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Whenever an experiment can be described classically, quantum physics must predict the same outcome. Intuitively, there is nothing quantum about an accelerating observer travelling through a vacuum. It is therefore not surprising that many…
This paper presents three non-linear observers on three examples of engineering interest: a chemical reactor, a non-holonomic car, and an inertial navigation system. For each example, the design is based on physical symmetries. This…
Smartphones equipped with sensors such as accelerometers, gyroscopes, and magnetometers offer valuable opportunities for physics education, allowing students to measure motion using their own devices. However, commonly used applications…
What happens when two synchronized clocks on a rigid beam are both given the exact same acceleration profile? Will they remain synchronized? What if we use a rigid-rod Rindler acceleration profile? The special relativity prediction…
This paper introduces a new mobile sensor scheduling problem, involving a single robot tasked with monitoring several events of interest that occur at different locations. Of particular interest is the monitoring of transient events that…
We show that starting with the fact that special relativity theory is concerned with a distortion of the observed length of a moving rod, without mentioning if it is a "contraction" or "dilation", we can derive the Lorentz transformations…
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…
The robust distributed state estimation for a class of continuous-time linear time-invariant systems is achieved by a novel kernel-based distributed observer, which, for the first time, ensures fixed-time convergence properties. The…
Doppler effect and Hubble effect in different models of space-time in the case of auto-parallel motion of the observer are considered. The Doppler effect and shift frequency parameter are specialized for the case of auto-parallel motion of…
Several new ideas related to Special and General Relativity are proposed. The black-box method is used for the synchronization of the clocks and the space axes between two inertial systems or two accelerated systems and for the derivation…
While the Unruh effect has traditionally been studied under the assumption of uniform acceleration, a simplification motivated by experimental considerations, it is not necessarily true for all non-inertial motions. We propose a novel…
This paper revisits the problems of estimating the position of an object moving in $n$ ($\geq 2$)-dimensional Euclidean space using velocity measurements and either direction or range measurements of one or multiple source points. The…
We demonstrate that, under orthographic projection and with a camera fixated on a point located on a rigid body, the rotation of that body can be analytically obtained by tracking only one other feature in the image. With some exceptions,…
In the rod and hole paradox as described by Rindler (1961 Am. J. Phys. 29 365-6), a rigid rod moves at high speed over a table towards a hole of the same size. Observations from the inertial frames of the rod and slot are widely different.…
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…
Rayleigh-B\'enard convection (RBC) is a fundamental problem of fluid dynamics, with many applications to geophysical, astrophysical, and industrial flows. Understanding RBC at parameter regimes of interest requires complex physical or…
We focus in this paper in the estimation of a target trajectory defined by whether a time constant parameter in a simple stochastic process or a random walk with binary observations. The binary observation comes from binary derivative…
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…
In the description of \emph{relative} motion in accelerated systems and gravitational fields, inertial and tidal accelerations must be taken into account, respectively. These involve a critical speed that in the first approximation can be…
Event cameras offer high temporal resolution and low latency, making them ideal sensors for high-speed robotic applications where conventional cameras suffer from image degradations such as motion blur. In addition, their low power…