  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.
