Related papers: Geometric Event-Based Relativistic Quantum Mechani…
We propose a novel framework for the quantum geometry of expectation values over arbitrary sets of operators and establish a link between this geometry and the eigenstates of Hamiltonian families generated by these operators. We show that…
The relativity to the measuring device in quantum theory, i.e. the covariance of local dynamical variables relative transformations to moving quantum reference frame in Hilbert space, may be achieved only by the rejection of super-selection…
Einstein's theory of general relativity is based on the premise that the physical laws take the same form in all coordinate systems. However, it still presumes a preferred decomposition of the total kinematic Hilbert space into local…
We describe a theory amalgamating quantum theory and general relativity through the identification of a continuous 4-dimensional spacetime arena constructed from the substructures of a generalised multi-dimensional form for proper time. In…
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…
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…
The identification of physical subsystems in quantum mechanics as compared to classical mechanics poses significant conceptual challenges, especially in the context of quantum gravity. Traditional approaches associate quantum systems with…
Non-relativistic quantum mechanics is shown to emerge from classical mechanics through the requirement of a relativity principle based on special transformations acting on position and momentum uncertainties. These transformations keep the…
This paper addresses the question why quantum mechanics is formulated in a unitary Hilbert space, i.e. in a manifestly complex setting. Investigating the linear dynamics of real quantum theory in a finite-dimensional Euclidean Hilbert space…
The quantum theory of ur objects postulates that all existing physical objects and their properties are constructed from fundamental objects called ur objects being described by an element of a two dimensional complex Hilbert space. This…
The observed probabilities of quantum mechanics possess a time asymmetry which is based on the truism that a state must be prepared before an observable can be measured in it. While Hilbert space quantum theory cannot incorporate this arrow…
We propose a new quantum approach for describing a system of $n$ interacting particles with variable mass connected by an unknown field with variable form ($n$-VMVF systems). Instead of assuming any particular nature for variation of the…
We consider some basic problems associated with quantum mechanics of systems having a time-dependent Hilbert space. We provide a consistent treatment of these systems and address the possibility of describing them in terms of a…
The purpose of this contribution is to give an introduction to quantum geometry and loop quantum gravity for a wide audience of both physicists and mathematicians. From a physical point of view the emphasis will be on conceptual issues…
This paper is the first of two papers devoted to formulation of quantum mechanics of a particle in a normal geodesic frame of reference in the general Riemannian space-time. Here canonical quantization of geodesic motion in the…
Having started with the general formulation of the quantum theory of the real scalar field (QFT) in the general Riemannian space--time $ V_{1,3} $, the general--covariant quasinonrelativistic quantum mechanics of a point-like spinless…
The relational version of the modal interpretation offers both a consistent quantum ontology and solution for quantum paradoxes within the framework of nonrelativistic quantum mechanics. In the present paper this approach is generalized for…
Quantum mechanics is among the most important and successful mathematical model for describing our physical reality. The traditional formulation of quantum mechanics is linear and algebraic. In contrast classical mechanics is a geometrical…
On the basis of the relativistic symmetry of Minkowski space, we derive a Lorentz invariant equation for a spread electron. This equation slightly differs from the Dirac equation and includes additional terms originating from the spread of…
This paper represents the second in a series of works aimed at reinvigorating the quantum geometrodynamics program. Our approach introduces a lattice regularization of the hypersurface deformation algebra, such that each lattice site…