  In order to ask for future concepts of relativity, one has to build upon the
original concepts instead of the nowadays common formalism only, and as such
recall and reconsider some of its roots in geometry. So in order to discuss
3-space and dynamics, we recall briefly Minkowski's approach in 1910
implementing the nowadays commonly used 4-vector calculus and related tensorial
representations as well as Klein's 1910 paper on the geometry of the Lorentz
group. To include microscopic representations, we discuss few aspects of
Wigner's and Weinberg's 'boost' approach to describe 'any spin' with respect to
its reductive Lie algebra and coset theory, and we relate the physical
identification to objects in $P^{5}$ based on the case $(1,0)\oplus(0,1)$ of
the electromagnetic field. So instead of following this -- in some aspects --
special and misleading 'old' representation theory, based on 4-vector calculus
and tensors, we provide and use an alternative representation based on line
geometry which -- besides comprising known representation theory -- is capable
of both describing (classical) projective geometry of 3-space as well as it
yields spin matrices and the classical Lie transfer. In addition, this geometry
is capable of providing a more general route to known Lie symmetries,
especially of the su(2)$\oplus$i~su(2) Lie algebra of special relativity, as
well as it comprises gauge theories and affine geometry. Thus it serves as
foundation for a future understanding of more general representation theory of
relativity based, however, on roots known from classical projective geometry
and $P^{5}$. As an application, we discuss Lorentz transformations in point
space in terms of line and Complex geometry, where we can identify them as...
