# Classical Mechanics WITHOUT determinism?

1. May 24, 2005

### ZapperZ

Staff Emeritus
First of all, a disclaimer. I am making NO vouch for the validity of this paper. I just found it an amusing read and thought it's a twist from what normally happens. Typically, we tend to think that classical mechanics, even classical statistics, is completely deterministic, and that only when we get to the quantum scale would such thing be an issue for debate.

But here, it seems to also apply to classical mechanics, where you get rather "predictable" dynamics even when one do not start off with a deterministic system.

http://arxiv.org/abs/quant-ph/0505143

Have a go at it and see what you think...

Zz.

2. May 24, 2005

### Juan R.

A note. Many people tends to think that classical mechanics is deterministic and quantum mechanics is indeterministic. Still is exactly the inverse.

Precisely Schrödinger equation is purely deterministic and indeterminism arises when there is contact with a measurer. Precisely the measurer is a classical object like emphasized by Böhr. If the measuring apparatus is a quantum object, the whole system is quantum one and perfectly described by a Schrödinger deterministic equation.

Precisely are the large systems where the deterministic formulation fails. precisely are large systems (some are called LPS).

Usual classical dynamics (e.g. newtonian one) is a formulation for classical systems when random components of equations are omited.

always one use

F = ma

one is using

<F> = m <a>

This is the theory of physical ensembles (does not confound with the theory of Gibbs ensembles)

And another note, the typical interpretation of classical statistical mechanics sound very very poor. It appears that you are supporting the old "coarse grained" interpretation of statistical mechanics is (really outdated) on the framework of physical and mathematical research in the topic.

About the paper. it is another paper about a very very old idea inspired in the first-decades-formulation-of-QM-supposition that a wave function is a kind of wave in the sense of classical physics.

Any attempt to derive QM from a supposed underlying deterministic classical newer found is comdemned to failure. All atempts including

http://arxiv.org/abs/quant-ph/0505143

omit lot of important stuff.

Note the emphasis on a single particle for obtain phy(x,t). People does not abandon that kind of uggly approach by conceptual or philosophical decades ago (on 1950 if i remember correctly)

By no talk about this approach contradicts special relativity (as required in relativistic quantum field theory), does not acomodate the existence of spin, and so forth, violate the dual representations, for example, in momentum eigenspace, etc.

The role of position operator confronts with Landau uncertainty rules for photons and relativistic electrons, etc, etc, etc, etc.

And finally we obtain a rare, rather incorrect, restricted formulation that obtains no new predictions and therefore the asumption of the existence of underlying deterministic trajectories is simply an act of faith.