Re: Determinacy in classical physics (naive question)

From: lubinok (somebody_at_somewhere.co)
Date: 07/17/04 

Date: Sat, 17 Jul 2004 23:57:47 GMT

"Laurent Fortel" <no.spam.please@free.fr> wrote in message
news:40f9629d$0$15270$636a15ce@news.free.fr...
> I am no physicist, but a maths teacher trying to use his vacations time
> to have a look again at the physics he learnt as an undergraduate...
> Preliminary notice : I am definitely not reasoning as a physicist (a
> theoretical physicist perhaps...) since physical reality is NOT the
> subject of my question. Indeed my question is rather a maths question.
>
> Try to Google with "classical physics" and "deterministic". Many sources
> (most of them quantum mechanics elementary expositories) will assert
> with no detail that "classical physics is deterministic". One at least
> precises that it means the classical theory of gravitation +
> electrodynamics
> http://online.redwoods.cc.ca.us/DEPTS/science/chem/storage/Schrod/
>
> What I am looking for is a precise (mathematically formalized, ideally)
> proposition meaning that "classical physics is deterministic", and some
> directions to look for a proof.
>
> Here is a tentative compendium of what I understand presently, any help
> to go further will be welcome.
>
> 1 - About gravitation :
>
> 1a) A finite set of massive particules interacting via gravitation, in a
> newtonian space-time.
>
> This is the only thing I fully understand. Elementary differential
> equations theory asserts clearly that if I know the position and the
> velocity of each particle at t=0, every position and velocity at t=t_0
> are implied. No problem on this one.
>
> 1b) Gravitation in a continuous universe.
>
> No idea whether this is a reasonable question (but it seemed to me an
> exercice easier than struggling with Maxwell's equations...)
>
> It seems easy to write down a non-relativistic gravitation theory
> replacing the finite massive particules m_i by a distribution of volumic
> mass mu(x,y,z,t), just adding down an equation for conservation of mass.
> Doing it so, the data would be mu(x,y,z,0) and the velocity field
> v(x,y,z,0) ; "deterministic" would mean that mu(x,y,z,t) and v(x,y,z,t)
> are thence uniquely determined for each t. This reminds me of no maths I
> have met, but might be well-known. Any directions of reading ?
>
> 2 - About electrodynamics :
>
> 2b) Maxwell equations in a continuous universe (newtonian space-time
> with aether, or special relativity that is the furthest I know...)
>
> Here I think I can write down a list of variables describing the
> universe at time t=0 (mu distribution of volumic mass ; rho distribution
> of charges ; velocity field). Then I can write a list of equations
> (Maxwell equations, Newton law linking derivatives of the velocity field
> and the formula for force, conservation of mass (conservation of charge
> being implied by Maxwell equations)). "Determinacy of classical
> mechanics" would seem to mean that when you give mu, rho and v for t=0,
> their values for all t are implied. But the maths underneath seem at
> least tricky ; how can it be that such an assumption is so universally
> "well-known" while its proof is so seldom shown ? Probably I have a
> completely false idea of what "determinacy of classical
> electromagnetism" mean. Help !
>
> 2a) (For memory only) Classical electrodynamics for a finite set of
> massive and charged particles.
>
> If I was able to write a set of equations describing that, like at 1a),
> I would probably understand what their "determinacy" means, using very
> simply differential equations theory. But I suppose this is hopeless, is
> it ?

Consider Chaos Theory.
It is mostly if not wholy based on classical theory.
The results are *highly inderministic*
Butterfly wings in the Amazon and all that........etc
l.