> I was mainly thinking of systems which are very sensitive to initial
> conditions. Therefore, the inability to make long-range predictions is true
> even if one were to know the initial conditions exactly.
>
I am sorry if I am missing your point, but I am not able to agree with the above.
To know the initial conditions exactly WOULD allow you to make long range
predictions since there would be no uncertainty that would diverge exponentially.
The sensitivity to initial conditions negates long term predictions solely because
there is always some uncertainty dx in the initial condition xo ; i.e. xo = xo +
dx. at t = 0, thus the dx term will "grow" exponentially in chaotic systems..
> I use deterministic chaos as an example where to us things appear to be
> governed by randomness whereas they are really not chance events at all.
This is true for classical dynamics of few particles but as you agree, untrue for
quantum. Yet, even in complex classical systems, genuine randomness - and hence
indeterminism - may occur due to the shear complexity of interactions, but the
quantum argument is more robust.
> I do realize that quantum mechanics does introduce probabilistic concepts as
> an inherent feature of nature. But can't we understand the origin of
> Planck's constant as resulting from God's hands partially shaking when
> creating the universe. [The former is partly on a humorous context but not
> quite so either.]
How much of the former is serious? I am not being flippant, for by it you seam to
be saying that God HAS created the universe with some inherent randomness (shaking
of the hand = initial condition uncertainty?) which agrees with our present
understanding of nature and the way I reconcile these notions.
> Quantum theory is not the final theory and so the
> underlying laws of Nature must somehow be consistent with the omniscience of
> God.
While quantum theory MAY not be the finial theory, it is practically so - assuming
one's definition of scientific knowledge is limited to what can be measured.
I do not view chance as being inconsistent with God's omniscience since even if
there is an infinite dimension to nature's fluctuations and hence possibilities,
God's knowledge and control are not threatened since even our mathematics implies
different levels of infinity! Furthermore, God's sovereignty in not impinged upon
since to role a 7 on a six sided die numbered 1 - 6 is impossible; this is one way
of interpreting what the verse "...God determines the outcome" means.
Sincerely
George
--George Andrews Jr.Assistant Professor PhysicsLeTourneau Universityandrewsg@letu.edu