Interpretation of the metric tensor components based on possible astrophysical implications

In this paper we shall consider the following question: ‘If the whole galactical system expands and if galaxies are separating away from one another just as much as they are separating from our galaxy, can we assume that such a reality will have repercussions on the formulation of basic physical laws in our surroundings?’ Considering a confirmative answer, we performed an attempt to find a physical interpretation of the perturbations of the metric tensor components. It was shown that they can be expressed in terms of the dilatation function which also appears to be one reason which prohibits the precise measurement of real time and distance. Considering that an observer in our wold knows nothing of the aperiodicity of atomic oscillations which ‘determine’ the unit of time, we discerned the meaning of time in two ways: (i) the time as it is accepted in special relativity and (ii) the ‘time’ based on the reading of clocks which suffer dilatation. The usual procedure for establishing equations of the gravitational field was then carried out. These equations reduce to those of the classical theory, if the dilatation function is proportional to Newtonian gravitational potential. On this basis, considering the Earth's expansion as a process which exists as a cosmological manifestation, we discussed the observed fact of the agreement between the rate of the Earth's radius and that of the universe, according to Hubble's law.