Re: DR.Ronald Mallett
In a recent paper by
Ken Olum and
Allen Everett[7] the authors claimed to have found problems with Mallett's analysis. One of their objections is that the
spacetime which Mallett used in his analysis contains a
singularity even when the power to the laser is off and is not the spacetime that would be expected to arise naturally if the circulating laser were activated in previously empty space. Mallett has not offered a published response to Olum and Everett, but in his book
Time Traveler he mentions that he was unable to directly model the
optical fiber or
photonic crystal which bends the light's path as it travels through it, so the light circulates around rather than moving in a straight line; as a substitute he chose to include a "line source" (a type of one-dimensional singularity) which would act as a "geometric constraint", bending spacetime in such a way that the light would circulate around on a
helix-shaped path in a vacuum
[8] (for an older solution involving an infinite cylinder which creates CTCs, in this case due to the cylinder's own rotation rather than light circulating around it, see the
Tipler cylinder). He notes that closed timelike curves are present in a spacetime containing both the line source and the circulating light, while they are not present in a spacetime containing only the line source, so that "the closed loops in time had been produced by the circulating flow of light, and not by the non-moving line source."
[9] However, he does not provide any additional argument as to why we should expect to see closed timelike curves in a different spacetime where there is no line source, and where the light is caused to circulate due to passing through a physical substance like a photonic crystal rather than circulating in a vacuum due to the curved spacetime around the line source.
Another objection by Olum and Everett is that even if Mallett's choice of spacetime were correct, the energy required to twist spacetime sufficiently would be huge, and that with lasers of the type in use today the ring would have to be much larger in circumference than the observable universe. At one point Mallett agreed that in a vacuum the energy requirements would be impractical but noted that the energy required goes down as the speed of light goes down. He then argued that if the light is slowed down significantly by passing it through a
medium (as in the experiments of
Lene Hau where light was passed through a
superfluid and slowed to about 17 metres per second) the needed energy would be attainable.
[10] However, the physicist
J. Richard Gott argues that slowing down light by passing it through a medium cannot be treated as equivalent to lowering the constant
c (the
speed of light in a vacuum) in the equations of General Relativity, saying:
[11]
One has to distinguish between the speed of light in a vacuum, which is a constant, and through any other medium, which can vary enormously. Light travels more slowly through water than through empty space, for example, but this does not mean that you age more slowly while scuba diving or that it is easier to twist space-time underwater.
The experiments done so far don't lower the speed of light in empty space; they just lower the speed of light in a medium and should not make it easier to twist space-time. Thus, it should not take any less mass-energy to form a black hole or a time machine of a given size in such a medium.
Later, Mallett abandoned the idea of using slowed light to reduce the energy, writing that, "For a time, I considered the possibility that slowing down light might increase the gravitational frame dragging effect of the ring laser ... Slow light, however, turned out not to be helpful for my research."
[12]
Finally, Olum and Everett note a theorem proven by
Stephen Hawking in a 1992 paper on the
Chronology Protection Conjecture,
[13] which demonstrated that according to General Relativity it should be impossible to create closed timelike curves in any finite region that satisfies the
weak energy condition, meaning that the region contains no
exotic matter with negative energy. Mallett's original solution involved a spacetime containing a line source of infinite length, so it did not violate this theorem despite the absence of exotic matter, but Olum and Everett point out that the theorem "would, however, rule out the creation of CTC's in any finite-sized approximation to this spacetime."
http://en.wikipedia.org/wiki/Ronald_Mallett
Typically I'm not too trusting of Wiki, but in this instance it's a good place to start.
