  The relative motion of material, point-like observers is analysed in terms of
coordinate maps between the respective rest-frame of each observer. Under the
assumption these maps are $C^{2}$-regular, conservation laws are deduced, which
in turn are found to yield wave equations familiar as scalar and spinor fields.
Wave-particle dualism is then understood as a property of these coordinate maps
as opposed to an inherent property of the point-like observers themselves.
Additionally it is shown that the relative acceleration of these observers can
only be realised in this context by the introduction of additional potential
fields. It is shown that if each observer is to be associated with an inertial
frame of reference, then the potential field is necessarily a massless gauge
field.
