Re: Determinacy in classical physics (naive question)

From: Andrew B. Park (novakyu_at_yahoo.com)
Date: 07/17/04 

Date: 17 Jul 2004 15:08:54 -0700

(snip)

I thought determinacy was much simpler than that. It simply means, when
you do an experiment, and repeat that same experiment under the same
conditions, you will get one, and only one "determined" result. (So, it
is possible, given that you know _exact_ initial velocities and
positions of _all_ the particles involved, as well as _exact_ forces
between them, the future of the interaction of those particles is
determined. Of course, QM does not allow this.)

The way QM is nondeterministic is in the uncertainty principle (well...
I think it's taken as an axiom--that or, you accept [x,p] = ihbar,
instead of [x,p]=0, as CM asserts,... you can start from either and
reach the other conclusion). This could be taken to mean that there is
no such thing as _exact_ velocity and position (or knowing it). You can
know _exact_ velocity only when you allow infinite uncertainty in
position (so, velocity has very little meaning... except maybe when you
get momentum out of that), and you can know _exact_ position only when
you allow infinite uncertainty in velocity--so you know where the
particle is exactly right now, but you have no idea where it's going
next.

So, determinacy is just that: the idea of knowing _exact_ positions,
velocities, and forces-being-acted on of all the particles. This isn't
something that can be derived from CM--it's one of the assumptions (and
if I recall my first semester of engineering physics correctly, an
implicit assumption) of CM.

Best wishes,

Andrew

PS. Oh, yeah--in QM, you can have _exactly same_ (as far as
theoretically possible, in any case) experimental setting, and your
experimental results from one experiment to the next will vary--only
the probability of getting certain result does not vary (and that's why
QM is a probabilistic theory, instead of a deterministic theory).

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