The Velocity of Light
| Scientific Paper | |
|---|---|
| Title | The Velocity of Light |
| Read in full | Link to paper |
| Author(s) | Louis Essen |
| Keywords | velocity of light, cavity resonator, metrology, electromagnetic units, radar |
| Published | 1952 |
| Journal | Science Progress |
| Volume | 40 |
| No. of pages | 17 |
| Pages | 54-70 |
Read the full paper here
Abstract
The importance of the velocity of light in the development of electrical theory and practice is sometimes overlooked and in this review special emphasis will therefore be given to this aspect of the work and to the determinations of the velocity by electrical methods. It will moreover be assumed at the outset that in accordance with theory the value is independent of the frequency of the waves. The electrical, radio, and optical methods are all measurements of the same constant and the different titles of the various papers are merely indications of the particular technique employed. If there are discrepancies in the results then the theory must be re-examined; but so far no significant discrepancies have been found...
Overview
This is a review article written by Louis Essen of the Electricity Division of the National Physical Laboratory at Teddington, at the moment when his own cavity-resonator work had just overturned the accepted value of c. It is not a theoretical paper: it is a critical survey of every serious determination of the speed of light from Roemer in 1676 to Bol at Stanford in 1950, organised by experimental method rather than by chronology, and closing with a full table of results and a pointed discussion of how experimenters report their errors.
Two claims run through it. The first is historical and mildly revisionist: Essen argues that the electrical measurements did not follow from electromagnetic theory but helped provoke it. Faraday suggested in 1846 that light is an electromagnetic radiation; Weber and Kohlrausch obtained an electrical value ten years later that agreed with Fizeau's optical one; and "Faraday's suggestion, and this experimental support, were much in Maxwell's mind when he wrote his famous paper on the electromagnetic field. It may be regarded as an experimental fact which stimulated the formulation of electromagnetic theory rather than as a deduction made from it, as is often supposed." The second is methodological and is the review's real payload: the accepted value adopted by Birge in 1941, 299,776 ± 4 km/s, was too low, its quoted error was too tight, and the community's confidence in it "can only hinder the progress in a subject". Essen's target is not any theory of light but the practice of quoting a probable error that conceals unexamined systematic error.
The methods surveyed
The measurement problem
Essen sets out the common structure first. All the determinations reduce to a measurement of distance and of a time interval, and the time intervals are far too short to be measured except by counting the regular vibrations of a tuning fork or quartz crystal against a frequency standard. He remarks on the leverage this gives: "the same proportional accuracy can be achieved in the measurement of a frequency of 1010 c/s ... as in the measurement of a frequency of 10−5 c/s". The measured quantity in a dielectric is v = c/√(με); in air √(με) exceeds unity by only about 3 × 10−4, so reduction to free space is easy for optical work, but in a cavity resonator the velocity is strongly affected by the apparatus and the free-space value must be extracted using electromagnetic theory. He therefore groups the methods as lumped electrical circuit, free wave, and guided wave.
Electrical circuit methods: the ratio of the units
More than twenty determinations were made by measuring the ratio of the electromagnetic to the electrostatic unit — historically an artefact of having defined charge and pole strength from Coulomb's Law and its magnetic analogue with the 4πε0 and 4πμ0 factors dropped. Essen quotes Maxwell's own 1868 introduction, which notes the ratio's importance "in the ordinary working of all submarine telegraph cables" before adding that the velocity of propagation of electromagnetic disturbances "according to my calculations is expressed by the very same number". Modern reading: the experiments measure 1/√(μ0ε0). The best of them, Rosa and Dorsey (1906), built capacitors as plates, spheres and cylinders whose capacitance could be computed from dimensions, measured them against resistance by a Maxwell bridge and a differential galvanometer, and combined this with the Lorenz determination of the absolute ohm — a metal disc rotated in the field of two coils of calculable mutual inductance. The observations spread over ±150 km/s but Rosa and Dorsey estimated a maximum uncertainty of ±30 km/s. Essen's judgement is that modern technique could reduce the random scatter but not the difficulty of constructing and computing the standards, so "it would not be easy to effect a worth-while improvement".
Free wave methods
Roemer and Bradley are early free-wave measurements but limited by observational error and by uncertainty in the distances. Galileo's shuttered-lantern attempt was, Essen says, sound in method and right in its surmise that light travels at a finite speed, and failed only on apparatus. Since a single transit cannot be timed, the experiments impose a periodic structure and look for a stationary effect: he gives the standing-wave analysis, with the resultant amplitude 2E cos 2π(z/λ + φ) × sin 2π(ft + φ) and nulls spaced λ/2, and then explains why this cannot be applied to light. Ordinary light sources are incoherent — short trains of random phase, which destroy the pattern — and although a Michelson interferometer circumvents that and reaches 2 parts in 108 on wavelength, "the second difficulty — that of measuring the frequency of light waves — has not yet been overcome."
The practical substitute is to chop the beam with a toothed wheel, rotating mirror, Kerr cell or vibrating quartz, and detect at the modulation frequency, giving c = 2d'f√(με)/(2n − 1) with a further correction because air is dispersive and the group velocity is what is measured. Essen's assessment of the most celebrated of these is unusually blunt. Michelson, Pease and Pearson (1935) used a mile-long evacuated pipe folded to a ten-mile path, but only 20 kc/s modulation, so their setting accuracy was no better than others'; the results showed "quite large unresolved systematic errors", and "in the circumstances it seems doubtful whether the use of an evacuated pipe was justified", since the total air effect is about 85 km/s and could have been computed to ±1 km/s from measured temperature, pressure and humidity. Their value, 299,774 ± 11 km/s, underpinned Birge's 1941 figure.
Bergstrand (1950) advanced the optical method decisively by combining 8 Mc/s modulation with a long path and superposing a 50 c/s square wave, producing two wave trains 180° out of phase and separated by 0.01 s, detected separately and balanced in opposition. This converted a flat minimum into a sharp zero, cut the spread to a few km/s, and gave 299,793.1 ± 0.25 km/s.
Radar is, Essen says, "perhaps the simplest in principle of all the methods": a pulse's round trip is read directly against a time base derived from a frequency standard. He reproduces a radar display from Jones and Cornford (1949) and describes the three systems used — Gee at 50 Mc/s, Oboe at 3000 Mc/s, Shoran at 300 Mc/s — all using a responder rather than a passive reflector. Aslakson's figure-of-eight flight technique, four crossings at 121° to the perpendicular, plus a plane flying the path to measure atmospheric conditions directly, supported a claimed ±2.4 km/s. A radio-wave Michelson interferometer at 3 cm or shorter, begun in Germany during the war and taken up by Culshaw at TRE and then the NPL, is described as promising but immature, its difficulty being that the wavelength is not negligible against the mirrors so diffraction corrections matter.
Essen flags a systematic trap peculiar to radio: the refractive index of water vapour at radio frequencies is much larger than that of dry air, unlike at optical frequencies, so humidity must be measured carefully. He and Froome had just measured the indices at 24,000 Mc/s and found Aslakson's assumed value slightly low and the British radar value "considerably too high, causing an error of 5 km/s in velocity" — and he recomputes the British results accordingly for his table.
Guided wave methods
Blondlot in 1891 measured wavelengths of 8 m and 35 m on Lecher wires by sliding a short-circuit reflector, obtaining 292,000 to 305,200 km/s. Mercier (1923), using continuous waves at 46–66 Mc/s on 11 m wires read by invar tape to 0.1 mm, obtained 299,575 km/s, becoming 299,782 ± 30 km/s in free space — "a remarkably careful piece of experimental work which seems however to have attracted little attention."
The cavity resonator is the same idea with a hollow tube. The phase velocity in a cylindrical guide exceeds c — by as much as 30 per cent at centimetric wavelengths — but is calculable from the frequency, the guide wavelength λg and the internal radius a through the Bessel-function cutoff condition, with a computable correction for field penetration into imperfectly conducting walls. Resonance can be set and measured to better than 1 part in 108. Essen describes the NPL apparatus of Essen and Gordon-Smith (1948) — "which first cast doubt on the accepted optical value of c" — and the later plunger-and-gauge-block version (Essen 1950), noting that using two resonance modes allows the effective diameter itself to be measured in terms of frequency, and that determining λg by differences between plunger positions cancels end effects. Bol's Stanford resonator calculated rather than eliminated the geometrical corrections, but was larger and lower in frequency, so surface imperfections mattered less.
Results
The tables collect the lot. From the ratio of the units: Weber and Kohlrausch 310,800 (1857) down through Maxwell's own 284,300 (1868) to Rosa and Dorsey 299,784 ± 30 (1906). By free wave: Roemer 300,000; Fizeau 315,300 ± 500; Foucault 298,000 ± 500; Michelson 299,802 ± 30 (1924) and 299,798 ± 4 (1926); Michelson, Pease and Pearson 299,774 ± 11; Bergstrand 299,793.1 ± 0.25; Aslakson 299,792 ± 2.4. By guided wave: Mercier 299,782 ± 30; Essen and Gordon-Smith 299,792 ± 3; Essen 299,792.0 ± 1; Bol 299,789.3 ± 0.4. Essen notes that Bearden and Watts, Stille and himself, weighing the evidence in different ways, all arrive at
- c = 299,790 km/s.
He closes on error reporting. Where the scatter is large, random error can be beaten down by repetition, but "in these circumstances it is impossible to make any experimental check of small systematic errors" — which is why both Birge and Dorsey, after careful study, landed on a value "which now appears to be considerably too low", and why Birge's ±4 km/s "appears to have given the radio engineer an altogether false impression of the accuracy of the optical results". His proposal is that limits be quoted in three parts: the standard deviation of individual observations, the systematic error from known causes, and an estimate of possible systematic error from causes not fully understood. The final observation is that the precision now reached turns these apparatus into instruments: "the velocity of light has therefore become a standard of measurement having applications in the field of metrology as well as those of electrical and radio engineering."
Assessment
This paper is sound on its own terms, and it is worth saying so plainly: it is a careful experimental review by the man who made the measurement that settled the question, and its judgements have held up. Essen's recommended value of 299,790 km/s sits 2.5 km/s — less than one part in 105 — below the value 299,792.458 km/s that was fixed by definition in 1983, and his own cavity-resonator result of 299,792.0 ± 1 km/s is closer still, well within its stated limit. His verdict that Birge's 299,776 ± 4 km/s was too low and too confident was correct, and his identification of the Michelson–Pease–Pearson experiment as impressive in scale but limited by a 20 kc/s modulation frequency and burdened with unresolved systematics is the assessment that has stood.
The methodological point is the more durable contribution, and it is the reason the paper still repays reading on a wiki devoted to scientific dissent. Essen's diagnosis is that the field went wrong not through fraud or incompetence but through a reporting convention: a "probable error" that quantifies scatter while saying nothing about the errors the experimenter has not thought of. The consequence he identifies — that a whole generation of radio engineers inherited a false impression of optical accuracy — is a clean case study in how a community can converge on a wrong number with high confidence. His three-part error proposal anticipates the modern separation of statistical from systematic uncertainty. It is also striking that the physicist who wrote this became, later in his career, one of the sharpest critics of the standard treatment of clocks and time in Special Relativity; the temperament on display here — insisting that a stated uncertainty be earned rather than assumed — is recognisably the same.
Two limitations are worth noting, neither of them faults in the work. The first is that Essen assumes at the outset, "in accordance with theory", that c is independent of frequency, and treats electrical, radio and optical determinations as measurements of one constant; this is a theoretical premise imported into an experimental review, and he says so honestly — "if there are discrepancies in the results then the theory must be re-examined; but so far no significant discrepancies have been found." The premise is what licenses the combined table, and a reader interested in dispersion of the vacuum will find that the paper's structure forecloses the question rather than testing it. The second is that the review does not engage the more interesting historical question raised by its own table: whether the drift of measured values — high in the 1850s, dipping through the 1930s, rising again after 1947 — reflects anything beyond changing systematics. Essen clearly takes the view that it does not, and his account of exactly which systematic error afflicted each of the low results (the air correction, the water-vapour index, the flat minimum) is the strongest available argument for that view. But he states it by demonstration rather than by argument, and readers who suspect a real variation in c will not find that hypothesis addressed here. What the paper does establish, thoroughly, is that the apparent stability of a published constant is no evidence at all about the size of its unexamined errors.