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To unify and clarify the persistently debated electromagnetic stress tensors(ST) and photon momenta, we establish a theory inspired by the Einstein-Laubformalism inside an arbitrary macroscopic object immersed in any complexmedium. Our generalized Einstein-Laub force and ST yield the total forceexperienced by any generic macroscopic object due to the internal fieldinteracting with its atoms, charges and molecules. Appropriate scenarios areestablished for the conservation of a newly proposed momentum that we callnon-mechanical generalized Einstein-Laub momentum, along with the kinetic andcanonical momenta of photons. Our theory remains valid even in a generallyheterogeneous or bounded embedding background medium without resorting tohidden momenta, and unambiguously identifies the existence domain, or validitydomain, of the STs and photon momenta proposed to date. This existence domainis the region either outside a macroscopic scatterer with only exterior fields,or at its interior with only inside fields. The appropriate identification ofsuch existence domain constitutes the basis of our unified theory. Finally, athought experiment is proposed, which shows that the appropriate force and thephoton momentum in the embedding medium can also be properly identified if thebackground is comparatively larger than the embedded scatterer. It alsoexplains the fully different roles of the Abraham and Minkowski photon momentain the embedding medium. Most importantly, our unified theory reveals that aunique formulation of the momentum conservation law is unfeasible, though ageneralized expression of the ST and momentum density is achievable in terms ofnew concepts that we introduce, namely, the effective polarization andeffective magnetization.

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