Competing Ideas in Quantum Measurement: The Search for a Perfect ``Theory of Everything''

Graeme Donald Robertson

This book has been written for eighteen year olds (or anyone who will listen) as an honest attempt to face their justified questionings and to offer them a metaphysical framework with which to confront the twenty-first century. It is vitally important that certain modes of thought are uprooted and new modes put in their place if mankind and planet Earth are not soon to suffer an historic global catastrophe. Apart from the continuing world-wide proliferation of conventional, chemical, biological and nuclear weaponry, the temperature of the planet has risen more rapidly in the last twenty-five years than it has since the year 900AD, which confirms global warming by some cause or other. These and the many intensifying human conflicts and natural disasters demand that some fundamental changes to our thinking are made as soon as possible. These 120 pages begin with an original examination of the quantum-theoretical understanding of reason (logic) and reality (existence) and find both to be at odds with common sense. A theory of everything is a reduction to a single grand idea! A quantum theory of everything is a mathematical theory of a consciousness realizing this grand idea! That is what this book tries to comprehend by means of five indisputable propositions.

Michael L. G. Redhead

T. R. Robinson

The natural numbers play a key role in axiomatic set theory and hence in the foundations of mathematics. The natural numbers also have a major role in quantum mechanics. The idea is explored that von Neumann's construction (vNC) of the natural numbers, within the framework of Zermelo-Fraenkel (ZF) axiomatic set theory, can serve as a blueprint for deriving some key basic equations of quantum mechanics. This approach obviates any need for quantizing classical mechanics and provides further support for the view that quantum mechanics is perfectly applicable to fields beyond those in physics for which it was originally intended.This article is part of the theme issue 'Quantum theory and topology in models of decision making (Part 1)'.

L. E. Ballentine

Hiromi Miyajima, Noritaka Shigei Masataka Fujisaki

In this paper, an algorithm of quantum associative memory is proposed using quantum search algorithms. In the associative memory, the problem is to find the data or the nearest data in the meaning of hamming distance from designated data. If the search data in memorized dataset is contained, the problem becomes data search one. In associative memory, it is difficult to find the nearest data in hamming distance. For searching any item in an unsorted database with N items, a classical takes O(N) steps but Grover’s quantum searching algorithm takes only O( p N) steps on perfect graph. By generalizing the idea, Ventura has proposed the associative memory model, but it does not solve the problem of finding the nearest data. On the other hand, quantum search algorithm with O( p N) steps on hypercube is also proposed. Therefore, the idea in this paper is formalizing the problem as quantum search algorithm in hypercube but not in the conventional perfect graph. First, we perform quantum search algorithm by considering quantum walk on hypercube. Further, it is observed search data or the nearest data by using the conventional algorithm with high probability.

Badis Ydri