Chaotic complexity vs. quantum indeterminacy

Damian Popolo <Damian.Popolo@newcastle.ac.uk> wrote on July 15, 2002:

>I found this posting extremely intresting but also rather confusing. ... Part
>of my confusion derives from Prugovecki's own statments.  One the one hand, he
>affirms that "the considered theory of "chaos" is actually still classical
>physics: the "chaos" is only apparent, since the underlying laws are still
>deterministic".  Hence, I would argue, the notion of 'deterministic chaos'.
>Nonetheless, on the other hand, Prugovecki affirms a few lines after that "It
>is this "fundamental indeterminacy" that distinguishes the ideas of chaos
>theory from those of quantum theory (although some physicists are considering
>the possibility of "quantum chaos."  What are we to understand in here?  Does
>chaos deal with and recognozes this fundamental indeterminacy of nature or
>not?  And if it does, how can it still be 'deterministic'?

Answers:

The theory of chaos has involved from the study of classical dynamical
systems, which is deterministic in the sense that, once the initial values
of certain observables are given (e.g., the positions and momenta of all
the interacting particles in a dynamical system) their subsequent values
are, in principle, completely determined by the differential equations
governing this behavior. In practice, however, one can measure such values
only within margins of error determined by the accuracy of the instruments
involved. So the question arose whether "small" margins of errors in the
initial conditions will result also in "small" margins of error in the
predicted values. The fact that this was no so even for relatively simple
nonlinear differential equations came as a great surprise in the 1960s, and
made some physicists aware of the limitations on the predictive power of
many classical theories since, although deterministic, the ensuing behavior
is so complex as to appear chaotic. However, if the accuracy of measurement
of the initial values could be increased indefinitely, the actual
trajectories could be also traced with increasing accuracy, and what
appears to be chaotic behavior would simply emerge as behavior of very
great complexity.

On he other hand, Heisenberg's uncertainty principle denies the possibility
of being able to increase indefinitely the accuracy of measurement of, say,
the simultaneous values of the positions and momenta of interacting quantum
particles, and their quantum states embody this fact. Thus, although the
Schroedinger equation is deterministic, in quantum theory there is a
fundamental indeterminacy present from the outset. The quantum measurement
problem is a very complex one, involving philosophy of science and
sophisticated mathematics as much as physics. An outline of the various
advocated points of view can be found in the recently published 1,000 pp
reference work FOUNDATIONS AND INTERPRETATIONS OF QUANTUM MECHANICS (World
Scientific, 2001) by B. Auletta.

Quantum theory undermines the philosophical foundations of 19th century
deterministic theories of human behavior, and especially of those
"materialistic" social doctrines which, influenced by Newtonian physics,
claimed that history is governed by deterministic laws which lead to
"historical necessities." In that indirect manner quantum theory is
relevant to social theory: it allows for free will, as opposed to causal
necessity, even if we assume that human beings are merely complex
aggregates of matter.