Astrophysics (Index)About

spacetime diagram

(Minkowski diagram)
(graph of simplified spacetime, with fewer space dimensions)

A spacetime diagram (or Minkowski diagram) is a graph of a simplified spacetime which can be used to show consequences of relativity, displaying plotted worldlines. The simplest is a 2-dimensional graph showing only a single dimension of space, i.e., a planar "cut" through 4-dimensional spacetime. Typically, time is represented as the vertical axis. 3-dimensional graphs are also used, showing two space dimensions.

It is common to scale the graph so the path light would take along this dimension shows as a 45-degree angle, i.e., movement at the speed of light. The slope of the line varies inversely with the speed of a small (point-like) object represented by the line, steeper being slower. Lines steeper than the speed-of-light angle can represent objects, i.e.,time-like lines, which could represent the position of the object at each time. Lines less steep than 45 degrees are impossible for a point-like object to follow: that would be exceeding the speed of light: such lines are termed space-like, to indicate in any frame of reference, there will be some space between any two separate points on the line: an object with enough length could sit on the line, interconnecting the points. Variations on the graph, including rotating axes, can be used to demonstrate the effect of differing frames of reference.

(diagram,relativity,cosmology,black holes)
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