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The term Minkowski diagram refers to a specific form of spacetime diagram frequently used in special relativity. A Minkowski diagram is a two-dimensional graphical depiction of a portion of Minkowski space , usually where space has been curtailed to a single dimension.
Hyperbolic motion can be visualized on a Minkowski diagram, where the motion of the accelerating particle is along the -axis. Each hyperbola is defined by x = ± c 2 / α {\displaystyle x=\pm c^{2}/\alpha } and η = α τ / c {\displaystyle \eta =\alpha \tau /c} (with c = 1 , α = 1 {\displaystyle c=1,\alpha =1} ) in equation ( 2 ).
Hermann Minkowski (1864–1909) found that the theory of special relativity could be best understood as a four-dimensional space, since known as the Minkowski spacetime. In physics, Minkowski space (or Minkowski spacetime) (/ m ɪ ŋ ˈ k ɔː f s k i,-ˈ k ɒ f-/ [1]) is the main mathematical description of spacetime in the absence of gravitation.
The simplest example of a Lorentzian manifold is flat spacetime, which can be given as R 4 with coordinates (,,,) and the metric = + + + =. These coordinates actually cover all of R 4 . The flat space metric (or Minkowski metric ) is often denoted by the symbol η and is the metric used in special relativity .
Commonly a Minkowski diagram is used to illustrate this property of Lorentz transformations. Elsewhere, an integral part of light cones is the region of spacetime outside the light cone at a given event (a point in spacetime). Events that are elsewhere from each other are mutually unobservable, and cannot be causally connected.
These curves must fall within a cone defined by light-like curves. In our definition above: world lines are time-like curves in spacetime. space-like curves falling outside the light cone. Such curves may describe, for example, the length of a physical object. The circumference of a cylinder and the length of a rod are space-like curves.
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 .
The canonical Lorentzian manifold is Minkowski spacetime, where = and is the flat Minkowski metric. The names for the tangent vectors come from the physics of this model. The names for the tangent vectors come from the physics of this model.