What are the mechanisms that cause the vacuum to be nonlinear to EM excitation? Consider a electromagnetic excitation that is confined in time, and locally looks like a plane-wave traveling in a vacuum:
$$
\mathbf{E}(\mathbf{r},t) = \mathbf{\hat{x}}E_0 \cos(\mathbf{k}\cdot\mathbf{r}-\omega t) f(\mathbf{k}\cdot\mathbf{r}-\omega t),
$$
where $f$ is some envelope function like a gaussian that confines the wave to a packet moving along the wave vector at the speed of light. Suppose a corresponding $\mathbf{H}$ field exists according to Maxwell's equations. The intensity of this wave is proportional to $E_0^2$, and for some reasonable, everyday ranges of intensity, the vacuum is approximately linear, i.e., it's electromagnetic properties don't vary with changes in the intensity of the wave, and we can do things like send twice as much power into a dish antenna pointed at space and expect twice as much power to reach our satellite. However, this wave carries mass-energy, and mass-energy curves spacetime, and spacetime curvature does affect the EM properties of the vacuum.
Furthermore, it seems to me that there is some intensity limit at which quantum effects, such as virtual particles, might come into play. Perhaps the high field intensity of the wave kicks a virtual particle/antiparticle pair into reality, in the process robbing the wave of some power.
My questions are:

*

*Am I correct in identifying the two mechanisms above (mass-energy curving spacetime and EM interaction with virtual particles) as ways in which the vacuum's properties react to EM wave intensity?

*Are there other mechanisms that can cause the vacuum to change properties depending on the intensity of EM waves?

*Do we have a concrete understanding of the energy scales at which these effects could be observed? Specifically, how much intensity in Watts/m$^2$ is required to see the various nonlinear effects?

*Have these nonlinear effects in vacuum been observed in experiment? Can you please point to some references that report the results of such experiments?

 A: *

*Pair production at high field strengths is the most important factor in the nonlinearity of the vacuum. Classical E&M is correct because the fine structure constant is a small dimensionless number $(\alpha\approx 1/137)$, thus perturbation theory gives small anomalies as compared to the classical (or non-relativistic QM) result.

We don't have a theory of quantum gravity, and we don't have any experimental observations of highly charged black holes, so we can't really expect that combining QFT and general relativity give the correct results. Remember that gravity is many orders of magnitude weaker than E&M as well as the strong and weak nuclear forces, so designing an experiment which tests such deviations from classical mechanics is difficult.


*Not until you reach (electroweak) unification energies, so that weak interactions generate Feynman diagrams which contribute appreciably to the perturbation theory result. This is why the muon anomalous magnetic moment can be computed to such high accuracy using only QED.


*The answers to this are in the vacuum polarization Wikipedia article:




*See the g-factor article or the muon anomaly article.

