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On the base of the Hamilton theory for the time-like photon in isotropicdielectric with refraction index n (S.Antoci, et.al, 2007), we suggestgeneralization of the Einstein-Plank-Richardson law for the value of the lightenergy quantum in medium:E=h*nu*n, where h is the Plank's constant, and nu isthe light frequency. By use of this new quantum law, we resolve the famouscontradiction between de Broglie and Einstein's theories, related with the oldAbraham-Minkowski dilemma in the definition of the photon momentum value p (inthe medium for n>1). We show that the same value p=p_a=E/(c*n)(c is the speedof light in vacuum) follows now from the both theories of de Broglie andEinstein, which complies with the theory of Abraham, but not with the theory ofMinkowski (where p=p_m=E*n/c). Based on the corpuscular approach with p=p_a andE=h*nu*n^2, we give new inference for the Snellius refraction law and resolvemore old corresponding corpuscular-wave Newton-Huygens dilemma. We show thateven for n-1<<1 the Abraham and Minkowski theories (with different p=p_a andp=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 theVavilov-Cherenkov radiation realization in the photon gas of the backgroundcosmic radiation, for which n-1=10^(-42) in the current epoch.

Generalization of the Einstein-Plank-Richardson law for the photon  energy in medium resolves Abraham-Minkowski dilemma in the electromagnetic  field theory statement