# Understanding Special Relativity: The Lorentz Transformation, Time Dilation, and Length Contraction

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The Lorentz transformation describes how two observers in relative motion can relate their measurements of space and time. This Demonstration illustrates the space and time axes for two observers, one at rest (black axes, red gridlines) and one in motion (blue axes and gridlines) for a single space-time event, time dilation, or length contraction. The coordinate axes can be shown for each observer, and the relative velocity can be changed at will.

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Contributed by: Frederick W. Strauch (August 2011)

Open content licensed under CC BY-NC-SA

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## Details

The Lorentz transformation between two reference frames with coordinates and , in relative motion with velocity , can be represented by , or the inverse , where and . The inverse transformation is used to plot gridlines of constant and .

See also:

http://en.wikipedia.org/wiki/Lorentz_transformation

http://en.wikipedia.org/wiki/Time_dilation

http://en.wikipedia.org/wiki/Length_contraction

## Permanent Citation