View source for Atomic Standards of Length and Time

{{Infobox paper
| title = Atomic Standards of Length and Time
| url = [http://www.naturalphilosophy.org/pdf/abstracts/abstracts_6383.pdf Link to paper]
| author = [[Louis Essen]]
| keywords = length, time, earth, Units, metre, second, krypton-86, caesium, metrology
| published = 1959
| journal = [[Science Progress]]
| volume = 47
| number = 186
| num_pages = 23
| pages = 209-229
}}

'''Read the full paper''' [http://www.naturalphilosophy.org/pdf/abstracts/abstracts_6383.pdf here]

==Abstract==

The units of measurement used in science for evaluating the fundamental quantities length and time are the metre and the second. Although originally related to a particular dimension of the Earth, the metre has since 1889 been defined as the distance, under specified conditions, between two parallel lines engraved on a platinum-iridium bar (the International Prototype Metre) which is carefully preserved in a vault at the International Bureau of Weights and Measures at Sevres in France. Two astronomical units of time are now recognised one, the mean solar second, which is related to the diurnal period of rotation of the Earth, and the other, more precisely defined and designated in 1956 as the second,* which is related to the period of revolution of the Earth about the Sun as represented by the duration of a particular tropical year. During the next few years there is every prospect that new definitions of the metre and the second will become adopted which will be expressed in terms of certain fundamental characteristics of the atom...

==Overview==

This is a joint review by H. Barrell and Louis Essen, both of the Standards Division of the National Physical Laboratory at Teddington, written at the moment when the two base units of physics were about to be cut loose from the Earth and from a metal bar and re-founded on atomic transitions. Barrell writes the length half, Essen the time half. The paper is a status report from the inside: Essen had built the world's first caesium atomic frequency standard at the NPL in 1955, and the recommendation to define the metre by a krypton-86 wavelength was already before the International Committee of Weights and Measures, awaiting the 11th General Conference of 1960. The authors accordingly write as advocates who have done the experiments, not as commentators.

The argument is a metrological one rather than a theoretical one, and its interest for readers of this wiki lies in what it establishes about the ''operational'' basis of measurement. Both the metre and the second, the authors insist, are "abstract conceptions" that "cannot be used as the practical bases of measurement until they have been defined" either by an arbitrary material artefact or by reference to a natural phenomenon. Everything else — including any physical law expressed in metres and seconds — rests on that choice of embodiment. The paper documents the moment when the embodiment shifted from the rotating and revolving Earth to the atom, and it records, almost in passing, the recognition that the atomic and astronomical time scales are not the same thing and may drift apart. Essen would spend much of the rest of his career pressing the implications of exactly that kind of operational scrupulousness against what he saw as the loose reasoning of [[Special Relativity]].

==The argument==

===Why the existing standards had become inadequate===

The reproducibility of the metre as embodied in the hierarchy of platinum-iridium line standards is put at between 200 and 300 parts in 10<sup>9</sup>, improvable perhaps to 100 parts in 10<sup>9</sup> with photoelectric microscope comparators. Beyond that limit the authors identify a structural weakness rather than a technical one: a material standard is "vulnerable to secular change, damage or destruction", so the defining artefact must be made practically inaccessible, and the whole system "may be subject to small but undisclosed secular variations of length". There is no internal check.

The astronomical time standards fail differently. They are permanent and available but imprecise. Averaging over one hundred days gives the mean solar second to about 1 part in 10<sup>9</sup>, but statistical analysis of quartz clock performance had already given "strong evidence that the rate of rotation of the Earth varies periodically throughout the year", and study of the periods of revolution of other solar-system bodies over two centuries showed the Earth's rotation had changed irregularly "by as much as 80 parts in 10<sup>9</sup>". This is why the ephemeris second, tied to the Earth's revolution about the Sun, was designated in 1956. But ephemeris time is measured less precisely than mean solar time and needs still longer averaging — it had then been determined to about 2.2 parts in 10<sup>9</sup> from three years of observation — and quartz clocks cannot be trusted to hold a uniform rate over such intervals. The unit so obtained is therefore only an average, whereas practical work needs the value "at a particular instant or over a short interval".

===The atomic principle===

Both new standards rest on the same two equations. A transition between atomic energy states ''E''<sub>2</sub> and ''E''<sub>1</sub> emits or absorbs radiation of frequency

''f'' = (''E''<sub>2</sub> − ''E''<sub>1</sub>)/''h''

and, propagating in vacuo at ''c'', of wavelength

''λ'' = ''ch''/(''E''<sub>2</sub> − ''E''<sub>1</sub>)

Since the right-hand quantities are fundamental constants, "any atomic radiation is potentially a standard of length or of frequency". The practical division of labour follows from magnitudes: optical lines at ~6 × 10<sup>14</sup> c/s cannot be compared with quartz oscillators at 10<sup>5</sup>–10<sup>6</sup> c/s, whereas hyperfine transitions near 10<sup>10</sup> c/s can be, so optical lines serve length and microwave lines serve frequency.

The limiting factor is line width, tabulated as natural width, Doppler width and pressure broadening. Natural and Doppler broadening are symmetrical and shift no mean wavelength; pressure broadening — subdivided into collision, resonance and interatomic Stark broadening — is asymmetrical and does displace the line. Self-reversal, in which cooler outer atoms absorb the core of a line emitted deeper in a discharge, can broaden a line or split it into an apparent doublet.

===The wavelength standard===

Babinet proposed light waves as a length basis in 1829; Michelson and Benoît first measured the metre in cadmium red wavelengths in 1892–3. Table 2 collects all nine determinations of the metre in terms of the cadmium red line ''λ''<sub>B</sub>. Their mean, 1 553 164.12 waves to the metre, gives ''λ''<sub>B</sub> = 6438.4696 × 10<sup>−10</sup> m — "by a convenient fluke" identical with the value adopted for spectroscopy in 1907 — with maximum deviation 260 parts in 10<sup>9</sup> and no trend with date, which the authors take as evidence that the hierarchy of metre standards is secularly stable.

The decisive technical advance was the use of pure isotopes of even atomic mass and charge, which have zero nuclear spin and so emit lines free of hyperfine structure and of isotope displacement. Terrien found the orange (6056 Å) and yellow-green (5650 Å) lines of krypton-86 to be "the sharpest ever known to have been produced from discharge lamps of the established kind", emitted from Engelhard's hot-cathode lamp run in a cryostat at the triple point of nitrogen (63 K). Table 3 gives five laboratories' vacuum wavelengths for three krypton-86 and three mercury-198 lines, agreeing in the last figures. The Consultative Committee recommended the krypton-86 orange line, the 2p<sub>10</sub>–5d<sub>5</sub> transition, giving

1 metre = 1 650 763.73 vacuum wavelengths

reproducible to about 1 part in 10<sup>9</sup>, two orders of magnitude better than the artefact. Practical calibration of existing metre bars would still be limited to about 10 parts in 10<sup>9</sup>.

===The frequency standard===

Two candidates are compared. The ammonia inversion line (''J'' = 3, ''K'' = 3) at 23 870 Mc/s, sharpened by the maser of Gordon, Townes and Zeiger and independently of Basov and Prokhorov, gains continuous coherence but its frequency "depends to a small extent on the electrical circuit and on the operating conditions", limiting definition to about ±10 parts in 10<sup>8</sup> — though Bonanomi and colleagues at Neuchâtel achieved a repetition accuracy of ±0.2 part in 10<sup>9</sup>.

The caesium beam standard, built on the Rabi–Kusch–Zacharias–Ramsey atomic-beam method, proved better. Oven, collimating slit, deflecting magnets of about 4000 oersted, two cavity resonators and a detector wire in a vacuum of 10<sup>−8</sup>–10<sup>−7</sup> mmHg suffice; line widths of 120 c/s were obtained, with 50 c/s in prospect from a long vertical machine then under construction at the NPL. Essen reports that the frequency was "independent of most of the parameters to an extraordinary degree", only the d.c. field and the cavity phasing needing care, both checkable with the standard itself, with accidental variations not expected to exceed a few parts in 10<sup>11</sup>.

Two independent reliability checks are reported. Intercomparison at the NPL against two commercial Atomichrons and one experimental National Company standard, of quite different construction, gave differences of 0.15–0.32 × 10<sup>−9</sup> with a standard deviation of 0.03 part in 10<sup>9</sup> (Table 4). Radio intercomparison via the Rugby MSF and GBR transmissions against the Atomichron at Camden, New York gave monthly differences of 0.0–0.8 parts in 10<sup>9</sup> (Table 5); daytime propagation errors on the 60 kc/s and 16 kc/s transmissions were held to a few parts in 10<sup>10</sup>. The joint NPL–U.S. Naval Observatory programme yielded the caesium ''F'',''m''(4,0)–''F'',''m''(3,0) zero-field frequency as 9 192 631 770 ± 20 c/s in terms of the ephemeris second — the number later frozen into the SI definition.

===Two time scales===

The authors resist collapsing the two kinds of time into one. The atomic standard is right for physics and radio engineering; the astronomical standard preserves continuity over the long spans of astronomy and gives the time of day for civil life. But "it would be undesirable and confusing to have two unrelated units of time", so a single unit combining both virtues is wanted. Until then any measurement better than a few parts in 10<sup>8</sup> must state which unit it uses — UT2, ephemeris time, or an atomic unit with its adopted line frequency stated. The NPL's own provisional value had already shifted from 9 192 631 830 c/s (referred to UT2 in June 1955) to 9 192 631 770 c/s (referred to ET).

==Assessment==

This is mainstream metrology written by two of its practitioners, and on its own terms it is sound; almost everything it forecasts happened. The krypton-86 metre was adopted in 1960 as predicted, and the caesium second was adopted in 1967 — one conference later than the authors' guess of 1966, and with the frequency they quote, 9 192 631 770, unchanged. The atomic-beam source they single out at the end as the most favoured future frequency standard did indeed displace the discharge lamp, and the 1983 redefinition of the metre by a fixed value of ''c'' went further than they anticipated by eliminating the wavelength standard altogether. Their prediction that mass would resist an atomic definition at 1 part in 10<sup>8</sup> held for another half-century; the Huntoon–Fano suggestion of founding a third base unit on the proton gyromagnetic ratio was not the route eventually taken.

What is genuinely valuable in the paper is its methodological discipline. The reliability of the caesium standard is not asserted from theory but established three ways: by deliberately varying design parameters and measuring the effect, by comparing physically dissimilar instruments built by different organisations, and by transatlantic radio comparison. The authors are candid that a maser's frequency is partly a property of its circuit rather than of the ammonia molecule, and equally candid that the artefact metre's stability can only be inferred, never checked, because the defining bar is deliberately inaccessible. This insistence that a unit is a defined operation, not a fact of nature, is the paper's most durable point.

Two limitations should be noted, neither a fault of the authors. First, the accuracy figures are reproducibility figures for the emitting source, not accuracy of the underlying transition, and the paper does not fully separate the two; the krypton lamp's 1 part in 10<sup>9</sup> depends on lamp temperature, pressure and excitation being held to specified conditions, with departures merely "calculable". Second, the paper touches but does not pursue the question it raises in its closing pages — whether the atomic and astronomical time scales differ in principle rather than merely in the Earth's irregularity. It cites Bullard's observation that this is "a matter of some cosmological interest" and leaves it there. That is the right editorial decision for a 1959 review, but it leaves the deeper issue untouched: once time is defined by a caesium hyperfine interval, statements about clock rates in relativity become statements about that interval, and the operational meaning of the relativistic time transformations has to be argued rather than assumed. Essen made precisely this complaint in his later critical work on relativity, notably ''[[The Special Theory of Relativity: A Critical Analysis]]'', where he objected that the theory's treatment of clocks and rods was not framed with the care that a metrologist would demand. Readers who come to this paper expecting that critique will not find it here — this is the constructive half of Essen's work, and it is the technical authority it earned him that gave his later objections their weight.

==See also==

* [[Louis Essen]]
* [[The Special Theory of Relativity: A Critical Analysis]]
* [[Time]]
* [[Speed of Light]]
* [[Planck Constant]]
* [[Doppler Effect]]
* [[Simultaneity]]

[[Category:Scientific Paper|atomic standards length time]]
[[Category:Time]]