Physical theories extant describe natural events using the concept of fields.  Fields are described mathematically by so-called laws that prescribe the characteristics of the fields such that the fields yield meaningful representations of experimental results.  To obtain experimental results, experiments establish local coincidence of events in spacetime.  Thus, the spacetime coordinates are implicit in physical theories.

An essential characteristic of the mathematical prescription is the requirement that theories and their predictions be invariant to changes in the coordinate systems.  Transformation laws ensure this characteristic.  Transformations include gauge transformations and coordinate transformations.  Proper transformations within acceptable theories leave predictions invariant.

Experimental properties are expressed in magnitudes and units.  Proper predictions of theory must, then, incorporate units consistently.  Different systems of units exist.  These systems are interconvertible.  The units are related to the physical properties by which experiments and theories work together to represent nature.

The coordinate of an event is not unique.  Rather, the coordinate depends upon the system of coordinates.  Coordinate systems are characterized by an origin and a metric.  The transformation that expresses the coordinate of an event in one coordinate system in terms of the coordinates of another coordinate system is a coordinate transformation.

Two coordinate systems that differ only in origin are related through a non-homogenous coordinate transformation.  That is, the difference between the coordinate of an event in one system and the coordinate of that event in the other coordinate system is a non-zero constant (non-homogeneous).