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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 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 = / and = / (with =, =) in equation ().
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]
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.
For easy visualizations of four dimensions, two space coordinates are often suppressed. An event is then represented by a point in a Minkowski diagram, which is a plane usually plotted with the time coordinate, say , vertically, and the space coordinate, say , horizontally. As expressed by F.R. Harvey
Minkowski diagram of the twin paradox. There is a difference between the trajectories of the twins: the trajectory of the ship is equally divided between two different inertial frames, while the Earth-based twin stays in the same inertial frame.
The Penrose diagram for Minkowski spacetime. Radial position is on the horizontal axis and time is on the vertical axis. Null infinity is the diagonal boundary of the diagram, designated with script 'I'. The metric for a flat Minkowski spacetime in spherical coordinates is = + +.