Related papers: Observers and Splitting Structures in Relativistic…
Although time is one of our most intuitive physical concepts, its understanding at the fundamental level is still an open question in physics. For instance, time in quantum mechanics and general relativity are two distinct and incompatible…
A method of designing observers and observer-based tracking controllers is proposed for nonlinear systems on manifolds via embedding into Euclidean space and transversal stabilization. Given a system on a manifold, we first embed the…
This paper explores the observability and estimation capability of dynamical systems using predominantly relative measurements of the system's state-space variables, with minimal to no reliance on absolute measurements of these variables.…
The resonant modes of two-dimensional elastic elliptical objects are studied from a modal formalism by emphasizing the role of the symmetries of the objects. More precisely, as the symmetry is broken in the transition from the circular disc…
We address the observability problem for ensembles that are described by probability distributions. The problem is to reconstruct a probability distribution of the initial state from the time-evolution of the probability distribution of the…
We present a general approach to quantum entanglement and entropy that is based on algebras of observables and states thereon. In contrast to more standard treatments, Hilbert space is an emergent concept, appearing as a representation…
The aim of this paper is to present the application of an approach to study contraction theory recently developed for piecewise smooth and switched systems. The approach that can be used to analyze incremental stability properties of…
I present an analysis of the physical assumptions needed to obtain the metric structure of space-time. For this purpose I combine the axiomatic approach pioneered by Robb with ideas drawn from works on Weyl's "Raumproblem". The concept of a…
We consider "unphysical", kinematic observables that do not commute with the constraints of a gauge system in the context of an extension of the system. We show that these observables, while not predictable, can nevertheless be said to have…
The usual formulation of time-dependent mechanics implies a given splitting $Y=R\times M$ of an event space $Y$. This splitting, however, is broken by any time-dependent transformation, including transformations between inertial frames. The…
Objectives: A systematic study on the general relativistic Poynting-Robertson effect has been developed so far by introducing different complementary approaches, which can be mainly divided in two kinds: (1) improving the theoretical…
We examine length measurement in curved spacetime, based on the 1+3-splitting of a local observer frame. This situates extended objects within spacetime, in terms of a given coordinate which serves as an external reference. The radar metric…
Recent advances in semiclassical gravity, both in our understanding of the gravitational path integral and the algebraic structure of a gravitating subregion, rely on the presence of an observer to obtain a nontrivial Hilbert space for…
A new approach to classical electrodynamics is presented, showing that it can be regarded as a particular case of the most general relativistic force field. In particular, at first it is shown that the structure of the Lorentz force comes…
We first develop systematic and comprehensive interval observer designs for linear time-invariant (LTI) systems, under standard assumptions of observability and interval bounds on the initial condition and uncertainties. Traditionally, such…
Defining gravitational subsystems has long been challenging due to the lack of the conventional notion of locality in gravity. In this work, we define gravitational subsystems from the observable spacetime subregions of a set of…
We consider spacetime to be a 4-dimensional differentiable manifold that can be split locally into time and space. No metric, no linear connection are assumed. Matter is described by classical fields/fluids. We distinguish electrically…
The Schr\"odinger equation in the presence of an external electromagnetic field is an important problem in computational quantum mechanics. It also provides a nice example of a differential equation whose flow can be split with benefit into…
The description of relativistic effects requires a preliminary definition of events localised in space-time while the clocks used for time definition and the fields used in synchronisation or localisation procedures are necessarily quantum…
The relativistic spinning particle model, proposed in [3,4], is analyzed in a Hamiltonian framework. The spin is simulated by extending the configuration space by introducing a light-like four vector degree of freedom. The model is heavily…