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Superluminal Transmission

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Definition: transport of some quantity with a velocity exceeding that of light in vacuum

German: Übertragung mit Überlichtgeschwindigkeit

Categories: general optics, physical foundations

How to cite the article; suggest additional literature

Under certain circumstances, light can propagate with a phase velocity or group velocity greater than c, the vacuum velocity of light. At a first glance, this may suggest the possibility of superluminal transmission of information – in striking contradiction with Einstein's theory of relativity, which shows that superluminal transmission would be associated with a violation of causality. However, careful inspection of the accepted physical theories (in particular, of Maxwell's theory of electromagnetism, Einstein's theory of relativity, and quantum electrodynamics) shows that these definitely do not allow any non-causal effects. Any attempt to demonstrate such effects on the basis of these theories must fail for logical reasons and is thus based on fundamental misconceptions, although the flaw may not always be easy to identify.

Two relatively simple examples of apparently (but not really) non-causal transmission are given here:

Of course, it is conceivable that the currently accepted physical theories, e.g. Einstein's theory of relativity, will have to be revised or replaced with newer theories, possibly even allowing for superluminal propagation. Such theories exist already, but so far there is no convincing evidence that could support the withdrawal of relativity in the favor of an alternative theory.


[1]A. Sommerfeld, “Ein Einwand gegen die Relativtheorie der Elektrodynamik und seine Beseitigung”, Phys. Zeitschr. 8, 841 (1907)
[2]C. G. B. Garrett and D. E. McCumber, “Propagation of a gaussian light pulse through an anomalous dispersion medium”, Phys. Rev. A 1 (2), 305 (1970)
[3]S. Chu and S. Wong, “Linear pulse propagation in an absorbing medium”, Phys. Rev. Lett. 48 (11), 738 (1982)
[4]A. M. Steinberg and R. Y. Chiao, “Dispersionless, highly superluminal propagation in a medium with a gain doublet”, Phys. Rev. A 49 (3), 2071 (1994)
[5]D. Mugnai et al., “Observation of superluminal behaviors in wave propagation”, Phys. Rev. Lett. 84 (21), 4830 (2000)
[6]L. J. Wang et al., “Gain-assisted superluminal light propagation”, Nature 406, 277 (2000)
[7]M. D. Stenner et al., “The speed of information in a ‘fast-light’ optical medium”, Nature 425, 695 (2003)
[8]M. S. Bigelow et al., “Superluminal and slow-light propagation in a room temperature solid”, Science 301, 200-202 (2003)
[9]M. D. Stenner et al., “Fast causal information transmission in a medium with a slow group velocity”, Phys. Rev. Lett. 94 (5), 053902 (2005)
[10]H. Jeong et al., “Direct observation of optical precursors in a region of anomalous dispersion”, Phys. Rev. Lett. 96 (14), 143901 (2006)
[11]J. D. Jackson, Classical Electrodynamics, Wiley, (1998)

(Suggest additional literature!)

See also: velocity of light, phase velocity, group velocity, causality
and other articles in the categories general optics, physical foundations

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