Nonlinear electrodynamics in vacuum remains a relatively unexplored topic, as the intensities required to reach the nonlinear regime make it difficult to test in the laboratory. There are thus several competing theories of nonlinear electrodynamics, distinct from each other in theory but not yet having been ruled out by experiment [1,2]. The standard theory (derived from QED) is the Heisenberg-Euler model, which treats vacuum as a polarizable medium through the production of virtual electron-positron pairs. This model has had success in explaining (for example) the Lamb shift in hydrogen, but in recent years significant discrepancies (of ~7σ) have appeared when applied to muonic hydrogen and muonic deuterium, where the heavier muon is 200 times closer to the nucleus and thus experiences a much stronger electric field [3,4].
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