The DOI matches its Crossref record; 37 of the 37 references it cites were found in a registry or an index.
Evolution without evolution: Dynamics described by stationary observables
Abstract
Because the time parameter in the Schr\"odinger equation is not observable, energy apparently obeys a superselection rule in the same sense that charge does. That is, observables must all commute with the Hamiltonian and hence be stationary. This means that it is consistent with all observations to assume that any closed system such as the Universe is in a stationary state. We show how the observed dynamic evolution of a system can be described entirely in terms of stationary observables as a dependence upon internal clock readings.
Overview
The claims and statistics of this paper haven’t been checked yet.
Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.
Integrity signals
Registry
Cites
Statistics
Verification
Claims the paper makes
The claims and statistics of this paper haven’t been checked yet.
Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.
Self-check
Percentages, sums and reported differences re-computed from the paper’s own numbers.
The self-check needs the paper’s full text.
Citations
Cites
Angular Momentum in Quantum Mechanics
Edmonds, A. R. (1957) · Princeton University Press eBooks · doi:10.1515/9781400884186 · Cited by 3,876
Elementary Theory of Angular Momentum
Rose, M. E., & Feld, B. T. (1957) · Physics Today · doi:10.1063/1.3060162 · Cited by 3,612
Quantum Theory of Gravity. I. The Canonical Theory
DeWitt, B. S. (1967) · Physical Review · doi:10.1103/physrev.160.1113 · Cited by 3,385
Elementary Theory of Angular Momentum
Pincherle, L. (1958) · Physics Bulletin · doi:10.1088/0031-9112/9/2/013 · Cited by 2,788
Gravitation: an Introduction to current research
Witten, L. (1962) · CERN Document Server (European Organization for Nuclear Research) · Cited by 2,004
Role of Conformal Three-Geometry in the Dynamics of Gravitation
York, J. W. (1972) · Physical Review Letters · doi:10.1103/physrevlett.28.1082 · Cited by 1,392
An algebraic approach to quantum field theory
Haag, R., & Kastler, D. (1964) · Journal of Mathematical Physics · doi:10.1063/1.1704187 · Cited by 1,250
PCT, spin and statistics, and all that
L.R. (1964) · Nuclear Physics · doi:10.1016/0029-5582(64)90049-5 · Cited by 1,000
Misner, C. W. (1969) · Physical Review Letters · doi:10.1103/physrevlett.22.1071 · Cited by 856
Gravitation—An introduction to current research
Kilmister, C. W. (1963) · Planetary and Space Science · doi:10.1016/0032-0633(63)90130-2 · Cited by 729
Cited by
Reference frames, superselection rules, and quantum information
Bartlett, S. D., Rudolph, T., & Spekkens, R. W. (2007) · Reviews of Modern Physics · doi:10.1103/revmodphys.79.555 · Cited by 827
TIME AND INTERPRETATIONS OF QUANTUM GRAVITY
KUCHAŘ, K. V. (2011) · International Journal of Modern Physics D · doi:10.1142/s0218271811019347 · Cited by 657
Time in quantum gravity: An hypothesis
Rovelli, C. (1991) · Physical Review D · doi:10.1103/physrevd.43.442 · Cited by 445
Quantum mechanics without time: A model
Rovelli, C. (1990) · Physical Review D · doi:10.1103/physrevd.42.2638 · Cited by 316
Rovelli, C. (1991) · Classical and Quantum Gravity · doi:10.1088/0264-9381/8/2/012 · Cited by 250
Metadata
- Authors
- Page, D. N., & Wootters, W. K.
- Venue
- Physical Review D
- Publisher
- American Physical Society (APS)
- Published
- 1983-06-15
- Volume
- 27
- Issue
- 12
- Pages
- 2885-2892
- ISSN
- 0556-2821 (ISSN-L)
- OpenAlex
- W2034864060
- Cited by
- 578
- References
- 37
- FWCI
- 0.00
- Type
- journal article
- Language
- en
- Open access
- closed
About these checks
Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.
Statistics and arithmetic are recomputed, not judged.
Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.
What counts as a claim ›How we measure confidence ›How we check this ›
Are you an author, or do you see a problem with this page? Request a review
How to cite
Cite CoChat for the checks on this page, and the paper for its own findings.
- This page
- CoChat. (2026). Citation check: Evolution without evolution: Dynamics described by stationary observables. https://app.cochat.ai/papers/10.1103/physrevd.27.2885
- The paper
- Page, D. N., & Wootters, W. K. (1983). Evolution without evolution: Dynamics described by stationary observables. Physical Review D. https://doi.org/10.1103/physrevd.27.2885
Data sources
Bibliographic data: Semantic Scholar, OpenAlex, Crossref.
Contains information from the Semantic Scholar Academic Graph Datasets, made available under the ODC Attribution License (ODC-BY 1.0).
Semantic Scholar’s data is described in: Kinney, R., et al. (2023). The Semantic Scholar Open Data Platform. arXiv:2301.10140.