2010/11/30 by Ian D. Lawrie · 5 citations
Mathematics · Physics and Astronomy · #Applied mathematics #Black Holes and Theoretical Physics #Classical mechanics #Cosmology #Hamiltonian constraint #Loop quantum cosmology #Loop quantum gravity #Mathematics #Noncommutative and Quantum Gravity Theories #Observability #Observable #Observer (physics) #Physics #Problem of time #Quantum #Quantum Mechanics and Applications #Quantum cosmology #Quantum gravity #Quantum mechanics #Statistical physics #Theoretical physics #Time evolution #Unobservable #gr-qc #hep-ph #hep-th #quant-ph
paper · pdf · doi:10.1103/physrevd.83.043503
published in Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields 83(4) (American Physical Society) · 21 pages, no figures; minor revisions and added references; matches version in Phys Rev D
openalex publication_date 2011/02/01 · arxiv created 2011/03/09 · arxiv updated 2011/03/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
A commonly adopted relational account of time evolution in generally covariant systems, and more specifically in quantum cosmology, is argued to be unsatisfactory, insofar as it describes evolution relative to observed readings of a clock that does not exist as a bona fide observable object. A modified strategy is proposed, in which evolution relative to the proper time that elapses along the worldline of a specific observer can be described through the introduction of a ``test clock,'' regarded as internal to, and hence unobservable by, that observer. This strategy is worked out in detail in the case of a homogeneous cosmology, in the context of both a conventional Schr"odinger quantization scheme, and a ``polymer'' quantization scheme of the kind inspired by loop quantum gravity. Particular attention is given to limitations placed on the observability of time evolution by the requirement that a test clock should contribute only a negligible energy to the Hamiltonian constraint. It is found that suitable compromises are available, in which the clock energy is reasonably small, while Dirac observables are reasonably sharply defined.