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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 non-exhaustive 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 105
1727 Bradley abberation of light 300 000*
*1 x 105
1848 Fizeau rotating toothed wheel 313 290
5 x 103
1850 Foucault rotating mirror 298 000
2 x 103
1857 Weber & Kohlrausch electrical constants 310 000
2 x 104
1868 Maxwell electrical constants 288 000
2 x 104
1875 Cornu rotating mirror 299 990
2 x 102
1880 Michelson rotating mirror 299 910
1.5 x 102
1883 Thomson electrical constants 282 000
2 x 104
1883 Newcomb rotating mirror 299 880
3 x 101
1901 Perrotin rotating mirror 299 777
3 x 101
1907 Rosa & Dorsey electrical constants 299 784
1 x 101
1923 Mercier standing waves on wires 299 782
3 x 101
1928 Mittelstaedt Kerr cell shutter 299 778
1 x 101
1932 Pease & Pearson rotating mirror 299 774
2 x 100
1940 Hüttel Kerr cell shutter 299 768
1 x 101
1941 Anderson Kerr cell shutter 299 776
6 x 100
1947 Jones & Conford Oboe radar 299 782
2.5 x 101
1950 Bol cavity resonator 299 789.3
4 x 10-1
1950 Essen cavity resonator 299 792.5
2.5 x 100
1951 Bergstrand Kerr cell shutter 299 793.1
3 x 10-1
1951 Alsakson Shoran radar 299 794.2
2.5 x 100
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 (1932-2002) 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 re-defined. The precision of time measurements was much higher then the precision with which the meter could be defined. Since the 17th 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:

  1. G.R. Fowles, Introduction to Modern Optics, 2nd Ed.; Dover publiction New York, NY, (1989).
  2. G.Woan, The Cambridge Handbook of Physics Formulas, Cambridge University Press, Cambrigre, UK (2000)
  3. 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, 433-604 (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); 605-622.
  4. L.Bergmann, C.Schaefer, Lehrbuch der Exp. Phys.; Vol III, 7th edition, DeGruyter (1978)
  5. D. B. Sullivan in http://nvl.nist.gov/pub/nistpubs/sp958-lide/191-193.pdf
  6. http://www.uark.edu/ua/pirelli/html/train_PW_CW.htm
  7. 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 Methane-Stabi-lized Laser, Phys. Rev. Lett. 29, (1972); 1346-1349

First published on the web: 10.11.2006.

Author: Thomas Nelis