Black Hole Quantum Computers

# Black Hole Quantum Computers - Black Hole Quantum Computers...

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Black Hole Quantum Computers Brian Brooks 2008-11-10 Most would agree that astronomy has nothing in common with computability. To a certain extent, black holes have nothing to do with computers. Traditionally, physics and computer science were divorced by a fundamental thesis, that algorithms could be distinguished independent of the physical world. Why should physics have anything to do with the ability to solve mathematical problems? Even further, what do black holes have to do with the physical nature of computational machinery? In this paper I strive to show how the quantum mechanics of black holes can be applied to the theory of computability. The research presented has been compiled in a fashion that stimulates a theoretical link between black holes and quantum computing known as black hole quantum computing. The desire to capture the complexities of mathematical reasoning and computation in a simple and powerful manner has been a major theme of 20 th Century mathematics[5]. In 1931, Kurt G¨odel proved that the leading formalization of mathematics, Principia Mathematica , was either an incomplete or inconsistent theory of the natural numbers. In other words, it contained statements that are neither provably true nor provably false. This theorem, known as G¨odel’s Incompleteness Theorem, shows that Hilbert’s program to ﬁnd a complete and consistent set of axioms for all of mathematics is impossible. G¨odel went further and argued that any mechanical method for describing a set of axioms and the rules by which theorems can be deduced can be translated into statements in arithmetic. From these statements, one could then construct new statements that attest to their own unprovability. As a consequence every such system of formalized statements would be incomplete[5]. This claim that no consistent formal system can prove all truths of arithmetic was seen as a negative result for mathematics. It was taken by many to show that there are statements in arithmetic whose truth is unknowable. Thus, a major limitation on the power of reasoning beyond mathematics. Although Godel’s argument was generally accepted, it relied upon a generalized formal system. Proving the absence of a mechanical method for doing something required a precise formalization of what mechanical 1

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computation is. In 1936, three inﬂuential methods of computation were developed: Alonzo Church’s lambda calculus, Steven Kleene’s recursive functions, and Alan Turing’s machines. All three systems were found to agree on which functions were computable, diﬀering in how they were to be computed. The mechanical action of Turing’s machines won people over in how to go about computing mathematical functions. This link between abstract computability and physical computability made Turing machines the standard model of computation[5]. In 1937, Turing published
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## This note was uploaded on 02/07/2011 for the course PHYS 101 taught by Professor Aster during the Spring '11 term at East Tennessee State University.

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Black Hole Quantum Computers - Black Hole Quantum Computers...

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