I did study physics, and our statistical physics lecture only derived thermodynamic laws.
We also had a somewhat shoddy derivation of Newton's Laws from the Schrödinger equation, but wasn't really satisfactory either, because it doesn't really answer the question when I can treat things classically.
What I'd really like (and haven't seen so far, but also haven't searched too hard) is the derivation of an error function that tells me how wrong I am to treat things classically, depending on some parameters (like number of particles, total mass, interaction strength, temperature, whatever is relevant).
(Another thing that drove me nuts in our QM classes where that "observations" where introduced as: a classical system couples to a quantum system. Which presupposes the existence of classical systems, without properly defining or delineating them. And here QM was supposed to be the more fundamental theory).
>What I'd really like (and haven't seen so far, but also haven't searched too hard) is the derivation of an error function that tells me how wrong I am to treat things classically, depending on some parameters (like number of particles, total mass, interaction strength, temperature, whatever is relevant).
There are plenty of ways to do this and things like Wigner functions literally calculate quantum corrections to classical systems.
But generally if you can't even measure a system before it's quantum state decoheres then it's quantum status is pretty irrelevant.
I.e. the time it takes for a 1 micrometer wide piece of dust to decohere is ~10^-31 s and it takes a photon ~10^12s to cross it's diameter. So it decoheres 10 billion billion times faster that a photon could even cross it.
The error is usually taken as ratio of wavelength to your desired precision, but in general depends on your use case, sometimes you have full precision all the way down, sometimes you have insufficient precision on astronomic scale. Quantum physics doesn't have an absolute scale cutoff.
We also had a somewhat shoddy derivation of Newton's Laws from the Schrödinger equation, but wasn't really satisfactory either, because it doesn't really answer the question when I can treat things classically.
What I'd really like (and haven't seen so far, but also haven't searched too hard) is the derivation of an error function that tells me how wrong I am to treat things classically, depending on some parameters (like number of particles, total mass, interaction strength, temperature, whatever is relevant).
(Another thing that drove me nuts in our QM classes where that "observations" where introduced as: a classical system couples to a quantum system. Which presupposes the existence of classical systems, without properly defining or delineating them. And here QM was supposed to be the more fundamental theory).