Ann Arbor Talk. 
Quantum Applications Symposium. July 2, 2001. www.erim.org/qas2001)

HOW MINDS CAN EFFECT QUANTUM BRAINS.

INTRODUCTION.

Quantum theory, unlike classical physical theory, is dynamically incomplete.
It is dynamically incomplete in two different ways. 
Both are well known.

The first way stems from the famous statistical aspect of quantum theory:

The outcomes of certain experimental procedures are not fixed by 
the dynamical rules of QT: 
only the relative probabilities of the various alternative 
possible outcomes are fixed. 

The second way stems from the equally famous introduction of into
physical theory of the "participant/observers".

But WHY are they introduced?

They are introduced because they play AN IMPORTANT FUNCTIONAL
ROLE in the orthodox Copenhagen formulation of the theory.

The problem is this: the statistical theory requires that 
A SPECIFIC CHOICE MUST BE MADE ABOUT WHICH ASPECT OF NATURE
WILL BE PROBED---WHICH QUESTION WILL BE ASKED---
before the stochastically characterized answer, or outcome, is delivered.

But this `selection of the question' is NOT determined WITHIN THE 
QUANTUM SYSTEM by the KNOWN laws of quantum theory.

The Orthodox Copenhagen Quantum Theory deals with this lacuna
by allowing  PARTICIPANT/OBSERVERS, who stand OUTSIDE the system
described by the quantum mathematics. to choose WHICH questions 
are put to nature, and WHEN these questions are put.

The participant/observers accomplish this by  "FREELY CHOOSING" which 
experimental procedure they set in place. 

These ideas lead to the wonderfully useful pragmatic quantum theory.

But placing of the participant/observer, and his instruments, 
outside the quantum mechanically described system divides the
dynamically unified physical universe into two differently described 
parts. This leads to problems at the level of principles.

Von Neumann resolved these problems by including the entire physical 
universe in the quantum system.

But then the question arises:

If the whole physical universe, including the body and the brain 
of every experimenter, is included in the quantum system then:

What fixes `which question is asked',
and `when is it  asked'?

What is the SELECTION PROCESS that answers these questions?

How does that selection process affect the physical world?

Those are the issues that I am concerned with.

My main conclusion is this:

Within von Neumann's formulation of quantum theory this 
selection process, which is NOT FIXED by the KNOWN laws
of physics, can strongly effect the behavior of a human 
brain.

I shall explain how this works.

But if this selection process has physical effects in human brains, 
then it presumably has physical effects in other systems as well.

Thus the pertinent question for this 
"Quantum Applications Symposium" is:

CAN WE BUILD SYSTEMS that exploit the physical power of 
this quantum selection process?

Learning how to use this process could be as 
important as learning how to use electricity.

2. MIND IN QUANTUM THEORY

So far I have not mentioned MIND.

But within the von Neumnn framework this selection process is 
understood as an effect of `mind' on `brain'.

Before explaining how `mind' can effect `brain' I must distinguish these two.

In brief: Brain is `Physical'; Mind is `Experiential'.

Quantum theory and classical physical theory are both built on the
concept of the ``state of a system''.  This state is described 
in terms of mathematical quantities that are localized in tiny regions 
of space, and evolve in time.  Things characterized in this way are 
classified as Physical.

Experiential things are EXPERIENCED FEELINGS: feelings of `pain',
`pleasure', `yellownesses', `effort', `knowings', and similar
`experiential-type qualities'.

Copenhagen and von Neuman quantum theory both consider experiential
qualities to be, themselves, REAL ASPECTS OF NATURE.

But how does mind enter into von Neumann quantum theory?

When von Neumann expands the quantum system to include the
entire physical universe the question arises:

What perform the essential dynamical functions that Copenhagen 
quantum theory had assigned to the participant/observer?

Von Neuman transferred the functions formerly assigned to
a participant/observer to an "abstract ego", which can be regarded 
as the mental aspect of the participant/observer. 

The selection process thereby becomes associated with mind.

Mind becomes associated with a dynamical process!

3. COMPARISON TO MIND IN CLASSICAL PHYSICS

The present state of philosophy of mind shows that classical physical 
theory does NOT provide an adequate foundation for a theory of nature
that includes minds. Briefly, classical theory leads to a choice between
either `epiphenomal minds' that can have no effect on the physical world,
or an `identity theory' that claims, for example, that a  `pain'
is `exactly the same thing' as some brain activity.

The epiphenomenal option is unsatisfactory for the following reason:
  
`Epiphenomenal consciousness' has no physical effects, and
hence has no possibility to evolve by natural selection.

The alternative `identity theory' option is unsatifactory within
classical physical theory for the following reason:

Classical physical theory is about spacio-temporal structures
built out of atomic particles, and electromagnetic and gravitational
fields. These spacio-temporal structures can have diverse
dynamical, logical, and mathematical properties that are in principle
consequences of the classical laws and principles, and the initial conditions.
But the principles of classical physical theory provide no way to deduce
from spacio-temporal structures the existence of experiential feelings.

The only virtue of identity theory is that it is the only way WITHIN
CLASSICAL PHYSICAL THEORY to avoid epiphenomenalism.
But quantum theory provides another way out.
 
4. MAJOR DYNAMICAL CHANGES INSTITUTED BY QUANTUM THEORY

Quantum theory institutes major dynamical changes in the following five items: 

1) MIND

2) MATTER

3) FREEDOM

4) WILL

5) LOCALITY

Before describing these changes I will say something about ``ontology''.

The founders of quantum theory held that the quantum mathematical 
should be treated as rules for computing (statistical) connections 
between what human participant/observers do and what they observe. 

Inquiries into `what is actually going on' were discouraged:
the theory was construed pragmatically , not ontologically.
 
However, von Neumann's formulation is amenable to a rationally coherent
"ontological" interpretation. I shall speak as if the
quantum state and its properties, as represented in von Neumann's
formulation, are faithful images of the true state of affairs.

I turn to the five features listed above.

1) MINDS are taken to be dynamically active realities. They are associated 
   with the dynamical functions of the participant/observers.
   As in the Copenhagen formulation, the dynamics is formulated
   like the  game of twenty questions: Each participant poses questions
   that can be answered `Yes' or `No'. An answer is immediately 
   delivered to the poser, and the state of the universe is `reset' so 
   that it conforms to that answer: all components of the physical
   state that are incompatible with that answer are obliterated. 
   The state thus becomes a `compendium' of `bits of information', 
   each injected into the quantum state in association with the 
   experiencing by some participant/observer of the delivered answer. 

2) MATTER, the stuff of the physical universe, becomes dynamically
   midway between mind and the old concept of matter.
   But how can anything lie midway between mind and old matter?
   Answer: The state of the universe becomes essentially a cloud of
   classical possibilities: each droplet in the cloud is similar to a 
   physically possible classical universe, and each resetting reduces 
   the cloud to a smaller cloud of possibilities. This new cloud then 
   spreads out due to the effects of the Heisenberg uncertainty principle, 
   with the individual droplets continually  dividing. 

3) FREEDOM is present. The CURRENTLY KNOWN laws of physics do not 
   determine WHICH QUESTION will be posed, or WHEN it will be posed: 
   Within contemporary physical theory these choices are FREE CHOICES.

4) WILL is causally efficacious. Exercising the just-mentioned freedom 
   can influence the course of physical events in the brain. 
   I shall explain presently how this works.

5) LOCALITY fails during the resettings. The process associated with an 
   experience acts over an extended region in the brain. Each experience
   "grasps" some whole MACROSCOPIC aspects of brain activity. 

5. THE BASIC VON NEUMANN EQUATIONS.

How does the dynamical process work? What are the basic equations?
  
Let {e} be the set of possible experiences associated with a brain B
(during some interval that lasts at least a few seconds)

The "question" associated with possible experience `e' is: Will `e' occur?

Let P_e be the projection operator associated with possible experience `e'. 

[A projection operator is  an operator P that satisfies PP=P]  

Let B(t) be the evolving state (density operator) of the brain B. 

[B(t) is formed by taking the trace of the state of the universe over 
all degrees of freedom except those of B.] 

Let Prob(e,t) be the probability that `e' will occur at time t if 
the question "Will `e' occur?" is posed at time t. Then

Prob(e,t)= Tr P_e B(t) P_e /Tr B(t),

where Tr means trace over the degrees of freedom of B.

[The quantities P_e and B(t) and their products can be represented by
N-by-N "matrices" (N-by-N arrays of numbers) with N infinite, and
the trace is the sum of the diagonal elements: it is the QT analog 
of the classical sum (integral) over all points in phase space.]

If the delivered answer is `Yes', then B(t) is reset to P_e B(t) P_e:

If `No' then B(t) is reset to (1-P_e)B(t)(1-P_e).

Note that the basic dynamical equations inject into the dynamics
   the operators P_e that implement our experiences:
[This is how Copenhagen and von Neumann quantum theory "explicitly"
connect the quantum mathematics to human experience.] 

These P_e's are nonlocal: they act over MACROSCOPIC portions of the 
   brain. 

Thus the experienced macroscopic features of the brain enter 
   into the dynamical evolution of the brain. 

6. ATTENTION AND `SELECTION OF THE QUESTION'.

When you attend to something you seek answers to questions about it.
These questions are ones that can be answered by possible experiences.

So one can naturally identify `attending to X' with asking "Will `e' occur?",
where `e' contains information about X.

This linkage ties the psychological concept of ATTENTION to the
quantum concept of SELECTION of the question.

7. HOW MENTAL EFFORT CAN INFLUENCE BRAIN BEHAVIOR?

Within von Neumann quantum theory a person's mental effort 
can influence the behavior of his brain? 

A mental effort to keep attention focussed of some topic feels
rather like a speeded-up posing of the question "Shall I continue
to think about this topic?" This question seems to be reverberating
in the background. But how could a repetitious asking of a question
have any effect on the observed system. In classical statistical
mechanics simply posing questions has no effect at all upon average values: 
i.e., upon values obtained by averaging over the possible answers. 

But in quantum theory simply asking a question repeatedly and rapidly,
without regard to the answer, can strongly influence the behaviour of 
the system being examined. 

This effect is known as  the Quantum Zeno Effect.

8. THE QUANTUM ZENO EFFECT.

Let the projection operator P=P_e  associated with experience `e'
project onto a subspace in which the degrees of freedom are changing
slowly on the time scale of the repetitious questioning.

If the original answer at time t=0 is `Yes', then the expectation 
value Prob (e, t) at the short time t later when the question is
asked again is

Tr P U(t)P B(0) P U(-t) P/ Tr P B(0) P 

~ Tr P (1 -iHt)P B(0) P (1 +iHt)P/ Tr P B(0) P 

~ 1 plus terms of order t squared.

This means that if the question is posed rapidly, the brain will be
nearly "frozen" in the subspace where the answer is `Yes', instead
of evolving out of that subspace, as it normally would do if the 
question were not being posed repeatedly and rapidly.

Notice that this effect does not depend on whether the state B(t)
is a pure state or a decoherent statistical mixture.

9. WILLIAM JAMES ON "WILL".

[In "The Principles of Psychology II"]
 
In the chapter on Will, in the
section entitled ``Volitional effort is effort of  attention'' 
James writes:

``Thus  we find that {\it we reach the  heart  of our inquiry  into volition
when we ask by what process is it that the thought of any given action
comes to prevail stably in the mind.}'' 

and later

``{\it  The essential achievement of the will, in short, when it is most 
`voluntary,'  is to attend to a difficult  object and hold it fast before
the  mind.   ...  Effort of attention is  thus the essential phenomenon
of will.''}

Still  later, James says:

``Everywhere, then, the function  of effort is the same:
to keep affirming and adopting the thought  which,  if left to  itself, would 
slip away.''

Thus the von Neumann fomulation of quantum theory can provide a dynamical 
explanation of the efficacy of volition, as it was understood by 
William James.
 
Note that no violation of the basic quantum principles is involved:
There is NO BAISING OR REVISION of the basic statistical rules.

The same theory explains also many intricate details of the psychological 
data on attention collected during the past several decades.
[See: http://www-physics.lbl.gov/~stapp/stappfiles.html.
Quantum Theory and the Role of Mind in Nature.
To be published in Foundations of Physics, October 2001]

Thus this quantum theory of mind-brain dynamics has nontrivial 
explanatory power.

This explanation gives to mind an actual causal influence on
brain: the causal efficacy of mind is not just some bizarre
illusion, as  it is in both classical physical theory, and the 
many minds/worlds interpretation.

10. PHILOSOPHICAL FOOTNOTE

Von Neumann's reference to the `abstract ego', which is the experiential 
residue remaining after the body and brain of the participant/observer
is put into the quantum system, can give the impression (to a classically 
oriented philosopher) that this residual experiential part must lie outside 
the physical universe. However, the physical universe of von Neumann's 
theory is not like the old substantive universe of classical physical 
theory. In von Neumann's theory, as I am construing it, the state of 
the universe, as it is represented in the theory, is regarded 
as a faithful image of a nature that has mindlike qualities:
The basic nature of the physical universe is to be a carrier of 
actualized experiences.
 
Within this framework an experience could reasonably be regarded as a 
process occurring in a brain, or to a brain, much as the identity theorists 
claim. But this process would now not be simply the mechanical occurrence of 
a pattern of brain activity: it would be rather the actualizing of 
that pattern; the process of instantiating, or "expressing", this 
particular pattern. 

11. GENERALIZING TO NON-HUMAN SYSTEMS.
 
The original Copenhagen interpretation regarded the quantum mathematics
as merely rules that allowed  human scientists to make computations
pertaining to correlations among their experiences.

Von Neuman made no effort to cancel this restriction to human beings.

But if the efficacious selection process is at work in human beings,
then analogs must surely must be present in other systems. 

Thus the question for this "Quantum Applications Symposium" is: 

Can we exploit this putative dynamical process?

Consider ANY system that is maintaining itself in a state of dynamic
equilibium with its environment.

There will generally be a continuum of states of equilibrium, or approximate
equilibrium, available to the system. When the external situation changes
the system is placed in some degree of stress: there may be a tendency for the
system to disintegrate. Some new collection of internal states may now become
stable, and the system will either make a transition to one of these, or 
perish.

Quantum mechanics must be applied in principle. A quantum calculation
would in principle yield the transition probabitities. 

But the predictions would be affected if  the system could initiate
internal reductions analogous to those occurring in human brains---
according to the theory outlined above.

But what is the general rule that selects the pertinent projection operators 
P, and the times t at which they act?

The simplest possible rule seems to be this:

Rule A:

Each selected operator P, time t, and system B  give a local maximum for

Tr P B(t)/Tr B(t)

as B and t vary, and the P vary over the set associated with
quasi-classical states of the coulomb field in the 
coulomb gauge. 

This rule speculative. 

But some such rule must be added, in order to complete von Neumann 
quantum theory, with respect to the essential selection function that 
Copenhagen quantum theory assigns to the participant/observers.

12. REMARKS CONCERNING RULE A.

1. Virtue vis-a-vis the Many-Worlds/Minds-Interpretation (MWI)
   with Environmental-Decoherence (ED).
   The MWI-ED approach has been examined in detail by Zurek.
   [Prog. Th. Phys. 89, 281-312 (1993)]
   The fatal flaw is that ED produces an overcomplete set of states.
   But in order for the statistical theory to work one must have
   definite projectors P: A continuum of non-orthogonal P will not
   do: probabilities will not add up to unity. There is no way
   to get definite projectors P out of the quantum mathematics
   itself, with the whole universe included in the quantum system.
   Some extra rule must be added. Rule A is a prototype.

2. The effect of ED will tend to decompose the state of B into a mixture
   of coherent states in coordinate space. A suitable P could
   be of the form 

   P PSI = P (Sum of |i>PSI_i over i in C)
         = Sum of |i>PSI_i over i in subset C(P) of C,

   where C is the index set of a minimal complete lattice 
   of `coherent' states |i>, and the PSI_i are the amplitudes
   associated with PSI, and also with P PSI for i in C(P).

3. The function of the brain,  honed by natural selection,
   is to interpret clues supplied by receptors, and create a
   "best" course of action. Thus the P's that generate the
   largest Tr P B(t)/Tr B(t) ought to be P's that select 
   quasi-classical subspaces that lead reliably to classically
   describable actions. That is the reason that I imposed
   the quasi-classical condition on the P's.  The state
   of the couloumb field in the coulomb (i.e., radiation)
   gauge is a natural candidate, because it changes more slowly
   and is defined instantaneously in terms of the positions of the charges.
   [Cf. J. Schwinger, Theory of Quantized Fields, Phys. Rev. 82, 914 (1951)
    S. Weinberg, The Quantum Theory of Fields I, Secs. 8.2 and 8.5]
   
4. If Rule A is indeed the rule that completes the quantum dynamics
   (apart from the statistical choice of answers/outcomes) 
   then we should be able to build devices that would exhibit
   the internal Quantum Zeno Effect, and control their own behaviours 
   (in ways we design) via the quantum selection process.
   This dynamics would act WITHIN the window of possibilities created
   by the Heisenberg uncertainty principle: it would create a dynamical
   structure within that window. 

5. By proposing a proto-type rule that is formulated exclusively in 
   terms of quantities appearing in the quantum formalism I do not mean 
   to exclude the possibility that the "true" rule might refer to a larger 
   structure in which the quantum structure is imbedded. 

   But it is scientifically reasonable to look first for a rule that refers 
   only the physical world as it is described within contemporary physics.