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On the Brightness of the Thomson Lamp. A Prolegomenon to Quantum Recursion Theory
, 2009
"... 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 accele ..."
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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 selfcontradictory feature of diagonalization, a generalized diagonal method allowing no quantum fixed points is proposed.
Randomness in Physics: Five Questions, Some Answers
, 2009
"... Despite provable unknowables in recursion theory, indeterminism and randomness in physics is confined to conventions, subjective beliefs and preliminary evidence. The history of the issue is very briefly reviewed, and answers to five questions raised by Zenil are presented. ..."
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Despite provable unknowables in recursion theory, indeterminism and randomness in physics is confined to conventions, subjective beliefs and preliminary evidence. The history of the issue is very briefly reviewed, and answers to five questions raised by Zenil are presented.
The diagonalization method in quantum recursion theory
, 2009
"... As quantum parallelism allows the effective corepresentation of classical mutually exclusive states, the diagonalization method of classical recursion theory has to be modified. Quantum diagonalization involves unitary operators whose eigenvalues are different from one. ..."
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As quantum parallelism allows the effective corepresentation of classical mutually exclusive states, the diagonalization method of classical recursion theory has to be modified. Quantum diagonalization involves unitary operators whose eigenvalues are different from one.
Centre for Discrete Mathematics and Theoretical Computer Science Quantum Interfaces
, 2000
"... Rational agents acting as observers use “knowables ” to construct a vision of the outside world. Thereby, they are bound by the information exchanged with what they consider as objects. The cartesian cut or, in modern terminology, the interface mediating this exchange, is again a construction. It se ..."
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Rational agents acting as observers use “knowables ” to construct a vision of the outside world. Thereby, they are bound by the information exchanged with what they consider as objects. The cartesian cut or, in modern terminology, the interface mediating this exchange, is again a construction. It serves as a “scaffolding, ” an intermediate construction capable of providing the necessary conceptual means. An attempt is made to formalize the interface, in particular the quantum interface and quantum measurements, by a symbolic information exchange. A principle of conservation of information is reviewed and a measure of information flux through the interface is proposed. We cope with the question of why observers usually experience irreversibility in measurement processes if the evolution is reversible, i.e., onetoone. And why should there be any meaningful concept of classical information if there is merely quantum information to begin with? We take the position here that the concept of irreversible measurement is no deep principle but originates in the practical inability to reconstruct a quantum state of the object. Many issues raised apply also to the quantum’s natural double, virtual reality.