Superluminal Motion: Fact or Fiction?
INTERACTION TIME THEORIES
Where velocity comes to the fore, is in the question of the time required for the barrier penetration to take place. How soon after incidence can an event, or a particle measurement, occur on the other side of the barrier? This time is known as the interaction or tunneling time. There are different theories of Quantum Mechanics. These theories are supposedly physically equivalent but suggest widely different answers.
Dilip K. Roy, in one of his many publications on the subject, defines this interaction time as the ratio between the barrier height and the energy of the particle. This definition is based simply on the Uncertainty principle which results from the mathematics of what is called a Fourier transformation. In the same definition, however, he makes a point not to assume the time is independent of the barrier width. This is because the probability for tunneling to take place at all depends directly upon this width. Wigner and Eisenbud, in an analysis of wave packet transmissions at Princeton in 1955, however, concluded that the tunneling time ould "reach a maximum beyond which it would stay the same no matter how thick the barrier". As quoted by Julian Brown, a science writer based in London, "this would imply that the effective tunneling velocity can ... increase without limit as the thickness of the barrier increases". Brown further notes that "although the probability of traveling through the barrier also falls off with increasing thickness, [according to Wigner and Eisenbud's theory] the few particle s that were able to pass through would do so without regard to Einstein's ultimate speed limit".
These promising statements, however, are only a few among a myriad of interaction time theories. In 1932, L. MacColl of Bell Laboratories stated, "when a particle tunnels through a barrier, it does so without any appreciable delay". According to Roy, "tunneling has sometimes been regarded to propagate with the speed of light...". Roy notes that the standard approaches on tunneling time "predict mutually contradictory estimates as regards tunneling time".
EXPERIMENTAL EVIDENCE
Aswith any theory, scientists require that an experiment be the ultimate source of information regarding the actual interaction time for a tunneling particle. But until recently, time measurement devices and experimental apparatus were not sufficient for the making of the precise measurements that these quantum mechanical experiments would require.
About ten years ago, Steven Chu and Stephen Wong at AT&T Bell Labs in New Jersey measured superluminal velocities for light pulses traveling through an absorbing material. In 1991, Anedio Ranfagni et al at the National Institute for Research into Electromagnetic Waves in Florence, Italy measured the speed of propagation for microwaves through a "forbidden zone" inside square metal w aveguides. The reported values were initially less than the speed of light, until the experiment was repeated in 1992 with thicker barriers. Also in 1992, Gnnter Nimtz and colleagues at the University of Cologne reported superluminal speeds for microwaves traversing a similar forbidden region.
In 1993. the most solid experimental evidence came from Chiao and his colleagues Aephraim Steinberg and Paul Kwiat at the University of California at Berkeley. Using the Hong-Ou-Mandel interferometer, they were able to measure the tunneling times of visible light. According to Brown, "the researchers found that the photons thattunneled their way through the optical filter arrived 1.5 femtoseconds sooner than the ones that traveled through air. The tunneling photons seemed to have traveled at 1.7 times the speed of light".
Similar experiments by Ferenc Krauss et al at the Technical University in Vienna in October of 1994 "strongly suggest that as they progressively increased the thickness of the barrier the tunneling time saturated toward a maximum value". In March of 1995, at a colloquium in Snowbird, Utah, Nimtz announced that he had sent a signal across twelve centimeters of space at 4.7 times the speed of light. The signal was a modulation in the frequency of his microwave source matching Mozart's 40th Symphony.
This announcement caused several respectable physicists to re-think the definition of a signal. Even Chaio and his colleagues were adamantly opposed to describing Nimtz' work as the sending of a signal.
IMPLICATIONS - SI6NALS AND CAUSALITY
Admittedly, however, Nimtz had sent something. Why was the bar of Mozart's symphony not a signal? The answer to this lies in the question of causality, and the concept of smoothly varying functions. If a wave packet's shape upon incidence is smooth and well- defined, it is a straightforward calculation to determine its shape after transmission. Because the final shape can be mathematically determined, the causality principle does not restrict the travel speed of the packet. Basically, since no useful information is being transmitted, it would not be possible to use the transmitted wave packet as a signal to shut off the original incident signal. Because of this, most scientists would not consider a smoothly varying function to be a signal. In fact, Choio and Steinberg were quick to point out that Nimtz' symphony was not a signal, but simply a smoothly varying pulse. It was predictable in its shape from the beginning. A sudden change in the shape would still travel at only fight speed, and only a sudden change, according to Chaio, could be regarded as a signal. As quoted by Brown, Chaio noted "Einstein causality rules out the propagation of any signal traveling faster than light, but it does not limit the group velocity of electromagnetic propagation". Other sources commenting on this idea of superluminal particle travel have similar conclusions. Landauer notes that "the few transmitted photons [in Chaio's experiment] arrive earlier than the velocity of light would allow . .. [however] that velocity is presumed not to represent the retardation between a cause and its effect". Though some scientists see hope of faster-than-light signal transmission with the work of Chaio, Nimtz, and others, there is much debate focused on the definition of a signal. The experiments conclusively show that music or photons can be sent faster than light, but only if a mathematical prediction of the results could be made in the first place. Most physicists still insist a "signal" is something which conveys unpredictable information, or that which would give rise to causality problems at superluminal velocities, but the results of the experiments are still astounding. "Einstein causality ... does not limit the group velocity of electromagnetic propagation", and with this, experimental verification of the existence of superluminal particle travel is found.
CONCLUSION
"Einstein causality rules out the propagation of any signal trawling faster than light, but it does not limit the group velocity of electromagnetic propagation."-Chaio
After considering the mathematical possibility of motion faster than light, we have concluded that Einstein Causality does not allow for the superluminal transmission of any useful information. In other words, one cannot send a signal backwards in time, ruling out all time travel and similar cause and effect disturbances. However, through the work of Chaio and other experimental physicists, conclusive evidence is given for faster-than-light transmission of smoothly varying functions such as that of a particle wave packet. This means that it is indeed possible for an object to have a velocity greater than that of light.