A unified theory correcting Einstein-Laub electrodynamics solves dilemmas in the photon momenta and electromagnetic stress tensors

To unify and clarify the persistently debated electromagnetic stress tensors (ST) and photon momenta, we establish a theory inspired by the Einstein-Laub formalism inside an arbitrary macroscopic object immersed in any complex medium. Our generalized Einstein-Laub force and ST yield the total force experienced by any generic macroscopic object due to the internal field interacting with its atoms, charges and molecules. Appropriate scenarios are established for the conservation of a newly proposed momentum that we call non-mechanical generalized Einstein-Laub momentum, along with the kinetic and canonical momenta of photons. Our theory remains valid even in a generally heterogeneous or bounded embedding background medium without resorting to hidden momenta, and unambiguously identifies the existence domain, or validity domain, of the STs and photon momenta proposed to date. This existence domain is the region either outside a macroscopic scatterer with only exterior fields, or at its interior with only inside fields. The appropriate identification of such existence domain constitutes the basis of our unified theory. Finally, a thought experiment is proposed, which shows that the appropriate force and the photon momentum in the embedding medium can also be properly identified if the background is comparatively larger than the embedded scatterer. It also explains the fully different roles of the Abraham and Minkowski photon momenta in the embedding medium. Most importantly, our unified theory reveals that a unique formulation of the momentum conservation law is unfeasible, though a generalized expression of the ST and momentum density is achievable in terms of new concepts that we introduce, namely, the effective polarization and effective magnetization.