Related papers: The Noncommutative Values of Quantum Observables
Dirac talked about q-numbers versus c-numbers. Quantum observables are q-number variables that generally do not commute among themselves. He was proposing to have a generalized form of numbers as elements of a noncommutative algebra. That…
Based on a recent relational formulation of quantum reference frame transformations, especially with a case of quantum spatial translations in particular, we analyzed how the `value' of an observable for a fixed state change. That is the…
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.…
A characteristical property of a classical physical theory is that the observables are real functions taking an exact outcome on every (pure) state; in a quantum theory, at the contrary, a given observable on a given state can take several…
The implications of the physical theory of quantum mechanics on the question of realism is much a subject of sustaining interest, while the background questions among physicists on how to think about all the theoretical notion and…
The best mathematical arguments against a realistic interpretation of quantum mechanics - that gives definite but partially unknown values to all observables - are analysed and shown to be based on reasoning that is not compelling. This…
Quantum correlations can be naturally formulated in a classical statistical system of infinitely many degrees of freedom. This realizes the underlying non-commutative structure in a classical statistical setting. We argue that the quantum…
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…
Measurement is an important scientific activity. In most of science, including classical physics, is may be understood as a way of finding out about the physical world and representing the results numerically. No-go theorems show that…
We give a review of concepts related to connection of classical and quantum theories, from the phase space perspective. Quantum theory is described by non-commutative operators of coordinates and momenta, results in values having a certain…
A central feature of quantum mechanics is the non-commutativity of operators used to describe physical observables. In this article, we present a critical analysis on the role of non-commutativity in quantum theory, focusing on its…
In this paper we consider the observables describing fundamental spatiotemporal properties and relations in the context of Quantum Gravity (QG). As we will show, in both Loop Quantum Gravity and in String Theory, these observables are…
Under the principle that quantum mechanical observables are invariant under relevant symmetry transformations, we explore how the usual, non-invariant quantities may capture measurement statistics. Using a relativisation mapping, viewed as…
Some notes about quantum physics, an interpretation if one wishes, are put forward, insisting on `closely following the mathematics/formalism, the `nuts and bolts of what quantum physics says'. These, basically well-known, issues seem to…
In this sequence of papers, noncommutative analysis is used to give a consistent axiomatic approach to a unified conceptual foundation of classical and quantum physics. The present Part I defines the concepts of observables, states and…
Physical quantities are assumed to take real values, which stems from the fact that an usual measuring instrument that measures a physical observable always yields a real number. Here we consider the question of what will happen if physical…
We propose that observables in quantum theory are properly understood as representatives of symmetry-invariant quantities relating one system to another, the latter to be called a reference system. We provide a rigorous mathematical…
The concept of number is fundamental to the formulation of any physical theory. We give a heuristic motivation for the reformulation of Quantum Mechanics in terms of non-standard real numbers called Quantum Real Numbers. The standard axioms…
Quantum theory is applicable, in principle, to both the microscopic and macroscopic realms. It is therefore worthwhile to investigate whether it is possible to evolve a quantum-compatible view of the properties and states of macroscopic…
We offer a fresh perspective on the relational interpretation of quantum mechanics as a way of thinking about the world described by quantum theory based on quantifiable notions of information. This allows us to provide a definition of a…