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In [[mathematical physics]], '''Minkowski space''' (or '''Minkowski spacetime''') ({{IPAc-en|m|ɪ|ŋ|ˈ|k|ɔː|f|s|k|i|,_|-|ˈ|k|ɒ|f|-}}<ref>[http://www.dictionary.com/browse/minkowski"Minkowski"] {{Webarchive|url=https://web.archive.org/web/20190622030121/https://www.dictionary.com/browse/minkowski |date=2019-06-22 }}. ''[[Random House Webster's Unabridged Dictionary]]''.</ref>) combines [[inertial]] [[space]] and [[time]] [[manifolds]] with a [[non-inertial reference frame]] of [[Spacetime|space and time]] into a [[four-dimensional]] model relating a position ([[inertial frame of reference]]) to the [[field (physics)|field]].
The model helps show how a [[spacetime interval]] between any two [[Event (relativity)|events]] is independent of the [[inertial frame of reference]] in which they are recorded. Mathematician [[Hermann Minkowski]] developed it from the work of [[Hendrik Lorentz]], [[Henri Poincaré]], and others
Minkowski space is closely associated with [[Albert Einstein|Einstein's]] theories of [[special relativity]] and [[general relativity]] and is the most common mathematical structure by which special relativity is formalized. While the individual components in Euclidean space and time might differ due to [[length contraction]] and [[time dilation]], in Minkowski spacetime, all frames of reference will agree on the total interval in spacetime between events.<ref group=nb>This makes spacetime distance an [[Invariant (physics)|invariant]].</ref> Minkowski space differs from [[Four-dimensional space|four-dimensional Euclidean space]]
In 3-dimensional [[Euclidean space]], the [[isometry group]] (the maps preserving the regular [[Euclidean distance]]) is the [[Euclidean group]]. It is generated by [[Rotation matrix|rotations]], [[Reflection (mathematics)|reflections]] and [[Translation (geometry)|translations]]. When time is appended as a fourth dimension, the further transformations of translations in time and [[Lorentz boost]]s are added, and the group of all these transformations is called the [[Poincaré group]]. Minkowski's model follows special relativity, where motion causes [[time dilation]] changing the scale applied to the frame in motion and shifts the phase of light.
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