It does happen, though. For example, until 1956 all evidence indicated that processes involving elementary particles would be essentially unchanged when the directions of the particles were replaced by their mirror-image directions. This "law of conservation of parity" was disproved when an elegant experiment performed by physicists at NIST showed that the mirror-images of a process were in fact distinguishable. See The Fall of Parity at NIST's web site for an account of the experiment.
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