Causal Discussion of Superluminal Pulses

Recent observations of "superluminal" light pulses were widely reported in the news media. Some reports noted that the observations do not contradict Einstein causality, but others were misleading. For example, one began by announcing that "scientists have apparently broken the universe's speed limit." Another unfortunate circumstance has been a cavalier derision of the work by other physicists.

In his "What's New" column on the American Physical Society's Web site, Robert Park¹ asked, "Whoa, is this the old phase-velocity stuff that has confused generations of physics students?" No, it is not. It is the group velocity that is found to be greater than c (the speed of light in a vacuum). A month and a half later, Park said,¹ "Charles Bennett at IBM Watson points out that this is little more than a confused rehash of an old story, where the peak of the wavepacket leaving the 'superluminal' medium is causally related to just the leading edge of the wave packet entering the medium." I would like to offer a different perspective.

Generations of physics students have been assured that, when the group velocity is either greater than c or negative, a pulse will be so distorted that group velocity is no longer a meaningful concept. (The implication that there would otherwise be a conflict with special relativity is incorrect, because the group velocity is not a signal velocity.) But in 1982, experiments were reported² in which pulses passed through an absorbing medium with little distortion and with a group velocity that "exceeds 3 × 10¹⁰ cm/s, equals ± ∞, or becomes negative." During the 1990s, Raymond Chiao, Paul Kwiat, and Aephraim Steinberg studied faster-than-c effects in the tunneling of single-photon wavepackets.³ Their experiments answered longstanding, subtle questions about how long it takes for a particle to tunnel across a barrier.

The experiments by L. J. Wang and colleagues,⁴ which attracted much of the recent publicity, demonstrate that the peak of the exit pulse can emerge from an amplifying medium before the original peak enters it, and this can occur with essentially no amplification, absorption, or pulse distortion.

Rolf Landauer, Thierry Martin, and others discussed related phenomena in the early 1990s for particular types of wavepackets, and Gerhard Diener⁵ in 1996 presented an especially clear analysis and proof that causality is preserved. While the possibility of reconstructing the complete pulse from an infinitesimally small tail might be regarded as an old story, it is certainly worthy of further study, especially in connection with quantum noise. I suspect that many physicists would agree with Landauer's comments⁶ that "the easy explanation [that the whole transmitted wave comes from the front end of the much larger incident wave] is unsatisfying," and that "our understanding of this is not what it deserves to be."