Related papers: A simple criterion for nonrotating reference frame…
We establish the conditions under which a conservation law associated with a non-invertible operator may be realized as a symmetry in quantum physics. As established by Wigner, all quantum symmetries must be represented by either unitary or…
We reformulate Classical Mechanics as a timeless relativistic theory. Readers are introduced to a new class of reference systems, the binate frames, where physical events are identified with four position-coordinates -- no clocks are used.…
Rotation of polarization in an external gravitational field is one of the effects of general relativity that can serve as a basis for its precision tests. A careful analysis of reference frames is crucial for a proper evaluation of this…
One important global topological property of a spacetime manifold is orientability. It is widely believed that spatial orientability can only be tested by global journeys around the Universe to check for orientation-reversing closed paths.…
The purpose of this note is to generalize the celebrated Ran and Reurings fixed point theorem to the setting of a space with a binary relation that is only transitive (and not necessarily a partial order) and a relation-complete metric. The…
As we typically teach in an introductory mechanics course, choosing a "good" reference frame with convenient axes may present a major simplification to a problem. Additionally, knowing some conserved quantities provides an extremely…
In axistationary asymptotically flat spacetimes zero angular momentum observers (ZAMOs) define an absolute standard of non--rotation locally, as can be verified by the absence of any Sagnac effect for these observers. Nevertheless, we argue…
A quantum frame is defined by a material object subject to the laws of quantum mechanics. The present paper studies the relations between quantum frames, which in the classical case are described by elements of the Poincare' group. The…
A characterization of regular topological fundamental groups yields a `no retraction theorem' for spaces constructed in similar fashion to the Hawaiian earring.
We examine the problem of motion of an oscillating mass object provided no external force is applied to it. Calculations directly lead to the conclusion that the body accelerates in each system of reference except for the rest reference…
We describe an explicitly non-contextual statistical model of hidden variables for the qutrit, which fully reproduces the predictions of quantum mechanics and, thus, bypasses the constraints imposed by the Kochen-Specker theorem and its…
Identity-homotopic self-homeomorphisms of a space of non-periodic 1-dimensional tiling are generalizations of orientation-preserving self-homeomorphisms of circles. We define the analogue of rotation numbers for such maps. In constrast to…
We established a fixed-point theorem for mapping satisfying a general contractive inequality of integral type depended an another function. This theorem substantially extend the theorem due to Branciari (2003) and Rhoades (2003)
The theory of Space rotations is introduced. The relativity principle is generalized to satisfy to reference frames rotating in 3D space. It is shown that the most postulates and limitations of quantum theories are consequences of this…
A theory of gravity with a generic action functional and minimally coupled to N matter fields has a nontrivial fixed point in the leading large N approximation. At this fixed point, the cosmological constant and Newton's constant are…
The concept of rigid reference frame and of constricted spatial metric, given in the previous work [\emph{Class. Quantum Grav.} {\bf 21}, 3067,(2004)] are here applied to some specific space-times: In particular, the rigid rotating disc…
A ``Wick rotation'' is applied to the noncommutative sphere to produce a noncommutative version of the hyperboloids. A harmonic basis of the associated algebra is given. It is noted that, for the one sheeted hyperboloid, the vector space…
We present a fully relativistic analysis of Bessel beams revealing some noteworthy features that are not explicit in the standard description. It is shown that there is a reference frame in which the field takes a particularly simple form,…
Some recent papers formulated sufficient conditions for the decomposition of matrix variances. A statement was that if we have one or two observables, then the decomposition is possible. In this paper we consider an arbitrary finite set of…
Recent modern space missions deliver invaluable information about origin of our universe, physical processes in the vicinity of black holes and other exotic astrophysical objects, stellar dynamics of our galaxy, etc. On the other hand,…