Minkowski space

Minkowski space is 4-dimensional quasi-Euclidean space (i.e., the set of points Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle (x,y,z,t)} ) together with the metric:

$c^{2}dt^{2}-dx^{2}-dy^{2}-dz^{2}$

It is called quasi-Euclidean because the metric coefficients for space and time are different, rather than always being positive for a true Euclidean space. Whether the time coefficient or the space coefficients should be the negative ones has been debated for a century. It doesn't matter in practice. The convention above (time is positive and space negative) was the one preferred by Einstein.

A vector v in Minkowski space is said to be time-like if $||v||^{2}>0$, light-like if $||v||^{2}=0$ and space-like if Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle ||v||^2 < 0} . The isometries of Minkowski space are the Lorentz transformations.

External links

• The Geometry of Special Relativity: The Minkowski Space - Time Light Cone