Generalization of the Einstein-Plank-Richardson law for the photon   energy in medium resolves Abraham-Minkowski dilemma in the electromagnetic   field theory statement
  On the base of the Hamilton theory for the time-like photon in isotropic dielectric with refraction index n (S.Antoci, et.al, 2007), we suggest generalization of the Einstein-Plank-Richardson law for the value of the light energy quantum in medium:E=h*nu*n, where h is the Plank's constant, and nu is the light frequency. By use of this new quantum law, we resolve the famous contradiction between de Broglie and Einstein's theories, related with the old Abraham-Minkowski dilemma in the definition of the photon momentum value p (in the medium for n>1). We show that the same value p=p_a=E/(c*n)(c is the speed of light in vacuum) follows now from the both theories of de Broglie and Einstein, which complies with the theory of Abraham, but not with the theory of Minkowski (where p=p_m=E*n/c). Based on the corpuscular approach with p=p_a and E=h*nu*n^2, we give new inference for the Snellius refraction law and resolve more old corresponding corpuscular-wave Newton-Huygens dilemma. We show that even for n-1<<1 the Abraham and Minkowski theories (with different p=p_a and p=p_m)may lead to very different conclusions. Thus, only the theory with p=p_a, contrary to the theory with p=p_m, allows the conclusion about the Vavilov-Cherenkov radiation realization in the photon gas of the background cosmic radiation, for which n-1=10^(-42) in the current epoch. 
Sergey G. Chefranov
physics.gen-ph