In General > s.a. Frequency; time; units [optical strontium clocks as candidates for a new definition of the second].
* Ideal clock: A clock that gives the time to unlimited accuracy, and measures proper time along its worldline, unaffected by acceleration.
* Atomic clocks: In general they work by shooting microwaves into a sample of cooled Cs atoms and reading out the microwave-absorption frequency which corresponds to a specific quantum transition for electrons in the Cs atoms; The microwave frequency setting is used to define the "second."
* Variants: In optical lattice clocks, millions of atoms are trapped and interrogated simultaneously, dramatically improving clock stability.
* Most precise: 2002, The NIST-F1, will have an accuracy of 1 part in 1015, 1 s in 30 Myr, used in the GPS; If one could cool the atoms to lower temperatures (thus reducing the blurring caused by their movement) or observe them for longer periods, the precision of the whole readout process (and the standardization of the second) would improve; NIST plans to have several SPARC "space clocks" in orbit in the next few years; 2006, The current accuracy of NIST-F1 is 1 s in 70 Myr, and is soon expected to reach 1 part in 1016; In the not-too-distant future, our ability to compare atomic frequency standards and clocks at different laboratories will be limited by our knowledge of the geoid; 2007, The current accuracy of the best NIST optical clock is 1 part in 1017; 2011, The accuracy and stability of the best terrestrial artificial clocks substantially exceed those of astronomical sources as timekeepers; 2020, The best lab-based clocks have a fractional uncertainty of 9.4 × 10−19, and the best transportable atomic clocks (used to measure gravitational redshift, for example) 5 × 10−18.
* Future: 2010, The use of Josephson junctions may lead to clocks with an accuracy of 1 part in 1019; The shortest time scale known so far is given by the lifetime of the Z boson, 10−25 s (its decay produces 45.5-GeV neutrinos); 2011, Some progress in finding nuclei with suitable energy levels for use as nuclear clocks; Optical lattice clocks hold great promise and aim at a 10−18 fractional accuracy.
@ Precision: Bergquist et al PT(01)mar [1 part in 1015]; news pw(08)mar [1 part in 1017]; Guéna et al PRL(11) [improving atomic fountain clocks]; Huntemann et al PRL(16) + news wired(16)feb [single-Yb-ion-clock with 1.1 × 10−18 relative frequency uncertainty]; news pt(20)may [transportable clocks]; news sn(21)mar [new atomic clocks accurate to within 10−17, and future redefinition of the second].

References > s.a. astronomy; fine-structure constant [variation]; quantum technology.
@ General: Aveni 89; Itano & Ramsey SA(93)jul; Hackman & Sullivan AJP(95)apr [RL]; Will gq/95 [and general relativity]; Barnett 98, 99; Kleppner PT(06)mar; Hartnett & Luiten RMP(11)-a1004 [astrophysical vs terrestrial clock stability]; Riehle Phy(12) [optical atomic clocks]; Datta Phys(21) [time intervals].
@ Atomic clocks: Jones 00 [I]; Audoin & Guinot 01; Gibbs SA(02)sep; Gill & Margolis pw(05)may [optical]; news pw(06)aug [T effect]; Camparo PT(07)nov; Appel Phy(09) [new technology]; Gibble Phy(10) [increased clock coherence time from interactions between atoms]; news ns(13)aug [used to simulate ultracold quantum systems]; Delva & Lodewyck a1308-proc [in metrology and geodesy]; news sn(14)mar [future atomic clocks connected into a global superclock]; Kessler et al PRL(14) [based on entangled qubits]; Akerman & Ozeri a1709 [atomic combination clocks]; news ns(19)may [new generation of Rb-based small-scale optical clocks]; > s.a. fine structure constant variations.
@ Nuclear clocks: news Phy(11)jun, ns(11)jun [work on Th-229 nuclei]; news ns(11)nov; Peik et al a2012 [and tests of fundamental physics].
@ Clock paradox: Iorio FPL(05) [in special and general relativity]; Jones & Wanex FPL(06)phy [static homogeneous metric].
@ Quantum clocks: Buzek et al PRL(99)qp/98; Chou et al PRL(10)-a0911 + news wired(10)feb [quantum-logic atomic clock]; Derevianko & Katori RMP(11) + news sn(11)oct [optical lattice clocks]; Hodges PRA(13) [electron spin states in diamond]; Gessner a1402 [ideal]; Tempel & Aspuru-Guzik NJP(14)-a1406 [Feynman's clock, for open quantum systems]; Zhou et al CQG(18)-a1802 [complementarity relation, and gravitational time lag]; Woods et al a1806 [more accurate than classical ones]; Paige et al PRL(20)-a1809, Khandelwal et al a1904 [time dilation and uncertainty]; > s.a. special-relativistic kinematics [time dilation].
@ And quantum mechanics: Salecker & Wigner PR(58); Frenkel qp/05; Myers & Madjid AP(14)-a1407 [conceptual]; Lock & Fuentes in(17)-a1609 [relativistic, semiclassical model]; Stupar et al a1806 [accuracy of time scales generated by clocks]; Smith a2004-GRF [quantum time dilation]; > s.a. measurements [time]; time in quantum mechanics; zeno effect.
@ And thermodynamics: Erker et al PRX(17)-a1609 & Short Phy(17) [thermodynamic cost of measuring time]; Milburn a2007; Pearson et al PRX(21) [classical].
@ And spacetime structure, gravitation: Ord & Mann IJTP(12) [finite-frequency clocks measure spacetime area]; Sinha & Samuel CQG(15)-a1401 [quantum limit on clock stability in a gravitational field]; Angélil et al PRD(14)-a1402 [miniaturization of extremely accurate atomic clocks and precise timing experiments by satellite missions]; Lindkvist et al SRep(15)-a1409 [motion-induced degradation of the precision of quantum clocks]; Lorek et al CQG(15)-a1503 [impossibility of ideal clocks in quantum field theory]; Castro-Ruiz et al PNAS(17)-a1507 [physical clocks and time measurement]; Bratek a1511 [relativistic ideal clock model]; Müller et al SSR(18)-a1702 [with high-performance clocks]; Gambini & Pullin JPC(20)-a2006 [minimum time uncertainty]; > see Chronogeometry; deformed uncertainty relations; gravitomagnetism [clock effect]; quantum gravity phenomenology; tests of general relativity.

* Huygens' experiment: In 1665 Christiaan Huygens observed that pendulum clocks hung on the same wall tend to sync up, with opposite phases.
@ General references: AS(90)303 [with computers]; Rowlands FPL(06) [and non-inertial observers].
@ Huygens' experiment: Bennett et al PRS(02) [modern analysis, model]; Kapitaniak et al PRP(12); news Huff(15)jul.
@ In special relativity: Anderson et al PRP(98); Russo NCB(06) [conventionality]; Nissim-Sabat a2004 [against conventionality?].
@ In general relativity: Bahder in(09)gq/04 [near Earth]; Wang et al PRD(16)-a1501 [satellite-based].
@ In quantum theory: Yurtsever & Dowling PRA(02)qp/00; Preskill qp/00; Giovannetti et al Nat(01)qp, PRL(01)qp, PRA(02)qp/01, PRA(02)qp/01, PRA(04); Boixo et al LP(06)qp [with decoherence].

Timekeeping > s.a. astronomy.
* History: Before atomic timekeeping, clocks were set to the skies; Since 1972, radio signals have been broadcasting atomic seconds, with leap seconds occasionally added to keep the signals synchronized with the actual rotation of Earth, which is less regular than atomic timekeeping (one is due to be added on 30 June 2012); > s.a. Vsauce YouTube video.
@ General references: Andrewes SA(02)sep; Eastman et al PASP(10)-a1005 [with better than one-minute accuracy, for astrophysical data]; Hobbs a1011-proc [pulsar-based timescale]; Seago et al a1111-conf [Colloquium on Decoupling Civil Timekeeping from Earth Rotation]; news pw(12)aug [using pulsars].
@ Calendars: Shimony 98 [fiction re Gregorian reform]; Richards 98 [history]; Aveni 02; Izquierdo Peña a0812 [Colombian Muisca calendar]; Mishra a1007 [in India]; Akrami a1111 [development of the Iranian calendar]; Sigismondi a1401 [on the need for the Gregorian reform].
@ Leap seconds: in Kleppner PT(06)mar; Finkleman et al AS(11)jul-a1106 [and Coordinated Universal Time]; news bbc(12)jan [debate].
@ History: Bartky 00 [XIX century America]; Audoin & Guinot 01; Vodolazhskaya AAT-a1309 [sundials of the Bronze Age]; Vodolazhskaya a1408 [ancient Egyptian methods for measuring time]; Sigismondi a1412 [synchronization and time zones].
@ Dating methods: Turney 07; news Cosmos(17)oct [luminescence dating]; > s.a. elements [carbon dating].

main pageabbreviationsjournalscommentsother sitesacknowledgements
send feedback and suggestions to bombelli at – modified 10 may 2021