Information transmittal, principle of relativity and mass energy relation

Relativistic transformations and their application to electrodynamics of a weakly accelerated electron considered in [A. Einstein, Zur Elektrodynamik der bewegter Körper, Annalen der Physik, 17 (1905) 891 921] are further analyzed in their relation to the principle of relativity, the concept of mass, and the mass energy equation. Alternative consideration in dynamics of weakly accelerated electrons demonstrates that the factors in longitudinal 3 and transverse 2 masses of an electron with the mass at rest naturally appear in observed accelerations as a result of relativistic transformations, without any deviation from the principle of relativity and the second Newtonʹs law of motion. As concerns the special relativity in accelerated motion, this allows us to retain the concept of mass as scalar characteristic of an accelerated body. It is argued that ``the principle of equivalence of the mass and energy of restʹʹ (Einstein) depends on the speed of the information transmitting signal by which the observation (measurement) is made (synchronization of clocks is achieved), so that relativistic equation E D mc2 appears as an image phenomenon which essentially depends on the propagation of light as a measuring signal and on its speed V D c as the critical parameter of Einsteinʹs relativistic transformations. It is demonstrated that the spherical waves considered by Einstein are distorted in real time, and the fundamental Lorentz invariant is not crisp, but presents a soft interval whose diameter is in the range of 30,000 km for time delays of 0.1 s in transmission of information. The results open new avenues for further research in the theory of relativity and its applications.