  It is shown in this paper that the difference between the two forms of
relativity - the ''true transformation (TT) relativity'' and - the ''apparent
transformation (AT) relativity'' is essentially caused by the difference in the
concept of \emph{sameness} of a physical system, i.e., of a physical quantity,
for different, relatively moving, observers. In the ''TT relativity'' the same
quantity for different inertial frames of reference is covariantly defined
four-dimensional (4D) tensor quantity, which transforms according to the
Lorentz transformation as the TT. In the ''AT relativity'' parts of a 4D tensor
quantity are often considered as the same quantity for different observers,
although they correspond to different quantities in 4D spacetime, and they are
not connected by the Lorentz transformation than by the AT. Then the true
transformations of a spacetime length and the apparent transformations of a
spatial distance (the Lorentz contraction) and of a temporal distance (the
usual dilatation of time) are examined in detail. It is proved that only the
true transformations of the spacetime length are in agreement with the special
relativity as the theory of a 4D spacetime with the pseudo-Euclidean geometry.

Classical Physics