On the nature of quantum geometrodynamics

Abstract

Classical gravitation, electromagnetism, charge, and mass are described in a preceding article in terms of curved empty space and nothing more. In advance of the detailed quantization of this pure Einstein-Maxwell geometrodynamics, an attempt is made here (1) to bring to light some of the most important properties to be expected for quantized geometrodynamics and (2) to assess whether this theory, without addition of any inventive elements, can contribute anything to the understanding of the elementary particle problem. Gravitational field fluctuations are concluded to have qualitatively new consequences at distances of the order of ( h ̷ G c 3 ) 1 2 = 1.6 × 10 −33 cm . They lead one to expect the virtual creation and annihilation throughout all space of pairs with electric charges of the order ∼( h ̷ c) 1 2 and energies of the order ( h ̷ c 5 G ) 1 2 = (2.18 × 10 −5 g)c 2 = 2.4 × 10 22 mc 2 . The problem is discussed, to what extent these charges can be identified with the unrenormalized or “undressed” charges of electron theory. Decisive for the future usefulness of quantum geometroydnamics is the question whether spin shows itself as an inevitable geometrical concomitant of quantization, or whether it and other ideas have to superposed on this purely geometrical description of nature.