Lorentz Transformation for a Rotating Square

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This Demonstration shows the deformation of a rotating square according to the Lorentz transformation from the frame of reference of a rocket (RFR) moving with a velocity . Beta () is the ratio , where is the speed of light, so goes from 0 to 1.


The plot shows images of a rotating square as taken by a hypothetical camera placed on the RFR, which is located at . The camera takes the photo when on the axis. The coordinate refers to the position in the laboratory frame of reference (LFR).

The value of the angular speed of the rotating square must be chosen with care. Its value of 0.2—chosen for convenience, in order not to exceed the speed of light—is in the arguments of the Sin[] and Cos[] functions. A speed greater than can lead to more than one root in the solutions of the equations and it would be impossible to plot the rotating square. Play with the value of the angular speed to make the square rotate with different velocities.

The longitude makes the shape of the square change from a square to a cross.


Contributed by: Carlos Anton Solanas (March 2011)
Open content licensed under CC BY-NC-SA



Snapshot 1: a rotating cross with the RFR at rest ()

Snapshot 2: by increasing , the square changes shape

Snapshot 3: in the limit as , the square becomes a vertical line, according to the Lorentz contraction

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