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The Minkowski metric η is the metric tensor of Minkowski space. It is a pseudo-Euclidean metric, or more generally, a constant pseudo-Riemannian metric in Cartesian coordinates. As such, it is a nondegenerate symmetric bilinear form, a type (0, 2) tensor.
The Minkowski distance or Minkowski metric is a metric in a normed vector space which can be considered as a generalization of both the Euclidean distance and the Manhattan distance. It is named after the Polish mathematician Hermann Minkowski .
In general relativity, the metric tensor (in this context often abbreviated to simply the metric) is the fundamental object of study. The metric captures all the geometric and causal structure of spacetime , being used to define notions such as time, distance, volume, curvature, angle, and separation of the future and the past.
Rindler chart, for = in equation (), plotted on a Minkowski diagram.The dashed lines are the Rindler horizons. The worldline of a body in hyperbolic motion having constant proper acceleration in the -direction as a function of proper time and rapidity can be given by [16]
The metric has signature ... (where x, y, z are the usual Cartesian coordinates) and the Minkowski metric tensor with metric signature (− + + +) is defined as
We will call it the Langevin-Landau-Lifschitz metric, and we can call this notion of distance radar distance "in the small". This metric was first given by Langevin , but the interpretation in terms of radar distance "in the small" is due to Lev Landau and Evgeny Lifshitz , who generalized the construction to work for the quotient of any ...
Spacetime algebra is a type of geometric algebra that is closely related to Minkowski space, and is equivalent to other formalisms of special relativity. It uses mathematical objects such as bivectors to replace tensors in traditional formalisms of Minkowski spacetime, leading to much simpler equations than in matrix mechanics or vector calculus.
The Poincaré group, named after Henri Poincaré (1905), [1] was first defined by Hermann Minkowski (1908) as the isometry group of Minkowski spacetime. [2] [3] It is a ten-dimensional non-abelian Lie group that is of importance as a model in our understanding of the most basic fundamentals of physics.