  Since almost all phenomena electrodynamics deal with have energy scales much
lower than the Higgs mass energy and intermediate boson energy, electrodynamics
of continuous media should be applicable and the constitutive relation of
spacetime/vacuum should be local and linear. What is the key characteristic of
the spacetime/vacuum? It is the Weak Equivalence Principle (WEP I) for
photons/wave packets of light which states that the spacetime trajectory of
light in a gravitational field depends only on its initial position and
direction of propagation, and does not depend on its frequency (energy) and
polarization, i.e. nonbirefringence of light propagation in spacetime/vacuum.
With this principle it is proved by the author in 1981 in the weak field limit,
and by Lammerzahl and Hehl in 2004 together with Favaro and Bergamin in 2011
without assuming the weak-field condition that the constitutive tensor must be
of the core metric form with only two additional degrees of freedom - the
pseudoscalar (Abelian axion or EM axion) degree of freedom and the scalar
(dilaton) degree of freedom (i.e. metric with axion and dilaton). In this
paper, we review this connection and the ultrahigh precision empirical tests of
nonbirefringence together with present status of tests of cosmic Abelian axion
and dilaton. If the stronger version of WEP is assumed, i.e. WEP II for photons
(wave packets of light) which states in addition to WEP I also that the
polarization state of the light would not change (e.g. no polarization rotation
for linear polarized light) and no amplification/attenuation of light, then no
Abelian (EM) axion and no dilaton, and we have a pure metric theory.
