Atomic clock - Knowledge

3367:. As the optical experimental clocks move beyond their microwave counterparts in terms of accuracy and stability performance, this puts them in a position to replace the current standard for time, the caesium fountain clock. In the future this might lead to redefining the caesium microwave-based SI second, and other new dissemination techniques at the highest level of accuracy to transfer clock signals will be required that can be used in both shorter-range and longer-range (frequency) comparisons between better clocks and to explore their fundamental limitations without significantly compromising their performance. The BIPM reported in December 2021 based on the progress of optical standards contributing to TAI the Consultative Committee for Time and Frequency (CCTF) initiated work towards a redefinition of the second expected during the 2030s. 14036: 3849:(2021), 3 options were considered for the redefinition of the second sometime around 2026, 2030, or 2034. The first redefinition approach considered was a definition based on a single atomic reference transition. The second redefinition approach considered was a definition based on a collection of frequencies. The third redefinition approach considered was a definition based on fixing the numerical value of a fundamental constant, such as making the Rydberg constant the basis for the definition. The committee concluded there was no feasible way to redefine the second with the third option, since no physical constant is known to enough digits currently to enable realizing the second with a constant. 382: 860:, which rely on the 1.4 GHz hyperfine transition in atomic hydrogen, are also used in time metrology laboratories. Masers outperform any commercial caesium clock in terms of short-term frequency stability. In the past, these instruments have been used in all applications that require a steady reference across time periods of less than one day (frequency stability of about 1 part in ten for averaging times of a few hours). Because some active hydrogen masers have a modest but predictable frequency drift with time, they have become an important part of the BIPM's ensemble of commercial clocks that implement International Atomic Time. 551: 3169: 3957:. Galileo started offering global Early Operational Capability (EOC) on 15 December 2016, providing the third, and first non-military operated, global navigation satellite system. Galileo System Time (GST) is a continuous time scale which is generated on the ground at the Galileo Control Centre in Fucino, Italy, by the Precise Timing Facility, based on averages of different atomic clocks and maintained by the Galileo Central Segment and synchronised with TAI with a nominal offset below 50 nanoseconds. According to the European GNSS Agency, Galileo offers 30 nanoseconds timing accuracy. 658: 46: 3291: 3935: 2342: 1241:) on a hyperfine transition, the field in the cavity oscillates, and the cavity is tuned for maximum microwave amplitude. Alternatively, in a caesium or rubidium clock, the beam or gas absorbs microwaves and the cavity contains an electronic amplifier to make it oscillate. For both types, the atoms in the gas are prepared in one hyperfine state prior to filling them into the cavity. For the second type, the number of atoms that change hyperfine state is detected and the cavity is tuned for a maximum of detected state changes. 3356:

oscillators are in slightly different environments. These are causing differing reactions to gravity, magnetic fields, or other conditions. This miniaturized clock network approach is novel in that it uses an optical lattice of strontium atoms and a configuration of six clocks that can be used to demonstrate relative stability, fractional uncertainty between clocks and methods for ultra-high-precision comparisons between optical atomic clock ensembles that are located close together in a metrology facility.

4353:(this corresponds to a 1 degree uncertainty in the radiation environment as seen by the atoms in NIST-F1). To improve the performance of the NIST primary frequency standard, we sought to reduce the uncertainty due to the BBR effect. To accomplish this goal and to better understand the accepted model of the BBR shift, we developed NIST-F2, a laser-cooled Cs fountain primary frequency standard in which the microwave cavity structure and flight tube operate at cryogenic temperatures ( 14030: 309: 1024: 13719: 4035:. Some manufacturers may label radio clocks as atomic clocks, because the radio signals they receive originate from atomic clocks. Normal low-cost consumer-grade receivers that rely on the amplitude-modulated time signals have a practical accuracy uncertainty of ± 0.1 second. This is sufficient for many consumer applications. Instrument grade time receivers provide higher accuracy. Radio clocks incur a propagation delay of approximately 1 1077: 4110: 726:. The closer the frequency is to the inherent oscillation frequency of the atoms, the more atoms will switch states. Such correlation allows very accurate tuning of the frequency of the microwave radiation. Once the microwave radiation is adjusted to a known frequency where the maximum number of atoms switch states, the atom and thus, its associated transition frequency, can be used as a timekeeping oscillator to measure elapsed time. 2231: 918: 1119: 2373:. The list contains the frequency values and the respective standard uncertainties for the rubidium microwave transition and for several optical transitions. These secondary frequency standards are accurate at the level of 10; however, the uncertainties provided in the list are in the range 10 – 10 since they are limited by the linking to the caesium primary standard that currently (2018) defines the second. 13729: 114: 3919:. Periodic corrections are performed to the on-board clocks in the satellites to keep them synchronized with ground clocks. The GPS navigation message includes the difference between GPST and UTC. As of July 2015, GPST is 17 seconds ahead of UTC because of the leap second added to UTC on 30 June 2015. Receivers subtract this offset from GPS Time to calculate UTC. 3027: 3034:'s strontium optical atomic clock is based on neutral atoms. Shining a blue laser onto ultracold strontium atoms in an optical trap tests how efficiently a previous burst of light from a red laser has boosted the atoms to an excited state. Only those atoms that remain in the lower energy state respond to the blue laser, causing the fluorescence seen here. 1768:("LO") are heterodyned to near zero frequency by harmonics of the repeating variation in feedback sensitivity to the LO frequency. The effect places new and stringent requirements on the LO, which must now have low phase noise in addition to high stability, thereby increasing the cost and complexity of the system. For the case of an LO with 2121: 769:. They do this by designing and building frequency standards that produce electric oscillations at a frequency whose relationship to the transition frequency of caesium 133 is known, in order to achieve a very low uncertainty. These primary frequency standards estimate and correct various frequency shifts, including relativistic 3081:. A major obstacle to developing an optical clock is the difficulty of directly measuring optical frequencies. This problem has been solved with the development of self-referenced mode-locked lasers, commonly referred to as femtosecond frequency combs. Before the demonstration of the frequency comb in 2000, 2688:

ion clock. These were the most accurate clocks that had been constructed, with neither clock gaining nor losing time at a rate that would exceed a second in over a billion years. In February 2010, NIST physicists described a second, enhanced version of the quantum logic clock based on individual ions

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atom moves at a much slower speed of 130 m/s due to its greater mass. The hyperfine frequency of caesium (~9.19 GHz) is also higher than other elements such as rubidium (~6.8 GHz) and hydrogen (~1.4 GHz). The high frequency of caesium allows for more accurate measurements. Caesium

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in the 1990s led to increasing accuracy of atomic clocks. Lasers enable the possibility of optical-range control over atomic states transitions, which has a much higher frequency than that of microwaves; while optical frequency comb measures highly accurately such high frequency oscillation in light.

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The March 2018 Quarterly Performance Report by the European GNSS Service Centre reported the UTC Time Dissemination Service Accuracy was ≤ 7.6 nanoseconds, computed by accumulating samples over the previous 12 months, and exceeding the ≤ 30 ns target. Each Galileo satellite has two passive

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JILA's 2017 three-dimensional (3-D) quantum gas atomic clock consists of a grid of light formed by three pairs of laser beams. A stack of two tables is used to configure optical components around a vacuum chamber. Shown here is the upper table, where lenses and other optics are mounted. A blue laser

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In a next phase, these labs strive to transmit comparison signals in the visible spectrum through fibre-optic cables. This will allow their experimental optical clocks to be compared with an accuracy similar to the expected accuracies of the optical clocks themselves. Some of these labs have already

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than mechanical devices. Atomic clocks can also be isolated from environmental effects to a much higher degree. Atomic clocks have the benefit that atoms are universal, which means that the oscillation frequency is also universal. This is different from quartz and mechanical time measurement devices

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The BIPM defines the unperturbed ground-state hyperfine transition frequency of the rubidium-87 atom, 6 834 682 610.904 312 6 Hz, in terms of the caesium standard frequency. Atomic clocks based on rubidium standards are therefore regarded as secondary representations of

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National metrology institutions maintain an approximation of UTC referred to as UTC(k) for laboratory k. UTC(k) is distributed by the BIPM's Consultative Committee for Time and Frequency. The offset UTC-UTC(k) is calculated every 5 days, the results are published monthly. Atomic clocks record UTC(k)

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In February 2022, scientists at the University of Wisconsin-Madison reported a "multiplexed" optical atomic clock, where individual clocks deviated from each other with an accuracy equivalent to losing a second in 300 billion years. The reported minor deviation is explainable as the concerned clock

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Twenty-first century experimental atomic clocks that provide non-caesium-based secondary representations of the second are becoming so precise that they are likely to be used as extremely sensitive detectors for other things besides measuring frequency and time. For example, the frequency of atomic

3997:(DSAC), a miniaturized, ultra-precise mercury-ion atomic clock, into outer space. NASA said that the DSAC would be much more stable than other navigational clocks. The clock was successfully launched on 25 June 2019, activated on 23 August 2019 and deactivated two years later on 18 September 2021. 3968:

The Galileo navigation message includes the differences between GST, UTC and GPST, to promote interoperability. In the summer of 2021, the European Union settled on a passive hydrogen maser for the second generation of Galileo satellites, starting in 2023, with an expected lifetime of 12 years per

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provides an alternative to the Global Positioning System (GPS) system and is the second navigational system in operation with global coverage and of comparable precision. GLONASS Time (GLONASST) is generated by the GLONASS Central Synchroniser and is typically better than 1,000 nanoseconds. Unlike

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The most accurate caesium clocks based on the caesium frequency of 9.19 GHz have an accuracy between 10–10. Unfortunately, they are big and only available in large metrology labs and not useful for factories or industrial environments that would use an atomic clock for GPS accuracy but cannot

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over 6 hours. Recently it has been proved that the quantum entanglement can help to further enhance the clock stability. In 2020 optical clocks were researched for space applications like future generations of global navigation satellite systems (GNSSs) as replacements for microwave based clocks.

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In 2017 JILA reported an experimental 3D quantum gas strontium optical lattice clock in which strontium-87 atoms are packed into a tiny three-dimensional (3-D) cube at 1,000 times the density of previous one-dimensional (1-D) clocks, such as the 2015 JILA clock. A comparison between two regions of

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The rare-earth element ytterbium (Yb) is valued not so much for its mechanical properties but for its complement of internal energy levels. "A particular transition in Yb atoms, at a wavelength of 578 nm, currently provides one of the world's most accurate optical atomic frequency standards," said

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A clock's quality can be specified by two parameters: accuracy and stability. Accuracy is a measurement of the degree to which the clock's ticking rate can be counted on to match some absolute standard such as the inherent hyperfine frequency of an isolated atom or ion. Stability describes how the

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changes and are not very accurate. The most accurate clocks use atomic vibrations to keep track of time. Clock transition states in atoms are insensitive to temperature and other environmental factors and the oscillation frequency is much higher than any of the other clocks (in microwave frequency

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Many of the newer clocks, including microwave clocks such as trapped ion or fountain clocks, and optical clocks such as lattice clocks use a sequential interrogation protocol rather than the frequency modulation interrogation described above. An advantage of sequential interrogation is that it can

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Hydrogen masers are used for flywheel oscillators in laser-cooled atomic frequency standards and broadcasting time signals from national standards laboratories, although they need to be corrected as they drift from the correct frequency over time. The hydrogen maser is also useful for experimental

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TAI is not distributed in everyday timekeeping. Instead, an integer number of leap seconds are added or subtracted to correct for the Earth's rotation, producing UTC. The number of leap seconds is changed so that mean solar noon at the Greenwich meridian does not deviate from UTC noon by more than

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excites the atoms between two of their energy levels. Having established the stability of the clocks, the researchers are studying external influences and evaluating the remaining systematic uncertainties, in the hope that they can bring the clock's accuracy down to the level of its stability. An

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Masuda, T.; Yoshimi, A.; Fujieda, A.; Fujimoto, H.; Haba, H.; Hara, H.; Hiraki, T.; Kaino, H.; Kasamatsu, Y.; Kitao, S.; Konashi, K.; Miyamoto, Y.; Okai, K.; Okubo, S.; Sasao, N.; Seto, M.; Schumm, T.; Shigekawa, Y.; Suzuki, K.; Stellmer, S.; Tamasaku, K.; Uetake, S.; Watanabe, M.; Watanabe, T.;

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effect has been well documented. Atomic clocks are effective at testing general relativity on ever smaller scales. A project to observe twelve atomic clocks from 11 November 1999 to October 2014 resulted in a further demonstration that Einstein's theory of general relativity is accurate at small

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in about two hours. According to Jun Ye, "this represents a significant improvement over any previous demonstrations". Ye further commented "the most important potential of the 3D quantum gas clock is the ability to scale up the atom numbers, which will lead to a huge gain in stability" and "the

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Hydrogen masers have superior short-term stability compared to other standards, but lower long-term accuracy. The long-term stability of hydrogen maser standards decreases because of changes in the cavity's properties over time. The relative error of hydrogen masers is 5 × 10 for periods of 1000

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National laboratories usually operate a range of clocks. These are operated independently of one another and their measurements are sometimes combined to generate a scale that is more stable and more accurate than that of any individual contributing clocks. This scale allows for time comparisons

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Liu, Liang; Lü, Desheng; Chen, Weibiao; Li, Tang; Qu, Qiuzhi; Wang, Bin; Li, Lin; Ren, Wei; Dong, Zuoren; Zhao, Jianbo; Xia, Wenbing; Zhao, Xin; Ji, Jingwei; Ye, Meifeng; Sun, Yanguang; Yao, Yuanyuan; Song, Dan; Liang, Zhaogang; Hu, Shanjiang; Yu, Dunhe; Hou, Xia; Shi, Wei; Zang, Huaguo; Xiang,

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techniques were needed to bridge the gap between radio and optical frequencies, and the systems for doing so were cumbersome and complicated. With the refinement of the frequency comb, these measurements have become much more accessible and numerous optical clock systems are now being developed

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In 2022, the best realisation of the second is done with caesium primary standard clocks such as IT-CsF2, NIST-F2, NPL-CsF2, PTB-CSF2, SU–CsFO2 or SYRTE-FO2. These clocks work by laser-cooling a cloud of caesium atoms to a microkelvin in a magneto-optic trap. These cold atoms are then launched

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The BIPM defines the unperturbed optical transition frequency of the hydrogen-1 neutral atom, 1 233 030 706 593 514 Hz, in terms of the caesium standard frequency. Atomic clocks based on hydrogen standards are therefore regarded as secondary representations of the

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von der Wense, Lars; Seiferle, Benedict; Laatiaoui, Mustapha; Neumayr, Jürgen B.; Maier, Hans-Jörg; Wirth, Hans-Friedrich; Mokry, Christoph; Runke, Jörg; Eberhardt, Klaus; Düllmann, Christoph E.; Trautmann, Norbert G.; Thirolf, Peter G. (5 May 2016). "Direct detection of the Th nuclear clock

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provides very accurate timing and frequency signals. A GPS receiver works by measuring the relative time delay of signals from a minimum of four, but usually more, GPS satellites, each of which has at least two onboard caesium and as many as two rubidium atomic clocks. The relative times are

2807:, which was better than existing 2019 optical atomic clock technology. Although a precise clock remains an unrealized theoretical possibility, efforts through the 2010s to measure the transition energy culminated in the 2024 measurement of the optical frequency with sufficient accuracy ( 2222:, and, for many of the newer clocks, is significantly larger. Analysis of the effect and its consequence as applied to optical standards has been treated in a major review (Ludlow, et al., 2015) that lamented on "the pernicious influence of the Dick effect", and in several other papers. 1244:

Most of the complexity of the clock lies in this adjustment process. The adjustment tries to correct for unwanted side-effects, such as frequencies from other electron transitions, temperature changes, and the spreading in frequencies caused by the vibration of molecules including

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clocks is altered slightly by gravity, magnetic fields, electrical fields, force, motion, temperature and other phenomena. The experimental clocks tend to continue to improve, and leadership in performance has shifted back and forth between various types of experimental clocks.

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Before TAI is published, the frequency of the result is compared with the SI second at various primary and secondary frequency standards. This requires relativistic corrections to be applied to the location of the primary standard which depend on the distance between the

1096:) and short-term stability. They are used in many commercial, portable and aerospace applications. Modern rubidium standard tubes last more than ten years, and can cost as little as US$ 50. Some commercial applications use a rubidium standard periodically corrected by a 842:

Primary frequency standards can be used to calibrate the frequency of other clocks used in national laboratories. These are usually commercial caesium clocks having very good long-term frequency stability, maintaining a frequency with a stability better than 1 part in

3612:, or even higher. They have better stabilities than microwave clocks, which means that they can facilitate evaluation of lower uncertainties. They also have better time resolution, which means the clock "ticks" faster. Optical clocks use either a single ion, or an 897:

when averaged over 15 minutes. Receivers allow the simultaneous reception of signals from several satellites, and make use of signals transmitted on two frequencies. As more satellites are launched and start operations, time measurements will become more accurate.

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in his 1873 Treatise on Electricity and Magnetism: 'A more universal unit of time might be found by taking the periodic time of vibration of the particular kind of light whose wave length is the unit of length.' Maxwell argued this would be more accurate than the

3980:. BeiDou Time (BDT) is a continuous time scale starting at 1 January 2006 at 0:00:00 UTC and is synchronised with UTC within 100 ns. BeiDou became operational in China in December 2011, with 10 satellites in use, and began offering services to customers in the 1955: 3984:

region in December 2012. On 27 December 2018 the BeiDou Navigation Satellite System started to provide global services with a reported timing accuracy of 20 ns. The final, 35th, BeiDou-3 satellite for global coverage was launched into orbit on 23 June 2020.

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Elwell, R.; Schneider, Christian; Jeet, Justin; Terhune, J. E. S.; Morgan, H. W. T.; Alexandrova, A. N.; Tran Tan, Hoang Bao; Derevianko, Andrei; Hudson, Eric R. (2 July 2024). "Laser excitation of the Th nuclear isomeric transition in a solid-state host".

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Grebing, Christian; Al-Masoudi, Ali; Dörscher, Sören; Häfner, Sebastian; Gerginov, Vladislav; Weyers, Stefan; Lipphardt, Burghard; Riehle, Fritz; Sterr, Uwe; Lisdat, Christian (2016). "Realization of a timescale with an accurate optical lattice clock".

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technology. Such clocks are also called optical clocks where the energy level transitions used are in the optical regime (giving rise to even higher oscillation frequency), which thus, have much higher accuracy as compared to traditional atomic clocks.

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Schuldt, Thilo; Gohlke, Martin; Oswald, Markus; Wüst, Jan; Blomberg, Tim; Döringshoff, Klaus; Bawamia, Ahmad; Wicht, Andreas; Lezius, Matthias; Voss, Kai; Krutzik, Markus; Herrmann, Sven; Kovalchuk, Evgeny; Peters, Achim; Braxmaier, Claus (July 2021).

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developed a series of seven caesium-133 microwave clocks named NBS-1 to NBS-6 and NIST-7 after the agency changed its name from the National Bureau of Standards to the National Institute of Standards and Technology. The first clock had an accuracy of

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The signal received from one satellite in a metrology laboratory equipped with a receiver with an accurately known position allows the time difference between the local time scale and the GNSS system time to be determined with an uncertainty of a few

633:. The second is expected to be redefined when the field of optical clocks matures, sometime around the year 2030 or 2034. In order for this to occur, optical clocks must be consistently capable of measuring frequency with accuracy at or better than 2954:. These four European labs are developing and host a variety of experimental optical clocks that harness different elements in different experimental set-ups and want to compare their optical clocks against each other and check whether they agree. 3833:

The only viable way to fix the Rydberg constant involves trapping and cooling hydrogen. Unfortunately, this is difficult because it is very light and the atoms move very fast, causing Doppler shifts. The radiation needed to cool the hydrogen

3059:, is a pioneer in exploiting the properties of a single ion held in a trap to develop clocks of the highest stability. The development of the first optical clock was started at NIST in 2000 and finished in 2006. See for a review up to 2020. 766: 1015:

reference tubes suitable for national standards currently last about seven years and cost about US$ 35,000. Primary frequency and time standards like the United States Time Standard atomic clocks, NIST-F1 and NIST-F2, use far higher power.

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In August 2016 the French LNE-SYRTE in Paris and the German PTB in Braunschweig reported the comparison and agreement of two fully independent experimental strontium lattice optical clocks in Paris and Braunschweig at an uncertainty of

2950:; and Italy's Istituto Nazionale di Ricerca Metrologica (INRiM) in Turin labs have started tests to improve the accuracy of current state-of-the-art satellite comparisons by a factor of 10, but it will still be limited to one part in 2970:

but these span much shorter distances than the European network and are between just two labs. According to Fritz Riehle, a physicist at PTB, "Europe is in a unique position as it has a high density of the best clocks in the world".

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The accuracy of atomic clocks has improved continuously since the first prototype in the 1950s. The first generation of atomic clocks were based on measuring caesium, rubidium, and hydrogen atoms. In a time period from 1959 to 1998,

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was proposed by Russian physicist Vladilen Letokhov in the 1960s. The theoretical move from microwaves as the atomic "escapement" for clocks to light in the optical range, harder to measure but offering better performance, earned

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Modern clocks such as atomic fountains or optical lattices that use sequential interrogation are found to generate type of noise that mimics and adds to the instability inherent in atom or ion counting. This effect is called the

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The time readings of clocks operated in metrology labs operating with the BIPM need to be known very accurately. Some operations require synchronization of atomic clocks separated by great distances over thousands of kilometers.

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Roslund, Jonathan D.; Cingöz, Arman; Lunden, William D.; Partridge, Guthrie B.; Kowligy, Abijith S.; Roller, Frank; Sheredy, Daniel B.; Skulason, Gunnar E.; Song, Joe P.; Abo-Shaeer, Jamil R.; Boyd, Martin M. (23 August 2023).

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Seiferle, B.; von der Wense, L.; Bilous, P.V.; Amersdorffer, I.; Lemell, C.; Libisch, F.; Stellmer, S.; Schumm, T.; Düllmann, C.E.; Pálffy, A.; Thirolf, P.G. (12 September 2019). "Energy of the Th nuclear clock transition".

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systematic uncertainty, which is equivalent to 50 picoseconds per day. A system of several fountains worldwide contributes to International Atomic Time. These caesium clocks also underpin optical frequency measurements.

641:. In addition, methods for reliably comparing different optical clocks around the world in national metrology labs must be demonstrated, and the comparison must show relative clock frequency accuracies at or better than 3212:. There are two reasons for the possibly better precision. Firstly, the frequency is measured using light, which has a much higher frequency than microwaves, and secondly, by using many atoms, any errors are averaged. 12579:

Bothwell, Tobias; Kennedy, Colin J.; Aeppli, Alexander; Kedar, Dhruv; Robinson, John M.; Oelker, Eric; Staron, Alexander; Ye, Jun (2022). "Resolving the gravitational redshift across a millimetre-scale atomic sample".

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Beloy, Kyle; Bodine, Martha I.; Bothwell, Tobias; Brewer, Samuel M.; Bromley, Sarah L.; Chen, Jwo-Sy; Deschênes, Jean-Daniel; Diddams, Scott A.; Fasano, Robert J.; Fortier, Tara M.; Hassan, Youssef S. (25 March 2021).

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Insensitivity to environmental effects. Due to its small size and the shielding effect of the surrounding electrons, an atomic nucleus is much less sensitive to ambient electromagnetic fields than is an electron in an

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radio transmitters. They are used at some long-wave and medium-wave broadcasting stations to deliver a very precise carrier frequency. Atomic clocks are used in many scientific disciplines, such as for long-baseline

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Marianna Safronova. The estimated uncertainty achieved corresponds to about one second over the lifetime of the universe so far, 15 billion years, according to scientists at the Joint Quantum Institute (JQI) and the

680:. The atomic clock was about the size of a grain of rice with a frequency of about 9 GHz. This technology became available commercially in 2011. Atomic clocks on the scale of one chip require less than 30 1055:). The output of the frequency synthesizer is amplified and applied to a chamber containing caesium gas which absorbs the microwaves. The output current of the caesium chamber increases as absorption increases. 3472: 8108:

Thielking, J.; Okhapkin, M.V.; Glowacki, P.; Meier, D.M.; von der Wense, L.; Seiferle, B.; Düllmann, C.E.; Thirolf, P.G.; Peik, E. (2018). "Laser spectroscopic characterization of the nuclear-clock isomer Th".

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Pedrozo-Peñafiel, Edwin; Colombo, Simone; Shu, Chi; Adiyatullin, Albert F.; Li, Zeyang; Mendez, Enrique; Braverman, Boris; Kawasaki, Akio; Akamatsu, Daisuke; Xiao, Yanhong; Vuletić, Vladan (16 December 2020).

534:. Timekeeping researchers are currently working on developing an even more stable atomic reference for the second, with a plan to find a more precise definition of the second as atomic clocks improve based on 2958:

established fibre-optic links, and tests have begun on sections between Paris and Teddington, and Paris and Braunschweig. Fibre-optic links between experimental optical clocks also exist between the American

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GPST is related to but differs from TAI (International Atomic Time) and UTC (Coordinated Universal Time). GPST remains at a constant offset from TAI (TAI – GPST = 19 seconds) and like TAI does not implement

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Greater number of atoms. Because of the aforementioned insensitivity to ambient fields, it is not necessary to have the clock atoms well-separated in a dilute gas. Current measurements take advantage of the

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The SI second is defined as a certain number of unperturbed ground-state hyperfine transitions of the caesium-133 atom. Caesium standards are therefore regarded as primary time and frequency standards.

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Brewer, S. M.; Chen, J.-S.; Hankin, A. M.; Clements, E. R.; Chou, C. W.; Wineland, D. J.; Hume, D. B.; Leibrandt, D. R. (15 July 2019). "Al Quantum-Logic Clock with a Systematic Uncertainty below 10".

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The heart of NIST's next-generation miniature atomic clock – ticking at high "optical" frequencies – is this vapor cell on a chip, shown next to a coffee bean for scale.

12285: 2777:" in the ultraviolet frequency range. In 2003, Ekkehard Peik and Christian Tamm noted this makes a clock possible with current optical frequency-measurement techniques. In 2012, it was shown that a 13758: 4009:

announced a drive to upgrade to the U.S. military timekeeping systems for greater precision over time when sensors do not have access to GPS satellites, with a plan to reach precision of 1 part in

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A redefinition must include improved optical clock reliability. TAI must be contributed to by optical clocks before the BIPM affirms a redefinition. A consistent method of sending signals, such as

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Santarelli, G.; Audoin, C.; Makdissi, A.; Laurent, P.; Dick, G.J.; Clairon, A. (1998). "Frequency stability degradation of an oscillator slaved to a periodically interrogated atomic resonator".

6536: 6446: 2220: 10333: 9713: 1283:(LO) for a time of perhaps a second or so. Analysis of the final state of the atoms is then used to generate a correction signal to keep the LO frequency locked to that of the atoms or ions. 2116:{\displaystyle \sigma _{y,\,{\rm {Dick}}}(\tau )\approx {\frac {\sigma _{y}^{\rm {LO}}}{\sqrt {2\ln(2)}}}\cdot \left|{\frac {\sin(\pi d)}{\pi d}}\right|\cdot {\sqrt {\frac {T_{c}}{\tau }}}.} 578:

The first advance beyond the precision of caesium clocks occurred at NIST in 2010 with the demonstration of a "quantum logic" optical clock that used aluminum ions to achieve a precision of

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As in the radio range, absorption spectroscopy is used to stabilize an oscillator—in this case, a laser. When the optical frequency is divided down into a countable radio frequency using a

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The performance of primary and secondary frequency standards contributing to International Atomic Time (TAI) is evaluated. The evaluation reports of individual (mainly primary) clocks are

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Dimarcq, Noel; Gertsvolf, Marina; Mileti, Gaetano; Bize, Sebastien; Oates, Christopher; Peik, Ekkehard; Calonico, Davide; Ido, Tetsuya; Tavella, Patrizia; Meynadier, Frédéric (2024).

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mathematically transformed into three absolute spatial coordinates and one absolute time coordinate. GPS Time (GPST) is a continuous time scale and theoretically accurate to about 14

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is reduced by temperature fluctuations. This led to the idea of measuring the frequency of an atom's vibrations to keep time much more accurately, as proposed by James Clerk Maxwell,

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McGrew, W. F.; Zhang, X.; Fasano, R. J.; Schaffer, S. A.; Beloy, K.; Nicolodi, D.; Brown, R. C.; Hinkley, N.; Milani, G.; Schioppo, M.; Yoon, T. H.; Ludlow, A. D. (6 December 2018).

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nowadays, for higher frequencies and narrower resonances in the oscillating fields. Kolsky, Phipps, Ramsey, and Silsbee used this technique for molecular beam spectroscopy in 1950.

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Zhang, Chuankun; Ooi, Tian; Higgins, Jacob S.; Doyle, Jack F.; von der Wense, Lars; Beeks, Kjeld; Leitner, Adrian; Kazakov, Georgy; Li, Peng; Thirolf, Peter G.; Schumm, Thorsten;

4618: 4094:. Accurate timekeeping is needed to prevent illegal trading ahead of time, in addition to ensuring fairness to traders on the other side of the globe. The current system known as 3639: 3391:

afford to build a whole metrology laboratory for one atomic clock. Researchers have designed a strontium optical clock that can be moved around in an air-conditioned car trailer.

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depends on the element that is stimulated. For example, calcium optical clocks resonate when red light is produced, and ytterbium clocks resonate in the presence of violet light.

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Higher frequency. All other things being equal, a higher-frequency transition offers greater stability for simple statistical reasons (fluctuations are averaged over more cycles).

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beam excites a cube-shaped cloud of strontium atoms located behind the round window in the middle of the table. Strontium atoms fluoresce strongly when excited with blue light.

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In June 2015, the National Physical Laboratory (NPL) in Teddington, UK; the French department of Time-Space Reference Systems at the Paris Observatory (LNE-SYRTE); the German

933:(TAI), then adding leap seconds as necessary. TAI is a weighted average of around 450 clocks in some 80 time institutions. The relative stability of TAI is around one part in 1943: 1058:

The remainder of the circuitry simply adjusts the running frequency of the VCXO to maximize the output current of the caesium chamber which keeps the oscillator tuned to the

10120: 9953: 5260:

Nicholson, T.L.; Campbell, S.L.; Hutson, R.B.; Marti, G.E.; Bloom, B.J.; McNally, R.L.; Zhang, W.; Barrett, M.D.; Safronova, M.S.; Strouse, G.F.; Tew, W.L. (21 April 2015).

2161: 1911: 1636: 815:

microwave transition and other optical transitions, including neutral atoms and single trapped ions. These secondary frequency standards can be as accurate as one part in

691:

The National Institute of Standards and Technology created a program NIST on a chip to develop compact ways of measuring time with a device just a few millimeters across.

10446: 5876: 1703: 1679: 1585: 1384: 9978:

T.L. Nicholson; S.L. Campbell; R.B. Hutson; G.E. Marti; B.J. Bloom; R.L. McNally; W. Zhang; M.D. Barrett; M.S. Safronova; G.F. Strouse; W.L. Tew; J. Ye (21 April 2015).

2369:

A list of frequencies recommended for secondary representations of the second is maintained by the International Bureau of Weights and Measures (BIPM) since 2006 and is

11539: 11170: 7759: 251:

of the involved atomic clocks is important because the smaller the error in time measurement, the smaller the error in distance obtained by multiplying the time by the

13934: 10480: 9070: 4078:

seconds. Given its quantum nature and the fact that time is a relativistic quantity, atomic clocks can be used to see how time is influenced by general relativity and

3606: 1754: 1357: 11771: 5585: 4310:

Thomas P. Heavner; Elizabeth A. Donley; Filippo Levi; Giovanni Costanzo; Thomas E. Parker; Jon H. Shirley; Neil Ashby; Stephan Barlow; Steven R. Jefferts (May 2014).

3492: 3359:

Optical clocks are currently (2022) still primarily research projects, less mature than rubidium and caesium microwave standards, which regularly deliver time to the

5825: 12193:"Definition and Realization of the System Time of COMPASS/BeiDou Navigation Satellite System, Chunhao Han, Beijing Global Information Center,(BGIC), Beijing, China" 7983:

Campbell, C.; Radnaev, A.G.; Kuzmich, A.; Dzuba, V.A.; Flambaum, V.V.; Derevianko, A. (2012). "A single ion nuclear clock for metrology at the 19th decimal place".

1863: 1836: 1727: 1656: 13857: 11829: 11765:"GLONASS Interface Control Document, Navigation radiosignal In bands L1, L2 (ICD L1, L2 GLONASS), Russian Institute of Space Device Engineering, Edition 5.1, 2008" 8943: 2753:

which current atomic clocks measure. Most nuclear transitions operate at far too high a frequency to be measured, but the exceptionally low excitation energy of

7456: 1609: 1279:, during which the atom or ion collections are analyzed, renewed and driven into a proper quantum state, after which they are interrogated with a signal from a 6172:

Jain, Pratik; Priya, Priyanka; Ram, T. V. S.; Parikh, K. S.; Bandi, Thejesh N. (1 December 2021). "Digital lock-in amplifier for space rubidium atomic clock".

5158: 1271:. When a clock is first turned on, it takes a while for the oscillator to stabilize. In practice, the feedback and monitoring mechanism is much more complex. 1267:

properties of the atomic transition frequency of the caesium can be used to tune the microwave oscillator to the same frequency, except for a small amount of

718:

An atomic clock is based on a system of atoms which may be in one of two possible energy states. A group of atoms in one state is prepared, then subjected to

12180: 6495: 6428:

J. A. Barnes, A. R. Chi, L. S. Cutler, D. J. Healey, D. B. Leeson, T. E. McGunigal, J. A. Mullen, W. L. Smith, R. Sydnor, R. F. C. Vessot, G. M. R. Winkler:

2357:, more stable and more reliable. The Cold Atom Clock Experiment in Space (CACES) testing a Cold Atom Clock in Earth orbit in microgravity conditions and the 12277: 5235: 665:

In addition to increased accuracy, the development of chip-scale atomic clocks has expanded the number of places atomic clocks can be used. In August 2004,

11800: 9036: 3101:

is also divided by that factor. Although the bandwidth of laser phase noise is generally greater than stable microwave sources, after division it is less.

12063: 9735: 3227:

over a 7-hour period was published on 22 August 2013. At this stability, the two optical lattice clocks working independently from each other used by the

50:

NIST physicists Steve Jefferts (foreground) and Tom Heavner with the NIST-F2 caesium fountain atomic clock, a civilian time standard for the United States

13765: 12644: 11851: 7561: 3340:

ability to scale up both the atom number and coherence time will make this new-generation clock qualitatively different from the previous generation".

3010:) apart at the NIST lab, its partner lab JILA, and the University of Colorado all in Boulder, Colorado over air and fiber optic cable to a precision of 781:

shift) and several other factors. The best primary standards currently produce the SI second with an accuracy approaching an uncertainty of one part in

11448: 9817: 7134: 3208:, which is as accurate as the experiment could measure. These clocks have been shown to keep pace with all three of the caesium fountain clocks at the 5440:

Bothwell, Tobias; Kennedy, Colin J.; Aeppli, Alexander; Kedar, Dhruv; Robinson, John M.; Oelker, Eric; Staron, Alexander; Ye, Jun (16 February 2022).

3188:

In 2013 optical lattice clocks (OLCs) were shown to be as good as or better than caesium fountain clocks. Two optical lattice clocks containing about

10329: 9709: 8171:

Yasuda, Y.; Yamaguchi, A.; Yoda, Y.; Yokokita, T.; Yoshimura, M.; Yoshimura, K. (12 September 2019). "X-ray pumping of the Th nuclear clock isomer".

1729:

over which the measurements are averaged increases from seconds to hours to days. The stability is most heavily affected by the oscillator frequency

6009: 3118:

These techniques allow the atoms or ions to be highly isolated from external perturbations, thus producing an extremely stable frequency reference.

145:. Electron states in an atom are associated with different energy levels, and in transitions between such states they interact with a very specific 11919: 11597: 10307: 6035: 4369: 1189: 11967: 11375:"Consultative Committee for Units (CCU) Report of the 25th meeting (21-23 September 2021) to the International Committee for Weights and Measures" 1199:

This definition makes the caesium oscillator the primary standard for time and frequency measurements, called the caesium standard. Following the

7535: 228:

to within one second while being based on clocks that are based on the definition of the second, though leap seconds will be phased out in 2035.

1764:

and is typically the primary stability limitation for the newer atomic clocks. It is an aliasing effect; high frequency noise components in the

499:

vibrations of the unperturbed ground-state hyperfine transition frequency of the caesium-133 atom. Prior to that it was defined by there being

129:(formerly HP) 5071A caesium beam clocks. The black units in the foreground are Microsemi (formerly Sigma-Tau) MHM-2010 hydrogen maser standards. 11884:"1 The Definition and Implementation of Galileo System Time (GST). ICG-4 WG-D on GNSS time scales. Jérôme Delporte. CNES – French Space Agency" 11682: 6918: 5624: 4664: 3505: 3287:". At this frequency uncertainty, this JILA optical lattice clock is expected to neither gain nor lose a second in more than 15 billion years. 3228: 2243: 742: 666: 420: 285: 11999: 11627: 9895:

Bloom, B. J.; Nicholson, T. L.; Williams, J. R.; Campbell, S. L.; Bishof, M.; Zhang, X.; Zhang, W.; Bromley, S. L.; Ye, J. (22 January 2014).

9374: 6811: 3400:

vertically by laser light. The atoms then undergo Ramsey excitation in a microwave cavity. The fraction of excited atoms are then detected by

965:, time signal transmitters, and speaking clocks. In addition, GNSS provides time information accurate to a few tens of nanoseconds or better. 873:(GNSS) provide a satisfactory solution to the problem of time transfer. Atomic clocks are used to broadcast time signals in the United States 9649: 6122: 2307: 762: 432: 371: 316: 10271: 10211:

S. L. Campbell; R. B. Hutson; G. E. Marti; A. Goban; N. Darkwah Oppong; R. L. McNally; L. Sonderhouse; W. Zhang; B. J. Bloom; J. Ye (2017).

9598: 7850:

Gao, Qi; Zhou, Min; Han, Chengyin; Li, Shangyan; Zhang, Shuang; Yao, Yuan; Li, Bo; Qiao, Hao; Ai, Di; Lou, Ge; Zhang, Mengya (22 May 2018).

7373: 7282: 7191: 6984: 6780: 5986: 961:

to no more than 100 nanoseconds. In some countries, UTC(k) is the legal time that is distributed by radio, television, telephone, Internet,

13850: 12669: 9627: 7955: 7166: 6099: 5821: 3360: 804: 3419: 1554:{\displaystyle \sigma _{y,\,{\rm {atoms}}}(\tau )\approx {\frac {\Delta \nu }{\nu _{0}{\sqrt {N}}}}{\sqrt {\frac {T_{\text{c}}}{\tau }}},} 11708: 10364: 10089: 5004: 3308:

in 1 hour of averaging time. This precision value does not represent the absolute accuracy or precision of the clock, which remain above

11945: 11742: 10631:

Brewer, S. M.; Chen, J.-S.; Hankin, A. M.; Clements, E. R.; Chou, C. W.; Wineland, D. J.; Hume, D. B.; Leibrandt, D. R. (15 July 2019).

7013: 5371:

Brewer, S. M.; Chen, J.-S.; Hankin, A. M.; Clements, E. R.; Chou, C. W.; Wineland, D. J.; Hume, D. B.; Leibrandt, D. R. (15 July 2019).

4289: 610:

in 2015. Scientists at NIST developed a quantum logic clock that measured a single aluminum ion in 2019 with a frequency uncertainty of

12033: 9433: 4668: 2353:

Most research focuses on the often conflicting goals of making the clocks smaller, cheaper, more portable, more energy efficient, more

12641: 12092: 9869: 9092: 9033: 7593: 5705: 5677: 5343: 4070:

between two layers of atoms separated by one millimeter using a strontium optical clock cooled to 100 nanokelvins with a precision of

11656: 582:. Optical clocks are a very active area of research in the field of metrology as scientists work to develop clocks based on elements 12419: 6744: 1104:). This achieves excellent short-term accuracy, with long-term accuracy equal to (and traceable to) the US national time standards. 14388: 12723: 9770: 5513: 11445: 10112: 10054: 9896: 5620: 5346: 3768: 13843: 13328: 13164: 5928: 4149: 1188:

of radiation corresponding to the transition between two energy levels of the ground state of the caesium-133 atom. In 1997, the

1044: 12348: 12199: 4747: 1756:. This is why optical clocks such as strontium clocks (429 terahertz) are much more stable than caesium clocks (9.19 GHz). 11374: 10558: 10387: 5849: 5592: 4824: 3946: 2712:, which is the first demonstration of such a clock with uncertainty below 10 and remains the most accurate clock in the world. 13788: 11890: 2282:. The goal is to redefine the second when clocks become so accurate that they will not lose or gain more than a second in the 12793: 12759: 11528: 11485: 9847: 9342: 9062: 7755: 7668: 5862: 5042: 4934: 4240: 4090:

Atomic clocks keep accurate records of transactions between buyers and sellers to the millisecond or better, particularly in

2947: 1036: 738: 424: 12695: 10472: 5733: 5059: 1291:

All timekeeping devices use oscillatory phenomena to accurately measure time, whether it is the rotation of the Earth for a

14357: 12546: 12520: 12371: 12254: 12228: 11764: 11568: 11196:

Koller, S. B.; Grotti, J.; Vogt, St.; Al-Masoudi, A.; Dörscher, S.; Häfner, S.; Sterr, U.; Lisdat, Ch. (13 February 2017).

8829:"Hyper-precise atomic clocks face off to redefine time – Next-generation timekeepers can only be tested against each other" 8780:"Hyper-precise atomic clocks face off to redefine time – Next-generation timekeepers can only be tested against each other" 5812: 3869:

The development of atomic clocks has led to many scientific and technological advances such as precise global and regional

3331:(a quantum gas for Fermi particles). The experimental data shows the 3D quantum gas clock achieved a residual precision of 9227: 3352:

Ye's strontium-87 clock has not surpassed the aluminum-27 or ytterbium-171 optical clocks in terms of frequency accuracy.

926:

between different clocks in the laboratory. These atomic time scales are generally referred to as TA(k) for laboratory k.

165:

The second, symbol s, is the SI unit of time. It is defined by taking the fixed numerical value of the caesium frequency,

4263: 3977: 3379: 621:

At JILA in September 2021, scientists demonstrated an optical strontium clock with a differential frequency precision of

405:

and microwave absorption signals. Unfortunately, this caused a side effect with a light shift of the resonant frequency.

12148: 12000:"Galileo Open Service and Search and Rescue – Quarterly Performance Reports, containing measured performance statistics" 11825: 3911:. However, most receivers lose accuracy in the interpretation of the signals and are only accurate to 100 nanoseconds. 2166: 1275:

accommodate much higher Q's, with ringing times of seconds rather than milliseconds. These clocks also typically have a

1039:(VCXO) that is tunable over a narrow range. The output frequency of the VCXO (typically 5 MHz) is multiplied by a 15080: 14626: 13751: 5736: 3374:

molecules were demonstrated at-sea on a naval vessel and operated continuously in the Pacific Ocean for 20 days in the

12502: 10582: 5646: 4627: 3324:

respectively. The 3D quantum gas strontium optical lattice clock's centerpiece is an unusual state of matter called a

15090: 14108: 6116: 5183: 4456: 2370: 1136: 363: 10826: 8669:

Seiferle, Benedict; von der Wense, Lars; Thirolf, Peter G. (2017). "Lifetime measurement of the Th nuclear isomer".

125:, which provides the time standard for the U.S. Department of Defense. The rack mounted units in the background are 3927: 3846: 1775: 428: 7041:; Donaldson, R W; Hope, E G; Bangham, M J (July 1973). "Hydrogen Maser Work at the National Physical Laboratory". 3002:

In 2021, NIST compared transmission of signals from a series of experimental atomic clocks located about 1.5

13278: 12933: 12117: 7815: 6607: 4904:"Paper 1.15: "Experiments with Separated Oscillatory Fields and Hydrogen Masers," (Nobel Lecture), N. F. Ramsey, 4195: 118: 11796: 9120: 8331: 4921:, World Scientific Series in 20th Century Physics, vol. 21, WORLD SCIENTIFIC, pp. 115–127, June 1998, 953:. The TAI time-scale is deferred by a few weeks as the average of atomic clocks around the world is calculated. 929:

Coordinated Universal Time (UTC) is the result of comparing clocks in national laboratories around the world to

401:

for electron energy level transitions in atoms using light. This technique is useful for creating much stronger

15008: 14835: 14181: 13157: 12055: 11852:"European GNSS (Galileo) Open Service Signal-In-Space Operational Status Definition, Issue 1.0, September 2015" 11388:

Ren, Wei; Li, Tang; Qu, Qiuzhi; Wang, Bin; Li, Lin; Lü, Desheng; Chen, Weibiao; Liu, Liang (18 December 2020).

9526:

Golovizin, A.; Tregubov, D.; Mishin, D.; Provorchenko, D.; Kolachevsky, N.; Kolachevsky, N. (25 October 2021).

6855:

Ren, Wei; Li, Tang; Qu, Qiuzhi; Wang, Bin; Li, Lin; Lü, Desheng; Chen, Weibiao; Liu, Liang (18 December 2020).

3943: 2358: 882: 758: 240: 10905: 5902: 808: 14362: 11858: 9505:

Schmittberger, Bonnie L. (21 April 2020). "A Review of Contemporary Atomic Frequency Standards". p. 13.

8649: 3765:. The Rydberg constant describes the energy levels in a hydrogen atom with the nonrelativistic approximation 3758:{\displaystyle R_{\infty }={\frac {m_{e}e^{4}}{8\varepsilon _{0}^{2}h^{3}c}}={\frac {m_{e}c\alpha ^{2}}{2h}}} 3094: 3073:

has led to a new generation of atomic clocks. These clocks are based on atomic transitions that emit visible

1249:. One way of doing this is to sweep the microwave oscillator's frequency across a narrow range to generate a 168: 154: 28: 12748:

Geng, Yilong; Liu, Shiyu; Yin, Zi; Naik, Ashish; Prabhakar, Balaji; Rosenblum, Mendel; Vahdat, Amin (2018).

11501: 11027:

Ludlow, Andrew D; Boyd, Martin M; Ye, Jun; Peik, Ekkehard; Schmidt, Piet O (2015). "Optical atomic clocks".

9793: 7085: 5708: 1397:

clock performs when averaged over time to reduce the impact of noise and other short-term fluctuations (see

827:. This is because the uncertainty in the central caesium standard against which the secondary standards are 381: 13240: 10142:

N. Huntemann; C. Sanner; B. Lipphardt; Chr. Tamm; E. Peik (8 February 2016). "Single-Ion Atomic Clock with

8487:. This feature is assigned to the excitation of the Th nuclear isomeric state, whose energy is found to be 2693:

and aluminium. Considered the world's most precise clock in 2010 with a fractional frequency inaccuracy of

2322:

cooling of the microwave interaction region; the largest source of uncertainty in NIST-F1 is the effect of

949:

of Earth. The values of the rotating geoid and the TAI change slightly each month and are available in the

355: 8330:

Tiedau, J.; Okhapkin, M. V.; Zhang, K.; Thielking, J.; Zitzer, G.; Peik, E.; et al. (29 April 2024).

3938:

Space Passive Hydrogen Maser used in ESA Galileo satellites as a master clock for an onboard timing system

2983:

via a newly established phase-coherent frequency link connecting Paris and Braunschweig, using 1,415

315:(right) and Jack Parry (left) standing next to the world's first caesium-133 atomic clock in 1955, at the 14317: 14297: 14243: 14128: 13964: 13531: 11473: 10297: 9472: 9066: 6634: 5030: 3581:

Optical clocks are based on forbidden optical transitions in ions or atoms. They have frequencies around

3276: 1088:

Rubidium standard clocks are prized for their low cost, small size (commercial standards are as small as

11915: 11593: 8744: 6489:

Quessada, A.; Kovacich, R. P.; Courtillot, I.; Clairon, A.; Santarelli, G.; Lemonde, P. (2 April 2003).

4013:. The Robust Optical Clock Network will balance usability and accuracy as it is developed over 4 years. 1410: 722:

radiation. If the radiation is of the correct frequency, a number of atoms will transition to the other

141:

that measures time by monitoring the resonant frequency of atoms. It is based on atoms having different

14789: 14766: 13984: 13969: 13907: 13886: 12883: 12863: 12396: 10632: 7483: 5372: 3279:

for an elevation change of 2 cm (0.79 in) on planet Earth that according to JILA/NIST Fellow

2914:. It is the large ratio between transition frequency and isomer lifetime which gives the clock a high 2750: 1101: 217: 10757:

Zheng, Xin; Dolde, Jonathan; Lochab, Varun; Merriman, Brett N.; Li, Haoran; Kolkowitz, Shimon (2022).

550: 14671: 14138: 13949: 13594: 13443: 13323: 12873: 12786: 8519:(4 September 2024). "Frequency ratio of the Th nuclear isomeric transition and the Sr atomic clock". 6288: 5953: 3903: 3899: 3364: 3162: 1916: 1097: 930: 874: 673:

that was 100 times smaller than an ordinary atomic clock and had a much smaller power consumption of

436: 370:

in 1949. This led to the first practical accurate atomic clock with caesium atoms being built at the

366:, and Isidor Rabi. He proposed the concept in 1945, which led to a demonstration of a clock based on 328: 269:

second) translates into an almost 30-centimetre (11.8 in) distance and hence positional error).

213: 150: 83: 12444: 6907: 6803: 2704:

In July 2019, NIST scientists demonstrated such an Al quantum logic clock with total uncertainty of

13293: 12003: 11686: 11619: 7852:"Systematic evaluation of a Yb optical clock by synchronous comparison between two lattice systems" 7086:"Proton Zemach radius from measurements of the hyperfine splitting of hydrogen and muonic hydrogen" 6286:

Ludlow, A.D.; Boyd, M.M.; Ye, J.; Peik, E.; Schmidt, P.O. (26 June 2015). "Optical atomic clocks".

5791: 4772:; Parry, J. V. L. (1955). "An Atomic Standard of Frequency and Time Interval: A Cæsium Resonator". 4696:; Parry, J. V. L. (1955). "An Atomic Standard of Frequency and Time Interval: A Cæsium Resonator". 3877:, which depend critically on frequency and time standards. Atomic clocks are installed at sites of 2129: 1868: 921:

Data points representing atomic clocks around the world that define International Atomic Time (TAI)

11325:

Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences

11271:

Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences

6772: 6103: 5978: 5761: 5680: 1614: 14398: 14176: 14078: 13994: 13989: 13549: 13200: 12470: 10395: 9591: 9382: 8671: 8412: 8339: 6972: 5662:

Lutwak, Robert (26–29 November 2007). "The Chip-Scale Atomic Clock — Prototype Evaluation".

4309: 3994: 3839: 1684: 1661: 1567: 1366: 1200: 1152: 670: 531: 293: 9623: 9146: 9095: 7159: 4384: 4345:

and is dominated by the uncertainty in the blackbody radiation (BBR) shift correction, which is

2991:) of telecom fibre-optic cable. The fractional uncertainty of the whole link was assessed to be 1192:(CIPM) added that the preceding definition refers to a caesium atom at rest at a temperature of 15070: 14666: 14619: 12903: 10081: 9736:"Ytterbium in quantum gases and atomic clocks: van der Waals interactions and blackbody shifts" 4091: 4067: 4055: 4031:

is a clock that automatically synchronizes itself by means of radio time signals received by a

3182: 3168: 3052: 1769: 1398: 767:

All-Russian Scientific Research Institute for Physical-Engineering and Radiotechnical Metrology

467: 456: 452: 406: 248: 12698: 11941: 11712: 10386:

G. Edward Marti; Ross B. Hutson; Akihisa Goban; Sara L. Campbell; Nicola Poli; Jun Ye (2018).

10356: 6684: 6410: 5540: 5209: 5085: 5008: 3588: 1732: 1335: 1326:

One of the most important factors in a clock's performance is the atomic line quality factor,

15013: 14551: 13732: 13364: 13309: 13263: 13248: 12893: 12749: 11734: 7816:"Recent Advances Concerning the Sr Optical Lattice Clock at the National Time Service Center" 7562:"Press release: NIST 'Quantum Logic Clock' Rivals Mercury Ion as World's Most Accurate Clock" 7006: 5236:"NIST's Second 'Quantum Logic Clock' Based on Aluminum Ion is Now World's Most Precise Clock" 4363: 4144: 4139: 4095: 3954: 3477: 2720: 2616: 2579: 2502: 1706: 1040: 847:

over a few months. The uncertainty of the primary standard frequencies is around one part in

413: 195:, the unperturbed ground-state hyperfine transition frequency of the caesium-133 atom, to be 12025: 11269:

National Physical Laboratory (2011). "When should we change the definition of the second?".

9527: 9444: 9415: 7590: 6747: 14921: 14822: 14812: 14802: 14731: 14378: 14292: 14118: 13979: 13615: 13584: 13033: 12928: 12779: 12599: 12085: 11332: 11278: 11126: 11046: 10993: 10939: 10867: 10780: 10723: 10597: 10526: 10414: 10239: 10169: 10009: 9921: 9539: 9391: 9279: 9185: 8983: 8899: 8840: 8791: 8690: 8348: 8256: 8192: 8128: 8066: 8002: 7931: 7863: 7712: 7636: 7591:

NIST's Second 'Quantum Logic Clock' Based on Aluminum Ion is Now World's Most Precise Clock

7508: 7331: 7240: 7110: 7050: 6504: 6360: 6307: 6249: 6181: 5463: 5291: 5167: 5107: 4969: 4781: 4705: 4653: 4564: 4517: 3950: 3870: 3123: 2539: 2469: 2434: 2323: 2260: 1841: 1821: 1712: 1641: 870: 657: 232: 216:(TAI), which is maintained by an ensemble of atomic clocks around the world. The system of 87: 11649: 11197: 10385: 7610:

C.W Chou; D. Hume; J.C.J. Koelemeij; D.J. Wineland & T. Rosenband (17 February 2010).

3343:

In 2018, JILA reported the 3D quantum gas clock reached a residual frequency precision of

3048: 3026: 8: 14588: 14383: 14238: 14103: 14055: 13489: 12948: 12908: 11968:"Galileo Initial Services – Open Service – Quarterly Performance Report Oct–Nov–Dec 2017" 9762: 6010:"Clock Experiment Shows a Fundamental Connection Between Energy Consumption and Accuracy" 3232: 3082: 2937:

and place the thorium ions in a solid, which allows billions of atoms to be interrogated.

2867: 2677: 2402: 2283: 1268: 1002:

Caesium has several properties that make it a good choice for an atomic clock. Whereas a

942: 789: 333: 324: 225: 13924: 12754:. 15th USENIX Symposium on Networked Systems Design and Implementation. pp. 81–94. 12603: 11336: 11323:

Gill, Patrick (28 October 2011). "When should we change the definition of the second?".

11282: 11147: 11130: 11104: 11050: 10997: 10943: 10871: 10784: 10727: 10601: 10530: 10418: 10243: 10173: 10013: 9925: 9543: 9395: 9283: 9189: 8987: 8903: 8844: 8795: 8694: 8352: 8260: 8196: 8132: 8070: 8006: 7935: 7867: 7716: 7640: 7335: 7244: 7114: 7054: 6660:"The atomic clock with the world's best long-term accuracy is revealed after evaluation" 6508: 6364: 6311: 6253: 6185: 5467: 5295: 5171: 5111: 4973: 4785: 4709: 4568: 4521: 3267:

evaluated the absolute frequency uncertainty of a strontium-87 optical lattice clock at

2934: 811:. This list contains the frequency values and respective standard uncertainties for the 15085: 14699: 14563: 14337: 14261: 14191: 13438: 13416: 13283: 13107: 13078: 13013: 13006: 12623: 12589: 11422: 11356: 11302: 11251: 11217: 11116: 11062: 11036: 11009: 10983: 10955: 10883: 10857: 10804: 10770: 10713: 10682: 10648: 10613: 10550: 10516: 10438: 10404: 10263: 10229: 10193: 10159: 10030: 9999: 9979: 9945: 9911: 9809: 9573: 9506: 9348: 9303: 9269: 9015: 8920: 8889: 8877: 8714: 8680: 8530: 8421: 8304: 8280: 8246: 8216: 8182: 8152: 8118: 8090: 8056: 8026: 7992: 7947: 7892: 7851: 7736: 7702: 7660: 7626: 7438: 7412: 7355: 7321: 7264: 7230: 7126: 7100: 7066: 6883: 6856: 6835: 6571: 6545: 6471: 6376: 6350: 6323: 6297: 6265: 6239: 6205: 6036:"New experiment: Clocks consuming more energy are more accurate… 'cause thermodynamics" 5628: 5552: 5495: 5453: 5422: 5388: 5320: 5281: 5261: 5131: 5097: 4880: 4797: 4721: 4478: 4448: 4412: 4115: 4051: 3416:

The advantage of optical clocks can be explained by the statement that the instability

2741:

One theoretical possibility for improving the performance of atomic clocks is to use a

1594: 1246: 1148: 1144: 962: 906: 902: 793: 402: 348: 231:

The accurate timekeeping capabilities of atomic clocks are also used for navigation by

69: 45: 10848:

N. Poli; C. W. Oates; P. Gill; G. M. Tino (13 January 2014). "Optical atomic clocks".

10058: 9173: 4436: 3290: 2715:

The accuracy of experimental quantum clocks has since been superseded by experimental

15033: 14612: 14411: 14276: 14093: 13798: 13793: 13519: 13398: 13298: 13151: 13054: 12958: 12755: 12627: 12615: 12554: 12338: 12192: 12156: 11481: 11427: 11409: 11348: 11294: 11243: 11235: 11152: 11066: 11013: 10959: 10887: 10808: 10796: 10758: 10739: 10686: 10674: 10666: 10617: 10554: 10542: 10430: 10267: 10255: 10220: 10185: 10035: 9937: 9813: 9684: 9577: 9565: 9557: 9480: 9407: 9352: 9338: 9307: 9295: 9209: 9201: 9037:"NIST Team Compares 3 Top Atomic Clocks With Record Accuracy Over Both Fiber and Air" 9019: 9007: 8999: 8971: 8925: 8858: 8809: 8706: 8364: 8284: 8272: 8220: 8208: 8144: 8094: 8082: 8018: 7951: 7897: 7879: 7740: 7728: 7652: 7430: 7347: 7268: 7256: 7070: 6888: 6719: 6563: 6490: 6463: 6380: 6327: 6269: 6209: 6197: 6112: 5868: 5858: 5499: 5487: 5479: 5426: 5414: 5406: 5325: 5307: 5135: 5123: 5038: 4985: 4930: 4885: 4867: 4739: 4582: 4533: 4452: 4416: 4404: 4400: 4332: 4079: 4040: 3962: 3934: 3325: 3209: 3134: 3056: 2967: 2889: 2685: 2264: 1300: 1264: 1071: 792:

in the device cannot be ignored. The standard is then considered in the framework of

774: 734: 697:

are currently (2022) designing atomic clocks that implement new developments such as

587: 448: 344: 337: 12751:

Exploiting a Natural Network Effect for Scalable, Fine-grained Clock Synchronization

11255: 10701: 10504: 10388:"Imaging Optical Frequencies with 100 μHz Precision and 1.1 μm Resolution" 10197: 9257: 8718: 8030: 7664: 7442: 7359: 7062: 6575: 6531: 6516: 6488: 6475: 4816: 4437:"James Clerk Maxwell, A treatise on electricity and magnetism, first edition (1873)" 3104:

The primary systems under consideration for use in optical frequency standards are:

2420: 514:

1900. The 1968 definition was updated in 2019 to reflect the new definitions of the

14556: 14302: 14281: 14233: 14196: 14009: 13637: 13625: 13453: 13421: 13253: 13122: 13038: 13028: 12943: 12607: 11883: 11417: 11401: 11360: 11340: 11306: 11286: 11231: 11227: 11142: 11134: 11054: 11001: 10947: 10875: 10788: 10731: 10662: 10658: 10605: 10534: 10442: 10426: 10422: 10247: 10181: 10177: 10025: 10017: 9949: 9929: 9839: 9801: 9547: 9399: 9330: 9287: 9193: 8991: 8915: 8907: 8848: 8799: 8702: 8698: 8540: 8521: 8435: 8431: 8360: 8356: 8309: 8264: 8237: 8200: 8173: 8156: 8136: 8074: 8047: 8014: 8010: 7939: 7887: 7871: 7830: 7794: 7724: 7720: 7648: 7644: 7422: 7343: 7339: 7252: 7248: 7130: 7118: 7058: 6952: 6878: 6868: 6834:

Jingfeng; Peng, Xiangkai; Wang, Yuzhu (2017). "Tests of Cold Atom Clock in Orbit".

6711: 6555: 6512: 6455: 6368: 6315: 6257: 6189: 5562: 5471: 5402: 5398: 5315: 5299: 5175: 5115: 4977: 4922: 4875: 4859: 4801: 4789: 4725: 4713: 4572: 4525: 4444: 4396: 4328: 4236: 4124: 3633: 3382:

have led to the world's first commercial rackmount optical clock in November 2023.

3090: 1765: 1224: 979: 539: 122: 11080: 9403: 9334: 8972:"Frequency ratio measurements at 18-digit accuracy using an optical clock network" 7611: 6659: 6593: 5664:

36th Annual Precise Time and Time Interval (PTTI) Systems and Applications Meeting

4311: 15075: 15049: 15018: 14916: 14779: 14287: 14266: 14098: 14070: 13835: 13699: 13564: 13541: 13509: 13461: 13448: 13411: 13393: 13023: 13018: 12506: 12250: 12224: 10113:"The most accurate clock ever built only loses one second every 15 billion years" 9528:"Compact magneto-optical trap of thulium atoms for a transportable optical clock" 7597: 7309: 7218: 5650: 3613: 3375: 3070: 2390: 2319: 2311: 2295: 2256: 1946: 1405: 1220: 1208: 1132: 685: 475: 460: 440: 398: 11557: 10879: 9977: 9258:"20 years of developments in optical frequency comb technology and applications" 8944:"Optical fibre link opens a new era of time-frequency metrology, 19 August 2016" 7943: 6372: 6261: 6060: 5514:"An atomic clock measured how general relativity warps time across a millimeter" 5441: 4903: 2341: 14878: 14719: 14704: 14676: 14651: 14643: 14583: 14342: 14332: 14271: 14228: 14060: 14050: 14019: 13919: 13891: 13774: 13642: 13632: 13431: 13303: 13273: 13258: 13043: 13001: 12996: 12868: 12611: 11138: 10927: 10792: 10609: 9322: 8995: 8544: 7875: 7426: 7122: 6685:"2016 Gets Longer with Extra Second Added to New Year Countdown | Sci-News.com" 6443: 6430: 5857:. Vol. 15. International Bureau of Weights and Measures. 2020. p. 9. 5566: 5475: 5119: 4926: 4164: 4159: 4032: 3887: 3883: 3066: 2915: 2746: 1443:. The limiting instability due to atom or ion counting statistics is given by 1228: 1113: 788:

It is important to note that at this level of accuracy, the differences in the

770: 702: 571: 390: 252: 236: 24: 12645:"JILA Atomic Clocks Measure Einstein's General Relativity at Millimeter Scale" 12278:"China's BeiDou navigation satellite, rival to US GPS, starts global services" 11058: 10735: 10538: 9805: 9763:"JILA Strontium Atomic Clock Sets New Records in Both Precision and Stability" 9291: 8268: 8204: 8140: 7084:

Dupays, Arnaud; Beswick, Alberto; Lepetit, Bruno; Rizzo, Carlo (August 2003).

6319: 5442:"Resolving the gravitational redshift across a millimetre-scale atomic sample" 5179: 1658:

is the averaging period. This means instability is smaller when the linewidth

1027:

Simplified block diagram of typical commercial cesium beam frequency reference

950: 15064: 15028: 14873: 14868: 14807: 14741: 14470: 14421: 14406: 14352: 14123: 13959: 13954: 13870: 13722: 13672: 13620: 13554: 13526: 13514: 13504: 13494: 13376: 13220: 13146: 13095: 13048: 12963: 12923: 12918: 12913: 12846: 12558: 12160: 11413: 11239: 10670: 10210: 9688: 9561: 9484: 9299: 9205: 9003: 8645: 7883: 7484:"What the world's most accurate clock can tell us about Earth and the cosmos" 7400: 6723: 5872: 5483: 5410: 5311: 5127: 4989: 4871: 4586: 4537: 4408: 4207:

One second in 13.8 billion years, the age of the universe, is an accuracy of

4174: 4169: 3858: 3216: 2778: 2736: 2724: 2669: 2663: 1193: 511: 385:

A caesium atomic clock from 1975 (upper unit) and battery backup (lower unit)

281: 13743: 11005: 10251: 9197: 7609: 7399:

Leute, J.; Huntemann, N.; Lipphardt, B.; Tamm, Christian (3 February 2016).

6957: 6944: 6559: 6098: 5586:"SA.45s CSAC Chip Scale Atomic Clock (archived version of the original pdf)" 5151:"Optical frequency combs: From frequency metrology to optical phase control" 4505: 14863: 14774: 14709: 14568: 14455: 14450: 14445: 14432: 13814: 13694: 13688: 13354: 13288: 13210: 13141: 12991: 12938: 12878: 12619: 11431: 11352: 11344: 11298: 11290: 11247: 11156: 10800: 10743: 10678: 10546: 10434: 10259: 10189: 10039: 9941: 9676: 9569: 9411: 9213: 9063:"Coping With Unusual Atomic Collisions Makes an Atomic Clock More Accurate" 9011: 8929: 8862: 8813: 8710: 8368: 8276: 8212: 8148: 8086: 8022: 7901: 7732: 7656: 7434: 7351: 7260: 6892: 6567: 6467: 6224: 6201: 6147: 5491: 5418: 5329: 4889: 4577: 4552: 4529: 4198:

have demonstrated a clock that will not lose a second in 300 billion years.

4154: 4054:

predicts that clocks tick slower deeper in a gravitational field, and this

3981: 3916: 3197: 3044: 2755: 1588: 1315: 1257: 1035:

beam frequency reference, timing signals are derived from a high stability

723: 394: 359: 308: 277: 221: 142: 12499: 11405: 10330:"JILA's 3-D Quantum Gas Atomic Clock Offers New Dimensions in Measurement" 10141: 10082:"Getting Better All the Time: JILA Strontium Atomic Clock Sets New Record" 9174:"Optical frequency combs: Coherently uniting the electromagnetic spectrum" 8313: 8299: 7799: 7782: 7401:"Frequency Comparison of Yb Ion Optical Clocks at PTB and NPL via GPS PPP" 6873: 5642: 5150: 5086:"On a definition of the SI second with a set of optical clock transitions" 4956:

Hellwig, Helmut; Evenson, Kenneth M.; Wineland, David J. (December 1978).

4847: 4610: 4551:

Rabi, I. I.; Zacharias, J. R.; Millman, S.; Kusch, P. (15 February 1938).

3838:— is also difficult. Another hurdle involves improving the uncertainty in 3200:

were able to stay in synchrony with each other at a precision of at least

901:

These methods of time comparison must make corrections for the effects of

15023: 14939: 14931: 14853: 14797: 14756: 14578: 14573: 14218: 14201: 14133: 14113: 13999: 13881: 13824: 13704: 13682: 13589: 13574: 13369: 13349: 13339: 13268: 13225: 13205: 13134: 12953: 12855: 12670:"An Ultra-Precise Clock Shows How to Link the Quantum World With Gravity" 10822: 10759:"Differential clock comparisons with a multiplexed optical lattice clock" 8654: 7105: 7038: 6412:

Local oscillator induced instabilities in trapped ion frequency standards

4863: 4769: 4693: 4134: 4129: 4036: 4028: 4022: 3878: 3571:{\displaystyle \sigma (\tau )={\frac {1}{2\pi f{\sqrt {NT_{int}\tau }}}}} 3098: 3063: 2270:

The next step in atomic clock advances involves going from accuracies of

1761: 1319: 1204: 828: 797: 527: 375: 312: 97: 20: 12308:"China puts final satellite for Beidou network into orbit – state media" 9933: 9710:"Blackbody Radiation Shift: Quantum Thermodynamics Will Redefine Clocks" 8911: 8078: 7308:

Huntemann, N.; Sanner, C.; Lipphardt, B.; Tamm, Chr. (8 February 2016).

6712:"How the U.S. Built the World's Most Ridiculously Accurate Atomic Clock" 6529: 3969:

satellite. The masers are about 2 feet long with a weight of 40 pounds.

2330: 2286:. To do so, scientists must demonstrate the accuracy of clocks that use 14982: 14944: 14858: 14830: 14593: 14546: 14530: 14416: 14322: 14143: 14004: 13974: 13912: 13599: 13499: 13406: 13381: 13184: 12968: 12125: 10021: 8233: 7835: 7405:

IEEE Transactions on Ultrasonics, Ferroelectrics, and Frequency Control

6537:

IEEE Transactions on Ultrasonics, Ferroelectrics, and Frequency Control

6447:

IEEE Transactions on Ultrasonics, Ferroelectrics, and Frequency Control

6399:, pages 221–230. Proceedings of the IEEE, Vol. 54, No 2, February 1966. 6394: 6148:"NIST Primary Frequency Standards and the Realization of the SI Second" 5303: 4957: 4611:"NIST Primary Frequency Standards and the Realization of the SI Second" 4319: 3908: 3078: 2921:

A nuclear energy transition offers the following potential advantages:

1250: 894: 778: 471: 256: 23:. For the clock as a measure for risk of catastrophic destruction, see 11389: 11171:"Vector Atomic brings world's first rackmount optical clock to market" 10951: 10702:"Atomic clock performance enabling geodesy below the centimetre level" 9897:"An optical lattice clock with accuracy and stability at the 10 level" 9552: 6945:"With better atomic clocks, scientists prepare to redefine the second" 6459: 6222: 6193: 4981: 4608: 3260:

improved optical lattice clock was described in a 2014 Nature paper.

1260:

to apply feedback to control long-term drift in the radio frequency.

1023: 14959: 14490: 14327: 14211: 14186: 14166: 14083: 14035: 14029: 14014: 13662: 13579: 13215: 13127: 13102: 13083: 12973: 10501: 9323:"Towards a High-Performance Optical Clock Based on Single 171-Yb Ion" 8043: 4793: 4717: 3328: 3154: 3146: 3138: 3130: 3003: 2984: 2845:) that an experimental optical nuclear clock can now be constructed. 2774: 2690: 2681: 2346: 2291: 2287: 1360: 1232: 1076: 1059: 741:(PTB) in Germany, the National Institute of Standards and Technology 730: 719: 694: 676: 603: 595: 591: 583: 555: 146: 126: 12420:"Working Overtime: NASA's Deep Space Atomic Clock Completes Mission" 10583:"Optical clock technologies for global navigation satellite systems" 8853: 8828: 8804: 8779: 6285: 3467:{\displaystyle \sigma \propto {\frac {\Delta f}{f}}{\frac {1}{S/N}}} 409:

and others managed to reduce the light shifts to acceptable levels.

14964: 14954: 14883: 14736: 14525: 14505: 14347: 14253: 14153: 13944: 13939: 13230: 13073: 12983: 12841: 12831: 12594: 11222: 11121: 10988: 10901: 10847: 10775: 10718: 10653: 10521: 10409: 10302: 10234: 10164: 9677:"How Super-Precise Atomic Clocks Will Change the World in a Decade" 9525: 9511: 9274: 8894: 8685: 8535: 8426: 8251: 8187: 8123: 8061: 7707: 7417: 7326: 7235: 6840: 5557: 5458: 5393: 5102: 4109: 3874: 2354: 1296: 1007: 1003: 854: 812: 750: 746: 698: 523: 419:

After 1956, atomic clocks were studied by many groups, such as the

11041: 10862: 10004: 9916: 7997: 7631: 7536:"The most precise atomic clock ever made is a cube of quantum gas" 7217:

Brewer, S.; Chen, J.-S.; Hankin, A.; Clements, E. (15 July 2019).

6550: 6418:. Precise Time and Time Interval (PTTI) Conference. Redondo Beach. 6355: 6302: 6244: 5286: 4043:. Many governments operate transmitters for timekeeping purposes. 1080:

A team of United States Air Force airmen carrying a rubidium clock

917: 14974: 14893: 14845: 14635: 14520: 14510: 14440: 14312: 14223: 14088: 13569: 13559: 13481: 13472: 13457: 13344: 13189: 13112: 12821: 11505: 5005:"Atomichron: The Atomic Clock from Concept to Commercial Product" 3923: 3284: 3158: 3150: 2315: 2230: 1308: 1292: 1118: 1032: 1011: 996: 992: 988: 878: 367: 289: 273: 73: 13359: 8875: 7917:"Nuclear laser spectroscopy of the 3.5 eV transition in Th" 6915:

ERASMUS Centre – Directorate of Human Spaceflight and Operations

6223:

N. Poli; C. W. Oates; ), P. Gill; G. M. Tino (13 January 2014).

3114:

atoms packed in a three-dimensional quantum gas optical lattice.

14911: 14751: 14661: 14515: 14465: 14460: 13667: 12826: 10972: 10633:"Al+27 Quantum-Logic Clock with a Systematic Uncertainty below 9172:

Diddams, Scott A.; Vahala, Kerry; Udem, Thomas (17 July 2020).

8516: 7219:"Al Quantum-Logic Clock with a Systematic Uncertainty below 10" 6085: 5373:"Al+27 Quantum-Logic Clock with a Systematic Uncertainty below 5060:"New Atomic Clocks May Someday Redefine the Length of a Second" 3931:

GPS, the GLONASS time scale implements leap seconds, like UTC.

3371: 3280: 3142: 3119: 1312: 1253: 1169: 886: 567: 559: 519: 515: 158: 12724:"TimeChainZ – Regulatory Reporting For High-Frequency Trading" 12471:"DARPA to launch programme for creating optical atomic clocks" 10052: 9894: 8107: 6594:"Ultraprecise atomic clock poised for new physics discoveries" 5979:"NIST Launches a New U.S. Time Standard: NIST-F2 Atomic Clock" 4290:"NIST Launches a New U.S. Time Standard: NIST-F2 Atomic Clock" 2318:. The increase in precision from NIST-F1 to NIST-F2 is due to 15003: 14998: 14949: 14686: 14656: 14495: 14307: 14206: 14161: 13677: 13426: 13117: 13065: 12547:"These Physicists Watched a Clock Tick for 14 Years Straight" 12181:

China Satellite Navigation Office, Version 2.0, December 2013

11558:"The Role of GPS in Precise Time and Frequency Dissemination" 8650:"A nuclear clock prototype hints at ultraprecise timekeeping" 7612:"Frequency Comparison of Two High-Accuracy Al Optical Clocks" 6635:"Accuracy of the NPL caesium fountain clock further improved" 5801:. Consultative Committee for Time and Frequency. 20 May 2019. 5792:"Mise en pratique for the definition of the second in the SI" 4654:"Time and frequency measurement at NIST: The first 100 years" 4006: 3401: 3074: 3039: 2799:

ion could provide a total fractional frequency inaccuracy of

1611:

is the number of atoms or ions used in a single measurement,

1304: 1237: 1174:

Since 1968, the SI has defined the second as the duration of

946: 857: 138: 59: 11268: 11101: 10298:"A Fermi-degenerate three-dimensional optical lattice clock" 10213:"A Fermi-degenerate three-dimensional optical lattice clock" 8668: 8329: 8169: 7307: 6773:"NIST launches a new US time standard: NIST-F2 atomic clock" 6083: 5259: 5148: 4039:

for every 300 kilometres (186 mi) of distance from the

3823:{\displaystyle E_{n}\approx -{\frac {R_{\infty }ch}{n^{2}}}} 2999:, making comparisons of even more accurate clocks possible. 2701:, it offers more than twice the precision of the original. 2333:

by the International Bureau of Weights and Measures (BIPM).

1043:

to obtain microwaves at the frequency of the caesium atomic

545: 423:(formerly the National Bureau of Standards) in the USA, the 14906: 14901: 14746: 14723: 14604: 14500: 14485: 14475: 13929: 13866: 12816: 12802: 12343: 12118:"ESA Adds System Time Offset to Galileo Navigation Message" 7982: 7398: 6980: 6591: 6530:

Westergaard, P.G.; Lodewyck, J.; Lemonde, P. (March 2010).

4337:

Currently, the type B fractional uncertainty in NIST-F1 is

4063: 3264: 3173: 3031: 3007: 2988: 2963: 2959: 2235: 1163: 754: 681: 599: 13935:

International Earth Rotation and Reference Systems Service

12578: 12445:"DARPA Aims for More Accurate Atomic Clock to Replace GPS" 11195: 8408: 7310:"Single-Ion Atomic Clock with 3×10 Systematic Uncertainty" 6061:"A Cesium Beam Frequency Reference for Severe Environment" 5538: 5439: 3993:

In April 2015, NASA announced that it planned to deploy a

3502:

is the signal-to-noise ratio. This leads to the equation

3283:

is "getting really close to being useful for relativistic

2364: 1332:, which is defined as the ratio of the absolute frequency 113: 14480: 12149:"Trying to Get Somewhere? An Atomic Clock May Be Helping" 10699: 8968: 8752:. EMMI Workshop: The Th Nuclear Isomer Clock. Darmstadt. 7509:"New type of atomic clock keeps time even more precisely" 7083: 7037: 4550: 2948:

German National Metrology Institute (PTB) in Braunschweig

2673: 819:; however, the uncertainties in the list are one part in 244: 12640: 12372:"NASA Technology Missions Launch on SpaceX Falcon Heavy" 12225:"China GPS rival Beidou starts offering navigation data" 10756: 10630: 9091: 9032: 8300:"Shedding Light on the Thorium-229 Nuclear Clock Isomer" 7692: 7216: 6532:"Minimizing the Dick effect in an optical lattice clock" 5704: 5676: 5370: 5342: 2263:, and laser cooling of atoms, which was demonstrated by 478:

released the 5060 rack-mounted model of caesium clocks.

12771: 12509:, National Institute of Standards and Technology, 2010. 12251:"China's Beidou GPS-substitute opens to public in Asia" 11820: 11818: 10579: 9840:"NIST Ytterbium Atomic Clocks Set Record for Stability" 9473:"The most accurate clock ever made runs on quantum gas" 6743: 5347:"NIST's Quantum Logic Clock Returns to Top Performance" 4852:

Journal of Research of the National Bureau of Standards

3231:

research team would differ less than a second over the

3176:'s 2013 pair of ytterbium optical lattice atomic clocks 3038:

The idea of trapping atoms in an optical lattice using

2383: 1404:

The instability of an atomic clock is specified by its

1006:

atom moves at 1,600 m/s at room temperature and a

470:

sold more than 50 units of the first atomic clock, the

296:

of 1 second in 300 million years (relative uncertainty

11444: 10473:"JILA Team Invents New Way to 'See' the Quantum World" 9441:

Physikalisch-Technische Bundesanstalt, Division Optics

9228:"Femtosecond-Laser Frequency Combs for Optical Clocks" 8746:

Concepts and Prospects for a Thorium-229 Nuclear Clock

8440:

a narrow, laser-linewidth-limited spectral feature at

7783:"Viewpoint: Ion Clock Busts into New Precision Regime" 5159:

IEEE Journal of Selected Topics in Quantum Electronics

4955: 4066:

measured the difference in the passage of time due to

3893: 3219:

atoms, a new record for stability with a precision of

2892:

is greater than the nuclear excitation energy, giving

486:

In 1968, the duration of the second was defined to be

11908: 9327:

2021 IEEE 6th Optoelectronics Global Conference (OGC)

8878:"A clock network for geodesy and fundamental science" 6608:"What Are Optical Clocks and Why Are They Important?" 6523: 6496:

Journal of Optics B: Quantum and Semiclassical Optics

3771: 3642: 3591: 3508: 3480: 3422: 3247:

better than previous experiments. The clocks rely on

2169: 2132: 1958: 1919: 1871: 1844: 1824: 1778: 1735: 1715: 1687: 1664: 1644: 1617: 1597: 1570: 1452: 1413: 1369: 1338: 286:

National Institute of Standards and Technology (NIST)

171: 11815: 11711:. GPS Operations Center. 30 May 2012. Archived from 10505:"Entanglement on an optical atomic-clock transition" 8514: 4817:"President Piñera Receives ESO's First Atomic Clock" 4105: 3861:, must be developed before the second is redefined. 3300:

the same 3D lattice yielded a residual precision of

807:(BIPM) provides a list of frequencies that serve as 208:

when expressed in the unit Hz, which is equal to s.

12694: 11556:Dana, Peter H.; Bruce M. Penro (July–August 1990). 9702: 8876:Paul-Eric Pottie, Gesine Grosche (19 August 2016). 6491:"The Dick effect for an optical frequency standard" 6281: 6279: 5732: 5580: 5578: 5576: 4661:

2001 IEEE International Frequency Control Symposium

4609:M.A. Lombardi; T.P. Heavner; S.R. Jefferts (2007). 4553:"A New Method of Measuring Nuclear Magnetic Moment" 3636:would involve fixing the value to a certain value: 3126:are used to cool the atoms for improved precision. 2306:accuracy was first reached at the United Kingdom's 1256:at the detector. The detector's signal can then be 16:

Clock that monitors the resonant frequency of atoms

13865: 11555: 11472: 9769:. National Institute of Standards and Technology. 9256:Fortier, Tara; Baumann, Esther (6 December 2019). 8389:, and the fluorescence lifetime in the crystal is 6482: 6171: 5029: 4441:Landmark Writings in Western Mathematics 1640–1940 3822: 3757: 3600: 3570: 3486: 3466: 3378:2022. These technologies originally funded by the 2730: 2215:{\displaystyle \sigma _{y,\,{\rm {atoms}}}(\tau )} 2214: 2155: 2115: 1937: 1905: 1857: 1830: 1810: 1748: 1721: 1697: 1673: 1650: 1630: 1603: 1579: 1553: 1435: 1378: 1351: 863: 532:2019 revision of the International System of Units 284:. The primary standard for the United States, the 187: 12243: 11960: 11709:"Notice Advisory to Navstar Users (NANU) 2012034" 9171: 6422: 4506:"Space Quantization in a Gyrating Magnetic Field" 4016: 3608:of typically 1 Hz, so the Q-factor is about 15062: 11934: 11026: 10930:(12 January 2014). "Timekeepers of the future". 10053:JILA Scientific Communications (21 April 2015). 9870:"New atomic clock sets the record for stability" 7978: 7976: 7513:MIT News | Massachusetts Institute of Technology 6276: 5573: 5541:"Roadmap towards the redefinition of the second" 1709:) is larger. The stability improves as the time 1190:International Committee for Weights and Measures 11973:. European GNSS Service Centre. 28 March 2018. 9467: 9465: 9321:Zuo, Yani; Dai, Shaoyao; Chen, Shiying (2021). 9054: 8373:The nuclear resonance for the Th ions in Th:CaF 8227: 6437: 5737:"Ion Optical Clocks and Precision Measurements" 3976:satellite navigation system is operated by the 3111:neutral atoms trapped in an optical lattice and 1203:, the definition of every base unit except the 733:laboratories maintain atomic clocks: including 327:proposed measuring time with the vibrations of 300:). NIST-F2 was brought online on 3 April 2014. 212:This definition is the basis for the system of 12747: 12330: 11526: 9375:"Single-atom optical clock with high accuracy" 9255: 8325: 8323: 8101: 4264:"The world is doing away with the leap second" 3255:and trapped in an optical lattice. A laser at 2941: 2870:, this pathway is energetically prohibited in 2668:In March 2008, physicists at NIST described a 2234:The historical accuracy of atomic clocks from 1318:. However all of these are easily affected by 421:National Institute of Standards and Technology 153:. This phenomenon serves as the basis for the 14620: 13851: 13773: 13759: 12787: 11826:"Galileo's contribution to the MEOSAR system" 10110: 9980:"Systematic evaluation of an atomic clock at 9504: 8662: 7973: 5615: 5613: 5262:"Systematic evaluation of an atomic clock at 4651: 3385: 3370:In July 2022, atomic optical clocks based on 2126:This expression shows the same dependence on 1811:{\displaystyle \sigma _{y}^{\rm {LO}}(\tau )} 1131:seconds. This makes hydrogen masers good for 412:Ramsey developed a method, commonly known as 11789: 10823:"BIPM Time Coordinated Universal Time (UTC)" 9462: 9434:"On Secondary Representations of the Second" 8291: 7849: 7501: 6100:International Bureau of Weights and Measures 5822:International Bureau of Weights and Measures 4368:: CS1 maint: DOI inactive as of June 2024 ( 3494:is the instability, f is the frequency, and 3361:International Bureau of Weights and Measures 1037:voltage-controlled quartz crystal oscillator 912: 879:Global Navigation Satellite System (GLONASS) 805:International Bureau of Weights and Measures 12500:"How Accurate is a Radio Controlled Clock?" 11387: 8320: 8163: 7756:"Optical Clock Precision Breaks New Ground" 7374:"Ytterbium 171 ion (688 THz) BIPM document" 7283:"Ytterbium 171 ion (642 THz) BIPM document" 6854: 6832: 4604: 4602: 4600: 4598: 4596: 3988: 3129:Atomic systems under consideration include 1303:, the vibrations of springs and gears in a 1158: 652: 481: 220:that is the basis of civil time implements 14627: 14613: 13858: 13844: 13766: 13752: 12794: 12780: 11944:. European GNSS Agency. 15 December 2016. 11478:TIME—From Earth Rotation to Atomic Physics 11198:"Transportable Optical Lattice Clock with 9862: 9785: 9372: 9320: 9060: 8508: 8393:, corresponding to an isomer half-life of 8037: 6408: 6007: 5954:"Temperature and Kinetic Energy – Answers" 5610: 5035:TIME—From Earth Rotation to Atomic Physics 4958:"Time, frequency and physical measurement" 4768: 4692: 4305: 4303: 3055:in 2005. One of 2012's Physics Nobelists, 1214: 44: 19:For a clock updated by radio signals, see 12593: 12217: 11683:"NOTICE ADVISORY TO NAVSTAR USERS (NANU)" 11650:"NAVSTAR GPS User Equipment Introduction" 11421: 11221: 11146: 11120: 11040: 10987: 10861: 10774: 10717: 10652: 10520: 10408: 10233: 10163: 10079: 10029: 10003: 9915: 9832: 9551: 9510: 9273: 8919: 8893: 8852: 8803: 8684: 8534: 8425: 8250: 8186: 8122: 8060: 7996: 7908: 7891: 7834: 7798: 7706: 7630: 7416: 7325: 7234: 7104: 6956: 6942: 6882: 6872: 6839: 6801: 6549: 6402: 6387: 6354: 6341:Poli, N (2014). "Optical atomic clocks". 6301: 6243: 5842: 5814:Explanatory Supplement of BIPM Circular T 5655: 5556: 5457: 5392: 5319: 5285: 5149:J. Ye; H. Schnatz; L.W. Hollberg (2003). 5101: 5037:. Weinheim: Wiley-VCH. pp. 191–195. 4879: 4576: 4282: 3845:In the Report of the 25th meeting of the 2181: 1970: 1464: 1363:to the linewidth of the resonance itself 708: 546:Metrology advancements and optical clocks 343:During the 1930s, the American physicist 14389:International Commission on Stratigraphy 12518: 12494: 12492: 12397:"NASA Activates Deep Space Atomic Clock" 11494: 11449:"Help with WWVB Radio Controlled Clocks" 11390:"Development of a space cold atom clock" 10926: 10354: 9794:"Precise atomic clock may redefine time" 9650:"PTB Optical nuclear spectroscopy of Th" 9431: 9368: 9366: 9364: 9362: 8332:"Laser Excitation of the Th-229 Nucleus" 7915:Peik, E.; Tamm, Chr. (15 January 2003). 7914: 7533: 6857:"Development of a space cold atom clock" 6396:Statistics of Atomic Frequency Standards 6033: 5681:"Success Story: Chip-Scale Atomic Clock" 5142: 5083: 4593: 4296:. 3 April 2014 – via www.nist.gov. 4261: 3933: 3394: 3289: 3167: 3025: 2340: 2251:, and the last clock had an accuracy of 2229: 1638:is the time required for one cycle, and 1393:that do not have a universal frequency. 1211:relies on the definition of the second. 1164:International System of Units definition 1117: 1075: 1022: 916: 656: 549: 380: 307: 224:to allow clock time to track changes in 117:The master atomic clock ensemble at the 112: 12417: 12369: 12146: 11318: 11316: 10332:(Press release). NIST. 5 October 2017. 9624:"PTB Time and Frequency Department 4.4" 8743:Peik, Ekkehard (25–27 September 2012). 8644: 8297: 7559: 6908:"Atomic clock ensemble in space (ACES)" 6587: 6585: 6431:Characterization of Frequency Stability 5900: 5786: 5784: 5782: 5233: 4300: 4150:Primary Atomic Reference Clock in Space 2365:Secondary representations of the second 1062:frequency of the hyperfine transition. 809:secondary representations of the second 259:or 1 billionth of a second (10 or 188:{\displaystyle \Delta \nu _{\text{Cs}}} 15063: 13789:Synchronous Motor and the Master Clock 12399:. NASA Jet Propulsion Laboratory (JPL) 12336: 11803:from the original on 13 September 2019 11594:"GPS time accurate to 100 nanoseconds" 9959:from the original on 17 September 2016 9251: 9249: 8826: 8777: 7019:from the original on 23 September 2015 6632: 6105:The International System of Units (SI) 5929:"NIST-F1 Cesium Fountain Atomic Clock" 5926: 5661: 5084:Lodewyck, Jérôme (16 September 2019). 5002: 4845: 4434: 4382: 4312:"First Accuracy Evaluation of NIST-F2" 2910:ions a long half-life on the order of 629:between atomic ensembles separated by 602:demonstrated a strontium clock with a 272:The main variety of atomic clock uses 14608: 13839: 13747: 12775: 12489: 12351:from the original on 10 December 2015 12288:from the original on 27 December 2018 12275: 12257:from the original on 27 December 2012 12056:"Rb Atomic Frequency Standard (RAFS)" 11574:from the original on 15 December 2012 11545:from the original on 25 October 2012. 10367:from the original on 14 December 2017 10295: 9716:from the original on 18 December 2012 9359: 8950:from the original on 14 November 2016 8549:The transition frequency between the 7753: 6987:from the original on 19 November 2011 6924:from the original on 25 December 2015 6084:National Physical Laboratory (2019). 6008:University, Lancaster (11 May 2021). 5851:BIPM Annual Report on Time Activities 5799:Bureau International Poids et Mesures 4674:from the original on 29 December 2019 4633:from the original on 12 February 2021 4479:"Milestones:First Atomic Clock, 1948" 4046: 2745:energy transition (between different 2255:. The clocks were the first to use a 1386:. Atomic resonance has a much higher 871:Global Navigational Satellite Systems 765:(NPL) in the United Kingdom, and the 739:Physikalisch-Technische Bundesanstalt 425:Physikalisch-Technische Bundesanstalt 13728: 12276:Varma, K. J. M. (27 December 2018). 12231:from the original on 3 February 2012 12205:from the original on 29 October 2020 12098:from the original on 28 October 2020 12066:from the original on 6 November 2018 11948:from the original on 15 January 2021 11896:from the original on 6 November 2016 11662:from the original on 21 October 2013 11480:. Weinheim: Wiley-VCH. p. 266. 11322: 11313: 10829:from the original on 4 November 2013 10561:from the original on 4 February 2021 10123:from the original on 27 January 2018 9876:from the original on 2 February 2014 9791: 9773:from the original on 8 December 2014 9656:from the original on 7 November 2017 9630:from the original on 7 November 2017 8759:from the original on 10 October 2021 8742: 7813: 7780: 7140:from the original on 14 January 2019 6689:Breaking Science News | Sci-News.com 6582: 6340: 6145: 5779: 5207: 4919:Spectroscopy With Coherent Radiation 4750:from the original on 17 October 2017 4503: 4430: 4428: 4426: 4262:Brumfiel, Geoff (27 November 2022). 4243:from the original on 7 December 2010 4181: 4085: 3275:, which corresponds to a measurable 3108:single ions isolated in an ion trap; 2684:. This clock was compared to NIST's 12634: 12337:Landau, Elizabeth (27 April 2015). 11980:from the original on 26 August 2019 11922:from the original on 29 August 2019 10470: 10355:Phillips, Julie (10 October 2017). 10336:from the original on 5 October 2017 10310:from the original on 6 October 2017 10092:from the original on 9 October 2015 9850:from the original on 23 August 2013 9820:from the original on 25 August 2013 9760: 9246: 9121:"The Prize's Legacy: Dave Wineland" 7762:from the original on 26 August 2019 6814:from the original on 9 October 2015 5989:from the original on 19 August 2016 5882:from the original on 14 August 2021 5831:from the original on 9 October 2022 5621:"Chip-Scale Atomic Devices at NIST" 4098:is only accurate to a millisecond. 3978:China National Space Administration 3965:atomic clocks for onboard timing. 3894:Global navigation satellite systems 3627: 2716: 566:Technological developments such as 535: 13: 12147:Belcher, David (1 November 2021). 11797:"Galileo begins serving the globe" 11777:from the original on 14 April 2016 11630:from the original on 21 March 2017 10357:"The Clock that Changed the World" 9674: 7814:Wang, Yebing (27 September 2018). 7807: 7774: 7747: 7686: 7534:Woodward, Aylin (5 October 2017). 7380:from the original on 2 August 2022 7289:from the original on 2 August 2022 7198:from the original on 2 August 2022 6703: 6139: 5077: 3947:Global Navigation Satellite System 3924:GLObal NAvigation Satellite System 3796: 3648: 3592: 3432: 2196: 2193: 2190: 2187: 2184: 2017: 2014: 1982: 1979: 1976: 1973: 1793: 1790: 1665: 1571: 1501: 1479: 1476: 1473: 1470: 1467: 1436:{\displaystyle \sigma _{y}(\tau )} 1370: 1286: 995:clock, developed in 1999, and the 463:and Frequency & Time Systems. 378:in collaboration with Jack Parry. 172: 14: 15102: 14109:Discrete time and continuous time 12418:Hartono, Naomi (1 October 2021). 12036:from the original on 6 March 2019 10908:from the original on 26 June 2015 10296:Beall, Abigail (5 October 2017). 9604:from the original on 27 June 2015 9147:"Optical Lattices: Webs of Light" 9096:"Optical Lattices: Webs of Light" 8827:Gibney, Elizabeth (2 June 2015). 8778:Gibney, Elizabeth (2 June 2015). 8475:) that decays with a lifetime of 8397:for a nucleus isolated in vacuum. 7674:from the original on 21 July 2011 7481: 7172:from the original on 4 March 2016 6943:Cartlidge, Edwin (1 March 2018). 6783:from the original on 6 April 2014 6592:University of Wisconsin-Madison. 5189:from the original on 6 March 2016 4908:(1989, The Nobel Foundation) and 4827:from the original on 1 April 2014 4423: 4000: 3021: 2657: 2302:The goal of an atomic clock with 1137:very long baseline interferometry 713: 374:in the United Kingdom in 1955 by 14034: 14028: 13727: 13718: 13717: 12741: 12716: 12688: 12662: 12572: 12544: 12538: 12512: 12463: 12437: 12411: 12389: 12363: 12300: 12269: 12185: 12174: 12140: 12110: 12078: 12048: 12030:Safran - Navigation & Timing 12018: 11992: 11876: 11844: 11832:from the original on 9 July 2016 11757: 11745:from the original on 2 June 2018 11727: 11701: 11675: 11642: 11612: 11600:from the original on 14 May 2012 11586: 11549: 11520: 11466: 11438: 11381: 11367: 11262: 11189: 11163: 11095: 11073: 11020: 10966: 10920: 10894: 10841: 10815: 10750: 10693: 10624: 10573: 10495: 10483:from the original on 17 May 2019 10464: 10452:from the original on 2 June 2020 10379: 10348: 10322: 10289: 10204: 10135: 10104: 10073: 10046: 9971: 9888: 9754: 9728: 9668: 9642: 9616: 9584: 9519: 9498: 9425: 9373:W.H. Oskay; et al. (2006). 9314: 9220: 9165: 9139: 9113: 9085: 9073:from the original on 5 June 2011 9026: 8962: 8936: 8869: 8820: 8771: 8736: 8638: 8563:excited state is determined as: 8402: 8298:Thirolf, Peter (29 April 2024). 7572:from the original on 2 June 2017 6709: 6174:Review of Scientific Instruments 6128:from the original on 4 June 2021 4449:10.1016/b978-044450871-3/50125-x 4385:"History of early atomic clocks" 4108: 4062:In 2021 a team of scientists at 3928:Russian Aerospace Defence Forces 3847:Consultative Committee for Units 2361:are examples of clock research. 1018: 347:built equipment for atomic beam 288:'s caesium fountain clock named 218:Coordinated Universal Time (UTC) 12370:Northon, Karen (25 June 2019). 10111:James Vincent (22 April 2015). 7843: 7603: 7584: 7553: 7527: 7475: 7449: 7392: 7366: 7301: 7275: 7210: 7184: 7152: 7077: 7031: 6999: 6965: 6936: 6905: 6899: 6848: 6826: 6795: 6765: 6737: 6677: 6652: 6633:Laboratory, National Physical. 6626: 6600: 6434:, NBS Technical Note 394, 1970. 6334: 6216: 6165: 6092: 6088:. National Physical laboratory. 6077: 6053: 6034:Vleugels, Anouk (23 May 2021). 6027: 6001: 5971: 5946: 5920: 5903:"NIST-F1 Cesium Fountain Clock" 5894: 5805: 5754: 5726: 5698: 5670: 5532: 5506: 5433: 5364: 5336: 5253: 5227: 5201: 5057: 5051: 5023: 4996: 4949: 4896: 4846:Ramsey, N.F. (September 1983). 4839: 4809: 4762: 4732: 4686: 4645: 4201: 4196:University of Wisconsin-Madison 4188: 3864: 3852: 3365:International Atomic Time (TAI) 2888:ions, as the second and higher 2866:atoms decay in microseconds by 2731:Nuclear (optical) clock concept 1938:{\displaystyle 0.4<d<0.7} 1591:linewidth of the clock system, 875:Global Positioning System (GPS) 864:Synchronization with satellites 445:Bureau International de l'Heure 14182:History of timekeeping devices 12519:lombardi (24 September 2009). 12314:. 23 June 2020. Archived from 12026:"Passive Hydrogen Maser (PHM)" 11232:10.1103/PhysRevLett.118.073601 10663:10.1103/physrevlett.123.033201 10427:10.1103/PhysRevLett.120.103201 10182:10.1103/PhysRevLett.116.063001 9761:Ost, Laura (22 January 2014). 8703:10.1103/PhysRevLett.118.042501 8436:10.1103/PhysRevLett.133.013201 8377:is measured at the wavelength 8361:10.1103/PhysRevLett.132.182501 8015:10.1103/PhysRevLett.108.120802 7725:10.1103/PhysRevLett.123.033201 7649:10.1103/PhysRevLett.104.070802 7560:Swenson, Gayle (7 June 2010). 7344:10.1103/PhysRevLett.116.063001 7253:10.1103/PhysRevLett.123.033201 5403:10.1103/physrevlett.123.033201 4740:"60 years of the Atomic Clock" 4619:Journal of Measurement Science 4544: 4497: 4471: 4443:, Elsevier, pp. 564–587, 4383:Ramsey, Norman F (June 2006). 4376: 4255: 4229: 4017:Time signal radio transmitters 3518: 3512: 2359:Atomic Clock Ensemble in Space 2209: 2203: 2070: 2061: 2039: 2033: 1995: 1989: 1805: 1799: 1492: 1486: 1430: 1424: 1010:atom moves at 510 m/s, a 759:University of Colorado Boulder 1: 9404:10.1103/PhysRevLett.97.020801 9335:10.1109/OGC52961.2021.9654373 7781:Dubé, Pierre (15 July 2019). 6804:"A New Era for Atomic Clocks" 6802:Laura Ost (4 February 2014). 4504:Rabi, I. I. (15 April 1937). 4222: 2326:from the warm chamber walls. 2314:clock and the United States' 2156:{\displaystyle T_{c}/{\tau }} 1906:{\displaystyle d=T_{i}/T_{c}} 773:linked to atomic motion, the 705:to reach greater accuracies. 397:developed a technique called 155:International System of Units 29:Atomic Clock (disambiguation) 14634: 12086:"GNSS Timescale Description" 12060:safran-navigation-timing.com 11620:"UTC to GPS Time Correction" 11529:"The Science of Timekeeping" 11476:; Seidelmann, P. K. (2009). 9792:Ball, Philip (9 July 2013). 7754:Wills, Stewart (July 2019). 7192:"Aluminum ion BIPM document" 6343:La Rivista del Nuovo Cimento 5901:swenson (29 December 1999). 5762:"How Do Atomic Clocks Work?" 5033:; Seidelmann, P. K. (2009). 4744:National Physical Laboratory 3871:navigation satellite systems 2308:National Physical Laboratory 2267:and his colleagues in 1978. 1865:, and where the duty factor 1838:, the interrogation time is 1631:{\displaystyle T_{\text{c}}} 1219:The core of the traditional 763:National Physical Laboratory 433:National Physical Laboratory 372:National Physical Laboratory 354:The accuracy of mechanical, 317:National Physical Laboratory 7: 14790:Internal combustion engines 14767:External combustion engines 14129:Gravitational time dilation 13965:Barycentric Coordinate Time 13532:Geological history of Earth 11502:"Global Positioning System" 11081:"BIPM work programme: Time" 10902:"BIPM work programme: Time" 10471:Ost, Laura (5 March 2018). 10080:Laura Ost (21 April 2015). 9067:National Science Foundation 5234:swenson (4 February 2010). 4101: 3585:, with a natural linewidth 3277:gravitational time dilation 2942:Clock comparison techniques 2751:atomic electron transitions 2336: 2225: 1698:{\displaystyle {\sqrt {N}}} 1674:{\displaystyle \Delta \nu } 1580:{\displaystyle \Delta \nu } 1379:{\displaystyle \Delta \nu } 1107: 1065: 951:BIPM Circular T publication 877:, the Russian Federation's 447:, abbreviated BIH), at the 10: 15107: 13985:Geocentric Coordinate Time 13970:Barycentric Dynamical Time 13908:Coordinated Universal Time 12884:Orders of magnitude (time) 12612:10.1038/s41586-021-04349-7 11685:. May 2017. Archived from 11139:10.1038/s41586-024-07225-2 10793:10.1038/s41586-021-04344-y 10610:10.1007/s10291-021-01113-2 9061:D. Lindley (20 May 2009). 8996:10.1038/s41586-021-03253-4 8545:10.1038/s41586-024-07839-6 7876:10.1038/s41598-018-26365-w 7427:10.1109/TUFFC.2016.2524988 7123:10.1103/PhysRevA.68.052503 6779:. nist.gov. 3 April 2014. 6155:NCSL International Measure 5476:10.1038/s41586-021-04349-7 4927:10.1142/9789812795717_0015 4848:"History of Atomic Clocks" 4401:10.1088/0026-1394/42/3/s01 4333:10.1088/0026-1394/51/3/174 4020: 3926:(GLONASS) operated by the 3873:, and applications in the 3632:A definition based on the 3380:U.S. Department of Defense 2734: 2661: 2259:, which was introduced by 1223:atomic clock is a tunable 1167: 1111: 1102:GPS disciplined oscillator 1069: 999:clock, developed in 2013. 977: 973: 669:scientists demonstrated a 303: 18: 15081:Electronic test equipment 15042: 14991: 14973: 14930: 14892: 14844: 14821: 14788: 14765: 14718: 14685: 14644:Classical simple machines 14642: 14539: 14430: 14397: 14371: 14252: 14152: 14139:Time-translation symmetry 14069: 14043: 14026: 13950:International Atomic Time 13900: 13877: 13807: 13781: 13775:Electric clock technology 13713: 13655: 13608: 13595:Time translation symmetry 13540: 13480: 13470: 13392: 13319: 13239: 13180: 13064: 12982: 12892: 12854: 12840: 12809: 12339:"Deep Space Atomic Clock" 12253:. BBC. 27 December 2012. 12227:. BBC. 27 December 2011. 11918:. European Space Agency. 11799:. European Space Agency. 11735:"Time References in GNSS" 11538:(1289). Hewlett Packard. 11504:. Gps.gov. Archived from 11059:10.1103/RevModPhys.87.637 11029:Reviews of Modern Physics 10880:10.1393/ncr/i2013-10095-x 10850:Rivista del Nuovo Cimento 10736:10.1038/s41586-018-0738-2 10539:10.1038/s41586-020-3006-1 10150:Systematic Uncertainty". 9806:10.1038/nature.2013.13363 9592:"Ytterbium BIPM document" 9292:10.1038/s42005-019-0249-y 8269:10.1038/s41586-019-1533-4 8205:10.1038/s41586-019-1542-3 8141:10.1038/s41586-018-0011-8 7944:10.1209/epl/i2003-00210-x 7160:"Strontium BIPM document" 7063:10.1088/0026-1394/9/3/004 6517:10.1088/1464-4266/5/2/373 6373:10.1393/ncr/i2013-10095-x 6320:10.1103/RevModPhys.87.637 6289:Reviews of Modern Physics 6262:10.1393/ncr/i2013-10095-x 6232:Rivista del Nuovo Cimento 5927:mweiss (26 August 2009). 5210:"Optical Frequency Combs" 5208:NIST (31 December 2009). 5180:10.1109/JSTQE.2003.819109 4335:(inactive 23 June 2024). 3904:United States Space Force 3900:Global Positioning System 3404:beams. These clocks have 3163:electromagnetic radiation 3161:. The color of a clock's 1098:global positioning system 931:International Atomic Time 913:International timekeeping 562:to measure time precisely 437:International Time Bureau 429:National Research Council 214:International Atomic Time 151:electromagnetic radiation 103: 93: 79: 65: 55: 43: 38: 15091:Time measurement systems 12801: 9329:. IEEE. pp. 92–95. 8497:(10)</sys> eV 7596:5 September 2010 at the 7007:"Rubidium BIPM document" 5567:10.1088/1681-7575/ad17d2 5120:10.1088/1681-7575/ab3a82 3989:Experimental space clock 3601:{\displaystyle \Delta f} 3386:Chip-scale atomic clocks 3363:(BIPM) for establishing 2962:lab and its partner lab 1949:can be approximated as 1749:{\displaystyle \nu _{0}} 1352:{\displaystyle \nu _{0}} 1159:Time measuring mechanism 1143:tests of the effects of 968: 653:Chip-scale atomic clocks 558:lattice clock that uses 482:Definition of the second 474:. In 1964, engineers at 292:, measures time with an 255:is (a timing error of a 27:. For other topics, see 15029:Check weighing machines 14399:Astronomical chronology 14372:Archaeology and geology 14079:Absolute space and time 13995:IERS Reference Meridian 13990:International Date Line 13901:International standards 13550:Absolute space and time 13201:Astronomical chronology 11828:. European Commission. 11527:David W. Allan (1997). 11394:National Science Review 11210:Physical Review Letters 11105:"Optical Clocks at Sea" 11006:10.1364/OPTICA.3.000563 10641:Physical Review Letters 10396:Physical Review Letters 10252:10.1126/science.aam5538 10152:Physical Review Letters 9740:Joint Quantum Institute 9383:Physical Review Letters 9198:10.1126/science.aay3676 8672:Physical Review Letters 8413:Physical Review Letters 8340:Physical Review Letters 7695:Physical Review Letters 7619:Physical Review Letters 7600:, NIST, 4 February 2010 7461:www.laserfocusworld.com 7314:Physical Review Letters 7223:Physical Review Letters 6973:"Unit of time (second)" 6958:10.1126/science.aat4586 6861:National Science Review 6560:10.1109/TUFFC.2010.1457 6225:"Optical Atomic Clocks" 5381:Physical Review Letters 4270:. National Public Radio 3995:Deep Space Atomic Clock 3961:hydrogen maser and two 3840:quantum electrodynamics 3487:{\displaystyle \sigma } 1770:Flicker frequency noise 1227:containing a gas. In a 1215:Tuning and optimization 1201:2019 revision of the SI 1153:gravitational red shift 943:equal gravity potential 881:, the European Union's 671:chip-scale atomic clock 572:optical frequency combs 435:in the United Kingdom, 323:The Scottish physicist 243:and the United States' 157:' (SI) definition of a 13782:Powerline synchronized 13600:Time reversal symmetry 12904:Italian six-hour clock 12699:"Keeping Time at NIST" 12505:7 January 2021 at the 11345:10.1098/rsta.2011.0237 11291:10.1098/rsta.2011.0237 9262:Communications Physics 6146:NIST (December 2007). 5649:7 January 2021 at the 5641:Available on-line at: 5627:. 2007. Archived from 5591:. 2011. Archived from 4652:D.B. Sullivan (2001). 4578:10.1103/physrev.53.318 4530:10.1103/physrev.51.652 4268:Weekend Edition Sunday 4092:high-frequency trading 4068:gravitational redshift 4056:gravitational redshift 3939: 3902:(GPS) operated by the 3824: 3759: 3602: 3572: 3488: 3468: 3296: 3183:University of Delaware 3177: 3053:Nobel Prize in Physics 3035: 2717:optical lattice clocks 2350: 2238: 2216: 2157: 2117: 1939: 1907: 1859: 1832: 1812: 1750: 1723: 1699: 1675: 1652: 1632: 1605: 1581: 1555: 1437: 1380: 1353: 1123: 1081: 1028: 922: 909:of a few nanoseconds. 709:How atomic clocks work 662: 563: 468:National Radio Company 466:During the 1950s, the 453:National Radio Company 427:(PTB) in Germany, the 407:Claude Cohen-Tannoudji 386: 320: 210: 189: 130: 119:U.S. Naval Observatory 15014:Seed-counting machine 14358:Weekday determination 14244:Sundial markup schema 13365:Time and fate deities 13310:The Unreality of Time 13249:A series and B series 12498:Michael A. Lombardi, 9992:Nature Communications 9094:(29 September 2020). 8882:Nature Communications 8556:ground state and the 8314:10.1103/Physics.17.71 7800:10.1103/physics.12.79 5274:Nature Communications 5003:Forman, Paul (1998). 4145:Network Time Protocol 4140:List of atomic clocks 3955:European Space Agency 3937: 3825: 3760: 3603: 3573: 3489: 3469: 3395:Redefining the second 3293: 3171: 3124:magneto-optical traps 3029: 2662:Further information: 2344: 2233: 2217: 2158: 2118: 1940: 1908: 1860: 1858:{\displaystyle T_{i}} 1833: 1831:{\displaystyle \tau } 1813: 1751: 1724: 1722:{\displaystyle \tau } 1707:signal to noise ratio 1700: 1676: 1653: 1651:{\displaystyle \tau } 1633: 1606: 1582: 1556: 1438: 1381: 1354: 1323:regime and higher). 1121: 1079: 1041:frequency synthesizer 1026: 920: 800:at a specific point. 729:A number of national 660: 553: 431:(NRC) in Canada, the 414:Ramsey interferometry 384: 311: 190: 163: 116: 14813:Nutating disc engine 14803:Reciprocating engine 14379:Chronological dating 14119:Theory of relativity 13980:Daylight saving time 13616:Chronological dating 13585:Theory of relativity 12929:Daylight saving time 12643:(16 February 2022). 11447:(11 February 2010). 11175:www.businesswire.com 10061:on 19 September 2015 8648:(4 September 2024). 6748:"Second: The Future" 5707:(11 December 2019). 5064:Smithsonian Magazine 4864:10.6028/jres.088.015 4823:. 15 November 2013. 3951:European GNSS Agency 3769: 3640: 3589: 3506: 3478: 3420: 2672:based on individual 2349:-based optical clock 2324:black-body radiation 2167: 2130: 1956: 1917: 1869: 1842: 1822: 1776: 1733: 1713: 1685: 1681:is smaller and when 1662: 1642: 1615: 1595: 1568: 1450: 1411: 1367: 1336: 1295:, the swinging of a 1231:clock the gas emits 1135:, in particular for 1045:hyperfine transition 777:of the environment ( 530:decided upon at the 336:, which defines the 169: 88:satellite navigation 14589:Time value of money 14384:Geologic time scale 14239:History of sundials 14104:Cosmological decade 14056:Greenwich Mean Time 13887:Orders of magnitude 12909:Thai six-hour clock 12604:2022Natur.602..420B 12521:"Radio Station WWV" 12475:Airforce Technology 11942:"Galileo Goes Live" 11406:10.1093/nsr/nwaa215 11337:2011RSPTA.369.4109G 11331:(1953): 4109–4130. 11283:2011RSPTA.369.4109G 11277:(1953): 4109–4130. 11131:2024Natur.628..736R 11051:2015RvMP...87..637L 10998:2016Optic...3..563G 10944:2014NatPh..10...82M 10872:2013NCimR..36..555P 10785:2022Natur.602..425Z 10728:2018Natur.564...87M 10602:2021GPSS...25...83S 10531:2020Natur.588..414P 10419:2018PhRvL.120j3201M 10277:on 15 December 2019 10244:2017Sci...358...90C 10174:2016PhRvL.116f3001H 10014:2015NatCo...6.6896N 9934:10.1038/nature12941 9926:2014Natur.506...71B 9544:2021OExpr..2936734G 9538:(22): 36734–36744. 9396:2006PhRvL..97b0801O 9284:2019CmPhy...2..153F 9190:2020Sci...369..367D 9153:. 29 September 2020 8988:2021Natur.591..564B 8912:10.1038/ncomms12443 8904:2016NatCo...712443L 8845:2015Natur.522...16G 8796:2015Natur.522...16G 8695:2017PhRvL.118d2501S 8379:148.3821(5) nm 8353:2024PhRvL.132r2501T 8261:2019Natur.573..243S 8197:2019Natur.573..238M 8133:2018Natur.556..321T 8079:10.1038/nature17669 8071:2016Natur.533...47V 8007:2012PhRvL.108l0802C 7961:on 16 December 2013 7936:2003EL.....61..181P 7924:Europhysics Letters 7868:2018NatSR...8.8022G 7717:2019PhRvL.123c3201B 7641:2010PhRvL.104g0802C 7336:2016PhRvL.116f3001H 7245:2019PhRvL.123c3201B 7115:2003PhRvA..68e2503D 7055:1973Metro...9..128E 6874:10.1093/nsr/nwaa215 6509:2003JOptB...5S.150Q 6409:Dick, G.J. (1987). 6365:2013NCimR..36..555P 6312:2015RvMP...87..637L 6254:2013NCimR..36..555P 6186:2021RScI...92l4705J 5766:www.timeanddate.com 5735:(29 October 2016). 5709:"Chip-Scale Clocks" 5679:(2 December 2020). 5468:2022Natur.602..420B 5296:2015NatCo...6.6896N 5172:2003IJSTQ...9.1041Y 5112:2019Metro..56e5009L 4974:1978PhT....31l..23H 4786:1955Natur.176..280E 4710:1955Natur.176..280E 4569:1938PhRv...53..318R 4522:1937PhRv...51..652R 4435:Achard, F. (2005), 4237:"USNO Master Clock" 4194:Researchers at the 3949:is operated by the 3842:/QED calculations. 3698: 3233:age of the universe 3062:The development of 2868:internal conversion 2670:quantum logic clock 2421: by definition 2382:Working frequency ( 2284:age of the universe 2022: 1913:has typical values 1798: 991:clocks include the 885:system and China's 790:gravitational field 325:James Clerk Maxwell 14836:Peaucellier-Lipkin 14564:Mental chronometry 14192:Marine chronometer 14044:Obsolete standards 13439:Rosy retrospection 13417:Mental chronometry 13241:Philosophy of time 12318:on 28 October 2020 12153:The New York Times 11916:"Galileo's clocks" 11177:. 13 November 2023 10022:10.1038/ncomms7896 9988:total uncertainty" 9872:. 27 August 2013. 9846:. 22 August 2013. 9234:. 18 December 2009 7856:Scientific Reports 7836:10.3390/app8112194 7515:. 16 December 2020 6691:. 23 December 2016 5304:10.1038/ncomms7896 5270:total uncertainty" 5011:on 21 October 2007 4116:Electronics portal 4082:at the same time. 4052:General relativity 4047:General relativity 3940: 3820: 3755: 3684: 3598: 3568: 3484: 3464: 3297: 3185:in December 2012. 3178: 3086:around the world. 3036: 2781:based on a single 2749:) rather than the 2351: 2239: 2212: 2153: 2113: 2003: 1935: 1903: 1855: 1828: 1818:is independent of 1808: 1779: 1746: 1719: 1695: 1671: 1648: 1628: 1601: 1577: 1551: 1433: 1376: 1349: 1269:experimental error 1265:quantum-mechanical 1247:Doppler broadening 1149:general relativity 1145:special relativity 1124: 1082: 1029: 963:fiber-optic cables 923: 907:general relativity 903:special relativity 794:general relativity 663: 564: 403:magnetic resonance 387: 351:frequency clocks. 349:magnetic resonance 321: 247:. The timekeeping 233:satellite networks 185: 131: 70:Telecommunications 15058: 15057: 15034:Riveting machines 14732:Archimedes' screw 14602: 14601: 14412:Nuclear timescale 14094:Continuous signal 13833: 13832: 13799:Synchronous motor 13794:Utility frequency 13741: 13740: 13651: 13650: 13626:Circadian rhythms 13444:Tense–aspect–mood 13299:Temporal finitism 13176: 13175: 13152:Grandfather clock 12761:978-1-939133-01-4 12676:. 25 October 2021 12588:(7897): 420–424. 12477:. 21 January 2022 12451:. 1 February 2022 12006:on 26 August 2019 11864:on 9 January 2017 11487:978-3-527-40780-4 11400:(12): 1828–1836. 11115:(8009): 736–740. 10952:10.1038/nphys2834 10769:(7897): 425–430. 10515:(7838): 414–418. 9742:. 5 December 2012 9553:10.1364/OE.435105 9421:on 17 April 2007. 9344:978-1-6654-3194-1 9035:(24 March 2021). 8982:(7851): 564–569. 8731:has been measured 8245:(7773): 243–246. 8181:(7773): 238–242. 8117:(7701): 321–325. 7093:Physical Review A 6867:(12): 1828–1836. 6460:10.1109/58.710548 6194:10.1063/5.0061727 5864:978-92-822-2280-5 5631:on 7 January 2008 5520:. 18 October 2021 5452:(7897): 420–424. 5044:978-3-527-40780-4 4982:10.1063/1.2994867 4936:978-981-02-3250-4 4915:, 541–552 (1990)" 4704:(4476): 280–282. 4667:. pp. 4–17. 4182:Explanatory notes 4086:Financial systems 4080:quantum mechanics 4041:radio transmitter 3974:BeiDou-2/BeiDou-3 3818: 3753: 3713: 3566: 3563: 3462: 3442: 3210:Paris Observatory 3057:David J. Wineland 3049:Theodor W. Hänsch 2968:Boulder, Colorado 2890:ionization energy 2848:Although neutral 2651: 2650: 2394:(typical clocks) 2274:to accuracies of 2108: 2107: 2082: 2043: 2042: 1693: 1625: 1604:{\displaystyle N} 1546: 1545: 1539: 1527: 1524: 1301:grandfather clock 1263:In this way, the 1207:and almost every 1072:Rubidium standard 775:thermal radiation 735:Paris Observatory 449:Paris Observatory 356:electromechanical 345:Isidor Isaac Rabi 340:for timekeeping. 338:mean solar second 241:Galileo Programme 182: 111: 110: 15098: 14737:Eductor-jet pump 14629: 14622: 14615: 14606: 14605: 14303:Dominical letter 14234:Equation of time 14197:Marine sandglass 14038: 14032: 14010:Terrestrial Time 13867:Time measurement 13860: 13853: 13846: 13837: 13836: 13768: 13761: 13754: 13745: 13744: 13731: 13730: 13721: 13720: 13638:Glottochronology 13478: 13477: 13394:Human experience 13254:B-theory of time 12852: 12851: 12796: 12789: 12782: 12773: 12772: 12766: 12765: 12745: 12739: 12738: 12736: 12734: 12720: 12714: 12713: 12711: 12709: 12697:(18 June 2020). 12692: 12686: 12685: 12683: 12681: 12666: 12660: 12659: 12657: 12655: 12638: 12632: 12631: 12597: 12576: 12570: 12569: 12567: 12565: 12542: 12536: 12535: 12533: 12531: 12516: 12510: 12496: 12487: 12486: 12484: 12482: 12467: 12461: 12460: 12458: 12456: 12449:The Defense Post 12441: 12435: 12434: 12432: 12430: 12415: 12409: 12408: 12406: 12404: 12393: 12387: 12386: 12384: 12382: 12367: 12361: 12360: 12358: 12356: 12334: 12328: 12327: 12325: 12323: 12304: 12298: 12297: 12295: 12293: 12273: 12267: 12266: 12264: 12262: 12247: 12241: 12240: 12238: 12236: 12221: 12215: 12214: 12212: 12210: 12204: 12197: 12189: 12183: 12178: 12172: 12171: 12169: 12167: 12144: 12138: 12137: 12135: 12133: 12128:on 28 March 2018 12124:. Archived from 12114: 12108: 12107: 12105: 12103: 12097: 12090: 12082: 12076: 12075: 12073: 12071: 12052: 12046: 12045: 12043: 12041: 12022: 12016: 12015: 12013: 12011: 12002:. Archived from 11996: 11990: 11989: 11987: 11985: 11979: 11972: 11964: 11958: 11957: 11955: 11953: 11938: 11932: 11931: 11929: 11927: 11912: 11906: 11905: 11903: 11901: 11895: 11888: 11880: 11874: 11873: 11871: 11869: 11863: 11857:. Archived from 11856: 11848: 11842: 11841: 11839: 11837: 11822: 11813: 11812: 11810: 11808: 11793: 11787: 11786: 11784: 11782: 11776: 11769: 11761: 11755: 11754: 11752: 11750: 11731: 11725: 11724: 11722: 11720: 11705: 11699: 11698: 11696: 11694: 11679: 11673: 11671: 11669: 11667: 11661: 11654: 11646: 11640: 11639: 11637: 11635: 11616: 11610: 11609: 11607: 11605: 11590: 11584: 11583: 11581: 11579: 11573: 11562: 11553: 11547: 11546: 11544: 11536:Application Note 11533: 11524: 11518: 11517: 11515: 11513: 11498: 11492: 11491: 11470: 11464: 11463: 11461: 11459: 11442: 11436: 11435: 11425: 11385: 11379: 11378: 11371: 11365: 11364: 11320: 11311: 11310: 11266: 11260: 11259: 11225: 11205: 11203: 11193: 11187: 11186: 11184: 11182: 11167: 11161: 11160: 11150: 11124: 11099: 11093: 11092: 11090: 11088: 11077: 11071: 11070: 11044: 11024: 11018: 11017: 10991: 10970: 10964: 10963: 10924: 10918: 10917: 10915: 10913: 10898: 10892: 10891: 10865: 10845: 10839: 10838: 10836: 10834: 10819: 10813: 10812: 10778: 10754: 10748: 10747: 10721: 10697: 10691: 10690: 10656: 10636: 10628: 10622: 10621: 10587: 10577: 10571: 10570: 10568: 10566: 10524: 10499: 10493: 10492: 10490: 10488: 10468: 10462: 10461: 10459: 10457: 10451: 10412: 10392: 10383: 10377: 10376: 10374: 10372: 10352: 10346: 10345: 10343: 10341: 10326: 10320: 10319: 10317: 10315: 10293: 10287: 10286: 10284: 10282: 10276: 10270:. Archived from 10237: 10217: 10208: 10202: 10201: 10167: 10149: 10147: 10139: 10133: 10132: 10130: 10128: 10108: 10102: 10101: 10099: 10097: 10077: 10071: 10070: 10068: 10066: 10057:. Archived from 10050: 10044: 10043: 10033: 10007: 9987: 9985: 9975: 9969: 9968: 9966: 9964: 9958: 9919: 9901: 9892: 9886: 9885: 9883: 9881: 9866: 9860: 9859: 9857: 9855: 9836: 9830: 9829: 9827: 9825: 9789: 9783: 9782: 9780: 9778: 9758: 9752: 9751: 9749: 9747: 9732: 9726: 9725: 9723: 9721: 9706: 9700: 9699: 9697: 9695: 9672: 9666: 9665: 9663: 9661: 9646: 9640: 9639: 9637: 9635: 9620: 9614: 9613: 9611: 9609: 9603: 9596: 9588: 9582: 9581: 9555: 9523: 9517: 9516: 9514: 9502: 9496: 9495: 9493: 9491: 9469: 9460: 9459: 9457: 9455: 9449: 9443:. Archived from 9438: 9429: 9423: 9422: 9420: 9414:. Archived from 9379: 9370: 9357: 9356: 9318: 9312: 9311: 9277: 9253: 9244: 9243: 9241: 9239: 9224: 9218: 9217: 9169: 9163: 9162: 9160: 9158: 9143: 9137: 9136: 9134: 9132: 9117: 9111: 9110: 9108: 9106: 9089: 9083: 9082: 9080: 9078: 9058: 9052: 9051: 9049: 9047: 9030: 9024: 9023: 8966: 8960: 8959: 8957: 8955: 8940: 8934: 8933: 8923: 8897: 8873: 8867: 8866: 8856: 8824: 8818: 8817: 8807: 8775: 8769: 8768: 8766: 8764: 8758: 8751: 8740: 8734: 8733: 8730: 8728: 8688: 8666: 8660: 8659: 8642: 8636: 8635: 8632: 8631: 8629: 8626: 8623: 8620: 8586: 8584: 8583: 8580: 8577: 8562: 8555: 8538: 8512: 8506: 8505: 8498: 8492: 8486: 8474: 8464: 8461: 8455: 8445: 8429: 8406: 8400: 8399: 8396: 8392: 8388: 8387:.409(7) THz 8386: 8380: 8336: 8327: 8318: 8317: 8308:. Vol. 17. 8295: 8289: 8288: 8254: 8231: 8225: 8224: 8190: 8167: 8161: 8160: 8126: 8105: 8099: 8098: 8064: 8041: 8035: 8034: 8000: 7980: 7971: 7970: 7968: 7966: 7960: 7954:. Archived from 7921: 7912: 7906: 7905: 7895: 7847: 7841: 7840: 7838: 7823:Applied Sciences 7820: 7811: 7805: 7804: 7802: 7778: 7772: 7771: 7769: 7767: 7751: 7745: 7744: 7710: 7690: 7684: 7683: 7681: 7679: 7673: 7634: 7616: 7607: 7601: 7588: 7582: 7581: 7579: 7577: 7557: 7551: 7550: 7548: 7546: 7531: 7525: 7524: 7522: 7520: 7505: 7499: 7498: 7496: 7494: 7479: 7473: 7472: 7470: 7468: 7463:. September 2001 7453: 7447: 7446: 7420: 7396: 7390: 7389: 7387: 7385: 7370: 7364: 7363: 7329: 7305: 7299: 7298: 7296: 7294: 7279: 7273: 7272: 7238: 7214: 7208: 7207: 7205: 7203: 7188: 7182: 7181: 7179: 7177: 7171: 7164: 7156: 7150: 7149: 7147: 7145: 7139: 7108: 7106:quant-ph/0308136 7090: 7081: 7075: 7074: 7035: 7029: 7028: 7026: 7024: 7018: 7011: 7003: 6997: 6996: 6994: 6992: 6969: 6963: 6962: 6960: 6940: 6934: 6933: 6931: 6929: 6923: 6912: 6903: 6897: 6896: 6886: 6876: 6852: 6846: 6845: 6843: 6830: 6824: 6823: 6821: 6819: 6799: 6793: 6792: 6790: 6788: 6769: 6763: 6762: 6760: 6758: 6746:(9 April 2019). 6741: 6735: 6734: 6732: 6730: 6707: 6701: 6700: 6698: 6696: 6681: 6675: 6674: 6672: 6670: 6656: 6650: 6649: 6647: 6645: 6630: 6624: 6623: 6621: 6619: 6612:Revolutionalized 6604: 6598: 6597: 6589: 6580: 6579: 6553: 6527: 6521: 6520: 6503:(2): S150–S154. 6486: 6480: 6479: 6441: 6435: 6426: 6420: 6419: 6417: 6406: 6400: 6391: 6385: 6384: 6358: 6338: 6332: 6331: 6305: 6283: 6274: 6273: 6247: 6229: 6220: 6214: 6213: 6169: 6163: 6162: 6152: 6143: 6137: 6136: 6135: 6133: 6127: 6111:(8th ed.), 6110: 6096: 6090: 6089: 6081: 6075: 6074: 6072: 6070: 6065: 6057: 6051: 6050: 6048: 6046: 6031: 6025: 6024: 6022: 6020: 6005: 5999: 5998: 5996: 5994: 5985:. 3 April 2014. 5975: 5969: 5968: 5966: 5964: 5958:www.grc.nasa.gov 5950: 5944: 5943: 5941: 5939: 5924: 5918: 5917: 5915: 5913: 5898: 5892: 5891: 5889: 5887: 5881: 5856: 5846: 5840: 5839: 5838: 5836: 5830: 5824:, 12 July 2021, 5819: 5809: 5803: 5802: 5796: 5788: 5777: 5776: 5774: 5772: 5758: 5752: 5751: 5749: 5747: 5730: 5724: 5723: 5721: 5719: 5702: 5696: 5695: 5693: 5691: 5674: 5668: 5667: 5659: 5653: 5640: 5638: 5636: 5617: 5608: 5607: 5605: 5603: 5597: 5590: 5582: 5571: 5570: 5560: 5536: 5530: 5529: 5527: 5525: 5510: 5504: 5503: 5461: 5437: 5431: 5430: 5396: 5376: 5368: 5362: 5361: 5359: 5357: 5345:(15 July 2019). 5340: 5334: 5333: 5323: 5289: 5269: 5267: 5257: 5251: 5250: 5248: 5246: 5231: 5225: 5224: 5222: 5220: 5205: 5199: 5198: 5196: 5194: 5188: 5166:(4): 1041–1058. 5155: 5146: 5140: 5139: 5105: 5081: 5075: 5074: 5072: 5070: 5055: 5049: 5048: 5027: 5021: 5020: 5018: 5016: 5007:. Archived from 5000: 4994: 4993: 4953: 4947: 4946: 4945: 4943: 4900: 4894: 4893: 4883: 4843: 4837: 4836: 4834: 4832: 4821:ESO Announcement 4813: 4807: 4805: 4794:10.1038/176280a0 4766: 4760: 4759: 4757: 4755: 4736: 4730: 4729: 4718:10.1038/176280a0 4690: 4684: 4683: 4681: 4679: 4673: 4658: 4649: 4643: 4642: 4640: 4638: 4632: 4615: 4606: 4591: 4590: 4580: 4548: 4542: 4541: 4501: 4495: 4494: 4492: 4490: 4475: 4469: 4468: 4467: 4465: 4432: 4421: 4420: 4380: 4374: 4373: 4367: 4359: 4356: 4352: 4350: 4344: 4342: 4316: 4307: 4298: 4297: 4286: 4280: 4279: 4277: 4275: 4259: 4253: 4252: 4250: 4248: 4233: 4216: 4214: 4212: 4205: 4199: 4192: 4125:Caesium standard 4118: 4113: 4112: 4077: 4075: 4012: 3837: 3829: 3827: 3826: 3821: 3819: 3817: 3816: 3807: 3800: 3799: 3789: 3781: 3780: 3764: 3762: 3761: 3756: 3754: 3752: 3744: 3743: 3742: 3730: 3729: 3719: 3714: 3712: 3708: 3707: 3697: 3692: 3679: 3678: 3677: 3668: 3667: 3657: 3652: 3651: 3634:Rydberg constant 3628:Rydberg constant 3623: 3619: 3611: 3607: 3605: 3604: 3599: 3584: 3577: 3575: 3574: 3569: 3567: 3565: 3564: 3559: 3558: 3540: 3525: 3493: 3491: 3490: 3485: 3473: 3471: 3470: 3465: 3463: 3461: 3457: 3445: 3443: 3438: 3430: 3411: 3409: 3350: 3348: 3338: 3336: 3323: 3321: 3315: 3313: 3307: 3305: 3274: 3272: 3258: 3254: 3251:atoms cooled to 3250: 3249:10 000 ytterbium 3246: 3242: 3240: 3226: 3224: 3207: 3205: 3195: 3193: 3091:femtosecond comb 3071:optical lattices 3017: 3015: 2998: 2996: 2982: 2980: 2953: 2935:Mössbauer effect 2913: 2909: 2908: 2907: 2900: 2899: 2887: 2886: 2885: 2878: 2877: 2865: 2864: 2863: 2856: 2855: 2844: 2842: 2838: 2835: 2832: 2826: 2824: 2821: 2818: 2815: 2812: 2806: 2804: 2798: 2797: 2796: 2789: 2788: 2772: 2770: 2769: 2762: 2761: 2711: 2709: 2700: 2698: 2645: 2640: 2638: 2635: 2632: 2629: 2626: 2608: 2603: 2601: 2598: 2595: 2592: 2589: 2571: 2566: 2564: 2561: 2558: 2555: 2552: 2549: 2531: 2526: 2524: 2521: 2518: 2515: 2512: 2494: 2489: 2487: 2484: 2481: 2478: 2462: 2457: 2455: 2452: 2449: 2446: 2443: 2427: 2419: 2417: 2414: 2411: 2376: 2375: 2371:available online 2345:An experimental 2331:published online 2312:caesium fountain 2305: 2281: 2277: 2273: 2261:Jerrod Zacharias 2257:caesium fountain 2254: 2250: 2221: 2219: 2218: 2213: 2202: 2201: 2200: 2199: 2162: 2160: 2159: 2154: 2152: 2147: 2142: 2141: 2122: 2120: 2119: 2114: 2109: 2103: 2102: 2093: 2092: 2087: 2083: 2081: 2073: 2053: 2044: 2023: 2021: 2020: 2011: 2002: 1988: 1987: 1986: 1985: 1944: 1942: 1941: 1936: 1912: 1910: 1909: 1904: 1902: 1901: 1892: 1887: 1886: 1864: 1862: 1861: 1856: 1854: 1853: 1837: 1835: 1834: 1829: 1817: 1815: 1814: 1809: 1797: 1796: 1787: 1766:local oscillator 1755: 1753: 1752: 1747: 1745: 1744: 1728: 1726: 1725: 1720: 1704: 1702: 1701: 1696: 1694: 1689: 1680: 1678: 1677: 1672: 1657: 1655: 1654: 1649: 1637: 1635: 1634: 1629: 1627: 1626: 1623: 1610: 1608: 1607: 1602: 1586: 1584: 1583: 1578: 1560: 1558: 1557: 1552: 1547: 1541: 1540: 1537: 1531: 1530: 1528: 1526: 1525: 1520: 1518: 1517: 1507: 1499: 1485: 1484: 1483: 1482: 1442: 1440: 1439: 1434: 1423: 1422: 1391: 1385: 1383: 1382: 1377: 1358: 1356: 1355: 1350: 1348: 1347: 1331: 1281:local oscillator 1225:microwave cavity 1187: 1185: 1182: 1179: 1122:A hydrogen maser 1095: 1093: 1054: 1052: 980:Caesium standard 936: 850: 846: 838: 834: 826: 822: 818: 784: 679: 648: 646: 640: 638: 632: 628: 626: 617: 615: 609: 598:. Scientists at 581: 540:Rydberg constant 509: 507: 504: 498: 497: 494: 491: 334:Earth's rotation 299: 276:atoms cooled to 268: 267: 263: 226:Earth's rotation 207: 206: 203: 200: 194: 192: 191: 186: 184: 183: 180: 123:Washington, D.C. 48: 36: 35: 15106: 15105: 15101: 15100: 15099: 15097: 15096: 15095: 15061: 15060: 15059: 15054: 15050:Spring (device) 15038: 15019:Vending machine 14987: 14969: 14926: 14888: 14840: 14817: 14784: 14780:Stirling engine 14761: 14714: 14681: 14638: 14633: 14603: 14598: 14535: 14426: 14393: 14367: 14248: 14148: 14099:Coordinate time 14071:Time in physics 14065: 14039: 14033: 14024: 13896: 13873: 13864: 13834: 13829: 13803: 13777: 13772: 13742: 13737: 13709: 13700:Time immemorial 13647: 13604: 13565:Coordinate time 13536: 13490:Geological time 13466: 13449:Time management 13412:Generation time 13396: 13388: 13333: 13315: 13235: 13194: 13172: 13060: 12978: 12895: 12888: 12844: 12836: 12805: 12800: 12770: 12769: 12762: 12746: 12742: 12732: 12730: 12728:www.chainzy.com 12722: 12721: 12717: 12707: 12705: 12693: 12689: 12679: 12677: 12674:Quanta Magazine 12668: 12667: 12663: 12653: 12651: 12639: 12635: 12577: 12573: 12563: 12561: 12543: 12539: 12529: 12527: 12517: 12513: 12507:Wayback Machine 12497: 12490: 12480: 12478: 12469: 12468: 12464: 12454: 12452: 12443: 12442: 12438: 12428: 12426: 12416: 12412: 12402: 12400: 12395: 12394: 12390: 12380: 12378: 12368: 12364: 12354: 12352: 12335: 12331: 12321: 12319: 12306: 12305: 12301: 12291: 12289: 12274: 12270: 12260: 12258: 12249: 12248: 12244: 12234: 12232: 12223: 12222: 12218: 12208: 12206: 12202: 12195: 12191: 12190: 12186: 12179: 12175: 12165: 12163: 12145: 12141: 12131: 12129: 12116: 12115: 12111: 12101: 12099: 12095: 12088: 12084: 12083: 12079: 12069: 12067: 12054: 12053: 12049: 12039: 12037: 12024: 12023: 12019: 12009: 12007: 11998: 11997: 11993: 11983: 11981: 11977: 11970: 11966: 11965: 11961: 11951: 11949: 11940: 11939: 11935: 11925: 11923: 11914: 11913: 11909: 11899: 11897: 11893: 11886: 11882: 11881: 11877: 11867: 11865: 11861: 11854: 11850: 11849: 11845: 11835: 11833: 11824: 11823: 11816: 11806: 11804: 11795: 11794: 11790: 11780: 11778: 11774: 11767: 11763: 11762: 11758: 11748: 11746: 11733: 11732: 11728: 11718: 11716: 11715:on 8 April 2013 11707: 11706: 11702: 11692: 11690: 11681: 11680: 11676: 11665: 11663: 11659: 11652: 11648: 11647: 11643: 11633: 11631: 11618: 11617: 11613: 11603: 11601: 11592: 11591: 11587: 11577: 11575: 11571: 11560: 11554: 11550: 11542: 11531: 11525: 11521: 11511: 11509: 11508:on 30 July 2010 11500: 11499: 11495: 11488: 11474:McCarthy, D. D. 11471: 11467: 11457: 11455: 11443: 11439: 11386: 11382: 11373: 11372: 11368: 11321: 11314: 11267: 11263: 11201: 11199: 11194: 11190: 11180: 11178: 11169: 11168: 11164: 11100: 11096: 11086: 11084: 11079: 11078: 11074: 11025: 11021: 10971: 10967: 10928:Margolis, Helen 10925: 10921: 10911: 10909: 10900: 10899: 10895: 10856:(12): 555–624. 10846: 10842: 10832: 10830: 10821: 10820: 10816: 10755: 10751: 10712:(7734): 87–90. 10698: 10694: 10634: 10629: 10625: 10585: 10578: 10574: 10564: 10562: 10500: 10496: 10486: 10484: 10469: 10465: 10455: 10453: 10449: 10390: 10384: 10380: 10370: 10368: 10353: 10349: 10339: 10337: 10328: 10327: 10323: 10313: 10311: 10294: 10290: 10280: 10278: 10274: 10228:(6359): 90–94. 10215: 10209: 10205: 10145: 10143: 10140: 10136: 10126: 10124: 10109: 10105: 10095: 10093: 10078: 10074: 10064: 10062: 10051: 10047: 9983: 9981: 9976: 9972: 9962: 9960: 9956: 9899: 9893: 9889: 9879: 9877: 9868: 9867: 9863: 9853: 9851: 9838: 9837: 9833: 9823: 9821: 9790: 9786: 9776: 9774: 9759: 9755: 9745: 9743: 9734: 9733: 9729: 9719: 9717: 9708: 9707: 9703: 9693: 9691: 9675:Norton, Quinn. 9673: 9669: 9659: 9657: 9648: 9647: 9643: 9633: 9631: 9622: 9621: 9617: 9607: 9605: 9601: 9594: 9590: 9589: 9585: 9524: 9520: 9503: 9499: 9489: 9487: 9471: 9470: 9463: 9453: 9451: 9450:on 23 June 2015 9447: 9436: 9430: 9426: 9418: 9377: 9371: 9360: 9345: 9319: 9315: 9254: 9247: 9237: 9235: 9226: 9225: 9221: 9170: 9166: 9156: 9154: 9145: 9144: 9140: 9130: 9128: 9119: 9118: 9114: 9104: 9102: 9090: 9086: 9076: 9074: 9059: 9055: 9045: 9043: 9031: 9027: 8967: 8963: 8953: 8951: 8942: 8941: 8937: 8874: 8870: 8854:10.1038/522016a 8839:(7554): 16–17. 8825: 8821: 8805:10.1038/522016a 8790:(7554): 16–17. 8776: 8772: 8762: 8760: 8756: 8749: 8741: 8737: 8726: 8724: 8723:A half-life of 8667: 8663: 8643: 8639: 8627: 8624: 8621: 8618: 8616: 8614: 8607: 8600: 8593: 8581: 8578: 8575: 8574: 8572: 8570: 8564: 8557: 8550: 8529:(8028): 63–70. 8513: 8509: 8502: 8496: 8490: 8488: 8484: 8480: 8476: 8472: 8468: 8462: 8459: 8457: 8453: 8449: 8443: 8441: 8407: 8403: 8395:1740(50) s 8394: 8390: 8384: 8382: 8378: 8376: 8334: 8328: 8321: 8296: 8292: 8232: 8228: 8168: 8164: 8106: 8102: 8055:(7601): 47–51. 8042: 8038: 7985:Phys. Rev. Lett 7981: 7974: 7964: 7962: 7958: 7919: 7913: 7909: 7848: 7844: 7818: 7812: 7808: 7779: 7775: 7765: 7763: 7752: 7748: 7691: 7687: 7677: 7675: 7671: 7614: 7608: 7604: 7598:Wayback Machine 7589: 7585: 7575: 7573: 7558: 7554: 7544: 7542: 7532: 7528: 7518: 7516: 7507: 7506: 7502: 7492: 7490: 7480: 7476: 7466: 7464: 7455: 7454: 7450: 7397: 7393: 7383: 7381: 7372: 7371: 7367: 7306: 7302: 7292: 7290: 7281: 7280: 7276: 7215: 7211: 7201: 7199: 7190: 7189: 7185: 7175: 7173: 7169: 7162: 7158: 7157: 7153: 7143: 7141: 7137: 7088: 7082: 7078: 7036: 7032: 7022: 7020: 7016: 7009: 7005: 7004: 7000: 6990: 6988: 6971: 6970: 6966: 6941: 6937: 6927: 6925: 6921: 6910: 6904: 6900: 6853: 6849: 6831: 6827: 6817: 6815: 6800: 6796: 6786: 6784: 6771: 6770: 6766: 6756: 6754: 6742: 6738: 6728: 6726: 6708: 6704: 6694: 6692: 6683: 6682: 6678: 6668: 6666: 6658: 6657: 6653: 6643: 6641: 6631: 6627: 6617: 6615: 6606: 6605: 6601: 6590: 6583: 6528: 6524: 6487: 6483: 6442: 6438: 6427: 6423: 6415: 6407: 6403: 6392: 6388: 6339: 6335: 6284: 6277: 6238:(12): 555–624. 6227: 6221: 6217: 6170: 6166: 6150: 6144: 6140: 6131: 6129: 6125: 6119: 6108: 6097: 6093: 6082: 6078: 6068: 6066: 6063: 6059: 6058: 6054: 6044: 6042: 6032: 6028: 6018: 6016: 6006: 6002: 5992: 5990: 5977: 5976: 5972: 5962: 5960: 5952: 5951: 5947: 5937: 5935: 5925: 5921: 5911: 5909: 5899: 5895: 5885: 5883: 5879: 5865: 5854: 5848: 5847: 5843: 5834: 5832: 5828: 5817: 5811: 5810: 5806: 5794: 5790: 5789: 5780: 5770: 5768: 5760: 5759: 5755: 5745: 5743: 5731: 5727: 5717: 5715: 5703: 5699: 5689: 5687: 5675: 5671: 5660: 5656: 5651:Wayback Machine 5634: 5632: 5619: 5618: 5611: 5601: 5599: 5595: 5588: 5584: 5583: 5574: 5537: 5533: 5523: 5521: 5512: 5511: 5507: 5438: 5434: 5374: 5369: 5365: 5355: 5353: 5341: 5337: 5265: 5263: 5258: 5254: 5244: 5242: 5232: 5228: 5218: 5216: 5206: 5202: 5192: 5190: 5186: 5153: 5147: 5143: 5082: 5078: 5068: 5066: 5056: 5052: 5045: 5031:McCarthy, D. D. 5028: 5024: 5014: 5012: 5001: 4997: 4954: 4950: 4941: 4939: 4937: 4910:Rev. Mod. Phys. 4902: 4901: 4897: 4844: 4840: 4830: 4828: 4815: 4814: 4810: 4767: 4763: 4753: 4751: 4738: 4737: 4733: 4691: 4687: 4677: 4675: 4671: 4656: 4650: 4646: 4636: 4634: 4630: 4613: 4607: 4594: 4557:Physical Review 4549: 4545: 4510:Physical Review 4502: 4498: 4488: 4486: 4477: 4476: 4472: 4463: 4461: 4459: 4433: 4424: 4381: 4377: 4361: 4360: 4354: 4348: 4346: 4340: 4338: 4314: 4308: 4301: 4288: 4287: 4283: 4273: 4271: 4260: 4256: 4246: 4244: 4235: 4234: 4230: 4225: 4220: 4219: 4210: 4208: 4206: 4202: 4193: 4189: 4184: 4179: 4114: 4107: 4104: 4088: 4073: 4071: 4049: 4025: 4019: 4010: 4003: 3991: 3896: 3888:radio astronomy 3867: 3855: 3835: 3812: 3808: 3795: 3791: 3790: 3788: 3776: 3772: 3770: 3767: 3766: 3745: 3738: 3734: 3725: 3721: 3720: 3718: 3703: 3699: 3693: 3688: 3680: 3673: 3669: 3663: 3659: 3658: 3656: 3647: 3643: 3641: 3638: 3637: 3630: 3621: 3617: 3614:optical lattice 3609: 3590: 3587: 3586: 3582: 3548: 3544: 3539: 3529: 3524: 3507: 3504: 3503: 3479: 3476: 3475: 3453: 3449: 3444: 3431: 3429: 3421: 3418: 3417: 3407: 3405: 3397: 3388: 3376:Exercise RIMPAC 3346: 3344: 3334: 3332: 3319: 3317: 3311: 3309: 3303: 3301: 3270: 3268: 3256: 3252: 3248: 3244: 3238: 3236: 3222: 3220: 3203: 3201: 3191: 3189: 3067:frequency combs 3024: 3013: 3011: 2994: 2992: 2978: 2976: 2951: 2944: 2911: 2906: 2904: 2903: 2902: 2898: 2896: 2895: 2894: 2893: 2884: 2882: 2881: 2880: 2876: 2874: 2873: 2872: 2871: 2862: 2860: 2859: 2858: 2854: 2852: 2851: 2850: 2849: 2840: 2836: 2833: 2830: 2828: 2822: 2819: 2816: 2813: 2810: 2808: 2802: 2800: 2795: 2793: 2792: 2791: 2787: 2785: 2784: 2783: 2782: 2768: 2766: 2765: 2764: 2760: 2758: 2757: 2756: 2754: 2747:nuclear isomers 2739: 2733: 2707: 2705: 2696: 2694: 2666: 2660: 2643: 2636: 2633: 2630: 2627: 2624: 2622: 2615:Optical clock ( 2606: 2599: 2596: 2593: 2590: 2587: 2585: 2578:Optical clock ( 2569: 2562: 2559: 2556: 2553: 2550: 2547: 2545: 2538:Optical clock ( 2529: 2522: 2519: 2516: 2513: 2510: 2508: 2501:Optical clock ( 2492: 2485: 2482: 2479: 2476: 2474: 2460: 2453: 2450: 2447: 2444: 2441: 2439: 2425: 2415: 2412: 2409: 2407: 2393: 2391:Allan deviation 2367: 2339: 2320:liquid nitrogen 2303: 2296:optical lattice 2279: 2275: 2271: 2252: 2248: 2228: 2183: 2182: 2174: 2170: 2168: 2165: 2164: 2148: 2143: 2137: 2133: 2131: 2128: 2127: 2098: 2094: 2091: 2074: 2054: 2052: 2048: 2013: 2012: 2007: 2001: 1972: 1971: 1963: 1959: 1957: 1954: 1953: 1947:Allan deviation 1918: 1915: 1914: 1897: 1893: 1888: 1882: 1878: 1870: 1867: 1866: 1849: 1845: 1843: 1840: 1839: 1823: 1820: 1819: 1789: 1788: 1783: 1777: 1774: 1773: 1740: 1736: 1734: 1731: 1730: 1714: 1711: 1710: 1688: 1686: 1683: 1682: 1663: 1660: 1659: 1643: 1640: 1639: 1622: 1618: 1616: 1613: 1612: 1596: 1593: 1592: 1569: 1566: 1565: 1536: 1532: 1529: 1519: 1513: 1509: 1508: 1500: 1498: 1466: 1465: 1457: 1453: 1451: 1448: 1447: 1418: 1414: 1412: 1409: 1408: 1406:Allan deviation 1387: 1368: 1365: 1364: 1343: 1339: 1337: 1334: 1333: 1327: 1289: 1287:Clock mechanism 1221:radio frequency 1217: 1183: 1180: 1177: 1175: 1172: 1166: 1161: 1133:radio astronomy 1116: 1110: 1091: 1089: 1074: 1068: 1050: 1048: 1021: 982: 976: 971: 934: 915: 866: 848: 844: 836: 832: 831:is one part in 824: 820: 816: 782: 716: 711: 674: 655: 644: 642: 636: 634: 630: 624: 622: 613: 611: 607: 579: 548: 510:seconds in the 505: 502: 500: 495: 492: 489: 487: 484: 476:Hewlett-Packard 461:Hewlett–Packard 399:optical pumping 319:in west London. 306: 297: 265: 261: 260: 204: 201: 198: 196: 179: 175: 170: 167: 166: 51: 32: 17: 12: 11: 5: 15104: 15094: 15093: 15088: 15083: 15078: 15073: 15056: 15055: 15053: 15052: 15046: 15044: 15040: 15039: 15037: 15036: 15031: 15026: 15021: 15016: 15011: 15006: 15001: 14995: 14993: 14989: 14988: 14986: 14985: 14979: 14977: 14971: 14970: 14968: 14967: 14962: 14957: 14952: 14947: 14942: 14936: 14934: 14928: 14927: 14925: 14924: 14919: 14914: 14909: 14904: 14898: 14896: 14890: 14889: 14887: 14886: 14881: 14879:Wind generator 14876: 14871: 14866: 14861: 14856: 14850: 14848: 14842: 14841: 14839: 14838: 14833: 14827: 14825: 14819: 14818: 14816: 14815: 14810: 14805: 14800: 14794: 14792: 14786: 14785: 14783: 14782: 14777: 14771: 14769: 14763: 14762: 14760: 14759: 14754: 14749: 14744: 14739: 14734: 14728: 14726: 14716: 14715: 14713: 14712: 14707: 14705:Pendulum clock 14702: 14697: 14691: 14689: 14683: 14682: 14680: 14679: 14677:Wheel and axle 14674: 14669: 14664: 14659: 14654: 14652:Inclined plane 14648: 14646: 14640: 14639: 14632: 14631: 14624: 14617: 14609: 14600: 14599: 14597: 14596: 14591: 14586: 14584:Time metrology 14581: 14576: 14571: 14566: 14561: 14560: 14559: 14549: 14543: 14541: 14540:Related topics 14537: 14536: 14534: 14533: 14528: 14523: 14518: 14513: 14508: 14503: 14498: 14493: 14488: 14483: 14478: 14473: 14468: 14463: 14458: 14453: 14448: 14443: 14437: 14435: 14428: 14427: 14425: 14424: 14419: 14414: 14409: 14403: 14401: 14395: 14394: 14392: 14391: 14386: 14381: 14375: 14373: 14369: 14368: 14366: 14365: 14360: 14355: 14350: 14345: 14340: 14335: 14330: 14325: 14320: 14315: 14310: 14305: 14300: 14295: 14290: 14285: 14279: 14274: 14269: 14264: 14258: 14256: 14250: 14249: 14247: 14246: 14241: 14236: 14231: 14229:Dialing scales 14226: 14221: 14216: 14215: 14214: 14204: 14199: 14194: 14189: 14184: 14179: 14174: 14169: 14164: 14158: 14156: 14150: 14149: 14147: 14146: 14141: 14136: 14131: 14126: 14121: 14116: 14111: 14106: 14101: 14096: 14091: 14086: 14081: 14075: 14073: 14067: 14066: 14064: 14063: 14061:Prime meridian 14058: 14053: 14051:Ephemeris time 14047: 14045: 14041: 14040: 14027: 14025: 14023: 14022: 14020:180th meridian 14017: 14012: 14007: 14002: 13997: 13992: 13987: 13982: 13977: 13972: 13967: 13962: 13957: 13952: 13947: 13942: 13937: 13932: 13927: 13922: 13917: 13916: 13915: 13904: 13902: 13898: 13897: 13895: 13894: 13889: 13884: 13878: 13875: 13874: 13863: 13862: 13855: 13848: 13840: 13831: 13830: 13828: 13827: 13822: 13817: 13811: 13809: 13805: 13804: 13802: 13801: 13796: 13791: 13785: 13783: 13779: 13778: 13771: 13770: 13763: 13756: 13748: 13739: 13738: 13736: 13735: 13725: 13714: 13711: 13710: 13708: 13707: 13702: 13697: 13692: 13685: 13680: 13675: 13670: 13665: 13659: 13657: 13653: 13652: 13649: 13648: 13646: 13645: 13643:Time geography 13640: 13635: 13633:Clock reaction 13630: 13629: 13628: 13618: 13612: 13610: 13606: 13605: 13603: 13602: 13597: 13592: 13587: 13582: 13577: 13572: 13567: 13562: 13557: 13552: 13546: 13544: 13538: 13537: 13535: 13534: 13529: 13524: 13523: 13522: 13517: 13512: 13507: 13502: 13497: 13486: 13484: 13475: 13468: 13467: 13465: 13464: 13451: 13446: 13441: 13436: 13435: 13434: 13432:time signature 13429: 13419: 13414: 13409: 13403: 13401: 13390: 13389: 13387: 13386: 13385: 13384: 13374: 13373: 13372: 13362: 13357: 13352: 13347: 13342: 13336: 13334: 13332: 13331: 13326: 13320: 13317: 13316: 13314: 13313: 13306: 13304:Temporal parts 13301: 13296: 13291: 13286: 13281: 13276: 13274:Eternal return 13271: 13266: 13261: 13259:Chronocentrism 13256: 13251: 13245: 13243: 13237: 13236: 13234: 13233: 13228: 13223: 13218: 13213: 13208: 13203: 13197: 13195: 13193: 13192: 13187: 13181: 13178: 13177: 13174: 13173: 13171: 13170: 13169: 13168: 13154: 13149: 13144: 13139: 13138: 13137: 13132: 13131: 13130: 13125: 13115: 13110: 13105: 13100: 13099: 13098: 13088: 13087: 13086: 13070: 13068: 13062: 13061: 13059: 13058: 13051: 13046: 13044:Hindu Panchang 13041: 13036: 13031: 13026: 13021: 13016: 13011: 13010: 13009: 13004: 12999: 12988: 12986: 12980: 12979: 12977: 12976: 12971: 12966: 12961: 12956: 12951: 12946: 12941: 12936: 12931: 12926: 12921: 12916: 12911: 12906: 12900: 12898: 12890: 12889: 12887: 12886: 12881: 12876: 12871: 12866: 12860: 12858: 12849: 12838: 12837: 12835: 12834: 12829: 12824: 12819: 12813: 12811: 12807: 12806: 12799: 12798: 12791: 12784: 12776: 12768: 12767: 12760: 12740: 12715: 12687: 12661: 12633: 12571: 12545:Chen, Sophia. 12537: 12511: 12488: 12462: 12436: 12410: 12388: 12362: 12329: 12299: 12268: 12242: 12216: 12184: 12173: 12139: 12122:insidegnss.com 12109: 12077: 12047: 12017: 11991: 11959: 11933: 11907: 11875: 11843: 11814: 11788: 11756: 11726: 11700: 11689:on 28 May 2017 11674: 11641: 11611: 11585: 11548: 11519: 11493: 11486: 11465: 11437: 11380: 11366: 11312: 11261: 11188: 11162: 11094: 11072: 11019: 10982:(6): 563–569. 10965: 10932:Nature Physics 10919: 10893: 10840: 10814: 10749: 10692: 10623: 10572: 10494: 10463: 10403:(10): 103201. 10378: 10347: 10321: 10288: 10203: 10134: 10103: 10072: 10045: 9998:(6896): 6896. 9970: 9910:(7486): 71–5. 9887: 9861: 9831: 9784: 9753: 9727: 9701: 9667: 9641: 9615: 9583: 9532:Optics Express 9518: 9497: 9461: 9432:Fritz Riehle. 9424: 9358: 9343: 9313: 9245: 9219: 9164: 9138: 9127:. 3 March 2017 9112: 9084: 9053: 9025: 8961: 8935: 8868: 8819: 8770: 8735: 8661: 8646:Conover, Emily 8637: 8612: 8605: 8598: 8591: 8568: 8507: 8500: 8494: 8482: 8478: 8470: 8466: 8451: 8447: 8401: 8391:630(15) s 8374: 8319: 8290: 8226: 8162: 8100: 8036: 7972: 7930:(2): 181–186. 7907: 7842: 7806: 7773: 7746: 7685: 7602: 7583: 7552: 7526: 7500: 7482:Ahmed, Issam. 7474: 7448: 7411:(7): 981–985. 7391: 7365: 7300: 7274: 7209: 7183: 7151: 7076: 7049:(3): 128–137. 7030: 6998: 6964: 6935: 6898: 6847: 6825: 6794: 6764: 6736: 6702: 6676: 6651: 6625: 6614:. 20 July 2021 6599: 6581: 6544:(3): 623–628. 6522: 6481: 6454:(4): 887–894. 6436: 6421: 6401: 6386: 6333: 6296:(2): 637–701. 6275: 6215: 6164: 6138: 6117: 6091: 6076: 6052: 6026: 6000: 5970: 5945: 5919: 5893: 5863: 5841: 5804: 5778: 5753: 5725: 5697: 5669: 5654: 5609: 5598:on 25 May 2013 5572: 5531: 5505: 5432: 5363: 5335: 5252: 5226: 5200: 5141: 5076: 5050: 5043: 5022: 4995: 4948: 4935: 4906:Les Prix Nobel 4895: 4858:(5): 301–320. 4838: 4808: 4761: 4731: 4685: 4644: 4592: 4543: 4516:(8): 652–654. 4496: 4485:. 14 June 2022 4470: 4457: 4422: 4375: 4327:(3): 174–182. 4299: 4281: 4254: 4227: 4226: 4224: 4221: 4218: 4217: 4200: 4186: 4185: 4183: 4180: 4178: 4177: 4172: 4167: 4165:Time metrology 4162: 4160:Speaking clock 4157: 4152: 4147: 4142: 4137: 4132: 4127: 4121: 4120: 4119: 4103: 4100: 4087: 4084: 4048: 4045: 4033:radio receiver 4021:Main article: 4018: 4015: 4002: 4001:Military usage 3999: 3990: 3987: 3895: 3892: 3884:interferometry 3866: 3863: 3854: 3851: 3815: 3811: 3806: 3803: 3798: 3794: 3787: 3784: 3779: 3775: 3751: 3748: 3741: 3737: 3733: 3728: 3724: 3717: 3711: 3706: 3702: 3696: 3691: 3687: 3683: 3676: 3672: 3666: 3662: 3655: 3650: 3646: 3629: 3626: 3597: 3594: 3562: 3557: 3554: 3551: 3547: 3543: 3538: 3535: 3532: 3528: 3523: 3520: 3517: 3514: 3511: 3483: 3460: 3456: 3452: 3448: 3441: 3437: 3434: 3428: 3425: 3396: 3393: 3387: 3384: 3253:10 microkelvin 3116: 3115: 3112: 3109: 3023: 3022:Optical clocks 3020: 2943: 2940: 2939: 2938: 2930: 2926: 2916:quality factor 2905: 2897: 2883: 2875: 2861: 2853: 2794: 2786: 2767: 2759: 2735:Main article: 2732: 2729: 2659: 2658:Quantum clocks 2656: 2649: 2648: 2646: 2641: 2620: 2612: 2611: 2609: 2604: 2583: 2575: 2574: 2572: 2567: 2543: 2535: 2534: 2532: 2527: 2506: 2498: 2497: 2495: 2490: 2472: 2466: 2465: 2463: 2458: 2437: 2431: 2430: 2428: 2423: 2405: 2399: 2398: 2395: 2387: 2380: 2366: 2363: 2338: 2335: 2227: 2224: 2211: 2208: 2205: 2198: 2195: 2192: 2189: 2186: 2180: 2177: 2173: 2151: 2146: 2140: 2136: 2124: 2123: 2112: 2106: 2101: 2097: 2090: 2086: 2080: 2077: 2072: 2069: 2066: 2063: 2060: 2057: 2051: 2047: 2041: 2038: 2035: 2032: 2029: 2026: 2019: 2016: 2010: 2006: 2000: 1997: 1994: 1991: 1984: 1981: 1978: 1975: 1969: 1966: 1962: 1934: 1931: 1928: 1925: 1922: 1900: 1896: 1891: 1885: 1881: 1877: 1874: 1852: 1848: 1827: 1807: 1804: 1801: 1795: 1792: 1786: 1782: 1743: 1739: 1718: 1692: 1670: 1667: 1647: 1621: 1600: 1576: 1573: 1562: 1561: 1550: 1544: 1535: 1523: 1516: 1512: 1506: 1503: 1497: 1494: 1491: 1488: 1481: 1478: 1475: 1472: 1469: 1463: 1460: 1456: 1432: 1429: 1426: 1421: 1417: 1375: 1372: 1346: 1342: 1288: 1285: 1229:hydrogen maser 1216: 1213: 1168:Main article: 1165: 1162: 1160: 1157: 1114:Hydrogen maser 1112:Main article: 1109: 1106: 1100:receiver (see 1070:Main article: 1067: 1064: 1053:.6317 MHz 1020: 1017: 978:Main article: 975: 972: 970: 967: 947:rotating geoid 914: 911: 865: 862: 771:Doppler shifts 715: 714:Time standards 712: 710: 707: 654: 651: 547: 544: 536:optical clocks 483: 480: 391:Alfred Kastler 305: 302: 280:that approach 253:speed of light 237:European Union 178: 174: 109: 108: 105: 101: 100: 95: 91: 90: 81: 77: 76: 67: 63: 62: 57: 56:Classification 53: 52: 49: 41: 40: 25:Doomsday Clock 15: 9: 6: 4: 3: 2: 15103: 15092: 15089: 15087: 15084: 15082: 15079: 15077: 15074: 15072: 15071:Atomic clocks 15069: 15068: 15066: 15051: 15048: 15047: 15045: 15041: 15035: 15032: 15030: 15027: 15025: 15022: 15020: 15017: 15015: 15012: 15010: 15007: 15005: 15002: 15000: 14997: 14996: 14994: 14992:Miscellaneous 14990: 14984: 14981: 14980: 14978: 14976: 14972: 14966: 14963: 14961: 14958: 14956: 14953: 14951: 14948: 14946: 14943: 14941: 14938: 14937: 14935: 14933: 14929: 14923: 14920: 14918: 14915: 14913: 14910: 14908: 14905: 14903: 14900: 14899: 14897: 14895: 14891: 14885: 14882: 14880: 14877: 14875: 14874:Water turbine 14872: 14870: 14869:Steam turbine 14867: 14865: 14862: 14860: 14857: 14855: 14852: 14851: 14849: 14847: 14843: 14837: 14834: 14832: 14829: 14828: 14826: 14824: 14820: 14814: 14811: 14809: 14808:Rotary engine 14806: 14804: 14801: 14799: 14796: 14795: 14793: 14791: 14787: 14781: 14778: 14776: 14773: 14772: 14770: 14768: 14764: 14758: 14755: 14753: 14750: 14748: 14745: 14743: 14742:Hydraulic ram 14740: 14738: 14735: 14733: 14730: 14729: 14727: 14725: 14721: 14717: 14711: 14708: 14706: 14703: 14701: 14698: 14696: 14693: 14692: 14690: 14688: 14684: 14678: 14675: 14673: 14670: 14668: 14665: 14663: 14660: 14658: 14655: 14653: 14650: 14649: 14647: 14645: 14641: 14637: 14630: 14625: 14623: 14618: 14616: 14611: 14610: 14607: 14595: 14592: 14590: 14587: 14585: 14582: 14580: 14577: 14575: 14572: 14570: 14567: 14565: 14562: 14558: 14555: 14554: 14553: 14550: 14548: 14545: 14544: 14542: 14538: 14532: 14529: 14527: 14524: 14522: 14519: 14517: 14514: 14512: 14509: 14507: 14504: 14502: 14499: 14497: 14494: 14492: 14489: 14487: 14484: 14482: 14479: 14477: 14474: 14472: 14469: 14467: 14464: 14462: 14459: 14457: 14454: 14452: 14449: 14447: 14444: 14442: 14439: 14438: 14436: 14434: 14433:units of time 14429: 14423: 14422:Sidereal time 14420: 14418: 14415: 14413: 14410: 14408: 14407:Galactic year 14405: 14404: 14402: 14400: 14396: 14390: 14387: 14385: 14382: 14380: 14377: 14376: 14374: 14370: 14364: 14363:Weekday names 14361: 14359: 14356: 14354: 14353:Tropical year 14351: 14349: 14346: 14344: 14341: 14339: 14336: 14334: 14331: 14329: 14326: 14324: 14321: 14319: 14318:Intercalation 14316: 14314: 14311: 14309: 14306: 14304: 14301: 14299: 14296: 14294: 14291: 14289: 14286: 14284:(lunar Hijri) 14283: 14280: 14278: 14275: 14273: 14270: 14268: 14265: 14263: 14260: 14259: 14257: 14255: 14251: 14245: 14242: 14240: 14237: 14235: 14232: 14230: 14227: 14225: 14222: 14220: 14217: 14213: 14210: 14209: 14208: 14205: 14203: 14200: 14198: 14195: 14193: 14190: 14188: 14185: 14183: 14180: 14178: 14175: 14173: 14170: 14168: 14165: 14163: 14160: 14159: 14157: 14155: 14151: 14145: 14142: 14140: 14137: 14135: 14132: 14130: 14127: 14125: 14124:Time dilation 14122: 14120: 14117: 14115: 14112: 14110: 14107: 14105: 14102: 14100: 14097: 14095: 14092: 14090: 14087: 14085: 14082: 14080: 14077: 14076: 14074: 14072: 14068: 14062: 14059: 14057: 14054: 14052: 14049: 14048: 14046: 14042: 14037: 14031: 14021: 14018: 14016: 14013: 14011: 14008: 14006: 14003: 14001: 13998: 13996: 13993: 13991: 13988: 13986: 13983: 13981: 13978: 13976: 13973: 13971: 13968: 13966: 13963: 13961: 13960:24-hour clock 13958: 13956: 13955:12-hour clock 13953: 13951: 13948: 13946: 13943: 13941: 13938: 13936: 13933: 13931: 13928: 13926: 13923: 13921: 13918: 13914: 13911: 13910: 13909: 13906: 13905: 13903: 13899: 13893: 13890: 13888: 13885: 13883: 13880: 13879: 13876: 13872: 13868: 13861: 13856: 13854: 13849: 13847: 13842: 13841: 13838: 13826: 13823: 13821: 13818: 13816: 13813: 13812: 13810: 13806: 13800: 13797: 13795: 13792: 13790: 13787: 13786: 13784: 13780: 13776: 13769: 13764: 13762: 13757: 13755: 13750: 13749: 13746: 13734: 13726: 13724: 13716: 13715: 13712: 13706: 13703: 13701: 13698: 13696: 13693: 13691: 13690: 13686: 13684: 13681: 13679: 13676: 13674: 13671: 13669: 13666: 13664: 13661: 13660: 13658: 13654: 13644: 13641: 13639: 13636: 13634: 13631: 13627: 13624: 13623: 13622: 13621:Chronobiology 13619: 13617: 13614: 13613: 13611: 13607: 13601: 13598: 13596: 13593: 13591: 13588: 13586: 13583: 13581: 13578: 13576: 13573: 13571: 13568: 13566: 13563: 13561: 13558: 13556: 13555:Arrow of time 13553: 13551: 13548: 13547: 13545: 13543: 13539: 13533: 13530: 13528: 13527:Geochronology 13525: 13521: 13518: 13516: 13513: 13511: 13508: 13506: 13503: 13501: 13498: 13496: 13493: 13492: 13491: 13488: 13487: 13485: 13483: 13479: 13476: 13474: 13469: 13463: 13459: 13455: 13452: 13450: 13447: 13445: 13442: 13440: 13437: 13433: 13430: 13428: 13425: 13424: 13423: 13420: 13418: 13415: 13413: 13410: 13408: 13405: 13404: 13402: 13400: 13395: 13391: 13383: 13380: 13379: 13378: 13377:Wheel of time 13375: 13371: 13368: 13367: 13366: 13363: 13361: 13358: 13356: 13353: 13351: 13348: 13346: 13343: 13341: 13338: 13337: 13335: 13330: 13327: 13325: 13322: 13321: 13318: 13312: 13311: 13307: 13305: 13302: 13300: 13297: 13295: 13292: 13290: 13287: 13285: 13282: 13280: 13277: 13275: 13272: 13270: 13267: 13265: 13262: 13260: 13257: 13255: 13252: 13250: 13247: 13246: 13244: 13242: 13238: 13232: 13229: 13227: 13224: 13222: 13221:Periodization 13219: 13217: 13214: 13212: 13209: 13207: 13204: 13202: 13199: 13198: 13196: 13191: 13188: 13186: 13183: 13182: 13179: 13167: 13166: 13162: 13161: 13160: 13159: 13155: 13153: 13150: 13148: 13147:Digital clock 13145: 13143: 13140: 13136: 13133: 13129: 13126: 13124: 13121: 13120: 13119: 13116: 13114: 13111: 13109: 13106: 13104: 13101: 13097: 13094: 13093: 13092: 13089: 13085: 13082: 13081: 13080: 13077: 13076: 13075: 13072: 13071: 13069: 13067: 13063: 13057: 13056: 13052: 13050: 13047: 13045: 13042: 13040: 13037: 13035: 13032: 13030: 13027: 13025: 13022: 13020: 13017: 13015: 13012: 13008: 13005: 13003: 13000: 12998: 12995: 12994: 12993: 12990: 12989: 12987: 12985: 12981: 12975: 12972: 12970: 12967: 12965: 12962: 12960: 12957: 12955: 12952: 12950: 12947: 12945: 12942: 12940: 12937: 12935: 12932: 12930: 12927: 12925: 12924:Relative hour 12922: 12920: 12919:24-hour clock 12917: 12915: 12914:12-hour clock 12912: 12910: 12907: 12905: 12902: 12901: 12899: 12897: 12891: 12885: 12882: 12880: 12877: 12875: 12872: 12870: 12867: 12865: 12862: 12861: 12859: 12857: 12853: 12850: 12848: 12843: 12839: 12833: 12830: 12828: 12825: 12823: 12820: 12818: 12815: 12814: 12812: 12808: 12804: 12797: 12792: 12790: 12785: 12783: 12778: 12777: 12774: 12763: 12757: 12753: 12752: 12744: 12729: 12725: 12719: 12704: 12700: 12696: 12691: 12675: 12671: 12665: 12650: 12646: 12642: 12637: 12629: 12625: 12621: 12617: 12613: 12609: 12605: 12601: 12596: 12591: 12587: 12583: 12575: 12560: 12556: 12552: 12548: 12541: 12526: 12522: 12515: 12508: 12504: 12501: 12495: 12493: 12476: 12472: 12466: 12450: 12446: 12440: 12425: 12421: 12414: 12398: 12392: 12377: 12373: 12366: 12350: 12346: 12345: 12340: 12333: 12317: 12313: 12309: 12303: 12287: 12283: 12279: 12272: 12256: 12252: 12246: 12230: 12226: 12220: 12201: 12194: 12188: 12182: 12177: 12162: 12158: 12154: 12150: 12143: 12127: 12123: 12119: 12113: 12094: 12087: 12081: 12065: 12061: 12057: 12051: 12035: 12031: 12027: 12021: 12005: 12001: 11995: 11976: 11969: 11963: 11947: 11943: 11937: 11921: 11917: 11911: 11892: 11885: 11879: 11860: 11853: 11847: 11831: 11827: 11821: 11819: 11802: 11798: 11792: 11773: 11766: 11760: 11744: 11740: 11739:navipedia.net 11736: 11730: 11714: 11710: 11704: 11688: 11684: 11678: 11672:Section 1.2.2 11658: 11651: 11645: 11629: 11625: 11621: 11615: 11599: 11595: 11589: 11570: 11566: 11559: 11552: 11541: 11537: 11530: 11523: 11507: 11503: 11497: 11489: 11483: 11479: 11475: 11469: 11454: 11450: 11446: 11441: 11433: 11429: 11424: 11419: 11415: 11411: 11407: 11403: 11399: 11395: 11391: 11384: 11376: 11370: 11362: 11358: 11354: 11350: 11346: 11342: 11338: 11334: 11330: 11326: 11319: 11317: 11308: 11304: 11300: 11296: 11292: 11288: 11284: 11280: 11276: 11272: 11265: 11257: 11253: 11249: 11245: 11241: 11237: 11233: 11229: 11224: 11219: 11216:(7): 073601. 11215: 11211: 11207: 11192: 11176: 11172: 11166: 11158: 11154: 11149: 11144: 11140: 11136: 11132: 11128: 11123: 11118: 11114: 11110: 11106: 11098: 11082: 11076: 11068: 11064: 11060: 11056: 11052: 11048: 11043: 11038: 11034: 11030: 11023: 11015: 11011: 11007: 11003: 10999: 10995: 10990: 10985: 10981: 10977: 10969: 10961: 10957: 10953: 10949: 10945: 10941: 10937: 10933: 10929: 10923: 10907: 10903: 10897: 10889: 10885: 10881: 10877: 10873: 10869: 10864: 10859: 10855: 10851: 10844: 10828: 10824: 10818: 10810: 10806: 10802: 10798: 10794: 10790: 10786: 10782: 10777: 10772: 10768: 10764: 10760: 10753: 10745: 10741: 10737: 10733: 10729: 10725: 10720: 10715: 10711: 10707: 10703: 10696: 10688: 10684: 10680: 10676: 10672: 10668: 10664: 10660: 10655: 10650: 10646: 10642: 10638: 10627: 10619: 10615: 10611: 10607: 10603: 10599: 10595: 10591: 10590:GPS Solutions 10584: 10576: 10560: 10556: 10552: 10548: 10544: 10540: 10536: 10532: 10528: 10523: 10518: 10514: 10510: 10506: 10498: 10482: 10478: 10474: 10467: 10448: 10444: 10440: 10436: 10432: 10428: 10424: 10420: 10416: 10411: 10406: 10402: 10398: 10397: 10389: 10382: 10366: 10362: 10358: 10351: 10335: 10331: 10325: 10309: 10305: 10304: 10299: 10292: 10273: 10269: 10265: 10261: 10257: 10253: 10249: 10245: 10241: 10236: 10231: 10227: 10223: 10222: 10214: 10207: 10199: 10195: 10191: 10187: 10183: 10179: 10175: 10171: 10166: 10161: 10157: 10153: 10138: 10122: 10118: 10114: 10107: 10091: 10087: 10083: 10076: 10060: 10056: 10049: 10041: 10037: 10032: 10027: 10023: 10019: 10015: 10011: 10006: 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8080: 8076: 8072: 8068: 8063: 8058: 8054: 8050: 8049: 8045:transition". 8040: 8032: 8028: 8024: 8020: 8016: 8012: 8008: 8004: 7999: 7994: 7991:(12) 120802. 7990: 7986: 7979: 7977: 7957: 7953: 7949: 7945: 7941: 7937: 7933: 7929: 7925: 7918: 7911: 7903: 7899: 7894: 7889: 7885: 7881: 7877: 7873: 7869: 7865: 7861: 7857: 7853: 7846: 7837: 7832: 7828: 7824: 7817: 7810: 7801: 7796: 7792: 7788: 7784: 7777: 7761: 7757: 7750: 7742: 7738: 7734: 7730: 7726: 7722: 7718: 7714: 7709: 7704: 7700: 7696: 7689: 7670: 7666: 7662: 7658: 7654: 7650: 7646: 7642: 7638: 7633: 7628: 7624: 7620: 7613: 7606: 7599: 7595: 7592: 7587: 7571: 7567: 7563: 7556: 7541: 7540:New Scientist 7537: 7530: 7514: 7510: 7504: 7489: 7485: 7478: 7462: 7458: 7452: 7444: 7440: 7436: 7432: 7428: 7424: 7419: 7414: 7410: 7406: 7402: 7395: 7379: 7375: 7369: 7361: 7357: 7353: 7349: 7345: 7341: 7337: 7333: 7328: 7323: 7319: 7315: 7311: 7304: 7288: 7284: 7278: 7270: 7266: 7262: 7258: 7254: 7250: 7246: 7242: 7237: 7232: 7228: 7224: 7220: 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6233: 6226: 6219: 6211: 6207: 6203: 6199: 6195: 6191: 6187: 6183: 6180:(12) 124705. 6179: 6175: 6168: 6160: 6156: 6149: 6142: 6124: 6120: 6118:92-822-2213-6 6114: 6107: 6106: 6101: 6095: 6087: 6080: 6062: 6056: 6041: 6040:TNW | Science 6037: 6030: 6015: 6011: 6004: 5988: 5984: 5980: 5974: 5959: 5955: 5949: 5934: 5930: 5923: 5908: 5904: 5897: 5878: 5874: 5870: 5866: 5860: 5853: 5852: 5845: 5827: 5823: 5816: 5815: 5808: 5800: 5793: 5787: 5785: 5783: 5767: 5763: 5757: 5742: 5738: 5734: 5729: 5714: 5710: 5706: 5701: 5686: 5682: 5678: 5673: 5665: 5658: 5652: 5648: 5644: 5630: 5626: 5622: 5616: 5614: 5594: 5587: 5581: 5579: 5577: 5568: 5564: 5559: 5554: 5550: 5546: 5542: 5535: 5519: 5515: 5509: 5501: 5497: 5493: 5489: 5485: 5481: 5477: 5473: 5469: 5465: 5460: 5455: 5451: 5447: 5443: 5436: 5428: 5424: 5420: 5416: 5412: 5408: 5404: 5400: 5395: 5390: 5386: 5382: 5378: 5367: 5352: 5348: 5344: 5339: 5331: 5327: 5322: 5317: 5313: 5309: 5305: 5301: 5297: 5293: 5288: 5283: 5279: 5275: 5271: 5256: 5241: 5237: 5230: 5215: 5211: 5204: 5185: 5181: 5177: 5173: 5169: 5165: 5161: 5160: 5152: 5145: 5137: 5133: 5129: 5125: 5121: 5117: 5113: 5109: 5104: 5099: 5095: 5091: 5087: 5080: 5065: 5061: 5054: 5046: 5040: 5036: 5032: 5026: 5010: 5006: 4999: 4991: 4987: 4983: 4979: 4975: 4971: 4968:(12): 23–30. 4967: 4963: 4962:Physics Today 4959: 4952: 4938: 4932: 4928: 4924: 4920: 4916: 4914: 4911: 4907: 4899: 4891: 4887: 4882: 4877: 4873: 4869: 4865: 4861: 4857: 4853: 4849: 4842: 4826: 4822: 4818: 4812: 4803: 4799: 4795: 4791: 4787: 4783: 4780:(4476): 280. 4779: 4775: 4771: 4765: 4749: 4745: 4741: 4735: 4727: 4723: 4719: 4715: 4711: 4707: 4703: 4699: 4695: 4689: 4670: 4666: 4662: 4655: 4648: 4629: 4625: 4621: 4620: 4612: 4605: 4603: 4601: 4599: 4597: 4588: 4584: 4579: 4574: 4570: 4566: 4562: 4558: 4554: 4547: 4539: 4535: 4531: 4527: 4523: 4519: 4515: 4511: 4507: 4500: 4484: 4480: 4474: 4460: 4458:9780444508713 4454: 4450: 4446: 4442: 4438: 4431: 4429: 4427: 4418: 4414: 4410: 4406: 4402: 4398: 4394: 4390: 4386: 4379: 4371: 4365: 4358: 4334: 4330: 4326: 4322: 4321: 4313: 4306: 4304: 4295: 4291: 4285: 4269: 4265: 4258: 4242: 4238: 4232: 4228: 4204: 4197: 4191: 4187: 4176: 4175:Optical clock 4173: 4171: 4170:Time transfer 4168: 4166: 4163: 4161: 4158: 4156: 4153: 4151: 4148: 4146: 4143: 4141: 4138: 4136: 4133: 4131: 4128: 4126: 4123: 4122: 4117: 4111: 4106: 4099: 4097: 4093: 4083: 4081: 4069: 4065: 4060: 4057: 4053: 4044: 4042: 4038: 4034: 4030: 4024: 4014: 4008: 3998: 3996: 3986: 3983: 3979: 3975: 3970: 3966: 3964: 3958: 3956: 3952: 3948: 3945: 3936: 3932: 3929: 3925: 3920: 3918: 3912: 3910: 3905: 3901: 3891: 3889: 3885: 3880: 3876: 3872: 3862: 3860: 3850: 3848: 3843: 3841: 3836:121.5 nm 3831: 3813: 3809: 3804: 3801: 3792: 3785: 3782: 3777: 3773: 3749: 3746: 3739: 3735: 3731: 3726: 3722: 3715: 3709: 3704: 3700: 3694: 3689: 3685: 3681: 3674: 3670: 3664: 3660: 3653: 3644: 3635: 3625: 3615: 3595: 3579: 3560: 3555: 3552: 3549: 3545: 3541: 3536: 3533: 3530: 3526: 3521: 3515: 3509: 3501: 3497: 3481: 3458: 3454: 3450: 3446: 3439: 3435: 3426: 3423: 3414: 3403: 3392: 3383: 3381: 3377: 3373: 3368: 3366: 3362: 3357: 3353: 3341: 3330: 3327: 3292: 3288: 3286: 3282: 3278: 3266: 3261: 3241:10 years 3234: 3230: 3218: 3217:ytterbium-171 3213: 3211: 3199: 3186: 3184: 3175: 3170: 3166: 3164: 3160: 3156: 3152: 3148: 3144: 3140: 3136: 3132: 3127: 3125: 3121: 3113: 3110: 3107: 3106: 3105: 3102: 3100: 3096: 3092: 3087: 3084: 3080: 3076: 3072: 3068: 3065: 3060: 3058: 3054: 3050: 3046: 3041: 3033: 3028: 3019: 3009: 3005: 3000: 2990: 2986: 2972: 2969: 2965: 2961: 2955: 2949: 2936: 2931: 2927: 2924: 2923: 2922: 2919: 2917: 2891: 2869: 2846: 2780: 2779:nuclear clock 2776: 2771: 2752: 2748: 2744: 2738: 2737:Nuclear clock 2728: 2726: 2725:ytterbium-171 2722: 2718: 2713: 2702: 2692: 2687: 2683: 2679: 2675: 2671: 2665: 2664:Quantum clock 2655: 2647: 2642: 2621: 2618: 2614: 2613: 2610: 2605: 2584: 2581: 2577: 2576: 2573: 2568: 2544: 2541: 2537: 2536: 2533: 2528: 2507: 2504: 2500: 2499: 2496: 2491: 2473: 2471: 2468: 2467: 2464: 2459: 2438: 2436: 2433: 2432: 2429: 2424: 2422: 2406: 2404: 2401: 2400: 2396: 2392: 2388: 2385: 2381: 2378: 2377: 2374: 2372: 2362: 2360: 2356: 2348: 2343: 2334: 2332: 2327: 2325: 2321: 2317: 2313: 2309: 2300: 2297: 2293: 2289: 2285: 2268: 2266: 2265:Dave Wineland 2262: 2258: 2245: 2237: 2232: 2223: 2206: 2178: 2175: 2171: 2149: 2144: 2138: 2134: 2110: 2104: 2099: 2095: 2088: 2084: 2078: 2075: 2067: 2064: 2058: 2055: 2049: 2045: 2036: 2030: 2027: 2024: 2008: 2004: 1998: 1992: 1967: 1964: 1960: 1952: 1951: 1950: 1948: 1932: 1929: 1926: 1923: 1920: 1898: 1894: 1889: 1883: 1879: 1875: 1872: 1850: 1846: 1825: 1802: 1784: 1780: 1771: 1767: 1763: 1757: 1741: 1737: 1716: 1708: 1690: 1668: 1645: 1619: 1598: 1590: 1589:spectroscopic 1574: 1548: 1542: 1533: 1521: 1514: 1510: 1504: 1495: 1489: 1461: 1458: 1454: 1446: 1445: 1444: 1427: 1419: 1415: 1407: 1402: 1400: 1394: 1390: 1373: 1362: 1344: 1340: 1330: 1324: 1321: 1317: 1316:crystal watch 1314: 1311:changes in a 1310: 1306: 1302: 1298: 1294: 1284: 1282: 1278: 1272: 1270: 1266: 1261: 1259: 1255: 1252: 1248: 1242: 1240: 1239: 1234: 1230: 1226: 1222: 1212: 1210: 1206: 1202: 1197: 1195: 1194:absolute zero 1191: 1171: 1156: 1154: 1150: 1146: 1140: 1138: 1134: 1128: 1120: 1115: 1105: 1103: 1099: 1086: 1078: 1073: 1063: 1061: 1056: 1046: 1042: 1038: 1034: 1025: 1019:Block diagram 1016: 1013: 1009: 1005: 1000: 998: 994: 990: 986: 981: 966: 964: 958: 957:0.9 seconds. 954: 952: 948: 944: 938: 932: 927: 919: 910: 908: 904: 899: 896: 890: 888: 884: 880: 876: 872: 861: 859: 856: 852: 840: 830: 814: 810: 806: 801: 799: 796:to provide a 795: 791: 786: 780: 776: 772: 768: 764: 760: 756: 752: 748: 744: 740: 736: 732: 727: 725: 721: 706: 704: 703:optical combs 700: 696: 692: 689: 687: 683: 678: 672: 668: 659: 650: 619: 606:precision of 605: 601: 597: 593: 589: 585: 576: 573: 569: 561: 557: 552: 543: 542:around 2030. 541: 537: 533: 529: 525: 521: 517: 513: 512:tropical year 479: 477: 473: 469: 464: 462: 458: 454: 450: 446: 442: 438: 434: 430: 426: 422: 417: 415: 410: 408: 404: 400: 396: 392: 383: 379: 377: 373: 369: 365: 361: 360:quartz clocks 357: 352: 350: 346: 341: 339: 335: 330: 326: 318: 314: 310: 301: 295: 291: 287: 283: 282:absolute zero 279: 275: 270: 266:1,000,000,000 258: 254: 250: 246: 242: 238: 234: 229: 227: 223: 219: 215: 209: 176: 162: 160: 156: 152: 148: 144: 143:energy levels 140: 136: 128: 124: 120: 115: 106: 102: 99: 96: 92: 89: 85: 82: 78: 75: 71: 68: 64: 61: 58: 54: 47: 42: 37: 34: 30: 26: 22: 15009:Agricultural 14864:Quasiturbine 14775:Steam engine 14710:Quartz clock 14695:Atomic clock 14694: 14569:Decimal time 14298:Astronomical 14177:Complication 14172:Atomic clock 14171: 13820:Atomic clock 13819: 13815:Quartz clock 13695:Time capsule 13689:Tempus fugit 13687: 13609:Other fields 13308: 13289:Perdurantism 13211:Calendar era 13163: 13156: 13142:Cuckoo clock 13090: 13079:astronomical 13053: 12879:Unit of time 12810:Key concepts 12750: 12743: 12731:. Retrieved 12727: 12718: 12706:. Retrieved 12702: 12690: 12678:. Retrieved 12673: 12664: 12652:. Retrieved 12648: 12636: 12585: 12581: 12574: 12562:. Retrieved 12550: 12540: 12528:. Retrieved 12524: 12514: 12479:. Retrieved 12474: 12465: 12453:. Retrieved 12448: 12439: 12427:. Retrieved 12423: 12413: 12401:. Retrieved 12391: 12379:. Retrieved 12375: 12365: 12353:. Retrieved 12342: 12332: 12320:. Retrieved 12316:the original 12311: 12302: 12290:. Retrieved 12282:livemint.com 12281: 12271: 12259:. Retrieved 12245: 12233:. Retrieved 12219: 12207:. Retrieved 12187: 12176: 12164:. Retrieved 12152: 12142: 12130:. Retrieved 12126:the original 12121: 12112: 12100:. Retrieved 12080: 12068:. Retrieved 12059: 12050: 12038:. Retrieved 12029: 12020: 12008:. Retrieved 12004:the original 11994: 11982:. Retrieved 11962: 11950:. Retrieved 11936: 11924:. Retrieved 11910: 11898:. Retrieved 11878: 11866:. Retrieved 11859:the original 11846: 11834:. Retrieved 11805:. Retrieved 11791: 11779:. 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Retrieved 10272:the original 10225: 10219: 10206: 10158:(6) 063001. 10155: 10151: 10137: 10125:. Retrieved 10116: 10106: 10094:. Retrieved 10085: 10075: 10063:. Retrieved 10059:the original 10055:"About Time" 10048: 9995: 9991: 9973: 9961:. Retrieved 9907: 9903: 9890: 9878:. Retrieved 9864: 9852:. Retrieved 9843: 9834: 9822:. Retrieved 9797: 9787: 9775:. Retrieved 9766: 9756: 9744:. Retrieved 9739: 9730: 9718:. Retrieved 9704: 9692:. Retrieved 9680: 9670: 9658:. Retrieved 9644: 9632:. Retrieved 9618: 9606:. Retrieved 9586: 9535: 9531: 9521: 9500: 9488:. Retrieved 9476: 9452:. Retrieved 9445:the original 9440: 9427: 9416:the original 9390:(2) 020801. 9387: 9381: 9326: 9316: 9265: 9261: 9238:21 September 9236:. Retrieved 9231: 9222: 9181: 9177: 9167: 9155:. Retrieved 9150: 9141: 9129:. Retrieved 9124: 9115: 9103:. Retrieved 9099: 9087: 9075:. Retrieved 9056: 9044:. Retrieved 9040: 9028: 8979: 8975: 8964: 8952:. Retrieved 8938: 8885: 8881: 8871: 8836: 8832: 8822: 8787: 8783: 8773: 8761:. 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