Related papers: Relativistic Positioning Systems
A key limitation of current multi-robot systems is a lack of relative localization, particularly in environments without GPS or motion capture systems. This article presents a centralized method for relatively localizing a 2D swarm using…
The standard formulation of quantum theory relies on a fixed space-time metric determining the localisation and causal order of events. In general relativity, the metric is influenced by matter, and is expected to become indefinite when…
Being able to measure time, whether directly or indirectly, is a significant advantage for an organism. It permits it to predict regular events, and prepare for them on time. Thus, clocks are ubiquitous in biology. In the present paper, we…
The relativity of Global Positioning System (GPS) pseudorange measurements is explored within the geometrical optics approximation in the curved space-time near Earth. A space-time grid for navigation is created by the discontinuities…
Machine perception is an important prerequisite for safe interaction and locomotion in dynamic environments. This requires not only the timely perception of surrounding geometries and distances but also the ability to react to changing…
In this article we outline the structure of a general relativistic astrometric model which has been developed to deduce the position and proper motion of stars from 1-microarcsecond optical observations made by an astrometric satellite…
Elementary particles, i.e. the basic constituents of nature, are characterized by quantum recurrences in time. The flow of time of every physical system can be therefore decomposed in elementary cycles of time. This allows us to enforce the…
I present a complete set of gauge invariant observables, in the context of general relativity coupled with a minimal amount of realistic matter (four particles). These observables have a straightforward and realistic physical…
While adhering to the formalism of Special and General Relativity, this paper considers the interpretation of clock rates and the rating of clocks in detail. We also pay particular attention to the crucial requirement of reciprocity between…
This paper studies the class of logarithmically completely monotonic (LCM) functions. These functions play an important role in characterising externally positive linear systems which find applications in important control problems such as…
We give a precise theoretical description of initially aligned sets of orthogonal gyroscopes which are transported along different paths from some initial point to the same final point in spacetime. These gyroscope systems can be used to…
There are a number of problematic features within the current treatment of time in physical theories, including the "timelessness" of the Universe as encapsulated by the Wheeler-DeWitt equation. This paper considers one particular…
In this note, we provide some categorical perspectives on the relativization construction arising from quantum measurement theory in the presence of symmetries and occupying a central place in the operational approach to quantum reference…
We discuss a systematic way in which a relational dynamics can be established relative to periodic clocks both in the classical and quantum theories, emphasising the parallels between them. We show that: (1) classical and quantum relational…
This tutorial, addressing physics teachers and undergraduate students, aims at clarifying some aspects of time in special relativity. In particular, time dilation is usually presented only as the well-known ratio of lab time over proper…
We provide a new algebraic solution procedure for the global positioning problem in $n$ dimensions using $m$ satellites. We also give a geometric characterization of the situations in which the problem does not have a unique solution. This…
Contrary to popular belief, the global positioning problem on earth may have more than one solutions even if the user position is restricted to a sphere. With 3 satellites, we show that there can be up to 4 solutions on a sphere. With 4 or…
A simple method to generate a two-dimensional binary grid pattern, which allows for absolute and accurate self-location in a finite planar region, is proposed. The pattern encodes position information in a local way so that reading a small…
The universality of the Laplace-Runge-Lenz symmetry in all rotationally symmetric systems is discussed. The independence of the symmetry on the type of interaction is proven using only the most generic properties of the Poisson brackets.…
We have previously shown (arXiv:1912.00033) that three approaches to relational quantum dynamics -- relational Dirac observables, the Page-Wootters formalism and quantum deparametrizations -- are equivalent. Here we show that this `trinity'…