Related papers: Quantum Measurements from a Logical Point of View
We describe a scheme of quantum mechanics in which the Hilbert space and linear operators are only secondary structures of the theory. As primary structures we consider observables, elements of noncommutative algebra, and the physical…
For the first time it is shown that the logic of quantum mechanics can be derived from Classical Physics. An orthomodular lattice of propositions, characteristic of quantum logic, is constructed for manifolds in Einstein's theory of general…
Every measurement determines a single value as its outcome, and yet quantum mechanics predicts it only probabilistically. The Kochen-Specker theorem and Bell's inequality are often considered to reject a realist view but favor a skeptical…
One of the most difficult problems in quantum mechanics is the analysis of the measurement processes. In this paper, we point out that many of these difficulties originate from the different roles of measurement outcomes and observable…
A resolution of the quantum measurement problem(s) using the consistent histories interpretation yields in a rather natural way a restriction on what an observer can know about a quantum system, one that is also consistent with some results…
Taking several statistical examples, in particular one involving a choice of experiment, as points of departure, and making symmetry assumptions, the link towards quantum theory developed in Helland (2005a,b) is surveyed and clarified. The…
I discuss a set of strong, but probabilistically intelligible, axioms from which one can {\em almost} derive the appratus of finite dimensional quantum theory. Stated informally, these require that systems appear completely classical as…
We consider categorical logic on the category of Hilbert spaces. More generally, in fact, any pre-Hilbert category suffices. We characterise closed subobjects, and prove that they form orthomodular lattices. This shows that quantum logic is…
In the absence of a satisfactory interpretation of quantum theory, physical law lacks physical basis. This paper reviews the orthodox, or Dirac-von Neumann interpretation, and makes explicit that Hilbert space describes propositions about…
Using a quantum like algebraic formulation we give proof of Kochen-Specker theorem. We introduce new criteria in order to account for the contextual nature of measurements in quantum mechanics.
The basic notions of quantum mechanics are formulated in terms of separable infinite dimensional Hilbert space $\mathcal{H}$. In terms of the Hilbert lattice $\mathcal{L}$ of closed linear subspaces of $\mathcal{H}$ the notions of state and…
Quantum mechanics has been subject to logical scrutiny since its inception. The behavior of quantum systems, which are fundamentally dissimilar from classical systems, often appears to point to a logical inconsistency in quantum mechanics,…
Analysing Quantum Measurement requires analysing the physics of amplification since amplification of phenomena from one scale to another scale is essential to measurement. There still remains the task of working this into an axiomatic…
The interpretation of quantum mechanics has been a problem since its founding days. A large contribution to the discussion of possible interpretations of quantum mechanics is given by the so-called impossibility proofs for hidden variable…
A number of issues related to measurement show that self-consistency is lacking in quantum mechanics as this theory has been generally understood. Each issue is presented as a point in this paper. Each point can be resolved by incorporating…
This article is an exploratory account of the the non-monotonic behaviour of conceptual associations in the light of context. Computational approximations of conceptual space are furnished by semantic space models which are emerging from…
A new approach to the problem of measurement in quantum mechanics is proposed. In this approach, the process of measurement is described in the Heisenberg picture and divided into two stages. The first stage is to transduce the measured…
The question about the existence of so-called ``hidden'' variables in quantum mechanics and the perception of the completeness of quantum mechanics are two sides of the same coin. Quantum analytical mechanics constitutes a completion of…
A version of quantum theory is derived from a set of plausible assumptions related to the following general setting: For a given system there is a set of experiments that can be performed, and for each such experiment an ordinary…
One of the most central and controversial element of quantum mechanics is the use of non zero vectors of a Hilbert space (or, more generally, of one dimension subspaces) for representing the state of a quantum system. In particular, the…