Photon and Graviton: Similarity and Distinctions

Two elementary particles—a photon and a graviton—responsible for interaction with physical objects of two long-range action fields electromagnetic and gravitational are considered. The similarity and distinction of these quantum particles are investigated. It is shown that these particles essentially differ from each other. First of all, they are in different spaces. The photon is in photon space, and the graviton is in Riemann’s space-time. Interaction of a photon and a mass body cannot be calculated in Euclidian space. Interaction of a graviton and a mass body can be calculated in the Euclidian space. Polarizing properties of a gravitational wave both in plane Minkowski’s space, and in curved Riemann’s space-time are in detail considered. The differential equation of a gravitational quantum oscillator is found and its solution is analyzed. Also, the quantum metrics of Riemann’s space-time in presence of graviton and its quantum numbers are found.