Related papers: Quantum Spaces are Modular
Classical mechanics, relativity, electrodynamics and quantum mechanics are often depicted as separate realms of physics, each with its own formalism and notion. This remains unsatisfactory with respect to the unity of nature and to the…
Different approaches are compared to formulation of quantum mechanics of a particle on the curved spaces. At first, the canonical, quasi-classical and path integration formalisms are considered for quantization of geodesic motion on the…
In quantum electrodynamics a classical part of the S-matrix is normally factored out in order to obtain a quantum remainder that can be treated perturbatively without the occurrence of infrared divergences. However, this separation, as…
As established by Sol\`er, Quantum Theories may be formulated in real, complex or quaternionic Hilbert spaces only. St\"uckelberg provided physical reasons for ruling out real Hilbert spaces relying on Heisenberg principle. Focusing on this…
In classical theory, the physical systems are elucidated through the concepts of particles and waves, which aim to describe the reality of the physical system with certainty. In this framework, particles are mathematically represented by…
Starting with the Hamiltonian formulation for spacetimes with two commuting spacelike Killing vectors, we construct a midisuperspace model for linearly polarized plane waves in vacuum gravity. This model has no constraints and its degrees…
A rather non-standard quantum representation of the canonical commutation relations of quantum mechanics systems, known as the polymer representation has gained some attention in recent years, due to its possible relation with Planck scale…
The fundamental axioms of the quantum theory do not explicitly identify the algebraic structure of the linear space for which orthogonal subspaces correspond to the propositions (equivalence classes of physical questions). The projective…
In this paper we analyze and discuss the historical and philosophical development of the notion of logical possibility focusing on its specific meaning in classical and quantum mechanics. Taking into account the logical structure of quantum…
Some recent experiments claim to show that any model in which a quantum state represents mere information about an underlying physical reality of the system must make predictions which contradict those of quantum theory. The present work…
Quantum physics is a linear theory, so it is somewhat puzzling that it can underlie very complex systems such as digital computers and life. This paper investigates how this is possible. Physically, such complex systems are necessarily…
The two essential ideas in this paper are, on the one hand, that a considerable amount of the power of quantum computation may be obtained by adding to a classical computer a few specialized quantum modules and, on the other hand, that such…
We define and study the notion of quantum polarity, which is a kind of geometric Fourier transform between sets of positions and sets of momenta. Extending previous work of ours, we show that the orthogonal projections of the covariance…
The canonical answer to the question posed is "Yes." -- tacitly assuming that quantum theory and the concept of spacetime are to be unified by `quantizing' a theory of gravitation. Yet, instead, one may ponder: Could quantum mechanics arise…
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…
The ontology proposed in this paper is aimed at demonstrating that it is possible to understand the counter-intuitive predictions of quantum mechanics while still retaining much of the framework underlying classical physics, the implication…
The basic problem of quantum cosmology is the definition of the quantum state of the universe, with appropriate boundary conditions on Riemannian three-geometries. This paper describes recent progress in the corresponding analysis of…
We discuss two topics that are usually considered to be exclusively "quantum": the Schroedinger equation, and the uncertainty principle. We show (or rather recall) that the Schroedinger equation can be derived from Hamilton's equations…
We propose that the Schrodinger equation results from applying the classical wave equation to describe the physical system in which subatomic particles play random motion, thereby leading to quantum mechanics. The physical reality described…
In previous works, we showed that both time and space can emerge from entanglement within a globally constrained quantum Universe, with no background coordinates. By extending the Page and Wootters quantum time formalism to include both…