The Dimensionless Constants of Physics

Quantum Gravity Meets &HPS

“…Also the solution of this question may be expected to reveal deeper knowledge of the relations, only intimated by Hilbert, holding between gravity and electricity, and of a further integration of these relations with the quantum hypothesis. (ibid., p. 750) 17 This interpretation is strengthened by the fact that Haas went on to consider the various possible combinations of other constants in other contexts, investigating the way they demarcate domains [51].…”

“…51 Taken together, when satisfied, these constraints are taken to reflect spacetime diffeomorphism invariance; together they tell us that the geometry of spacetime is not affected by the 49 It is possible that this approach was developed by DeWitt using material he'd had to master for his work in higher-dimensional Lagrangian hydrodynamics, in which one has to consider a mesh that forms a dynamical background for the materials one is studying. 50 Donald Salisbury has investigated the early history of the canonical quantization formalism, with its introduction of 'constraints' (on which see below): [85; 86].…”

“…However, he entirely omits from his story equally crucial work by Paul Weiss (a student of Max Born and Paul Dirac): [106; 107]. 51 Hamiltonian constraints, in general relativity, constitute an infinite set of relations holding between the canonical variables of the theory (the spatial metric and its conjugate: (gµν , p µν )). Any choice of physical variables must satisfy these constraints on some initial hypersurface.…”