相关论文: Observables II : Quantum Observables

We start with a discussion of the use of mathematics to model the real world then justify the role of Hilbert space formalism for such modelling in the general context of quantum logic. Following this, the incompleteness of the…

In Quantum Physics there are circumstances where the direct measurement of particular observables encounters diffculties; in some of these cases, however, its value can be evaluated, i.e. it can be inferred by measuring another observable…

Quantum theory famously entails the existence of incompatible measurements; pairs of observables which cannot be simultaneously measured to arbitrary precision. Incompatibility is widely regarded to be a uniquely quantum phenomenon, linked…

In ordinary Quantum Mechanics only ideally instantaneous observations of a quantity or a set of compatible quantities are usually considered. In an old paper of our group in Milano a formalism was introduced for the continuous monitoring of…

A non-commuting measurement transfers, via the apparatus, information encoded in a system's state to the external "observer". Classical measurements determine properties of physical objects. In the quantum realm, the very same notion…

The role of time in quantum mechanics is discussed. The differences between ordinary observables and an observable which corresponds to the time of an event is examined. In particular, the time-of-arrival of a particle to a fixed location…

A goal of most interpretations of quantum mechanics is to avoid the apparent intrusion of the observer into the measurement process. Such intrusion is usually seen to arise because observation somehow selects a single actuality from among…

One of the hallmarks of quantum theory is the realization that distinct measurements cannot in general be performed simultaneously, in stark contrast to classical physics. In this context the notions of coexistence and joint measurability…

We analyse the wave function collapse as seem by two distinct observers (with identical detectors) in relative motion. Imposing that the measurement process demands information transfer from the system to the detectors, we note that…

Classical, Quantum and Relativistic mechanics elect time and space as fundamentals, extracting the measure of motion -velocity- from this static space-time platform. Conversely, the timelessness of Statistical mechanics computes the…

In many a traditional physics textbook, a quantum measurement is defined as a projective measurement represented by a Hermitian operator. In quantum information theory, however, the concept of a measurement is dealt with in complete…

The kinematical foundations of Schwinger's algebra of selective measurements were discussed in a previous paper (arXiv:1905.12274) and, as a consequence of this, a new picture of quantum mechanics based on groupoids was proposed. In this…

A source of much difficulty and confusion in the interpretation of quantum mechanics is a ``naive realism about operators.'' By this we refer to various ways of taking too seriously the notion of operator-as-observable, and in particular to…

Some results are reviewed and developments are presented on the study of Time in quantum mechanics as an observable, canonically conjugate to energy. Operators for the observable Time are investigated in particle and photon quantum theory.…

Given a physical quantum system described by a Hilbert H, for any bounded quantum observable (a bounded self-adjoint operator) T it is possible to define several ''hidden observable'' functions f:H->R associated to T and for any quantum…

It is shown that quantum mechanics is noncontextual if quantum properties are represented by subspaces of the quantum Hilbert space (as proposed by von Neumann) rather than by hidden variables. In particular, a measurement using an…

We study a family of physical observable quantities in quantum gravity. We denote them W functions, or n-net functions. They represent transition amplitudes between quantum states of the geometry, are analogous to the n-point functions in…

We begin by defining mutually unbiased (MU) observables on a finite dimensional Hilbert space. We also consider the more general concept of parts of MU observables. The relationships between MU observables, value-complementary observables…

We show how quantum mechanics can be understood as a space-time theory provided that its spatial continuum is modelled by a variable real number (qrumber) continuum. Such a continuum can be constructed using only standard Hilbert space…

We propose an exercise in which one attempts to deduce the formalism of quantum mechanics solely from phenomenological observations. The only assumed inputs are obtained through sequential probing of quantum systems; no presuppositions…