Results 1  10
of
13
Notes on a Paulian idea: foundational, historical, anecdotal and forwardlooking thoughts on the quantum
"... This document is the first installment of three in the Cerro Grande Fire Series. The Cerro Grande Fire left many in the Los Alamos community acutely aware of the importance of backing up the hard drive. I could think of no better instrument for the process than LANL itself. This is a collection of l ..."
Abstract

Cited by 11 (4 self)
 Add to MetaCart
This document is the first installment of three in the Cerro Grande Fire Series. The Cerro Grande Fire left many in the Los Alamos community acutely aware of the importance of backing up the hard drive. I could think of no better instrument for the process than LANL itself. This is a collection of letters written to various friends and colleagues
Contexts in quantum, classical and partition logic
 In Handbook of Quantum Logic
, 2006
"... Contexts are maximal collections of comeasurable observables “bundled together ” to form a “quasiclassical miniuniverse. ” Different notions of contexts are discussed for classical, quantum and generalized urn–automaton systems. PACS numbers: 02.10.v,02.50.Cw,02.10.Ud ..."
Abstract

Cited by 8 (7 self)
 Add to MetaCart
(Show Context)
Contexts are maximal collections of comeasurable observables “bundled together ” to form a “quasiclassical miniuniverse. ” Different notions of contexts are discussed for classical, quantum and generalized urn–automaton systems. PACS numbers: 02.10.v,02.50.Cw,02.10.Ud
Generalizations of Kochen and Specker’s theorem and the effectiveness of Gleason’s theorem
 Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics 35, 177194
, 2004
"... Abstract. Kochen and Specker’s theorem can be seen as a consequence of Gleason’s theorem and logical compactness. Similar compactness arguments lead to stronger results about finite sets of rays in Hilbert space, which we also prove by a direct construction. Finally, we demonstrate that Gleason’s th ..."
Abstract

Cited by 3 (1 self)
 Add to MetaCart
Abstract. Kochen and Specker’s theorem can be seen as a consequence of Gleason’s theorem and logical compactness. Similar compactness arguments lead to stronger results about finite sets of rays in Hilbert space, which we also prove by a direct construction. Finally, we demonstrate that Gleason’s theorem itself has a constructive proof, based on a generic, finite, effectively generated set of rays, on which every quantum state can be approximated. 1. Gleason’s Theorem and Logical Compactness Kochen and Specker’s (1967) theorem (KS) puts a severe constraint on possible hiddenvariable interpretations of quantum mechanics. Often it is considered an improvement on a similar argument derived from Gleason (1957) theorem (see, for example, Held. 2000). This is true in the sense that KS provide an explicit construction of a finite set of rays on which no twovalued homomorphism exists. However, the fact that there is such a finite set follows from Gleason’s theorem using a simple logical compactness argument (Pitowsky 1998, a similar point is made in Bell 1996). The existence of finite sets of rays with other interesting features
PLURALISM IN MATHEMATICS
, 2004
"... We defend pluralism in mathematics, and in particular Errett Bishop’s constructive approach to mathematics, on pragmatic grounds, avoiding the philosophical issues which have dissuaded many mathematicians from taking it seriously. We also explain the computational value of interval arithmetic. ..."
Abstract

Cited by 2 (1 self)
 Add to MetaCart
We defend pluralism in mathematics, and in particular Errett Bishop’s constructive approach to mathematics, on pragmatic grounds, avoiding the philosophical issues which have dissuaded many mathematicians from taking it seriously. We also explain the computational value of interval arithmetic.
Constructive Mathematics and Quantum Physics
, 1999
"... This paper is dedicated to the memory of Prof. Gottfried T. Ru ttimann ..."
Abstract

Cited by 1 (0 self)
 Add to MetaCart
(Show Context)
This paper is dedicated to the memory of Prof. Gottfried T. Ru ttimann
Foundational, Historical, Anecdotal and ForwardLooking Thoughts on the Quantum Selected Correspondence, 1995–2001
, 2001
"... This document is the first installment of three in the Cerro Grande Fire Series. The Cerro Grande Fire left many in the Los Alamos community acutely aware of the importance of backing up the hard drive. I could think of no better instrument for the process than LANL itself. This is a collection of l ..."
Abstract
 Add to MetaCart
This document is the first installment of three in the Cerro Grande Fire Series. The Cerro Grande Fire left many in the Los Alamos community acutely aware of the importance of backing up the hard drive. I could think of no better instrument for the process than LANL itself. This is a collection of letters written to various friends and colleagues
A DEFENCE OF MATHEMATICAL PLURALISM
, 2004
"... We approach the philosophy of mathematics via a discussion of the differences between classical mathematics and constructive mathematics, arguing that each is a valid activity within its own context. ..."
Abstract
 Add to MetaCart
We approach the philosophy of mathematics via a discussion of the differences between classical mathematics and constructive mathematics, arguing that each is a valid activity within its own context.
A Constructivist Perspective on Physics
, 2002
"... This paper examines the problem of extending the programme of mathematical constructivism to applied mathematics. I am not concerned with the question of whether conventional mathematical physics makes essential use of the principle of excluded middle, but rather with the more fundamental question o ..."
Abstract
 Add to MetaCart
This paper examines the problem of extending the programme of mathematical constructivism to applied mathematics. I am not concerned with the question of whether conventional mathematical physics makes essential use of the principle of excluded middle, but rather with the more fundamental question of whether the concept of physical infinity is constructively intelligible. I consider two kinds of physical infinity: a countably infinite constellation of stars and the infinitely divisible spacetime continuum. I argue (contrary to Hellman) that these do not pose any insuperable problem for constructivism, and that constructivism may have a useful new perspective to offer on physics. References ...