相关论文: How to Measure a Beable

A complete theory of overmeasurement by measuring refinements of observables is presented. It encompasses a wider set of functions of observ- ables (coarsenings) . Thus the theory has a broad potential application.It is applied to a…

Individual choices often depend on the order in which the decisions are made. In this paper, we expose a general theory of measurable systems (an example of which is an individual's preferences) allowing for incompatible (non-commuting)…

The concept of measurability of functions on a charge space is generalised for functions taking values in a uniform space. Several existing forms of measurability generalise naturally in this context, and new forms of measurability are…

John Bell once argued that one ought to select, out of the 'observables' of quantum theory, some subset of 'beables' that can be consistently ascribed determinate values. Moreover, this subset should be selected so as to guarantee (among…

``Weak'', ``protective'', and ``delayed observation'' measurements are analyzed in the framework of the Bohm interpretation of quantum theory. It is argued that the above varieties of measurements manifest some difficulties of the Bohm…

Many systems in biology, physics, and engineering are modeled by nonlinear dynamical systems where the states are usually unknown and only a subset of the state variables can be physically measured. Can we understand the full system from…

Gathering data through measurements is at the basis of every experimental science. Ideally, measurements should be repeatable and, when extracting only coarse-grained data, they should allow the experimenter to retrieve the finer details at…

In the standard von Neumann interaction used in Quantum measurements, the chosen observable to which the environment (apparatus) entangles is exactly reproduced in the state of the environment, thereby decohering the quantum system in the…

Measurement is an integral part of modern science, providing the fundamental means for evaluation, comparison, and prediction. In the context of visualization, several different types of measures have been proposed, ranging from approaches…

In this contribution I review rigorous formulations of a variety of limitations of measurability in quantum mechanics. To this end I begin with a brief presentation of the conceptual tools of modern measurement theory. I will make precise…

In this paper we develop a notion of measure theory over boolean toposes which is analogous to noncommutative measure theory, i.e. to the theory of von Neumann algebras. This is part of a larger project to study relations between topos…

Quantum-mechanical interpretation-related implications of the theory of unitary premeasurement [1] on complete measurement (objectification or collapse included) are investigated in the present article with a view to give an affirmative…

The question of what should be meant by a measurement is tackled from a mathematical perspective whose physical interpretation is that a measurement is a fundamental process via which a finite amount of classical information is produced.…

We report an inconsistency found in probability theory (also referred to as measure-theoretic probability). For probability measures induced by real-valued random variables, we deduce an "equality" such that one side of the "equality" is a…

The quantum mechanical measurement process is considered. A hypothetical concept of irrational dynamical variables is proposed. A possible definition of measurement is discussed along with a mathematical method to calculate experimental…

Spaces of quasi-invariant measures supplied with different topologies are studied. Their embeddings, projective decompositions, conditions for their metrizability are investigated. Theorems about convergence of nets of quasi-invariant…

The realistic interpretation of classical theory assumes that every classical system has well-defined properties, which may be unknown to the observer but are nevertheless part of reality and can in principle be revealed by measurements.…

Two theorems with applications to the quantum theory of measurements are stated and proven. The first one clarifies and amends von Neumann's Measurement Postulate used in the Copenhagen interpretation of quantum mechanics. The second one…

An analysis of quantum measurement is presented that relies on an information-theoretic description of quantum entanglement. In a consistent quantum information theory of entanglement, entropies (uncertainties) conditional on measurement…

A limitation on simultaneous measurement of two arbitrary positive operator valued measures is discussed. In general, simultaneous measurement of two noncommutative observables is only approximately possible. Following Werner's formulation,…