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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You can drag the space-time event (black dot) and see its and coordinates by mousing over it.

Time dilation is the phenomenon whereby two observers disagree on the time interval between two events: moving clocks run slowly. Here the proper time of a moving observer (in blue) corresponds to a longer (dilated) time for an observer a