Abstract :
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.
