Where does the classical limit begin?

[hawkingfan]

I'm thinking about where the classical limit would begin in terms of a particle's rest mass. If we start at the smallest mass scales consisting of subatomic particles, we would have to use quantum mechanics (due to the significant wave nature of particles with small momenta). If we consider heavier things such as atoms, and some molecules, we can still use quantum mechanics. If we go farther into macroscopic things such as a speck of sand, a baseball, etc, then we use classical mechanics. Exactly where do we stop using classical mechanics. Can bacteria qualify as classical particles to a good approximation? What about smaller things like viruses? Is classical mechanics good enough or is too innacurate?

 

[Winzer]

As far as I know there is no EXACT scale where the transition from classical to quantum takes place. There are fuzzy regions where phenomenon can be modeled semi-classically, etc.

You might find http://en.wikipedia.org/wiki/Mesoscopic_physics" wiki article on Mesoscopic Physics interesting.

 

[alxm]

The quantum-chemical perspective may be illuminating:
Within QC, nuclei are typically modeled as being wholly classical or semi-classical.
For the dynamics of hydrogen transfer in some situations, the effect of proton tunneling can be measured, but even then it can be regarded more as a correction to the classical behavior. For heaver elements (Z > Be or so) I don't even think it's measurable in 'ordinary' circumstances. Obviously you have BECs, and double-slit diffraction has been measured for C60, but the former is a rather extreme circumstance and the latter effect isn't enough to be chemically significant.

So all electronic and chemical properties of an atom/molecule (bonding, ionization potentials, etc) all radiation/matter interactions, intermolecular energy transfer of other sorts, all electron kinetics, and some proton kinetics are quantum-mechanical. Vibrational and rotational energy levels are well treated semi-classically. Molecular structure, large scale molecular motion/diffusion, chemical reaction rates etc are classical.

For instance, the relative energies of chemical compounds and 'activated complexes' (in transition-state theory) are entirely quantum-mechanical in their origin. But the resulting equilibria and reaction rates are well-described with classical statistical themodynamics once you know the energies.

Ask me what the vibrational energy levels of a molecule are, and I have to use QM to some extent to get the answer, even if it means a simplified harmonic-oscillator or Morse potential (i.e. a semi-classical description is fine as long as I can ignore vibronic coupling, in other words, as long as the electrons don't get involved too much). But the distribution of the vibrational levels in a system? Classical stat-mech. The origin of the vibrational potential-well? Quantum mechanical.

In short it all meshes together nicely. You don't just stop using QM at one level and switch to classical (or vice versa), there's a range of semi-classical models that bridge the gap.

 

[sweet springs]

Hi.
How about Compton wavelength λ=h/mc for your purpose? Compton wavelength of the electron is 2.4263102175±33×10−12 meters according to Wiki. This is the limit of position measurement of the particle. Your effort to measure beyond the limit cause particle-antiparticle pairs and make measurement of the position mess. If you handle particle in motion, Δx Δp > h'/2 gives you another larger scale of quantum/classical transition, Δｘ～10−10 meters for electron in atom. 　
Regards.