Faster-than-light - Justifications - Faster Light (Casimir Vacuum and Quantum Tunnelling)

Faster Light (Casimir Vacuum and Quantum Tunnelling)

Raymond Y. Chiao was first to measure the quantum tunnelling time, which was found to be between 1.5 to 1.7 times the speed of light.

Einstein's equations of special relativity postulate that the speed of light in a vacuum is invariant in inertial frames. That is, it will be the same from any frame of reference moving at a constant speed. The equations do not specify any particular value for the speed of the light, which is an experimentally determined quantity for a fixed unit of length. Since 1983, the SI unit of length (the meter) has been defined using the speed of light.

The experimental determination has been made in vacuum. However, the vacuum we know is not the only possible vacuum which can exist. The vacuum has energy associated with it, unsurprisingly called the vacuum energy. This vacuum energy can perhaps be changed in certain cases. When vacuum energy is lowered, light itself has been predicted to go faster than the standard value c. This is known as the Scharnhorst effect. Such a vacuum can be produced by bringing two perfectly smooth metal plates together at near atomic diameter spacing. It is called a Casimir vacuum. Calculations imply that light will go faster in such a vacuum by a minuscule amount: a photon traveling between two plates that are 1 micrometer apart would increase the photon's speed by only about one part in 1036. Accordingly there has as yet been no experimental verification of the prediction. A recent analysis argued that the Scharnhorst effect cannot be used to send information backwards in time with a single set of plates since the plates' rest frame would define a "preferred frame" for FTL signalling. However, with multiple pairs of plates in motion relative to one another the authors noted that they had no arguments that could "guarantee the total absence of causality violations", and invoked Hawking's speculative chronology protection conjecture which suggests that feedback loops of virtual particles would create "uncontrollable singularities in the renormalized quantum stress-energy" on the boundary of any potential time machine, and thus would require a theory of quantum gravity to fully analyze. Other authors argue that Scharnhorst's original analysis which seemed to show the possibility of faster-than-c signals involved approximations which may be incorrect, so that it is not clear whether this effect could actually increase signal speed at all.

The physicists Günter Nimtz and Alfons Stahlhofen, of the University of Cologne, claim to have violated relativity experimentally by transmitting photons faster than the speed of light. They say they have conducted an experiment in which microwave photons—relatively low energy packets of light—travelled "instantaneously" between a pair of prisms that had been moved up to 3 ft (1 m) apart. Their experiment involved an optical phenomenon known as "evanescent modes", and they claim that since evanescent modes have an imaginary wave number, they represent a "mathematical analogy" to quantum tunnelling. Nimtz has also claimed that "evanescent modes are not fully describable by the Maxwell equations and quantum mechanics have to be taken into consideration." Other scientists such as Herbert G. Winful and Robert Helling have argued that in fact there is nothing quantum-mechanical about Nimtz's experiments, and that the results can be fully predicted by the equations of classical electromagnetism (Maxwell's equations).

Nimtz told New Scientist magazine: "For the time being, this is the only violation of special relativity that I know of." However, other physicists say that this phenomenon does not allow information to be transmitted faster than light. Aephraim Steinberg, a quantum optics expert at the University of Toronto, Canada, uses the analogy of a train traveling from Chicago to New York, but dropping off train cars at each station along the way, so that the center of the ever shrinking main train moves forward at each stop; in this way, the speed of the center of the train exceeds the speed of any of the individual cars.

Herbert G. Winful argues that the train analogy is a variant of the "reshaping argument" for superluminal tunneling velocities, but he goes on to say that this argument is not actually supported by experiment or simulations, which actually show that the transmitted pulse has the same length and shape as the incident pulse. Instead, Winful argues that the group delay in tunneling is not actually the transit time for the pulse (whose spatial length must be greater than the barrier length in order for its spectrum to be narrow enough to allow tunneling), but is instead the lifetime of the energy stored in a standing wave which forms inside the barrier. Since the stored energy in the barrier is less than the energy stored in a barrier-free region of the same length due to destructive interference, the group delay for the energy to escape the barrier region is shorter than it would be in free space, which according to Winful is the explanation for apparently superluminal tunneling.

A number of authors have published papers disputing Nimtz's claim that Einstein causality is violated by his experiments, and there are many other papers in the literature discussing why quantum tunneling is not thought to violate causality.

It was later claimed by the Keller group in Switzerland that particle tunneling does indeed occur in zero real time. Their tests involved tunneling electrons, where the group argued a relativistic prediction for tunneling time should be 500-600 attoseconds (an attosecond is one quintillionth (10−18) of a second). All that could be measured was 24 attoseconds, which is the limit of the test accuracy. Again, though, other physicists believe that tunneling experiments in which particles appear to spend anomalously short times inside the barrier are in fact fully compatible with relativity, although there is disagreement about whether the explanation involves reshaping of the wave packet or other effects.