No thing goes faster than light

The observation of a light pulse leaving a gas-filled chamber before it had even arrived sparked a media frenzy, yet the laws of physics have remained intact.

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.

At almost 300 000 km s¹, the cosmic speed limit, c, is one of the most widely known constants in physics. A massive object needs infinite energy to reach c, while massless particles like photons always carry their energy at precisely the speed of light. More importantly, the relativistic notion of simultaneity makes it clear that no information can travel faster than light without throwing all our concepts of cause and effect into disarray. Relativity teaches us that if two spacetime events are separated so that they cannot be connected by any signal travelling at c or less, then different observers will disagree as to which of the two events came first. Since most physicists still believe that cause needs to precede effect, we conclude that no information can be transmitted faster than the speed of light.

Nevertheless, velocities greater than c can be observed. Suppose a lighthouse illuminates a distant shore. The rotating lamp moves quite slowly, but the spot on the opposite shore travels at a far greater velocity. If the shore were far enough away, the spot could even move faster than light. However, this moving spot is not a single "thing". Each point along the coastline receives its own spot of light from the lighthouse, and any information travels from the lighthouse at c, rather than along the path of the moving spot. Such phenomena are described as the "motion of effects", and are not forbidden by relativity.

In optics, the possibility of superluminal velocities was with us throughout the 20th century. The overall velocity (or "group velocity") of an optical pulse passing through a medium is determined by the way the refractive index varies for the different frequencies that make up the pulse. Since the peak of the pulse occurs when all the frequencies add up in phase, the peak can be delayed by a large amount if each component experiences a very different refractive index (see figure 1a).

When the energy of the optical pulse differs from the energy difference between two electronic energy levels in the atoms of the medium (i.e. when the light is far from resonance), the refractive index increases with frequency. This "normal" dispersion reduces the group velocity below c. Roughly speaking, an atom may temporarily absorb a photon, even though the light is not exactly at resonance, and re-emit it some time later, thus slowing down the light.

However, the behaviour of the light pulse is very different closer to the absorption line, where the refractive index decreases with increasing frequency. This behaviour leads to so-called anomalous dispersion in which the sign of the delay changes, which means that the group velocity can exceed c. This problem was treated in a classic analysis by Arnold Sommerfeld and Léon Brillouin, who pointed out that the strong absorption and distortion that occur at the resonant frequency generally make the group velocity a meaningless concept. They demonstrated that neither information nor energy can travel faster than light in this region. Throughout most of the 20th century, this was usually accepted as the last word on superluminal group velocities.

However, the field was revived in 1970 by Geoffrey Garrett and Dean McCumber, then both at Bell Laboratories in the US. They showed that it should be possible to observe an undistorted Gaussian pulse with a group velocity exceeding the speed of light, or even with a negative group velocity, provided the pulse has a narrow bandwidth and the region though which it travels is short. This effect was dramatically confirmed in an experiment by Steven Chu and Stephen Wong, then also at Bell Labs, in 1982 (Phys. Rev. Lett. 48 738).

Although Sommerfeld and Brillouin's conclusion that neither energy nor information travels faster than c remains valid, the group velocity is not entirely meaningless. The smooth Gaussian waveform is reshaped by the absorber, leading to a peak at precisely the time predicted by the group velocity. As for the energy, most of it is absorbed by the medium, and the sensible conclusion is that the transmitted energy comes from the leading edge of the incident pulse, which never travels faster than the speed of light.

Conventional wisdom slowly began to adapt to the idea that superluminal group velocities need not imply that the pulses are extremely distorted, as long as most of the energy in the pulse is absorbed. This absorption makes it possible for the velocity of the energy propagation, like the velocity of the information, to remain less than the speed of light regardless of the superluminal speed of a peak.

Over the past ten years, similar superluminal effects have been studied in connection with quantum-tunnelling experiments. In such experiments, the transmitted energy is once again quite small (R Y Chiao and A M Steinberg 1997 Progress in Optics XXXVII 347).

In contrast, the NEC team creates a region of anomalous dispersion in a nearly transparent medium. Wang and co-workers do this by pumping energy into the caesium vapour to create a kind of optical amplifier. First a laser is used to pump most of the caesium atoms into a particular spin state. Next, two additional pump lasers are used to lend energy to the atoms. These atoms can amplify light from yet another "probe" laser by making an electronic transition in which they absorb "pump" energy and re-emit it into the probe beam. There are two specific frequencies at which such a probe can be amplified in this way. By replacing absorption with amplification, the NEC team can swap the regions of normal and anomalous dispersion (see figure 1b). A region halfway between the two amplification lines appears where there is little loss, amplification or distortion. Here the group velocity becomes negative and nearly constant. Indeed, Wang and co-workers measured a group velocity of c/310. In other words, a pulse travelling a distance, L, is advanced by 310L/c.

The meaning of a negative group velocity is illustrated in figure 2. Within the cell, the peak of the pulse travels backwards relative to the direction it is moving in outside the cell. Long before the incident light pulse reaches the cell, two peaks appear at the far end: one travelling away from the cell at c, the other travelling back towards the entrance. This second pulse travels 300 times more slowly and is timed to meet up with the incident peak. The transmitted pulse travelling at c appears to leave the cell some 60 ns before the incident pulse arrives, enough time for it to travel an additional 20 metres.

What is shocking is that such an effect has been observed for the first time without a great deal of attenuation, amplification or distortion of the pulse. It appears as though energy has, in fact, travelled faster than light.

Of course, this is not the case. The effect observed at NEC only works in the presence of an amplifying medium, i.e. a medium that stores energy. In this case the energy is stored in the pump-laser beams. The caesium atoms are prepared in a state that allows them to transfer energy from these beams to the signal beam. The faster-than-light propagation occurs because the pump beams preferentially amplify the leading edge of the incident pulse, lending power to the signal and being repaid by absorbing some of the energy in its trailing edge. (It is important to note that even the dramatic 60 ns advance is only one fiftieth of the width of the pulse.) This is exactly analogous to the intuitive explanation of normal dispersion, except that in this case the atoms temporarily amplify the light pulse rather than absorb it.

A fascinating suggestion is that this experiment might work even for a pulse composed of only a single photon. However, there has been a good deal of controversy over how to discuss the information transmitted through such a system by a single-photon pulse, and many subtle issues remain.

Although relativity emerges unscathed from these experiments, our understanding of exactly which velocities are limited (or not) by c continues to evolve. And even though neither energy nor information is transmitted faster than light in experiments like the one at the NEC, it has already been proposed that the effects may one day be useful in compensating propagation delays in electronic systems.

For the time being, physicists will kept be busy trying to clarify their intuition about relativity and learning how to accurately describe the information carried in real optical or electronic pulses.

Author
Aephraim M Steinberg is in the Department of Physics, University of Toronto, Canada

I do agree with you, but I don't think it was a scientist that said it. For the life of me I don't recall who it was. It could have been a politician for all I can remember.
It is akin to the gentleman who was Head of the U.S. Patent Office in 1927 (I think) who said, "Everything that can be invented, has been invented."
I was only pointing out that it is ridiculous to speak in absolutes considering Man's record of achievement.

The theoretical equations themselves are differential equations. Their sol'n involves solving an integral by whatever method.

Eulers method is a simple method of numerically solving differential equations that does not involve an integral in any sense.

Eulers Method

I apologize. I went back and read my original reply # 27 and I got it wrong.
The quote I remember was "Man will never be able to travel faster than the speed of sound."
I misquoted the quote, and when the opportunity presents itself, I will attempt to find the source.

So basically, to get from one side of the univers to the other using a worm hole, the universe would have to be spherical? You would have to be able to bend two points in space to the point that they are right next to each other?

OK, but the belief that "man" would never travel faster than sound had a purely technological basis. Propeller driven aircraft can't reach the speed of sound for theoretical reasons, rockets seemed hopelessly unreliable, and jet aircraft required major redesign.

The speed of light is not just a barrier. It will not be overcome unless our understanding of physics is overturned.

I might add that Newton's laws of gravity quickly ran into problems with observed data -- the orbit of Mercury, for example. No such observational hiccups exist for the speed of light.

I'm quite familiar with numerical solutions to diffeqs. They are used to find particular solutions where it's difficult, or impossible to find a closed form solution, or they are used in automated computer controls. At any rate any numerical method amounts to finding the value of a particular solution, an antiderivative, an area, or integral. Study Euler's method again, it finds the area under the unknown curve y with the initial conditions and knowledge of y^'.

I was just kidding around. We are all friends here. I am truly sorry if I offended you or anyone else with my (oftentimes tacky) sense of humor. Take care, God bless, and have a wonderful rest of the day.

Where we see the Sun to be does not matter; it's where the sun actually is that matters in orbital dynamics. And if the "speed of gravity" is the same as the speed of light, the apparent mass of the sun will be about 2 degrees off from where the earth is trying to orbit around. In very short order the orbit will go chaotic.

I think this assumes the conclusion. If the speed of gravity propagates at the speed of light then why would the earth try to orbit 2 degrees off? Why wouldn't it orbit around where the sun appears to be?

"No such observational hiccups exist for the speed of light. "

Except maybe for a gravity lens. I know that a sufficient gravitational field can alter the path but can it alter the speed?
Isn't it a logical argument that if light can be slowed down by some outside force, then it can be sped up by some outside force? Just postulating.

At any rate any numerical method amounts to finding the value of a particular solution, an antiderivative, an area, or integral.

Finding the numerical solution of an equation is not the same thing as finding the value of an integral.

Study Euler's method again, it finds the area under the unknown curve y with the initial conditions and knowledge of y'.

No it does not. Eulers method works by *approximating* the area under a curve. Eulers method does not involve integrals in any sense. Without the existence of definite integrals in this numerical solution the corresponding feynman diagrams just would not arise.

What do you think?

I think I'll have another beer.

Ask Edwin Hubble, he'll know the answer.

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