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Objectivity (frame invariance)
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Objectivity (frame invariance) : ウィキペディア英語版
Objectivity (frame invariance)
The concept of objectivity in science . 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.
== Euclidean transformation ==
Physical processes can be described by an observer denoted by 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 (x_0,t_0) and (x,t) where x is a position vector and t 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 Q(t) in a way such that the distance between the pairs is kept the same. Therefore one can write:
:\ x^
*-x_0^
*=Q(t)(x-x_0).
By introducing a vector C(t) and a real number \alpha denoting the time shift, the relationship between x and x^
* can be expressed
:\ x^
*=c(t)+Q(t)x \quad \text \quad c(t)=x_0^
*-Q(t)x_0 \quad \text \quad \alpha=t^
*-t=t_0^
*-t_0.

The one-to-one mapping connection of the pair (x,t) with its corresponding pair (x^
*, t^
*) is referred to as a Euclidean transformation.

抄文引用元・出典: フリー百科事典『 ウィキペディア(Wikipedia)
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