Résumé
Que signifie « maintenant » à la plus grande échelle ? Cette revue expose ce que la relativité générale fixe du temps, quelles horloges l’observation utilise réellement et trois lectures courantes du temps cosmologique, avec le désaccord qu’une revue achevée devrait trancher.
Mots-clésgeneral relativity, cosmological time, redshift, clocks
Texte intégral
Introduction
General relativity is precise about how clocks behave and silent about which clock a cosmological statement is timed against. That silence is not a defect; it is the part of the subject a review has to make explicit.
The record is arranged so that theory comes first, observation second, and the interpretation last. Putting interpretation last keeps the review from arguing about definitions before the reader knows which quantities are measurable.
This is a specimen: no result is claimed, and every numeric slot is left open.
What the theory fixes
The theory fixes the relation between a clock and the metric along its worldline. Everything else — simultaneity, ordering, duration — is a statement about a family of worldlines, and therefore about a choice.
Reading the equation as a definition of what a clock measures, rather than as a law about time itself, is the move that makes the rest of the review tractable.
Clocks that observation can use
Observation does not have a clock in the abstract; it has observables. Table 1 sorts three common ones by the quantity they actually constrain, which is also the reason they disagree when the background changes.
| Clock | Observable | Limits it meets |
|---|---|---|
| atomic | frequency ratio | local systematics |
| pulsar | arrival time | dispersion and noise |
| expansion | redshift | model dependence |
Table 1. Observable clocks and the quantity each constrains. Layout demonstration only.
The third row is the one the review spends its time on: the expansion clock is not a device, it is an inference, and an inference needs a model before it can be read as a duration.
Three readings of cosmic time
The literature can be read as offering three positions, which differ less about the mathematics than about what a cosmological statement is about: the universe as a whole, an observer, or a class of observers.
- Cosmic time as a global parameter fixed by symmetry.
- Cosmic time as a proper time along a chosen family of observers.
- Cosmic time as a bookkeeping device with no physical claim.
The specimen does not choose among them. Naming the three is the contribution of the arranged version; a finished review would say which observational programme could distinguish them, if any.
What a finished review adds
A completed version would add a reference list long enough to be useful, a table of observational constraints with real uncertainties, and a section that states plainly which disagreements are linguistic and which are physical.
References
- Misner, C. W., Thorne, K. S., and Wheeler, J. A. (1973). Gravitation. W. H. Freeman.
- Wald, R. M. (1984). General Relativity. University of Chicago Press.
- Ellis, G. F. R., and van Elst, H. (1999). Cosmological models. In Theoretical and Observational Cosmology, 1–116.