相关论文: A Topos Perspective on State-Vector Reduction

This paper is the fourth in a series whose goal is to develop a fundamentally new way of building theories of physics. The motivation comes from a desire to address certain deep issues that arise in the quantum theory of gravity. Our basic…

A rigorous theory of quantum state reduction, the state change of the measured system caused by a measurement conditional upon the outcome of measurement, is developed fully within quantum mechanics without leading to the vicious circle…

The theory of quantum mechanics is examined using non-standard real numbers, called quantum real numbers (qr-numbers), that are constructed from standard Hilbert space entities. Our goal is to resolve some of the paradoxical features of the…

Essential elements of quantum theory are derived from an epistemic point of view, i.e., the viewpoint that thetheory has to do with what can be said about nature. This gives a relationship to statistical reasoning and to other areas of…

This is a series of lecture notes explaining topos theory and its application in physics.

In the current debate referring to the construction of a tenable background independent theory of Quantum Gravity we introduce the notion of topos-theoretic relativization of physical representability and demonstrate its relevance…

A phenomenological model for the calculation of reduction probabilities of a superposition of several states is presented. The approach bases only the idea that quantum state reduction has its origin in a mutual physical interaction between…

The notion of state reduction employed by the standard quantum theory of measurement is difficult to accept for two reasons: It leaves open where and when the reduction takes place and it does not give any objective conditions under which…

Topos quantum theory provides representations of quantum states as direct generalizations of the probability distribution, namely probability valuation. In this article, we consider extensions of a known bijective correspondence between…

In this paper we present the two-state vector formalism of quantum mechanics. It is a time-symmetrized approach to standard quantum theory particularly helpful for the analysis of experiments performed on pre- and post-selected ensembles.…

The basic notion of how topoi can be utilized in physics is presented here. Topos and category theory serve as valuable tools which extend our ordinary set-theoretical conceptions, can further the study of quantum logic and give rise to new…

Topos theory has been suggested first by Isham and Butterfield, and then by Isham and Doering, as an alternative mathematical structure within which to formulate physical theories. In particular, it has been used to reformulate standard…

We show how probabilities can be treated as truth values in suitable sheaf topoi. The scheme developed in this paper is very general and applies to both classical and quantum physics. On the quantum side, the results are a natural extension…

The development of quantum information theory has renewed interest in the idea that the state vector does not represent the state of a quantum system, but rather the knowledge or information that we may have on the system. I argue that this…

In the reductionistic approach, mechanisms are divided into simpler parts interconnected in some standard way (e.g. by a mechanical transmission). We explore the possibility of porting reductionism in quantum operations. Conceptually, first…

The relation between quantum measurement and thermodynamically irreversible processes is investigated. The reduction of the state vector is fundamentally asymmetric in time and shows an observer-relatedness which may explain the double…

In the topos approach to quantum theory, the spectral presheaf plays the role of the state space of a quantum system. We show how a notion of entropy can be defined within the topos formalism using the equivalence between states and…

In a previous preprint (quant-ph/0012122) we introduced a ``contextual objectivity" formulation of quantum mechanics (QM). A central feature of this approach is to define the quantum state in physical rather than in mathematical terms, in…

The goal of this paper is to summarise the first steps in developing a fundamentally new way of constructing theories of physics. The motivation comes from a desire to address certain deep issues that arise when contemplating quantum…

This paper is the first in a series whose goal is to develop a fundamentally new way of constructing theories of physics. The motivation comes from a desire to address certain deep issues that arise when contemplating quantum theories of…