Clocks |

**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 10^{15},
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
10^{16}; 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
10^{17}; 2011, The accuracy and stability of the best terrestrial
artificial clocks substantially exceed those of astronomical sources as timekeepers.

* __Future__: 2010, The use of Josephson junctions
may lead to clocks with an accuracy of 1 part in 10^{19};
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 10^{15}];
news pw(08)mar
[1 part in 10^{17}];
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].

**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];
Erker et al PRX(17)
& Short Phy(17) [thermodynamic cost of measuring time].

@ __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];
> s.a. fine structure constant variations.

@ __Nuclear clocks__: news Phy(11)jun,
ns(11)jun [work on Th-229 nuclei];
news ns(11)nov.

@ __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 a1802 [complementarity relation, and gravitational time lag];
Woods et al a1806 [more accurate than classical ones].

@ __And quantum mechanics__: Salecker & Wigner PR(58);
Frenkel qp/05;
Myers & Madjid AP(14)-a1407 [conceptual];
Erker et al a1609 [fundamental limitations and resources];
Lock & Fuentes a1609 [relativistic, semiclassical model];
Stupar et al a1806 [accuracy of time scales generated by clocks];
> s.a. measurements [time]; time in quantum mechanics;
zeno effect.

@ __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 a1507 [physical clocks and time measurement]; Bratek a1511 [relativistic ideal clock model]; Müller et al SSR(18)-a1702 [with high-performance clocks]; > see Chronogeometry; deformed uncertainty relations; gravitomagnetism [clock effect]; quantum gravity phenomenology; tests
of general relativity.

**Synchronization**

* __ 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].

@ __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).

@ __ 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].

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