Minkowski metric

In mathematical physics, Minkowski space or Minkowski spacetime is a combination of 3-dimensional Euclidean space and time into a 4-dimensional manifold where the spacetime interval between any two events is independent of the inertial frame of reference in which they are recorded. Although initially developed by mathematician Hermann Minkowski for Maxwell's equations of electromagnetism, the mathematical structure of Minkowski spacetime was shown to be an immediate consequence of the postulates of special relativity.

Minkowski space is closely associated with Einstein's theory of special relativity, and is the most common mathematical structure on which special relativity is formulated. While the individual components in Euclidean space and time will often differ due to length contraction and time dilation, in Minkowski spacetime, all frames of reference will agree on the total distance in spacetime between events. Because it treats time differently than it treats the three spatial dimensions, Minkowski space differs from four-dimensional Euclidean space.

In 3-dimensional Euclidean space (e.g. simply space in Galilean relativity), the isometry group (the maps preserving the regular Euclidean distance) is the Euclidean group. It consists of rotations, reflections, and translations. When time is amended as a fourth dimension, the further transformations of translations in time and Galilean boosts are added, and the group of all these transformations is called the Galilean group. All Galilean transformations preserve the 3-dimensional Euclidean distance. This distance is purely spatial. Time differences are separately preserved as well. This changes in the spacetime of special relativity, where space and time are interwoven.

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