Date: Mon, 21 Oct 2002 17:41:24 -0700 (PDT)
From: stapp@thsrv.lbl.gov
Reply-To: hpstapp@lbl.gov
To: Kathryn Blackmond Laskey <klaskey@gmu.edu>
Subject: Re: Quantum Theory of the Human person (fwd)

On Fri, 18 Oct 2002, Kathryn Blackman's Laskey wrote:

> Dear Henry,
> 
> I hope all is well with you.
> 
> Thanks very much for sending me this abstract.
> 
> Regarding the book "The Mindful Universe" you sent recently, where is 
> that being published?

It is still under construction. I've already had several offers
to publish it, but I'm holding off on deciding until the manuscript
is more readable to more people, and perhaps addresses more completely
the questions you ask below.
 
> I would appreciate your answering a question I have.
> 
> There is much disagreement in the literature about the reduction 
> process and how it works, including controversy over whether there is 
> any such thing as reduction.  I have read numerous statements from 
> physicists that measurement involves interaction of a quantum system 
> with its environment, and is (it is asserted) therefore "nothing but" 
> Schrodinger evolution on a larger system.

This is wishful thinking not backed up by adequate supporting math.

This is essentially the Everett Approach. I have published my reasons for
claiming that this approach, after a half century of dedicated effort by
very many physicists, has not yet succeeded, technically.
[Can. J. Phys. 2002 SEP v80 N9 The basis problem in many-worlds theories,
pp.1043-105] 

It is indeed widely advertized that the interaction with the 
environment solves the measurement problem, But I do not believe
that the principal workers in that area (Zurek, Zeh, Joos)
actually make the claim that the whole theory has really been
worked out. I believe that the details have not been worked out 
satisfactorily , and that the gaps are significant, and are 
sufficient to undercut any strong claim that the Schroedinger equation
alone (and this includes the enviromental decoherence) is 
actually sufficient, by itself, to tie the evolving state vector
to well-defined probabilities for human experiences, which is
what the orthodox (Copenhagen and von Neumann) formulations
achieve by explicitly introducing a second process tied to experiential
realities.



The reason, in brief, that a second process tied to experiential
realities is needed is that if the universe has been evolving 
since the big bang solely under the influence of the Schroedinger
equation then every object and every human brain would now be, due
to the uncertainty conditions on the original atoms, represented
by a smeared out cloud, by an amorphous continuum. But in order to
extract from a quantum state a set of probabilities pertaing to 
human experiences, and hence to give well defined empirical
meaning to the quantum state, one must specify a basis: one must 
separate the space of the observing system into a set of discrete 
orthogonal subspaces corresponding to different "observations"; 
i.e., into orthogonal subspaces corresponding to different distinguishable  
experiences. But there is no detailed suggestion as to how 
a set of particular orthogonal projection operator P are to be
specified on the basis of the amorphous state of the brain and
the continuous action of the Schroedinger evolution. 

The problem, basically, is that a (proper) subspace is a set
of zero measure. For example, a subspace of dimension one in 
a visualizable space of three dimensions consists of a single
line in the three-dimentional space. The definition of this
subspace must distinguish the vectors that lie along that line
from vectors that deviate from that direction by the the tiniest 
amount. But how can a continuous amorphous structure distinguish
one direction from those lying arbitrarily close to it? 
[For a higher-dimension example one can think of a plane in a three
dimensional space: again almost all points arbitrarily close
to any point in the plane will lie outside the plane.] Moreover,
the projection operator P cannot be local (confined to a point, 
as contrasted to a smeared out region.) So how can a nonlocal
P be specified by a local process (the Schroedinger evolution
operator) acting upon a completely amorphous structure, the 
evolved state. The founders (and von Neumann) seemed to recognize 
clearly this basic problem of principle, and they introduced 
a second process to resolve it. Any claim to have resolved
this claring problem of principle without bringing in another 
process (besides the Schoedinger equation) needs to be 
spelled out in detail. But this has not been done. Rather,
the environmental decoherence effect has been pointed to as
some sort of panacea. But that effect does not resolve the
problem at issue, but rather heightens it, by making it
effectively impossible, or nearly impossible, to use 
empirical data to shed any light on the matter. The 
environmental decoherence effect quickly reduces the density
matrix of macroscopic systems to NEAR diagonal form, but the
slightly off-diagonal elements in coordinate space hold
the continuum of diagonal states together in a continuous interlocked
structure. This structure does not break up purely dynamically into
a set of discrete regions. Any rule that breaks up this linked amorphous
structure in coordinate space into a  set of discrete parts associated 
with distinguishable experiences would seem very difficult if 
not impossible to achieve solely by the dynamical process specified
by to the Schroedinger equation alone.

In any case this extraction of discrete subspaces from the 
amorphous evolving quantum state needs to be described by those who 
claim that the Schroedinger equation alone is enough. 


> Bohm and Hiley say this in 
> describing their hidden variable theory.  

Bohm's pilot-wave model is another way to add onto the raw
theory an extra process to tie the raw theory into human
experiences in a quantitative way.

The main objection to that theory is that, in spite of
long-term intensive effort, it has not been generalized
to cover relativistic cases involving particle
creation and annihilation. Also, the connection of that theory
to experiment was based on the presumption that when the macroscopic
level of "pointers" was reached, the experience of the observer would
correspond to the branch of the pointer wave function that was "occupied
by the "trajectory". (Notice that this involves a second process, which
is explicitly linked to consciousness.) But this linkage is cast into 
doubt by examples in which the trajectory goes through one detector but
it is the faraway dectector that fires. [ Dewdney, Hardy, and Squires,
Phys. Lett. A 184 (1993) 6-11] 

I once asked Bohm how he answered Einstein's charge that his model
was "too cheap". He said that he agreed! And notice that the last two
chapters of his book with Hiley tries to go beyond this model. And 
he, like I, saw the need to deal more adequately with Consciousness, 
and wrote several late papers on the subject. And Hiley
is working on ideas that seem quite different from the old pilot-
wave model. I do not think any physicist actually working in the area
claims that the pilot-wave model really exists in the relativistic
domain.

> Others also say this, 
> including people who don't subscribe to the Bohm pilot wave + 
> particle ontology, such as Carver Mead in "Collective 
> Electrodynamics," who gives a fairly well worked-out example of a 
> quantum oscillator jumping an energy level, and how this can be 
> explained by systems that briefly cross phases, exchange energy, then 
> go out of phase again.


This book is checked out at UCB and is being ordered for me from UCSC.
But in any case quantum theory explains well how information is
transferred to measuring devices. But those clean descriptions
are the BASIS of the measurement problem, not the solution.
They do  not explain how some object whose location is  represented by a 
(center-of-mass) wave function that is spread out over meters is 
experienced as being located at nearly a point, and with some well 
defined associated probability. If the device location is smeared out 
then for each of a large continuum of device locations the device will 
record the object as being "here." [Suppose the device has in addition to 
its detecting ability also the capacity to determine and record its 
location, and to correlated that information to the "detection" event.] 

Its the same problem as before. Orthodox theory allows the detector to be 
placed in some particular location corresponding to some particular 
experience because the observer places it there, but an observer governed 
solely by the Schroedinger equation has nothing definite about him: the 
entire situation is a continuous smear with no dynamically defined 
dividing lines. Some additional principle connected to the mind-brain
connection is needed.  

> Dorit Ahranov in her review article on quantum 
> computing also says that measurement involves Schrodinger evolution 
> of the system and its environment.  R. Mirman says "Wavefunctions 
> don't collapse, oversimplifications do... Perhaps what collapses is 
> not the statefunction, but common sense...  Discontinuity cannot be 
> true, and it is not.  <aside from KBL... didn't people once think it 
> could not be true that -1 had a square root, or that numbers could be 
> less than zero?>  But carelessness unfortunately can be true and too 
> often is, and certainly can make discontinuity appear true."  He goes 
> on to amplify: "If for example we consider an object striking a 
> screen forming a spot, the statefunction of the system after the 
> formation, the product of that of the struck atom plus all objects 
> attracted to it and the scattered object, is found from the initial 
> one using Schrodinger's equation, and if so found would be seen to 
> vary continuously.  In principle it is possible to calculate final 
> (perhaps extremely complicated) statefunctions from initial ones, and 
> the entire transformation from one statefunction to another is 
> completely continuous.  Never is there a sudden change or collapse. 
> Any such appearances result from ignoring the (continuous) 
> intermediate stages by regarding these as happening instantaneously."
 
Yes! If process II is the whole story then there never is a sudden 
change or collapse! Exactly true! But the continuousness of
that Process II evolution is closely tied to the fact that in a 
universe evolving exclusively via the Schr. Eq., ever since the big bang,
the detector is everywhere, and the observer's brain is a smeared out
continuum of possibilities. I once, long ago, characterized the 
many-worlds solution as shifting the whole measurement problem onto 
the mind-brain problem, about which it says nothing. For the theory,
to be meaningful it must be tied to probabistic statements about 
alternative possible experiences. But the smeared-out state
of the brain does not cleanly separate vectors from other vectors
that differ from them by very tiny amounts. What principle, involving
nothing but the evolving amorphous state, separates the space of brain
states into othogonal subspaces?

I do not claim that this problem has no solution. But Mirman's observation
that a world evolving via the Schroedinger equantion alone is evolving
continuously does not SOLVE the measurement problem: it CREATES the 
measurement problem.  Certainly, Heisenberg and Pauli and von Neumann
understood that a world evolving according to a universally valid Schr. 
Eq. would evolve continuously. And they also understood that that did not 
resolve the problem. I have absolutely no doubt that von Neumann 
understood very well also the essential features of environmental 
decoherence: they are all clearly displayed in his work. Yet in order to
get an empirically  meaninful theory he brought in Process I. 

> 
> Mathematically, wouldn't it always be possible to embed a system in a 
> larger system, and construct a Hamiltonian for the larger system such 
> that measurement events occurred on the smaller system as a 
> consequence of Schrodinger evolution on the larger system?  Is there 
> a way to test empirically whether the wavefunction "collapses" or 
> whether it's "just Schrodinger evolution of a larger system?"  Or are 
> we discussing religious faith?
> 
> Thanks!
> 
> Kathy
> 

The whole von Neumann approach involves assuming that the entire
physical universe, without Process I interventions, evolves in 
accordance with Process II. That is the starting point. This will
certainly generate continuous evolution of "measurement" type
processes in subsystems. That is all automatic, and essentially trivial.
The problem, if no Process I  interventions are included,
is to tie the amorphous structure generated by Process II to human
experience. That is a nontrivial mathematical problem that has
hardly even been addressed by many worlders (some unsuccessful
attempts were discussed in my Can. J. Phys. article) much less
solved. I think the top people see the problem, but they tend not
to emphasize it, but rather to hide it, and the followers are thus
unaware that there is a basic unsolved problem that renders the theory
a nontheory. at least now. But extracting discreteness from
an amorphous structure cannot be deemed a trivial matter.

As regards tests. it is certainly the case that living
systems that exploit the Quantum Zeno Effect in the way I
am suggesting, would tend to be more stable and directed than
a system evolving under the action of the Process II (Schr. Eq.)
alone. So there are, in principle, important empirical differences.

Actually, a properly constructed many world theory COULD be
essentially equivalent to the von Neumann theory. The point is that
a properly constructed many-worlds (actually one-world, many-minds)
theory needs, I believe, to specify orthogonal projection operators
corresponding to different distinguishable experiences, for only in this
way can the theory be adequately connected to experience. Suppose the 
aspects of the brain associated with these P's are being periodically
monitored/observed by another part of the brain (e.g., the prefrontal 
cortex). This monitoring would act like a measurement, and be represented
by a von Neumann Process I within the part of the space associated with
the original set of P's. And perhaps the monitoring action could itself
be associated with other experiences, for example, with a feeling of effort
or of high-level control of attention. 

The point here is that I have continually stressed that Process I 
is not controlled by any KNOWN law. But further developments MIGHT
tie it into Process II, plus some identifications of the connection
of the P's with experiences. But in the absence of any specific 
suggestion as to how this would work it seems to me that von Neumann's
formulation is the best available theory. A mind-brain theory based upon
it would almost surely fit into a future theory that provides an adequate
explanation of the causal structure lying behind Process I.