How small does a system have to be for QM to be necessary?

[dRic2]

If we are talking bout a single atom QM is obviously necessary, but when we are talking about a bunch of molecules (like gases/fluids) statistical mechanics works fine too. I remember it has something to do with $\hbar$ but I don't remember much and I can not quantify it.

Thanks

 

[ZapperZ]

If we are talking bout a single atom QM is obviously necessary, but when we are talking about a bunch of molecules (like gases/fluids) statistical mechanics works fine too. I remember it has something to do with $\hbar$ but I don't remember much and I can not quantify it.

Thanks

It has nothing to do with size. It has everything to do with the size of coherence. Remember that in a superconductor, the entire supercurrent is a "quantum object" and exhibit quantum properties. That's is relatively big. In the Delft-Stony Brook experiment, a scale of 10¹¹ particles exhibit quantum superposition properties. Particles as big as buckyballs have undergone interference effects. And we haven't even touched the superposition with mirrors.

Certainly, the larger the object, the more difficult it is to maintain coherence throughout the entire entity. But again, there's nothing that we know of so far that limits this size. So technically, the effects of quantum properties are all around us. We just do not notice it because the lack of coherence washes out many of their fingerprints that we expect.

Zz.

 

[dRic2]

I'm don't know very much about conductors but I liked how you proved the point.

It has nothing to do with size. It has everything to do with the size of coherence.

This bring back to my mind something I read a while ago in Feynman's "Six Easy Pieces". There are some interesting thoughts about this. I really enjoyed the reading (even though it is supposed to be divulgative).

In the Delft-Stony Brook experiment, a scale of $10^11$ particles exhibit quantum superposition properties.

Very interesting. I just did a quick search on google and I was wondering: isn't this about entanglement? Probably I'm wrong but I use "superposition" to address the property of wavefunctions to be combined ($ψ = Σc_nψ_n$), am I wrong?

Anyway I should probably rephrase my question: when QM is needed to make accurate calculations (except for electromagnetic phenomena)? For example, if I want to analyze the properties like thermal conductivity or activation energy of a reaction or density of a substance or behavior of a flame (some random example that comes to my mind) do I need QM? Because classical mechanics still works fine for that kind of things.

I think QM is useful only in stuff like superconductors or laser or something like that.

 

[dRic2]

I think QM is useful only in stuff like superconductors or laser or something like that

Because here you are playing with electrons... I feel like big molecules doesn't show enough QM effects

 

[f95toli]

Anyway I should probably rephrase my question: when QM is needed to make accurate calculations (except for electromagnetic phenomena)?

There is no straightforward answer to that question. The physical size of the system has -as ZapperZ has already pointed out- nothing to do with it; there are plenty of examples of very large systems that can only be described using QM. A nice example would be the microwave cavities used in cavity-QED experiments; these are about the size of a orange (or even larger) but when cooled to a low enough temperature their EM properties can only be described using QM.

Another -more recent example- would be the small quantum computers (20-50 qubits) that are now being demonstrated; the chips are typically 10x10mm2 or so (i.e. in many cases larger than CMOS circuits) but the interaction between the different elements of the circuits (qubits, resonators etc) can only be described using QM.

Roughly speaking it has to do with which property you are interested in and how well insulated you system is from the environment. Electromagnetic properties are fairly "easy" to get into the "QM realm" but there are also lots of examples of mechanical (MEMS) resonators that exhibit e.g. superposition of states and these are so large that you can easily see them in a normal optical microscope.

 

[Vanadium 50]

I feel like

I don't think this is a very good argument. Nature is not compelled to arrange itself in a way you find favorable.

If you want to understand heat capacities of metals - bulk metals that you can hold in your hand - the classical model of Drude is off by something like 100. You need to treat the electrons quantum mechanically to get the right answer. If it weren't for QM, you couldn't use pots and pans when cooking.

 

[dRic2]

Thank you for the replies. I know my question is kind of silly and vague and if you wonder how it got into my mind here's the explanation.

I've always been a classical physics guy. Last year I started to get involved in QM with some courses at the university, but it felt like an "elitist" (google translate) subject, maybe because I'm totally ignorant in electronics and related stuff. So, since QM was born basically to explain the hydrogen atom and light phenomena, I thought that QM comes in hand for the small things.

I also noticed lots of example (not all) proposed involves electronics (which I've never studied), so this explains my lack of knowledge in the field