Fabio Falchi

I describe a simple method to calculate Earth dimensions using only local measurements and observations. I used modern technology (a digital photo camera and Google Earth) but the exact same method can be used without any aid, with naked eye observations and distances measured by walking, and so it was perfectly accessible to Ancient Greek science.

Read more at https://arxiv.org/abs/2007.02111

# Feynman Lectures on the Strong Interactions

**Richard P. Feynman, James M. Cline**

These twenty-two lectures, with exercises, comprise the extent of what was meant to be a full-year graduate-level course on the strong interactions and QCD, given at Caltech in 1987-88. The course was cut short by the illness that led to Feynman’s death. Several of the lectures were finalized in collaboration with Feynman for an anticipated monograph based on the course. The others, while retaining Feynman’s idiosyncrasies, are revised similarly to those he was able to check. His distinctive approach and manner of presentation are manifest throughout. Near the end he suggests a novel, nonperturbative formulation of quantum field theory in D dimensions. Supplementary material is provided in appendices and ancillary files, including verbatim transcriptions of three lectures and the corresponding audiotaped recordings.

Read more at https://arxiv.org/abs/2006.08594

# Packing Moons Inside the Earth

**Sunil K. Chebolu**

Using ideas of sphere packing problem we estimate the number of solid moons that can be packed inside the Earth, assuming that both the Moon and the Earth are perfect sphere.

Read more at https://arxiv.org/abs/2006.00603

# 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.”

Read more https://arxiv.org/abs/2005.10671

# 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.

Read more at https://arxiv.org/abs/2005.05472

# 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.

Read more at https://arxiv.org/abs/2005.04240

# 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.

Read more at https://arxiv.org/pdf/2004.11850.pdf