lightspeeds.RdContains historical determinations of the speed of light from many studies from Fizeau's toothed wheel in 1849, to determinations using stabilized lasers in 1983. Methods, year of study, authors, information on mechanisms used, as well as other remarks are recorded. The estimated speed of light is recorded for each study as well as the authors' determination of the error of their measurement.
The data are of particular value since in 1974 the speed of light was defined to be 299,792.458 kilometres per second (in vacuo). The data therefore provide a rare case where the `true value` is known.
Also, the values might be grouped by the different methods were used over time to estimate the speed of light. In this way, the data provide a useful case study to discuss methods of meta-analysis as well.
A data frame with 81 rows and 11 variables
The general method used to determine the speed of light (see details for more on this).
Year in which the determination was made.
First researcher named as conducting the study (surname, or prefixed with initials if surname not unique).
Second researcher named, if any.
Third researcher named, if any.
Fourth researcher named, if any.
Type of mechanism used (see details below).
More detail on mechanism used (see details below).
Remark on some detail of the study or method used.
The determined speed of light in air in kilometres per second.
The error of the estimate (in km/second) as reported by the researchers (see details below).
The row order of the values follow their order of appearence in the paper given as reference below.
See reference for details.
On the meaning of the error variable, from the reference:
"This error is rarely a standard deviation. Nor is it based solely on measurements taken
in the study. Instead, it is a number out together bt the researchers from a number
of possible sources and is very subjective. It is not uncommon for subsequent researchers
to examine in detail the results of a given study and to arrive at a different value
of the error. Finally, physicists are accustomed to reporting the probable error which
can be interpreted as approximately 0.6745 times the standard deviation of the estimate."
On the meaning of variables related to method, also from the reference:
Optical: These methods are based on having a light beam leave a source, strike a rotating
mirror or pass through the spaces of a toothed wheel, travel some considerable distance to
be reflected back (again striking the rotating mirror or passing through the spaces of a
toothed wheel) to near the original soource. The speed of rotation must be just right and
is used in the determination of the speed of light. Precision of estimation could ve increased
by increasing the distance the light had to travel (from source to stationary mirror and back) or
by increasing the speed of rotation.
Electrical: This method is introduced after the electromagnetic theory of light was developed.
Light could now be thought of as electromagnetic radiation. As such measures of the speed of any
electromagnetic radiation in vacuo would also be legitimate measures of the speed of light (in vacuo).
Moreover the ratio of electrostatic to electromagnetic units of measurement of electrical quantities could
be taken to be measurements of the speed of light.
Electro-optical: These are based largely on the same principle as the toothed wheel in optical
methods which effectively use a mechanical shutter to switch light on and off.
With the electro-optical methods, non-mechanical shutters are used to much more rapidly (and
in a more finely controlled way) alternate the light and so increase the precision.
The Kerr cell consists of two electrodes immersed in a liquid like nitrobenzene. When high
voltage is applied to the electrodes, the polarity of light passing through the cell changes
from planar to elliptical. Switching between high and low voltage effects the shutter.
The quartz modulator passes sound waves through a crystal to change its refractive index.
An acoustic frequency can be found to produce a diffraction grating for light passing through the
crystal; double that frequency and the diffraction grating dissappears. Switching between the two
frequencies produces the shutter effect.
Radio wave: Understanding light to be electromagetic radiation also means that radio waves can
be used in place of visible light to make measurements of its speed.
Radar sends a short pulse of high frequency radio waves from a source to a distant object and
measures the time taken to receive the reflected wave from the distant object. Knowing the
actual distance allows a determination of the speed of the radio wave (or light).
The cavity resonator sends high frequency radio waves down a hollow cylinder sealed at both ends.
The cylinder resonates if its length is a whole number multiple of the half-wavelength of the
radio wave. The speed of light (in the medium within the cylinder or cavity) can be determined
from the dimensions of the cylinder (cavity).
Geodetic: These are improvements on the Kerr cell technology to make it capable of measuring
geodetic distances. The resulting (commercial) instrument was called a Geodimeter. With known
distances these instruments could be turned around to be used to provide measures of the speed of
light. The Tellurometer was another instrument invented to determine geodetic distances.
The principal difference between it and the Geodimeter is that it used microwave radiation to
carry the signal.
Spectroscopy: Bombarding molecules with electromagnetic radiation causes them to
absorb enough energy to change various states.
Bombarding molecules with microwave radiation changes their
rotational state, with infra-red radiation their vibrational state. Quantum theory
allows the measurement of these to changed states to be turned into a determination of the
speed of light. Different studies bombarded different molecules.
Ultrasonic modulation: This method can be regarded as an improvement on the quartz modulator.
Instead of acoustic waves on a crystal, a diffraction grating is produced with ultrasonic waves
in a liquid. Turning the diffraction grating on and off produces the shutter.
Interferometry: A single source light bean is split in two. Each travels some distance, is
reflected, and returns to the source. The two are made to travel different distances and
the amount by which they are out of phase with one another upon return, together with the
difference in distances travelled, can be turned into a measure of the speed of light.
Instead of visible light, radio waves or micro waves were used.
Stabilized lasers: In interferometry there can be some uncertainty in the measure of the
wavelengths used. With stabilized lasers using a technique called sub-Doppler saturated
absorption spectroscopy it became possible to fix the frequency (and hence the wavelength)
of some lasers within a very narrow range of the electromagnetic spectrum. Such lasers are
called stabilized lasers and have nice short wavelengths (micrometres) that allow more precise
measurements of the speed of light.
R.W. Oldford 1994, `The speed of light: A case study in empirical problem solving`, Unpublished manuscript. <doi:10.13140>
R.W. Oldford