Possibility to Realize an Accelerated Turing Machine
Abstract
Takaaki Musha
In mathematics and computer science, an accelerated Turing machine is a hypothetical computational model related to Turing machines, which can perform a countable infinite number of computational steps within a finite time. It is also called a Zeno machine, a concept proposed independently by B. Russdel, R. Blake and H. Weyl, which performs its first computational step in one unit of time and each subsequent step in half the time of the step before, allowing an infinite number of steps of computation to be completed within a finite interval of time [1,2]. However, such a machine cannot be physically realized, from the standpoint of the Heisenberg uncertainty principle, because the energy to perform the computation will be exponentially increasing as the computational speed is accelerating. Thus, the Zeno machine is considered a mere mathematical concept with no possibility to realize it in the physical world. Contrary to this conclusion, the author can show the possibility to realize a real accelerated Turing machine, by utilizing superluminal particles instead of subliminal particles, which are related to evanescent photons, and also a metamaterial circuit.
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