On the brightness of the Thomson lamp. A prolegomenon to quantum recursion theory

Details On the brightness of the Thomson lamp. A prolegomenon to quantum recursion theory On the brightness of the Thomson lamp. A prolegomenon to quantum recursion theory

2009-04-10

arxiv.org/abs/0904.1649v2

Lecture Notes in Computer Science Vol. 5715, ed. by C.S. Calude, et al. (Springer, Berlin, Heidelberg, 2009)

Physics

Quantum Physics

11 pages, 1 figure, revised and accepted for UC09

Scientific paper

10.1007/978-3-642-03745-0_26

Some physical aspects related to the limit operations of the Thomson lamp are discussed. Regardless of the formally unbounded and even infinite number of "steps" involved, the physical limit has an operational meaning in agreement with the Abel sums of infinite series. The formal analogies to accelerated (hyper-) computers and the recursion theoretic diagonal methods are discussed. As quantum information is not bound by the mutually exclusive states of classical bits, it allows a consistent representation of fixed point states of the diagonal operator. In an effort to reconstruct the self-contradictory feature of diagonalization, a generalized diagonal method allowing no quantum fixed points is proposed.

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