Group Velocity Is Not Signal Velocity

August 2003, page 14

Recently, I have seen an increasing number of papers in which scientists claim to have proven extraordinary phenomena by applying the concept of group velocity to the anomalous dispersion of waves. Two of the greatest wave theorists of all time, Arnold Sommerfeld and Léon Brillouin, have dealt with the subject.

In separate papers, Sommerfeld and Brillouin wrote that, in anomalous dispersion, the group velocity cannot be the signal velocity.¹ Indeed, in anomalous dispersion, the group velocity goes through both negative and positive infinite values. It also goes through values greater than the speed of light² (as does the phase velocity).

References

1. A. Sommerfeld, Annalen der Physik 44, 177 (1914); L. Brillouin, Annalen der Physik 44, 203 (1914). For a lucid English-language digest of the two papers, see ref. 2, p. 334.
2. J. A. Stratton, Electromagnetic Theory, McGraw-Hill, New York (1941), p. 339, _1fig. 63.

Max J. Lazarus

(m.lazarus@lancaster.ac.uk)

University of Lancaster

Lancaster, England

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Group Velocity Is Not Signal Velocity

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