Deriving relativistic momentum and energy

We present a new derivation of the expressions for momentum and energy of a relativistic particle. In contrast to the procedures commonly adopted in textbooks, the one suggested here requires only the knowledge of the composition law for velocities along one spatial dimension, and does not make use of the concept of relativistic mass, or of the formalism of four-vectors. The basic ideas are very general and can be applied also to kinematics different from the Newtonian and Einstein ones, in order to construct the corresponding dynamics.Comment: 15 pages, 2 figure

Interlaboratory comparison reveals state of the art in microplastic detection and quantification methods

In this study, we investigate the current accuracy of widely used microplastic (MP) detection methods through an interlaboratory comparison (ILC) involving ISO-approved techniques. The ILC was organized under the prestandardization platform of VAMAS (Versailles Project on Advanced Materials and Standards) and gathered a large number (84) of analytical laboratories across the globe. The aim of this ILC was (i) to test and to compare two thermo-analytical and three spectroscopical methods with respect to their suitability to identify and quantify microplastics in a water-soluble matrix and (ii) to test the suitability of the microplastic test materials to be used in ILCs. Two reference materials (RMs), polyethylene terephthalate (PET) and polyethylene (PE) as powders with rough size ranges between 10 and 200 μm, were used to press tablets for the ILC. The following parameters had to be assessed: polymer identity, mass fraction, particle number concentration, and particle size distribution. The reproducibility, SR, in thermo-analytical experiments ranged from 62%–117% (for PE) and 45.9%–62% (for PET). In spectroscopical experiments, the SR varied between 121% and 129% (for PE) and 64% and 70% (for PET). Tablet dissolution turned out to be a very challenging step and should be optimized. Based on the knowledge gained, development of guidance for improved tablet filtration is in progress. Further, in this study, we discuss the main sources of uncertainties that need to be considered and minimized for preparation of standardized protocols for future measurements with higher accuracy

Begründung der Lorentz-Gruppe allein mit Symmetrie-und Relativitäts-Annahmen

Abstract Aus dem Relativitätsprinzip folgt ohne Verwendung des empirischen Prinzips von der Konstanz der Lichtgeschwindigkeit, daß die Lorentz-Transformation die einzig denkbare Alternative zur (raumzeitlich asymmetrischen) Galilei-Transformation ist.</jats:p