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

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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

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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

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

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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

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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

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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.

Read also https://arxiv.org/pdf/2004.08236.pdf

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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.

Read more at https://arxiv.org/pdf/2004.06084.pdf

Quantum technology is seeing a remarkable explosion in interest due to a wave of successful commercial technology. As a wider array of engineers and scientists are needed, it is time we rethink quantum educational paradigms. Current approaches often start from classical physics, linear algebra, or differential equations. This chapter advocates for beginning with probability theory. In the approach outlined in this chapter, there is less in the way of explicit axioms of quantum mechanics. Instead the historically problematic measurement axiom is inherited from probability theory where many philosophical debates remain. Although not a typical route in introductory material, this route is nonetheless a standard vantage on quantum mechanics. This chapter outlines an elementary route to arrive at the Schrödinger equation by considering allowable transformations of quantum probability functions (density matrices). The central tenet of this chapter is that probability theory provides the best conceptual and mathematical foundations for introducing the quantum sciences.

Read more at https://arxiv.org/pdf/2003.09330.pdf ]]>

I study the physical nature of traces (or memories). Surprisingly, (i) systems separation with (ii) temperature differences and (iii) long thermalization times, are sufficient conditions to produce macroscopic traces. Traces of the past are ubiquitous because these conditions are largely satisfied in our universe. I quantify these thermodynamical conditions for memory and derive an expression for the maximum amount of information stored in such memories, as a function of the relevant thermodynamical parameters. This mechanism transforms low entropy into available information.

Read more at https://arxiv.org/pdf/2003.06687.pdf ]]>

When a massive star dies in a supernova, the explosion is only the beginning of the end. Most of the stellar matter is thrown far and wide, but the star’s iron-filled heart remains behind. This core packs as much mass as two Suns and quickly shrinks to a sphere that would span the length of Manhattan. Crushing internal pressure — enough to squeeze Mount Everest to the size of a sugar cube — fuses subatomic protons and electrons into neutrons.

Astronomers know that much about how neutron stars are born. Yet exactly what happens afterwards, inside these ultra-dense cores, remains a mystery. Some researchers theorize that neutrons might dominate all the way down to the centre. Others hypothesize that the incredible pressure compacts the material into more exotic particles or states that squish and deform in unusual ways.

Now, after decades of speculation, researchers are getting closer to solving the enigma, in part thanks to an instrument on the International Space Station called the Neutron Star Interior Composition Explorer (NICER).

Last December, this NASA space observatory provided astronomers with some of the most precise measurements ever made of a neutron star’s mass and radius1,2, as well as unexpected findings about its magnetic field1,3. The NICER team plans to release results about more stars in the next few months. Other data are coming in from gravitational-wave observatories, which can watch neutron stars contort as they crash together. With these combined observations, researchers are poised to zero in on what fills the innards of a neutron star.

For many in the field, these results mark a turning point in the study of some of the Universe’s most bewildering objects. “This is beginning to be a golden age of neutron-star physics,” says Jürgen Schaffner-Bielich, a theoretical physicist at Goethe University in Frankfurt, Germany.

Launched in 2017 aboard a SpaceX Falcon 9 rocket, the US$62-million NICER telescope sits outside the space station and collects X-rays coming from pulsars — spinning neutron stars that radiate charged particles and energy in enormous columns that sweep around like beams from a lighthouse. The X-rays originate from million-degree hotspots on a pulsar’s surface, where a powerful magnetic field rips charged particles off the exterior and slams them back down at the opposing magnetic pole.

NICER detects these X-rays using 56 gold-coated telescopes, and time-stamps their arrival to within 100 nanoseconds. With this capability, researchers can precisely track hotspots as a neutron star whips around at up to 1,000 times per second. Hotspots are visible as they swing across the object. But neutron stars warp space-time so strongly that NICER also detects light from hotspots facing away from Earth. Einstein’s general theory of relativity provides a way to calculate a star’s mass-to-radius ratio through the amount of light-bending. That and other observations allow astrophysicists to pin down the masses and radii of the deceased stars. Those two properties could help in determining what is happening down in the cores.

**Deep, dark mystery**

Neutron stars get more complicated the deeper one goes. Beneath a thin atmosphere made mostly of hydrogen and helium, the stellar remnants are thought to boast an outer crust just a centimetre or two thick that contains atomic nuclei and free-roaming electrons. Researchers think that the ionized elements become packed together in the next layer, creating a lattice in the inner crust. Even further down, the pressure is so intense that almost all the protons combine with electrons to turn into neutrons, but what occurs beyond that is murky at best (see ‘Dense matter’).

Crucially, each possibility would push back in a characteristic way against a neutron star’s colossal gravity. They would generate different internal pressures and therefore a larger or smaller radius for a given mass. A neutron star with a Bose–Einstein condensate centre, for instance, is likely to have a smaller radius than one made from ordinary material such as neutrons. One with a core made of pliable hyperon matter could have a smaller radius still.

“The types of particles and the forces between them affect how soft or squashy the material is,” says Anna Watts, a NICER team member at the University of Amsterdam.

Differentiating between the models will require precise measurements of the size and mass of neutron stars, but researchers haven’t yet been able to push their techniques to fine-enough levels to say which possibility is most likely. They typically estimate masses by observing neutron stars in binary pairs. As the objects orbit one another, they tug gravitationally on each other, and astronomers can use this to determine their masses. Roughly 35 stars have had their masses measured in this way, although the figures can contain error bars of up to one solar mass. A mere dozen or so have also had their radii calculated, but in many cases, the techniques can’t determine this value to better than a few kilometres — as much as one-fifth of the size of a neutron star.

NICER’s hotspot method has been used by the European Space Agency’s XMM-Newton X-ray observatory, which launched in 1999 and is still in operation. NICER is four times more sensitive and has hundreds of times better time resolution than the XMM-Newton. Over the next two to three years, the team expects to be able to use NICER to work out the masses and radii of another half a dozen targets, pinning down their radii to within half a kilometre. With this precision, the group will be well placed to begin plotting out what is known as the neutron-star equation of state, which relates mass to radius or, equivalently, internal pressure to density.

If scientists are particularly lucky and nature happens to serve up especially good data, NICER might help eliminate certain versions of this equation. But most physicists think that, on its own, the observatory will probably narrow down rather than completely rule out models of what happens in the mysterious objects’ cores.

“This would still be a huge advance on where we are now,” says Watts.

**Field lines**

NICER’s first target was J0030+0451, an isolated pulsar that spins roughly 200 times per second and is 337 parsecs (1,100 light years) from Earth, in the constellation Pisces….

… read more at https://www.nature.com/articles/d41586-020-00590-8