Objectivity (frame invariance)

The concept of objectivity in science means that qualitative and quantitative descriptions of physical phenomena remain unchanged when the phenomena are observed under a variety of conditions. For example, physical processes (e.g. material properties) are invariant under changes of observers; that is, it is possible to reconcile observations of the process into a single coherent description of it.

Physical processes can be described by an observer denoted by ${\displaystyle O}$. In Euclidean three-dimensional space and time, an observer can measure relative positions of points in space and intervals of time.

Consider an event in Euclidean space characterized by the pairs ${\displaystyle (x_{0},t_{0})}$ and ${\displaystyle (x,t)}$ where ${\displaystyle x}$ is a position vector and ${\displaystyle t}$ is a scalar representing time. This pair is mapped to another one denoted by the ${\displaystyle *}$ superscript. This mapping is done with the orthogonal time-dependent second order tensor ${\displaystyle Q(t)}$ in a way such that the distance between the pairs is kept the same. Therefore, one can write:

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