Point of Demarcation between Quantum and Classical Behavior

[Twodogs]

[Moderator's note: spin off from previous thread due to topic change.]

Reading here that in QM it is not possible to explicitly define path, yet it seems in the everyday world that path can be sufficiently defined so as to land a rover on Mars. Is that ultimately illusory or is there a point of demarcation between the realms. Disregard if is this is off topic. Thanks.

 

[vanhees71]

The Mars rover is a many-body system, and "many" here means really "many"! Note that 12g carbon is about 1mol consisting of about $6 \cdot 10^{23}$ $^{12}\text{C}$ atoms.

Of course you cannot solve the quantum many-body problem for all these particles in minute detail using quantum mechanics or even relativistic quantum field theory to also describe the atomic nuclei as bound states of quarks and gluons, etc.

To handle the Mars rover you need an effective theory for the relevant, macroscopic degrees of freedom, which are a only a few, i.e., you can coarse grain the detailed dynamics tremendously. After all you end up with classical Newtonian mechanics for a body moving in the (also Newtonian) gravitational field of the Sun and the planets of our solar system.

There's no contradiction between the classical theories of physics, which are approximations of the fundamental physics adequate for a pretty large realm of applicability, including "rocket science" :-).

 

[Twodogs]

The Mars rover is a many-body system, and "many" here means really "many"! Note that 12g carbon is about 1mol consisting of about $6 \cdot 10^{23}$ $^{12}\text{C}$ atoms.

Of course you cannot solve the quantum many-body problem for all these particles in minute detail using quantum mechanics or even relativistic quantum field theory to also describe the atomic nuclei as bound states of quarks and gluons, etc.

To handle the Mars rover you need an effective theory for the relevant, macroscopic degrees of freedom, which are a only a few, i.e., you can coarse grain the detailed dynamics tremendously. After all you end up with classical Newtonian mechanics for a body moving in the (also Newtonian) gravitational field of the Sun and the planets of our solar system.

There's no contradiction between the classical theories of physics, which are approximations of the fundamental physics adequate for a pretty large realm of applicability, including "rocket science" :-).

Thanks.
I watched a tutorial in which a post doc worked through the math suggesting that there is a mass/energy bound to the quantum realm. By his reckoning, a speck of dust floating in a light breeze is outside the quantum realm by twenty orders of magnitude. Not sure I have expressed it clearly here, but wonder if there is an approximate demarcation - classical/quantum.

 

[A. Neumaier]

wonder if there is an approximate demarcation - classical/quantum.

Typically, systems with 10000 to a million atoms are in the grey zone in between. But it depends on the accuracy with which you want to model things.

 

[vanhees71]

Hm, wait for ever better experiments :-).

 

[Vanadium 50]

Point of demarcation? You mean a spot where om one side behavior is purely classical and on the other purely quantum? There is no such point.

Further, some systems never become purely classical. You cannot understand the specific heats of metals with classical electron behavior. The fact that you can buy an oven mitt at all is proof of quantum mechanics.

 

[Demystifier]

The fact that you can buy an oven mitt at all is proof of quantum mechanics.

Can you elaborate a bit, why is QM necessary to understand how oven mitt works?

 

[PeroK]

Can you elaborate a bit, why is QM necessary to understand how oven mitt works?

I thought that buy was the operative word. I.e. that somehow the success of global capitalism was proof of QM.

 

[Vanadium 50]

Classically, the specific heat of metals is very high, so it would take many hours or days for a cookie tray to heat up. No need for an oven mitt after 30 minutres - you could just grab it. (Further, if it did heat up, there would be so much heat present that the nearby area would become an oven and the mitt would be useless)

 

[A. Neumaier]

Classically, the specific heat of metals is very high, so it would take many hours or days for a cookie tray to heat up. No need for an oven mitt after 30 minutres - you could just grab it. (Further, if it did heat up, there would be so much heat present that the nearby area would become an oven and the mitt would be useless)

Nevertheless, engineers use successfully classical physics to describe the thermodynmaical and elastic properties of metals. The prediction of material properties requires quantum physics, but not the macroscopic consequences of these properties.

 

[Vanadium 50]

So?

My point is that there is no point in which the specific heat of metals is anywhere near its classical limit. There is no "point of demarcation".

 

[A. Neumaier]

So?

My point is that there are different possible interpretations of what a quantum/classical boundary means, and one of them has a meaningful though somewhat fuzzy answer. So it is likely that the OP meant that.

 

[vanhees71]

The funny thing is that in a way both points of view are right. You can of course describe the thermodynamics of a piece of metal classically taking the specific heat simply as an empirical input ("phenomenological thermodynamics").

On the other hand it's true that the failure of the classical Drude model to explain the deviation from the Dulong-Petite prediction for the contribution of the "free electrons" (conduction electrons) to the heat capacity:

https://en.wikipedia.org/wiki/Free_electron_model

At room temperature you can usually neglect the contribution from the conduction electrons due to quantum degeneracy and are left with the Dulong-Petit value from the lattice vibrations alone, $3Nk$:

https://en.wikipedia.org/wiki/Dulong–Petit_law

The explanation for this discrepancy to the classical Drude model is one of the earliest application of Fermi statistics and is due to Sommerfeld, extending the classical model to the Drude-Sommerfeld model.

I guess that's what @Vanadium 50 is referring to.