We review the available conceptual, theoretical and experimental evide
nce according to which physical media in general, with particular refe
rence to the hyperdense media in the interior of hadrons, alter the Mi
nkowskian spacetime with local speeds of light which are generally sub
luminal for media of low density (such as planetary atmospheres), and
superluminal for media of high density (such as hadrons). We show that
the isominkowskian geometry can provide the only known geometrization
of the spacetime of physical media which is: (1) universal, in the se
nse of applying for all possible signature-preserving spacetimes; (2)
direct, in the sense of holding within the given inertial frame of the
observer for all possible spacetimes; (3) invariant, in a way equival
ent to that of the conventional spacetime; (4) axiom-preserving, thus
permitting the preservation of the axioms of the special relativity an
d their extension to arbitrary speeds; and (5) an agreement with the a
vailable preliminary experimental data. Specific experiments are discu
ssed in detail for the resolution of the still open problems of the sp
acetime and related basic laws holding in the interior of the hyperden
se hadrons.