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In 1983 the 17th CGPM decided to redefine the metre as used in the SI system of units in order to solve problems with obtaining a sufficiently precise realisation of the previous definition of the metre.[1] The definition reads: "The metre is the length of the path travelled by light in vacuum during a time interval of 1/299 792 458 of a second." This definition has the effect that the speed of light now takes an exact value of 299 792 458 metres per second.

History

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The speed of light, usually denoted c nowadays, has been subject of speculation or investigation for millennia. However the nature of c, as a universal physical constant, was only established by the development of special relativity in 1905. This left the value of c, as with all physical constants, as a subject of further refinement by measurement.

Since, by 1975, similar laser-based measurements of c agreed with each other with an uncertainty comparable to that of the "realization of the metre", the 15th Conférence Générale des Poids et Mesures recommended using 299792458 m/s for "the speed of propagation of electromagnetic waves in vacuum".[2]. The recommendation was adopted in 1983 by the 17th CGPM, by their definition of the metre as the length of the path traveled by light in vacuum during a time interval of 1/299,792,458 of a second.[3] Further reasons for using this definition are stated in Resolution 1.[1] A popular account of the decision from that time is provided in the New Scientist.[4]

Consequences

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The effect of this definition gives the speed of light in vacuum an exact value in metric units, namely 299,792,458 metres/second. This can be regarded as a conversion factor[5] between the second and the metre. The value of 299,792,458 m/s is approximately the measured value of the speed of light based upon the pre-1983 definition of the metre,[6] and was selected in part to result in minimal dislocation of standards.[7] According to NIST:[8] “In all of these changes in definition, the goal was not only to improve the precision of the definition, but also to change its actual length as little as possible.” Thus, within the SI system of units, the speed of light is now a defined constant[9] and no longer something to be measured.[10] Improved experimental techniques do not affect the metric value of the speed of light, but do result in a better realization of the metre, i.e. recalibration of the measuring instruments involved.[11][12] Because the second is defined in terms of atomic transitions that can be measured accurately, the new definition, being a ratio of measured times, allows for a definition of the metre with greater accuracy in practical measurement than one based on a ratio of lengths determined using a fringe count of interference patterns.[13]

Rather than measure a time-of-flight, one implementation of this definition is to use a recommended source with established frequency f, and delineate the metre in terms of the wavelength λ of this light as determined using the defined numerical value of c and the relationship λ = c / f.[14] Practical realizations of the metre use recommended wavelengths of visible light in a laboratory vacuum with corrections being applied to take account of actual conditions such as diffraction, gravitation or imperfection in the vacuum.

Increased accuracy

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Accuracy of interferometers vs. length measured. After Webb and Jones.[15]

In the second half of the 20th century much progress was made in increasing the accuracy of measurements of the speed of light, first by cavity resonance techniques and later by laser interferometer techniques. In 1972, using the latter method, a team at the US National Institute of Standards and Technology (NIST) laboratories in Boulder, Colorado determined the speed of light to be c = 299792456.2±1.1 m/s.[16][10] Almost all the uncertainty in this measurement of the speed of light was due to uncertainty in the length of the metre.[16][10][2]

Since 1960, the metre had been defined as a given number of wavelengths of the light of one of the spectral lines of krypton,[Note 1] but the profile of the chosen spectral line was not perfectly symmetrical.[16][10] This made its wavelength, and hence the length of the metre, ambiguous, because the definition did not specify what point on the line profile it referred to. [Note 2] There were other problems in using the krypton source. For example, one problem is the coherence length of this source of 78 cm, which complicates its use for measuring longer lengths.[Note 3] By way of contrast, some He-Ne lasers have a coherence length of about 75 km, making such sources very attractive for measurement of long distances.[22][23]

Hence the krypton discharge was not the best source for determining the metre. An alternative would be to select a better source, for example the caesium 133 atomic transition selected in 1967 for the standard of time.[24] However, laser technology was rapidly evolving and new and better sources were being devised; a standard was desirable that could keep abreast of such developments, and allow adoption of new sources that were more precise or more practical as they evolved.[Note 4]

The introduction of many sources required a methodology for comparison. The wavelength of the sources could be compared, but using interferometry to measure wavelengths was subject to some serious errors.[Note 5] On the other hand the measurement of frequencies had become very good.[13] Since frequency and wavelength were related by the speed of propagation, a comparison of the frequencies of sources was tantamount to a comparison of wavelengths, but more accurate. The only issue was to insure that the speed of propagation was the same in all such comparisons, which led to the adoption of the speed of light in vacuum as the standard of speed of propagation.

In 1975, considering that similar measurements of c agreed with each other and their uncertainty was comparable to that in the realization of the metre, the 15th Conférence Générale des Poids et Mesures (CGPM) recommended using 299792458 m/s for "the speed of propagation of electromagnetic waves in vacuum".[2] In 1983, because the definition of the metre in terms of the Kr86 transition at 6057Å did not allow a sufficiently precise realization of it for all requirements, the 17th CGPM adopted the 1975 recommendation: "the length of the path travelled by light in vacuum during a time interval of 1⁄299792458 of a second".[1] The effect of this definition gives the speed of light the exact value 299792458 m/s.[7][8] As a result, in the SI system of units the speed of light is now a defined constant.[9] Improved experimental techniques do not affect the value of the speed of light in SI units, but do result in a more precise realisation of the metre.[11][12]

With this definition, the remaining uncertainties in the realization of the metre are now (i) the uncertainties in the radiations, now tabulated and kept current in the mis en pratique;[28] (ii) the uncertainties in the realization of "vacuum" (or, equivalently, uncertainties in the corrections implemented to account for the medium employed) and (iii) the uncertainty in interferometry in establishing a wavelength. This last is no better than use of a better source and the old definition of the metre as a number of wavelengths of a specific transition. However, the flexibility in choice of source and the ability to let the standard evolve with improved precision of the sources are the determining factors in making the change in definition.

Does the definition preclude some measurements?

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The special theory of relativity is based upon a number of postulates concerning properties of the speed of light.[29] In the present SI units system where the speed of light has a defined value of c = 299,792,458 m/s exactly, can these postulates continue to be tested as experimental technique improves? For example, does the definition of c as an exact value mean that any test of whether light is isotropic, dispersionless, etc. is placed beyond test, by definition? The answer is: ‘No. What is placed beyond test is the defined value of c, not any experimental investigations.’

For example, consider the hypothetical observation of anisotropy.[30] In the SI system of units, the anisotropy would take the form of the metre having different lengths in different directions. Of course, a standard of length cannot be allowed to be uncertain in this way, so the effect of this hypothetical observation would be a change in the definition of the metre, to add a directional correction. At the same time, however, the explanation of this anisotropy would be attempted by improvements in theory, and quite possibly the successful explanation would be that the physical phenomenon of the speed of travel of light was anisotropic. The physical phenomenon of the speed of travel of light must be kept separate in our thinking from the numerical value of c in the SI system of units. (This distinction might be a good reason to use the symbol c0 for the SI conversion factor instead of c, as is recommended by the CGPM.)

In sum, tests of the special theory of relativity, for example, are not impeded by an exact definition of c in the SI system of units. The experiments show up as tests of the adequacy of the definition of the metre. Any necessary changes in this definition due to future experimental results will be accompanied eventually by theoretical explanations, and these theories may indeed invoke as yet undiscovered properties of the speed of travel of light.

References

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  1. ^ a b c "Resolution 1". Conférence Générale des Poids et Mesures. BIPM. 1983. Retrieved 2009-08-23. Cite error: The named reference "Resolution_1" was defined multiple times with different content (see the help page).
  2. ^ a b c Resolution 2 of the 15th CGPM. BIPM. 1975. Retrieved 2009-09-09. {{cite book}}: |work= ignored (help)
  3. ^ "Base unit definitions: Meter". NIST. Retrieved 2009-08-22.
  4. ^ Tom Wilkie (Oct 27, 1983). "Time to remeasure the metre". New Scientist. Vol. 100. Reed Business Information. pp. 258 ff. ISSN 0262-4079.
  5. ^ Jespersen, J; Fitz-Randolph, J; Robb, J (1999). From Sundials to Atomic Clocks: Understanding time and frequency (Reprint of National Bureau of Standards 1977, 2nd ed.). Courier Dover. p. 280. ISBN 0486409139. One fallout of the new definition was that the speed of light was no longer a measured quantity; it became a defined quantity. The reason is that, by definition, a meter is the distance light travels in designated length of time, so however we label that distance - one meter, five meters, whatever -- the speed of light is automatically determined. And measuring length in terms of time is a prime example of how defining one unit in terms of another removes a constant of nature by turning c into a conversion factor whose value is fixed and arbitrary.
  6. ^ Stuart Gregson, John McCormick, Clive Parini (2007). Principles of planar near-field antenna measurements. Institution of Engineering and Technology. p. 22. ISBN 978-0863417368. In 1975 the 15th CGPM, Resolution 2(CR 103 and Metrologia, 1975, 11 179-180) adopted the speed of propagation of EM waves in vacuum as 299,792,458 m/s where the estimated uncertainty is ±4 × 10−9{{cite book}}: CS1 maint: multiple names: authors list (link)
  7. ^ a b Edwin F. Taylor, John Archibald Wheeler (1992). Spacetime physics: introduction to special relativity (2nd ed.). Macmillan. ISBN 0716723271. Cite error: The named reference "Wheeler" was defined multiple times with different content (see the help page).
  8. ^ a b Penzes, WB (2009). "Time Line for the Definition of the Meter". NIST. Retrieved 2010-01-11.
  9. ^ a b Jespersen, J; Fitz-Randolph, J; Robb, J (1999). From Sundials to Atomic Clocks: Understanding time and frequency (Reprint of National Bureau of Standards 1977, 2nd ed.). Courier Dover. p. 280. ISBN 0486409139. Cite error: The named reference "Jespersen" was defined multiple times with different content (see the help page).
  10. ^ a b c d e Sullivan, DB. "Speed of Light From Direct Frequency and Wavelength Measurements" (PDF). NIST. p. 191. Retrieved 2009-08-22. A consequence of this definition is that the speed of light is now a defined constant, not to be measured again....This way of defining the meter has proven to be particularly robust, since unlike a definition based on a standard such as the krypton lamp, length measurement can be continuously improved without resorting to a new definition. Cite error: The named reference "NIST_pub" was defined multiple times with different content (see the help page).
  11. ^ a b Steve Adams (1997). Relativity: an introduction to space-time physics. CRC Press. p. 140. ISBN 0748406212. One peculiar consequence of this system of definitions is that any future refinement in our ability to measure c will not change the speed of light (which is a defined number), but will change the length of the meter! Cite error: The named reference "Adams" was defined multiple times with different content (see the help page).
  12. ^ a b Wolfgang Rindler (2006). Relativity: special, general, and cosmological (2nd ed.). Oxford University Press. p. 41. ISBN 0198567316. Note that … improvements in experimental accuracy will modify the meter relative to atomic wavelengths, but not the value of the speed of light! Cite error: The named reference "W_Rindler" was defined multiple times with different content (see the help page).
  13. ^ a b PH Sydenham (2003). "Standards and calibration of length". In Walt Boyes (ed.). Instrumentation reference book (3rd ed.). Butterworth-Heinemann. p. 56. ISBN 0750671238. Time standards (parts in 1014 uncertainty) are more reproducible in terms of uncertainty than length (parts in 109)
  14. ^ A list of the resulting wavelengths based upon these frequencies and λ = c/f is found at BIPM mise-en-pratique, method b.
  15. ^ Colin E. Webb, Julian D. C. Jones (2004). "Figure D2.1.15: Accuracy limits for laser interferometry". Handbook of Laser Technology and Applications: Applications. Taylor & Francis. p. 1741. ISBN 0750309660.
  16. ^ a b c d Evenson, K. M.; Wells, J. S.; Petersen, F. R.; Danielson, B. L.; Day, G. W.; Barger, R. L.; Hall, J. L. (1972). "Speed of Light from Direct Frequency and Wavelength Measurements of the Methane-Stabilized Laser". Physical Review Letters. 29 (19): 1346–49. doi:10.1103/PhysRevLett.29.1346.{{cite journal}}: CS1 maint: date and year (link)
  17. ^ Resolution 6 of the 11th CGPM. BIPM. 1960. Retrieved 2009-10-18. {{cite book}}: |work= ignored (help)
  18. ^ Stephen A. Dyer (2001). Survey of instrumentation and measurement. Wiley-IEEE. p. 461. ISBN 047139484X.
  19. ^ Ernest G. Wolff (2004). Introduction to the Dimensional Stability of Composite Materials. DEStech Publications, Inc. p. 345. ISBN 1932078223.
  20. ^ PS Mishra (2009). "Spatial coherence and temporal coherence". Biophysics. VK(India) Enterprises. p. 543. ISBN 978-93-80006-43-7.
  21. ^ Wolfgang Demtröder (2008). "§2.8: Coherence properties of radiation fields". Laser spectroscopy: Basic principles (4th ed.). Springer. pp. 42ff. ISBN 978-3540734154.
  22. ^ Daniel Malacara, Brian J. Thompson (2001). Handbook of optical engineering. CRC Press. p. 67. ISBN 0824799607.
  23. ^ Benjamin Austin Barry (1988). Construction measurements, Volume 1987 (2nd ed.). Wiley-Interscience. p. 117. ISBN 047183663X.
  24. ^ Claude Audoin, Bernard Guinot (2001). The measurement of time: time, frequency, and the atomic clock. Cambridge University Press. ISBN 0521003970.
  25. ^ "Recommendation 1 (CI-2007) Revision of the Mise en pratique list of recommended radiations" (PDF). Comité International des Poids et Mesures 96th meeting (November 2007). BIPM. 2007. p. 185. Retrieved 20010-07-30. {{cite web}}: Check date values in: |accessdate= (help)
  26. ^ F. B. Dunning, Randall G. Hulet (1997). Atomic, molecular, and optical physics: electromagnetic radiation. Academic Press. p. 316. ISBN 0124759777.
  27. ^ Victor Nascov (2005). "§25.2: Optical interferometry overview". In Günter Wilkening, Ludger Koenders (ed.). Nanoscale calibration standards and methods: dimensional and related measurements in the micro- and nanometer range. Wiley-VCH. pp. 332 ff. ISBN 352740502X.
  28. ^ The mise en pratique is continually revised to keep abreast of improvements in sources and techniques, suggesting additional standards and revising old ones. The revision of 2002 is more extensive than most, summarizing the reasoning behind the introduction of new sources, and recapitulating the earlier resolutions. It can be found at "RECOMMENDATION 1 (CI-2002): Revision of the practical realization of the definition of the metre" (PDF). 91st Meeting of the CIPM. BIPM. 2002. Retrieved 2010-07-22.
  29. ^ Bertfried Fauser, Jürgen Tolksdorf, Eberhard Zeidler (2007). Quantum gravity: mathematical models and experimental bounds. Birkhäuser. p. 21. ISBN 978-3764379773.{{cite book}}: CS1 maint: multiple names: authors list (link)
  30. ^ The isotropy of the speed of light can be monitored using a rotating resonator: see Sven Herrmann, Alexander Senger, Evgeny Kovalchuk, Holger Müller, and Achim Peters (2005). "Test of the isotropy of the speed of light using a continuously rotating optical resonator" (PDF). Phys Rev Lett. 95 (15): 150401. doi:10.1103/PhysRevLett.95.150401. PMID 16241700.{{cite journal}}: CS1 maint: multiple names: authors list (link)

Notes

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  1. ^ From 1960 to 1983, the metre was defined as "the length equal to 1,650,763.73 wavelengths in vacuum of the radiation corresponding to the transition between the levels 2p10 and 5d5 of the krypton-86 atom."[17]
  2. ^ The value of 299792456.2±1.1 m/s quoted above assumes that the definition of the metre is to be applied to the centre of gravity of the krypton line, however if the maximum-intensity point of the line were used instead, the result would be 299792458.7±1.1 m/s.[16][10]
  3. ^ Beyond a coherence length, no interference pattern can be observed. The coherence length is longer, the narrower the spectral width of the source.[18] The coherence length of the gas discharge krypton source is described by Wolff,[19] and by Mishra.[20] An excellent general discussion is found in Demtröder.[21]
  4. ^ For example, the 2007 mise en pratique adopted frequencies of molecules in the optical telecommunications region that had been determined by femtosecond comb-based frequency measurements for the first time.[25]
  5. ^ Among the more serious sources of error in interferometry are beam collimation, alignment, refractive index correction and fractional fringe determination.[26] A theoretical discussion of the limits of interferometer accuracy is found in Wilkening & Koenders.[27]
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