Einstein utilized Lorentz invariance from Maxwells equations to modify mechanical laws and establish the special theory of relativity. Similarly, we may have a different theory if there exists another covariance of Maxwells equations. In this paper,
we find such a new transformation where Maxwells equations are still unchanged. Consequently, Veselagos metamaterial and other systems have negative phase velocities without double negative permittivity and permeability can be described by a unified theory. People are interested in the application of metamaterials and negative phase velocities but do not appreciate the magnitude and significance to the spacetime conception of modern physics and philosophy.
Abraham-Minkowski dilemma concerning the momentum of light within dielectric materials has persisted over 100 years[1]-[2] and conflicting experiments were reported until recently[3]-[4]. We perform a reversed Fizeau experiment to test the compositio
n law of light speeds in media and the result accords with extended Lorentz transformations where the light speed c is changed to c/n. This is a crucial evidence that Minkowskis formulation p=nE/c should be correct although the momentum is not measured directly. By the way, the energy velocity of an electromagnetic field transferred along good conductors may be much faster than c and people have broken the light barrier for a very long time.
A resolution of the Abraham-Minkowski dilemma is presented that other constant velocities can play the role of c in the theory of relativity. For example, in 2005 electrons of graphene were discovered to behave as if the coefficient is a Fermi veloci
ty. Then we propose a conjecture for neutrinos to avoid the contradiction among two-component theory, negative rest mass-square and oscillation.
