Using the diagram of space-time, which represents intersections of the spheres depicting the front of an electromagnetic wave in the resting and moving frames with a plane going through the centres of the spheres, and the assumption that a quantum (photon) of spherical electromagnetic wave maintains its entity during the propagation of the wave, it is derived a quantum equation of the Doppler effect: sqrt(1-beta^2) tau^2 - 2 cos(gamma) tau(0) tau + sqrt(1-beta^2) tau(0)^2 = 0, where "tau(0)" and "tau" are the periods of an electromagnetic wave in the frames of the source and the receiver, "beta" is the relative speed of the frames divided by the speed of light in free space, and "gamma" is the angle of aberration (the difference of the angles of slope of a ray in the frames of the source and the receiver). It is maintained that despite the differences between the obtained equation and Einstein’s expression for the Doppler shift, the equation of time dilation doesn’t need any alteration. Inapplicability of some fundamental principles of the special relativity to finite distances as well as inherent uncertainties in the measurements of space and time intervals is discussed.