Relativistic spring-mass system

Rodrigo Andrade e Silva, Andre G. S. Landulfo, George E. A. Matsas, Daniel A. T. Vanzella

The harmonic oscillator plays a central role in physics describing the dynamics of a wide range of systems close to stable equilibrium points. The nonrelativistic one-dimensional spring-mass system is considered a prototype representative of it. It is usually assumed and galvanized in textbooks that the equation of motion of a relativistic harmonic oscillator is given by the same equation as the nonrelativistic one with the mass M at the tip multiplied by the relativistic factor 1/(1−v2/c2)1/2. Although the solution of such an equation may depict some physical systems, it does not describe, in general, one-dimensional relativistic spring-mass oscillators under the influence of elastic forces. In recognition to the importance of such a system to physics, we fill a gap in the literature and offer a full relativistic treatment for a system composed of a spring attached to an inertial wall, holding a mass M at the end.

Read more at https://arxiv.org/pdf/1810.13365.pdf

Quantum treatment of Verlinde’s entropic force conjecture

A. Plastino, M. C. Rocca, G. L. Ferri
Verlinde conjectured that gravitation is an emergent entropic force. This surprising conjecture was proved in [Physica A 505 (2018) 190] within a purely classical context. Here, we appeal to a quantum environment to deal with the conjecture in the case of bosons and consider also the classical limit of quantum mechanics (QM)….
Read more at https://arxiv.org/pdf/1808.01330.pdf

The Hawking temperature, the uncertainty principle and quantum black holes

blackhole1

A static black hole. The horizon (H ) is at a distance RS from the singularity (S).

Jorge Pinochet
In 1974, Stephen Hawking theoretically discovered that black holes emit thermal radiation and have a characteristic temperature, known as the Hawking temperature. The aim of this paper is to present a simple heuristic derivation of the Hawking temperature, based on the Heisenberg uncertainty principle. The result obtained coincides exactly with Hawking’s original finding. In parallel, this work seeks to clarify the physical meaning of Hawking’s discovery. This article may be useful as pedagogical material in a high school physics course or in an introductory undergraduate physics course.
Read more at https://arxiv.org/pdf/1808.05121.pdf

The twin paradox: the role of acceleration

J. Gamboa, F. Mendez, M. B. Paranjape, Benoit Sirois
The twin paradox, which evokes from the the idea that two twins may age differently because of their relative motion, has been studied and explained ever since it was first described in 1906, the year after special relativity was invented. The question can be asked: “Is there anything more to say?” It seems evident that acceleration has a role to play, however this role has largely been brushed aside since it is not required in calculating, in a preferred reference frame, the relative age difference of the twins. Indeed, if one tries to calculate the age difference from the point of the view of the twin that undergoes the acceleration, then the role of the acceleration is crucial and cannot be dismissed. In the resolution of the twin paradox, the role of the acceleration has been denigrated to the extent that it has been treated as a red-herring. This is a mistake and shows a clear misunderstanding of the twin paradox.
Read more at https://arxiv.org/pdf/1807.02148.pdf

The Physics of baking good Pizza

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Heat transfer mechanisms in the pizza oven

Andrey Varlamov, Andreas Glatz, Sergio Grasso
Physical principles are involved in almost any aspect of cooking. Here we analyze the specific process of baking pizzas, deriving in simple terms the baking times for two different situations: For a brick oven in a pizzeria and a modern metallic oven at home. Our study is based on basic thermodynamic principles relevant to the cooking process and is accessible to undergraduate students. We start with a historical overview of the development and art of pizza baking, illustrate the underlying physics by some simple common examples, and then apply them in detail to the example of baking pizza.
Read more at https://arxiv.org/ftp/arxiv/papers/1806/1806.08790.pdf

Longest Straight Line Paths on Water or Land on the Earth

longest

Longest Sailable Straight Line Path on Earth


Rohan Chabukswar, Kushal Mukherjee
There has been some interest recently in determining the longest distance one can sail for on the earth without hitting land, as well as in the converse problem of determining the longest distance one could drive for on the earth without encountering a major body of water. In its basic form, this is an optimisation problem, rendered chaotic by the presence of islands and lakes, and indeed the fractal nature of the coasts. In this paper we present a methodology for calculating the two paths using the branch-and-bound algorithm.
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Longest Drivable Straight Line Path on Earth

Read more at https://arxiv.org/pdf/1804.07389.pdf