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A spacelike spacetime interval hence provides a measure of proper distance, i.e. the true distance = . Likewise, a timelike spacetime interval gives the same measure of time as would be presented by the cumulative ticking of a clock that moves along a given world line.
Spacetime is equipped with an indefinite non-degenerate bilinear form, called the Minkowski metric, [2] the Minkowski norm squared or Minkowski inner product depending on the context. [nb 2] The Minkowski inner product is defined so as to yield the spacetime interval between two events when given their coordinate difference vector as an ...
The interval imparts information about the causal structure of spacetime. When <, the interval is timelike and the square root of the absolute value of is an incremental proper time. Only timelike intervals can be physically traversed by a massive object.
A spacetime diagram is a graphical illustration of locations in space at various times, especially in the special theory of relativity.Spacetime diagrams can show the geometry underlying phenomena like time dilation and length contraction without mathematical equations.
This is a list of well-known spacetimes in general relativity. [1] Where the metric tensor is given, a particular choice of coordinates is used, but there are often other useful choices of coordinate available.
The interval, s 2, between two events is defined as: = (spacetime interval), where c is the speed of light, and Δr and Δt denote differences of the space and time coordinates, respectively, between the events.
This is done by means of the metric tensor, which allows for determining the causal structure of spacetime. The difference (or interval) between two events can be classified into spacelike, lightlike and timelike separations. Only if two events are separated by a lightlike or timelike interval can one influence the other.
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 ...