Related papers: Completing the quantum formalism in a contextually…
All our statements about the physical world are expressed in terms of everyday notions and thus in terms of classical physics. This necessity is behind each of our attempt to extract meaning out of empirical data and to communicate this…
In quantum physics the term `contextual' can be used in more than one way. One usage, here called `Bell contextual' since the idea goes back to Bell, is that if $A$, $B$ and $C$ are three quantum observables, with $A$ compatible (i.e.,…
In this paper we attempt to discuss what has Kochen-Specker (KS) theorem to say about physical invariance and quantum individuality. In particular, we will discuss the impossibility of making reference to objective physical properties…
Quantum mechanics, one of the most successful theories in the history of science, was created to account for physical systems not describable by classical physics. Though it is consistent with all experiments conducted thus far, many of its…
We are dealing in this work with such formal and conceptual extensions of nonrelativistic quantum mechanics (QM) which contain QM with its standard formalism and interpretation as a subtheory. QM is here primarily equivalently reformulated…
The Copenhagen Interpretation describes individual systems, using the same Hilbert space formalism as does the statistical ensemble interpretation (SQM). This leads to the well-known paradoxes surrounding the Measurement Problem. We extend…
We describe a system of axioms that, on one hand, is sufficient for constructing the standard mathematical formalism of quantum mechanics and, on the other hand, is necessary from the phenomenological standpoint. In the proposed scheme, the…
In spite of the very common opinion we show that QM is not complete and that it is possible to create prequantum models providing finer description of physical reality than QM. There exists (at least in theoretical models) dispersion free…
Contemporary scientific perspectivism is re-evaluated and extended to a comprehensive perspectivist methodology and 'mediated' realistic epistemology, especially, with reference to quantum mechanics. In the present study, this is realized…
In analogy with conventional quantum mechanics, non-commutative quantum mechanics is formulated as a quantum system on the Hilbert space of Hilbert-Schmidt operators acting on non-commutative configuration space. It is argued that the…
The mechanism of describing quantum states by standard probability (tomographic one) instead of wave function or density matrix is elucidated. Quantum tomography is formulated in an abstract Hilbert space framework, by means of the identity…
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…
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…
The original purpose of measurements is to provide us with information about a previously unknown physical property of the system observed. In the Hilbert space formalism of quantum mechanics, this physical meaning of measurement…
We begin by discussing ``What exists?'', i.e. ontology, in Classical Physics which provided a description of physical phenomena at the macroscopic level. The microworld however necessitates a introduction of Quantum ideas for its…
The notion that any physical quantity is defined and measured relative to a reference frame is traditionally not explicitly reflected in the theoretical description of physical experiments where, instead, the relevant observables are…
The most peculiar, specifically quantum, features of quantum mechanics --- quantum nonlocality, indeterminism, interference of probabilities, quantization, wave function collapse during measurement --- are explained on a logical-geometrical…
The existence of contextuality in quantum mechanics is a fundamental departure from the classical description of the world. Currently, the quest to identify scenarios which cannot be more contextual than quantum theory is at the forefront…
This paper presents a comprehensive perspective of the metric of quantum states with a focus on the background independent metric structures. We also explore the possibilities of geometrical formulations of quantum mechanics beyond the…
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…