TOPICS
Search

Minkowski Space


Minkowski space is a four-dimensional space possessing a Minkowski metric, i.e., a metric tensor having the form

 dtau^2=-(dx^0)^2+(dx^1)^2+(dx^2)^2+(dx^3)^2.

Alternatively (though less desirably), Minkowski space can be considered to have a Euclidean metric with imaginary time coordinate x^0=ict where c is the speed of light (by convention c=1 is normally used) and where i is the imaginary number i=sqrt(-1). Minkowski space unifies Euclidean three-space plus time (the "fourth dimension") in Einstein's theory of special relativity.

In equation (5) above, the metric signature (1,3) is assumed; under this assumption, Minkowski space is typically written R^(1,3). One may also express equation (5) with respect to the metric signature (3,1) by reversing the order of the positive and negative squared terms therein, in which case Minkowski space is denoted R^(3,1).

The Minkowski metric induces an inner product, the four-dimensional Lorentzian inner product (sometimes referred to as the Minkowski inner product), which fails to be positive definite (Ratcliffe 2006).


See also

Euclidean Metric, Four-Vector, Lorentzian Inner Product, Lorentz Tensor, Lorentz Transformation, Metric Tensor, Metric Signature, Minkowski Metric, Positive Definite Quadratic Form, Twistor, Twistor Space

Portions of this entry contributed by Christopher Stover

Explore with Wolfram|Alpha

References

Ratcliffe, J. G. Foundations of Hyperbolic Manifolds. New York: Springer, 2006.Thompson, A. C. Minkowski Geometry. New York: Cambridge University Press, 1996.

Referenced on Wolfram|Alpha

Minkowski Space

Cite this as:

Stover, Christopher and Weisstein, Eric W. "Minkowski Space." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/MinkowskiSpace.html

Subject classifications