Related papers: Classical and Quantum Mechanics with Poincare-Snyd…
We apply the many-particle Schr\"{o}dinger-Newton equation, which describes the co-evolution of an many-particle quantum wave function and a classical space-time geometry, to macroscopic mechanical objects. By averaging over motions of the…
The paper contains further development of the idea of field quantization introduced in M. Czachor, J. Phys. A: Math. Gen. {\bf 33} (2000) 8081-8103. The formalism is extended to the relativistic domain. The link to the standard theory is…
We give an introductory overview of the classical Poincar\'e gauge theory of gravity formulated on the spacetime manifold that carries the Riemann-Cartan geometry with nontrivial curvature and torsion. After discussing the basic…
Since the advent of quantum mechanics we have mainly been concerned with its predictions from the perspective of an external observer. This is in strong contrast to the theory of general relativity, where the physics is governed by the…
Extra dimensions are introduced: 3 in Classical Mechanics and 6 in Relativistic Mechanics, which represent orientations, resulting from rotations, of a particle, described by quaternions, and leading to a 7-dimensional, respectively…
Because of the non-locality of quantum entanglement, realist approaches to completing quantum mechanics have implications for our conception of space. Quantum gravity also is expected to predict phenomena in which the locality of classical…
The recently introduced consistent discrete lattice formulation of canonical general relativity produces a discrete theory that is constraint-free. This immediately allows to overcome several of the traditional obstacles posed by the…
The relationship between classical and quantum theory is of central importance to the philosophy of physics, and any interpretation of quantum mechanics has to clarify it. Our discussion of this relationship is partly historical and…
Relational mechanics is a reformulation of mechanics (classical or quantum) for which space is relational. This means that the configuration of an $N$-particle system is a shape, which is what remains when the effects of rotations,…
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…
We attempt to contribute some novel points of view to the "foundations of quantum mechanics", using mathematical tools from "quantum probability theory" (such as the theory of operator algebras). We first introduce an abstract algebraic…
The Problem of Time in Quantum Gravity is analyzed from a classical presymplectic perspective. In the first part of the paper the Three Space Approach to General Relativity is introduced via the Barbour-Foster-\'O Murchadha action and the…
The objective of this series of three papers is to axiomatically derive quantum mechanics from classical mechanics and two other basic axioms. In this first paper, Schreodinger's equation for the density matrix is fist obtained and from it…
We postulate that physical states are equivalent under coordinate transformations. We then implement this equivalence principle first in the case of one-dimensional stationary systems showing that it leads to the quantum analogue of the…
Quantum particles in a potential are described by classical statistical probabilities. We formulate a basic time evolution law for the probability distribution of classical position and momentum such that all known quantum phenomena follow,…
Quantum technology is seeing a remarkable explosion in interest due to a wave of successful commercial technology. As a wider array of engineers and scientists are needed, it is time we rethink quantum educational paradigms. Current…
The geometro-stochastic method of quantization provides a framework for quantum general relativity, in which the principal frame bundles of local Lorentz frames that underlie the fibre-theoretical approach to classical general relativity…
Classical and quantum physics represent two distinct theories; however, quantum physics is regarded as the more fundamental of the two. It is posited that classical mechanics should arise from quantum mechanics under certain limiting…
In this tenth paper of the series we aim at showing that our formalism, using the Wigner-Moyal Infinitesimal Transformation together with classical mechanics, endows us with the ways to quantize a system in any coordinate representation we…
This work deals with the questions of absolute space and relativity. In particular, an alternative derivation of the effects described by special relativity is provided, which is based on a description that assumes a privileged reference…