Extropy, nonunitarity and representation

Date: Tue, 6 Aug 1996 00:55:31 -0700 (PDT)
From: Joel Henkel <jhenkel@juno.com>
To: quantum-d@teleport.com
Subject: Extropy, nonunitarity and representation

I would like to respond to Ed Close's 8/1/96 comments by amplifying my
use of the term extropy...

I. Definitions

Ed Close wrote:

>Our definitions are similar.  The word "extropy" is defined on Page 36
>of my book (see following quotes) and was used to describe the mirror
>image of entropy.

>     "...the organizing force existing prior to relative motion...
>       Ex = before or beyond, tropy = turning or relative motion.

In contrast, my definition as the number of partitions of Hilbert space
is a statistical one, dimensionless and corresponding to the thermodynamic
probability, W, in the statistical measure of thermodynamical entropy, S
= k log W, where W is the number of microstates or complexions in the
macrostate of a mechanical system. My definition is meta-mechanical in
the sense that the ensemble of mechanical systems transcends the usual
approach of quantum mechanics--to describe single, isolated physical
systems.

Entropy is defined only within a single "mechanical" partition of Hilbert
space, since it describes the distribution of probability within the
possible states of a single mechanical system. Extropy is defined over
the whole "meta-mechanical" partitioned Hilbert space, since it is a
measure of the number of partitions in the space.

II. Approaches

Ed goes on to describe his approach,

>In my work, extropy is treated from a different mathematical
>perspective, utilizing an adaptation and extension of G. Spencer
>Brown's calculus of indications, which I call the calculus of
>distinctions.  This approach is, in my opinion, superior to
>conventional mathematics because it applies prior to enumeration
>and quantification, and allows us to include the act of the drawing
>of distinctions, which is a function of consciousness, in the
>objective description of phenomena.  All extropy, from the order
>exhibited in quantum phenomena to the multitude of systems of
>structure making up the entire universe, is ultimately described
>in terms of distinctions drawn by a conscious observer.  Therefore,
>extropy, and in fact every description of reality, is actually
>defined in reference to a conscious observer.

The key notion here is

 *it applies prior to enumeration and quantification, and allows
  us to include the act of the drawing of distinctions, which
  is a function of consciousness, in the objective description
  of phenomena.*

I handle the notion of "drawing distinction" as choosing a particular
mechanical physical system--a state function spanning an entire Hilbert
space--from an ensemble of unitarily-inequivalent systems. The ensemble
is represented mathematically as a structured or partitioned Hilbert
space, filled with all possible systems *that are yet to be distinguished*.
David Peat discusses this in his book, *The Philosopher's Stone*, pg.
133,

  "But we are now about to enter a nonunitary world that goes
  even beyond this, for in a nonunitary transformation, a
  quantum system dissolves into a world of novelty and
  potentiality. With each nonunitary transformation, Hilbert
  space dissolves and reforms. And with each transformation,
  radical change, evolution, and modification become
  possible. A nonunitary transformation could be pictured,
  for example, as allowing a quantum system access to totally
  new vectors that have never existed in that Hilbert space
  before. Within a nonunitary transformation, a quantum
  system opens itself to true novelty."

Peat gives non-unitary physics a kind of "meta-mechanical"
character--beyond the usual "mechanical" unitary quantum system.

III. The Conscious Observer

Ed ties extropy to a conscious observer,

>Therefore, extropy, and in fact every description of reality, is
>actually defined in reference to a conscious observer.

My approach also involves a conscious observer. However, I tie the notion
of consciousness to a specific biophysical description of all living
organisms. This description gives the capability of making distinctions
to organisms in general. I define an organism's consciousness in this
context as the ability to generate a *representation* of its environment.
Generation of a representation requires the act of making distinctions.

Ed touches on this point in terms of *open organizing systems*.

>Conceptually, entropy is a measure of uniformity, or lack of structure,
>defined within a closed physical system.  Conversely, extropy is a
>measure of recognizable patterns, i.e., order, or structure.  Defining
>extropy as a meta-mechanical concept, and describing it in terms of
>matrices which can connect partitions of Hilbert space through non-
>unitary transformations, appears to be a reasonable way to accommodate
>open, organizing systems that borrow energy from surrounding systems to
>create and sustain order and structure.

There is an explicit biophysical meta-mechanical model describing how even
a single-celled organism can "borrow energy from surrounding systems to
create and sustain order and structure*. (See Del Giudice 1988 pg. 58.)
The model is meta-mechanical, since living organisms are open systems,
continually interacting with their environments, and so must deal with
unitarily-inequivalent states. Conventional quantum mechanics deals only
with closed isolated physical systems. The meta-mechanical model uses
quantum field theory to describe the borrowing in terms of *spontaneous
symmetry-breaking*, a non-unitary process in which filamentary microtubules
within a cell can perform the act of making distinctions through the
selection of a specific ground state, a Goldstone mode. A Goldstone mode
is a form of Bose condensation, here, a collective coherence of oriented
water dipole moments. Thus, Goldstone modes are capable of representing
their environments through the medium of ordered water. The key is that
the environment itself can be described in terms of oriented dipole moments,
for example, the dipole moments of biochemical molecular species swimming
in the water near cells. This allows a *representation in kind*, using the
same kind of elements to form patterns.

IV. Extropy as a measure of complexity in a single cell's representation

Extropy, or the number of Hilbert space partitions, in the case of a cell's
"representation in kind", can be set to equal the number of Goldstone
modes required to cover the range of external (environmental) biochemical
molecular (dipole moment) vibration frequencies. In principle, (ideal QFT
conditions) this number is infinite--the number of different possible
ground states. In actuality, various constraints should reduce this to
some large, but finite, number.

V. References

F. David Peat, *The Philosopher's Stone: Chaos, Synchronicity, and the
Hidden Order of the World*, Bantam Books, 1991

E. Del Giudice, S. Doglia, M. Milani and G. Vitiello, Structures,
Correlations, and Electromagnetic Interactions in Living Matter: Theory
and Applications, in *Biological Coherence and Response to External
Stimuli* H. Frohlich ed, Springer Verlag, (1988), pgs 49-64}