Related papers: Can we measure structures to a precision better th…
This article briefly summarizes the motivations for -- and recent progress in -- searching for cosmological configurations within string theory, with a focus on how much we might reasonably hope to learn about fundamental physics from…
The study of the additive volume of sets can be reduced to the case of one-dimensional sets. The exact values of the volume of extremal sets are given as a conjecture.
We begin by revisiting a paper of Erd\H{o}s and Fishburn, which posed the following question: given $k\in \mathbb{N}$, what is the maximum number of points in a plane that determine at most $k$ distinct distances, and can such optimal…
The recent Planck Legacy 2018 release has confirmed the presence of an enhanced lensing amplitude in CMB power spectra compared to that predicted in the standard $\Lambda$CDM model. A closed universe can provide a physical explanation for…
Kempf et al. in Ref. [1] have formulated a Hilbert space representation of quantum mechanics with a minimal measurable length. Recently it has been revealed, in the context of doubly special relativity, that a test particles' momentum…
In this note we examine the volume of the convex hull of two congruent copies of a convex body in Euclidean $n$-space, under some subsets of the isometry group of the space. We prove inequalities for this volume if the two bodies are…
The space-time metric is widely believed to be subject to stochastic fluctuations induced by quantum gravity at the Planck scale. This work is based on two different phenomenological approaches being currently made to this topic, and…
There is a big gap between the charming principles ideas and the real implementation of a diagnostic. In this lecture we review some details that make the difference between a good and bad measurement, highlighting also the relation between…
It is argued that the fundamental length scale for the quantum dynamics of spacetime need not be equal to the Planck length. Possibly, this new length scale is related to a nonvanishing cosmological constant or vacuum energy density.
If a physical significance should be attributed to the cosmological large number relationship obtained from Sciama's formulation of Mach's Principle, then a number of interesting physical conclusions may be drawn. The Planck length is…
Time-like and space-like invariant space-time intervals are used to analyse measurements of spatial and temporal distances defined by two spatially-separated clocks. The time dilatation effect is confirmed, but not `relativity of…
Porosity and dimension are two useful, but different, concepts that quantify the size of fractal sets and measures. An active area of research concerns understanding the relationship between these two concepts. In this article we will…
Protective measurements, which we have introduced recently, allow to measure properties of the state of a single quantum system and even the Schr\"odinger wave itself. These measurements require a protection, sometimes due to an additional…
We carry out a systematic study of the bounds that can be set on Planck-scale deformations of relativistic symmetries and CPT from precision measurements of particle and antiparticle lifetimes. Elaborating on our earlier work [1] we discuss…
Trying to combine standard quantum field theories with gravity leads to a breakdown of the usual structure of space-time at around the Planck length, 1.6*10^{-35} m, with possible violations of Lorentz invariance. Calculations of…
The question of what should be meant by a measurement is tackled from a mathematical perspective whose physical interpretation is that a measurement is a fundamental process via which a finite amount of classical information is produced.…
Precision measurements of electroweak observables provide stringent tests of the Standard Model structure and an accurate determination of its parameters. A brief overview of the present experimental status is presented. A more extensive…
We examine the level of agreement between low redshift weak lensing data and the CMB using measurements from the CFHTLenS and Planck+WMAP polarization. We perform an independent analysis of the CFHTLenS six bin tomography results of Heymans…
A bounded subset of a normed linear space is said to be (diametrically) complete if it cannot be enlarged without increasing the diameter. A complete super set of a bounded set $K$ having the same diameter as $K$ is called a completion of…
We prove that any closed map between metrizable spaces can be extended to a closed map between completely metrizable spaces with the same extensional dimension.