Related papers: State Vector Reduction as a Shadow of a Noncommuta…
A phenomenological model for the calculation of reduction probabilities of a superposition of several states is presented. The approach bases only the idea that quantum state reduction has its origin in a mutual physical interaction between…
The description of a closed quantum system is extended with the identification of an underlying substructure enabling an expanded formulation of dynamics in the Heisenberg picture. Between measurements a ``state point" moves in an…
Non-commutative spacetime and quantum groups have been argued to capture non-classical features of spacetime and its symmetries in the low-energy limit of quantum gravity. In this letter, we show that employing the $SU_q(2)$ quantum group…
Each scheme of state reconstruction comes down to parametrize the state of a quantum system by expectation values or probabilities directly measurable in an experiment. It is argued that the time evolution of these quantities provides an…
We compute numerically the time evolution of simple semiclassical states describing homogeneous and isotropic spatial geometries in quantum-reduced loop gravity under a deparametrized formulation of the dynamics, in which a reference matter…
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…
We continue our program of unifying general relativity and quantum mechanics in terms of a noncommutative algebra ${\cal A}$ on a transformation groupoid $\Gamma = E \times G$ where $E$ is the total space of a principal fibre bundle over…
The basic concept of the two-state vector formalism, which is the time symmetric approach to quantum mechanics, is the backward evolving quantum state. However, due to the time asymmetry of the memory's arrow of time, the possible ways to…
In Noncommutative Geometry, as in quantum theory, classically real variables are assumed to correspond to self-adjoint operators. We consider the relaxation of the requirement of self-adjointness to mere symmetry for operators $X_i$ which…
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…
A unified conceptual foundation of classical and quantum physics is given, free of undefined terms. Ensembles are defined by extending the `probability via expectation' approach of Whittle to noncommuting quantities. This approach carries…
The quantum-mechanical state vector is not directly observable even though it is the fundamental variable that appears in Schrodinger's equation. In conventional time-dependent perturbation theory, the state vector must be calculated before…
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…
Space of states of PT symmetrical quantum mechanics is examined. Requirement that eigenstates with different eigenvalues must be orthogonal leads to the conclusion that eigenfunctions belong to the space with an indefinite metric. The self…
The noncommutative spectral action extends our familiar notion of commutative spaces, using the data encoded in a spectral triple on an almost commutative space. Varying a rather simple action, one can derive all of the standard model of…
We survey some results relating noncommutative geometry to the class field theory of number fields. These results appear within the context of quantum statistical mechanics where some arithmetic properties of a given number field can be…
These are expanded lecture notes of a mini-course whose objectives were to introduce the basic concepts, constructions and techniques of noncommutative geometry, as well as their uses as a framework for modelling quantum spacetime. Key…
The conventional view, that Einstein was wrong to believe that quantum physics is local and deterministic, is challenged. A parametrised model, Q, for the state vector evolution of spin 1/2 particles during measurement is developed. Q draws…
According to quantum theory, pure physical states correspond to equivalence classes of state vectors, where any two members of one class differ by a complex factor. The point is that such a factor does not change the probability for the…
A rigorous theory of quantum state reduction, the state change of the measured system caused by a measurement conditional upon the outcome of measurement, is developed fully within quantum mechanics without leading to the vicious circle…