Re: [asa] Results of Cameron's Survey

From: George Murphy <GMURPHY10@neo.rr.com>
Date: Mon Jun 29 2009 - 19:22:16 EDT

Iain -

If it's just a matter of studying solutions of a system of DEs then there's
no need to make any connection with quantum theory. But if the Lorenz
system is supposed to describe trurbulent flow under some conditions (which
was, I believe, why Lorenz originally focused on it) then there is - because
the fluid is made up of molecules to which QM & the uncertainty relation
applies.

Shalom
George
http://home.roadrunner.com/~scitheologyglm

----- Original Message -----
From: "Iain Strachan" <igd.strachan@gmail.com>
To: "George Murphy" <GMURPHY10@neo.rr.com>
Cc: <asa@calvin.edu>
Sent: Monday, June 29, 2009 6:44 PM
Subject: Re: [asa] Results of Cameron's Survey

On Mon, Jun 29, 2009 at 5:10 PM, George Murphy <GMURPHY10@neo.rr.com> wrote:
>
> Iain -
>
> This gets into the murky area of the interface between classical chaos
> theory & quantum mechanics, where I claim no great expertise. Since
> quantum mechanics is linear there's no "quantum chaos" in a
> straightforward sense. But in specifying the initial conditions more &
> more precisely for a classical system, as you suggest below, you'll
> eventually get to the limit specified by the uncertainty principle, &
> below that point you can't go. With a strong interpretation of QM even God
> can't because the uncertainty principle is not just about limits on what
> we can measure but is a statement that position-momentum pairs that
> violate it don't exist.

Ah yes, of course I'd forgotten the quantum uncertainty. But that
only applies to things like position and momentum (which would of
course apply to my Lorenz Attractor example - initial conditions).
However it would not apply to the fine-tuning of the constants of the
universe. Hence there are constants in the Lorenz attractor (this
from the Wikipedia page):

## Lorenz Attractor equations solved by ODE Solve
## x' = sigma*(y-x)
## y' = x*(rho - z) - y
## z' = x*y - beta*z
function dx = lorenzatt(X,T)
    rho = 28; sigma = 10; beta = 8/3;
    dx = zeros(3,1);
    dx(1) = sigma*(X(2) - X(1));
    dx(2) = X(1)*(rho - X(3)) - X(2);
    dx(3) = X(1)*X(2) - beta*X(3);
    return
end

Note that the line starting rho = 28 specifies not the initial
conditions, but the constants of the system. One might imagine there
is much greater scope for fine adjustments of these. Different values
of rho give very different behaviour of the system.

So generalising to the Universe, maybe the Creator has much more fine
choice over things such as Planck's constant , or the Fine Structure
Constant than would be allowed by Quantum uncertainty.

Iain

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Received on Mon Jun 29 19:23:19 2009

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