equivalence principle – is equivalent to a system of motionless bodies Σ2 located in a uniform
Lemma. In an eigensystem of uniformly accelerated points, distances do not change.
Indeed, the equivalence principle establishes identity of laws of a system of equally accelerated
points and a uniform gravitational field but a distance between motionless points in a gravitational
field does not depend on time2.
Conclusion. We must not only refuse from intuitive suggestions but also apply methods of
the general relativity theory instead of the special one for investigation of non-inertial reference
3. In the non-relativistic physics, a description of a uniform field of any nature is not
difficult at all. Meantime, a description of a uniform field of accelerations or of an equivalent-to-
it gravitational field is beyond scope of possibilities of the special relativity theory. In particular,
readings of standard clocks in an accelerated system depend not only on their velocity but also on
their spatial location [5, 6]. Formally, this law is put in the form of the asymptotical equation for
the proper time in the points of the accelerated system and time in a convected system
where is acceleration. This ratio explains why the motion equation (1) is inappropriate for the
The methods of the general relativity theory allow describing a motion in the fullest form.
For a transfer from the motion equation of the special relativity theory to the motion equation of
the general relativity theory, it is needed – in the equation – to replace the ordinary differentiation
with the covariant one:
In order to obtain a motion equation in electromagnetic fields, it is necessary to replace
with . Now as a component in the motion equation, there is a metric of a reference
system. More to it, for a motion description in curvilinear coordinates, we need nothing except for