Related papers: Observables in the General Boundary Formulation
We introduce contextual values as a generalization of the eigenvalues of an observable that takes into account both the system observable and a general measurement procedure. This technique leads to a natural definition of a general…
A framework allowing for perturbative calculations to be carried out for quantum field theories with arbitrary smoothly curved boundaries is described. It is based on an expansion of the heat kernel derived earlier for arbitrary mixed…
The notion of equality between two observables will play many important roles in foundations of quantum theory. However, the standard probabilistic interpretation based on the conventional Born formula does not give the probability of…
Quantum observables can be identified with vector fields on the sphere of normalized states. The resulting vector representation is used in the paper to undertake a simultaneous treatment of macroscopic and microscopic bodies in quantum…
We show that the theory of operator quantum error correction can be naturally generalized by allowing constraints not only on states but also on observables. The resulting theory describes the correction of algebras of observables (and may…
We show that the real massive Klein-Gordon theory admits a description in terms of states on various timelike hypersurfaces and amplitudes associated to regions bounded by them. This realizes crucial elements of the general boundary…
A certain generalization of the mathematical formalism of quantum mechanics beyond operator algebras is considered. The approach is based on the concept of conditional probability and the interpretation of the Lueders - von Neumann quantum…
Quantum estimation theory provides optimal observations for various estimation problems for unknown parameters in the state of the system under investigation. However, the theory has been developed under the assumption that every observable…
A simple model of quantum particle is proposed in which the particle in a {\it macroscopic} rest frame is represented by a {\it microscopic d}-dimensional oscillator, {\it s=(d-1)/2} being the spin of the particle. The state vectors are…
The final version of a new approach to quantum theory is formulated in this paper. The basis is taken to be theoretical variables, variables that may be accessible or inaccessible, i.e., it may be possible or impossible for an observer to…
The questions of describing observables and observation in quantum gravity appear to be centrally important to its physics. A relational approach holds significant promise, and a classification of different types of relational observables…
We propose a mathematical structure, based on a noncommutative geometry, which combines essential aspects of general relativity and quantum mechanics, and leads to correct "limiting cases" of both these theories. We quantize a groupoid…
We recast the action principle of four dimensional General Relativity so that it becomes amenable for perturbation theory which doesn't break general covariance. The coupling constant becomes dimensionless (G_{Newton} \Lambda) and extremely…
The program of a physical concept of information is outlined in the framework of quantum theory. A proposal is made for how to avoid the introduction of axiomatic observables. The conventional (collapse) and the Everett interpretations of…
We examine the longstanding problem of introducing a time observable in Quantum Mechanics; using the formalism of positive-operator-valued measures we show how to define such an observable in a natural way and we discuss some consequences.
In this paper we report some results on the expectation values of a set of observables introduced for 3-dimensional Riemannian quantum gravity with positive cosmological constant, that is, observables in the Turaev-Viro model. Instead of…
A realist description of our universe requires a twofold concept of locality. On one hand, there are the strictly Einstein-local interactions which generate the time evolution. On the other hand, the quantum state space calls for a…
This is an attempt to create a consistent and non-trivial extension of quantum theory, describing in detail the quantum measurement process. A tentative but concrete model is presented, based on the concept of multiple…
The description of relativistic effects requires a preliminary definition of events localised in space-time while the clocks used for time definition and the fields used in synchronisation or localisation procedures are necessarily quantum…
Quantum field theory currently has a single standard mathematical characterization (the Standard Model), but no single accepted conceptual framework to interpret the mathematics. Many of these conceptualizations rely on intuitive concepts…