  Of the various formalisms developed to treat relativistic phenomena, those
based on Clifford's geometric algebra are especially well adapted for clear
geometric interpretations and computational efficiency. Here we study
relationships between formulations of special relativity in the spacetime
algebra (STA) Cl{1,3} of Minkowski space, and in the algebra of physical space
(APS)Cl{3}. STA lends itself to an absolute formulation of relativity, in which
paths, fields, and other physical properties have observer-independent
representations. Descriptions in APS are related by a one-to-one mapping of
elements from APS to the even subalgebra STA+ of STA. With this mapping,
reversion in APS corresponds to hermitian conjugation in STA. The elements of
STA+ are all that is needed to calculate physically measurable quantities
because only they entail the observer dependence inherent in any physical
measurement. As a consequence, every relativistic physical process that can be
modeled in STA also has a representation in APS, and vice versa. In the
presence of two or more inertial observers, two versions of APS present
themselves. In the absolute version, both the mapping to STA+ and hermitian
conjugation are observer dependent, and the proper basis vectors are persistent
vectors that sweep out timelike planes. In the relative version, the mapping
and hermitian conjugation are then the same for all observers. Relative APS
gives a covariant representation of relativistic physics with spacetime
multivectors represented by multiparavectors. We relate the two versions of APS
as consistent models within the same algebra.
