How does Classical Determinism Result from QM?

[Karl G.]

First, I'll start with the analogy of GR approaching the Newtonian Model under weak field conditions. Likewise, could somebody give an explanation of how the probabilistic nature of QM approaches the seemingly deterministic nature of classical mechanics in the macroscopic domain?

 

[alxm]

Karl, you keep asking questions on QM that are answered in just about every comprehensive textbook. Did you actually make any effort to find the answer yourself before asking?

See, e.g. Landau-Lifschitz, "Quantum Mechanics", Chapter 1 §6 - "The passage to the limiting case of classical mechanics."
It's not very hard.

 

[ZapperZ]

First, I'll start with the analogy of GR approaching the Newtonian Model under weak field conditions. Likewise, could somebody give an explanation of how the probabilistic nature of QM approaches the seemingly deterministic nature of classical mechanics in the macroscopic domain?

This is not that easy to explain, and it is still a highly-studied area of QM. We still do not see a clear-cut region when there is a transition (or cross-over) between QM and classical world.

The most popular explanation for the cause of QM to classical transition is decoherence. See, for example:

Johannes Kofler and Časlav Brukner, "Classical World Arising out of Quantum Physics under the Restriction of Coarse-Grained Measurements", Phys. Rev. Lett. 99, 180403 (2007).

Others, such as Roger Penrose, http://discovermagazine.com/2005/jun/cover" where the quantum system actually couples with gravity (or "gravitons" - still highly speculative and that's why it is a controversial).

So this is not that simple.

Zz.

 

[Bob_for_short]

It is not that simple but not too complicated either.

Let us consider a non relativistic electron moving in a potential and/or magnetic field. While moving it radiates randomly many photons so its position (speaking in the classical language) is fluctuating. If you sum up all these quantum events (that is called the inclusive cross section), you obtain the classical picture. In other words, the classical picture is the inclusive QM one. See my publication on this subject at arxiv:0806.2635, "Atom as a "Dressed" Nucleus" by Vladimir Kalitvianski, available also in the Central European Journal of Physics, Volume 7, N 1, pp. 1-11, 2009.

One can also understand "inclusive" as an "average over fluctuations".

Bob.

 

[StatusX]

In terms of deriving the equations of classical mechanics as a limit of those of quantum mechanics, the most direct way is through the formulation of classical mechanics using the http://en.wikipedia.org/wiki/Hamilton%E2%80%93Jacobi_equation" . This is an equation that looks very similar to the one that the phase of a wavefunction satisfies, and exactly matches it in the limit h->0.

As far as how determinism arises in this limit, remember that when h->0, all the relevant observables commute, so one can (roughly) say that you have simultaneous eigenstates of everything, and so there's no collapse or uncertainty.

 

[nikman]

An alternative, or complementary approach to traditional decoherence (already noted above) is to describe macroscopic emergence from an informatics perspective. We live in a coarse-grained world because we're coarse-grained measuring instruments. This idea annoys some people because it's kind of Copenhageny, out of Anton Zeilinger's IQOQI group in Vienna.

http://arxiv.org/pdf/quant-ph/0609079v3

Essentially the same material but adapted from a PowerPoint presentation:

http://www.fjfi.cvut.cz/workshop/Wor...asurements.pdf A recent We Beg To Differ, or Back To Decoherence:

http://arxiv.org/abs/0806.3558

 

[camboy]

There is good detailed explanation in lecture 2 of http://www.tcm.phy.cam.ac.uk/~mdt26/pilot_waves.html" from hidden variables perspective..