Visualizing The Transformations in Minkowski Space
Lorentz transformations can be depicted on the Minkowski light cone spacetime diagram.
Accelerating particle (curved worldline). Lorentz transformations on the Minkowski light cone spacetime diagram, for one space and one time dimension.The yellow axes are the rest frame of an observer, the blue axes correspond to the frame of a moving observer
The red lines are world lines, a continuous sequence of events: straight for an object travelling at constant velocity, curved for an object accelerating. Worldlines of light form the boundary of the light cone.
The purple hyperbolae indicate this is a hyperbolic rotation, the hyperbolic angle ϕ is called rapidity (see below). The greater the relative speed between the reference frames, the more "warped" the axes become. The relative velocity cannot exceed c.
The black arrow is a displacement four-vector between two events (not necessarily on the same world line), showing that in a Lorentz boost; time dilation (fewer time intervals in moving frame) and length contraction (shorter lengths in moving frame) occur. The axes in the moving frame are orthogonal (even though they do not look so).
Read more about this topic: Lorentz Transformation
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