Contra MWI (Many World Interpretation)
I had mentioned to Jeff Schwartz and to Ken Augustyn that
I was thinking about writing a paper about the problems
with MWI, and they both encouraged me to focus my energies
on that project, rather than on other matters that seem to be
soaking up my time.
This message is not that paper, but is rather a first
informal chat about the subject.
A first point is too obvious and oft-mentioned to bear
repeating in the literature, But I'll mention it here:
If every possible experience occurs in parallel then what
does it mean to say that the relative probabilities of
two alternative possible experiences is not unity?
The initial argument that I made to myself back in 1959,
when the reading of von Neumann's book caused me to imagine
a many-minds solution of the measurement problem, was this:
Imagine flipping a coin a hundred billion times. Simple
calculations show that, although the possibilities range
from all heads to all tails, a huge proportion of the
possible sequences will lie in the interval in which the
ratio of heads to tails is unity to within 1%. The fraction
of the possible sequences in which the ratio is, say,
6:4 to within 1% is very-very tiny.
But suppose the coin is "loaded" so the relative probability
of heads to tails is 6:4. Then the huge proponderance
of the actually occurring sequences will in all likelihood
be concentrated in the interval where the ratio is 6:4
to within 1%, even though only a tiny-tiny fraction of
the possible *sequences* lie within that interval.
Thus if we have a situation in which each outcome is either
a head or a tail one can form a clear idea of what the
consequence would likely be if the relative
probability of heads to tails is 6:4.
But if heads and tails BOTH occur in parallel then what
is the meaning of saying that the ratio of heads to tails
is 6:4?
What one needs in order to explain the (quantum) data
is this: The "experience of the observer" in a quantum
situation where the predicted relative probability
of "heads" to "tails" is 6:4 will almost certainly be
that the ratio of heads to tails in a run of one
hundred billions flips lies within 1% of
6:4, even though only a miniscule fraction
of the possible sequences lie in that interval.
There is not much difficulty understanding this result
if each flip gives either a head or a tail. But
how does one understand that one's experiences will
almost surely be 6:4 heads to tails to within 1%
if ALL possible experiences occur in parallel,
and the experiences of finding the 6:4 ratio to within
1% are only a minute fraction of the possible
experiences?
It all comes down to the question of what does
"statistical weight" means in a situation
where all things happen in parallel. What does it mean to
say that my experience will almost surely be `such
and such' when the contrary experiences are occurring
in parallel, and are vastly more numerous.
The MWI answer is simply:
THAT is the mysterious quantum postulate!
And this mystery is preferable to instantaneous action
at a distance, and the need for new rules associated
with the entry of consciousness into the dynamics of
conscious systems.
However, this MWI postulate IS mysterious, whereas
the idea of the existence of a temporal "now"
extending over the universe, even though we do
not have direct empirical access to it, was clear
enough to generations of eithteenth and
nineteenth century scientists: that idea is not
intrinsically mysterious. Nor is it intrinsically
mysterious that there should be rules for how our
minds work, and how minds are connected to brains.
Another thing about the MWI that
IS mysterious is that, because this multi-morld is
micro-deterministic, there is no logical or dynamical
need for anything not strictly entailed by the
micro-physical conditions, and hence no need for,
or causal role for, what our feelings seem to us to be.
Consciousness, as we directly know it, becomes an inert
spectator: experiences per se have no functional role in
nature. As in the *classical* deterministic case there
is no reason for the "seemings to be" that we directly
experience, and call "pleasure" and "pain", to exist at all,
or, if they do exist, to be associated, in general, with
physical activities that benefit and injure our
survival prospects, respectively. Nor can the
"seeming to be" that we call "effort" make any
difference. The MWI, like the classical model governed
completely by microlocal dynamical laws, leads to the
conclusion that these most immediately and directly known
aspects of reality, namely pleasure, pain, and effort,
either are fundamentally different from the "seemings to be"
that they are defined to be, or can have no effect upon
our physical actions.
The effort to build science on micro-deterministic
physical theories that either contradict the empirical evidence
(as in the case of classical physical theory) or
that postulate infinitudes of forever empirically inaccessible parallel
branches of reality (MWI) both lead directly to the invalidation
of the foundations of our conscious dealings with the world, whereas
the alternative of building our conception of reality on a formulation
of physical theory that maintains close contact with the empirical
data (vN/W), provides both a natural place for us in reality, and
a way for us to know reality, and for our knowings to act upon the rest
of reality. And it does these things without invoking any fundamental
mysteries.
A basic technical problem with MWI [which really should be called
MMI (Many Minds Interpretation) because the problem is to explain
the statistical structure exhibited in our human experiences] has to do
with the characterization or definition of an "observing system" within
a physical universe that evolves always in accordance with the
Schroedinger equation. The basic problem is that in a universe
that evolves with no collapses the state of the universe is going to be
an amorphous glob: any state of a human being will be part of a continuum
of similar human beings with slightly different states, maybe with more
or less particles, with slightly different histories, with slightly
shifted locations, etc., in an amorphous superposition or mixture.
These states, since they form continua, will overlap: they will not
be orthogonal. To make the statistical formulas of quantum theory work
we need to have projection operators that are associated with human
experiences. But if the state contains a continuum of human-body
possibilities, all existing in parallel, and if each projection
operator P in some *physically defined* class corresponds to an
experience, and each (1-P) corresponds to an associated contradictory
experience, then the set of pertinent P's must form a continuum, as do
the (1-P)'s. But then the probability formula
Prob P = Tr PS/Tr S
will give FINITE values for a continuum of P's, which gives a wildly
infinite total probability. The whole quantum probability calculus
breaks down.
This difficulty is avoided in the vN/W QT, as I define it, because
experiences are taken as primary realities, rather than mere
re-expressions of physical structures. This allows one to
talk first of a set {E_i} of experientially distinct experiences, and
then define the associated set {P_i}={P(E_i)} of orthogonal P_i's:
P_i P_j = P_j P_i =0. I do not believe that it makes sense to
introduce such P_i's in an amorphous universe just building on
physical properties alone. For there is no lattice or discrete
structure defined by the physics alone in an amorphous
universe.
[As I have just described it, the vN/W QT would seem to require
a sort of Platonic Realm of pre-existing ideas {E_i}.
However, it is possible to maintain the idea of co-evolving
realms of mind and matter by supposing that each distinct E_i
in the set {E_i} came into existence in conjunction with an existing
physical correlate. But once an E_i is created any subsequently
added E_j must correspond to a P_j that is orthogonal to all those
P_i's already specified.]
Anyone who thinks that decoherence (coupled perhaps with
consistent histories) gives a coherent well worked out MMI or MWI
ought to consider the problems described by Zurek in
Prog. Theor. Phys 89, 281-312 (1993)
The more recent review by Zurek
(Phil. Trans. R. Soc. Lond. A (1998) 356, 1793-1821)
also stresses the incompleteness of the program.
He stresses the problem of how the universe is to be split
into systems (observing systems and 'the environment') in a unique
way. That problem is connected to the problem that I emphasized
of extracting the discrete "basis states" required for the application
of the probability calculus from an amorphous glob. He describes
his report as "still only a report of partial progress".
So the growing aura that MWI is somehow already satisfactorily
worked out is not based on fact.
Of course, people working on quantum computation are not
involved with the basic problem of collapse, which comes in
unavoidably only at the level of the interface between human brains
and human experiences. But they ARE acutely concerned with environmental
decoherence, which acts very much like a collapse, but in principle can
be suppressed. When they assert that they believe that the Schroedinger
holds (no collapses) they are probably speaking primarily about the world of
quantum computers, not primarily about the vastly different, and vastly more
problematic, realm of human brains, or they have not really examined
the problems that Zurek has been trying (still not successfully) to resolve.
Or maybe they are just blissfully optimistic. But Zurek has been
doggedly trying to make it work for two decades, so it must be
admitted that there are some deeply nontrivial problems with MWI.
From stapp@thsrv.lbl.gov Thu Apr 12 20:54:25 2001
Date: Thu, 12 Apr 2001 20:51:18 -0700 (PDT)
From: stapp@thsrv.lbl.gov
Reply-To: hpstapp@lbl.gov
To: Stanley Klein
Cc: hpstapp@lbl.gov, kleinlist , bdj10@cam.ac.uk,
brucero@cats.ucsc.edu, ghrosenb@ai.uga.edu, hameroff@u.arizona.edu,
Jeffrey M. Schwartz , keith@imprint.co.uk,
Kathryn Blackmond Laskey , phayes@ai.uwf.edu
Subject: Re: EPR-Bohr-Bell and nonlocatity
On Thu, 12 Apr 2001, Stanley Klein wrote:
>
> 2. Could you remind me briefly why Bohm and many minds (many worlds)
> aren't also ontologies (quite ugly ones I'd say, but still
> ontologies).
>
>
They are ontologies, but neither has a real theory of consciousness.
Neither one has any place for "free will", since no questions are put to
nature. The known laws determine the course of events, and there is no
possibility for efficacious mind because there are no collapse events.
These theories were designed to keep mind from having any effect:
they are efforts to extend the epiphenomal character of mind found in
classical mechanics into quantum theory. Bohm theory had no place
for mind, but Bohm tried to bring it in, in some later papers, by
introducing an infinite tower of Guider waves, each controlling the
one below it. Somehow the infinity gave consciouness. But I believe
that a satisfactory theory of consciousness should not replace
consciousness by something else! A satisfactory theory of consciousness
must have the experiences that we directly feel, and report in
psychological language, as elements of the theory. And these elements
must be tied into the mathematics of quantum theory. This is possible
in the von Neumann formulation
because the mathematics of quantum theory is about bits of information,
and thoughts are felt, or mentally grasped, informational structures.
Many-minds theory is nominally about "mind" in the sense that it
resolves the "collapse" problem of quantum theory by denying that there
are collapses, and thus places the whole burden of reconciling that with
the fact that we do not experience all the things that are then present
in the universe, by appealing to a theory of mind, which, however, has
never been worked out. The first question is why does mind exist at all in
that theory since everthing else is determined without acknowledging mind.
But the real problem is to recover the results of the von Neumann theory,
which gives the empirically validated prediction about experiences, given
an observer/participant who askes well defined questions that are supposed
to correspond to well defined experiences, when the full dynamics is given
by the Schroedinger equation. The problem, there, is that the projection
operators P, which are needed to make the computations, define
SUBSPACES. An example of a subspace is the plane containing the x and y
axes in a three dimensional space. One can see that, given any vector in
the subspace, the tiniest shift of that vector in certain directions will
move that vector out of the subspace. But the evolution of the state of
the universe since the beginning of time, under the control of the
Schroedinger equation is going to be a smeared out structure with no
sharp boundaries or edges. How, therefore, can the state of the universe
itself, evolving in this way, ever lead to well-defined subspaces? The
whole mathematical structure needed to get the validated predictions
collapses in ruins.
In the von Neumann theory one has projection
operators, which have two eigenvalues, 0 and 1, and hence two answers
to the associated question, according to the basic rule of quantum theory.
One has therefore "bits" of information, and the notion that a potential
experience that grasps this bit of information either occurs or does not
occur. But this whole structure depends on the supposition that something
picks out a definite projection operator P. It seems obvious the
Schroedinger equation cannot do it. Stated differently, if the state
of the universe is the result of an uninterrupted Schroedinger evolution
since the big bang then the problem even defining individuals is already
enormous, and the further explaining of how the set of orthogonal projection
operators P corresponding to a definite set of mutually exclusive possible
experiences is going to be determined by the amorphous structure of the
state vector alone is daunting task that has not yet been performed.
So I claim that the many worlds/mind interpretation throws the whole
interpretational problem onto the problem of creating a theory of mind,
or minds, without real collapses, but the huge difficulties in doing
this have not even begun to be solved.
von Neumann's formulation is, I claim, the only quantum theory
that gives an adequate theory of consciousness and the brain.
Henry
From stapp@thsrv.lbl.gov Fri Apr 13 20:51:31 2001
Date: Fri, 13 Apr 2001 20:47:42 -0700 (PDT)
From: stapp@thsrv.lbl.gov
Reply-To: hpstapp@lbl.gov
To: Stanley Klein
Cc: hpstapp@lbl.gov, kleinlist , bdj10@cam.ac.uk,
brucero@cats.ucsc.edu, ghrosenb@ai.uga.edu, hameroff@u.arizona.edu,
Jeffrey M. Schwartz , keith@imprint.co.uk,
Kathryn Blackmond Laskey , phayes@ai.uwf.edu
Subject: Re: same predictions?
On Fri, 13 Apr 2001, Stanley Klein wrote:
> [Stan]
> > > 2. Could you remind me briefly why Bohm and many minds (many worlds)
> > > aren't also ontologies (quite ugly ones I'd say, but still
> > > ontologies).
> > >
> >[Henry]
> >They are ontologies, but neither has a real theory of consciousness.
>
>
> Thanks Henry. That's what I had thought about them being ontologies.
> I think some people strongly feel that Bohm has implications for
> consciousness (e.g. either the Bohm point or the 'pilot wave' being
> the mental).
>
> Now let me ask whether the three ontologies (Bohm, many minds, vN/W)
> make the same predictions. I had previously thought that they do.
> However, now I'm not so sure. In 'many minds' the choice of branch is
> random. In vN/W the choice doesn't seem to be random but rather comes
> from the mental realm. So maybe the two predictions regarding the
> outcome of mental effort are different. Or do you think they have
> same predictions?
>
> Stan
>
Dear Stan,
Bohm's original nonrelativistic model was designed to make the same
pedictions as vN/W. It does so, however, only if supplemented by
an extra postulate that associates consciousness with the
classical universe defined by the moving "Bohm point". This is a bit
of a problem because classical physics does not have any "rational"
connection between mind and matter. The great virtue of the quantum
approach to mind/matter is that the two aspects are naturally entwined
right from the start in mutually supportive roles. The original Bohm
model does not have this feature. Also, all the classical universe
enter co-equally into all of the dynamics, and hence it is unnatural
to single out ONE of the infinite ensemble as completely different
from all the others, in that it has this mysterious consciousness
attached to it, with this attachment having no effect on anything.
But in any case, that model is nonrelativistic: its PREDICTIONS
do not satisfy the empirical facts. Thus it is ruled out.
Bohm recognized this, right from the start, and noted that one
would have to do just what was done in the orthodox approach:
go over to field theory. It sounded at first plausible that, just
as ordinary quantum theory could be made relativistic by going over to
a relativistic field theory, so could his addendum to it.
However, the attempt to actually do so, made in his book,
"The Undivided Universe", revealed problems: He did not fully
demonstrate that he could apply his ideas to our basic
relativistic quantum field theory, QED. For this reason one cannot
claim that Bohm theory gives the same predictions as the relativistic
vN/W-Tomonaga-Schwinger theory. Bohm theory has, I believe, not really
been fully defined at the level of QED.
But let me pass over that point, and suppose the Bohm model
is well defined for the case of a human brain
How do we test the idea that of the billions of classical brains that,
according to Bohm's theory, effectively combine to make the quantum
state of the brain, exactly one carries (epiphenomenal) consciousness?
Let us think of the problem in the context of the OCD
patient whose brain is overwhelmed with the flood of signals
that are impelling him to wash his hands still one more time.
A competing rational thought briefly breaks through: "it would
be better, in the long run, to tend to the roses in the garden."
Now there is at least in principle a big difference between
what Bohm would say happens and what vN/W-QZE says happens.
Bohm theory would say that since this thought has flashed
into the mind the "preferred" Bohm point (or trajectory)
must be in a particular position, within the cloud of positions
that consitute the brain [let us ignore the rest of the universe].
The rest of the brain trajectories are still present, but engender no
consciousness.
The fact that the "consciouness-trajectory" is off in one
corner does not influence the motions of any of these virtual worlds.
But in the vN/W theory the fact that this thought has flashed means that
the actual (quantum) world is a world that is compatible with the fact
that this thought has occurred.
In nV/W the QZE effect, generated by the thought, can now "hold in place
the theraputic idea of moving to the garden", and thereby actually
change the evolution of the state of the brain from what the
Schroedinger equation specifies, whereas in Bohm's theory the presence of
consciousness on the trajectory has no effect on anything.
So the actual evolutions will be different in the two theories.
But suppose the evidence supports the vN/W QZE prediction
that the theraputic thought can hold itself in place.
The Bohmist can say that due to the complexity of the brain
one cannot actually compute what the Schroedinger equation would say.
Thus he could say that the brain was, due to its prior
conditioning, holding part of itself in place, and that the thought that
"I shall, by the force of my will, resist the OCD urges, and hold in
place the thought of moving to the garden", which Bohm's theory would say
is attached to the trajectory, would be an effect of the brain on the
stream of consciousness associated with the consciousness-bearing
trajectory.
Of course, it is totally fantastic that the brain should create
this epiphenomenal illusion. What is point such silliness?
What I expect to happen is that as neuroscience and psychophysics
develop, and more and more information begins to accumulate about
the differences in the way the brain behaves when consciousness
and conscious effort is present, as contrasted to brain behavior
when conscious processes are not present, it will become evident
that a lot of details are in accord with what would be expected
from vN/W QT. So the theory will become a useful tool.
[I am suddenly reminded of Gell-mann's early pronouncements
that the idea of "quarks" was merely a useful tool---that
quarks should not to be construed ontologically---and the present-day
blurring of that distinction by physicists]
If the behaviors of brains "seem" to be such that thoughts affect
brain actions in certain specific ways, and the alternative proposal that
this "seeming to be" is some sort of illusion, which cannot "yet"
be explained, and if the "seeming" connections are naturally
explainable as "true" connections within the framjework
of basic physics, then it becomes reasonable at some point
to start talking as if the seeming connections are real connections,
and drop the inane search for an explanation of the mysterious
"illusion".
So I am saying that the brain is such a complex system that it
is too much to demand that some single clean "crucial" experiment
will decide between the vN/W QT and Bohm's model, even though
the predicted brain behaviours differ. The vN/W QT specifies a
direct linkage between mind and brain that seems to fit both
the empirical facts and the basic principle of QT, whereas Bohm theory
needs to explain why it is that the presence of the "consciousness
trajectory" SEEMS to influence brain behaviour when the equations
do not entail it. [How does the presence of the "consciousness
trajectory" account for the "seeming" power of the thought to
keep attention focussed on the garden, when the attachment of
consciousness to the trajectory was just a ad hoc epiphenomenal
add on?]
[Bohm was undoubtedly aware of these problems, because
he later tried to bring in consciousness in ways that were very
different from the original simple ideas that some single
trajectory was real, and hence specified the branch that was
"observed" by the observer. He tried later to give consciousness
some overlording power. A guider field to guide the field that
guided the field that .... guided the classical universe.
But this deeper theory of consciousness was never worked out in
enough detail to permit clear predictions. Nor is it clear how these
"higher fields" are related to our conscious thoughts, which
is what a theory of consciousness ought to be about.]
Similar problems arise in the many-minds case. This theory
pushes all the interpretational difficulties onto a theory
of mind, which is not provided. It is the vN/W theory
that directly relate the mathematical formulas of QT
to experiences and that is validated by the empirical data.
So THAT theory is the touchstone to reality, and the many-minds
theory must connect onto that theory, and justify it without
using anything other than the Schroedinger equation. That's a tall
order. The many-minds theory must deduce the relevance of the
projection operators P on which vN/W QT [and Copenhagen QT]
is based, and explain how the state of world that is really the
amorphous structure that has grown out of the Schroedinger
evolution since the big bang manages to generate realms of
experiences that conform to the vN/W rules.
Decoherence helps a little bit, but not enough to do the job.
The state of a system that are naturally defined by environmental
decoherence effects are the so-called coherent states, which
are beautifully connected to classical physics. That is an
encouraging first step. But closely neighboring coherent state
are far from being orthonormal. And if two such states are each
coupled to an environment and the combined system evolves unitarily
then the inner product of the two states remains what it was.
So there always remains continuums of overlapping states:
environmental decohence does not separate the amorphous state
on the universe into distinct realms to which the vN/W rules of
interpretation apply.
So the many-minds interpretation does not exist. To make it
exist one needs a whole superstructure to place on top of
the Schroedinger evolution, a superstructure that will justify
the vN/W-Copenhagen rules of computation and interpretation.
I very much doubt that any such superstructure can be constructed
that does not smuggle in ad hoc rules that go beyond what
the Schroedinger equation entails. So the details
of the predictions could depend on those other features.
So in answer to the question of whether vN/W QT and
Many-Minds QT make the same predictions I answer
that the latter does not curently exist. To the exent that
it could be made an adequate theory it would have to justify
the vN/W rules at the practical level, at least to a good
approximation. But I do not see how the theory is going to be able
to avoid bringing in the outside question poser; I do not believe
that the state of the universe evolving via the Scroedinger
equation can, by itself, justify of the vN/W rules.
without admitting an outside "question poser", or something
equivalent to it.
Since the vN-Tomonaga-Schwinger relativistic quantum field theory
is the fundamental relativistic quantum theory that gives a clear
basis for the interpretation of the formulas, and since the
yet-to-be-created many-minds interpretation must presumably
justify it, at least at the pragmatic level, I propose taking
the former theory as basic, at least until the latter theory
becomes well defined.