Position space versions of Magueijo-Smolin doubly special relativity proposal and the problem of total momentum

We present and discuss two different possibilities to construct position space version for Magueijo-Smolin (MS) doubly special relativity proposal. The first possibility is to start from ordinary special relativity and then to define conserved momentum in special way. It generates MS invariant as well as nonlinear MS transformations on the momentum space, leading to consistent picture for one-particle sector of the theory. The second possibility is based on the following observation. Besides the nonlinear MS transformations, the MS energy-momentum relation is invariant also under some inhomogeneous linear transformations. The latter are induced starting from linearly realized Lorentz group in five-dimensional position space. Particle dynamics and kinematics are formulated starting from the corresponding five-dimensional interval. There is no problem of total momentum in the theory. The formulation admits two observer independent scales, the speed of light, $c$, and $k$ with dimension of velocity. We speculate on different possibilities to relate $k$ with fundamental constants. In particular, expression of $k$ in terms of vacuum energy suggests emergence of (minimum) quantum of mass.Comment: Latex twice, 14 pages, revised in accordance with the version publishedin Phys. Rev.

On the connection between Lenz's law and relativity

In this work, we demonstrate explicitly the unified nature of electric and magnetic fields, from the principles of special relativity and Lorentz transformations of the electromagnetic field tensor. Using an operational approach we construct the tensor and its corresponding transformation law, based on the principle of relativity. Our work helps to elucidate concepts of advanced courses on electromagnetism for primary-level learners and shows an alternative path to derive the Lenz's law based solely on relativity arguments.Comment: 6 pages, 4 figure

A Comment on the Classical Electron Self-Energy

This paper is devoted to the analysis of the divergence of the electron self-energy in classical electrodynamics. To do so, we appeal to the theory of distributions and a method for obtaining corresponding extensions. At first sight, electrostatics implies a divergence once we treat the electron as a charged point particle. However, our construction shows that its self-energy turns out to be an undetermined constant upon renormalization. Appealing to empirical results we may fix its value, demanding, for example, that all its mass comes from an electrostatic origin.Comment: 20 pages, no figures. Shorter and published version, in accordance to reviewers suggestion

Is time the real line?

This paper is devoted to discussing the topological structure of the arrow of time. In the literature, it is often accepted that its algebraic and topological structures are that of a one-dimensional Euclidean space $\mathbb{E}^1$, although a critical review on the subject is not easy to be found. Hence, leveraging on an operational approach, we collect evidences to identify it structurally as a normed vector space $(\mathbb{Q}, |\cdot|)$, and take a leap of abstraction to complete it, up to isometries, to the real line. During the development of the paper, the space-time is recognized as a fibration, with the fibers being the sets of simultaneous events. The corresponding topology is also exposed: open sets naturally arise within our construction, showing that the classical space-time is non-Hausdorff. The transition from relativistic to classical regimes is explored too.Comment: 26 pages, 9 figures. Misprints corrected and minor adjustments according to the review proces

One Hundred Years Later: Stern-Gerlach Experiment and Dimension Witnesses

Inspired by the one-hundredth anniversary of the seminal works of Stern and Gerlach, our contribution is a proposal of how to use their famous experiment in a more contemporary perspective. Our main idea is to re-cast the experiment in the modern language of prepare-and-measure scenarios. By doing so, it is possible to connect geometric and algebraic aspects of the space of states with the physical space. We also discuss possible simulations of the SG experiment as well as some experimental properties of the experiment revealed at the statistical level. Merging a more modern perspective with a paradigmatic experiment, we hope this paper can serve as an entry door for quantum information theory and the foundations of quantum mechanics.Comment: 23 pages, 6 figures. Minor adjustments, according to referee suggestion

Generalization of the Extended Lagrangian Formalism on a Field Theory and Applications

Formalism of extended Lagrangian represent a systematic procedure to look for the local symmetries of a given Lagrangian action. In this work, the formalism is discussed and applied to a field theory. We describe it in detail for a field theory with first-class constraints present in the Hamiltonian formulation. The method is illustrated on examples of electrodynamics, Yang-Mills field and non-linear sigma model.Comment: 17 pages, to be published in Phys. Rev.