Figure 1
Posted on 01/24/2002 8:55:55 AM PST by vannrox
No thing goes faster than light
Physics in Action: September 2000
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.
Long-held theories
| Figure 1 |
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.
Experimental breakthroughs
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.
 Figure 2 |
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
Another simple numerical technique applicable to differential equations is the Monte Carlo method -- which once again does not involve integrals in any sense.
Ridiculous. That is only an apparent motion caused by the Earth's rotation. The gravitational potential experienced by the Earth does not depend upon how fast it is rotating.
Let's suppose that the Earth rotated once every 16 minutes. Do you really suppose that the Earth would be flung away from the sun, because the sun's "apparent" position was 180 degrees out of phase?
Or Hillary heading for campaign money?
...so goes the *theory*.
LOL.
Sorry guy but you're not making much sense. It sounds like you're well meaning, but the more you try to explain away these problems the more it sounds like you're grasping for straws. Presumably you have studied Quantum Field Theory at the graduate level -- everything I have stated would seem quite obvious. I'm certainly no expert but this is all pretty basic.
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?
The sun travels about 2 degrees across the sky in 8 minutes.
Understood.
Thus the sun appears 2 degrees from where it actually is in the sky.
What do you mean where it "really is"? The whole point of relativity is that there is no absolute position apart from what we observe.
If gravity propagated at C, the earth would be trying to orbit around *that* point, not the *real* sun.
If gravity propagated at C there would be no "real" sun at some seperate location from the observed sun.
Several hundred years of math has shown that this leads to unstable orbits.
Only because this argument falsely assumes there is some "real" location different from the observed location. Assuming there is some "real" location for the sun where gravity is concerned, apart from the location we observe, presupposes the conclusion that gravity propagates instantaneously. It therefore isn't evidence for it.
Since the mass of a particle increases as it approaches c, perhaps a very sensitive gravity wave detector placed near a powerful particle accelerator could detect the gravity from a pulse of these briefly massive particles.
OK, I was only assuming your 2 degrees was right, I don't know what it is.
Here is a typical definition.
"The Monte Carlo method provides approximate solutions to a variety of mathematical problems by performing statistical sampling experiments on a computer. The method applies to problems with no probabilistic content as well as to those with inherent probabilistic structure. Among all numerical methods that rely on N-point evaluations in M-dimensional space to produce an approximate solution, the Monte Carlo method has absolute error of estimate that decreases as N superscript -1/2 whereas, in the absence of exploitable special structure all others have errors that decrease as N superscript -1/M at best."
It is a statistical method and does *NOT* involve, "finding the minimum energy for a term, or sum."
Are you just making this up as you go along?
Once again the "conceptual equivalent of an integration" is not the same thing as an integral. There will not exist any integrals in this solution.
USING THE MONTE CARLO METHOD YOU WOULD NEVER GET AN EXPANSION OF INTEGRAL TERMS WITH CORRESPONDING FEYNMAN DIAGRAMS.
Try to think it through more carefully and reply to what has been emphasized above.
Huh? You've got it backwards. There are no physical interactions "proposed in the theory". The so called physical interactions are a shorthand picture language for describing the integrals.
Actually, I should point out that what you state above does not even make sense. What "physical interactions" are proposed in the theory? The "theory" consists of expanding out a perturbation series used in solving the original QFT equations.
"Feynman diagrams describe point-like interactions; there is only one diagram for e+ e- annihilation to a photon (one vertex, three legs). Remember Feynman diagrams are only tools to represent rather complex integrations - the physics is the physics we get from the Universe, the math is the modelling (QM, perturbation theory, Hamiltonian, integration), the Feynmen diagram is the mnemonic."
But that argument is flawed for the same reason. Let's suppose there are two points along Earth's orbit, A and B. The Earth passes from point A to point B at some angular velocity, and you assert that there will be problem caused by the size of this angular velocity.
Now let's suppose that there's another mass travelling along the Earth's orbit, but travelling at a much smaller angular velocity. (Now, don't get hung up on the fact that this isn't a possible orbit. I'm supporting this mass by dangling it from a long, massless chain hanging off the planet Neptune, so there.) Here's the key: the gravitational potential caused by the sun at points A and B is exactly the same for both the Earth and the dangling mass. It's a function of where the sun is in relation to points A and B, and not at all a function of how fast the Earth or the dangling mass move.
The only way the speed of gravity enters into the equation is if the sun undergoes an acceleration with respect to points A and B, in which case the change in the field propagates at the speed of light.
Here's something else to consider: if your argument worked for gravity, it would also work in exactly the same way for electromagnetism. The motions of electrons around the atomic nucleus would be unstable for the same reason, only it would be far more pronounced because the electrons move at more relativistic velocities. But in spite of the measurably finite speed of light, the motions of the electons are exquisitely stable.
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