Quanta, Logic And Spacetime: Variations On Finkelstein’s Quantum Relativity

Offering a brief description of Finkelstein’s approach to quantum theory and some of its ramifications, this text specifically examines his suggestion that some sort of quantum-set-like structure should underlie our macroscopic perception of spacetime, developing it to the point where a proportion of fundamental physics (for a massless world) may be formally derived from the ground up. In detail, a model of what Finkelstein has called a quantum net , in conjunction with a single Schwinger-like dynamical principle, gives rise to the standard Langrangians for: massless Dirac fermions; general relativity; and Yang-Mills fields for the gauge groups SU(n), n = 3,4. These Langrangians emerge replete with (Feynman) gauge-fixing terms and ghost fields.