Related papers: What is the reference frame of an accelerated obse…
Based on a recent relational formulation of quantum reference frame transformations, especially with a case of quantum spatial translations in particular, we analyzed how the `value' of an observable for a fixed state change. That is the…
The relative motion of material, point-like observers is analysed in terms of coordinate maps between the respective rest-frame of each observer. Under the assumption these maps are $C^{2}$-regular, conservation laws are deduced, which in…
We propose a simple nonlinear observer for estimating the attitude and velocity of a rigid body from the measurements of specific acceleration, angular velocity, magnetic field (in body axes), and linear velocity (in body axes). It is…
A free system, considered to be a comparison system, allows for the notion of objective existence and inertial frame. Transformations connecting inertial frames are shown to be either Lorentz or generalized Galilei.
We revisit the long standing problem of analyzing an inertial electric charge from the point of view of uniformly accelerated observers in the context of semi-classical gravity. We choose a suitable set of accelerated observers with respect…
One version of the principle of equivalence, as originally formulated by Einstein, states that ``gravity" can be mimicked locally by going to an ``accelerated frame of reference". As highlighted by Synge, the physical content of this…
The interval of a flat Minkowski space is invariant with respect to the previously found three-dimensional transformation for point rotating coordinate systems. The assumption that our space is an object of point rotation at a frequency…
Due to the Unruh effect, accelerated and inertial observers differ in their description of a given quantum state. The implications of this effect are explored for the entropy assigned by such observers to localized objects that may cross…
Besides the defining space-time symmetries (homogeneity and isotropy) of inertial frames, the derivation of Lorentz transformation requires postulating the principle of relativity and the existence of a finite speed limit. In this article,…
The special theory of relativity teaches us that, although distinct inertial frames perceive the same dynamical laws, space and time intervals differ in value. We revisit the problem of time contraction using the paradigmatic model of a…
Everyday experience with centrifugal forces has always guided thinking on the close relationship between gravitational forces and accelerated systems of reference. Once spatial gravitational forces and accelerations are introduced into…
We probe the thermodynamic structure of gravity at local scales. In any general curved spacetime, it is possible to transform to a local inertial frame at any point such that the metric is flat up to quadratic order where the curvature at…
It is shown that the force in relativistic mechanics is not only the cause of acceleration of particle relative to an inertial frame of reference, but also the cause of change of the course of time along the particle's trajectory. Therein…
It has been argued by R. T. Cahill and others that a Michelson interferometer in "gas mode" - in which the light paths are through an included gaseous medium - are able to detect and have detected an absolute frame of reference. It is shown…
Motivated by drone autonomous navigation applications we address a novel problem of velocity-aided attitude estimation by combining two linear velocity components measured in a body-fixed frame and a linear velocity component measured in an…
We study an area distance in the Riemannian spacetime with expansion, vorticity and acceleration. It is shown that this observable depends on expansion, deceleration and acceleration parameters to third order in redshift, as well as on…
In the extensive literature dealing with the relativistic phenomenon of Thomas rotation several methods have been developed for calculating the Thomas rotation angle of a gyroscope along a circular world line. One of the most appealing…
We present a relativistic space-time diagram that displays in true magnitudes the readings (daytimes) of two inertial reference frames clocks. One reference frame is the rest frame for one clock. This diagram shows that two events…
We consider the following questions: when do there exist quaternionic frames with given frame spectrum and given frame vector norms? When such frames exist, is it always possible to interpolate between any two while fixing their spectra and…
The clock time t' of an accelerating observer, simultaneous with the measured clock time t of an inertial observer,is easily established in special relativity (as proper time) by the well-known time-dilation formula for t'(t). In this work,…