From ggglobus@UCI.EDU Wed Mar 3 10:26:51 1999
Date: Tue, 2 Mar 1999 10:52:38 -0800
From: gordon g globus
Subject: [q-mind] Stapp's Knowledge (reply to Severinghaus)--Henry Stapp
From: Henry Stapp
Subject: Stapp's Knowledge (Stapp replies to Severinghaus)
[Ed]
I'd like to ask Stapp to reconcile the apparent "incoherence"
between many S_b's and S. So far, all I've seen is a sort of --
'Well, this is a pragmatic-idealistic approach I'm doing' -- which
reads more as a trivial cop out than an informative reply. I
qualify 'incoherence' because I'm not sure of the best term here;
it does seem to me that many observers will have different
knowledge states from each other, and perhaps all will differ from S,
even if we make reasonable restrictions (leave out the riff-raff and
the blatantly ignorant, for instance).
[Stapp]
The description of the orthodox position as "pragmatic-idealistic" does not
constitute a mathematical description of the formalism, or prove anything
about its coherence. To do that one must get down to the nuts and bolts
level of the formalism. I do not have the space here to give a course in
quantum theory, but I think simplest example will go a long way toward
answering Ed's query. But one can be sure, of course, that the likes of
Heisenberg, Pauli, Dirac, Born, von Neumann, and Wigner, under the challenge
of Einstein, Schroedinger and, initially, a huge physics establishment, would
not accept the orthodox position if it were incoherent. Even Einstein
reluctantly
admitted that, although he could not accept the claim of the completeness of
the orthodox theory, he could not deny its coherence.
A look at my recently posted `Theory of Presponse' might be useful, but I
shall stick here to the orthodox theory, ala vN/W, rather than the
modifications of it discussed there.
Consider first the paradigmatic simple idealized measurement case.
Suppose the instrument has a possible response R identified by the projection
operator P. That is, PP = P, and the system represented by S is in
a state such that the response is R if and only if S = PSP.
Suppose the system S initially is in the state S = aP + b(1-P), where a and b
are two real positive numbers.
Suppose two observers examine the instrument. Let Q be the projection operator
that projects onto those states of the body/brain of the first observer that
include
a neural correlate of his recognizing that the response of the instrument is R.
That is,
1. QQ = Q,
2. Q acts on the degrees of freedom that represent the body/brain of
observer 1.
3. Observer 1 experiences that the instrument response is R
if and only if S_1 = Q S_1 Q and S = Q S Q. Here S_1 is the state of
observer 1 and is S_1 = Trace_1 S, where Trace_1 represents the trace
over all
degrees of freedom other than those the represent the body/brain of
observer 1.
Let T represent the projection operator on the degrees of freedom of the
body/brain second observer that is analogous to Q:
1. TT = T,
2. T acts on the degrees of freedom that represent the body/brain of
observer 2.
3. Observer 2 experiences that the instrument response is R
if and only if S_2 = T S_2 T and S = T S T. Here S_2 is the state of
observer 2, and is S_2 = Trace_2 S, where Trace_2 represents the trace
over all
degrees of freedom other than those the represent the body/brain of
observer 2.
The operators P, Q, and T act on different degrees of freedom, and hence
commute: the order in which the appear in a product does not matter.
If both observers examine the instrument then the state S of the entire
system becomes, due to the interactions between the instrument and the
observer
S = aPQT + b(1-P)(1-Q)(1-T).
This is the core of vonNeumann's theory of measurement.
If the first observer has an experience that constitutes his recognition
that the response of the instrument is R, then there will be a reduction
of the state to one compatible with this increment in knowledge: this is the
core idea of the Copenhagen interpretation. This reduction takes the above S
to
S' = QSQ.
The property QQ = Q given above yields immediately:
S' = aPQT
This entails also
S'_1 = aQ Trace_1 PT,
and hence
S'_1 = Q S'_1 Q.
The form S' = aPQT entails also that
S'_2 = T S'2 T, and
S' = T S' T.
Hence the experience second observer will be that the response of the
instrument is R: the experiences of the two observers will "cohere"!
This example covers only the simplest idealized example, but the conclusion
about the coherence of the experiences of different observers pertaining to
the features of their common environment observed by both is general.
[Ed]
Also, does knowledge really (that is at the fine grained
practical reality of how humans do true mental work) occur in
increments? This seems counter-intuitive to me, from my current
naive intuitive position. Yes, we can *take* things that way to
some reasonable and practical extent, but is that the way the
mind/brain truly works at the "level" of knowledge?
[Stapp]
I defer to the works of someone far more expert than I on
the nature of our stream of consciousness. William James
spent a lot of time researching this matter. In a brief summary
of an extensive investigation he writes:
``a discrete composition is what actually obtains
in our perceptual experience. We either perceive nothing, or something that
is there in sensible amount. This fact is what in psychology is known as the
law of the `threshold'. Either your experience is of no content, of no change,
or it is of a perceptual amount of content or change. Your acquaintance with
reality grows literally by buds or drops of perception. Intellectually and on
reflection you can divide these into components, but as immediately given they
come totally or not at all.''
[Ed]
Finally, it seems that as knowledge increases (whether
incrementally or not) S, its possible determinable states
(projections?), gets more and more constrained, that is, reduced.
What can be said, or hazarded without engaging in pure fantasy,
about the ultimate limits on this process (that is, on just
how small this domain could in principle become) and its form?
[Stapp}
No need to engage in speculation. The quantum formalism is very explicit on
this
point: the limit is given by Heisenberg's uncertainty principle.
This limit is implicit in the mathematical formalism itself: it is not
imposed ad hoc.
The limiting possible forms are inherent in the mathematics.