set of relevant facts, such as when the measurement is 
actually made but we are as yet ignorant of its result. Probabilities associated 
with the possible results of unperformed measurements are objective just in case 
all relevant facts are taken into account.\cite{Mohrhoff00}

There is, accordingly, a need to distinguish between performed measurements 
and their actual results on the one hand, and unperformed measurements and 
their possible results on the other. But this has nothing to do with the fact that 
the results of performed measurements are usually  {\it known} to someone. The 
difference between performed and unperformed measurements is not that the 
results of the latter are not known or perceived. The difference is that 
unperformed measurements are not performed!

The bottom line, so far, is that  {\it there isn't any problem that could be solved 
by dragging consciousness into discussions of QM}. The questions that 
consciousness is supposed to answer are pseudo-questions.

What about the converse? If consciousness does not help us understand QM, 
maybe QM can help us understand consciousness? (The underlying idea here is 
what philosopher David Chalmers has called the ``law of minimization of 
mystery'': ``consciousness is mysterious and quantum mechanics is mysterious, 
so maybe the two mysteries have a common source''\cite{Chalmers}). The 
mystery of consciousness is essentially the question of how it relates to the 
material world---how anything material can be conscious, and how anything can 
be conscious of the material world. What seems obvious to me is that as long as 
no-one has any clear idea about what QM is trying to tell us about the material 
world, it would be premature, if not outright foolish, to turn to QM for answers 
to these profound and fascinating questions.

Beginning with Fritjof Capra's popularization of the idea that physicists and 
Eastern mystics have something common to talk about, these questions---as well 
as the equally profound and fascinating problem of making sense of QM---have 
been obfuscated by concoctions of mysticism and QM dished out by numerous 
woolly masters. Among these {\it The Self-Aware Universe} by Goswami et 
al.\cite{Goswami} presents a worst-case scenario, not least because of the truths 
it contains---and makes a mockery of by buttressing them with absurdities, 
fallacies, and {\it non sequiturs}.\cite{Lloyd} ``To hitch a religious philosophy to 
contemporary science'' may not be, as Bernstein maintains, ``a sure route to 
obsolescence''.\cite{Bernstein} But to hitch it to a travesty of QM certainly is.

I am not opposed to the notion that physicists and mystics have something 
common to talk about. Yet they cannot do so profitably unless they cease to be 
muddleheaded about their respective domains. It seems to me that in the end 
physics will of its own accord converge with a spiritual philosophy that strictly 
holds its ground if both remain faithful to their principles. The words of the 
German poet Schiller are pertinent here: ``Enmity be between you! Too soon it is 
for alliance.~/ Search along separate paths, for that is how truth comes to light.''

``That which thinks not by the mind [or, that which one thinks not with the 
mind], that by which the mind is thought, know that to be the Brahman and not 
this which men follow after here,'' the Kena Upanishad~\cite{Kena} admonishes 
us. There is a consciousness beyond mind, and Goswami is absolutely right when 
he asserts that consciousness transcends both matter and mind. But to refer to 
this transcendent consciousness as ``quantum mind'' is ludicrous (as ludicrous as 
Zohar and Marshall's ``quantum self''\cite{Zohar,Zoharcmt} and Chopra's ``quantum 
healing''\cite{Chopra,Chopracmt}), and so is his supporting tale: Perception consists of the 
collapse of a possibility wave in the presence of awareness. The subject 
consciousness of the experience arises with the chosen brain state both of which 
exist only as possibility until the collapse. The observer forces the many 
possibilities into a single, manifested actuality by the very act of observation. The 
brain is a measuring instrument which collapses the infinite and eternal 
quantum mind into concreteness as manifested through individual experience. 
The universe exists as formless potentia in myriad possible branches in the 
transcendent domain. And so on  {\it ad nauseam}. As one reviewer remarked, 
``he sounds like Madame Blavatsky with a hangover''.\cite{Kirkus}

Now that we have disposed of the pseudo-problems and of some of their 
gratuitous answers (answers that do not involve consciousness have also been 
given), we are ready to address a real problem. How can a particle go through 
two slits without going through a particular slit and without being divided into 
parts that go through different slits? For this is what happens in a two-slit 
experiment whenever nothing indicates the slit taken by a particle. This problem 
arises from a mismatch between space and the way we tend to think about space. 
Ask yourself how you think about the empty regions $L$ and $R$ inside the two 
slits. No doubt you will consider them different, separate, distinct. This is why 
the behavior of particles in two-slit experiments baffles us. If a particle goes 
through both slits without going through a particular slit then the distinctness of 
$L$ and $R$ implies that the particle has two parts, one that goes through $L$ 
and another that goes through $R$. Since, in fact, the particle does not get 
divided by its passage through the slits, $L$ and $R$ cannot be distinct. That's 
what baffles us.

But think again. How are $L$ and $R$ different? You may say, well, they are in 
different places. So where are these different places? If you contemplate this 
question long enough, you will realize that you are poised either for a tautology 
or for an infinite regress. Either: $L$ is where $L$ is. Or: $L$ is inside another 
region $L'$, which is inside another region $L''$, and so on  {\it ad infinitum}. 
The root of the problem is that we keep switching between two inconsistent 
modes of thinking. If we ask about the position of~$L$, we treat $L$ as a  {\it 
thing} to which a position---a  {\it property}---can be attributed. If we answer 
that $L$ is in~$L$, we treat $L$ both as an object with a position and as the 
position of an object. If we reply that $L$ is in $L'$, we treat $L'$ as a property 
of~$L$. If we then ask about the position of~$L'$, we switch back to thinking of 
$L'$ as a thing to which properties can be attributed.

The problem has an easy solution: Stop thinking about regions of space as if they 
were  {\it things}. The regions $L$ and $R$ are  {\it properties} that may or may 
not be possessed. $L$~(that is, the property of being inside $L$) is possessed just 
in case there is a thing $T$ inside~$L$. Saying (A)~``$T$~is inside~$L$'' seems 
to be different from saying (B)~``$T$~has the property~$L$'' because 
proposition~(A) seems to imply that $L$ is a  {\it thing} that contains~$T$. But, 
in fact, $L$~is not a thing, and (A) says exactly what (B) is saying. Much the 
same applies to (numerically exact) positions: We tend to think of them as points, 
and we tend to think of these points as things to which positions can be 
attributed. In reality they do not  {\it have} positions, they  {\it are} positions, 
and positions are not  {\it things} but  {\it properties} that may or may not be 
possessed by things. As such they do not exist (in the material world) unless there 
are material objects to which they can be attributed.

Back to our particle. At the time it went through the slits it wasn't inside $L$, it 
wasn't inside $R$, and it didn't consist of two parts, one inside $L$ and one 
inside~$R$. As long as you assume that space is a thing that has parts---and once 
you start thinking that way you end up thinking that any finite region of space 
has infinitely many distinct parts,---you just can't make sense of this. But it is 
wrong to conceive of space as a thing that has parts because it is logically 
inconsistent to think of properties as if they were things. The behavior of 
particles in two-slit experiments forces us to acknowledge a fallacy we have been 
committing with impunity because the world of classical physics was consistent 
with it.

So space is not a thing that has parts but a set of positions. If we take into 
account that all positions are {\it relative} positions,\cite{relpos} we arrive at the 
conclusion that  {\it space is the totality of relative positions that exist between 
material objects}. (Another word for ``relative position'' is  {\it spatial relation}.) 
QM further takes into account that a position measurement can never 
distinguish between more than a finite number of finite regions, so that only 
finite regions are available as attributes. Attributable positions are always finite 
regions such as $L$ and~$R$. If a particle goes through both slits, neither $L$ 
nor $R$ is attributable to it, nor does it have parts to which the regions $L$ and 
$R$ are separately attributable. What  {\it is} attributable to the particle is the 
region $L$+$R$ that is ``made up of'' $L$ and~$R$.

{\it Made up of} $L$ and~$R$? Doesn't this imply that $L$ and $R$ are distinct 
parts of $L$+$R$? It does not, for $L$+$R$ is a property rather than a thing 
that has parts. It is possible that $L$+$R$ is attributable to a particle while 
neither $L$ nor $R$ is attributable to anything. In this case the distinction we 
make between ``The particle went through~$L$'' and ``The particle went 
through~$R$'' is a distinction that Nature does not make; it corresponds to 
nothing in the material world; it exists solely in our heads.

Thus our spontaneous, untaught way of thinking about space---as a thing that 
has parts---is wrong. And so is the way in which students of physics, to this very 
day, are being taught to think about space, namely as a manifold of intrinsically 
distinct point individuals. It involves the same fallacy, namely to think of 
conceptually distinct properties as if they were intrinsically distinct things. And 
if these students stumble over the behavior of particles in two-slit experiments, 
they are warned not to waste their time wondering. ``Do not keep saying to 
yourself, if you can possibly avoid it, 'But how can it be like that?' because you 
will go 'down the drain' into a blind alley from which nobody has yet escaped. 
Nobody knows how it can be like that.''\cite{Feynman} Nobody knows because 
everybody has been taught the wrong way of thinking about space.

This sorry state of affairs warrants an inquiry into its neurophysiological and 
psychological roots. You probably know that a certain area of the retina (known 
as the blind spot) lacks light-sensitive cells. You don't see an object if its optical 
image falls on this area. If the object is a black cross on white paper, you only see 
a white area, and if the paper is red, you see a red area instead. No visual 
information reaches your brain from this area, yet sometimes it looks white and 
sometimes it looks red. Here is why: The brain analyses the data it receives from 
both eyes by detecting  {\it contrasts}. It ``sees'' the edges of more or less 
homogeneously colored and evenly lit regions, where all but the most gradual 
variations in brightness and/or color occur. These regions themselves are not 
(directly) seen but are  {\it filled in} on the basis of changes in brightness and 
color occurring across their boundaries. The region containing the blind spot is 
uniformly filled in just like any other contrast-free region.

The way in which the brain processes visual information guarantees that the 
result---the phenomenal world---is a world of objects that are bounded by 
surfaces. The  {\it phenomenal} world---the world as we perceive it---therefore 
conforms to the ``cookie cutter paradigm''\cite{MohrhoffCCP,BCCP} (CCP) 
according to which the world's synchronic multiplicity rests on surfaces that 
carve up space in the manner of three-dimensional cookie cutters. The parts of 
any material object---including the world as a whole---are defined by the parts of 
the space it ``occupies'', and the parts of space are defined by delimiting and 
separating surfaces. This seems self-evident because this is how we perceive the 
world because this is how the brain analyses visual information.

We are prone to think that the mind works as it does because the brain works as 
it does, but in any spiritual conception of the world it must be the other way 
round. To understand why the brain works as it does we need to know why the 
mind works as it does.

There is, we said, a consciousness beyond mind. For the most detailed account of 
this consciousness and its relation to both matter and mind---as well as the most 
solidly founded on experience---we turn to Sri Aurobindo. In the Aurobindonian 
scheme of things, the world is an evolving manifestation of Brahman. Mind ({\it 
manas}) is the highest creative principle hitherto evolved but not by any means 
the highest. The original creative principle and dynamic link between Brahman 
and the world is supermind ({\it vijnana}). The creative action of the supermind 
is primarily qualitative and infinite and only secondarily quantitative and finite. 
Mind is the agent of this secondary action---limiting, defining, dividing, 
individualizing. Here is how Sri Aurobindo describes the characteristic action of 
mind, or  {\it mental} consciousness:
\begin{quote}
Mind in its essence is a consciousness which measures, limits,  {\it cuts out} forms 
of things from the indivisible whole and contains them  {\it as if each were a 
separate integer}. Even with what exists only as obvious parts and fractions, 
mind establishes this fiction of its ordinary commerce that they are  {\it things 
with which it can deal separately} and not merely as aspects of a whole\ldots It is 
this essential characteristic of Mind which conditions the workings of all its 
operative powers, whether conception, perception, sensation or the dealings of 
creative thought. It conceives, perceives, senses things  {\it as if rigidly cut out 
from a background or a mass} and employs them as fixed units\ldots\cite{LD}
\end{quote}
This characteristic action of mental consciousness is the real reason why the 
phenomenal world conforms to the CCP, and why we find it so hard  {\it not} to 
think of space itself as a thing that has parts. As long as we take the parts of 
matter to be defined by the parts of space, the parts of space are logically prior to 
the parts of matter; hence they exist independently of matter; hence space is a 
thing that has parts. Moreover, since it is in the nature of mind to deal with parts 
as if they were things that exist by themselves, rather than by virtue of some 
process of division or differentiation, space would be infinitely divided if it did 
conform to the mental outlook. The idea that  {\it all} (conceivable) parts of space 
exist by themselves inevitably leads to the contemporary physicist's conception of 
space as a manifold of intrinsically distinct point individuals.

The characteristic action of mental consciousness is also the reason why we are 
by nature materialists, for the essence of materialism is the idea that  {\it 
multiplicity is fundamental}. Mind deals with parts, in both perception and 
conception, ``as if each were a separate integer''. The essential function of the 
concept of ``matter'' is to betoken the separate existence of each part.

It will be illuminating to contrast two misconceptions arising from the mind's 
way of dealing with the world with what QM has to say---if we allow it to say 
what it has to say and do not force it into a conceptual framework that renders it 
incomprehensible. The first is that if there are ultimate parts---that is, if things 
are ultimately made of partless parts---then these have the form of a point. If the 
physical world were created along the lines laid down by the CCP, the shapes of 
things would be bounding surfaces, and matter would be an extended stuff 
bounded by surfaces. A material object would have as many parts as the space it 
occupies, and an object without parts---a particle like the electron---would be a 
bit of stuff with the form of a point.

The second misconception is that things are re-identifiable. Let me illustrate this 
with another experiment, a two-particle collision. Initially we have two incoming 
particles, one heading northward and one heading southward, and after the 
collision we have, per assumption, two outgoing particles, one heading eastward 
and one heading westward. Here re-identifiability means that each outgoing 
particle is identifiable with one of the incoming particles: The outgoing particle 
heading eastward is identical with either the incoming particle heading 
southward or the incoming particle heading northward. This is implied by the 
separate matter tokens that the mind places into things in order to account for 
their separate existences.

Now let's hear what QM has to say. QM, recall, forces us to conceive of space in 
the only logically consistent way, as the totality of spatial relations existing 
between material objects. Let's distinguish between the external spatial relations 
of an object and its internal spatial relations. (The  {\it external} spatial relations 
of an object $O$ are those between $O$ and objects that have no parts in 
common with $O$. The  {\it internal} spatial relations of $O$ are those between 
$O$'s own constituent parts.) The  {\it position} of $O$, properly conceived, is 
any of $O$'s external spatial relations. The  {\it form} of $O$, properly 
conceived, consists of the spatial relations between its parts. By this definition, an 
object that lacks parts, and therefore lacks internal spatial relations,  {\it also 
lacks a form}.

To convince yourself that the ultimate constituents of matter are  {\it formless} 
rather than pointlike, try to imagine a single pointlike object. As you imagine a 
pointlike object, you also imagine a spatial expanse in which this object is 
situated. You cannot imagine a point without imagining a space that surrounds 
or contains it. A point is a form, and the existence of a form implies the existence 
of space. But you are asked to imagine a  {\it single} pointlike object---not any 
other thing, nor any of this object's relations to other things. So you must not 
imagine its external spatial relations. And since a pointlike object lacks parts and 
therefore lacks internal spatial relations, your mental picture must not contain  
{\it any} spatial relations. But space is a set of spatial relations, so your mental 
picture must not contain space. And since the existence of a form implies the 
existence of space, your mental picture must not contain any form. The upshot is 
that the existence of a pointlike form is inconsistent with the proper way of 
thinking about space---as a set of spatial relations.

If you find it hard to conceive of electrons as formless objects, join the club. But 
keep in mind that no-one has ever seen an electron. By looking at the traces it 
has left one can see  {\it where} it has been but one cannot see its  {\it form}. 
Experiments can only establish the absence of evidence of internal spatial 
relations, which by itself is consistent with either a pointlike form or no form at 
all. So on the principle of theoretical parsimony alone (Occam's razor) we should 
consider it pointless to attribute to an electron the form of a point.

And what does QM have to say about our collision experiment? It tells us in 
unmistakable terms that if the particles are of the same type and their spins (if 
they have) are not antiparallel, then the outgoing particle heading eastward is  
{\it neither the same as nor different from either of the incoming particles}. In 
this case the distinction between ``$E$ is identical with $N$'' and ``$E$ is 
identical with $S$'' (where $E$ stands for the outgoing particle heading 
eastward and $N$ and $S$ stand for the incoming particles) is another 
distinction that Nature does not make; it corresponds to nothing in the material 
world; it exists solely in our heads. In other words, the particles are  {\it not 
re-identifiable}.

Now recall that re-identifiability is implied by the separate matter tokens that 
the mind places into things in order to account for their separate existences. 
What QM tells us here is that  {\it there are no separate matter tokens}. 
Consequently, if we consider particles of the same type, and if we consider them 
in themselves, out of relation to each other, we must consider them identical not 
just in the weak sense of exact similarity but  {\it in the strong sense of numerical 
identity}. (Identical twins are genetically identical in the weak sense; they have 
exactly similar genes. The evening star and the morning star are identical in the 
strong sense; they are one and the same planet.)

This strong identity is not confined to particles of the same type. The properties 
by which particles can be distinguished are either relational (like positions) or 
dynamic (characteristic of their interactions, like charges) or comparative (like 
mass ratios---the mass of a single particle has no physical significance). Hence if 
we consider the fundamental particles of matter in themselves, out of relation to 
each other, we must not consider them many. In themselves they lack 
distinguishing characteristics. The nonexistence of separate matter tokens 
therefore implies that in themselves they are one and the same thing.

We must accept that being one thing, or many things, or identical things, or 
different things does not, in reality, have the absolute meaning that it has for the 
mind. These are relative notions. Two particles can be one thing in one sense, two 
identical things in another sense, and two different things in yet another sense. 
Considered in themselves, all fundamental particles are one and the same 
thing~$X$. Because of the spatial relations that exist between $X$ and~$X$, they 
are also many identical things. (A multiplicity of relations implies at least the 
appearance---Shankara might say the illusion---of a multiplicity of relata.) And 
to the extent that they possess distinguishing properties, they are also different 
things.

Then what is $X$? $X$~is what every  {\it existing} fundamental particle 
intrinsically is. But, as I have just pointed out, physics knows nothing of  {\it 
intrinsic} properties; the scientifically knowable properties of particles are 
extrinsic~\cite{extrinsic} (relational, dynamic, or comparative). All we can say of 
an existing fundamental particle  {\it in itself} is that  {\it it exists}. Hence $X$ is  
{\it existence pure and simple}. And since existence ({\it sat}) is one of the three 
principal characterizations ({\it sat-chit-ananda}) of Brahman, the identification 
$X$=Brahman seems justified.

For integral Vedantists the world is a manifestation of Brahman. QM tells us 
something about how this manifestation is effected. By entering into spatial 
relations with itself, formless Brahman acquires the aspect of a multiplicity of formless 
particles. Along with the particles, space and forms come into existence, for space 
is the totality of existing spatial relations (between Brahman and Brahman), and 
forms are particular sets of such relations.

Space contains---in the proper, set-theoretic sense of ``containment''---the forms of all 
things that have forms. It does not contain material objects over and above their 
forms;  {\it a fortiori} it does not contain the formless ``constituents'' of matter. 
Physical space exists  {\it between} the fundamental particles. And since what 
exists at either end of each spatial relation is Brahman, spatial relations are  {\it 
internal} to Brahman. QM tells us that the physical world is  {\it both constituted 
by Brahman and suspended within Brahman}, if by ``Brahman'' we mean a pure 
existence which enters into spatial relations with itself. Note that the second 
aspect of Brahman, consciousness ({\it chit}), does  {\it not} figure in the 
intersection of Vedanta and QM.

The world is differentiated both spacewise (spatial relations warrant distinctions 
between ``here'' and ``there'') and timewise (temporal relations warrant 
distinctions between ``now'' and ``then''). The temporal differentiation is 
effected by  {\it change}, for time and change are coimplicates: A timeless world 
cannot change, and a changeless world is temporally undifferentiated and 
therefore timeless. In my opinion, the quintessential message of QM is that there 
are limits to the world's spatial and temporal differentiation. The world is only 
finitely differentiated. This too conflicts with the CCP, for the latter implies that 
the world is infinitely differentiated spacewise (as we have seen) and therefore 
also timewise.\cite{diff} QM tells us how and to what extent the world is spatially 
and temporally differentiated. As long as our thinking adheres to the CCP and 
we assume, accordingly, that the world is infinitely differentiated to begin with, 
we cannot but fail to get its message.

In an infinitely differentiated world, spatial relations are determinate quantities; 
they possess definite values. In a finitely differentiated world, spatial relations 
are indeterminate quantities; they possess fuzzy values. The proper 
conceptualization of indefiniteness requires the use of statistical concepts, and 
this is why quantum mechanics is formally a statistical theory, concerned with 
probabilities. But why is the world only finitely differentiated? Why do spatial 
relations have fuzzy values? The answer is that, for all we know, this is the only 
consistent way to ``fluff out matter''---to create material objects of finite size 
using a finite number of formless particles, or to manifest finite forms using a 
finite number of spatial relations. If you are Brahman, and you want to create 
spatially extended objects by entering into spatial relations with yourself, you 
have no choice but to let these relations have fuzzy values.

A possible way of giving quantum mechanics in a nutshell is to say that there are 
limits to the objective reality of mental distinctions. Recall Sri Aurobindo's 
characterization of mind. Mind is the agent of division, of differentiation. When 
it is employed by supermind, the original creative principle, mind is used 
judiciously. The mind's tendency to divide  {\it ad infinitum} is checked. But 
when mind is separated in its self-awareness from its supramental parent and left 
to run wild, as it is in us, it not only divides  {\it ad infinitum} but also fails to 
recognize itself as the instrument of the division. It takes the resulting 
multiplicity for the original truth or fact. That is why mental consciousness is 
inherently reductionistic, atomistic, and therefore materialistic.

According to quantum mechanics, the original truth or fact is unity, rather than 
multiplicity. Multiplicity is contingent and emergent. Quantum physics thus is 
the opposite of materialistic. There are, recall, no separate matter tokens. And 
since ``matter'' essentially connotes the existence of such tokens,  {\it there is no 
matter}. There is a substance---exactly one---and this is Brahman. QM describes 
a world that is created top-down, by a process of differentiation, rather than 
bottom-up, by a process of aggregation. In doing so it reveals that the creative 
principle to which the world owes its existence is supramental rather than 
mental, for supermind, characteristically, proceeds from the One to the Many by 
differentiation or particularization, while mind proceeds from the Many to at 
best a semblance of unity by aggregation.

Now that we know what QM is trying to tell us about matter, we can touch on 
the question of how consciousness relates to matter. QM has nothing to say on 
this subject, so we turn to (Sri Aurobindo's integral) Vedanta. Brahman is at 
once pure existence ({\it sat}) and pure consciousness ({\it chit}). We may 
characterize it either as an intrinsically indeterminate existence with the power 
to determine itself or as an intrinsically contentless consciousness with the power 
to give itself content. There is a supreme way of being, or of being conscious, to 
which these two characterizations are equally adequate. Up there there isn't any 
difference between Brahman qua existence and Brahman qua consciousness. The 
same is true at the other end of the great ``Chain of Being'', except that here 
existence is formless and consciousness lacks content. Each particle is Brahman, 
and therefore each particle is, indistinguishably, a pure existence and a pure 
consciousness. The question no longer is how anything material can be conscious. 
Instead we must ask how consciousness acquires content, or how 
undifferentiated consciousness=being differentiates into content-filled 
consciousness and form-determined being. In this way, as serveral 
panpsychists~\cite{Griffin,HutShep,Rosenberg,Seager,deQuin}
have argued, the hard problem of consciousness~\cite{Chalmers} becomes solvable.

The bottom line: As long as you attempt to straitjacket QM into materialistic 
modes of thinking (which is what the woolly masters do as persistently as the 
next physicist), and it makes no sense. Place it into a Vedantic framework of 
thought, and it makes perfect sense. Let it speak for itself, and it takes you a long 
way toward a Vedantic conception of the world.

\begin{thebibliography}{99}%===============================
\bibitem{probaone}
This ideas appears to receive support from another frequently voiced 
misconception, according to which a property is actually possessed by a physical 
system if the probability of obtaining this property as the result of a 
measurement is one. On this view, $p\,($R$,t)=1$ implies that the alpha is inside 
region $R$ at the time~$t$, and this suggests that the probability $p\,($R$,t)$ tells 
us something about what exists or obtains at the time~$t$. But the notion that 
probability one is sufficient for the possession of a property $q$ is manifestly 
false, for if $q$ is not actually obtained as the result of a measurement, it is 
possible in general to perform a different measurement and obtain a result that is 
incompatible with the possession of~$q$.

\bibitem{Popper}
Karl $R$. Popper, {\it Quantum Theory and the Schism in Physics} (Rowan \& 
Littlefield, Totowa, NJ, 1982), edited by W.W. Bartley,~III.

\bibitem{Heisenberg}
Werner Heisenberg, {\it Physics and Philosophy} (Harper and Row, New York, 
1958), Chap.~3.

\bibitem{Shimony}
Abner Shimony, ``Conceptual Foundations of Quantum Mechanics'', in {\it The 
New Physics} (Cambridge University Press, Cambridge, 1989), edited by Paul 
Davies, pp. 373--95.

\bibitem{Treiman}
Sam Treiman, {\it The Odd Quantum} (Princeton University Press, Princeton, 
NJ, 1999), p.~188. Dozens of similar phrases can be found in the literature.

\bibitem{LonBau}
Fritz London and Edmond Bauer, ``The theory of observation in 
quantum mechanics'', in {\it Quantum Theory and Measurement}, edited 
by John A. Wheeler and Wojciech H. Zurek (Princeton University 
Press, Princeton, NJ, 1983), pp. 217--59.

\bibitem{vNeu}
John von Neumann, {\it Mathematical Foundations of Quantum 
Mechanics} (Princeton University Press, Princeton, 1955).

\bibitem{Wigner}
Eugene P. Wigner, ``Remarks on the mind-body question'', in {\it The Scientist Speculates} 
(Heinemann, London, 1961), edited by I.J. Good, pp. 284--302.

\bibitem{Page}
Don N. Page, ``Sensible quantum mechanics: Are probabilities only in 
the mind?'', {\it Int. J. Mod. Phys.} D5, 583--96 (1996).

\bibitem{Stapp}
Henry Pierce Stapp, {\it Mind, Matter, and Quantum Mechanics} 
(Springer, Berlin, 1993).

\bibitem{Squires}
Euan Squires, {\it Conscious Mind in the Physical World} (Adam Hilger, New York, 1990).

\bibitem{Lockwood}
Michael Lockwood, {\it Mind, Brain and the Quantum} (Basil Blackwell, 
Oxford, 1989).

\bibitem{Albert}
David Z. Albert, {\it Quantum Mechanics and Experience} (Harvard 
University Press, Cambridge, MA, 1992).

\bibitem{Mohrhoff00}
Ulrich Mohrhoff, ``What quantum mechanics is trying to tell us'', {\it American 
Journal of Physics} 68/8 (2000), 728--45; e-Print quant-ph/9903051.

\bibitem{Chalmers}
David J. Chalmers, ``Facing up to the problem of consciousness'', {\it Journal of 
Consciousness Studies} 2/3 (1995), 200-219.

\bibitem{Goswami}
M. Goswami, $R$.E. Reed, A. Goswami, and F.A. Wolf, {\it The Self-Aware 
Universe: How Consciousness Creates the Material World} (J.P. Tarcher, Los 
Angeles, 1995).

\bibitem{Lloyd}
Peter B. Lloyd, ``Discussion of Amit Goswami's {\it Science Within 
Consciousness}'', {\tt 
http://easyweb.easynet.co.uk/\~{}ursa/philos/ goswami.htm}.

\bibitem{Bernstein}
Jeremy Bernstein, ``A cosmic flow'', American Scholar, Winter 1978/79, 6-8.

\bibitem{Kena}
Sri Aurobindo, {\it The Upanishads: Texts, Translations, and Commentaries} 
(Sri Aurobindo Ashram, Pondicherry, 1981), p.~102.

\bibitem{Zohar}
Danah Zohar and I.N. Marshall, {\it Quantum Self: Human Nature and Consciousness 
Defined by the New Physics} (Quill, 1991).

\bibitem{Zoharcmt}
I do not deny the existence of a self radically different from the referent of folk 
believes about the self, but only that this has anything to do with QM.

\bibitem{Chopra}
Deepak Chopra, {\it Quantum Healing: Exploring the Frontiers of Mind Body Medicine}
(Bantam Books, 1990).

\bibitem{Chopracmt}
By the same token, I do not deny possibilities of healing (both transitive and 
intransitive) that are beyond the ken of present-day medical science, but only 
that they have anything to do with QM.

\bibitem{Kirkus}
Kirkus Reviews (New York), March 1, 1993.

\bibitem{relpos}
To specify the position of an object, we must say where it is in relation to another 
object that serves as a reference point.

\bibitem{Feynman}
Richard P. Feynman, {\it The Character of Physical Law} (MIT Press, 
Cambridge, MA, 1967), p.~129.

\bibitem{MohrhoffCCP}
Ulrich Mohrhoff, ``Quantum mechanics and the cookie cutter paradigm'', 
e-Print quant-ph/0009001.

\bibitem{BCCP}
Ulrich Mohrhoff, ``Beyond the cookie cutter paradigm'', forthcoming in the 
Proceedings of the 2nd International Conference on Integral Psychology, 
Pondicherry, 4--7 January 2001.

\bibitem{LD}
Sri Aurobindo, {\it The Life Divine}, SABCL Vol. 18 (Sri Aurobindo Ashram, 
Pondicherry, 1970), p.~162; italics added.

\bibitem{extrinsic}
This use of ``extrinsic'' differs from the more specific use of the term in 
Refs.~\cite{Mohrhoff00} and \cite{MohrhoffCCP}.

\bibitem{diff}
In a world that is infinitely differentiated spacewise all objects have exact 
positions. In such a world a moving object passes through infinitely many 
distinct states in any finite time span. Hence such a world is infinitely 
differentiated timewise.

\bibitem{Griffin}
D.R. Griffin, ``Panexperientialist physicalism and the mind-body problem'', {\it 
Journal of Consciousness Studies} 4/3 (1997), 248--68.

\bibitem{HutShep}
P. Hut and R. Shepard, ``Turning the hard problem upside down and sideways'', {\it Journal of Consciousness Studies} 3/4 (1996), 313--29.

\bibitem{Rosenberg}
G.H. Rosenberg, ``Rethinking nature: a hard problem within the hard problem'', {\it Journal of Consciousness Studies} 3/1 (1996), 76--88.

\bibitem{Seager}
W. Seager, ``Consciousness, information and panpsychism'', {\it Journal of Consciousness 
Studies} 2/3 (1995), 272--88.

\bibitem{deQuin}
C. de Quincey, ``Consciousness all the way down?'', {\it Journal of Consciousness 
Studies} 1/2 (1994), 217--29.

\end{thebibliography} 
\end{document}


quant-ph0102047.extracted_bib
\begin{thebibliography}{99}%===============================
\bibitem{probaone}
This ideas appears to receive support from another frequently voiced 
misconception, according to which a property is actually possessed by a physical 
system if the probability of obtaining this property as the result of a 
measurement is one. On this view, $p\,($R$,t)=1$ implies that the alpha is inside 
region $R$ at the time~$t$, and this suggests that the probability $p\,($R$,t)$ tells 
us something about what exists or obtains at the time~$t$. But the notion that 
probability one is sufficient for the possession of a property $q$ is manifestly 
false, for if $q$ is not actually obtained as the result of a measurement, it is 
possible in general to perform a different measurement and obtain a result that is 
incompatible with the possession of~$q$.

\bibitem{Popper}
Karl $R$. Popper, {\it Quantum Theory and the Schism in Physics} (Rowan \& 
Littlefield, Totowa, NJ, 1982), edited by W.W. Bartley,~III.

\bibitem{Heisenberg}
Werner Heisenberg, {\it Physics and Philosophy} (Harper and Row, New York, 
1958), Chap.~3.

\bibitem{Shimony}
Abner Shimony, ``Conceptual Foundations of Quantum Mechanics'', in {\it The 
New Physics} (Cambridge University Press, Cambridge, 1989), edited by Paul 
Davies, pp. 373--95.

\bibitem{Treiman}
Sam Treiman, {\it The Odd Quantum} (Princeton University Press, Princeton, 
NJ, 1999), p.~188. Dozens of similar phrases can be found in the literature.

\bibitem{LonBau}
Fritz London and Edmond Bauer, ``The theory of observation in 
quantum mechanics'', in {\it Quantum Theory and Measurement}, edited 
by John A. Wheeler and Wojciech H. Zurek (Princeton University 
Press, Princeton, NJ, 1983), pp. 217--59.

\bibitem{vNeu}
John von Neumann, {\it Mathematical Foundations of Quantum 
Mechanics} (Princeton University Press, Princeton, 1955).

\bibitem{Wigner}
Eugene P. Wigner, ``Remarks on the mind-body question'', in {\it The Scientist Speculates} 
(Heinemann, London, 1961), edited by I.J. Good, pp. 284--302.

\bibitem{Page}
Don N. Page, ``Sensible quantum mechanics: Are probabilities only in 
the mind?'', {\it Int. J. Mod. Phys.} D5, 583--96 (1996).

\bibitem{Stapp}
Henry Pierce Stapp, {\it Mind, Matter, and Quantum Mechanics} 
(Springer, Berlin, 1993).

\bibitem{Squires}
Euan Squires, {\it Conscious Mind in the Physical World} (Adam Hilger, New York, 1990).

\bibitem{Lockwood}
Michael Lockwood, {\it Mind, Brain and the Quantum} (Basil Blackwell, 
Oxford, 1989).

\bibitem{Albert}
David Z. Albert, {\it Quantum Mechanics and Experience} (Harvard 
University Press, Cambridge, MA, 1992).

\bibitem{Mohrhoff00}
Ulrich Mohrhoff, ``What quantum mechanics is trying to tell us'', {\it American 
Journal of Physics} 68/8 (2000), 728--45; e-Print quant-ph/9903051.

\bibitem{Chalmers}
David J. Chalmers, ``Facing up to the problem of consciousness'', {\it Journal of 
Consciousness Studies} 2/3 (1995), 200-219.

\bibitem{Goswami}
M. Goswami, $R$.E. Reed, A. Goswami, and F.A. Wolf, {\it The Self-Aware 
Universe: How Consciousness Creates the Material World} (J.P. Tarcher, Los 
Angeles, 1995).

\bibitem{Lloyd}
Peter B. Lloyd, ``Discussion of Amit Goswami's {\it Science Within 
Consciousness}'', {\tt 
http://easyweb.easynet.co.uk/\~{}ursa/philos/ goswami.htm}.

\bibitem{Bernstein}
Jeremy Bernstein, ``A cosmic flow'', American Scholar, Winter 1978/79, 6-8.

\bibitem{Kena}
Sri Aurobindo, {\it The Upanishads: Texts, Translations, and Commentaries} 
(Sri Aurobindo Ashram, Pondicherry, 1981), p.~102.

\bibitem{Zohar}
Danah Zohar and I.N. Marshall, {\it Quantum Self: Human Nature and Consciousness 
Defined by the New Physics} (Quill, 1991).

\bibitem{Zoharcmt}
I do not deny the existence of a self radically different from the referent of folk 
believes about the self, but only that this has anything to do with QM.

\bibitem{Chopra}
Deepak Chopra, {\it Quantum Healing: Exploring the Frontiers of Mind Body Medicine}
(Bantam Books, 1990).

\bibitem{Chopracmt}
By the same token, I do not deny possibilities of healing (both transitive and 
intransitive) that are beyond the ken of present-day medical science, but only 
that they have anything to do with QM.

\bibitem{Kirkus}
Kirkus Reviews (New York), March 1, 1993.

\bibitem{relpos}
To specify the position of an object, we must say where it is in relation to another 
object that serves as a reference point.

\bibitem{Feynman}
Richard P. Feynman, {\it The Character of Physical Law} (MIT Press, 
Cambridge, MA, 1967), p.~129.

\bibitem{MohrhoffCCP}
Ulrich Mohrhoff, ``Quantum mechanics and the cookie cutter paradigm'', 
e-Print quant-ph/0009001.

\bibitem{BCCP}
Ulrich Mohrhoff, ``Beyond the cookie cutter paradigm'', forthcoming in the 
Proceedings of the 2nd International Conference on Integral Psychology, 
Pondicherry, 4--7 January 2001.

\bibitem{LD}
Sri Aurobindo, {\it The Life Divine}, SABCL Vol. 18 (Sri Aurobindo Ashram, 
Pondicherry, 1970), p.~162; italics added.

\bibitem{extrinsic}
This use of ``extrinsic'' differs from the more specific use of the term in 
Refs.~\cite{Mohrhoff00} and \cite{MohrhoffCCP}.

\bibitem{diff}
In a world that is infinitely differentiated spacewise all objects have exact 
positions. In such a world a moving object passes through infinitely many 
distinct states in any finite time span. Hence such a world is infinitely 
differentiated timewise.

\bibitem{Griffin}
D.R. Griffin, ``Panexperientialist physicalism and the mind-body problem'', {\it 
Journal of Consciousness Studies} 4/3 (1997), 248--68.

\bibitem{HutShep}
P. Hut and R. Shepard, ``Turning the hard problem upside down and sideways'', {\it Journal of Consciousness Studies} 3/4 (1996), 313--29.

\bibitem{Rosenberg}
G.H. Rosenberg, ``Rethinking nature: a hard problem within the hard problem'', {\it Journal of Consciousness Studies} 3/1 (1996), 76--88.

\bibitem{Seager}
W. Seager, ``Consciousness, information and panpsychism'', {\it Journal of Consciousness 
Studies} 2/3 (1995), 272--88.

\bibitem{deQuin}
C. de Quincey, ``Consciousness all the way down?'', {\it Journal of Consciousness 
Studies} 1/2 (1994), 217--29.

\end{thebibliography}