The True Rotational Symmetry of Space The following deep,
elegant, and beautiful explanation of the true rotational
symmetry of space comes from the late Sidney Coleman, as
presented to his graduate physics class at Harvard. This
explanation takes the form of a physical act that you will
perform yourself. Although elegant, this explanation is verbally
awkward to explain, and physically awkward to perform. It may
need to be practised a few times. So limber up and get ready:
you are about to experience in a deep and personal way the true
rotational symmetry of space! At bottom, the laws of physics are
based on symmetries, and the rotational symmetry of space is one
of the most profound of these symmetries. The most rotationally
symmetric object is a sphere. So take a sphere such as a
soccer—or basket-ball that has a mark, logo, or unique lettering
at some spot on the sphere. Rotate the sphere about any axis:
the rotational symmetry of space implies that the shape of the
sphere is invariant under rotation. In ad