Determining the Speed of Light
The speed of light is one of the most important constants in physical science. In
addition to the basic role it plays in the theory of relativity, its value is required for
work in photonics, electronics, electromagnetism, quantum theory and nuclear
physics. For this reason, a great deal of time and energy has been devoted to its
determination.
Although its measurement has occupied many scientists from the time of Galileo to
the present day, it was the work of British physicist, Louis Essen, that led to the present
accepted value and the subsequent re-definition of the unit of length (metre) in terms
of the speed of light.
Louis Essen is better known for building the first operational atomic clock in 1955
but he was also aware that there was an urgent need for better long-range radionavigation aids at the end of the Second World War; and knowing the exact value of
the speed of light was as important as precise time measurement for determining the
location of an aircraft, ship or submarine.
Essen worked at the National Physical Laboratory, Teddington, UK (NPL) during
the war and his experience with radar and microwave devices, especially the cavity
resonator, enabled him to develop a non-optical method of measuring the speed of
light.
In 1946, he published a new value of the speed of light in vacuum (299,792 ± 3 km/
s) that was 16 km/s higher than the then accepted value. His findings caused a great
deal of controversy at the time and were not accepted for several years. I have
reproduced a part of my father-in-law’s memoirs below in which he describes how he
came to be involved in measuring the speed of light.
Ray Essen
Memoirs of Louis Essen
The exact value of the speed of light was needed during the Second World War for
microwave applications such as radar and aircraft radio-navigation systems. NPL
(Britain’s national measurement institute) occasionally received enquiries from people
working on radar who were concerned about the best value to use and the telephone
operators usually directed the callers to me.
At first, I gave the textbook value of 299,800 km/s or, if a higher accuracy seemed
appropriate, 299,776 ± 4 km/s, which was the value that Raymond Birge at the
University of California in Berkeley had derived in 1941 from a statistical appraisal of
earlier optical determinations.
These enquiries set me thinking about the speed of light and how accurately it was
actually known. My work with cavity wavemeters led me to believe that I could
measure its value with a higher accuracy than could be determined by optical
methods.
Albert A Michelson
The accepted value for the speed of light before the Second World War was based
largely on the results of Michelson and his co-workers in the USA, and particularly on
his last experiment made in 1935. This was performed with the encouragement and
support of international bodies; it was costly and widely publicised. One feature which
made it costly, and was thought to be in its favour, was that the light path was confined
in an evacuated pipe 1.6-km long to eliminate the effect of the refractive index of the
air which reduces the speed by about 0.03 percent. Previous measurements had all
been made in air and corrected for refractive index, which was calculated from the
atmospheric conditions at the time. The reviewers’ faith in the result was strengthened
by the fact that four subsequent determinations made by different scientists in different
countries were in close agreement with it.
A study of the original papers convinced me that the value was not nearly so well
established as was thought. The actual precision of measurement was low and the
results were an average of many, sometimes thousands, of individual measurements,
always an unsatisfactory procedure. The authors of these papers made no great claims
for the accuracy of their results and pointed out that unexplained discrepancies were
present.
Cavity Resonator Method
My experience made me confident that the speed of light could be obtained far more
accurately as well as far more simply by measuring the dimensions and resonant
frequency of a specially constructed microwave cavity wavemeter. The setting to
resonance is so precise that a single measurement would be more accurate than the
average of the large numbers taken in the optical determinations and the high
precision would make it possible to investigate and eliminate the effect of small
systematic errors.
In view of its importance in radio navigation I started a more systematic study of the
speed of light as a side-line to my normal duties. At the end of the Second World War,
NPL already had a full programme of work intended to assist in the recovery of
Britain’s industry and a new determination of the speed of light was not considered to
be of high priority. Consequently, I was initially obliged to undertake this work in my
spare time and no objections were raised. I devised an experimental method that
enabled me to assemble most of the necessary apparatus from old pieces of warsurplus equipment.
A visitor from the USA mentioned that William Webster (‘Bill’) Hansen at Stanford
University was contemplating a similar measurement. But it is no bad thing to
duplicate work of this kind and, although Hansen was one of the pioneers of cavity
resonator theory, NPL was better equipped on the technical side. We had then the best
frequency standards and microwave measuring experience in the world, a splendid
workshop where the resonator could be made and a metrology department where its
dimensions could be measured. All these facilities were situated in the same grounds
and collaboration between the staff was encouraged.
This last point proved to be most important. There was a slight discrepancy between
some of the metrological measurements which were discussed with the head of the
department. In the course of the discussions it occurred to him that there might also be
a systematic error. The internal diameter had been measured by their standard method
in which two small balls at the ends of the arms of a feeler gauge slide over the curved
surface. The pressure of the balls on the surface causes a slight depression that must be
corrected for, and as the gauges usually tested are all made from steel a standard
correction is included in the calculations. But our resonator was made of copper, a
softer metal, and a larger correction should be applied. His suspicions were correct and
a small but significant error was avoided through the close relationship between our
departments.
The frequency measurements were made with the help of Albert Gordon-Smith, a
skilled and meticulously careful experimenter. Our result, published in 1946, was 16
km/s higher than the accepted value, which was much more interesting than if it had
been confirmed. It did not surprise us but everyone else was very sceptical, even our
Director, who, while congratulating us on the work, suggested that we would no doubt
get the correct result when we had perfected the technique.
The radar establishments in the UK and the USA, who were the people most
concerned, continued to use the old value for several years showing that scientists can
get fixed ideas on poor evidence and refused to relinquish them. No result had been
published from Stanford but a report in a popular journal suggested that the result was
going to confirm the optical value. I was planning a visit to the USA at that time so our
Director suggested that I should go and see them. Unfortunately, I found that Hansen
was in hospital with pneumonia which proved fatal. His colleagues were not in a
position to give a value but later when it was published in a short note it was quite
near to the NPL result, being 3 km/s lower.
Revised Method of Measurement
There was now a post-war reshuffle of staff and I moved back to the Electricity
Division where, in 1950, I was able to repeat the speed-of-light measurement with a
different form of resonator. The weakest point of the first experiment seemed to be the
measurement of the dimensions. Apart from the metrological difficulty, it was known
that the electric and magnetic fields penetrated the surfaces of the cavity resonator
which increased the effective size of the metal cylinder. The penetration is zero for
perfect conductors but it is not negligible for copper (used in the first experiment)
despite it being one of the best conductors we have.
I calculated the correction factor from transmission-line theory but the computer
genius, Alan Turing who was then working at NPL, repeated the calculation elegantly
and rigorously for me from waveguide theory. I found later that it had been calculated
and published in a French journal. In any case, I managed to eliminate most of the
correction by a suitable design of cavity resonator. The length could be altered by a
piston and the wavelength found by the distance between two successive resonances,
thus eliminating the effect of penetration in the end faces. Then, by using a number of
different frequencies and different modes of resonance, it was possible to eliminate the
diameter from the calculations or, expressed differently, to measure the diameter in
terms of length and frequency. It was clearly a more complicated and difficult
experiment than before and I was fortunate in securing the help of our excellent
workshops and of Eric Hope, another skilled electronic expert to replace GordonSmith, whom I had lost in the move.
Another change I made – and I mention this to show how difficult it is to make the
right compromise – was to construct the resonator from steel, because being a harder
material it is easier to grind the diameter to an exact size and uniformity. Against this
advantage it is a poor conductor and, therefore, had to be silver-plated. We had been
assured that this could be done uniformly but the result fell short of our expectations
and it is doubtful whether there was any overall gain in changing from copper to steel.
The two ways of obtaining the diameter: (1) direct metrological measurement corrected
for skin penetration, and (2) indirect measurement from lengths and frequencies, were
in good accord and the final result agreed exactly with that obtained before with the
limit of error reduced to 1 km/s.
[The memoirs of Louis Essen are published in full in ‘The Birth of Atomic Time’ by Ray
Essen (ISBN: 978-178456-167-3), available from most online book sellers].
Postscript
In 1952 the speed of light in vacuum (denoted c0 or simply c), as measured by Essen,
was adopted by the Assembly of the International Union of Scientific Radiotelegraphy
(USRI), which recommended this value for all scientific work. In 1957 USRI and the
International Union of Geodesy and Geophysics (IUGG) endorsed USRI’s earlier
recommendation and adopted the value of 299,792.5 ±0.4 km/s.
In 1975, after further experimental results were available, the 15th General
Conference on Weights and Measures (CGPM) in Paris recommended a value of
299,792,458 m/s. Finally, on 21 October 1983, the 17th CGPM re-defined the metre in
the International System of Units (SI) as being “the length of the path travelled by light
in vacuum during a time interval of 1/299,792,458 of a second.” As a result, the
numerical value of the speed of light in vacuum is now fixed exactly by the definition
of the metre.