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A spacetime diagram is typically drawn with only a single space and a single time coordinate. Fig. 2-1 presents a spacetime diagram illustrating the world lines (i.e. paths in spacetime) of two photons, A and B, originating from the same event and going in opposite directions. In addition, C illustrates the world line of a slower-than-light ...
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.
Spacetime topology is the topological structure of spacetime, a topic studied primarily in general relativity. This physical theory models gravitation as the curvature of a four dimensional Lorentzian manifold (a spacetime) and the concepts of topology thus become important in analysing local as well as global aspects of spacetime.
In a curved spacetime, assuming spacetime is globally hyperbolic, it is still true that the future light cone of an event includes the boundary of its causal future (and similarly for the past). However gravitational lensing can cause part of the light cone to fold in on itself, in such a way that part of the cone is strictly inside the causal ...
The dashed line is the spacetime trajectory ("world line") of the particle. The balls are placed at regular intervals of proper time along the world line. The solid diagonal lines are the light cones for the observer's current event, and they intersect at that event. The small dots are other arbitrary events in the spacetime.
This means that the symmetry group of space time is a de Sitter group rather than the Poincaré group. This results in spacetime being slightly curved even in the absence of matter or energy. This residual curvature is caused by a cosmological constant to be determined by observation.
Rather than an invariant time interval between two events, there is an invariant spacetime interval. Combined with other laws of physics, the two postulates of special relativity predict the equivalence of mass and energy , as expressed in the mass–energy equivalence formula E = m c 2 {\displaystyle E=mc^{2}} , where c {\displaystyle ...
In Minkowski space there is only one geodesic that connects any given pair of events, and for a time-like geodesic, this is the curve with the longest proper time between the two events. In curved spacetime, it is possible for a pair of widely separated events to have more than one time-like geodesic between them.