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Physics World

No thing goes faster than light

Aephraim M. Steinberg

Published Sep 1, 2000• 9 citations
Publisher

Abstract

Nothing can travel faster than light. Despite a recent raft of reports in the media, this statement is as true now as it ever was. Nonetheless, experiments over the past 20 years have been forcing us to re-examine what we mean by the word "nothing". In the latest experiment, a group of researchers at the NEC Research Institute in Princeton, US, observed the peak of a laser pulse leave a small cell filled with caesium gas before it had even entered the cell (L J Wang, A Kuzmich and A Dogariu 2000 Nature 406 277). Apparently, the peak of this pulse is simply not the kind of "thing" to which Einstein's famous law applies.

DOI
10.1088/2058-7058/13/9/23

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arXiv:physics/0209012•Sep 4, 2002•1 citation
Nothing can travel faster than light. Despite a recent raft of reports in the media, this statement is as true now as it ever was. Nonetheless, experiments over the past 20 years have been forcing us to re-examine what we mean by the word "nothing". In the latest experiment, a group of researchers at the NEC Research Institute in Princeton, US, observed the peak of a laser pulse leave a small cell filled with caesium gas before it had even entered the cell (L J Wang, A Kuzmich and A Dogariu 2000 Nature 406 277). Apparently, the peak of this pulse is simply not the kind of "thing" to which Einstein's famous law applies.
In two models it is shown that a light pulse propagates from a vacuum into certain media with velocity greater than that of a light in a vacuum (c). By numerical calculation the propagating properties of such a light are given. Recently L. J. Wang and his collaborators in their experiment [1] have found that the group velocity of a laser pulse in particularly prepared atomic caesium gas can much exceed that of light in a vacuum (c). Here we will explore the problem from a theoretical piont of view. Many years ago A. Sommerfeld rigorously proved [2] that the velocity of light pulse can not exceed c in absorption media. We call this conclusion as basic theorem afterwardz. In the following we will first examine why usually the basic theorem holds and in what condition it will be violated. Then two models are proposed, where with precise numerical calculation we will show that the basic theorem is indeed violated. Therefore the properties of light propagating in media of the models are given. We believe that these properties may appears in more realistic models. 1 Let a light pulse propagating along x axis toward its positive direction in a vacuum (x < 0), at time t = 0 arriving at x = 0, and then entering into a medium (x ≥ 0) afterwards. At x = 0, the amplitude of the light pulse changes with time t as ⎨ F(t) t ≥ 0 f(t) = ⎩ 0 t < 0. Usually f(t) can be rigorously expressed in Fourier integration as f(t) = Re A(n)e −int dn. (2) 0 For simplicity suppose there is no reflection of light at x = 0. The amplitude of the light pulse entering into the medium (x ≥ 0) is [2] f(t, x) = Re A(n)e −int+ikx dn, (3)
Peaceful coexistence For a hundred years, physicists trumpeted the celestial speed limit. Einstein has shown, they said, that nothing travels faster than light. But for a generation now, there has been stunning experimental evidence that hints that some mysterious influences are travelling faster than light. Contemporary physics rests on two great pillars. Einstein's theories describe the large-scale structure of space and time. Quantum theory describes the small-scale behaviour of matter within space and time: the behaviour of molecules, atoms and other particles. Roughly, one describes the container, and the other the contents. Although research continues, the two traditions are so much at variance that no one has been able to combine them into a single, unified theory or “theory of everything”. Quantum theory emerged piecemeal over many years and its development was driven by experimental results and mathematical guesses. Like most committee efforts, quantum theory was a patchwork of conflicting motivations and strategies. There is one central obstacle to unification: even today no one really understands quantum theory. For many years, relativity and quantum theory led a peaceful coexistence. The mysteries of quantum theory were dramatized by a series of paradoxes, but the theory worked very well and never threatened to contradict and overthrow its rival. But now things are changing. Recent experiments are revealing that quantum theory is even more strange than expected. Sometimes it appears as a great, conceptual black hole that sucks down into it every attempt to clarify the foundations of physics.
WHETHER we use it to estimate how far away a thunderstorm is, or simply take it for granted that we can have a conversation with someone on the other side of the world, we all know that light travels extremely fast. Indeed, special relativity teaches us that nothing in the universe can ever move faster than the speed of light in a vacuum: 2,99792,458ms -1 . However, there is no such limitation on how slowly light can travel. For the last few years, researchers have been routinely slowing light to just a few metres per second, and have recently even stopped it dead in its tracks so that it can be stored for future use.
In early 1999, a news article in the prestigious journal Nature led off with the announcement, "€œAn experiment with atoms at nanokelvin temperatures has produced the remarkable observation of light pulses traveling at velocities of only 17 m/s."€ The review continued with the understatement, "Observation of light pulses propagating at a speed no faster than a swiftly moving bicycle...comes as a surprise."€ These findings (and their review) marked the beginning of the current wave of interest in the field that has come to be called "€œslow light.â€" When we refer to "the speed of light," we typically mean c, the phase velocity of light in a vacuum, or the speed of propagation of the phase fronts of monochromatic light. The phase fronts travel more slowly through a material, propagating at the speed c/n, where n is the index of refraction of the medium. However, this ordinary slowing of the phase velocity is not slow light. "€œSlow light"€ and "€œfast light"€ refer to changes in the group velocity of light in a medium. A pulse of light can be decomposed mathematically into a group of monochromatic waves at slightly different frequencies, as in Fig. 19.1. In a dispersive material, these monochromatic waves travel at different speeds. When one views the propagation of the pulse as a whole, its apparent velocity depends on the extent of the spread of individual monochromatic-wave velocities. Each monochromatic wave travels at its own phase velocity, while the pulse travels at the group velocity. Of course, the group velocity of a pulse of light is not a new concept. The field of slow and fast light has drawn on theory and developments from the work of Sommerfeld and Brillouin from 1907 to 1914, experiments with early laser amplifiers in 1966, and other work done through the end of the 20th century. (For more of the history behind slow and fast light, see Refs. 8 and 9.)