Objectivity (frame Invariance) - Euclidean Transformation

Euclidean Transformation

Physical processes can be described by an observer denoted by . 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 and where is a position vector and is a scalar representing time. This pair is mapped to another one denoted by the superscript. This mapping is done with the orthogonal time-dependent second order tensor in a way such that the distance between the pairs is kept the same. Therefore one can write:

By introducing a vector and a real number denoting the time shift, the relationship between and can be expressed

The one-to-one mapping connection of the pair with its corresponding pair is referred to as a Euclidean transformation.