Minkowski Space

In mathematical physics, Minkowski space or Minkowski spacetime (named after the mathematician Hermann Minkowski) is the mathematical setting in which Einstein's theory of special relativity is most conveniently formulated. In this setting the three ordinary dimensions of space are combined with a single dimension of time to form a four-dimensional manifold for representing a spacetime.

In theoretical physics, Minkowski space is often contrasted with Euclidean space. While a Euclidean space has only spacelike dimensions, a Minkowski space also has one timelike dimension. Therefore the symmetry group of a Euclidean space is the Euclidean group and for a Minkowski space it is the Poincaré group.

The spacetime interval between two events in Minkowski space is either:

  1. space-like,
  2. light-like ('null') or
  3. time-like.

Read more about Minkowski SpaceHistory, Structure, Alternative Definition, Lorentz Transformations and Symmetry, Causal Structure, Reversed Triangle Inequality, Locally Flat Spacetime

Other articles related to "space, minkowski space, minkowski":

Twistor Space
... In mathematics, twistor space is the complex vector space of solutions of the twistor equation ... According to Andrew Hodges, twistor space is useful for conceptualizing the way photons travel through space, using four complex numbers ... He also posits that twistor space may aid in understanding the asymmetry of the weak nuclear force ...
Representation Theory Of The Poincaré Group
... In a physical theory having Minkowski space as the underlying spacetime, the space of physical states is typically a representation of the Poincaré group ... field theory, the physical states are sections of a Poincaré-equivariant vector bundle over Minkowski space ... The equivariance condition means that the group acts on the total space of the vector bundle, and the projection to Minkowski space is an equivariant map ...
Minkowski Space - Locally Flat Spacetime
... Strictly speaking, the use of the Minkowski space to describe physical systems over finite distances applies only in the Newtonian limit of systems without ... Nevertheless, even in such cases, Minkowski space is still a good description in an infinitesimal region surrounding any point (barring gravitational singularities) ... is described by a curved 4-dimensional manifold for which the tangent space to any point is a 4-dimensional Minkowski space ...
Kinetic Momentum - Relativistic Mechanics - Four-vector Formulation
... that include time as a fourth coordinate along with the three space coordinates ... of -1 or by keeping time a real quantity and embedding the vectors in a Minkowski space ... In a Minkowski space, the scalar product of two four-vectors U = (U0,U1,U2,U3) and V = (V0,V1,V2,V3) is defined as In all the coordinate systems, the (contravariant ...
Anomaly (physics) - Global Anomalies - Large Gauge Transformations - The Witten Anomaly
... In SU(2) gauge theory in 4 dimensional Minkowski space, a gauge transformation corresponds to a choice of an element of the special unitary group SU(2) at each point in spacetime ... If the 3-sphere at infinity is identified with a point, our Minkowski space is identified with the 4-sphere ... Thus we see that the group of gauge transformations vanishing at infinity in Minkowski 4-space is isomorphic to the group of all gauge transformations on the 4-sphere ...

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