Related papers: The Generalised Liar Paradox: A Quantum Model and …
In previous work, the author extended the Poincare Lie algebra to include a four position operator as a natural extension to a large fifteen parameter Lie algebra of operators. We here propose to generalize the metric contained in those…
The paper attempts to convince that the orthodox interpretation of quantum mechanics does not contradict philosophical realism by throwing light onto certain properties of quantum systems that seem to have escaped attention as yet. The…
Building on earlier work, we further develop a formalism based on the mathematical theory of frames that defines a set of possible phase-space or quasi-probability representations of finite-dimensional quantum systems. We prove that an…
We derive the Hilbert space formalism of quantum mechanics from epistemic principles. A key assumption is that a physical theory that relies on entities or distinctions that are unknowable in principle gives rise to wrong predictions. An…
The true dynamical randomness is obtained as a natural fundamental property of deterministic quantum systems. It provides quantum chaos passing to the classical dynamical chaos under the ordinary semiclassical transition, which extends the…
Progress in the new information-theoretic process physics is reported in which the link to the phenomenology of general relativity is made. In process physics the fundamental assumption is that reality is to be modelled as self-organising…
Quantum mechanics is a fundamentally probabilistic theory (at least so far as the empirical predictions are concerned). It follows that, if one wants to properly understand quantum mechanics, it is essential to clearly understand the…
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…
This paper presents a generalization of quantum mechanics from conventional Hilbert space formalism to Banach space one. We construct quantum theory starting with any complex Banach space beyond a complex Hilbert space, through using a…
The first of the two related papers analising and explaining the origin, manifestations and parodoxical features of the quantum potential (QP) from the non-relativistic and relativistic point of view. QP arises in the quantum Hamiltonian,…
Some mathematical theories in physics justify their explanatory superiority over earlier formalisms by the clarity of their postulates. In particular, axiomatic reconstructions drive home the importance of the composition rule and the…
Recently, some attention has been paid to falsifying the Leggett model, in which global probabilities characterizing a quantum state are represented by a combination of factorisable distributions. This idea was even verified in experiments,…
The question of a hidden variable interpretation of quantum contextuality in the Mermin-Peres square is considered. The Kochen-Specker theorem implies that quantum mechanics may be interpreted as a contextual hidden variable theory. It is…
We consider some generalization of the theory of quantum states and demonstrate that the consideration of quantum states as sheaves can provide, in principle, more deep understanding of some well-known phenomena. The key ingredients of the…
Quantum mechanics is formulated as a geometric theory on a Hilbert manifold. Images of charts on the manifold are allowed to belong to arbitrary Hilbert spaces of functions including spaces of generalized functions. Tensor equations in this…
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…
According to the Kolmogorovian Censorship Hypothesis, everything that quantum theory says about the world in the language of the quantum mechanical Hilbert space formalism is actually about relationships between ordinary relative…
In a predicative framework from basic logic, defined for a model of quantum parallelism by sequents, we characterize a class of first order domains, termed {\em virtual singletons}, which allows a generalization of the notion of duality,…
Quantum cognition in decision-making is a recent and rapidely growing field. In this paper we develop an expected utility theory in a context of non-classical (quantum) uncertainty. We replace the classical state space with a Hilbert space…
We propose a formal reconstruction of quantum mechanics grounded not in external mathematical abstractions, but in the structured dynamics of subjective experience. The Qualia Abstraction Language (QAL) models physical systems as evolving…