Updates from outer space: from Earth to K2-18 b

There are some interesting news about the research of exoplanets, but the first step starting from our planet, the Earth. Indeed, Evelyn Macdonald and Nicolas Cowan used the satellite Scicast to detect the transit spectrum of our planet. The idea is to deduce the atmosphere composition, obtaining the Earth's organic signature, and in this way data to confront with exoplanets transit spectrum.

Macdonald, E. J., & Cowan, N. B. (2019). An empirical infrared transit spectrum of Earth: opacity windows and biosignatures. Monthly Notices of the Royal Astronomical Society, 489(1), 196-204. doi:10.1093/mnras/stz2047

About two weeks after the pubblication of the previous paper, an international team of astronomers have discovered water vapor in the atmosphere of K2-18 b, an exoplanet that orbit in the habitable zone of the red dwarf K2-18. While it was initially considered a mini-Neptune on its 2015 discovery, the improved data on K2-18b has classified it as a super-Earth, although its size and density make it unlikely to be composed entirely of rocky iron and silicates.

Tsiaras A., Waldmann I. P., Tinetti G., Tennyson J., Yurchenko S. N. (2019). Water vapour in the atmosphere of the habitable-zone eight-Earth-mass planet K2-18 b. Nature Astronomy. doi:10.1038/s41550-019-0878-9

Breakthrough Prize 2020: Physics and Mathematics

2020 Breakthrough Prize in Fundamental Physics to the Event Horizon Telescope Collaboration, for the first image of a supermassive black hole, taken by means of an Earth-sized alliance of telescopes.

Using eight sensitive radio telescopes strategically positioned around the world in Antarctica, Chile, Mexico, Hawaii, Arizona and Spain, a global collaboration of scientists at 60 institutions operating in 20 countries and regions captured an image of a black hole for the first time. By synchronizing each telescope using a network of atomic clocks, the team created a virtual telescope as large as the Earth, with a resolving power never before achieved from the surface of our planet. One of their first targets was the supermassive black hole at the center of the Messier 87 galaxy – its mass equivalent to 6.5 billion suns. After painstakingly analyzing the data with novel algorithms and techniques, the team produced an image of this galactic monster, silhouetted against hot gas swirling around the black hole, that matched expectations from Einstein's theory of gravity: a bright ring marking the point where light orbits the black hole, surrounding a dark region where light cannot escape the black hole's gravitational pull.

2020 Breakthrough Prize in Mathematics to Alex Eskin, for revolutionary discoveries in the dynamics and geometry of moduli spaces of Abelian differentials, including the proof of the "magic wand theorem" with Maryam Mirzakhani.

Eskin teamed with famed Iranian mathematician and Fields Medalist, Maryam Mirzakhni, to prove a theorem about dynamics on moduli spaces. Their tour de force, published in 2013 after five years of labor, is a result with many consequences. One addresses the longstanding problem: If a beam of light from a point source bounces around a mirrored room, will it eventually reach the entire room – or will some parts remain forever dark? After translating the problem to a highly abstract multi-dimensional setting, the two mathematicians were able to show that for polygonal rooms with angles which are fractions of whole numbers, only a finite number of points would remain unlit. Mirzakhani passed away in 2017, at age 40, after fighting breast cancer for several years.

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via Breakthrough Prize

The greatest shapeshifter in the world

In the third episode of Season 3, Supergirl and J'onn J'onzz go to Mars, the red planet.

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Spacetime analogies

The elastic sheet model is one of the most used model for telling general relativity. It allows to show as smaller balls "orbit" around the larger ball in the center of the sheet in a way similar to the planets, at least until the balls lose energy due to friction and finally fall into the "gravitational wall".
This way to see the general relativity is directly connected with the embedded diagrams and Flamm paraboloids, the mathematical way to see the spacetime deformations. But this analogy has some problems not only because is inaccurate like all analogies, but also becuase it could be confusing about distorced space and spacetime especially among students. So we can ask: why is the sheet deformed? Because of the weight? This fact implies the use of a circluar argument: usinf gravity to explain gravity! But if the ball isn't in spacetime, where is it?⁽¹⁾

Come back on the road

Due to some family problems, 2017 was a difficult year and all my online activities, particularly blogs, had a considerable decrease in content. As for Doc Madhattan the effects were seen especially in the last months of 2017 and in 2018, when the last post came out in august.
In june of this year, almost a year later, I resumed posting also on this blog with the death of Murray Gell-Mann. However, I still had no idea if and how to regularly resume publications. Then the case wanted that, thanks to the first photograph of a quantum entaglement, I am selected among the contents of the week of Science Seeker, and this gives me the incentive to resume curating the contents also on this blog!
The program, which I hope to maintain, is to publish a couple of articles a month: in this way I should be able to keep up the pace, placing it between work and articles for my other italian blogs. As for the contents, I would like first of all to recover some of the notes that have remained in draft in all these months of silence, so try to write new contents from scratch. Probably I will also decrease the amount of mathematics present here on Doc Madhattan: the idea is also to take up my column on Mathematics in Europe, so probably the mathematical posts here will be an extract with the link to the complete article.
ON the other hand, physics will have all the space needed here on Doc Madhattan.
I hope that taking this road again may be even longer and more enjoyable than the one that was interrupted a year ago.

The great question about the Hubble constant

The Hubble-Lemaitre law is the mathematical formula bout the expanding universe. One of the collateral results of Einstein's theory of relativity was an expanding and non-static universe, a result that, in a first time, Einstein himself had disavowed. Yet various observations made in the second half of the 20s of the twentieth century instead confirmed the hypothesis of cosmic expansion^{(1, 2)}. \[z = H_0 \frac{D}{c}\] where $c$ is the speed of light, $H_0$ is the Hubble constant, while $z$ and $D$ are the light's redshift and the distance of the galaxy from the observer. The redshift, in particular, is due to the Doppler effect applied to electromagnetic waves. For example, when you hear the siren of an ambulance, it will seem to you stronger or weaker if approaching or moving away from your position. An electromagnetic wave, like light, instead will be closer to blue or red depending on whether it is closer to or away from the observer.
So, it has a certain importance to measure the redshift of the galaxies around us: evidently a null or little redshift was a clue to a static universe, otherwise we live in a dynamic universe, as you can see from the image present in the historical Hubble article⁽²⁾:

Imaging quantum entanglement

The main object of a paper published a couple of days ago on Science is to find an answer to the following question:

what kind of imaging process could reveal a Bell inequality?

The experimental set-up used a $\beta$-Barium Borate crystal pumped by a (quasi-cotinuous) laser. The pairs of entagled photons generated are subsequently separated on a beam splitter and propagate into two distinct optical systems like LIGO interferometer.
The results is the production of some images that shots the Bell inequality violation, like the following image:

Moreover, our demonstration shows that one can detect the signature of a Bell-type behavior within a single image acquired by an imaging setup. By demonstrating that quantum imaging can generate high-dimensional images illustrating the presence of Bell-type entanglement, we benchmark quantum imaging techniques against the most fundamental test of quantum mechanics.

Moreau, P. A., Toninelli, E., Gregory, T., Aspden, R. S., Morris, P. A., & Padgett, M. J. (2019). Imaging Bell-type nonlocal behavior. Science Advances, 5(7), eaaw2563. doi:10.1126/sciadv.aaw2563