Can a Computer be "Pushed" to Perform Faster-Than-Light?

We propose to “boost” the speed of communication and computation by immersing the computing environment into a medium whose index of refraction is smaller than one, thereby trespassing the speedof-light barrier. The Church-Turing and the Cook-Karp theses, as well as other, more general limits on computation, are under permanent “scrutiny” [cf. e.g., Davis (1958, p 11) or Deutsch (1985, p. 5)] by the physical sciences. Some recent issues which have been raised comprise Zeno-squeezed accelerated time scales (Weyl, 1949; Hogarth, 1992; Durand-Lose, 2005; Németi & Dávid, 2006; Svozil, 2009) enabling the construction of “infinity machines” capable of hypercomputation (Davis, 2006; Doria & Costa, 2006; Ord, 2006), counterfactual computation (Mitchison & Jozsa, 2001) and cryptography (Noh, 2009) based on quantum counterfactuals (Elitzur & Vaidman, 1993; Vaidman, 2007), as well as the dissipation limits to computation (Leff & Rex, 1990). Here we shall consider the possibility to speed up optical (Chiao & Milonni, 2002) computations and communication by transgressing the speed of light barrier in vacuum. Note that, although the speed of light barrier