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We consider the ADM splitting of the Einstein-Hilbert action in fivedimensions in the presence of matter that can be either a "point particle", ora set of scalar fields. The Hamiltonian, being a linear superposition ofconstraints, is equal to zero. Upon quantization, we obtain the Schr\"odingerequation for a wave functional, \Psi, that depends on the matter degrees offreedom, and on the 5D gravity degrees of freedom. After the Kaluza-Kleinsplitting, the functional Schr\"odinger equation decomposes so that it containsa part due to 4D gravity, a part due to electrodynamics, and a part due tomatter. Depending on choice of the matter term, we obtain two differentversions of a modified quantum electrodynamics. In one version, timeautomatically appears, and there is no problem with infinite vacuum energydensity of matter fields, whereas in the other version such problems exist.

Wheeler-DeWitt Equation in Five Dimensions and Modified QED