Related papers: Length measurement of a moving rod by a single obs…
We show that quantum mechanics and general relativity imply the existence of a minimal length. To be more precise, we show that no operational device subject to quantum mechanics, general relativity and causality could exclude the…
We present an approach to estimate the operational distinguishability between an entangled state and any separable state directly from measuring an entanglement witness. We show that this estimation also implies bounds on a variety of other…
Measuring dependence between random variables is a fundamental problem in Statistics, with applications across diverse fields. While classical measures such as Pearson's correlation have been widely used for over a century, they have…
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…
We provide a short proof that the Wasserstein distance between the empirical measure of a n-sample and the estimated measure is of order n^-(1/d), if the measure has a lower and upper bounded density on the d-dimensional flat torus.
We present a definition of time measurement based on high energy photons and the fundamental length scale, and show that, for macroscopic time, it is in accord with the Lorentz transformation of special relativity. To do this we define…
We show that an unification of quantum mechanics and general relativity implies that there is a fundamental length in Nature in the sense that no operational procedure would be able to measure distances shorter than the Planck length.…
The paper treats the issue of the length of a rotating circumference as seen from on board the moving disk and from an inertial reference frame. It is shown that, properly defining a measuring process, the result is in both cases 2piR thus…
We give a closed expression for the Minkowski (1+1)-dimensional metric in the radar coordinates of an arbitrary non-inertial observer O in terms of O's proper acceleration. Knowledge of the metric allows the non-inertial observer to perform…
Ng and van Dam have argued that quantum theory and general relativity give a lower bound of L^{1/3} L_P^{2/3} on the uncertainty of any distance, where L is the distance to be measured and L_P is the Planck length. Their idea is roughly…
We establish some deviation inequalities, moment bounds and almost sure results for the Wasserstein distance of order p $\in$ [1, $\infty$) between the empirical measure of independent and identically distributed R d-valued random variables…
We consider a Markov chain on $\mathbb{R}^d$ with invariant measure $\mu$. We are interested in the rate of convergence of the empirical measures towards the invariant measure with respect to various dual distances, including in particular…
We obtain estimates of all components of the velocity of a 3D rigid body moving in a viscous incompressible fluid without any symmetry restriction on the shape of the rigid body or the container. The estimates are in terms of suitable norms…
The article presents a comparative analysis of the accuracy of the distance to the observed object for geometric methods in noisy observations of bearings-only information.
In this paper, we prove that two different observers don't equally measure the distance between two points A and B. For this, we introduce some postulates and obtain a new formula to show distance between A and B. In this formula, radius of…
We present a derivation of the relativistic length-contraction formula based on Lorentz space-time transformations on non-simultaneous events. Our derivation avoids the disputable story about the stationary observer and its simultaneous…
The full characterization of a stringed musical instrument requires measuring the motion of the strings in at least two dimensions. Traditionally this has been done using electromagnetic means or by optical transmission. However in many…
The question of optimally approximating an arbitrary probability measure in the Wasserstein distance by a discrete one with uniform weights is considered. Estimates are obtained for the optimal approximation distance, with an explicit rate…
The visualisation of objects moving at relativistic speeds has been a popular topic of study since Special Relativity's inception. While the standard exposition of the theory describes certain shape-changing effects, such as the…
The attitude of a rigid body evolves on the three-dimensional special orthogonal group, and it is often estimated by measuring reference directions, such as gravity or magnetic field, using an onboard sensor. As a single direction…