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The most well-known class of spacetime diagrams are known as Minkowski diagrams, developed by Hermann Minkowski in 1908. Minkowski diagrams are two-dimensional graphs that depict events as happening in a universe consisting of one space dimension and one time dimension. Unlike a regular distance-time graph, the distance is displayed on the ...
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.
Rindler chart, for = in equation , plotted on a Minkowski diagram. The dashed lines are the Rindler horizons The dashed lines are the Rindler horizons The worldline of a body in hyperbolic motion having constant proper acceleration α {\displaystyle \alpha } in the X {\displaystyle X} -direction as a function of proper time τ {\displaystyle ...
A curve in is the image of a path or, more properly, an equivalence class of path-images related by re-parametrisation, i.e. homeomorphisms or diffeomorphisms of . When M {\displaystyle M} is time-orientable, the curve is oriented if the parameter change is required to be monotonic .
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 ).
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.
Minkowski–Bouligand dimension; Minkowski diagram; Minkowski distance; Minkowski functional; Minkowski inequality; Minkowski space. Null vector (Minkowski space) Minkowski plane; Minkowski's theorem; Minkowski's question mark function; Abraham–Minkowski controversy; Hasse–Minkowski theorem; Minkowski separation theorem; Smith–Minkowski ...
In a classical 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. Therefore, the Poincaré group also acts on the space of sections.