Related papers: Navigation in Curved Space-Time
In this paper we establish a generally and globally valid coordinate system in curved space-time with the simultaneous hypersurface orthogonal to the time coordinate. The time coordinate can be preseted according to practical evolving…
Commuting and noncommuting space-time coordinates in a class of deformed special relativity theories are investigated. Their momentum space representation, transformation behaviour, space-time algebra, invariants and the corresponding field…
We show that Maxwell's electromagnetism can be mapped into the Born-Infeld theory in a curved space-time, which depends only on the electromagnetic field in a specific way. This map is valid for any value of the two lorentz invariants $F$…
Time-averaged two-point currents are derived and shown to be spatially invariant within domains of local translation or inversion symmetry for arbitrary time-periodic quantum systems in one dimension. These currents are shown to provide a…
We consider defining time as a function of a cyclical field, an abstraction of a clock. The definition of time corresponds to a novel interpretation of the relationship between space-time coordinates of observers at different locations in…
We consider a modified version of four-dimensional electrodynamics, which has a photonic Chern-Simons-like term with spacelike background vector in the action. Light propagation in curved spacetime backgrounds is discussed using the…
On the basis of a "local" principle of equivalence of general relativity, we consider a navigation in a kind of "4D-ocean" involving measurements of conformally invariant physical properties only. Then, applying the Pfaff theory for PDE to…
Space-time-modulated systems have attracted significant interest over the past decade due to their ability to manipulate electromagnetic waves in unprecedented ways. Here, we introduce a new type of space-time-modulated structure, the…
We show that there exists a duality between the local coordinates and the solutions of the Klein-Gordon equation in curved spacetime in the same sense as in the Minkowski spacetime. However, the duality in curved spacetime does not have the…
Clock synchronization is the backbone of applications such as high-accuracy satellite navigation, geolocation, space-based interferometry, and cryptographic communication systems. The high accuracy of synchronization needed over…
The dynamics of spinning particles in curved space-time is discussed, emphasizing the hamiltonian formulation. Different choices of hamiltonians allow for the description of different gravitating systems. We give full results for the…
In the covariant canonical approach to classical physics, each point in phase space represents an entire classical trajectory. Initial data at a fixed time serve as coordinates for this ``timeless'' phase space, and time evolution can be…
Uncertainty relations for particle motion in curved spaces are discussed. The relations are shown to be topologically invariant. New coordinate system on a sphere appropriate to the problem is proposed. The case of a sphere is considered in…
In general relativity, cosmology and quantum field theory, spacetime is assumed to be an orientable manifold endowed with a Lorentz metric that makes it spatially and temporally orientable. The question as to whether the laws of physics…
Space-time coordinates in DSR theories with two invariant scales based on a dispersion relation with an energy independent speed of light are introduced by the demand, that boost and rotation generators are invariant under a transformation…
In 1948, Schwinger developed a local Lorentz covariant formulation of relativistic quantum electrodynamics in space-time which is fundamentally inconsistent with any delocalized interpretation of quantum mechanics. An interpretation…
We present a variant of a Global Navigation Satellite System called a Relativistic Positioning System (RPS), which is based on emission coordinates. We modelled the RPS dynamics in a space-time around Earth, described by a perturbed…
A theory for wave mechanical systems with local inversion and translation symmetries is developed employing the two-dimensional solution space of the stationary Schr\"odinger equation. The local symmetries of the potential are encoded into…
A quantum navigation problem concerns the identification of a time-optimal Hamiltonian that realises a required quantum process or task, under the influence of a prevailing `background' Hamiltonian that cannot be manipulated. When the task…
A possible model for quantum kinematics of a test particle in a curved space-time is proposed. Every reasonable neighbourhood V_e of a curved space-time can be equipped with a nonassociative binary operation called the geodesic…