A novel method is proposed for a laboratory test of the time independence of the fine-structure constant and of the electron to proton mass ratio, employing only electromagnetic resonators. For a resonator made out of, Imp through the a dielectric ionic or molecular crystal, the resonance frequencies depend on the product a alpha (2)rootm(e)/m(p) index of refraction. A test of the time independence of alpha and m(e)/m(p) can be performed by a search for a long-term change in the difference of two resonance frequencies exhibiting different dispersion. The method can be advantageously implemented with a single resonator. The prospects of implementation using optical resonators, systematic effects, and experimental requirements for a test at the level of 4 x 10(-15)/yr relative variation in a or m(e)/m(p) are discussed. On the experimental side, birefringent monolithic sapphire optical resonators with high-reflectivity mirrors are fabricated and characterized. The measurements of optical materials with ultralow absorption loss (ppm/cm level), required for the proposed method. are also reported.
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