Related papers: Elementary Quantum Mechanics in a Space-time Latti…
It is the matter of fact that quantum mechanics operates with notions that are not determined in the frame of the mechanics' formalism. Among them we can call the notion of "wave-particle" (that, however, does not appear in both classical…
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…
Within a theory of the existing fundamental length on the order of Planck's a high-energy deformation of the General Relativity for the space with horizon has been constructed. On this basis, Markov's work of the early eighties of the last…
The suspicion that the existence of a minimal uncertainty in position measurements violates Lorentz invariance seems unfounded. It is shown that the existence of such a nonzero minimal uncertainty in position is not only consistent with…
Some aspects of the interpretation of quantum theory are discussed. It is emphasized that quantum theory is formulated in the Cartesian coordinate system; in other coordinates the result obtained with the help of the Hamiltonian formalism…
One of the main challenges in physics today is to merge quantum theory and the theory of general relativity into a unified framework. Various approaches towards developing such a theory of quantum gravity are pursued, but the lack of…
We show how quantum mechanics can be understood as a space-time theory provided that its spatial continuum is modelled by a variable real number (qrumber) continuum. Such a continuum can be constructed using only standard Hilbert space…
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…
The quantum mechanical formalism for position and momentum of a particle in a one dimensional cyclic lattice is constructively developed. Some mathematical features characteristic of the finite dimensional Hilbert space are compared with…
A Planck-scale minimal observable length appears in many approaches to quantum gravity. It is sometimes argued that this minimal length might conflict with Lorentz invariance, because a boosted observer could see the minimal length further…
It is commonly accepted that the combination of quantum mechanics and general relativity gives rise to the emergence of a minimum uncertainty both in space and time. The arguments that support this conclusion are mainly based on…
The particle in a box is a simple model that has a classical Hamiltonian $H=p^2$ (using $2m=1$), with a limited coordinate space, $-b<q<b$, where $0<b<\infty$. Using canonical quantization, this example has been fully studied thanks to its…
We analyze the quantum phenomenon arising from the interaction of a spinless charged particle with a rotating cosmic string, under the action of a static and uniform magnetic field parallel to the string. We calculate the energy levels of…
In relativistic quantum field theory with local interactions, charge is locally conserved. This implies local conservation of probability for the Dirac and Klein-Gordon wavefunctions, as special cases; and then in turn for non-relativistic…
This paper argues that the requirement of applicableness of quantum linearity to any physical level from molecules and atoms to the level of macroscopic extensional world, which leads to a main foundational problem in quantum theory…
Planck scale physics represents a future challenge, located between particle physics and general relativity. The Planck scale marks a threshold beyond which the old description of spacetime breaks down and conceptually new phenomena must…
Various theories that aim at unifying gravity with quantum mechanics suggest modifications of the Heisenberg algebra for position and momentum. From the perspective of quantum mechanics, such modifications lead to new uncertainty relations…
There are four reasons why our present knowledge and understanding of quantum mechanics could be regarded as incomplete. Firstly, the principle of linear superposition has not been experimentally tested for position eigenstates of objects…
This paper presents a simple model that mimics quantum mechanics (QM) results in terms of probability fields of free particles subject to self-interference, without using Schr\"{o}dinger equation or wavefunctions. Unlike the standard QM…
This review consists of two parts. The first part establishes certain astrophysical bounds on the smoothness of classical spacetime. Some of the best bounds to date are based on the absence of vacuum Cherenkov radiation in ultrahigh-energy…