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\large {\bf
PARANORMAL IS ABNORMAL ACTION

OF MIND ON MATTER.\\
 
ONE NEEDS FIRST A THEORY OF 

NORMAL ACTION OF MIND ON MATTER.\\

CLASSICAL THEORY INADEQUATE:

NO `MIND' IN THE DYNAMICS.\\

QUANTUM THEORY IS FORMULATED

AS A THEORY OF MIND-MATTER

INTERPLAY!\\

SIMPLER THAN CLASSICAL PHYSICS!\\

I SHALL:\\

1. SHOW HOW QUANTUM THEORY
 
OF MIND-MATTER IS CONSTRUCTED.\\

2. DO TWO IMPORTANT MIND-MATTER

CALCULATIONS.\\ 
 
3. LOOK AT RAMIFICATIONS FOR PARANORMAL.
\newpage
IN QUANTUM THEORY NUMBERS GET

REPLACED BY MATRICES (OPERATORS).

1. AB CAN DIFFER FROM AB

2. Tr A = `A NUMBER'.\\

I SHALL DO THE CALCULATIONS WITHOUT

USING ANYTHING ABOUT MATRICES

BEYOND WHAT I HAVE JUST TOLD YOU.
\newpage
  VON NEUMANN-WIGNER QUANTUM THEORY.\\
   
  THE EVOLVING STATE OF THE UNIVERSE
 
  IS REPRESENTED BY A ``MATRIX'' S(t).\\
  
  EACH POSSIBLE EXPERIENCE IS 

  REPRESENTED IN THE THEORY BY A
 
  MATRIX P THAT SATISFIES PP=P.\\
   
  EACH ACTUAL EXPERIENCE IS

  REPRESENTED BY A ``REDUCTION''\\ 
  
  S(t+) = PS(t-)P\\
  
  THIS REDUCTION:

  1. "SAVES" A HIGH-LEVEL NEURAL ACTIVITY
 
  2. "ELIMINATES" COMPETING ACTIVITIES.\\

  THE ``SAVED'' PATTERN INITIATES A BRAIN
 
  ACTION THAT CORRESPONDS TO THE

  EXPERIENCE:

  THE SAVED PATTERN TENDS TO CAUSE 

  SUBSEQUENT EXPERIENCES TO CONFORM TO 
 
  THE  EXPECTATIONS AND  INTENTIONS 

  EMBEDDED IN THE EXPERIENCE
\newpage
  THE THEORY IS FORMULATED AS A 
 
  DYNAMICAL INTERPLAY BETWEEN 

 ``PARTICIPANTS'' AND  ``NATURE''\\

  THE TRIPARTITE  DYNAMICS:\\
    
    I.   A PARTICIPANT ASKS A YES-NO 
 
    QUESTION.\\

    II. NATURE RETURNS AN ANSWER, 

    `YES' OR `NO'.\\
    
   III. BETWEEN THESE INTERVENTIONS THE 
    
    STATE  EVOLVES DETERMINISTICALLY.\\


    TYPICAL QUESTIONS:

** AM I\\
``SEEING THE POINTER MOVE TO THE RIGHT''?\\
 
** AM I\\
``FEELING MY ARM RISE''?\\

** AM I

``INTENDING TO RAISE MY ARM''?
\newpage     

DETAILS:\\

    I. EACH YES-NO QUESTION IS 
    
REPRESENTED BY A MATRIX  P
 
    SATISFYING PP=P.

       ``ASKING'' IS REPRESENTED BY THE

        ``VON NEUMANN PROCESS I'':

        S(t)= PS(t-)P + (1-P)S(t-)(1-P)\\ 

    II. NATURE ANSWERS:\\
        
        
      `YES' MEANS S(t+)= PS(t) = PS(t-)P. 

        THE PROBABILITY OF `YES' IS 

        [P]=Tr PS(t)/TrS(t).\\
      
        `NO' MEANS S(t+)=(1-P)S(t)
          
        =(1-P)S(t-)(1-P).

        THE PROBABILITY OF `NO' IS 

        [1-P]=Tr (1-P)S(t)/TrS(t)\\

      
    III. BETWEEN JUMPS
 
S(t')=exp(-iH(t'-t)) S(t) exp(-iH(t-t'))\\
                
          FOR ``SMALL'' (t'-t), 

  S(t') ~= (1-iH(t'-t)) S(t) (1-iH(t-t')) 


\newpage
DERIVATION OF A LOCALITY RESULT.\\

LET QUESTIONS P AND Q BE ASKED AT 

THE SAME TIME IN DIFFERENT REGIONS.\\

PQ=QP \\ 

A KEY LOCALITY RESULT:

[Q] IS NOT AFFECTED BY `ASKING P'.

PROOF:

[Q]=Tr Q(PSP + (1-P)S(1-P))/DENOM

 = Tr Q[P S + (1-P)S]/Tr[PS+(1-P)S]/DENOM

  = Tr Q S/Tr S.\\

[USE Tr AB = Tr BA, PQ = QP, and PP=P.]\\

THE TOP LINE IS [Q] IF QUESTION P IS 

ASKED AND THE ANSWER IS NOT KNOWN.\\

THE BOTTOM LINE IS [Q] IF  

QUESTION P IS NEVER ASKED.\\

CONCLUSION: ASKING ``THERE'' DOES NOT
 
AFFECT THE PROBABILITY OF EXPERIENCE Q

OCCURRING ``HERE''.

\newpage

THE SECOND KEY RESULT.\\

THE QUANTUM ZENO EFFECT.\\
 
CAUSED BY RAPID REPETITION

OF THE SAME QUESTION P.\\
 
S(t')~= P (1-iH(t'-t))
 
   (PS(t)P + (1-P)S(t)(1-P))

        (1-iH(t-t')) P

   + (1-P) (1-iH(t'-t)) 

   (PS(t)P + (1-P)S(t)(1-P)) 

    (1-iH(t-t')) (1-P)\\


H ENTERS IN FOUR WAYS:

 PHP, (1-P)H(1-P), PH(1-P), (1-P)HP.\\

LOOK AT PH(1-P) CONTRIBUTION.

P(1-iH(t'-t))(1-P)= -iPH(1-P) (t'-t)

IT APPEARS WITH THE FACTOR
 
(1-P)(1-iH(t-t'))P= -i(1-P)HP (t-t')\\

EACH PH(1-P) AND EACH (1-P)HP APPEARS
 
WITH AT LEAST TWO POWERS OF (t'-t).\\ 
\newpage
LET INTERVAL T BE DIVIDED BY 

`ASKINGS' INTO n INTERVALS T/n.\\

LINEAR TERMS IN T/n GIVE n T/n:

ZEROTH ORDER IN n.\\

n CONTRIBUTIONS SECOND ORDER 

IN T/n : n/nn GOES TO ZERO.\\
 
PH(1-P) AND (1-P)HP DROP OUT:\\

H REPLACED BY PHP + (1-P)H(1-P).\\

NO P --- (1-P) transitions.\\

S GETS TRAPPED IN  PSP, 

OR IN (1-P)S(1-P)\\

THIS IS THE QUANTUM ZENO EFFECT.

\newpage
SIGNIFICANCE OF QZE

IT GIVES AN IMPORTANT QUANTUM
EFFECT OF MIND ON MATTER.

The environmental decoherence reduces the state S(t) to
effectively a statistical mixture of almost-classical\\ states.
This mixture, if it evolved according to the rules of classical
mechanics, would evolve (at least to first order) according to

  S(t') = exp -iH(t'-t) S(t) exp -iH(t-t')

BUT THEN THERE IS NO SUPPRESSION of the PH(1-P) and (1-P)HP
contributions to the evolution of this mixture. There is no confinement:
no focussing of attention. For there are no quantum jumps in the classical
mechanics case, and it was these jumps, which are a quantum effect,
that PRODUCED THE DEVIATION from the classical spreading.

\newpage
MAXIMALLY PREDICTIVE FORM OF THEORY.

MINIMIZE INPUT FROM PARTICIPANT.\\

LET \{P\}(t) BE SET OF P's THAT 

THE PARTICIPANT CAN ASK AT TIME t.\\
 
[THESE P's ACT ON THE DEGREES OF
 
FREEDOM OF PARTICIPANT.]\\

DEFINE:

P(t)= THE P IN \{P\}(t) 

THAT MAXIMIZES Tr P S(t).\\

ASSERT THAT PARTICIPANT CAN ONLY 

CONSENT OR VETO P(t).\\

SUPPOSE (BY VIRTUE OF ITS SURVIVAL

VALUE) THAT EACH P TENDS TO CREATE

CONDITIONS FOR SELF REPLICATION.\\

AND SUPPOSE `RAPIDITY OF ASKING'

IS CONTROLLED BY MENTAL EFFORT.\\

THEN MENTAL EFFORT WILL, VIA QZE,

TEND TO KEEP ATTENTION FOCUSSED.

\newpage

TIE-IN TO PSYCHOLOGY.

Wm. James. in "Psychology: The Briefer Course"
 
Ch. Attention: Sect. Attention and Free Will.

``I have spoken as if our attention were wholly 
determined by neural conditions. I believe that the array of {\it things}
we can attend to is so determined. No object can {\it catch} our attention
except by the neural machinery. But the {\it amount} of the attention which
an object receives after it has caught our attention is another question.
It often takes effort to keep mind upon it. We feel that we can make more 
or less of the effort as we choose. If this feeling be not deceptive, 
if our effort be a spiritual force, and an indeterminant one, then of 
course it contributes coequally with the cerebral conditions to the result.
Though it introduce no new idea, it will deepen and prolong the stay in 
consciousness of innumerable ideas which else would fade more quickly
away. The delay thus gained might not be more than a second in duration---
but that second may be critical; for in the rising and falling 
considerations in the mind, where two associated systems of them are
nearly in equilibrium it is often a matter of but a second more or 
less of attention at the outset, whether one system shall gain force to
occupy the field and develop itself and exclude the other, or be excluded 
itself by the other. When developed it may make us act, and that act may 
seal our doom. When we come to the chapter on the Will we shall see that 
the whole drama of the voluntary life hinges on the attention, slightly 
more or slightly less, which rival motor ideas may receive. ...''  

Posing a question is the act of attending. 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:

{\it  ``Consent to the idea's undivided presence, this is effort's sole 
achievement.''} ...``Everywhere, then, the function  of effort is the same:
to keep affirming and adopting the thought  which,  if left to  itself, would 
slip away.''
  
The vN/W theory, with the Quantum Zeno Effect incorporated, 
explains the mind-brain features that are the basis of James's 
conception of the action of human volition on brain process.

\newpage
EXAMPLE: How does your mental action raise your arm?

The set or sequence of P(t)'s is being offered to the mental aspect of the 
participant-observer by his body-brain. If raising the arm might be 
appropriate in the current circumstance then the question "Am I experiencing 
an intention to raise my arm?" is likely to be put forth by the brain. 
If consented to, not vetoed, this question will be asked. If effort is applied,
the same question will be asked in rapid succession. Attention will become 
focussed on the idea of raising the arm. According to James's ideo-motor 
theory, the action of raising the arm will be initiated (in the brain) by 
this dwelling of attention on the idea. 

The answer given by nature might be No! Then there will be some more
searching. But if raising the arm is by far the most appropriate
action under the circumstance, then the probability for a Yes answer---
with this probability ground out by the mechanical (survival-honed) evolution
---should be high.

If the initial answer is No, and all other alternatives are "bad",
on the basis of the mechanically conditioned criteria, then the question
should get posed again soon. Maybe this time it will get caught by QZE.

CONCLUSION:
 
von Neumann-Wigner quantum theory provides the rudiments of a neat 
and simple framework for studying mind-brain interaction. It has 
significant explanatory power: it explains immediately the essential 
features of volition described by Wm. James.

\newpage

WHAT ABOUT PARANORMAL?\\

CONCLUSION I. (LOCALITY)\\

NORMAL THEORY ENTAILS THAT
 
PROBABILITIES FOR FARAWAY EXPERIENCES

ARE NOT INFLUENCED BY MENTAL EFFORT

HERE.\\ \\
 
[I am assuming here, on the basis of the claimed evidence
for NO FALL-OFF AT ALL with either distance or time displacement,
that NO DIRECT PHYSICAL CONNECTION is responsible for the
purported effects.]

\newpage
CONCLUSION II:

Distant effects can be obtained by modifying the theory 
slightly:

Mental Effort: 

S$\rightarrow$ [(1+s)PSP + (1-P)S(1-P)] ,    small s 

This violates  normal quantum theory.

It would permit SIGNALS to be sent faster-than-light, 
in violation of ideas from the theory of relativity.

But if experiments really do conflict with this conclusion, 
then the modification proposed above is one conceivable way out.

It would mean that mental process can influence not only which questions are
asked, and when they are asked---which appears to be all that is needed to 
explain the NORMAL effects of mind on matter---but also can BIAS THE 
PROBABILITIES away from what quantum theory specifies. That would be a 
direct violation of present-day quantum theory, but would at least be a 
well defined and calculable small violation of the normal rules.

\newpage
CONCLUSION III.

A more plausible possibility would be to suppose that the
measuring devices are extentions of the human participant,
as more or less suggested by the Copenhagen approach. This would allow,
in principle, the P to act not only upon certain high-level degrees of
freedom of the brain, but also on some degrees of freedom of the
device. This would perhaps allow paranormal effects to come in
without actually directly violating the basic quantum rules.
One would be exploiting, instead, the looseness of quantum theory
pertaining to the choice of P in the vN process S$\rightarrow$ PSP + (1-P)S(1-P).

Since the choice of question P is already
a mental operation, it would more naturally be open to mental influence.
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