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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.
The dotted horizontal line represents the set of points regarded as simultaneous with the origin by a stationary observer. This diagram is drawn using the (x, t) coordinates of the stationary observer, and is scaled so that the speed of light is one, i.e., so that a ray of light would be represented by a line with a 45° angle from the x axis.
Where Einstein referred to "an observer who takes the train as his reference body" or "an observer located at the origin of the coordinate system", this group of modern writers says, for example, "an observer is represented by a coordinate system in the four variables of space and time" [3] or "the observer in frame S finds that a certain event ...
This template includes collapsible lists. To set it to display one particular list while keeping the remainder collapsed (i.e. hidden apart from their headings), use: {{Spacetime|cTopic=(listname)}} …where listname is one of the following (do not include any quotemarks nor parentheses): Introduction, Types, Mathematics, Relation to gravity
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 ...
In the k-calculus methodology, distances are measured using radar.An observer sends a radar pulse towards a target and receives an echo from it. The radar pulse (which travels at , the speed of light) travels a total distance, there and back, that is twice the distance to the target, and takes time , where and are times recorded by the observer's clock at transmission and reception of the ...
The vierbein field, , has two kinds of indices: labels the general spacetime coordinate and labels the local Lorentz spacetime or local laboratory coordinates. The vierbein field or frame fields can be regarded as the "matrix square root" of the metric tensor , g μ ν {\displaystyle g^{\mu \nu }\,} , since in a coordinate basis,
This form is local for an observer sandwiched between the black hole and the cosmological horizon, which reveal their presence as the two horizons at z = −R and z = R respectively. The coordinate z can be replaced by a global coordinate for the 1 + 1-dimensional de Sitter space part, and then the metric can be written as: