Related papers: Frames of Reference and Some of its Applications
Composite quantum systems can be decomposed into subsystems in many different inequivalent ways. We call a particular decomposition a meronomic reference frame for the system. We apply the ideas of quantum reference frames to characterize…
In a companion paper (Jonsson and Westman, Class. Quantum Grav. 23 (2006) 61), a generalization of optical geometry, assuming a non-shearing reference congruence, is discussed. Here we illustrate that this formalism can be applied to a…
This paper is an exploration of the nuanced realm of reference frames within the framework of General Relativity. Our analysis exposes a violation of Earman's SP1 principle in scenarios involving fields that are dynamically uncoupled, a…
In standard quantum mechanics, reference frames are treated as abstract entities. We can think of them as idealized, infinite-mass subsystems which decouple from the rest of the system. In nature, however, all reference frames are realized…
The general construction of extended refrence frames for noninertial observers in flat space is studied. It is shown that, if the observer moves inertially before and after an arbitrary acceleration and rotation, the region where reference…
Originally introduced in connection with general relativistic Coriolis forces, the term $\textit{frame-dragging}$ is associated today with a plethora of effects related to the off-diagonal element of the metric tensor. It is also frequently…
In A. Poltorak's concept, the reference frame in General Relativity is a certain manifold equipped with a connection. The question under consideration here is whether it is possible to join two events in the space-time by a time-like…
A framed surface is a smooth surface in the Euclidean space with a moving frame. By using the moving frame, we can define Bertrand framed surfaces as the same idea as Bertrand framed curves. Then we find the caustics and involutes as…
One approach to ease the construction of frames is to first construct local components and then build a global frame from these. In this paper we will show that the study of the relation between a frame and its local components leads to the…
Quantum reference frame transformations have been proposed to provide a means by which to translate descriptions of quantum systems relative to each other. At present, there are several differing frameworks for describing quantum reference…
The paper proposes a generalization of the Park transform based on the Frenet frame, which is a special set of coordinates defined in differential geometry for space curves. The proposed geometric transform is first discussed for three…
The purpose of the dynamics of moving systems is to search for the mathematical model that describes the link between the resultant applied force, that is the cause, and the speed of system that is the effect. This mathematical link…
A model for reference use in communication is proposed, from a representationist point of view. Both the sender and the receiver of a message handle representations of their common environment, including mental representations of objects.…
Frame theory is an exciting, dynamic and fast paced subject with applications in numerous fields of mathematics and engineering. In this paper we study Continuous Frame and introduce Continuous Frame with $C^{\ast}$-valued bounds. Also, we…
An observer at rest in a uniformly accelerated reference frame experiences a parallel gravitational field, where the rays of light are formed as circular arcs instead of being straight lines. We deduce how a sphere at rest in the Rindler…
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…
We will introduce formal frames of manifolds, which are a generalization of ordinary frames. Their fundamental properties are discussed. In particular, canonical forms are introduced, and torsions are defined in terms of them as a…
We present a method for constructing all bounded rational motions that frame a space curve $\mathbf{r}(t)$. This means that the motion guides an orthogonal frame along the curve such that one frame axis is in direction of the curve tangent.…
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…
This work introduces the framed curvature flow, a generalization of both the curve shortening flow and the vortex filament equation. Here, the magnitude of the velocity vector is still determined by the curvature, but its direction is given…