# When are quantum corrections significant for EM?

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1. Apr 23, 2015

### itssilva

As a rule of thumb, we might say that quantum theory becomes essential when we're analyzing systems at small distances (of the order of atomic sizes or less) and few enough particles (suppose particle number is conserved, as in QM); however, the world as a whole is quantum, and even a system which can succesfully be described by the classical framework is amenable to have its predicted values (energies, position expectation, etc) corrected to a small degree; such is also with electrodynamics.
However, I haven't been able to figure under which conditions you HAVE to consider the quantum nature of the EM field to have reasonable agreement with experiment, at the same level as in, we can't adequately describe electrons in atoms with classical mechanics. I know, for instance, of the existence of the Lamb shift, but overall it's a tiny correction to the relativistic energy eigenvalues of the hydrogen atom; are all quantum corrections of the EM field doomed to be small like it, or are there some conditions - particularly within atomic physics - under which they lead to results very distinct from the classical/semiclassical approach?

2. Apr 23, 2015

### Staff: Mentor

I think that is an important effect.
You cannot describe chemical bonds with classical electromagnetism. Macroscopic properties depend on those chemical structures. You can replace the detailed desciption with effective models, but there is no way to describe anything solid or liquid on a fundamental level with classical mechanics.

3. Apr 24, 2015

### ChrisVer

Well, I am not sure about that but...
If you consider the photon quantum field as infinite many harmonic oscillators (HO), the answer can be seen for when an HO can be treated classically... I think the right answer is when the number of your modes is way too large (so for example the energy $E_{N}$ will be almost the same with $E_{N+1}$ (discrete energies become continuous).
So my guess: when you say you have many photons whose energies are too large. I guess the measure is put by $\hbar$?

4. Apr 26, 2015

### itssilva

Indeed; but according to what I learned in my grad course, chemical bonds exist mainly because of exchange effects due to the antisymmetric nature of electronic wavefunctions. I was thinking something a little bolder, like: can photons be made to create chemical bonds based mainly on the quantum nature of the EM field? Semiclassicaly, there are computational reports that indicate the viability of making new types of chemical bonding with strong magnetic fields (http://www.sciencemag.org/content/337/6092/327.figures-only), but, as far as quantized EM fields contribute in stuff like this, I know zippo. There's this field theory (http://en.wikipedia.org/wiki/Euler–Heisenberg_Lagrangian) used to calculate photon-photon scattering under external strong fields, but even there the effects are tiny, so my hopes regarding significant photon-matter quantum corrections seem further down the drain.

5. Apr 27, 2015

### vanhees71

In atomic physics you start with the description of the atomic nucleus as a (static) classical field (Coulomb field in zeros approximation). Generally, you come pretty far with the semiclassical approximation (quantum theory of charged particles with the electromagnetic field treated classically). Particularly the often used photoelectric effect is well-described in this approximation. Contrary to claims in many textbooks it's not proof of the quantization of the electromagnetic field. In atomic physics the most famous radiation-correction effect is the Lambshift, which started the whole development of modern QFT (renormalization of QED; Shelter Island and Pocono conferences in the late 1940ies with Feynman and Schwinger as the main contributors; also closely followed by the Swiss contribution by Pauli and Weisskopf).

6. Apr 27, 2015

### itssilva

So, am I to assume all quantum corrections in a theory involving atoms are expected to be of the order of the Lamb shift, regardless of experimental conditions (strong external EM field or whatnot) ? More broadly, is there any situation (say, in quantum optics) where quantum electrodynamics needs to be used for us to be able to make decent predictions? Like mentioned in post #4, photon-photon scattering is hard to detect even under external strong fields...

7. Apr 28, 2015

### vanhees71

Sure, in Quantum Optics a lot is about the quantum nature of the em. field. Many of the most precise tests of quantum theory are done with photons, particularly concerning entanglement with biphotons, the violation of the Bell inequality and related issues.