Information transmittal, relativity and gravitation
Special relativity considered in [Albert Einstein, Zur Elektrodynamik der bewegte Krper, Ann. Phys. 17 (1905) 891921], and gravitation, studied in a series of papers, notably in [Albert Einstein, Zum gegenwrtigen Stnde des Gravitationsproblemen, Phys. Z. 14 (1913) 12491262], are further analyzed regarding the principle of relativity, gravitation, and the notion of mass. The energy relation derived by Einstein from the relativistic Maxwell equations is applied to potential energy W(x) W ( x ) of the gravitational field along the right line for which Einsteins transformations are valid. This defines the intensity G ( x ) = d W / d x of the relativistic force of gravity along a right line of observation in the gravitational field. The force is proportional to the observed  acceleration according to the formula ? G ( x ) = ? ? ? ? = ? x t t ? 3 where ? ? is the inert  mass in the second Newtons law of motion and ? ? is the charge (mass) in the relativistic electromagnetic (gravitational) field. In everyday life, we see that all bodies visually fall under gravity (i.e. in a common gravitational field) with the same observed acceleration ??? ? ? ? as if having equal inert and gravitational masses: ?/?=1 ? / ? = 1 , with respect to the synchronized time ? ? . However, if the principle of relativity extended by Einstein to the case of the uniformly accelerated rectilinear motion is valid, then this relation should also be true with respect to xtt x t t , that is, (?/?)?3=1 ( ? / ? ) ? 3 = 1 , in proper time t t of a still observer and of the carrying system (falling body), thus, depending on velocity v v at which the acceleration ??? ? ? ? is measured. This means that the inert mass ? ? and the gravitational mass ? ? can be considered equal only  at v=0 v = 0 , and otherwise are related by the equation ?=??3?? ? = ? ? 3 ? ? , where Einsteins calibration factor ?=[1?(v/V)2]?0.5?1,|v| 0 v > 0 , then the observed  gravitational mass ? ? is greater  than the inert mass ? ? . The increase of mass is concurrent with the increase of tensions that at high velocities v?V v ? V induce overheating in the particle accelerators and colliders. To comply with the nature of observation, the information transmittal signals are incorporated in the Lorentz invariant of the 4D 4 D geometry, leading to the local invariants of relativistic dynamics that include gravitation and the speed of signals used in observation of moving bodies. With the same communication signals, those invariants hold for the synchronized time and coordinates of moving systems irrespective of their relative velocities. A procedure is developed for measurement and computation of the accelerations produced by variable gravitational and/or electromagnetic fields through the measurements of velocities of a moving body, so that the motion of the body and the field of forces acting on it can be fully identified. The results open new avenues for research in the theory of relativity and its applications.
gravitation inert and gravitational masses relativistic invariants