Quantum gravity: Meaning and measurement

Abstract

A discussion of the meaning of a physical concept cannot be separated from discussion of the conditions for its ideal measurement. We assert that quantization is no more than the invocation of the quantum of action in the explanation of some process or phenomenon, and does not imply an assertion of the fundamental nature of such a process. This leads to an ecumenical approach to the problem of quantization of the gravitational field. There can be many valid approaches, each of which should be judged by the domain of its applicability to various phenomena. If two approaches have overlapping domains, the relation between them then itself becomes a subject of study. We advocate an approach to general relativity based on the unimodular group, which emphasizes the physical significance and measurability of the conformal and projective structures. A discussion of the method of matched asymptotic expansions, and of the weakness of terrestrial sources compared with astrophysical and cosmological sources, leads us to suggest theoretical studies of gravitational radiation based on retrodiction (observation) rather than prediction (experimentation).

The Present Situation in Quantum Theory and its Merging with General Relativity

“…This theory questioned applicability of the standard law of large numbers. The existence of the limit (10) in Q p , typically implies nonexistence of such a limit in R. 18 Thus reconsideration of QT on the basis the "genuine p-adic model" should lead to reconsideration of the role and interpretation of probability in QT. The first steps in this direction were done in author's works [59], [54], [66] (the latter paper is devoted to the p-adic probabilistic treatment of the EPR-experiment).…”

“…2 There has been some valuable work done in this direction, see, in particular, [10]. 3 Only recently quantum information was coupled with QFT-foundations [11]- [15].…”

“…The latter is endowed with so called weak topology. 10 The systems of vectors (e 1 , ..., e n , ...) and functionals (f 1 , ..., f n , ...) are biorthogonal bases. The expansion (2) can be written as…”