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Position Four-Vector

The contravariant four-vector arising in special and general relativity,

x^mu=[x^0; x^1; x^2; x^3]=[ct; x; y; z],
(1)

where c is the speed of light and t is time. Multiplication of two four-vectors gives the spacetime interval

I=g_(munu)x^mux^nu
(2)
=(x^0)^2-(x^1)^2-(x^2)^2-(x^3)^2
(3)
=(ct)^2-(x^1)^2-(x^2)^2-(x^3)^2.
(4)

See also

Four-Vector, Lorentz Transformation, Quaternion

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Cite this as:

Weisstein, Eric W. "Position Four-Vector." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/PositionFour-Vector.html

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