Space of Minkowski

In a space of Minkowski , name of its inventor, a not is reference mark by four Coordonnée S (X, there, Z, ct), the three coordinates of space and the coordinate of Temps.

In this space, dimension relating to time is imaginary pure, whereas the three other coordinates (space) are real.

The metric Tenseur of the space of Minkowski is thus (if one takes as convention which time is the first coordinate):

g = \ begin {pmatrix} - 1&0&0&0 \ \ 0&1&0&0 \ \ 0&0&1&0 \ \ 0&0&0&1 \ end {pmatrix}

The pseudonorme of two points of this space is defined by:

r^ {2} = (x_ {1} - x_ {2}) ^ {2} + (y_ {1} there _ {2}) ^ {2} + (z_ {1} - z_ {2}) ^ {2} - c^ {2} (t_ {1} - t_ {2}) ^ {2}

It is noted that it is null if a luminous ray can pass by these two points. From a physical point of view, an observer sees only objects which are with a null pseudonorme of him.

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