Casimir Forces: An Exact Approach for Periodically Deformed Objects

A novel approach for calculating Casimir forces between periodically deformed objects is developed. This approach allows, for the first time, a rigorous non-perturbative treatment of the Casimir effect for disconnected objects beyond Casimir's original two-plate configuration. The approach takes into account the collective nature of fluctuation induced forces, going beyond the commonly used pairwise summation of two-body van der Waals forces. As an application of the method, we exactly calculate the Casimir force due to scalar field fluctuations between a flat and a rectangular corrugated plate. In the latter case, the force is found to be always attractive.Comment: 4 pages, 3 figure

A Hypercomputation in Brouwer's Constructivism

In contrast to other constructivist schools, for Brouwer, the notion of "constructive object" is not restricted to be presented as `words' in some finite alphabet of symbols, and choice sequences which are non-predetermined and unfinished objects are legitimate constructive objects. In this way, Brouwer's constructivism goes beyond Turing computability. Further, in 1999, the term hypercomputation was introduced by J. Copeland. Hypercomputation refers to models of computation which go beyond Church-Turing thesis. In this paper, we propose a hypercomputation called persistently evolutionary Turing machines based on Brouwer's notion of being constructive.Comment: This paper has been withdrawn by the author due to crucial errors in theorems 4.6 and 5.2 and definition 4.