Quantum entanglement - human bodies - self-knowledge - catalog of articles - unconditional love

The golden autumn foliage of the trees shone brightly. The rays of the evening sun touched the thinned tops. The light broke through the branches and created a spectacle of bizarre figures flashing on the wall of the university “camper.”

Sir Hamilton's thoughtful gaze slowly slid, watching the play of chiaroscuro. A real melting pot of thoughts, ideas and conclusions was going on in the head of the Irish mathematician. He understood perfectly well that the explanation of many phenomena using Newtonian mechanics is like a play of shadows on a wall, deceptively intertwining figures and leaving many questions unanswered. “Perhaps it is a wave... or perhaps a stream of particles,” the scientist thought, “or light is a manifestation of both phenomena. Like figures woven from shadow and light.”

The beginning of quantum physics

It is interesting to watch great people and try to understand how great ideas are born that change the course of evolution of all mankind. Hamilton is one of those who stood at the origins of quantum physics. Fifty years later, at the beginning of the twentieth century, many scientists were studying elementary particles. The knowledge gained was contradictory and uncompiled. However, the first shaky steps were taken.

Understanding the microworld at the beginning of the twentieth century

In 1901, the first model of the atom was presented and its inconsistency was shown from the position of conventional electrodynamics. During the same period, Max Planck and Niels Bohr published many works on the nature of the atom. Despite their painstaking work, there was no complete understanding of the structure of the atom.

A few years later, in 1905, the little-known German scientist Albert Einstein published a report on the possibility of the existence of a light quantum in two states - wave and corpuscular (particles). In his work, arguments were given to explain the reason for the failure of the model. However, Einstein's vision was limited by the old understanding of the atomic model.

After numerous works by Niels Bohr and his colleagues, a new direction was born in 1925 - a kind of quantum mechanics. The common expression “quantum mechanics” appeared thirty years later.

What do we know about quanta and their quirks?

Today, quantum physics has come quite far. Many different phenomena have been discovered. But what do we really know? The answer is presented by one modern scientist. “You can either believe in quantum physics or not understand it,” is the definition. Think about it for yourself. It will be enough to mention such a phenomenon as quantum entanglement of particles. This phenomenon plunged the scientific world into a state of complete bewilderment. An even bigger shock was that the paradox that arose was incompatible with Einstein.

The effect of quantum entanglement of photons was first discussed in 1927 at the Fifth Solvay Congress. A heated argument arose between Niels Bohr and Einstein. The paradox of quantum entanglement has completely changed the understanding of the essence of the material world.

It is known that all bodies consist of elementary particles. Accordingly, all phenomena of quantum mechanics are reflected in the ordinary world. Niels Bohr said that if we do not look at the Moon, then it does not exist. Einstein considered this unreasonable and believed that an object exists independently of the observer.

When studying the problems of quantum mechanics, one should understand that its mechanisms and laws are interconnected and do not obey classical physics. Let's try to understand the most controversial area - quantum entanglement of particles.

Quantum entanglement theory

To begin with, it is worth understanding that quantum physics is like a bottomless well in which you can find anything. The phenomenon of quantum entanglement at the beginning of the last century was studied by Einstein, Bohr, Maxwell, Boyle, Bell, Planck and many other physicists. Throughout the twentieth century, thousands of scientists around the world actively studied and experimented with this.

The world is subject to the strict laws of physics

Why such interest in the paradoxes of quantum mechanics? Everything is very simple: we live subject to certain laws of the physical world. The ability to “bypass” predestination opens a magical door behind which everything becomes possible. For example, the concept of "Schrodinger's Cat" leads to the control of matter. Teleportation of information caused by quantum entanglement will also become possible. The transmission of information will become instantaneous, regardless of distance.
This issue is still under study, but has a positive trend.

Analogy and understanding

What is unique about quantum entanglement, how to understand it, and what happens when it happens? Let's try to figure it out. To do this, you will need to conduct some kind of thought experiment. Imagine that you have two boxes in your hands. Each of them contains one ball with a stripe. Now we give one box to the astronaut, and he flies off to Mars. Once you open a box and see that the stripe on the ball is horizontal, then the ball in another box will automatically have a vertical stripe. This will be quantum entanglement expressed in simple words: one object predetermines the position of another.

However, it should be understood that this is only a superficial explanation. In order to obtain quantum entanglement, the particles must have the same origin, like twins.

It is very important to understand that the experiment will be disrupted if someone before you had the opportunity to look at at least one of the objects.

Where can quantum entanglement be used?

The principle of quantum entanglement can be used to transmit information over long distances instantly. Such a conclusion contradicts Einstein's theory of relativity. It says that the maximum speed of movement is inherent only in light - three hundred thousand kilometers per second. Such transfer of information makes it possible for physical teleportation to exist.

Everything in the world is information, including matter. Quantum physicists came to this conclusion. In 2008, based on a theoretical database, it was possible to see quantum entanglement with the naked eye.

This once again suggests that we are on the threshold of great discoveries - movement in space and time. Time in the Universe is discrete, so instantaneous movement over vast distances makes it possible to get into different time densities (based on the hypotheses of Einstein and Bohr). Perhaps in the future this will be a reality just like the mobile phone is today.

Aetherdynamics and quantum entanglement

According to some leading scientists, quantum entanglement is explained by the fact that space is filled with a kind of ether - black matter. Any elementary particle, as we know, exists in the form of a wave and a corpuscle (particle). Some scientists believe that all particles reside on a “canvas” of dark energy. This is not easy to understand. Let's try to figure it out another way - by association.

Imagine yourself on the seashore. Light breeze and weak wind. Do you see the waves? And somewhere in the distance, in the reflections of the sun's rays, a sailboat is visible.
The ship will be our elementary particle, and the sea will be the ether (dark energy).
The sea can be in motion in the form of visible waves and drops of water. In the same way, all elementary particles can be simply the sea (its integral part) or a separate particle - a drop.

This is a simplified example, everything is somewhat more complicated. Particles without the presence of an observer are in the form of a wave and do not have a specific location.

A white sailboat is a distinct object; it differs from the surface and structure of the sea water. In the same way, there are “peaks” in the ocean of energy, which we can perceive as a manifestation of the forces known to us that shaped the material part of the world.

The microworld lives by its own laws

The principle of quantum entanglement can be understood if we take into account the fact that elementary particles are in the form of waves. Having no specific location and characteristics, both particles reside in an ocean of energy. At the moment the observer appears, the wave “transforms” into an object accessible to touch. The second particle, observing the equilibrium system, acquires opposite properties.

The described article is not aimed at succinct scientific descriptions of the quantum world. The ability of an ordinary person to comprehend is based on the accessibility of understanding the presented material.

Particle physics studies the entanglement of quantum states based on the spin (rotation) of an elementary particle.

In scientific language (simplified) - quantum entanglement is defined by different spins. In the process of observing objects, scientists saw that only two spins can exist - along and across. Oddly enough, in other positions the particles do not “pose” to the observer.

A new hypothesis - a new view of the world

The study of microcosm - the space of elementary particles - has given rise to many hypotheses and assumptions. The effect of quantum entanglement prompted scientists to think about the existence of some kind of quantum microlattice. In their opinion, at each node - the point of intersection - there is a quantum. All energy is an integral lattice, and the manifestation and movement of particles is possible only through the nodes of the lattice.

The size of the “window” of such a lattice is quite small, and measurement with modern equipment is impossible. However, in order to confirm or refute this hypothesis, scientists decided to study the movement of photons in a spatial quantum lattice. The point is that a photon can move either straight or in zigzags - along the diagonal of the lattice. In the second case, having covered a greater distance, he will spend more energy. Accordingly, it will differ from a photon moving in a straight line.

Perhaps over time we will learn that we live in a spatial quantum lattice. Or this assumption may turn out to be incorrect. However, it is the principle of quantum entanglement that indicates the possibility of the existence of a lattice.

In simple terms, in a hypothetical spatial “cube” the definition of one face carries with it a clear opposite meaning of the other. This is the principle of preserving the structure of space - time.

Epilogue

To understand the magical and mysterious world of quantum physics, it is worth taking a close look at the development of science over the past five hundred years. Previously, it was believed that the Earth was flat, not spherical. The reason is obvious: if you take its shape as round, then the water and people will not be able to hold on.

As we can see, the problem existed in the lack of a complete vision of all the forces at play. It is possible that modern science does not have enough vision of all the acting forces to understand quantum physics. Gaps in vision give rise to a system of contradictions and paradoxes. Perhaps the magical world of quantum mechanics contains the answers to the questions posed.

Quantum entanglement

Quantum entanglement is the basis of future technologies such as the quantum computer and quantum cryptography, and has also been used in experiments on quantum teleportation. In theoretical and philosophical terms, this phenomenon represents one of the most revolutionary properties of quantum theory, since it can be seen that the correlations predicted by quantum mechanics are completely incompatible with the ideas of the seemingly obvious locality of the real world, in which information about the state of the system can transmitted only through its immediate environment. Different views on what actually happens during the process of quantum mechanical entanglement lead to different interpretations of quantum mechanics.

Background

In 1935, Einstein, Podolsky and Rosen formulated the famous Einstein-Podolsky-Rosen Paradox, which showed that due to connectivity, quantum mechanics becomes a nonlocal theory. Einstein famously ridiculed coherence, calling it “a nightmare of action at a distance. Naturally, non-local connectivity refuted the TO postulate about the limiting speed of light (signal transmission).

On the other hand, quantum mechanics has an excellent track record of predicting experimental results, and in fact even strong correlations due to the phenomenon of entanglement have been observed. There is a way that seems to successfully explain quantum entanglement - the “hidden parameter theory” approach, in which certain but unknown microscopic parameters are responsible for the correlations. However, in 1964, J. S. Bell showed that it would still be impossible to construct a “good” local theory in this way, that is, the entanglement predicted by quantum mechanics can be experimentally distinguished from the results predicted by a wide class of theories with local hidden parameters . The results of subsequent experiments provided stunning confirmation of quantum mechanics. Some checks show that there are a number of bottlenecks in these experiments, but it is generally accepted that these are not significant.

Connectivity leads to an interesting relationship with the principle of relativity, which states that information cannot travel from place to place faster than the speed of light. Although two systems may be separated by a large distance and be entangled, it is impossible to transmit useful information through their connection, so causality is not violated by entanglement. This happens for two reasons:
1. the results of measurements in quantum mechanics are fundamentally probabilistic in nature;
2. The quantum state cloning theorem prohibits statistical testing of entangled states.

Reasons for the influence of particles

In our world, there are special states of several quantum particles - entangled states in which quantum correlations are observed (in general, correlation is the relationship between events above the level of random coincidences). These correlations can be detected experimentally, which was done for the first time over twenty years ago and is now routinely used in a variety of experiments. In the classical (that is, non-quantum) world, there are two types of correlations - when one event causes another, or when they both have a common cause. In quantum theory, a third type of correlation arises, associated with the nonlocal properties of entangled states of several particles. This third type of correlation is difficult to imagine using familiar everyday analogies. Or maybe these quantum correlations are the result of some new, hitherto unknown interaction, thanks to which entangled particles (and only they!) influence each other?

It is immediately worth emphasizing the “abnormality” of such a hypothetical interaction. Quantum correlations are observed even if the detection of two particles separated by a large distance occurs simultaneously (within the limits of experimental error). This means that if such an interaction takes place, then it should propagate extremely quickly in the laboratory frame of reference, at superluminal speed. And from this it inevitably follows that in other reference systems this interaction will be generally instantaneous and will even act from the future to the past (though without violating the principle of causality).

The essence of the experiment

Geometry of the experiment. Pairs of entangled photons were generated in Geneva, then the photons were sent along fiber optic cables of equal length (marked in red) to two receivers (marked by the letters APD) separated by 18 km. Image from the discussed Nature article

The idea of ​​the experiment is as follows: we will create two entangled photons and send them to two detectors, spaced as far apart as possible (in the experiment described, the distance between the two detectors was 18 km). In this case, we will make the paths of photons to the detectors as identical as possible, so that the moments of their detection are as close as possible. In this work, the detection moments coincided with an accuracy of approximately 0.3 nanoseconds. Quantum correlations were still observed under these conditions. This means, if we assume that they “work” due to the interaction described above, then its speed should exceed the speed of light by a hundred thousand times.
Such an experiment, in fact, was carried out by the same group before. The only novelty of this work is that the experiment lasted a long time. Quantum correlations were observed continuously and did not disappear at any time of the day.
Why is it important? If a hypothetical interaction is carried by some medium, then this medium will have a dedicated frame of reference. Due to the rotation of the Earth, the laboratory frame of reference moves relative to this frame of reference at different speeds. This means that the time interval between two events of detection of two photons will be different all the time for this medium, depending on the time of day. In particular, there will be a moment when these two events for this environment will seem simultaneous. (Here, by the way, the fact from the theory of relativity is used that two simultaneous events will be simultaneous in all inertial frames of reference moving perpendicular to the line connecting them).

If quantum correlations are carried out due to the hypothetical interaction described above and if the speed of this interaction is finite (even arbitrarily large), then at this moment the correlations would disappear. Therefore, continuous observation of correlations throughout the day would completely close this possibility. And repeating such an experiment at different times of the year would close this hypothesis even with infinitely fast interaction in its own dedicated reference frame.

Unfortunately, this could not be achieved due to the imperfection of the experiment. In this experiment, it takes several minutes of signal accumulation to say that correlations are actually being observed. The disappearance of correlations, for example, for 1 second, this experiment could not notice. That is why the authors could not completely close the hypothetical interaction, but only received a limit on the speed of its propagation in their selected reference frame, which, of course, greatly reduces the value of the result obtained.

Maybe...?

The reader may ask: if the hypothetical possibility described above is nevertheless realized, but the experiment simply overlooked it due to its imperfection, does this mean that the theory of relativity is incorrect? Could this effect be used for superluminal transmission of information or even for movement in space?

No. The hypothetical interaction described above serves a single purpose - these are the “gears” that make quantum correlations “work.” But it has already been proven that using quantum correlations it is impossible to transmit information faster than the speed of light. Therefore, whatever the mechanism of quantum correlations, it cannot violate the theory of relativity.
© Igor Ivanov

See Torsion fields.
The foundations of the Subtle World are physical vacuum and torsion fields. 4. MENTAL BODY.
DNA and the WORD living and dead.
Quantum entanglement.
Quantum theory and telepathy.
Treatment with the Power of Thought.
Suggestion and Self-Hypnosis.
Mental treatment.
Subconscious reprogramming.

Copyright © 2015 Unconditional love

Quantum entanglement is a phenomenon in which the subsystems of some previously unified quantum mechanical system, being separated by a distance from each other, continue to influence each other. In this case, a change in the state of one system affects another system. The phenomenon is essentially quantum in nature and has no classical analogue.

Coffee gets cold, buildings collapse, eggs break, and stars fizzle out in a Universe that seems destined to degrade into a state of uniform gray known as thermal equilibrium. The astronomer-philosopher Sir Arthur Eddington in 1927 cited the gradual spread of energy as evidence of the irreversible "arrow of time".

But to the bewilderment of generations of physicists, the arrow of time does not seem to follow from the basic laws of physics, according to which moving forward in time is the same as moving backward. According to these laws, if one knew the paths of all the particles in the universe and reversed them, energy would accumulate rather than disperse: cold coffee would spontaneously heat up, buildings would be reassembled from debris, and sunlight would be collected back into the sun.

“We are strong in classical physics,” Sandu Popescu, a professor of physics at the University of Bristol in the UK, told QuantaMagazine. “If I knew more, could I turn the tide of events, put together all the molecules of the broken egg?” Of course, the professor says that the arrow of time is not controlled by human ignorance. And yet, since the birth of thermodynamics in the 1850s, the only known approach to calculating the propagation of energy has been to formulate the statistical distribution of unknown particle trajectories and show that, over time, ignorance blurs the picture of things.

Physicists have now identified the fundamental source of the arrow of time. Energy dissipates and objects come into equilibrium, they say, because elementary particles become intertwined when they interact - a strange effect called quantum entanglement. “We can finally understand why a cup of coffee balances in a room,” says Tony Short, a quantum physicist at Bristol. “Confusion accumulates between the state of the coffee cup and the state of the room.” Popescu, Short and their colleagues Noah Linden and Andreas Winter reported the discovery in the journal Physical Review E in 2009, arguing that objects achieve equilibrium, or a state of uniform distribution of energy, for an infinite amount of time through quantum mechanical entanglement with their environment. A similar discovery was published by Peter Reiman of the University of Bielefeld in Germany a few months earlier in Physical Review Letters. Short and colleagues strengthened the argument in 2012 by showing that entanglement causes equilibrium in finite time. Also, in a work published on arXiv.org in February, two separate groups took the next step by calculating that most physical systems equilibrate quickly, in a time proportional to their size.

If the new line of research is correct, the story of the arrow of time begins with the quantum mechanical idea that, at its core, nature is inherently uncertain. An elementary particle lacks specific physical properties and is determined only by the probabilities of being in certain states. For example, at a certain moment a particle may have a 50 percent chance of spinning clockwise and a 50 percent chance of spinning counterclockwise. An experimentally verified theorem by Northern Irish physicist John Bell states that there is no “true” state of a particle; probabilities are the only thing that can be used to describe it. Quantum uncertainty inevitably leads to entanglement, the supposed source of the arrow of time.

When two particles interact, they can no longer be described by separate, independently evolving probabilities called “pure states.” Instead, they become entangled components of a more complex probability distribution that is described by the two particles together. The system as a whole is in a pure state, but the state of each of the individual particles is “mixed”. The two particles may be light years apart, but the spin of each particle will be correlated with the other. Albert Einstein described it well as “spooky action at a distance.” “Entanglement is, in a sense, the essence of quantum mechanics,” or the laws governing interactions at subatomic scales, Brunner says. This phenomenon underlies quantum computing, quantum cryptography and quantum teleportation.

The idea that entanglement could explain the arrow of time first occurred to Seth Lloyd thirty years ago, when he was a 23-year-old philosophy graduate from Cambridge University with a Harvard degree in physics. Lloyd realized that quantum uncertainty, and how it spreads as particles become increasingly entangled, could replace human uncertainty (or ignorance) in the old classical proofs as the true source of the arrow of time. Using the well-known quantum mechanical approach, in which units of information are the basic building blocks, Lloyd spent several years studying the evolution of particles in terms of the shuffling of ones (1s) and zeros (0s). He found that as particles become increasingly entangled with each other, the information that described them (1 for clockwise spin, and 0 for counterclockwise spin, for example) would be transferred to describe the system of entangled particles as a whole. It is as if the particles gradually lost their individual autonomy and became pawns of a collective state. At this point, Lloyd discovered, the particles enter a state of equilibrium, their states stop changing, like a cup of coffee cooling to room temperature. “What's really going on? Things are becoming more connected. The arrow of time is the arrow of increasing correlations.”

“When Lloyd proposed the idea in his thesis, the world was not ready,” says Renato Renner, head of the Institute for Theoretical Physics at ETH Zurich. - Nobody understood him. Sometimes you need ideas to come at the right time.” In 2009, a proof by a team of Bristol physicists struck a chord with quantum information theorists, opening up new ways to apply their methods. It showed that as objects interact with their environment—the way particles in a cup of coffee interact with air, for example—information about their properties “leaks out and gets smeared with the environment,” Popescu explains. This local loss of information causes the coffee's state to stagnate, even as the net state of the entire room continues to evolve. With the exception of rare random fluctuations, the scientist says, “his condition ceases to change over time.” It turns out that a cold cup of coffee cannot spontaneously heat up. Basically, as the pure state of the room evolves, the coffee may suddenly "become unmixed" with the air and enter the pure state. But there are so many more mixed states available in coffee than pure ones that this will almost never happen—the universe will end sooner than we can witness it. This statistical improbability makes the arrow of time irreversible.

“Essentially, entanglement opens up a huge space for you,” Popescu comments. - Imagine that you are in a park, in front of you is a gate. As soon as you enter them, you will find yourself in a huge space and get lost in it. You’ll never return to the gate either.”
In the new story of the arrow of time, information is lost through the process of quantum entanglement, rather than due to a subjective lack of human knowledge, resulting in the equilibration of a cup of coffee and a room. The room eventually equilibrates with the outside environment, and the environment - even more slowly - drifts toward equilibrium with the rest of the universe. The thermodynamic giants of the 19th century viewed this process as a gradual dissipation of energy that increases the overall entropy, or chaos, of the universe. Today, Lloyd, Popescu and others in the field see the arrow of time differently. In their opinion, information becomes increasingly diffuse, but never completely disappears. Although entropy increases locally, the overall entropy of the universe remains constant and zero.

“The universe as a whole is in a pure state,” says Lloyd. “But its individual parts, being entangled with the rest of the universe, remain mixed.”

“There's nothing in these works that explains why you start at the gate,” Popescu says, returning to the park analogy. “In other words, they do not explain why the original state of the universe was far from equilibrium.” The scientist hints that this question relates to the nature of the Big Bang.
Despite recent progress in calculating equilibration times, the new approach still cannot be used to calculate the thermodynamic properties of specific things like coffee, glass or exotic states of matter.

“The point is to find the criteria under which things behave like a window pane or a cup of tea,” Renner says. “I think I will see more work in this direction, but there is still a lot of work ahead.”
Some researchers have expressed doubt that this abstract approach to thermodynamics will ever be able to accurately explain how specific observable objects behave. But conceptual advances and new mathematical formalism are already helping researchers ask theoretical questions in thermodynamics, such as the fundamental limits of quantum computers and even the ultimate fate of the universe.

Twenty-six years after the epic failure of Lloyd's idea for the arrow of time, he is delighted to witness its rise and tries to apply the ideas of his last work to the paradox of information falling into a black hole.

According to scientists, our ability to remember the past but not the future, another manifestation of the arrow of time, can also be seen as increasing correlations between interacting particles. When you read something from a piece of paper, the brain correlates the information through photons that reach the eyes. Only from this moment will you be able to remember what is written on paper. As Lloyd notes: “The present can be defined as the process of relating (or making correlations) with our surroundings.” The backdrop for the steady growth of entanglements throughout the universe is, of course, time itself. Physicists stress that despite great strides in understanding how changes occur in time, they are not one iota closer to understanding the nature of time itself or why it is different from the other three dimensions of space. Popescu calls this mystery “one of the greatest mysteries in physics.”

“We can discuss the fact that an hour ago our brain was in a state that correlated with fewer things,” he says. “But our perception that time is passing is a completely different matter. Most likely, we will need a revolution in physics that will reveal this secret to us.”

It's an elegant and powerful concept. It suggests that time is an emergent phenomenon that appears in reality due to the nature of quantum entanglement. And it exists only for observers inside our universe. Any godlike observer outside of it will see a static, unchanging universe, as the earlier quantum Wheeler-DeWitt equation previously predicted. Of course, we have no way of obtaining an observer outside our universe and we have no chance of ever confirming this theory. At least that was the case until today. Recently, Ekaterina Moreva of the Istituto Nazionale di Ricerca Metrologica in Turin, Italy, and several of her colleagues were able to experimentally test Page and Wouters' ideas for the first time. And they demonstrated that time is indeed an emergent phenomenon for internal observers, but it does not exist for external observers.

This experiment involves creating a toy universe consisting of a pair of entangled photons and an observer who can measure their state in one of two ways. In the first, the observer measures the evolution of the system by entangling himself with it. In the second, a godlike observer measures evolution against an external clock that is completely independent of the toy universe.

The experiment itself is quite straightforward. Each of the entangled photons has a polarization that can be changed by passing through a birefringent plate. In the first case, the observer measures the polarization of one photon, thus becoming entangled with it. It then compares the result with the polarization of the second photon. The difference he receives will be the measure of time.

In the second case, both photons also pass through birefringent plates, which change their polarization. However, in this case, the observer only measures the global properties of both photons by comparing them with an independent clock.

In this case, the observer cannot notice any difference between the photons without ending up in a state of confusion with one of them. And if there is no difference, the system appears static to him. In other words, time does not arise in it.

This is a very impressive experiment. Appearance is a popular concept in science. In particular, physicists have recently become interested in the idea that gravity is also such an emergent phenomenon. And from here there was only one step left to the idea of ​​a similar mechanism for the emergence of time. What emergent gravity lacks, of course, is an experimental demonstration to show how it works in practice. This is why Moreva's work is so important - it is the first in the world to place an abstract and exotic idea on a stable experimental basis. Perhaps the most important result of this work is that it was the first to demonstrate that quantum mechanics and general relativity are not so incompatible.

The next step will be further development of the idea, in particular at the macroscopic level. It is one thing to show how time arises in photons, and another to understand how it arises for people. Quantum mechanics has already penetrated quite deeply into related scientific fields. In an attempt to explain life itself in terms of quantum theory, it even gave birth to its own biology. But until now, no one has dared to directly state that the effect of entanglement lies at the very core of living beings - inside the DNA helix.

The newborn quantum biology is not officially recognized as a scientific discipline. However, it has already become one of the most interesting and exciting topics of advanced research. For example, revealing the important role of quantum effects in a number of biological processes, such as photosynthesis. The new study was conducted by a group of physicists from the National University of Singapore (NSU). Elizabeth Rieper and her colleagues proceeded from the fact that the DNA double helix does not disintegrate precisely due to the principle of quantum entanglement.

To test their bold theory, scientists built a simplified theoretical model of DNA on a computer. In it, each nucleotide consists of a cloud of electrons around a central, positively charged nucleus. This "negative" cloud can move relative to the core, creating a dipole. In this case, the displacement of the cloud back and forth leads to the formation of a harmonic oscillator.

Ripert and his colleagues became interested in what would happen to the vibrations of the clouds (phonons) when the base pairs created a DNA double helix. According to scientists, when nucleotide pairs form, their combined clouds should theoretically vibrate in the opposite direction to the cloud from the neighboring pair to ensure the stability of the entire structure. Since phonons are essentially quantum objects, they can exist as a superposition of states and can become entangled. Scientists began by assuming the absence of any thermal effects affecting the spiral from the outside. “It is clear that chains of pairwise coupled harmonic oscillators can only be entangled at zero temperature,” says Ripert. In their article, which has not yet been published in scientific journals, physicists provide evidence that the entanglement effect, in principle, can occur at room temperature. And perhaps this is because the wavelength of the described phonons is close to the size of the DNA helix. This allows so-called standing waves to form (a phenomenon known as phonon capture). After this, phonons cannot “escape.” This effect will not be particularly significant for a giant molecule unless it extends throughout the entire helix. However, computer modeling carried out by Ripert and his friends demonstrates that the effect is truly colossal.

Each electron cloud in a base pair not only vibrates in concert with the movements of its neighbors - the phonons are in a superposition of states. And the general picture of all such oscillations in DNA is described by quantum laws: along the entire chain, nucleotide oscillators oscillate synchronously - this is a manifestation of quantum entanglement. The overall motion of the spiral turns out to be zero.

Model of a DNA helix with a fragment with two adjacent base pairs enlarged. The electron clouds in the two extreme positions of their oscillations are highlighted in blue, the directions of which are indicated by arrows (illustration by Rieper et al.). If you try to describe this model exclusively within the framework of classical physics, then none of the above can happen: a “classical” spiral should vibrate chaotically and fall apart. According to researchers, it is quantum effects that are responsible for the “gluing” of DNA. But, as in the case of the theory of cosmic ripples - the ambitious “twin sister” of the current work (admittedly, occupied with objects of the macrocosm), the main question is not original: how to prove this conclusion? No answer yet. Ripert's team ends their paper with the intriguing idea that entanglement somehow directly affects the way information is "read" from DNA. They say that in the future this will be tested and used experimentally. How exactly – no one can even guess yet.

Despite some degree of speculativeness, the assumption put forward by physicists excited many minds. After all, quantum effects have already been found in the most unexpected places, for example in an electrical circuit, but so far no one has made claims of such a scale - microscopic and at the same time incredibly important.

In light of the above, a person who spends a lot of effort on entangling several qubits in a solid body looks funny, because he does not suspect that the most striking example of such a system is himself.

Quantum entanglement

There are so many good articles on the Internet that help to develop adequate ideas about “entangled states” that it remains to make the most suitable selections, building the level of description that seems acceptable for a worldview site.

Topic of the article: Many people are close to the idea that all the fascinating quirks of entangled states could be explained this way. We mix the black and white balls, without looking, pack them into boxes and send them in different directions. We open the box on one side, look: a black ball, after which we are 100% sure that there is a white ball in the other box. That's all:)

The purpose of the article is not a strict immersion in all the features of understanding “entangled states”, but to compile a system of general ideas, with an understanding of the main principles. This is exactly how you should treat everything stated above :)

Let's immediately set the defining context. When specialists (and not debaters far from this specificity, even scientists in some ways) talk about the entanglement of quantum objects, they mean not that it forms one whole with some connection, but that one object becomes quantum characteristics exactly the same as the other (but not all, but those that allow identity in a pair according to Pauli’s law, so the spin of a mated pair is not identical, but mutually complementary). Those. This is not a connection or a process of interaction, even though it can be described by a general function. This is a characteristic of a state that can be “teleported” from one object to another (by the way, there is also a widespread misinterpretation of the word “teleport”). If you don’t decide on this right away, you can go very far into mysticism. Therefore, first of all, everyone who is interested in the issue must be clearly sure of what exactly is meant by “confusion.”

What this article was started for comes down to one question. The difference in the behavior of quantum objects from classical ones is manifested in the only so far known verification method: whether a certain verification condition is met or not - Bell’s inequality (more details below), which for “entangled” quantum objects behaves as if there is a connection between objects sent in different directions. But the connection seems to be not real, because... neither information nor energy can be transferred.

Moreover, this connection does not depend neither from distance nor from time: if two objects were “entangled”, then, regardless of the safety of each of them, the second behaves as if the connection still exists (although the presence of such a connection can only be detected by measuring both objects, such a measurement can be separated in time: first measure, then destroy one of the objects, and measure the second later. For example, see R. Penrose). It is clear that any type of “connection” becomes difficult to understand in this case and the question arises as follows: can the law of probability of the loss of the measured parameter (which is described by the wave function) be such that the inequality is not violated at each end, and with general statistics at both ends - was violated - and without any connection, naturally, except for the connection by an act of general emergence.

I’ll give the answer in advance: yes, it can, provided that these probabilities are not “classical”, but operate with complex variables to describe a “superposition of states” - as if simultaneously finding all possible states with a certain probability for each.

For quantum objects, the descriptor of their state (wave function) is exactly that. If we talk about describing the position of an electron, then the probability of finding it determines the topology of the “cloud” - the shape of the electron orbital. What is the difference between classical and quantum?

Let's imagine a rapidly rotating bicycle wheel. Somewhere on it there is a red disk for the side headlight reflector, but we only see a denser shadow of the blur in this place. The probability that by putting a stick in the wheel, the reflector will stop in a certain position from the stick is simply determined: one stick - one certain position. We put two sticks in, but only the one that is a little earlier will stop the wheel. If we try to stick our sticks completely simultaneously, ensuring that there is no time between the ends of the stick touching the wheel, then some uncertainty will appear. “There was no time” between interactions with the essence of the object - the whole essence of understanding quantum miracles :)

The speed of “rotation” of what determines the shape of the electron (polarization - the propagation of electrical disturbance) is equal to the maximum speed with which anything can propagate in nature (the speed of light in a vacuum). We know the conclusion of the theory of relativity: in this case, the time for this disturbance becomes zero: there is nothing in nature that could happen between any two points of propagation of this disturbance; time for it does not exist. This means that the disturbance is able to interact with any other “sticks” influencing it without wasting time - simultaneously. And the probability of what result will be obtained at a specific point in space during interaction must be calculated by a probability that takes into account this relativistic effect: Due to the fact that there is no time for an electron, it is not able to choose the slightest difference between two “sticks” during interaction with them and does it simultaneously from its “point of view”: an electron passes through two slits simultaneously with a different wave density in each and then interferes with itself as two superimposed waves.

Here is the difference in the descriptions of probabilities in classical and quantum: Quantum correlations are “stronger” than classical ones. If the result of a coin falling out depends on many influencing factors, but in general they are uniquely determined so that you just need to make an exact machine for throwing out coins, and they will fall the same way, randomness has “disappeared”. If you make an automaton that pokes into an electron cloud, then the result will be determined by the fact that each poke will always hit something, only with a different density of the essence of the electron in this place. There are no other factors other than the static distribution of the probability of finding the measured parameter in the electron, and this is determinism of a completely different kind than in the classics. But this is also determinism, i.e. it is always calculable, reproducible, only with a singularity described by the wave function. Moreover, such quantum determinism concerns only a holistic description of a quantum wave. But, due to the absence of its own time for the quantum, it interacts absolutely randomly, i.e. there is no criterion to predict in advance the result of measuring the totality of its parameters. In this sense, e (in the classical view) is absolutely non-deterministic.

The electron really and truly exists in the form of a static formation (and not a point rotating in orbit) - a standing wave of electric disturbance, which has another relativistic effect: perpendicular to the main plane of “propagation” (it’s clear why in quotes:) an electric field arises also a static region of polarization, which is capable of influencing the same region of another electron: magnetic moment. Electric polarization in an electron gives the effect of an electric charge, its reflection in space in the form of the possibility of influencing other electrons - in the form of a magnetic charge, which cannot exist in itself without an electric one. And if in an electrically neutral atom the electric charges are compensated by the nuclear charges, then the magnetic ones can be oriented in one direction and we get a magnet. More in-depth ideas about this are in the article .

The direction in which the magnetic moment of the electron will be directed is called spin. Those. spin is a manifestation of the method of superimposing a wave of electrical deformation on itself with the formation of a standing wave. The numerical value of the spin corresponds to the characteristic of the wave superimposing itself. For the electron: +1/2 or -1/2 (the sign symbolizes the direction of the lateral shift of polarization - the “magnetic” vector).

If there is one electron on the outer electron layer of an atom and suddenly another one joins it (the formation of a covalent bond), then they, like two magnets, immediately rise to position 69, forming a paired configuration with a bond energy that must be broken in order to again share these electrons. The total spin of such a pair is 0.

Spin is a parameter that plays an important role when considering entangled states. For a freely propagating electromagnetic quantum, the essence of the conditional parameter “spin” is still the same: the orientation of the magnetic component of the field. But it is no longer static and does not lead to the emergence of a magnetic moment. To fix it, you need not a magnet, but a polarizer slit.

To get some ideas about quantum entanglement, I suggest reading the popular and short article by Alexey Levin: Passion at a distance . Please follow the link and read before proceeding :)

So, specific measurement parameters are realized only during measurement, and before that they existed in the form of that probability distribution, which constituted the statics of the relativistic effects of the dynamics of the propagation of polarization of the microworld, visible to the macroworld. To understand the essence of what is happening in the quantum world means to penetrate into the manifestations of such relativistic effects, which in fact give a quantum object the properties of being simultaneously in different states until the moment of specific measurement.

An “entangled state” is a completely deterministic state of two particles that have such an identical dependence of the description of quantum properties that consistent correlations appear at both ends, due to the peculiarities of the essence of quantum statics, which have consistent behavior. Unlike macro statistics, in quantum statistics it is possible to preserve such correlations for objects separated in space and time and previously consistent in parameters. This is manifested in the statistics of the fulfillment of Bell's inequalities.

How is the wave function (our abstract description) of the unentangled electrons of two hydrogen atoms different (even though its parameters are generally accepted quantum numbers)? Nothing except that the spin of the unpaired electron is random without violating Bell's inequalities. In the case of the formation of a paired spherical orbital in a helium atom, or in the covalent bonds of two hydrogen atoms, with the formation of a molecular orbital generalized by two atoms, the parameters of the two electrons turn out to be mutually consistent. If entangled electrons are split and they begin to move in different directions, then a parameter appears in their wave function that describes the displacement of the probability density in space as a function of time - the trajectory. And this does not at all mean that the function is smeared in space, simply because the probability of finding an object becomes zero at some distance from it and there is nothing left behind to indicate the probability of finding an electron. This is especially obvious if the pair is separated in time. Those. two local and independent descriptors arise, moving particles in opposite directions. Although it is still possible to use one general descriptor, it is the right of the one who formalizes it :)

In addition, the environment of the particles cannot remain indifferent and is also subject to modification: the descriptors of the wave function of the particles of the environment change and participate in the resulting quantum statistics through their influence (giving rise to phenomena such as decoherence). But usually almost no one thinks of describing this as a general wave function, although this is also possible.

Many sources provide detailed information on these phenomena.

M.B. Mensky writes:

"One of the purposes of this article... is to substantiate the view that there is a formulation of quantum mechanics in which no paradoxes arise and in which all the questions that physicists usually ask can be answered. Paradoxes arise only when a researcher is not satisfied with this “physical” level of theory, when he poses questions that are not customary to pose in physics, in other words, when he takes it upon himself to try to go beyond the boundaries of physics. ...The specific features of quantum mechanics associated with entangled states were first formulated in connection with the EPR paradox, but at present they are not perceived as paradoxical. For people who work professionally with quantum mechanical formalism (i.e., for most physicists), there is nothing paradoxical either in EPR pairs or even in very complex entangled states with a large number of terms and a large number of factors in each term. The results of any experiments with such states are, in principle, easy to calculate (although technical difficulties in calculating complex entangled states are, of course, possible)."

Although, it must be said, in discussions about the role of consciousness, conscious choice in quantum mechanics, Mensky turns out to be the one who takes " take the courage to try to go beyond the boundaries of physics". This is reminiscent of attempts to approach the phenomena of the psyche. As a quantum professional, Mensky is good, but in the mechanisms of the psyche he, like Penrose, is naive.

Very briefly and conditionally (only to grasp the essence) about the use of entangled states in quantum cryptography and teleportation (since this is what amazes the imagination of grateful viewers).

So, cryptography. You need to send the sequence 1001

We use two channels. According to the first, we send an entangled particle, and according to the second, information about how to interpret the received data in the form of one bit.

Let us assume that there is an alternative to the possible state of the used quantum mechanical parameter spin in conditional states: 1 or 0. Moreover, the probability of their occurrence with each released pair of particles is truly random and does not convey any meaning.

First transfer. When measuring Here it turned out that the particle has state 1. This means that the other has state 0. So that volume At the end of receiving the required unit, we transmit bit 1. There they measure the state of the particle and, to find out what it means, add it to the transmitted 1. They get 1. At the same time, they check by white that the entanglement has not been broken, i.e. info was not intercepted.

Second gear. The result is again a state of 1. The other has a 0. We transmit the information - 0. Add it up and get the required 0.

Third gear. The state here is 0. There, that means - 1. To get 0, we transmit 0. We add, we get 0 (in the least significant digit).

Fourth. Here - 0, there - 1, it needs to be interpreted as 1. We pass the information - 0.

That's the principle. Interception of the info channel is useless due to a completely uncorrelated sequence (encryption of the state of the first particle with a key). Interception of an obfuscated channel - disrupts reception and is detected. Transmission statistics from both ends (the receiving end has all the necessary data on the transmitted end) according to Bell determines the correctness and non-interception of the transmission.

This is what teleportation is all about. There is no arbitrary imposition of a state on a particle there, but only a prediction of what this state will be after (and only after) the particle here is removed from the connection by measurement. And then they say that there was a transfer of a quantum state with the destruction of the complementary state at the starting point. Having received information about the state here, you can adjust the quantum mechanical parameter in one way or another so that it turns out to be identical to the one here, but here it will no longer be, and they are talking about implementing the ban on cloning in a bound state.

It seems that there are no analogues of these phenomena in the macrocosm, no balls, apples, etc. from classical mechanics cannot serve to interpret the manifestation of this nature of quantum objects (in fact, there are no fundamental obstacles to this, which will be shown below in the final link). This is the main difficulty for those who want to receive a visible “explanation”. This does not mean that such a thing is not imaginable, as is sometimes stated. This means that you need to work quite painstakingly on relativistic concepts, which play a decisive role in the quantum world and connect the world of quantum with the macro world.

But this is not necessary either. Let us recall the main task of the representation: what should be the law of materialization of the measured parameter (which is described by the wave function) so that the inequality is not violated at each end, and with general statistics, it is violated at both ends. There are many interpretations for understanding this, using auxiliary abstractions. They talk about the same thing in different languages ​​of such abstractions. Of these, two are the most significant in terms of the correctness shared among the bearers of ideas. I hope that after what has been said it will be clear what is meant :)

Copenhagen interpretation from an article about the Einstein-Podolsky-Rosen paradox:

" (EPR paradox) - an apparent paradox... In fact, let’s imagine that on two planets at different ends of the Galaxy there are two coins that always fall out the same way. If you record the results of all the tosses and then compare them, they will coincide. The drops themselves are random and cannot be influenced in any way. It is impossible, for example, to agree that heads are one and tails are zero, and thus transmit binary code. After all, the sequence of zeros and ones will be random at both ends of the wire and will not carry any meaning.

It turns out that there is an explanation for the paradox that is logically compatible with both the theory of relativity and quantum mechanics.

One might think that this explanation is too implausible. It's so strange that Albert Einstein never believed in a "god who plays dice." But careful experimental tests of Bell's inequalities have shown that there are non-local accidents in our world.

It is important to emphasize one already mentioned consequence of this logic: measurements over entangled states will only not violate the theory of relativity and causality if they are truly random. There should be no connection between the circumstances of measurement and the disturbance, not the slightest pattern, because otherwise the possibility of instantaneous transmission of information would arise. Thus, quantum mechanics (in the Copenhagen interpretation) and the existence of entangled states prove the presence of indeterminism in nature."

In a statistical interpretation, this is shown through the concept of “statistical ensembles” (same):

From the point of view of statistical interpretation, the real objects of study in quantum mechanics are not individual microobjects, but statistical ensembles of microobjects located in the same macroconditions. Accordingly, the phrase “a particle is in such and such a state” actually means “the particle belongs to such and such a statistical ensemble” (consisting of many similar particles). Therefore, the choice of one or another sub-ensemble in the initial ensemble significantly changes the state of the particle, even if there was no direct impact on it.

As a simple illustration, consider the following example. Let's take 1000 colored coins and throw them on 1000 sheets of paper. The probability that a “heads” imprint on a randomly selected sheet of paper is equal to 1/2. Meanwhile, for sheets on which coins lie “tails” up, the same probability is equal to 1 - that is, we have the opportunity to indirectly establish the nature of the imprint on paper, looking not at the sheet itself, but only at the coin. However, the ensemble associated with such an “indirect measurement” is completely different from the original one: it no longer contains 1000 sheets of paper, but only about 500!

Thus, a refutation of the uncertainty relationship in the EPR “paradox” would be valid only if for the original ensemble it was possible to simultaneously select a non-empty subensemble both on the basis of momentum and on the basis of spatial coordinates. However, it is precisely the impossibility of such a choice that is confirmed by the uncertainty relation! In other words, the EPR “paradox” in fact turns out to be a vicious circle: it presupposes in advance the incorrectness of the fact being refuted.

Option with a “superluminal signal” from a particle A to the particle B is also based on ignoring the fact that the probability distributions of the values ​​of the measured quantities characterize not a specific pair of particles, but a statistical ensemble containing a huge number of such pairs. Here, as a similar one, we can consider the situation when a colored coin is thrown onto a sheet in the dark, after which the sheet is pulled out and locked in a safe. The probability that “heads” is imprinted on the sheet is a priori equal to 1/2. And the fact that it will immediately turn into 1 if we turn on the light and make sure that the coin lies “tails” up does not at all indicate the ability of our gaze to mist chemically influence items locked in the safe.

More details: A.A. Pechenkin Ensemble interpretations of quantum mechanics in the USA and USSR.

And one more interpretation from http://ru.philosophy.kiev.ua/iphras/library/phnauk5/pechen.htm:

Van Fraassen's modal interpretation assumes that the state of a physical system changes only causally, i.e. in accordance with the Schrödinger equation, however, this state does not uniquely determine the values ​​of physical quantities detected during measurement.

Popper gives here his favorite example: a children's billiard (a board covered with needles, on which a metal ball rolls down from above, symbolizing a physical system - the billiard itself symbolizes an experimental device). When the ball is at the top of the billiard, we have one disposition, one predisposition to reach some point at the bottom of the board. If we fixed the ball somewhere in the middle of the board, we changed the specification of the experiment and received a new predisposition. Quantum mechanical indeterminism is preserved here in full: Popper stipulates that billiards are not a mechanical system. We are unable to trace the trajectory of the ball. But “wave packet reduction” is not an act of subjective observation, it is a conscious redefinition of the experimental situation, a narrowing of the conditions of experience.

Let's summarize the facts

1. Despite the absolute randomness of the loss of paramert when measuring entangled pairs of particles in the mass, consistency is manifested in each such pair: if one particle in the pair turns out to have spin 1, then the other particle in the pair has the opposite spin. This is understandable in principle: since in a paired state there cannot be two particles that have the same spin in the same energy state, then when they split, if consistency is preserved, then the spins remain consistent. As soon as the spin of one is determined, the spin of the other becomes known, despite the fact that the randomness of the spin in measurements from either side is absolute.

Let me briefly clarify the impossibility of completely identical states of two particles in one place in space-time, which in the model of the structure of the electron shell of an atom is called the Pauli principle, and in the quantum mechanical consideration of consistent states - the principle of the impossibility of cloning entangled objects.

There is something (yet unknown) that actually prevents a quantum or its corresponding particle from being in one local state with another - completely identical in quantum parameters. This is realized, for example, in the Casimir effect, when virtual quanta between the plates can have a wavelength no greater than the gap. And this is especially clearly realized in the description of an atom, when the electrons of a given atom cannot have identical parameters in all respects, which is axiomically formalized by the Pauli principle.

On the first, closest layer there can only be 2 electrons in the form of a sphere (s-electrons). If there are two of them, then they have different spins and are paired (entangled), forming a common wave with binding energy that must be applied to break this pair.

In the second, more distant and higher energy level, there can be 4 “orbitals” of two paired electrons in the form of a standing wave shaped like a volumetric figure eight (p-electrons). Those. greater energy occupies more space and allows several already connected pairs to be adjacent. The second layer differs energetically from the first layer by 1 possible discrete energy state (the more outer electrons, describing a spatially larger cloud, also have higher energy).

The third layer already spatially allows you to have 9 orbits in the shape of a quatrefoil (d-electrons), fourth - 16 orbits - 32 electrons, form which also resemble volumetric eights in different combinations ( f-electrons).

Electron cloud shapes:

a – s-electrons; b – p-electrons; c – d-electrons.

This set of discretely different states - quantum numbers - characterize the possible local states of electrons. And this is what comes of it.

When two electrons have different spinsoneenergy level (although this is not fundamentally necessary: http://www.membrana.ru/lenta/?9250) pair, a common “molecular orbital” is formed with a lower energy level due to energy and bonding. Two hydrogen atoms each sharing an unpaired electron form a common overlap of these electrons—a (simple covalent) bond. As long as it exists, truly two electrons have a common consistent dynamics - a common wave function. How long? “Temperature” or something else that can compensate for the bonding energy breaks it. The atoms fly apart with electrons no longer sharing a common wave, but still in a complementary, mutually consistent state of entanglement. But there is no connection anymore :) This is the moment when it is no longer worth talking about the general wave function, although the probabilistic characteristics in terms of quantum mechanics remain the same as if this function continued to describe the general wave. This precisely means maintaining the ability to manifest consistent correlation.

A method for producing entangled electrons through their interactions is described: http://www.scientific.ru/journal/news/n231201.html or popularly-schematically - in http://www.membrana.ru/articles/technic/2002/02/08/170200.html : " To create an "uncertainty relationship" of electrons, that is, to "confuse" them, you need to make sure that they are identical in all respects, and then shoot these electrons into a beam splitter. The mechanism “splits” each of the electrons, bringing them into a quantum state of “superposition”, as a result of which the electron is equally likely to move along one of two paths.".

2. With statistics of measurements on both sides, the mutual consistency of randomness in pairs can lead to a violation of Bell’s inequality under certain conditions. But not through the use of some special, as yet unknown quantum mechanical entity.

The following short article (based on the ideas presented by R. Pnrose) allows us to trace (show the principle, example) how this is possible: The relativity of Bell's inequalities or the New Mind of the Naked King. This is also shown in the work of A.V. Belinsky, published in Advances in Physical Sciences: Bell's theorem without the assumption of locality. Another work by A.V. Belinsky for consideration by those interested: Bell’s theorem for trichotomous observables, as well as a discussion with D.P.S., Prof., Acad. Valery Borisovich Morozov (a generally recognized luminary of the forums of the physics department of the FRTK-MIPT and the “dubinushki”), where Morozov offers for consideration both of these works by A.V. Belinsky: Experience of Aspect: a question for Morozov. And in addition to the topic about the possibility of violations of Bell's inequalities without introducing any long-range action: Modeling using Bell's inequality.

Please note that “The Relativity of Bell’s Inequalities or the New Mind of the Naked King”, as well as “Bell’s Theorem without the Assumption of Locality” in the context of this article do not pretend to describe the mechanism of quantum mechanical entanglement. The task is shown in the last sentence of the first link: “There is no reason to refer to the violation of Bell’s inequalities as an indisputable refutation of any model of local realism.” those. the limit of its use is the theorem stated at the beginning: “There may exist models of classical locality in which Bell’s inequalities will be violated.” There are additional explanations about this in the discussion.

I’ll also give you a model from myself.
“Violation of local realism” is just a relativistic effect.
Nobody (normal) argues with the fact that for a system moving at the maximum speed (the speed of light in vacuum) there is neither space nor time (the Lorentz transformation in this case gives zero time and space), i.e. for a quantum it is both here and there at once, no matter how distant it may be there.
It is clear that entangled quanta have their own starting point. And electrons are the same quanta in a state of a standing wave, i.e. existing here and there simultaneously for the entire lifetime of the electron. All properties of quanta turn out to be predetermined for us, those who perceive it from the outside, that’s why. We are ultimately made up of quanta, which are both here and there. For them, the speed of interaction propagation (maximum speed) is infinitely high. But all these infinities are different, just like the different lengths of segments, although each has an infinite number of points, but the ratio of these infinities gives the ratio of lengths. This is how time and space appear for us.
For us, local realism is violated in experiments, but for quanta it is not.
But this discrepancy does not affect reality in any way because we cannot practically take advantage of such an infinite speed. Neither information, nor, especially matter, is transmitted indefinitely quickly during “quantum teleportation”.
So all this is just jokes of relativistic effects, nothing more. They can be used in quantum cryptography or something else, but cannot be used for real long-range action.

Let's look at the essence of what Bell's inequalities show.
1. If the orientation of the meters at both ends is the same, then the spin measurement result at both ends will always be opposite.
2. If the orientation of the meters is opposite, then the result will be the same.
3. If the orientation of the left meter differs from the orientation of the right one by less than a certain angle, then point 1 will be realized and the coincidences will be within the probability predicted by Bell for independent particles.
4. If the angle exceeds, then point 2 and the coincidences will be greater than the probability predicted by Bell.

Those. at a smaller angle we will obtain predominantly opposite values ​​of the spins, and at a larger angle we will obtain predominantly identical ones.
Why this happens with spin can be imagined, keeping in mind that the spin of an electron is a magnet, and is also measured by the orientation of the magnetic field (or in a free quantum, spin is the direction of polarization and is measured by the orientation of the gap through which the plane of rotation of the polarization should fall).
It is clear that by sending magnets that were initially linked and retained their mutual orientation when sent, we will influence them with a magnetic field during measurement (turning them in one direction or another) in the same way as happens in quantum paradoxes.
It is clear that when encountering a magnetic field (including the spin of another electron), the spin is necessarily oriented in accordance with it (mutually opposite in the case of the spin of another electron). That is why they say that “spin orientation occurs only during measurement,” but at the same time it depends on its initial position (in which direction to rotate) and the direction of influence of the meter.
It is clear that no long-range actions are required for this, just as it is not necessary to prescribe such behavior in the initial state of the particles.
I have reason to believe that so far, when measuring the spin of individual electrons, intermediate spin states are not taken into account, but only predominantly along the measuring field and against the field. Examples of methods: , . It is worth paying attention to the date of development of these methods, which is later than the experiments described above.
The given model, of course, is simplified (in quantum phenomena, spin is not exactly the material magnets, although they provide all the observed magnetic phenomena) and does not take into account many nuances. Therefore, it is not a description of a real phenomenon, but shows only a possible principle. And he also shows how bad it is to simply trust descriptive formalism (formulas) without understanding the essence of what is happening.
Moreover, Bell's theorem is correct in the formulation from Aspek's article: “it is impossible to find a theory with an additional parameter that satisfies the general description and that reproduces all the predictions of quantum mechanics.” and not at all in Penrose’s formulation: “it turns out that it is impossible to reproduce the predictions of quantum theory in this (non-quantum) way.” It is clear that in order to prove the theory according to Penrose, it is necessary to prove that it is not possible to violate Bell’s inequalities using any models other than a quantum mechanical experiment.

This is a somewhat exaggerated, one might say vulgar example of interpretation, simply to show how one can be deceived in such results. But let’s make it clear what Bell wanted to prove and what actually happens. Bell created an experiment showing that in entanglement there is no pre-existing “algorithm”, no pre-built correlation (as opponents insisted at that time, saying that there are some hidden parameters that determine such a correlation). And then the probabilities in his experiments should be higher than the probability of an actually random process (why is well described below).
BUT in fact they simply have the same probabilistic dependencies. What does it mean? This means that it is not at all a predetermined, given connection between the fixation of a parameter and a measurement that takes place, but such a result of fixation comes from the fact that the processes have the same (complementary) probabilistic function (which, in general, directly stems from quantum mechanical concepts), the essence which is the realization of a parameter when fixed, which was not defined due to the absence of space and time in its “reference frame” due to the maximum possible dynamics of its existence (relativistic effect formalized by Lorentz transformations, see Vacuum, quanta, matter).

This is how Brian Greene describes the methodological essence of Bell's experiment in his book The Fabric of the Cosmos. Each of the two players received many boxes, each with three doors. If the first player opens the same door as the second in a box with the same number, then it flashes with the same light: red or blue.
The first player Scully assumes that this is ensured by the flash color program embedded in each pair depending on the door, the second player Mulder believes that the flashes follow with equal probability, but are somehow connected (by non-local long-range action). According to the second player, experience decides everything: if the program - then the probability of identical colors when different doors are randomly opened should be more than 50%, contrary to the truth of random probability. He gave an example why:
Just to be specific, let's imagine that the program for the sphere in a separate box produces blue (1st door), blue (2nd door) and red (3rd door) colors. Now, since we both choose one of the three doors, there are a total of nine possible combinations of doors that we can choose to open for a given box. For example, I can choose the top door on my box, while you can choose the side door on your box; or I can choose the front door and you can choose the top door; and so on."
"Yes, sure." – Scully jumped. “If we call the top door 1, the side door 2, and the front door 3, then the nine possible door combinations are simply (1,1), (1,2), (1,3), (2,1), ( 2,2), (2,3), (3,1), (3,2) and (3,3)."
"Yes, that's right," Mulder continues. - "Now the important point: Of these nine possibilities, we note that five combinations of doors - (1,1), (2,2), (3,3), (1,2) and (2,1) - lead to The result is that we see the spheres in our boxes flashing with the same colors.
The first three door combinations are the ones in which we choose the same doors, and as we know, this always results in us seeing the same colors. The other two door combinations (1,2) and (2,1) result in the same colors, since the program dictates that the spheres will flash one color - blue - if either door 1 or door 2 is open. So, since 5 is more than half of 9, that means that for more than half—more than 50 percent—of the possible combinations of doors we can choose to open, the orbs will flash the same color."
"But wait," Scully protests. - “This is just one example of a special program: blue, blue, red. In my explanation, I assumed that boxes with different numbers can and in general will have different programs.”
"Really, it doesn't matter. The conclusion is valid for any of the possible programs.

And this is indeed true if we are dealing with a program. But this is not at all the case if we are dealing with random dependencies for many experiences, but each of these accidents has the same form in each experiment.
In the case of electrons, when they were initially bound in a pair, which ensures their completely dependent spins (mutually opposite) and fly apart, this interdependence, of course, remains with a complete overall picture of the true probability of precipitation and in the fact that it is impossible to say in advance how the spins of the two turned out electrons in a pair is impossible until one of them is determined, but they “already” (if one can say so in relation to something that does not have its own metric of time and space) have a certain relative position.

Further in Brian Greene's book:
there is a way to examine whether we have inadvertently come into conflict with the SRT. The common property of matter and energy is that, when transferred from place to place, they can transmit information. Photons, traveling from a radio transmitting station to your receiver, carry information. Electrons traveling through Internet cables to your computer carry information. In any situation where something—even something unidentified—is implied to be moving faster than the speed of light, the safe test is to ask whether it is, or at least can, convey information. If the answer is no, the standard reasoning goes through that nothing exceeds the speed of light and SRT remains uncontested. In practice, physicists often use this test to determine whether some subtle process violates the laws of STR. Nothing survived this test.

As for the approach of R. Penrose and so on. interpreters, then from his work Penrouz.djvu I will try to highlight that fundamental attitude (worldview) that directly leads to mystical views about nonlocality (with my comments - black tsaeta):

It was necessary to find a way that would allow one to separate truth from assumptions in mathematics - some formal procedure, using which one could say with confidence whether a given mathematical statement is true or not (objection see Aristotle's Method and Truth, criteria of truth). Until this problem is properly resolved, one can hardly seriously hope for success in solving other, much more complex problems - those that concern the nature of the forces that move the world, no matter what relationship these same forces may have with mathematical truth. The realization that the key to understanding the universe lies in irrefutable mathematics is perhaps the first of the most important breakthroughs in science in general. The ancient Egyptians and Babylonians guessed about mathematical truths of various kinds, but the first stone in the foundation of mathematical understanding...
... for the first time, people had the opportunity to formulate reliable and obviously irrefutable statements - statements whose truth is beyond doubt today, despite the fact that science has stepped far forward since then. For the first time, people discovered the truly timeless nature of mathematics.
What is this - mathematical proof? In mathematics, a proof is an impeccable reasoning that uses only the techniques of pure logic. (pure logic does not exist. Logic is an axiomatic formalization of patterns and relationships found in nature) allowing one to make an unambiguous conclusion about the validity of a particular mathematical statement based on the validity of any other mathematical statements, either established in advance in a similar way, or not requiring proof at all (special elementary statements, the truth of which, in general opinion, is self-evident, are called axioms) . The proven mathematical statement is usually called a theorem. This is where I don’t understand him: there are also theorems that are simply stated but not proven.
... Objective mathematical concepts should be thought of as timeless objects; there is no need to think that their existence begins the moment they appear in one form or another in the human imagination.
... Thus, mathematical existence differs not only from physical existence, but also from the existence that our conscious perception is capable of endowing an object with. However, it is clearly related to the last two forms of existence - i.e., physical and mental existence connection is a completely physical concept, what does Penrose mean here?- and the corresponding connections are as fundamental as they are mysterious.
Rice. 1.3. Three “worlds” - Plato’s mathematical, physical and mental - and three fundamental mysteries connecting them...
... So, according to the one shown in Fig. 1.3 diagram, the entire physical world is governed by mathematical laws. We will see in later chapters of the book that there is strong (if incomplete) evidence to support this view. If we believe this evidence, then we have to admit that everything that exists in the physical Universe, down to the smallest detail, is indeed governed by precise mathematical principles - perhaps equations. I'm just quietly goofing around here....
...If this is so, then our physical actions are completely and completely subordinated to such universal mathematical control, although this “control” still allows for a certain randomness in behavior, governed by strict probabilistic principles.
Many people begin to feel very uncomfortable from such assumptions; I myself, to admit, these thoughts cause some anxiety.
... Perhaps, in a sense, the three worlds are not separate entities at all, but only reflect various aspects of some more fundamental TRUTH (emphasis added) that describes the world as a whole - a truth about which we currently have no idea concepts. - clean Mystic....
.................
It even turns out that there are areas on the screen that are inaccessible to particles emitted by the source, despite the fact that the particles could quite successfully enter these areas when only one of the slits was open! Although the spots appear on the screen one at a time in localized positions, and although each encounter of a particle with a screen can be associated with a specific act of emission of the particle by the source, the behavior of the particle between the source and the screen, including the ambiguity associated with the presence of two slits in the barrier, is similar to the behavior of a wave in which the wave When a particle collides with the screen, it feels both slits at once. Moreover (and this is especially important for our immediate purposes), the distance between the stripes on the screen corresponds to the wavelength A of our wave-particle, related to the momentum of the particles p by the previous formula XXXX.
All this is quite possible, a sober-minded skeptic will say, but this does not force us to carry out such an absurd-looking identification of energy and impulse with some operator! Yes, that’s exactly what I want to say: an operator is just a formalism for describing a phenomenon within its certain framework, and not an identity with the phenomenon.
Of course, it doesn’t force us, but should we turn away from a miracle when it appears to us?! What is this miracle? The miracle is that this apparent absurdity of the experimental fact (waves turn out to be particles, and particles turn out to be waves) can be brought into the system with the help of a beautiful mathematical formalism, in which momentum is actually identified with “differentiation along the coordinate”, and energy with “ differentiation with respect to time."
... This is all great, but what about the state vector? What prevents us from recognizing that it represents reality? Why are physicists often extremely reluctant to accept this philosophical position? Not just physicists, but those who have everything in order with a holistic worldview and are not inclined to engage in underdetermined reasoning.
.... If you wish, you can imagine that the photon wave function leaves the source in the form of a clearly defined wave packet of small sizes, then, after meeting the beam splitter, it is divided into two parts, one of which is reflected from the splitter, and the other is transmitted through it, for example, in a perpendicular direction. In both, we forced the wavefunction to split into two parts in the first beam splitter... Axiom a 1: quantum is not divisible. A person who talks about halves of a quantum outside its wavelength is perceived by me with no less skepticism than a person who creates a new universe with each change in the state of the quantum. Axiom a 2: the photon does not change its trajectory, and if it has changed, then this is re-emission of the photon by the electron. Because a quantum is not an elastic particle and there is nothing from which it would bounce. For some reason, in all descriptions of such experiments, these two things are avoided to be mentioned, although they have a more basic meaning than the effects that are described. I don’t understand why Penrose says this, he cannot but know about the indivisibility of the quantum, moreover, he mentioned this in the double-slit description. In such miraculous cases, one must still try to remain within the framework of the basic axioms, and if they come into some kind of contradiction with experience, this is a reason to think more carefully about the methodology and interpretation.
Let's accept for now, at least as a mathematical model of the quantum world, this curious description, according to which a quantum state evolves for some time in the form of a wave function, usually “smeared” throughout space (but with the possibility of focusing in a more limited area), and then, when the measurement is made, this state turns into something localized and well-defined.
Those. they are seriously talking about the possibility of something being spread out over several light years with the possibility of instantaneous mutual change. This can be presented purely abstractly - as the preservation of a formalized description on each side, but not in the form of some real entity represented by the nature of the quantum. Here there is a clear continuity of the idea about the reality of the existence of mathematical formalisms.

That is why I perceive both Penrose and other similar promistically-minded physicists very skeptically, despite their very loud authority...

In S. Weinberg's book Dreams of a Final Theory:
The philosophy of quantum mechanics is so irrelevant to its real use that one begins to suspect that all deep questions about the meaning of measurement are in fact empty, generated by the imperfection of our language, which was created in a world practically governed by the laws of classical physics.

In the article What is locality and why is it not in the quantum world? , where the problem is summarized based on recent events by Alexander Lvovsky, an employee of the RCC and a professor at the University of Calgary:
Quantum nonlocality exists only within the framework of the Copenhagen interpretation of quantum mechanics. According to it, when a quantum state is measured, it collapses. If we take as a basis the many-worlds interpretation, which says that the measurement of a state only extends the superposition to the observer, then there is no nonlocality. This is just an illusion of an observer who “does not know” that he has entered an entangled state with a particle at the opposite end of the quantum line.

Some conclusions from the article and its existing discussion.
Currently, there are many interpretations of different levels of sophistication, trying not just to describe the phenomenon of entanglement and other “non-local effects”, but to describe assumptions about the nature (mechanisms) of these phenomena - i.e. hypotheses. Moreover, the prevailing opinion is that it is impossible to imagine anything in this subject area, and it is only possible to rely on certain formalizations.
However, these same formalizations, with approximately equal convincingness, can show anything the interpreter wants, right down to describing the emergence of a new universe every time at a moment of quantum uncertainty. And since such moments arise during observation, bringing consciousness is like a direct participant in quantum phenomena.
For a detailed justification - why this approach seems completely wrong - see the article Heuristics.
So, every time the next cool mathematician begins to prove something like the unity of nature of two completely different phenomena based on the similarity of their mathematical description (well, for example, this is seriously done with Coulomb’s law and Newton’s law of gravity) or “explain” quantum entanglement to special “ dimension" without representing its real embodiment (or the existence of meridians in the formalism of earthlings), I will keep it ready :)

• Translation

Quantum entanglement is one of the most complex concepts in science, but its basic principles are simple. And once understood, entanglement opens the way to a better understanding of concepts such as the many worlds in quantum theory.

An enchanting aura of mystery surrounds the concept of quantum entanglement, as well as (somehow) the related requirement of quantum theory that there must be “many worlds.” And yet, at their core, these are scientific ideas with down-to-earth meaning and specific applications. I would like to explain the concepts of entanglement and many worlds as simply and clearly as I know them.

I

Entanglement occurs in situations in which we have partial information about the state of two systems. For example, two objects can become our systems – let’s call them kaons. "K" will stand for "classical" objects. But if you really want to imagine something concrete and pleasant, imagine that these are cakes.

Our kaons will have two shapes, square or round, and these shapes will indicate their possible states. Then the four possible joint states of the two kaons will be: (square, square), (square, circle), (circle, square), (circle, circle). The table shows the probability of the system being in one of the four listed states.

We will say that kaons are “independent” if knowledge about the state of one of them does not give us information about the state of the other. And this table has such a property. If the first kaon (cake) is square, we still don't know the shape of the second one. Conversely, the form of the second tells us nothing about the form of the first.

On the other hand, we will say that two kaons are entangled if information about one of them improves our knowledge about the other. The second tablet will show us strong confusion. In this case, if the first kaon is round, we will know that the second one is also round. And if the first kaon is square, then the second one will be the same. Knowing the shape of one, we can unambiguously determine the shape of the other.

The quantum version of entanglement looks essentially the same - it is a lack of independence. In quantum theory, states are described by mathematical objects called wave functions. The rules that combine wave functions with physical possibilities give rise to very interesting complications that we will discuss later, but the basic concept of entangled knowledge that we demonstrated for the classical case remains the same.

Although brownies cannot be considered quantum systems, entanglement in quantum systems occurs naturally, such as after particle collisions. In practice, unentangled (independent) states can be considered rare exceptions, since correlations arise between them when systems interact.

Consider, for example, molecules. They consist of subsystems - specifically, electrons and nuclei. The minimum energy state of a molecule, in which it usually exists, is a highly entangled state of electrons and nucleus, since the arrangement of these constituent particles will not be independent in any way. When the nucleus moves, the electron moves with it.

Let's return to our example. If we write Φ■, Φ● as wave functions describing system 1 in its square or round states and ψ■, ψ● for wave functions describing system 2 in its square or round states, then in our working example all states can be described , How:

Independent: Φ■ ψ■ + Φ■ ψ● + Φ● ψ■ + Φ● ψ●

Entangled: Φ■ ψ■ + Φ● ψ●

The independent version can also be written as:

(Φ■ + Φ●)(ψ■ + ψ●)

Note how in the latter case the brackets clearly separate the first and second systems into independent parts.

There are many ways to create entangled states. One is to measure a composite system that gives you partial information. One can learn, for example, that two systems have agreed to be of the same form without knowing which form they have chosen. This concept will become important a little later.

The more common effects of quantum entanglement, such as the Einstein-Podolsky-Rosen (EPR) and Greenberg-Horn-Seilinger (GHZ) effects, arise from its interaction with another property of quantum theory called the complementarity principle. To discuss EPR and GHZ, let me first introduce this principle to you.

Up to this point, we have imagined that kaons come in two shapes (square and round). Now let’s imagine that they also come in two colors – red and blue. Considering classical systems such as cakes, this additional property would mean that the kaon could exist in one of four possible states: red square, red circle, blue square, and blue circle.

But quantum cakes are quantons... Or quantons... They behave completely differently. The fact that a quanton in some situations may have different shapes and colors does not necessarily mean that it simultaneously has both shape and color. In fact, the common sense that Einstein demanded of physical reality does not correspond to experimental facts, as we will soon see.

We can measure the shape of a quanton, but in doing so we will lose all information about its color. Or we can measure the color, but lose information about its shape. According to quantum theory, we cannot measure both shape and color at the same time. No one's view of quantum reality is complete; we have to take into account many different and mutually exclusive pictures, each of which has its own incomplete picture of what is happening. This is the essence of the principle of complementarity, as formulated by Niels Bohr.

As a result, quantum theory forces us to be careful in attributing properties to physical reality. To avoid contradictions, we must admit that:

A property does not exist unless it is measured.
Measurement is an active process that changes the system being measured

II

Albert Einstein, Boris Podolsky and Nathan Rosen (EPR) described a surprising effect that occurs when two quantum systems become entangled. The EPR effect combines a special, experimentally achievable form of quantum entanglement with the principle of complementarity.

An EPR pair consists of two quantons, each of which can be measured in shape or color (but not both at once). Suppose we have many such pairs, all of them the same, and we can choose what measurements we make on their components. If we measure the shape of one member of an EPR pair, we are equally likely to get a square or a circle. If we measure color, we are equally likely to get red or blue.

Interesting effects that seemed paradoxical to EPR arise when we measure both members of the pair. When we measure the color of both members, or their shape, we find that the results are always the same. That is, if we discover that one of them is red and then measure the color of the second, we also discover that it is red - and so on. On the other hand, if we measure the shape of one and the color of the other, no correlation is observed. That is, if the first one was a square, then the second one could be blue or red with equal probability.

According to quantum theory, we will obtain such results even if the two systems are separated by a huge distance and the measurements are carried out almost simultaneously. The choice of measurement type at one location appears to affect the state of the system at another location. This “frightening action at a distance,” as Einstein called it, apparently requires the transmission of information—in our case, information about a measurement being made—faster than the speed of light.

But is it? Until I know what results you got, I don't know what to expect. I get useful information when I know your result, not when you take a measurement. And any message containing the result you receive must be transmitted in some physical way, slower than the speed of light.

With further study, the paradox collapses even more. Let's consider the state of the second system if the measurement of the first gave a red color. If we decide to measure the color of the second quanton, we get red. But by the principle of complementarity, if we decide to measure its shape when it is in the "red" state, we have an equal chance of getting a square or a circle. Therefore, the result of EPR is logically predetermined. This is simply a restatement of the principle of complementarity.

There is no paradox in the fact that distant events are correlated. After all, if we put one of two gloves from a pair into boxes and send them to different ends of the planet, it is not surprising that by looking in one box, I can determine which hand the other glove is intended for. Likewise, in all cases, the correlation of EPR pairs must be recorded on them when they are nearby so that they can withstand subsequent separation, as if having memory. The strangeness of the EPR paradox is not in the possibility of correlation itself, but in the possibility of its preservation in the form of additions.

III

Each individual experimenter obtains random results. Measuring the shape of a quanton, he obtains with equal probability a square or a circle; when measuring the color of a quanton, it is equally likely to be red or blue. So far everything is ordinary.

But when experimenters get together and compare the results, the analysis shows a surprising result. Let's say we call the square shape and red color “good”, and the circles and blue color “evil”. Experimenters find that if two of them decide to measure shape and the third decides to measure color, then either 0 or 2 of the measurements are “evil” (i.e., round or blue). But if all three decide to measure a color, then either 1 or 3 dimensions are evil. This is what quantum mechanics predicts, and this is exactly what happens.

Question: Is the amount of evil even or odd? Both possibilities are realized in different dimensions. We have to abandon this issue. It makes no sense to talk about the amount of evil in a system without relating it to how it is measured. And this leads to contradictions.

The GHZ effect, as physicist Sidney Coleman describes it, is “a slap in the face from quantum mechanics.” It breaks down the conventional, experiential expectation that physical systems have predetermined properties independent of their measurement. If this were so, then the balance of good and evil would not depend on the choice of measurement types. Once you accept the existence of the GHZ effect, you will not forget it, and your horizons will be expanded.

IV

We talk about “entangled histories” when it is impossible for a system to be assigned a certain state at each moment in time. Just as in traditional entanglement we rule out possibilities, we can create entangled histories by making measurements that collect partial information about past events. In the simplest entangled stories we have one quanton that we study at two different points in time. We can imagine a situation where we determine that the shape of our quanton was square both times, or round both times, but both situations remain possible. This is a temporal quantum analogy to the simplest versions of entanglement described earlier.

Using a more complex protocol, we can add a little extra detail to this system, and describe situations that trigger the "many-worlds" property of quantum theory. Our quanton can be prepared in the red state, and then measured and obtained in blue. And as in the previous examples, we cannot permanently assign a quanton the property of color in the interval between two dimensions; It does not have a specific form. Such stories realize, in a limited but completely controlled and precise way, the intuition inherent in the many-worlds picture of quantum mechanics. A certain state can be divided into two contradictory historical trajectories, which then connect again.

Erwin Schrödinger, the founder of quantum theory, who was skeptical about its correctness, emphasized that the evolution of quantum systems naturally leads to states, the measurement of which can give extremely different results. His thought experiment with "Schrodinger's cat" postulates, as we know, quantum uncertainty, taken to the level of influence on feline mortality. Before measuring, it is impossible to assign the property of life (or death) to a cat. Both, or neither, exist together in an otherworldly world of possibility.

Everyday language is ill-suited to explain quantum complementarity, in part because everyday experience does not include it. Practical cats interact with surrounding air molecules, and other objects, in completely different ways, depending on whether they are alive or dead, so in practice the measurement takes place automatically, and the cat continues to live (or not live). But the stories describe the quantons, which are Schrödinger's kittens, with confusion. Their full description requires that we consider two mutually exclusive trajectories of properties.

Controlled experimental implementation of entangled stories is a delicate thing, since it requires the collection of partial information about quantons. Conventional quantum measurements typically collect all the information at once—determining an exact shape or a precise color, for example—rather than obtaining partial information several times. But it can be done, albeit with extreme technical difficulties. In this way we can assign a certain mathematical and experimental meaning to the extension of the concept of “many worlds” in quantum theory, and demonstrate its reality.