Symmetry-Induced Disappearance of Reality: The Leibniz Effect

The philosopher Leibniz proposed a paradox to Newton’s friend Clarke: suppose that the universe existed twice in perfect symmetry; then it nevertheless would exist only once. Leibniz’s ‘principle of the identity of the indiscernible’ was first taken seriously by Weyl, the theoretician of symmetry. Weyl saw that a test may be possible if perfectly equal particles exist. The symmetry then exists in position space, a space more abstract than real space. However, since the former is only a way of talking about the latter, the absurd collapse would still make itself felt in reality. A mobile made of two equal balls captures it all, generating stunning illusions of switching identities. They become reality if the two balls are perfectly equal. Symmetry is stronger than classical logic.