Physics and the Pythagorean Theorem

James Overduin, Richard Conn Henry
Pythagoras’ theorem lies at the heart of physics as well as mathematics, yet its historical origins are obscure. We highlight a purely pictorial, gestalt-like proof that may have originated during the Zhou Dynasty. Generalizations of the Pythagorean theorem to three, four and more dimensions undergird fundamental laws including the energy-momentum relation of particle physics and the field equations of general relativity, and may hint at future unified theories. The intuitive, “pre-mathematical” nature of this theorem thus lends support to the Eddingtonian view that “the stuff of the world is mind-stuff.”
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Click to access 2005.10671.pdf

Pi from the sky

A null test of general relativity from a population of gravitational wave observations
Carl-Johan Haster
Our understanding of observed Gravitational Waves (GWs) comes from matching data to known signal models describing General Relativity (GR). These models, expressed in the post-Newtonian formalism, contain the mathematical constant π. Allowing π to vary thus enables a strong, universal and generalisable null test of GR. From a population of 22 GW observations, we make an astrophysical measurement of π=3.115+0.048−0.088, and prefer GR as the correct theory of gravity with a Bayes factor of 321. We find the variable π test robust against simulated beyond-GR effects.

Click to access 2005.05472.pdf

Dark Matter Capture by Atomic Nuclei

Bartosz Fornal, Benjamin Grinstein, Yue Zhao
We propose a new strategy to search for a particular type of dark matter via nuclear capture. If the dark matter particle carries baryon number, as motivated by a class of theoretical explanations of the matter-antimatter asymmetry of the universe, it can mix with the neutron and be captured by an atomic nucleus. The resulting state de-excites by emitting a single photon or a cascade of photons with a total energy of up to several MeV. The exact value of this energy depends on the dark matter mass. We investigate the prospects for detecting dark matter capture signals in current and future neutrino and dark matter direct detection experiments.

Click to access 2005.04240v1.pdf

Hawking for beginners

A dimensional analysis activity to perform in the classroom
Jorge Pinochet
In this paper we present a simple dimensional analysis exercise that allows us to derive the equation for the Hawking temperature of a black hole. The exercise is intended for high school students, and it is developed from a chapter of Stephen Hawking’s bestseller A Brief History of Time.

Click to access 2004.11850.pdf

Chirality Through Classical Physics

Chris L. Lin
Chirality, or handedness, is a topic that is common in biology and chemistry, yet is rarely discussed in physics courses. We provide a way of introducing the topic in classical physics, and demonstrate the merits of its inclusion – such as a simple way to visually introduce the concept of symmetries in physical law – along with giving some simple proofs using only basic matrix operations, thereby avoiding the full formalism of the three-dimensional point group.
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Click to access 2004.08236.pdf

Comments on magnetic black holes

Juan Maldacena
We discuss aspects of magnetically charged black holes in the Standard Model. For a range of charges, we argue that the electroweak symmetry is restored in the near horizon region. The extent of this phase can be macroscopic. If Q is the integer magnetic charge, the fermions lead to order Q massless two dimensional fermions moving along the magnetic field lines. These greatly enhance Hawking radiation effects.


Click to access 2004.06084.pdf