Terrell rotation

This behaviour was described independently by both Roger Penrose and James Edward Terrell.

Since the Lorentz transform does not depend on the acceleration, the visual appearance of the object depends only on the instantaneous velocity, and not the acceleration of the observer.Terrell's and Penrose's papers pointed out that although special relativity appeared to describe an "observed contraction" in moving objects, these interpreted "observations" were not to be confused with the theory's literal predictions for the visible appearance of a moving object.

A previously popular description of special relativity's predictions, in which an observer sees a passing object to be contracted (for instance, from a sphere to a flattened ellipsoid), was wrong.

These papers pointed out that some existing discussions of special relativity were flawed and "explained" effects that the theory did not actually predict – while these papers did not change the actual mathematical structure of special relativity in any way, they did correct a misconception regarding the theory's predictions.

A representation of the Terrell effect can be seen in the physics simulator "A Slower Speed of Light," published by MIT.

Comparison of the measured length contraction of a cube versus its visual appearance. The view is from the front of the cube at a distance four times the length of the cube's sides, three-quarters of the way from bottom to top, as projected onto a vertical screen (so that the vertical lines of the cube may initially be parallel).
A globe, moving at various speeds to the right, is observed from three diameters distance from its nearest point on the surface (marked by a red cross). The left image shows the globe's measured, Lorentz-contracted shape. The right image shows the visual appearance of the globe.