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In the rigorous mathematical formulation of special relativity, we suppose that the universe exists on a four-dimensional spacetime M. Individual points in spacetime are known as events ; physical objects in spacetime are described by worldlines (if the object is a point particle) or worldsheets (if the object is larger than a point).
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 physics, spacetime, also called the space-time continuum, is a mathematical model that fuses the three dimensions of space and the one dimension of time into a single four-dimensional continuum. Spacetime diagrams are useful in visualizing and understanding relativistic effects, such as how different observers perceive where and when events ...
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 field equations of general relativity are not parameterized by time but formulated in terms of spacetime. Many of the issues related to the problem of time exist within general relativity. At the cosmic scale, general relativity shows a closed universe with no external time. These two very different roles of time are incompatible. [4]
Frame-dragging: Rotating masses "drag along" the spacetime around them. Expansion of the universe: The universe is expanding, and certain components within the universe can accelerate the expansion. Technically, general relativity is a theory of gravitation whose defining feature is its use of the Einstein field equations.
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 ...
In relativity, if translations mix up nontrivially with rotations, but the universe is still homogeneous and isotropic, the only option is that spacetime has a uniform scalar curvature. If the curvature is positive, the analog of the sphere case for the two-dimensional creatures, the spacetime is de Sitter space and its symmetry group is the de ...