QED vacuum as a classical dielectric medium?

Question

I have heard this analogy a few times, particularly in the context of vacuum polarization. To what extent can the QED vacuum be modeled as a classical dielectric medium? Can one compute effective linear and nonlinear susceptibilities of this medium from QED? I am aware of the Born-Infeld theory and its relation to QED vacuum polarization, but I am also interested in higher-order effects like photon-photon scattering, which would involve third-order nonlinear susceptibility.

Answer 1

WP quote:

"When Planck's constant is hypothetically allowed to approach zero, QED vacuum is converted to classical vacuum, which is to say, the vacuum of classical electromagnetism."

As long you fulfill the above condition you should be able to reach the same results with the $ε_{0}$, $μ_{0}$, classical dielectric vacuum using QED.

By nullifying the Planck's constant space is no more quantized and becomes a continuum.

Note: Classical vacuum is not a material medium, but a reference state used to define the SI units. Its permittivity is the electric constant and its permeability is the magnetic constant, both of which are exactly known by definition, and are not measured properties. See Mackay & Lakhtakia, p. 20, footnote 6

Answer 2

Yes. This is seen more clearly when the charge and field amplitudes are set in SI units, instead of Gaussian, which mixes in the permittivity with the charge and fields and obfuscates the true nature and significance of what renormalization is and what it is doing: the renormalization coefficient $Z_3$ goes with the permittivity $ε_0$, not with the charge or field amplitudes. It is not the charges and fields that are being renormalized, and "dressed", in QED, but the permittivity - and therefore the vacuum itself. Only the Gaussian "charges" and "fields" are being dressed, because of their mixing the permittivity into their respective definitions.

I lay this out more fully in my reply here: Gaussian Unit Of Charge And Force.

An analogous statement can also be made about gauge fields.

In another reply you will see the (obvious) non-sequitur that the vacuum is "not a material medium, but a reference state used to define SI units" - which says nothing and means nothing, with respect to this question and is therefore irrelevant. In addition to being irrelevant, it is also false - since 2019. The items now put on the A-list by SI are Planck's constant and the electron charge, in place of That Kilogram Bar in Paris and the vacuum permeability (and, by extension: the vacuum permittivity, since vacuum light speed was and still is on the A-list). Right now, both vacuum permittivity and vacuum permeability are free-running, relative to the SI system, constrained only by their product being calibrated relative to SI units.

Neither permittivity nor permeability are used to calibrate or define SI units, any longer.

But in any case, being on the A-list does not make you, somehow, "less real", "less physical", "conventional" or contrived, and such arguments are non-sense. Otherwise, you'd be forced to now say that about Planck's constant and the electron charge, since 2019. Humans are not part of the Q continuum. They don't define the coefficients that govern the universe, but only measure them and calibrate their units to them.