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Mathematics Links Quantum Encryption and Black Holes

Mathematics Links Quantum Encryption and Black Holes  86

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

KOI-5Ab, the curious planet that orbits in a system of three suns

KOI-5Ab, the curious planet that orbits in a system of three suns 99
Photo: (Caltech / R. Hurt (IPAC))

To us, the Sun alone seems perfectly normal, but our solar system is actually a strange exception.

Most stars in the Milky Way galaxy have at least one companion star. In a system 1,800 light-years away, astronomers have finally confirmed the existence of a gas giant planet orbiting stars in a triple star system.

Called KOI-5, the system is located in the constellation Cygnus, and the exoplanet was confirmed ten years after it was first detected by the Kepler space telescope.

In fact, the planet – now known as KOI-5Ab – was discovered by Kepler when it began operations back in 2009.

“KOI-5Ab was dropped because it was difficult and we had thousands of other candidates,” astronomer David Siardi of NASA’s Exoplanet Science Institute said.

“There were lighter dives than the KOI-5Ab, and every day we learned something new from Kepler, so the KOI-5 was almost forgotten.”

Exoplanet hunters tend to avoid the complexities of multi-star systems; of the more than 4,300 exoplanets confirmed to date, less than 10 percent are multi-star systems, although such systems dominate the galaxy. As a result, little is known about the properties of exoplanets in multi-star systems compared to those orbiting a lone star.

After Kepler’s discovery, Chardy and other astronomers used ground-based telescopes such as the Palomar Observatory, Keck Observatory, and the Gemini North Telescope to study the system. By 2014, they had identified two companion stars, KOI-5B and KOI-5C.

Scientists were able to establish that the planet KOI-5Ab, is a gas giant that is about half the mass of Saturn and 7 times the size of Earth, and is in a very close five-day orbit around KOI-5A. KOI-5A and KOI-5B, both of roughly the same mass as the Sun, form a relatively close binary system with an orbital period of about 30 years.

KOI-5Ab, the curious planet that orbits in a system of three suns 100

A third star, KOI-5C, orbits the binary system at a much greater distance, with a period of about 400 years – slightly longer than Pluto’s 248-year orbit.

“By studying this system in more detail, perhaps we can understand how planets are created in the universe.”

The discovery was announced at the 237th meeting of the American Astronomical Society.

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Space

Why the universe does not fit into science

Why the universe does not fit into science 101
Photo: YouTube

Science can be compared to an artist painting what he has never seen, or to a writer describing other people’s travels: objects that he has never seen, places where he has never been. Sometimes such scientific “arts” turn out to be beautiful and interesting, but most of them will forever remain only theories, because they are beyond human capabilities.

In fact, science has the right only to speculate: how our universe appeared, how old it is, how many stars and other objects it contains.

Universe model

Why the universe does not fit into science 102

How many stars are there in the sky?

With an unarmed eye, a person can see about nine thousand stars in the sky in one cloudless and moonless night. And armed with binoculars or a telescope, much more – up to several million. However, this is much less than their true number in the universe. Indeed, only in our one galaxy (the Milky Way) there are about 400 billion stars. The exact amount, of course, is not known to science. And the visible universe contains about 170 billion galaxies.

It is worth clarifying that scientists can see the universe 46 billion light years deep in all directions. And the visible (observable) universe includes the space accessible to our eyes from the moment of the Big Explosion. In other words, only this (accessible to human perception) space science refers to our universe. Science does not consider everything that follows.

It is believed that there are supposedly a ceptillion (10 to 24 degrees) stars in our universe. These are theoretical calculations based on the approximate size and age of the universe. The origin of the universe is explained by the Big Bang theory. This is why the universe is constantly expanding and the more time passes, the more complex the universe and its components become.

Why the universe does not fit into science 103

It is not entirely correct to consider and perceive this scientific theory “head-on”. Scientists always claim that that explosion was not exactly an explosion, and the point that exploded was not the only one. After all, it was everywhere, because space did not exist then. And in general – everything happened quite differently from what is described in the Big Bang theory, but all other descriptions of the origin of the universe are even more incredible and inaccurate.

Separate but interconnected

That which is beyond the reach of human perception is usually discarded by science, or recognized as non-existent. Recognizing one thing, science does not want to recognize the existence of the other, although everything in our world is interconnected and is not able to exist separately – by itself.

Each object of the universe is a part of it much more than an independent, separate object.

Any person, like any material object of our world, consists of components: organs, cells, molecules, atoms. And each of its constituent parts can represent the whole world. Separate, and at the same time connected with all the others.

However, science, as a rule, perceives all the components of the universe – people, animals, plants, objects, the Earth, the Sun, other planets and stars – as separate subjects, thereby limiting itself.

Why the universe does not fit into science 104

Even what is considered the visible universe, one of the atoms of which could be called our solar system, is not subject to the boundaries of human perception. But perhaps the atom is an exaggeration, and our solar system is not even an atom, but one of its elements!

How, being so far from the truth, can one reason about something with the degree of probability with which science tries to reason about the origin of the universe?

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Space

An unexplained wobble shifts the poles of Mars

An unexplained wobble shifts the poles of Mars 105

The red planet sways from side to side like a whirligig when it loses speed. The new study allowed scientists to notice that the poles of Mars deviate slightly from the axis of rotation of the planet. On average, they move 10 cm from the center with a period of 200 days.

Such changes are called the Chandler Oscillations  – after the American astronomer Seth Chandler, who discovered them in 1891. Previously, they were only seen on Earth. It is known that the displacement of the poles of rotation of our planet occurs with a period of 433 days, while the amplitude reaches 15 meters. There is no exact answer why this is happening. It is believed that the fluctuations are influenced by processes in the ocean and the Earth’s atmosphere.

Chandler’s wobbles on Mars are equally perplexing. The authors of the study discovered them by comparing data from 18 years of studying the planet. The information was obtained thanks to three spacecraft that orbit the Red Planet: Mars Odyssey, Mars Reconnaissance Orbiter and Mars Global Surveyor. 

Since Mars has no oceans, it is likely that the Red Planet’s wobbly rotation is due to changes in atmospheric pressure. This is the first explanation that researchers have shared. In the future, there should be new details about the fluctuations that have so interested the scientific community.

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