Bonne lecture,
trouvé sur le site de Derkeley Lab, Physic Division:
http://www-physics.lbl.gov/~stapp/presponse.txt
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From ggglobus@UCI.EDU Wed Mar 3 10:27:26 1999
Date: Tue, 2 Mar 1999 08:05:24 -0800
From: gordon g globus <ggglobus@UCI.EDU>
Subject: [q-mind] Theory of Presponse--Henry Stapp
From: Henry Stapp <stapp@thsrv.lbl.gov>
Subject: Theory of Presponse
This is a reply to some recent queries from Stan Klein and Chris Nunn
about my way of providing a theoretical framework for understanding the
presponse effects of the kind reported by Bierman.
I have been reluctant to post much about my theory of presponse because
I do not want my theory to be regarded as an unorthodox theory, or a theory
of paranormal phenomena. I believe it to be a rational carrying forward of the
ideas of the Copenhagen interpretation in the ontological direction
developed by von Neumann and Wigner. My theory is design to be an orthodox
theory of the mind/body system, in this Copenhagen/vonNeumann/Wigner sense,
and it predicts no presponse, (assuming, of course, that the selection of the
picture is indeed isolated in such a way as to have no direct forward causal
influence on the brain of the subject prior to the presentation of the
picture to the subject.)
But there is great interest on this forum [q-mind] in the Bierman presponse
experiments. Whether or not the claims will be borne out, the experiments do
have enough of the trappings of good science to be not dismissable out of hand.
If the presponse effects of the kind reported by Bierman turn out
to be a real feature of nature, then, as Stan says, we are at the dawn of
a new age in science.
There is, then, a question of how the claimed effects could be reconciled with
contemporary orthodox science: What is the simplest and most parsimonious
modification of orthodox theory that could accommodate them? Must the
orthodox ideas of Copenhagen and von Neumann/Wigner be rejected in favor of
a radically different foundation?
I shall describe here how the addition of small non-hermitian contributions
to the Hamiltonian of the brain of the conscious subject can lead to
presponse effects of the kind Bierman reports.
Let P represent a projection operator that acts on the degrees of freedom
of the subject, and projects onto the neural correlates of a strong possible
experiential response to a wild picture.
Let Q represent a projection operator that act on the degrees of freedom
of the brain of the experimenter, and projects onto the neural correlates
of the experimenter's experiencing of an instrumental reading that indicates
a presponse in the body/brain of the subject.
In accordance with the orthodox approach, the theory is about correlations of
experiences of observers, and about the computable predictions of quantum
theory pertaining to these correlations.
The interaction of the body/brain of the subject with the instruments that
probe this body/brain induces a correlation between this body/brain and
the brain of the experimenter who observes the instruments. For definiteness
let me take the state of the full system to be the correlated state
S = QP + (1-Q)(1-P).
This says that the experience associated with Q occurs if and only if
the experience associated with P occurs. It expresses the correlation between
subject and experimenter brought about by the experimenters witnessing is the
results of the instumental probing of the subjects body/brain. This simplest
form is an idealization designed to allow me to bring out in a simple way
the essential logical points.
The projection operators P and Q act on different degrees of freedom and
hence commute: PQ = QP. Both P and Q are projection operators:
PP=P, and QQ=Q.
The expectation value of Q is, according to orthodox QM,
<Q> = Trace QS/Trace S = Trace QP / [Trace QP + Trace (1-P)(1-Q)],
where the second form follows immediately from two applications of
QQ = Q.
The orthodox theory allows the brain of the subject to undergo a local
unitary evolution after the interaction with the instruments:
S --> USV where V is the complex conjugate transpose of U.
The unitarity requirement is UV = VU = 1.
If the subject's brain state has evolved in this way then the expectation
value of Q would be
<Q>' = Trace QUSV /Trace USV.
U and Q act in different independent subspsaces and hence U commutes with Q:
QU = UQ. And for any (bounded) X and Y, Trace XY = Trace YX. But then one
can deduce immediately from the rules I have just stated that <Q> = <Q>':
the unitary evolution of the subject's brain state after the probing does not
effect the value of the observable <Q>: the statistical properties of the
observations by the experimenter are independent of what happens in the
brain/body of the subject after the probing of that brain/body that is
completed.
This is exactly what normal ideas about causal connections demand: the above
calculation, which should be understandable to any high school graduate, shows
immediately how this `normal' prediction about causal connections comes
automatically and easily out of the orthodox theory.
But what happens if an experience associated with either P or 1-P occurs
in the stream of consciousness of the subject. If the outcome of Nature's
Choice between the experience associated with P and the experience associated
with 1-P is not known then the orthodox theory says that you must add the
contributions to <Q> from the two possibilities. Hence the theory predicts
<Q>'' = Trace Q[PSP + (1-P)S(1-P)/Trace [PSP+ (1-P)S(1-P)].
A trivial calculation then shows that <Q>'' = <Q>
Hint: P(1-P) = 0 is another version of the definition (PP = P)
of a projection operator, and so is (1-P)(1-P) = (1-P).
The fact the the subject has had an experience DOES change the state, even
if one does not know which of the two possible experiences has actually
occurred. But if no information is included about which experience occurs then
the expectation value of Q will be just the same as if the subject has had no
experience. This means that the statistical properties of the experimenter's
experiences will not reveal anything about what is happening in the brain/mind
of the subject: orthodox theory predicts that there will be no presponse of
the kind reported by Bierman. The reader should be able to actually
understand the quantum mechanical calculation that leads to this conclusion.
To accommodate the Bierman data let us depart from the orthodox demand that
the evolution between reduction events be unitary. Physicists have
conducted test designed to check unitarity in various physical systems
and have detected no violations of unitarity in the systems studied, to the
accuracy measured. So it is recognized that the unitarity property, although
very basic to orthodox theory, is something that conceivably could fail, and
that should therefore be tested. The existence of a precursive effect would,
if the other aspects of the experiment are as represented, be a test of
unitarity.
Suppose after the probing is completed the brain of the subject
evolves via a transformation that is non-unitary, say:
S --> [fP + (1-P)]S[Pf + (1-P)], where f is a number not equal to 1.
(This could be the consequence of a small non-hermitian term in the
Hamiltonian that acts in the part of configuration space that is associated
with the neural correlates picked out by P.)
Then the expectation value of Q is
<Q>(f) = Trace Q [fP + (1-P)]S[Pf + (1-P)]/Trace [fP + (1-P)]S[Pf + (1-P)]
= ff Trace QP/[ff Trace QP + Trace (1-Q)(1-P)]
This depends upon f, and hence upon what is happening in the brain of the
subject after the probing is completed.
If the subject has an experience corresponding to P or to (1-P)
but it is not known whether it is P or (1-P) then the expectation value
of Q is
<Q>(f)' = Trace Q [fPSPf + (1-P)S(1-P)]/ Trace [fPSPf + (1-P)S(1-P)].
The rules defined above allow one easily to deduce that
<Q>(f) = <Q>(f)';
Assume that if the picture shown to the subject is `mild', rather than
`wild', then none of the possible responses of the subject will lie
in the very special part of configuration space where the non-hermitian
part of the Hamiltion is coming into play, so that f is effectively 1
for the mild pictures. This would account for an effect of the kind
reported by Bierman.
On the other hand, if the experimenter does his witnessing before the
the body/brain of the subject receives any information about the picture,
and hence before the brain evolves into the part of configuration space
where the non-hermitian term comes into play then
<Q>b = Trace Q[QSQ +(1-Q)S(1-Q)]/Trace [QSQ +(1-Q)S(1-Q)]
= Trace QS /Trace S = Trace QP/ Trace [QP + (1-Q)(1-P)]
= <Q>.
The Bierman presponse disappears under this early-viewing condition.
The point is that the calculation is to be carried out at the time the
observations of the experimenter are made, and if this time is prior to the
time that non-hermitian interaction comes into play the the state S before
that aberation occurs should be used.
Before turning to the queries of Stan and Chris, I use this example to
illustrate the main points of the orthodox interpretation.
1. Notice that the theory is explicity about our experiences. This dependence
on our experiences does not put the theory into some abstract never-never
land. Exactly the opposite! Making the theory about our experiences takes the
theory OUT of a realm of abstract ideas, related to what we know only
via some external (to the theory) metaphysical postulate of mysterious origin
--- i.e., the mysterious occurrence of conscious experience in a world defined
in terms that seems to provide no dynamical need or role for this other
kind of stuff --- and puts what we know explicitly into the formalism in
a practical way. It ties the theory securely to what we know, which is, on
the one hand, what we can describe to our colleagues about what we have done
(how we have set up the instruments) and what we have learned (how the
instruments have reponded), and, on the other hand, the subject's description
of his feelings associated with his witnessing of the picture.
2. The first kind of description relies on Kantian categories of thought,
such as spacetime, and more specifically about our ideas of objects located
in spacetime. These categories of thought enter only as an underpinning of
the experimenter's description, in ordinary language, refined by the concepts
of classical physical theory, what he is doing with instruments and what he
is learning from them. There is no description of any thing-in-itself beyond
our experiences, and the quantum theoretical description that allows us
to compute correlations among our experiences. This quantum description
can be viewed as an objective representation of certain properties of a
total reality that includes our conscious thoughts.
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