Landmarks: Breaking the Mirror
Symmetry is a cherished principle in theoretical physics. For example, the mirror reflection of any physical process appears to operate according to the same laws as its real-world counterpart. So it was a huge surprise in the 1950s when researchers showed in the Physical Review that mirror symmetry doesn’t always apply. They found that reactions involving the weak nuclear force, such as the radioactive decay of cobalt-60, can violate parity conservation, as the mirror symmetry is known. The discovery marked the abrupt introduction of symmetry breaking into fundamental physics.
The weaker the interaction the stronger the symmetry breakings. Gravitation is by far the weakest interaction. Covariance with respect to reflection in space and time is not required by the Poincaré group of Special Relativity or the Einstein group of General Relativity. External symmetry (coupled to rotation and translation) parity is not a Noetherian symmetry. There is every reason to believe left and right shoes vacuum free fall along non-identical trajectories.
One can obtain opposite parity atomic mass distributions and an apparatus sufficiently sensitive to detect Equivalence Principle violation thereform. Perform a parity Eötvös experiment by opposing chemically identical single crystal test masses of enantiomorphic space groups P3(1)21 and P3(2)21 quartz (lighter atoms) or cinnabar (heavier atoms). Sombody should probe spacetime geometry with test mass geometry. Somebody should look.