  The concept of a physical space, which actualizes Euclidean geometry, is not
confined to the statics of solids but extensible to the phenomena where
Newtonian mechanics is valid, defining its concept of time. The laws of
propagation of electromagnetic disturbances modify Newtonian formalism for
sufficiently fast free motions within each spatial domain of its validity for
slow motions and introduce the extended concept of time by uniting those of
Newtonian which can exist in different spatial domains of their validity.
  A boost direction for a pair of physical spaces is that spatial direction in
one of the spaces along which the other space moves. Free motions of point
particles make an instrumentation for identifying the boost direction as well
as events on a straight line along that direction. The concept of a boost
direction secures the physics-based formulation of the basic relativity
effects, which eventually results in the relation between two arbitrary spaces
in terms of their position vectors and time of a given event.
  The obtained transformation rules for the components of the position vector
differ from the vector-like relationship known in the literature because the
latter actually deals with column vectors made of Cartesian coordinates of true
vectors and appears identical to a coordinate transformation referred to as a
boost.
  Within the physics-based approach, the transformation of coordinates implies
specifying coordinate systems in each frame in terms of physical
objects/directions. This yields a logically consistent and physically
meaningful presentation of the coordinate transformations commonly exploited in
the special relativity theory, which makes manifestations of those
transformations evident. Specifically, for a Cartesian coordinate system
subjected to a boost, the coordinate-free technique of reasoning allows one to
evaluate its apparent distortion easily.
