Question

Is Continuous Localization Enough to Explain the Quantum/Classical Divide?

Answer 1

Fundamentally/foundationally, all physics is quantum. However, to use quantum mechanics to describe the fall of the apple would be ludicrous. …but why?

Well, of course is ℏℏ the hallmark signature of all that is quantum, right? So, for any particular system and process, we must compare any and all commensuratecharacteristic observable quantities of the system with ℏℏ, and see where we stand. So, how about that apple? It has about 0.100 kg, and let’s say that it is about 2.00 m above ground, and weighs about (0.100×9.81)(0.100×9.81)N… but none of that is commensurate with ℏ=1.05×10−34ℏ=1.05×10−34J·s. Well, the gravitational potential energy of that apple which would get converted into kinetic energy were it to fall on my head, 1 m above ground, as I sit under it equals m⋅g⋅h=(0.100⋅9.81⋅1=0.981)m·g·h=(0.100·9.81·1=0.981)J. …not there yet, but getting closer. The apple will be falling 2h/g−−−−√=(2⋅1.00/9.81−−−−−−−−−−√≈0.4522h/g=(2·1.00/9.81≈0.452s, which gives us an estimate of (Hamilton’s action) for the apple-falling-process: Saf=∫0.4520dt L≈0.443Saf=∫00.452dt L≈0.443J·s. Ta-dah! This is a characteristic of the process at hand, and it is a goody-good 34–35 orders of magnitude bigger than ℏℏ, which implies that quantum corrections to observables in this process are likely to be suppressed by powers of (ℏ/Saf)(ℏ/Saf), which is obviously negligible.

Now repeat this analysis with grains of rice, sand, … all the way down to atoms.

And then re-think the answer, and notice that it is a bit of a cheat: I compared the (Hamilton’s) action, SafSaf, with ℏℏ. But, what if I’m measuring the energy? Or the time of fall? Or the impulse? … which is why I wrote “are likely to be suppressed…” Also, the considered system may well have other observables that are commensurate with ℏℏ; angular momentum comes to mind… (For giggles: compare the angular momentum of a typical pirouetting ballerina and a spinning ammonia molecule to ℏℏ.)

Answer 2

that decoherence is only accepted up to a certain level, or for certain specific situations, otherwise its an obvious route, so, I would appreciate any answers to sort this out for me. I am not sure its the same question Sean is asking, apologies if it is.