Physicists have proven the impossibility of existence. Physicists have proven the impossibility of effective classical simulation of some quantum systems

The hypothesis about a computer simulation of our universe was put forward in 2003 by the British philosopher Nick Bostrom, but has already received its followers in the person of Neil deGrasse Tyson and Elon Musk, who expressed that the probability of the hypothesis is almost 100%. It is based on the idea that everything that exists in our universe is the product of a simulation, like the experiments carried out by machines in the Matrix trilogy.

Simulation theory

The theory believes that, given a sufficient number of computers with large computing power, it becomes possible to simulate in detail the entire world, which will be so believable that its inhabitants will have consciousness and intelligence.

Based on these ideas, we can assume: what is stopping us from living in a computer simulation? Maybe a more advanced civilization is conducting a similar experiment, having received the necessary technologies, and our entire world is a simulation?

Many physicists and metaphysicians have already created convincing arguments in favor of the idea, citing various mathematical and logical anomalies. Based on these arguments, we can assume the existence of a space computer model.

Mathematical refutation of the idea

However, two physicists from Oxford and the Hebrew University of Jerusalem, Zohar Ringel and Dmitry Kovrizhin, proved the impossibility of such a theory. They published their findings in the journal Science Advances.

After simulating a quantum system, Ringel and Kovrizhin found that simulating just a few quantum particles would require enormous computational resources, which, due to the nature of quantum physics, would increase exponentially with the number of simulated quanta.

To store a matrix describing the behavior of 20 spins of quantum particles, a terabyte of RAM will be required. Extrapolating this data over just a few hundred spins, we find that to create a computer with this amount of memory would require more atoms than the total number of atoms in the universe.

In other words, given the complexity of the quantum world we observe, it can be proven that any proposed computer simulation of the universe will fail.

Or maybe it’s a simulation after all?

On the other hand, continuing philosophical reasoning, a person will quickly come to the question: “Is it possible that more advanced civilizations deliberately put this complexity of the quantum world into the simulator in order to lead us astray?” To this Dmitry Kovrizhin answers:

This is an interesting philosophical question. But it is outside the scope of physics, so I would prefer not to comment on it.

Is it really possible for a moving physical object to exist that has zero energy? From the point of view of common sense, this is impossible, because movement itself is kinetic energy. This rather obvious physical fact was challenged by the concept of quantum space-time crystals, which was proposed in 2012 by physicist and Nobel Prize winner Frank Wilczek of the Massachusetts Institute of Technology. These space-time crystals are theoretical quantum systems that undergo periodic oscillations while in a standard state, the lowest energy state.

The idea of ​​​​creating a quantum space-time crystal turned out to be so attractive that a group of physicists from the University of California at Berkeley even began preparing to create an experimental setup in which the role of the crystal was played by calcium ions trapped in a ring ion trap. Under the influence of an extremely weak magnetic field, the calcium ions would begin to rotate slowly, while being in their lowest energy state. Theoretically, the rotation of such a system can continue indefinitely, even after the thermal death of the Universe, because such a system does not absorb or emit energy.

But, like any exotic physical theory, the theory of space-time crystals, in addition to its adherents, also has ardent opponents. One of the opponents of this theory is the famous physicist Patrick Bruno, who works at the European Synchrotron Radiation Facility laboratory located in Grenoble, France. Bruno has more than once pointed out some “holes” in the theory of space-time crystals, and not so long ago he left this theory unturned, creating his own “stopping theory”, which completely excludes the possibility of endless rotation of a wide class of systems located in standard state, which can be called space-time crystals.

According to Bruno's theory, the concept of space-time crystals has two main disadvantages. First, the rotating solitron (unit wave pulse) that Wilczek describes in his model is not in a standard state, but in a higher energy state. Secondly, a system that performs rotational motion, even if it is in a standard state, can radiate energy into the surrounding space in the form of electromagnetic waves, which in itself contradicts the law of conservation of energy.

As the main argument of his theory, Bruno demonstrates that setting a ring system of quantum particles around a magnetic trap ring will in any case increase the energy of the entire system, moving it from the standard to a higher energy state. Bruno considers the proof of this to be the description of rotating systems described in the works of Nobel Laureate Anthony Leggett, who studied the properties of rotating superfluids, liquids with an infinite fluidity coefficient.

Bruno believes his first argument should not come as a surprise, since a theory developed in 1964 by another Nobel laureate, Walter Kohn, states that insulating materials are completely insensitive to magnetic fluxes and their changes. Since quantum space-time crystals are modeled as Wigner crystals, and Wigner crystals are known to be insulators, magnetic flux and magnetic field will not be able to cause the space-time crystal system to rotate.

“I believe that by developing my “stopping theory”, I put an end to the theory of the possibility of the existence of rotating space-time crystals. I am sorry that a lot of my time and the time of other scientists was wasted on this initially incorrect theory. I have no plans to continue work in this direction, but if anyone comes up with alternative options that do not contradict existing theories, I will be glad to return to this topic again,” writes Bruno.

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Scientists at Oxford University have refuted the theory that the world exists in a computer simulation. Zohar Ringel and Dmitry Kovrizhin worked on the study.

Our species is much older than scientists previously thought Scientists have studied the DNA of fossils that were found in Morocco and concluded that the species homo sapiens appeared between 260 and 350,000 years ago. This was reported by the NY Post. Previously, the oldest known fossilized remains of our species were thought to be fossils from Ethiopia dating back about 200,000 years.

Scientists have denied that a computer can create such a large number of simultaneous actions.

Ringel and Kovrizhin calculated that just storing information about a few hundred electrons would require computer memory, which would require more atoms than there are in the Universe.

The study proved that it is impossible to simulate such a system on a classical computer, but quantum computers will probably be able to handle this one day.

American businessman and inventor Elon Musk is one of the adherents of the matrix theory. He believes that humanity lives in a simulation of the real world.

As Musk argued, video games are developing very quickly and people are already creating a different reality through them and can control it. Therefore, the probability that humanity lives in basic reality is one in billions.

Read also: Nobel Prize in Physics awarded for the discovery of gravitational waves

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Our species is much older than scientists previously thought Scientists have studied the DNA of fossils that were found in Morocco and concluded that the species homo sapiens appeared between 260 and 350,000 years ago. This was reported by the NY Post. Previously, the oldest known fossilized remains of our species were thought to be fossils from Ethiopia dating back about 200,000 years.

"Biological clock" wins Nobel Prize in Medicine

The prize winners were US scientists Jeffrey Hall, Michael Rosbash and Michael Young. The names of the Nobel Prize laureates were announced today in Stockholm. This was reported on Twitter by the Nobel Committee. The prize winners were US scientists Jeffrey Hall, Michael Rosbash and Michael Young for their discovery of the molecular mechanisms that control circadian rhythms. Circadian rhythms help control sleep, nutrition, hormone production and blood pressure.

Nobel Prize in Physics was given for the discovery of gravitational waves

US scientists Rainer Weiss, Kip Thorne and Barry Barish received the 2017 Nobel Prize in Physics Today, American scientists Rainer Weiss, Barry Barish and Kip Thorne received the Nobel Prize in Physics for the discovery of gravitational waves by the LIGO detector. This was reported on Twitter by the Nobel Committee. Last year, David Thoules, Duncan Haldane and Michael Kosterlitz received the Nobel Prize in Physics "for their theoretical discoveries in topological phase transitions and the topological phases of matter."

The Ministry of Natural Resources initiates research into the moose population in Ukraine

According to Semerak, if information about threats to the existence of moose is confirmed, the department will return to the ongoing dialogue on a hunting ban. The Ministry of Ecology and Natural Resources will initiate scientific research on the European moose population in Ukraine. This was stated by the Minister of Ecology and Natural Resources Ostap Semerak during a joint press conference of the Ministry of Natural Resources and the Ministry of Agrarian Policy, the government portal reports. “The discussion about banning moose hunting is not over.

Turkish archaeologists claim to have found the grave of Santa Claus

An intact tomb was found in the underground premises of the Church of St. Nicholas in the area of ​​​​the Turkish city of Demre. Turkish archaeologists reported that they had allegedly found the burial place of St. Nicholas the Wonderworker, but so far they could not get to his remains. The BBC reports this. It is reported that the intact tomb was found in the underground premises of the Church of St. Nicholas near the Turkish city of Demre, in the southwestern province of Antalya.

Scientists have found a way to destroy HIV-infected cells

KYIV. October 13. UNN. Modified DNA immune cells, which were invented by American molecular biologists, began to recognize cells infected with HIV and destroy them before the virus begins to destroy the immune system. Scientists have successfully conducted research on mice, reports UNN with reference to PLoS Pathogens. These transgenic T cells can protect the animal’s body from the recurrence of infection after antiretroviral drugs are stopped. read also: 136 thousand people are infected with HIV in Ukraine.

Scorpios can “tune” their venom for defense and attack.

Scientists have come to the conclusion that prolonged exposure to appropriate environmental conditions leads to changes in the composition of venom in scorpions. Scorpions are attacked by animals that are usually significantly larger than them in size, and the victims of scorpions themselves are mainly smaller insects. Therefore, scorpions have learned to subtly adjust the poisonous mixture to their current needs, Naked Science reports.

Scientists have measured the Milky Way

KYIV. October 14. UNN. According to the latest measurements, the size of the Milky Way galaxy is 66.5 thousand light years. Science writes about this, reports UNN. It is noted that this was previously impossible, since direct measurements of distances to astronomical sources rely on parallax, which can usually only be measured relative to neighboring objects. The long side of the Milky Way could not be measured accurately because the parallax is very small and interstellar dust blocks optical light from these regions.

Scientists: Hallucinogenic mushrooms may help with depression

Psilocybin suppresses the amygdala, which is largely responsible for emotions such as fear and anxiety. Psilocybin, a substance found in magic mushrooms, can “reset” the brain of a person with severe chronic depression, increasing hopes for future treatment. These are the conclusions of a study conducted by a group of scientists from Imperial College London, reports the BBC. In a small study, 19 patients were given a single dose of psilocybin.

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Sign-preserving operations on two-dimensional meshes

Zohar Ringel, Dmitry L. Kovrizhin / Science advances

In some quantum systems, the sign problem is fundamentally unsolvable. This means that they cannot be effectively simulated on classical computers. Two physicists, including a scientist from the Kurchatov Institute, showed that such a problem arises due to gravitational anomalies in systems with bosonic degrees of freedom, for example, in the fractional Hall effect. Article published in the magazine Science Advances.

It is traditionally believed that all problems that can be solved efficiently on a classical computer can be solved just as efficiently on a quantum computer, but not vice versa. For example, effective classical simulators have not yet been found for many systems with bosonic degrees of freedom, which arise naturally when studying models of interacting quantum many-body systems. In the new work, scientists showed that the absence of such simulations is not due to a lack of ingenuity of researchers, but to the fundamental impossibility of their existence.

The authors of the article note that proving the impossibility of classical simulations in general is a poorly defined problem. They therefore showed that fundamental problems arise when using the most common method of numerical research in the field, the quantum Monte Carlo method. The main tool of this method is the generating functional (partition function, not to be confused with the partition function from statistical mechanics). Knowing it, using differentiation it is easy to find the correlation functions of the system. However, it turns out that calculating the functional is not always possible due to the sign problem when the phases of the integrands change rapidly.

The main idea of ​​the physicists' proof is based on the concept of anomalies. Anomalies are peculiar effects that occur when the symmetry that is present at the level of classical field theory is broken at the level of quantum field theory. Both the usual Hall effect and the temperature effect (Righi-Leduc effect, thermal Hall effect) can be understood in terms of anomalies - charge and gravitational (gravitational anomaly, the adjective “gravitational” appears due to the general covariance of the theory, and not due to gravitational effects ) respectively.

Often, when connecting anomalous theories to static gauge fields, one finds that gauge field fluxes give rise to complex phase factors in the generating functional. This makes it impossible to construct a generating functional without the sign problem, in which complex phases are prohibited by definition. However, this is not always the case and there are various counterexamples. The subtlety is that complex phases may arise not in the original theory, but as a result of adding a gauge field flux.

Physicists carried out the proof that for the classical generating functional in the 2+1-dimensional theory of the bosonic fractional quantum Hall effect on a plane or on a torus it is impossible to get rid of the sign problem in three steps. To begin with, they established that gravitational anomalies cause chiral excitations at the boundary of the volume under study. They then showed that the existence of a spatially isolated chiral channel in this theory forbidden provided that the translation operator and the Perron-Frobenius operator are non-negative. At the same time, the existence of an unsigned generating functional (that is, one in which there is no sign problem) leads to the non-negativity of these operators. Thus, the resulting contradiction indicates the impossibility of avoiding the sign problem in this theory.

The physicists then looked at frustrated quantum systems, in which states similar to those produced by the fractional Hall effect appear when time-reversal symmetry is spontaneously broken. For example, such systems include Kagome quantum antiferromagnets. In general, the above reasoning applies to them, although some additional microscopic assumptions must be made.

Thus, scientists have shown that for a wide class of quantum systems, when calculating using the quantum Monte Carlo method, it is fundamentally impossible to get rid of the sign problem. This means that such systems cannot be effectively simulated using conventional, classical computers. Perhaps this obstacle can be overcome in the future with the help of quantum computers.

Recently we talked about how physicists solved the sign problem in the 1+1-dimensional Thirring model using a neural network.

Dmitry Trunin