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

TL;DR

This paper explores the physical and quantum informational aspects of the Thomson lamp limit, connecting it to infinite series, accelerated computation, and recursion theory, and proposing a quantum diagonalization method.

Contribution

It introduces a quantum perspective on the Thomson lamp limit, linking it to recursion theory and proposing a new diagonalization method without quantum fixed points.

Findings

Physical limits align with Abel sums of infinite series

Quantum information enables consistent fixed point representations

A generalized diagonal method without quantum fixed points is proposed

Abstract

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.