相关论文: Observables II : Quantum Observables
An observable on a quantum structure is any $\sigma$-homomorphism of quantum structures from the Borel $\sigma$-algebra into the quantum structure. We show that our partial information on an observable known only for all intervals of the…
In this paper we find a simple rule to reproduce the algebra of quantum observables using only the commutators and operators which appear in the Koopman-von Neumann (KvN) formulation of classical mechanics. The usual Hilbert space of…
Descriptions of classical mechanics in Hilbert space go back to the work of Koopman and von Neumann in the 1930s. Decades later, van Hove derived a unitary representation of the group of contact transformations which recently has been used…
Observables and instruments have played significant roles in recent studies on the foundations of quantum mechanics. Sequential products of effects and conditioned observables have also been introduced. After an introduction in Section~1,…
The notion coexistence of quantum observables was introduced to describe the possibility of measuring two or more observables together. Here we survey the various different formalisations of this notion and their connections. We review…
We discuss the notion about physical quantities as having values represented by real numbers, and its limiting to describe nature to be understood in relation to our appreciation that the quantum theory is a better theory of natural…
Newtonian and Schrodinger dynamics can be formulated in a physically meaningful way within the same Hilbert space framework. This fact was recently used to discover an unexpected relation between classical and quantum motions that goes…
With approaching quantum/noncommutative models for the deep microscopic spacetime in mind, and inspired by our recent picture of the (projective) Hilbert space as the model of physical space behind basic quantum mechanics, we reformulate…
In the Contextuality-by-Default theory random variables representing measurement outcomes are labeled contextually, i.e., not only by what they measure but also under what conditions (in what contexts) the measurements are made, including…
In a parametrized and constrained Hamiltonian system, an observable is an operator which commutes with all (first-class) constraints, including the super-Hamiltonian. The problem of the frozen formalism is to explain how dynamics is…
Bohmian mechnaics is the most naively obvious embedding imaginable of Schr\"odingers's equation into a completely coherent physical theory. It describes a world in which particles move in a highly non-Newtonian sort of way, one which may at…
For any pair of bounded observables $A$ and $B$ with pure point spectra, we construct an associated "joint observable" which gives rise to a notion of a joint (projective) measurement of $A$ and $B$, and which conforms to the intuition that…
The existence of incompatibility is one of the most fundamental features of quantum theory, and can be found at the core of many of the theory's distinguishing features, such as Bell inequality violations and the no-broadcasting theorem. A…
A measuring apparatus is described by quantum mechanics while it interacts with the quantum system under observation, and then it must be given a classical description so that the result of the measurement appears as objective reality.…
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 present a reformulation of quantum mechanics in terms of probability measures and functions on a general classical sample space and in particular in terms of probability densities and functions on phase space. The basis of our proceeding…
This paper considers a generalization of the notion of quantum observables in ontological models of quantum mechanics. Within this framework it is possible to construct physical models where quantum noncommutativity can arise dynamically.…
Thought experiments about the physical nature of set theoretical counterexamples to the axiom of choice motivate the investigation of peculiar constructions, e.g. an infinite dimensional Hilbert space with a modular quantum logic. Applying…
The concept of intrinsic and operational observables in quantum mechanics is introduced. In any realistic description of a quantum measurement that includes a macroscopic detecting device, it is possible to construct from the statistics of…
In Quantum Physics it is not always possible to directly perform the measurement of an obsevable; in some of these cases, however, its value can be {\sl detected}, i.e. it can be inferred by measuring {\sl another} observable characterized…