Feb1-10, 10:43 PM
Can the Casimir effect be used to enable a finite length Tipler cylinder to allow for CTCs?
Stephen Hawking proved that a functioning Tipler cylinder could not be built unless it either (1) was infinitely long or (2) violated the weak energy condition, meaning that the region can contain no exotic matter with negative energy. However, if a Tipler cylinder could be built, it has been shown in a solution to the equations of general relativity to allow for the possibility of closed timelike curves (CTCs) via frame dragging (http://en.wikipedia.org/wiki/Tipler_cylinder).
Now, here's where I thought of the Casimir effect. Morris, Thorne and Yurtsever pointed out that the quantum mechanics of the Casimir effect can be used to produce a locally mass-negative region of space-time (http://en.wikipedia.org/wiki/Casimir..._and_wormholes).
Now, clearly the Tipler cylinder is an outcome of a solution to general relativity (as is frame dragging, which I'm not sure has been experimentally verified yet), whereas the Casimir effect is a well-established result in quantum mechanics. A mature, complete quantum theory of gravity might rule out even the theoretical possibility of a Tipler cylinder.
But assuming frame dragging really occurs in nature (and despite conclusive evidence there is no reason to believe that it doesn't), could a Tipler cylinder of finite length be constructed by somehow exploiting the fact that the Casimir effect can produce a locally mass-negative region of space-time (i.e. fulfilling the role for which some negative energy form of "exotic matter" might otherwise be required)? And if so, what, roughly, might this setup look like? Obviously if it would be possible to construct it is way beyond our technical capabilities at this time, but it is interesting to consider, and it is an area where general relativity and quantum mechanics sort of "collide".
Hope that all makes sense!
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