Geometro-Stochastic Quantum Gravity

Abstract

The decision as to what is observable in a physical theory affects in a most fundamental manner its interpretation, and even the future course of its structural development. Hence, some recent studies (Howard and Stachel, 1989) of the development by Einstein of classical general relativity (CGR) during the 1907–1915 period have devoted particular attention to the question as to what are the quantities that are “observable” in CGR. These studies point to a fundamental feature of CGR, that underlies its principle of equivalence (Norton, 1989), and which eventually led Einstein to adopting in CGR the principle of general covariance, despite some temporary reservations that stemmed from his well-known “hole” argument1. This fundamental general covariance feature of CGR reflects the fact that the only fundamental observable entities in CGR are spacetime coincidences (Norton, 1987), which are represented by the points of a Lorentzian manifold. In Einstein’s own words: “All our space-time verifications invariably amount to a determination of space-time coincidences. If, for example, events consisted merely in the motion of material points, then ultimately nothing would be observable but the meetings of two or more of these points.” (Einstein, 1916, 1952, p. 117) — emphasis added.