When do classical mechanics and electromagnetics stop working?

[jmheer]

I've heard that classical mechanics and electromagnetics are not applicable at small sizes in particle physics.
1) At what size and energy levels are they no longer considered to be applicable at all?
2) What range of size and energy levels could be considered a "transition" area where both classical and quantum are applicable to some degree?
3) What determines the "cut-off" between areas of applicability?

Thanks!
-Joe Heer

 

[berkeman]

What have you found in your reading so far?

Certainly classical models do not work for electron orbitals in atoms, correct? Can you say why not?

 

[PeterDonis]

I've heard

Where? Can you give any specific references?

 

[Nugatory]

What determines the "cut-off" between areas of applicability?

There’s no cut-off. There are phenomena such as the beam splitting demonstrated by the Stern-Gerlach experiment or the stability of atoms which are predicted by quantum mechanics and inexplicable by classical mechanics - naturally we apply QM to these.

Large collections of atoms (cannonballs and clouds and people and just about everything else that we encounter in our daily lives) do not usually exhibit such behavior so we apply classical mechanics to these - not because QM isn’t applicable but because the math is way easier.

 

[jmheer]

What have you found in your reading so far?

Certainly classical models do not work for electron orbitals in atoms, correct? Can you say why not?

As I understand it, the classical Rutherford & Bohr models where electrons are treated as point particles orbiting a nucleus do not work because the electrons would undergo centripetal acceleration to stay in orbit, and accelerating point charges radiate (Larmor equation). So the electrons would lose energy and quickly spiral into the nucleus.

 

[jmheer]

There’s no cut-off. There are phenomena such as the beam splitting demonstrated by the Stern-Gerlach experiment or the stability of atoms which are predicted by quantum mechanics and inexplicable by classical mechanics - naturally we apply QM to these.

Large collections of atoms (cannonballs and clouds and people and just about everything else that we encounter in our daily lives) do not usually exhibit such behavior so we apply classical mechanics to these - not because QM isn’t applicable but because the math is way easier.

So if I understand what you are saying:
1) Quantum mechanics always applies, at all size and energy scales, but is not used for larger scales because of the complexity of the math.
2) Classical mechanics, which has much easier math, is not used for certain classes of problems because the classical methods that we have don't work for those classes of problems.

 

[Nugatory]

but is not used for larger scales

Most often it is not the size scale (quantum mechanical effects can affect observations at interstellar distances, as in the Hanbury-Brown-Twiss effect) but rather the number of particles involved. It's difficult to keep a large number of particles in the coherent superposition required to demonstrate quantum mechanical effects so we seldom find objects composed of a large number of particles behaving non-classically. There are exceptions, such as superfluidity and superconductivity, but it requires extraordinary efforts to get the system into a state where these appear.

tl;dr: Stop looking for a "cutoff", instead understand for each problem whether neglecting quantum mechanical effects is an acceptable approximation.

 

[vanhees71]

I've heard that classical mechanics and electromagnetics are not applicable at small sizes in particle physics.
1) At what size and energy levels are they no longer considered to be applicable at all?

For point particles classical mechanics and electromagnetics do not consistently work already at the one-particle level. There is no self-consistent description of the accelerated motion of a classical point charge, because the radiation-reaction problem has not been fully solved after more than a century of effort. The best one can do is to use the Landau-Lifshitz approximation of the Lorentz-Abraham-Dirac Equation. This is a result in first-order perturbation theory for the radiation reaction.

The problem is satisfactorily solved by the renormalization of QED, valid to all orders in perturbation theory.

2) What range of size and energy levels could be considered a "transition" area where both classical and quantum are applicable to some degree?

There is no fundamental transition in dependence of the size of systems known. There are macroscopic quantum phenomena for macroscopic objects like superconductivity or suprafluidity, where the collective behavior of a many-body system must be described quantum-theoretically.

 

[nightvidcole]

`Quantum effects become significant when you can make measurements precisely enough that Δx Δp ~ ℏ , or ΔE Δt ~ ℏ , where the uncertainties are defined based on the precision of your measurement. Somewhat relatedly, quantum effects show up when the dynamics of the system (such as its oscillation frequency) are so sensitive to the motion that you can easily observe a change in the system's energy on the order ΔE ~ ℏω , where ω is the classical (angular) frequency. The same applies when you can easily observe a change in the system's momentum on the order Δp ~ ℏk with k being a wavenumber relevant to the system (or the equivalent lattice vector, in the case of diffraction from a crystal).