Related papers: Can we measure structures to a precision better th…
There exists, in general, no unique definition of the size (volume, area, etc., depending on dimension) of a soliton. Here we demonstrate that the geometric volume (area etc.) of a soliton is singled out in the sense that it exactly…
Observations in Quantum Mechanics are subject to complex restrictions arising from the principle of energy conservation. Determining such restrictions, however, has been so far an elusive task, and only partial results are known. In this…
We derive bounds on the volume of an inclusion in a body in two or three dimensions when the conductivities of the inclusion and the surrounding body are complex and assumed to be known. The bounds are derived in terms of average values of…
An overview of space tests searching for small deviations from special relativity arising at the Planck scale is given. Potential high-sensitivity space-based experiments include ones with atomic clocks, masers, and electromagnetic…
The recent measurements of the Cosmic Microwave Background Anisotropies provided by the Planck satellite experiment have significantly improved the constraints on several cosmological parameters. In this brief paper we point out a small but…
We propose a measure of shape which is appropriate for the study of a complicated geometric structure, defined using the topology of neighborhoods of the structure. One aspect of this measure gives a new notion of fractal dimension. We…
The measurement of distance between two objects is generalized to the case where the objects are no longer points but are one-dimensional. Additional concepts such as non-extensibility, curvature constraints, and non-crossing become central…
Capacitance measurement is a useful technique in studying quantum devices, as it directly probes the local particle charging properties, i.e. the system compressibility. Here we report one approach which can measure capacitance from mK to…
According to general relativity, clocks are the basic measuring devices needed to probe spacetime geometry. However, it is generally accepted that the mass of clocks capable of measuring small time intervals must be bounded from below. In…
In 2011, a discrepancy between the values of the Planck constant measured by counting Si atoms and by comparing mechanical and electrical powers prompted a review, among others, of the measurement of the spacing of $^{28}$Si {220} lattice…
Noncommutativity of the spacetime coordinates has been explored in several contexts, mostly associated to phenomena at the Planck length scale. However, approaching this question through deformation theory and the principle of stability of…
We discuss how the bounds on observation associated with the Planck units would affect an observers perception of a black hole. By simply imposing Planck scale quantities as the lower bounds for length, time, and mass of black hole…
The measurement of the Avogadro constant opened the way to a comparison of the watt-balance measurements of the Planck constant with the values calculated from the quotients of the Planck constant and the mass of a particle or an atom.…
A structured collection of thought provoking conclusions about space and time is given. Using only the Compton wavelength lambda = hbar / m c and the Schwarzschild radius r_s = 2 G m / c^2, it is argued that neither the continuity of…
Conventional wisdom holds that any region of 3-space contains infinitely many points, and the Planck length scale determines the uncertainty in every measurement of distance between two separate points. Against such a backdrop, this…
Precision measurements of the fundamental constants are tour de force of basic metrology, where the useful information is usually beyond the last digit of the measured value. They challenge theoretical models and measurement technologies…
Improved measurements of the proton's structure are now possible thanks to significant technical advances that allow us to probe the proton with polarized photons. These measurements have shown that the proton is not as simple as previously…
This article is a survey of recent results on slicing inequalities for convex bodies. The focus is on the setting of arbitrary measures in place of volume.
Space-based clock-comparison experiments can provide Planck-scale sensitivity to many parameters for Lorentz and CPT violation that are difficult to measure on Earth. The principal advantages are a reduced timescale for data collection,…
A brief summary of the objections to the relational nature of inertial mass, gravitational mass and electric charge is presented. The objections are refuted by showing that the measurement process of comparing an instrument reference clock…