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Mathematics Links Quantum Encryption and Black Holes

A proposed mathematical proof that outlines the way information behaves in coded messages may have implications for black holes. The proof suggests that the radiation spit out by black holes may retain information on the dark behemoths.

The research focuses on encoding communications in quantum mechanical systems. But it also connects to a long-standing question for physicists: What happens to all the stuff that falls into a black hole, and is it possible to retrieve any information about the black hole?

A group of researchers from Switzerland and Canada, led by Frédéric Dupuis, showed that it’s possible to encode large messages with relatively small quantum encryption keys, which are keys made up of subatomic particles or photons. But the result implies something else: If someone could pull out information that is encrypted quantum mechanically in a message between two parties, the same feat should work in nature.

Coding with particles

Quantum encryption relies on the idea that any measurement made on subatomic particles changes the particles’ states; quantum mechanics says that these tiny particles are always in a state of uncertainty, until a measurement pushes the particle into one state or another.

The upshot is that subatomic particles can be used as a “foolproof” key that allows only the intended party to decode an encoded message. If anyone tries to decipher the key — by eavesdropping on the message, for instance — the two parties involved would know about it, and could change keys. That’s because any attempt to measure the key would change the information in it.

But this security isn’t absolute; it is possible for an eavesdropper to find out what the key is. With a certain number of quantum bits, or qubits, from the key, which for example might contain a dozen bits, the message can be decoded. Until a person acquires a threshhold number of bits, though, the information in the message is “locked.”

“We can make the amount of information in the [message or the key] right before it unlocks arbitrarily small,” said Jan Florjanczyck, now at the University of Southern California and one of the paper’s co-authors.

Ordinarily, to make a quantum key completely secure, one would have to use a key that is as big as the message. Since this isn’t practical, encryption schemes all use keys that are smaller than the message itself. For example, in primitive encryption, such as a cipher, the key itself is short, while the message is much longer. (The “pigpen” cipher, for instance, used by children, is 26 characters, each of which substitutes for a letter, while the message itself will be longer).

The short key allows patterns to show up that a decoder can crack. Modern encryption is much more sophisticated, but the principle is similar.

The new paper by Dupuis and his co-authors showed that one can still get good security even with a relatively short key in quantum communications.

Decoding black holes

What does quantum encryption have to do with black holes? The key concept is information.

In quantum encryption, one encodes information in quantum states. Just as one can measure quantum states to decode a message, one can measure quantum states to find out information about an object. And one of the fundamental pieces of quantum information theory is that such information can’t be destroyed.

Black holes suck up matter and emit a small amount of radiation, called Hawking radiation after Stephen Hawking, who first outlined the concept. This radiation takes energy away from a black hole. And with that energy, goes mass, because energy and mass are the same in physics.

But a black hole’s mass comes from all the stuff that has fallen into it. That means the photons emitted as Hawking radiation should carry some information about the black hole, because quantum information can’t be copied or destroyed. For a long time, though, many physicists thought there wasn’t any way to decipher that information, because the black hole had “scrambled” it. The decoding feat would be like trying to reconstruct a building that had been ground to dust. More recently, however, scientists, including Hawking, have changed their minds — the information is there, but one just needs to figure out how to decode it.

That’s where proofs like those by Dupuis and his colleagues come in. If one can “decode” the information contained in the quantum states of photons from a black hole, one can retrieve information about whatever was dropped into the black hole. And if it is possible to encode large messages with small keys, adjusting how much information one needs to unlock the message, it’s also possible to do that with the quantum bits that come out of a black hole.

“We can only say that such a decoding process exists, not whether it is easy to perform or whether the decoding might happen naturally,” Florjanczyck said.

That is, to gather information about a coffee cup dropped into a black hole last week, for example, one might need to have started gathering photons from the cup back when it formed. That would be the only way to get enough information to do the decoding.

“It’s a very interesting piece of work,” said Wolfgang Tittel, research chair in quantum secured communication at the University of Calgary in Alberta, Canada. “This kind of work links the very large with the very small.”

Original article on LiveScience.

http://www.space.com/22879-mathematics-links-quantum-encryption-black-holes.html

Space

Voyager 2 has discovered something amazing: Denser space outside the solar system

In November 2018, after a 41-year voyage, Voyager 2 crossed the boundary beyond which the Sun’s influence ends, and entered interstellar space. But the mission of the little probe is not yet complete – it continues to make amazing discoveries

Perhaps the probes have found some kind of traffic jam at the edge of the solar system. The Voyager flight continues and we will soon find out what it was.

Voyager 2 discovered something amazing: as the distance from the Sun increases, the density of space increases.

Voyager 1, which entered interstellar space in 2012, transmitted similar indicators to Earth. New data have shown that the increase in density may be a feature of the interstellar medium.

The solar system has several boundaries, one of which, called the heliopause, is determined by the solar wind, or rather by its significant weakening. The space inside the heliopause is the heliosphere, and the space outside is the interstellar medium. But the heliosphere is not round. It looks more like an oval, in which the solar system is at the leading edge, and a kind of tail stretches behind it.

Both Voyagers crossed the heliopause at the leading edge, but within 67 degrees heliographic latitude and 43 degrees longitude apart.

Interstellar space is usually considered a vacuum, but this is not entirely true. The density of matter is extremely small, but it still exists. In the solar system, the solar wind has an average density of protons and electrons from 3 to 10 particles per cubic centimeter, but it is lower the further from the Sun.

The average concentration of electrons in the interstellar space of the Milky Way is estimated to be about 0.037 particles per cubic centimeter. And the plasma density in the outer heliosphere reaches approximately 0.002 electrons per cubic centimeter. When the Voyager probes crossed the heliopause, their instruments recorded the electron density of the plasma through plasma oscillations.

Voyager 1 crossed the heliopause on August 25, 2012 at a distance of 121.6 astronomical units from the Earth (121.6 times the distance from Earth to the Sun – about 18.1 billion km). When he first measured plasma oscillations after crossing the heliopause on October 23, 2013 at a distance of 122.6 astronomical units (18.3 billion km), he found a plasma density of 0.055 electrons per cubic centimeter.

After flying another 20 astronomical units (2.9 billion kilometers), Voyager 1 reported an increase in the density of interstellar space to 0.13 electrons per cubic centimeter.

Voyager 2 crossed the heliopause on November 5, 2018 at a distance of 119 astronomical units (17.8 billion kilometers. On January 30, 2019, it measured plasma oscillations at a distance of 119.7 astronomical units (17.9 billion kilometers), finding that the density plasma is 0.039 electrons per cubic centimeter.

In June 2019, Voyager 2’s Instruments showed a sharp increase in density to about 0.12 electrons per cubic centimeter at a distance of 124.2 astronomical units (18.5 billion kilometers).

What caused the increase in the density of space? One theory is that the lines of force of the interstellar magnetic field become stronger with distance from the heliopause. This can cause electromagnetic ion cyclotron instability. Voyager 2 did detect an increase in the magnetic field after crossing the heliopause.

Another theory is that the material carried away by the interstellar wind should slow down in the heliopause, forming a kind of plug, as evidenced by the weak ultraviolet glow detected by the New Horizons probe in 2018, caused by the accumulation of neutral hydrogen in the heliopause.

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Space

NASA has banned fighting and littering on the moon

New details of the agreement signed by representatives of a number of countries on the development of the moon and the extraction of minerals within the framework of the Artemis program have appeared. Reported by the National Aeronautics and Space Administration (NASA).

So, astronauts involved in the mission are prohibited from littering and fighting on the territory of a natural satellite of the Earth.

So, we present to you the new rules for being on the Moon:

Everyone comes in peace;

Confidentiality is prohibited, all launched objects must be identified and registered;

All travel participants agree to help each other in case of emergencies;

All received data is transferred to the rest of the participants, and space systems must be universal;

Historic sites must be preserved and all rubbish must be disposed of;

Rovers and spacecraft should not interfere with other participants.

“”It is important not only to go to the moon with our astronauts, but also that we bring our values ​​with us,” said Mike Gold, acting head of NASA’s international and inter-agency relations.

According to him, violators of the above rules will be asked to “just leave” the territory of the moon.

The effect of these principles so far applies to eight signatory countries of the agreement: the USA, Australia, Canada, Italy, Japan, Luxembourg, the United Arab Emirates and the United Kingdom. Countries other than China can join if they wish.

 It should be noted that at the moment NASA is prohibited from signing any bilateral agreements with the PRC leadership.

The first NASA mission to the moon, known as “Artemis 1”, is scheduled for 2021 without astronauts, and “Artemis 2” will fly with a crew in 2023.

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Space

Methane snow found on the tops of Pluto’s equatorial mountains

Scientists believe that it arose as a result of the accumulation of large amounts of methane at an altitude of several kilometers above the surface of the planet.

In the images of the Cthulhu region – a dark region in the equatorial regions of Pluto – planetary scientists have found large reserves of methane snow that covers the peaks of local mountains and hills. It formed quite differently from how snow forms on Earth, astronomers write in the scientific journal Nature Communications.

“The white caps on the tops of Pluto’s mountains did not arise from the cooling of air currents that rise along the slopes into the upper atmosphere, as it happens on Earth, but from the accumulation of large amounts of methane at an altitude of several kilometers above Pluto’s surface. This gas condensed on the mountain tops, “the scientists write.

We owe almost everything we know about Pluto to the New Horizons interplanetary station. It was launched in January 2006, and in mid-July 2015 the station reached the Pluto system. New Horizons flew just 13 thousand km from the dwarf planet, taking many photographs of its surface. 

New Horizons data indicated an interesting feature of Pluto – in its depths, a giant subglacial ocean of liquid water can be hidden. It can be a kind of engine of those geological processes, traces of which can be seen on the surface of a dwarf planet. Because of this discovery of New Horizons, many discussions began among planetary scientists. Scientists are trying to understand how such a structure could have arisen, as well as to find out the appearance of Pluto in the distant past.

Members of the New Horizons science team and their colleagues from France, led by planetary scientist from NASA’s Ames Research Center (USA) Tanguy Bertrand, have discovered another unusual feature of Pluto. They studied the relief of one of the regions of the dwarf planet – the Cthulhu region. This is what astronomers call a large dark region at Pluto’s equator, which is whale-like in shape and is covered in many craters, mountains and hills.

Snow in Pluto’s mountains

By analyzing images of these structures taken by the LORRI camera installed on board New Horizons, astronomers have noticed many blank spots on the slopes of the highest mountain peaks. Having studied their composition, scientists have found that they consist mainly of methane.

Initially, planetary scientists assumed that these are deposits of methane ice. However, Bertrand and his colleagues found that the slopes and even the tops of Pluto’s equatorial mountains are actually covered not only with ice, but also with exotic methane snow that forms right on their surface.

Planetary scientists came to this conclusion by calculating how methane behaves in Pluto’s atmosphere. In doing so, they took into account how the molecules of its gases interact with the sun’s rays and other heat sources. It turned out that at the equator of Pluto, at an altitude of 2-3 km from its surface, due to the special nature of the movement of winds, unique conditions have formed, due to which snow is formed from methane vapor.

Unlike Earth, where such deposits are formed as a result of the rise of warm air into the upper atmosphere, on Pluto this process goes in the opposite direction – as a result of contact of the cold surface of the peaks and slopes of mountains with warm air masses from the relatively high layers of the dwarf planet’s atmosphere.

Previously, as noted by Bertrand and his colleagues, scientists did not suspect that this was possible. The fact is that they did not take into account that due to the deposition of even a small amount of methane snow and ice, the reflectivity of the peaks and slopes of mountains in the Cthulhu region increases. As a result, their surface temperature drops sharply, and snow forms even faster.

Scientists suggest that another mysterious feature of Pluto’s relief could have arisen in a similar way – the so-called Tartarus Ridges, located east of the Sputnik plain. A distinctive feature of this mountainous region is strange peaks that are shaped like skyscrapers or blades. Bertrand and his colleagues suggest that these peaks are also methane ice deposits that grow “from top to bottom.”

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