CLASSICAL AND RELATIVISTIC FORCES OF INERTIA

It is shown that -- in contrast to the classical physics and special relativity -- the self-consistency of general relativity requires that the forces of inertia follow unambiguously from the field equations as inductive gravitationM effects of the cosmic matter and that this requirement is perfectly satisfied, without supplementary hypotheses, for the Einstein universe, in full agreement with Mach's principle. The pseudo-Euclidean space-time geometry adopted for inertial frames in special relativity is commonly regarded as given a priori and thus valid even in completely empty universe. Consequently, the additional forces appearing in noninertial frames are in special relativity as well as in classical physics fictitious forces deprived of any material source. This non-Machian feature does not change by generally covariant formulation of the equations of motion. The standpoint of general relativity, inspired by Mach's ideas, is quite different. Einstein's theory of gravitation and inertia may be compatible with the general principle of relativity only if the inertial frames are distinguished by the very fact that they move without acceleration relative to the cosmic matter and if the field equations give the observed forces of inertia as real gravitational effects due to the actual universe. Unfortunately, the present cosmological knowledge does not yield sufficient information about the global properties of the universe and general relativity itself cannot derive them theoretically. Thus it is conceivable that some physicists perceive Mach's principle with considerable scepticism and regard the origin of inertia as physically inexplicable. In my opinion, however, the Gordian knot of gravity and inertia was cut by the genius of Einstein at one blow in his first cosmological paper [1]. He assigned to the universe the simplest thinkable properties: homogeneity, symmetry, isotropy, and invariability in time. So he arrived at a closed static universe with constant curvature in which a generalized law of inertia is valid if and only if the density of matter does not vanish. I was able to show in a previous paper [2] that Einstein's universe creates a gravitational field with constant scalar potential of the type of Seeliger, equal to the square of light velocity taken with negative sign, so that the so called Machian feed-back condition is fulfilled in Einstein's cosmology. In the present paper, I use the principle of general covariance in order to find an exact solution of the field equations which gives the space-time metric for a noninertial frame moving, without rotation, along a curvilinear trajectory with arbitrarily variable velocity. The main implication of this solution is the existence of all kinds of inertial *) Technickd 4, Praha 6, Czechoslovakia.