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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.
Two methods of construction are obvious from Fig. 3-2: the x-axis is drawn perpendicular to the ct′-axis, the x′ and ct-axes are added at angle φ; and the x′-axis is drawn at angle θ with respect to the ct′-axis, the x-axis is added perpendicular to the ct′-axis and the ct-axis perpendicular to the x′-axis. In a Minkowski diagram ...
If is negative, the spacetime interval is said to be spacelike. Spacetime intervals are equal to zero when =. In other words, the spacetime interval between two events on the world line of something moving at the speed of light is zero. Such an interval is termed lightlike or null. A photon arriving in our eye from a distant star will not have ...
The Poincaré group consists of all coordinate transformations of Minkowski space that do not change the spacetime interval between events.For example, if everything were postponed by two hours, including the two events and the path you took to go from one to the other, then the time interval between the events recorded by a stopwatch that you carried with you would be the same.
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 interval is often denoted =. The interval d s 2 {\displaystyle ds^{2}} imparts information about the causal structure of spacetime . When d s 2 < 0 {\displaystyle ds^{2}<0} , the interval is timelike and the square root of the absolute value of d s 2 {\displaystyle ds^{2}} is an incremental proper time .
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]
Subdivision of Minkowski spacetime with respect to a point in four disjoint sets. The light cone , the causal future , the causal past , and elsewhere . The terminology is defined in this article.