Speed of Light
The speed of light is a subject that has been
intensively studied over the last centuries: Today it is assumed to
be constant and is one of the basic physical constants.
Light is today understood as one from of electromagnetic energy.
We will start by considering a space free of matter, charges etc.
: the vacuum. The electromagnetic state of space is specified by
two vector fields the electrical field E and the magnetic
field H. In the static situation, when the fields do not vary
in time, the two fields are independent. However, when these two
fields are variable in time, in the dynamic situation, they influence
each other. A variation in the magnetic field will induce a change
in the electrical field and vice versa. Their interdependence has
been first properly described by James Clark Maxwell in the today
well kown Maxwell equations for the vacuum.
The two curl equation link the two vector fields and their time
derivatives. A change in the magnetic field will induce a curl of
the electric field. The equivalent is valid for a change in the
electric field. The divergence equations indicate the absence of
point charges in the vacuum. The divergence of the magnetic field
is always zero, because magnet monopoles do not exist in nature,
at least they have not been observed yet.
The constant mu is called the permeability of the vacuum. Its value
is defined to be 4pi 10^{7} henry per meter (Hm^{1})
The other constant epsilon is the permitivity of the vacuum is of
8.854187817... x10^{12} farads per meter (Fm^{1}).
These values, however, depend on the units used.
The two constants, mu and epsilon, are closely linked to the speed
of light. Maxwells equation can be decoupled. Combinig the curl
and divergence equations, using a little mathematical gymnastics
we find the a classical second order differential equation, known
as the wave or Laplace equation.
In the following tabel a nonexhaustive list of experimental determinations
of the speed of light is given to demonstrate the long history of
this scientific effort.
Date 
Experimenter 
Experimental technique 
Result (kms^{1}) 
Exp. uncertainty (kms^{1}) 

1676 
Römer 
eclipse of Jupiter moons 
214 459 
^{*}1 x 10^{5} 
1727 
Bradley 
abberation of light 
300 000^{*} 
^{*}1 x 10^{5} 
1848 
Fizeau 
rotating toothed wheel 
313 290 
5 x 10^{3} 
1850 
Foucault 
rotating mirror 
298 000 
2 x 10^{3} 
1857 
Weber & Kohlrausch 
electrical constants 
310 000 
2 x 10^{4} 
1868 
Maxwell 
electrical constants 
288 000 
2 x 10^{4} 
1875 
Cornu 
rotating mirror 
299 990 
2 x 10^{2} 
1880 
Michelson 
rotating mirror 
299 910 
1.5 x 10^{2} 
1883 
Thomson 
electrical constants 
282 000 
2 x 10^{4} 
1883 
Newcomb 
rotating mirror 
299 880 
3 x 10^{1} 
1901 
Perrotin 
rotating mirror 
299 777 
3 x 10^{1} 
1907 
Rosa & Dorsey 
electrical constants 
299 784 
1 x 10^{1} 
1923 
Mercier 
standing waves on wires 
299 782 
3 x 10^{1} 
1928 
Mittelstaedt 
Kerr cell shutter 
299 778 
1 x 10^{1} 
1932 
Pease & Pearson 
rotating mirror 
299 774 
2 x 10^{0} 
1940 
Hüttel 
Kerr cell shutter 
299 768 
1 x 10^{1} 
1941 
Anderson 
Kerr cell shutter 
299 776 
6 x 10^{0} 
1947 
Jones & Conford 
Oboe radar 
299 782 
2.5 x 10^{1} 
1950 
Bol 
cavity resonator 
299 789.3 
4 x 10^{1} 
1950 
Essen 
cavity resonator 
299 792.5 
2.5 x 10^{0} 
1951 
Bergstrand 
Kerr cell shutter 
299 793.1 
3 x 10^{1} 
1951 
Alsakson 
Shoran radar 
299 794.2 
2.5 x 10^{0} 
1952 
Froome 
microwave interferometry 
299 792.6 
7 x 10^{1} 
1972 
Evenson & Wells 
hetrodyn laser experiment 
299 792.456 2 
1.1 x 10^{4} 
^{*}these values are estimated. Sources used for the
for this page did not provide the exact value.Hints to find them
are welcome! The uncertainty in determination of the speed of light
based on astromic measurements are usually linked to the uncertainty
in the distance between sun and earth 
When looking at the table one not only notices the impressive improvement
in the experimental precision that has been achieved over the years.
It is even more important that the experiments lead to the same
result independent of the technique employed for the determination.
This further supports the idea that the speed of electromagnetic
waves is independent of the type of EM radiation used for the experiment.
The last experiment in the list, by Ken M. Evenson (19322002)
and Joe Wells from the National Institute of Standards and Technology in Boulder,
Co, has most likely been the last in a long series of determination
of the speed of light. In fact following Ken Evenson's experiment
the standard meter had to be redefined. The precision of time measurements
was much higher then the precision with which the meter could be
defined. Since the 17^{th }Conférence Générale
des Poids et Mesures in 1983 the meter is defined as the distance
light travels in 1/299 792 458 s, i.e. the speed of light has turned
in to a basic constant (c=299 792 458 ms^{1}) and the meter
has turned into the inverse of time (scaled by c). The odd number
for the speed of light was chosen to change the definition of the
meter as little as possible from the former value.
References:
 G.R. Fowles, Introduction to Modern
Optics, 2nd Ed.; Dover publiction New York, NY, (1989).
 G.Woan, The Cambridge Handbook of Physics Formulas,
Cambridge University Press, Cambrigre, UK (2000)

E. B. Rosa and N. E. Dorsey, A new determination of the ratio of the
electromagnetic to the electrostatic unit of electricity, Bull. Bur. Stand .3, 433604
(1907); A comparison of the various methods of determining the ratio of
the electromagnetic to the electrostatic unit of electricity, Bull. Bur. Stand. 3; (1907); 605622.
 L.Bergmann, C.Schaefer, Lehrbuch der Exp. Phys.;
Vol III, 7^{th} edition, DeGruyter (1978)
 D. B. Sullivan in http://nvl.nist.gov/pub/nistpubs/sp958lide/191193.pdf
 http://www.uark.edu/ua/pirelli/html/train_PW_CW.htm

K. M. Evenson, J. S. Wells, F. R. Petersen, B. L. Danielson, G. W. Day,
R. L. Barger, and J. L. Hall, Speed of Light from Direct Frequency and
Wavelength Measurements of the MethaneStabilized Laser, Phys. Rev. Lett. 29, (1972); 13461349
First published on the web: 10.11.2006.
Author: Thomas Nelis
