×

Jumping identities of particles. (English) Zbl 0981.00500

Summary: The relationship between equality and identity is one of the unsolved problems in science. Leibniz’s approach which goes back to Spinoza stresses real space. Suppose there are several identical universes present in an otherwise empty absolute space: then this is equivalent to only a single universe existing. Weyl realized that Leibniz’s group-theoretic result in real space remains valid in a more abstract space – configuration space. Suppose mathematically equal particles exist: then configuration space possesses Leibniz’s symmetry. The collapse down to a single surviving sub-universe occurs in this space as well. Consequences for the real space in which the particles live follow. The boundaries between adjacent sub-universes in configuration space correspond to well-defined relative positions in real space. Therefore at certain points in real space the particles exchange their identities. If the 2 equal particles live \(n\) a ring, the swap occurs under two conditions: coincidence and “anti-coincidence.” When the particles pass through opposing positions on the ring, they exhange their identities in a jump. The “leapswap” has implications ranging from chemistry to personal identity.

MSC:

00A30 Philosophy of mathematics
00A99 General and miscellaneous specific topics
PDFBibTeX XMLCite