What is quantum entanglement in simple words? Teleportation - is it possible? Has the possibility of teleportation been experimentally proven? What is Einstein's nightmare? In this article, you will get answers to these questions.

We often see teleportation in science fiction films and books. Have you ever wondered why what the writers came up with eventually becomes our reality? How do they manage to predict the future? I don't think it's an accident. Often science fiction writers have extensive knowledge of physics and other sciences, which, combined with their intuition and extraordinary imagination, helps them build a retrospective analysis of the past and simulate future events.

From the article you will learn:

• What is quantum entanglement?

concept "quantum entanglement" emerged from a theoretical assumption that follows from the equations of quantum mechanics. It means this: if 2 quantum particles (they can be electrons, photons) turn out to be interdependent (entangled), then the connection is preserved, even if they are spread to different parts of the Universe

The discovery of quantum entanglement explains to some extent the theoretical possibility of teleportation.

In short, then back quantum particle (electron, photon) is called its own angular momentum. Spin can be represented as a vector, and the quantum particle itself can be represented as a microscopic magnet.

It is important to understand that when no one observes a quantum, for example, an electron, then it has all the values ​​of the spin at the same time. This fundamental concept of quantum mechanics is called "superposition".

Imagine that your electron is spinning clockwise and counterclockwise at the same time. That is, it is in both spin states at once (spin up vector/spin down vector). Represented? OK. But as soon as an observer appears and measures his state, the electron itself determines which spin vector it should take - up or down.

Want to learn how to measure the spin of an electron? It is placed in a magnetic field: electrons with a spin against the direction of the field, and with a spin in the direction of the field, will deviate in different directions. The spins of photons are measured by directing them to a polarizing filter. If the spin (or polarization) of a photon is "-1", then it does not pass through the filter, and if it is "+1", then it passes.

Summary. As soon as you have measured the state of one electron and determined that its spin is “+1”, then the electron bound or “entangled” with it takes on the value of spin “-1”. And instantly, even if it is on Mars. Although before measuring the state of the 2nd electron, it had both spin values ​​simultaneously ("+1" and "-1").

This paradox, proved mathematically, did not please Einstein. Because it contradicted his discovery that there is no speed greater than the speed of light. But the concept of entangled particles proved: if one of the entangled particles is on Earth, and the 2nd is on Mars, then the 1st particle at the time of measuring its state instantly (faster than the speed of light) transmits information to the 2nd particle, what is the value of the spin her to accept. Namely, the opposite.

Einstein's dispute with Bohr. Who is right?

Einstein called "quantum entanglement" SPUCKHAFTE FERWIRKLUNG (German) or frightening, ghostly, supernatural action at a distance.

Einstein disagreed with Bohr's interpretation of the quantum entanglement of particles. Because it contradicted his theory that information cannot travel faster than the speed of light. In 1935 he published an article describing thought experiment. This experiment was called the "Einstein-Podolsky-Rosen Paradox".

Einstein agreed that bound particles could exist, but came up with another explanation for the instantaneous transfer of information between them. He said "entangled particles" more like a pair of gloves. Imagine that you have a pair of gloves. You put the left one in one suitcase, and the right one in the second. You sent the 1st suitcase to a friend, and the 2nd to the moon. When a friend receives the suitcase, he will know that the suitcase contains either a left or a right glove. When he opens the suitcase and sees that there is a left glove in it, he will instantly know that it is the right one on the Moon. And this does not mean that a friend influenced the fact that the left glove was in the suitcase and does not mean that the left glove instantly transmitted information to the right one. It only means that the properties of the gloves were originally the same from the moment they were separated. Those. entangled quantum particles initially contain information about their states.

So who was Bohr right, who believed that bound particles transmit information to each other instantly, even if they are spaced over great distances? Or Einstein, who believed that there is no supernatural connection, and everything is predetermined long before the moment of measurement.

This dispute moved to the realm of philosophy for 30 years. Has the dispute been resolved since then?

Bell's theorem. Dispute resolved?

John Clauser, while still a graduate student at Columbia University, in 1967 found the forgotten work of the Irish physicist John Bell. It was a sensation: it turns out Bell broke the deadlock between Bohr and Einstein. He proposed to test both hypotheses experimentally. To do this, he proposed building a machine that would create and compare many pairs of entangled particles. John Clauser began to develop such a machine. His machine could create thousands of pairs of entangled particles and compare them according to various parameters. The experimental results proved Bohr right.

And soon the French physicist Alain Aspe conducted experiments, one of which concerned the very essence of the dispute between Einstein and Bohr. In this experiment, the measurement of one particle could directly affect another only if the signal from the 1st to the 2nd passed at a speed exceeding the speed of light. But Einstein himself proved that this was impossible. There was only one explanation left - an inexplicable, supernatural connection between the particles.

The results of the experiments proved that the theoretical assumption of quantum mechanics is correct. Quantum entanglement is a reality ( Quantum Entanglement Wikipedia). Quantum particles can be bound despite vast distances. The measurement of the state of one particle affects the state of the 2nd particle located far from it, as if the distance between them did not exist. Supernatural communication at a distance is happening in reality.

The question remains, is teleportation possible?

Is teleportation confirmed experimentally?

Back in 2011, Japanese scientists teleported photons for the first time in the world! Instantly moved from point A to point B a beam of light.

If you want everything that you read about quantum entanglement to be sorted out in 5 minutes, watch this video, a wonderful video.

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Refers to "Theory of the Universe"

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 appropriate selections, building the level of description that seems acceptable for a worldview site.

Subject of the article: many people are close to the idea that all the bewitching quirks of entangled states could be explained in this way. We mix black and white balls, without looking we pack them in 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 it is white 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 the compilation of a system of general ideas, with an understanding of the main principles. That's the way it's supposed to be about everything :)

Let's set the defining context right away. When experts (and not discussants who are far from this specificity, even if they are scientists in some respects) talk about the entanglement of quantum objects, they do not mean that it forms a single whole with some kind of 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 an entangled pair is not identical, but mutually complementary). Those. this is no connection and no process of interaction, even if it can be described common function. This is a characteristic of a state that can be “teleported” from one object to another (by the way, here too, the misinterpretation of the word “teleport” is also common). If you do not immediately decide on this, then you can go very far into mysticism. Therefore, in the first place, everyone who is interested in the issue should be clearly sure what exactly is meant by "confusion".

What this article was started for is reduced to one question. The difference between the behavior of quantum objects and classical objects is manifested in the only method of verification so far known: whether or not a certain verification condition is met - 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, as it were, is not real, because. neither information nor energy can be transmitted.

Moreover, this relationship does not depend neither distance nor time: if two objects were "confused", then, regardless of the safety of each of them, the second one behaves as if the connection still exists (although the presence of such a connection can only be detected when 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 kind of "connection" becomes difficult to understand in this case, and the question arises as follows: can the law of the probability of falling out of the measured parameter (which is described by the wave function) be such that inequality is not violated at each of the ends, and with general statistics from both ends - was violated - and without any connection, of course, except for the connection by an act of general emergence.

I will give an answer in advance: yes, maybe, 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 just 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?

Imagine a rapidly spinning bicycle wheel. There is a red side reflector disk attached to it somewhere, but we can only see a denser shadow of blur in this place. The probability that by putting a stick into the wheel, the reflector will stop in a certain position away from the stick is simply determined: one stick - one position. Sunem two sticks, but only the one that appears a little earlier will stop the wheel. If we try to stick the sticks completely simultaneously, achieving that there is no time between the ends of the stick that come into contact with the wheel, then some uncertainty will appear. In "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 an electron (polarization - the propagation of an electrical disturbance) is equal to the limiting speed with which anything can propagate in nature at all (the speed of light in a vacuum). We know the conclusion of the theory of relativity: in this case, the time for this perturbation becomes zero: there is nothing in nature that could be realized between any two points of propagation of this perturbation, there is no time for it. This means that the perturbation is able to interact with any other "sticks" that affect it without spending time - simultaneously. And the probability of what result will be obtained at a particular point in space during the interaction should be calculated by the 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 the two "sticks" during the interaction with them and does it simultaneously from its own "point of view": an electron passes through two slots simultaneously with a different wave density in each and then interferes with itself as two superimposed waves.

Here is the difference between the descriptions of probabilities in the classics and quants: quantum correlations are "stronger" than classical ones. If the result of a coin drop depends on many influencing factors, but in general they are uniquely determined in such a way that one has only to make an accurate machine for throwing coins, and they will fall in the same way, then the randomness "disappeared". If we 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 electron's essence in this place. There are no other factors, except for the static distribution of the probability of finding the measured parameter in the electron, and this is a determinism of a completely different kind than in the classics. But this is also determinism; it is always calculable, reproducible, only with a singularity described by the wave function. At the same time, such quantum determinism concerns only a holistic description of the quantum wave. But, in view of the absence of proper time for a 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 meaning of e (in the classical view), it is absolutely non-deterministic.

The electron really and really exists in the form of a static formation (and not a point rotating in orbit) - a standing wave of electrical perturbation, in which there is one more relativistic effect: perpendicular to the main plane of "propagation" (it is clear why in quotation marks:) electric field there is also a static region of polarization, which is able to influence the same region of another electron: the 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 does not exist by itself without an electric one. And if in an electrically neutral atom the electric charges are compensated by the charges of the nuclei, then the magnetic ones can be oriented in one direction and we will get a magnet. For a deeper understanding of this - in the article .

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

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

Spin is the 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 magnetic moment. To fix it, you need not a magnet, but a polarizer slot.

To seed ideas about quantum entanglements, I suggest reading a popular and short article by Alexei Levin: Passion in the distance . Please follow the link and read before continuing :)

So, specific measurement parameters are realized only during measurement, and before that they existed in the form of the probability distribution that constituted the statics of the relativistic effects of the microcosm polarization propagation dynamics visible to the macrocosm. 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 the quantum object the properties of being simultaneously in different states until the moment of a particular 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 a consistent behavior. In contrast to macrostatistics, in quantum statistics it is possible to preserve such correlations for objects that are separated in space and time and previously coordinated in terms of parameters. This is manifested in the statistics of the fulfillment of Bell's inequalities.

What is the difference between the wave function (our abstract description) of unentangled electrons of two hydrogen atoms (despite the fact that its parameters will be 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 the 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 the entangled electrons are split, and they start moving in different directions, then a parameter appears in their wave function that describes the displacement of the probability density in space from time - the trajectory. And this does not mean at all that the function is spread out in space, simply because the probability of finding an object becomes zero at some distance from it, and nothing remains behind to indicate the probability of finding an electron. This is all the more evident in the case of the pair being spaced apart in time. Those. there are two local and independent descriptors of particles moving in opposite directions. Although one general descriptor can still be used, it is the right of the one who formalizes :)

In addition, the environment of 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 by their influence (giving rise to such phenomena as decoherence). But usually it never occurs to anyone to describe this as a general wave function, although this is also possible.

In many sources you can get acquainted with these phenomena in detail.

M.B. Mensky writes:

"One of the purposes of this article... is to substantiate the point of view that there is a formulation of quantum mechanics in which no paradoxes arise and within which all the questions that physicists usually ask can be answered. Paradoxes arise only when the researcher is not satisfied with this "physical" level of theory, when he raises questions that are not accepted in physics, in other words, when he takes the liberty of trying to go beyond the limits 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 the 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 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 reasoning about the role of consciousness, conscious choice in quantum mechanics, Mensky turns out to be the one who takes " take the liberty of trying to go beyond physics". This is reminiscent of attempts to approach the phenomena of the psyche. Mensky is good as a quantum professional, 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 (because this is what strikes the imagination of grateful viewers).

So, cryptography. You need to send the sequence 1001

We use two channels. On the first one we start up an entangled particle, on the second - information on how to interpret the received data in the form of one bit.

Suppose that there is an alternative possible state of the used quantum mechanical parameter spin in conditional states: 1 or 0. In this case, the probability of their falling out with each released pair of particles is truly random and does not convey any meaning a.

First transfer. When measuring here it turned out that the state of the particle is 1. This means that the other one has 0. In order to volume at the end to get 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. infa is not intercepted.

Second transfer. The state 1 came out again. The other one has 0. We pass info - 0. We add it up, we get the required 0.

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

Fourth. Here - 0, there - 1, it is necessary that it be interpreted as 1. We pass information - 0.

Here in this principle. Interception of the info channel is useless due to a completely uncorrelated sequence (encryption with the state key of the first particle). Interception of a tangled channel - disrupts reception and is detected. The 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 about. There is no arbitrary imposition of a state on a particle, but only a prediction of what this state will be after (and only after) the particle here is taken out of the connection by measurement. And then they say, like, 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, one can in one way or another correct the quantum mechanical parameter so that it turns out to be identical to the one here, but it will no longer be here, and one speaks of the fulfillment of the ban on cloning in a bound state.

It seems that no analogues of these phenomena in the macrocosm, no balls, apples, etc. from classical mechanics cannot serve to interpret the manifestation of such a 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 get a visible "explanation". This does not mean that such a thing is not conceivable, as is sometimes claimed. This means that it is necessary to work quite painstakingly on relativistic representations, which play a decisive role in the quantum world and connect the world of quantums with the macro world.

But this is not necessary either. Let us recall the main task of 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 common statistics from both ends it is violated. There are many interpretations for understanding this using auxiliary abstractions. They talk about the same thing different languages such abstractions. Of these, two are the most significant in terms of correctness shared among the carriers of representations. 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... Indeed, let's imagine that on two planets in different parts of the Galaxy there are two coins that always fall out in the same way. If you log the results of all the flips, and then compare them, they will match. The drops themselves are random, they can not be influenced in any way. It is impossible, for example, to agree that an eagle is a unit, and a tail is a zero, and thus transmit a binary code. After all, the sequence of zeros and ones will be random on both ends of the wire and will not carry any meaning.

It turns out that the paradox has an explanation 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 playing 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 consequence of this logic already mentioned: measurements over entangled states will not violate relativity and causality only if they are truly random. There should be no connection between the circumstances of the measurement and the disturbance, not the slightest regularity, because otherwise there would be the possibility of instantaneous transmission of information. Thus, quantum mechanics (in the Copenhagen interpretation) and the existence of entangled states prove the existence of indeterminism in nature."

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

From the point of view of statistical interpretation, the real objects of study in quantum mechanics are not single micro-objects, but statistical ensembles of micro-objects that are in the same macro conditions. Accordingly, the phrase "the 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 subensemble 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 drop them on 1000 sheets of paper. The probability that an “eagle” is imprinted on a sheet randomly chosen by us is 1/2. Meanwhile, for sheets on which coins lie “tails” up, the same probability is 1 - that is, we have the opportunity to indirectly establish the nature of the print 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, the refutation of the uncertainty relation in the “paradox” of EPR would be valid only if for the original ensemble it would be 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 affirmed by the uncertainty relation! In other words, the “paradox” of the EPR actually turns out to be a vicious circle: it presupposes the falsity of the refuted fact.

Variant with a "superluminal signal" from a particle A to a 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 situation, 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 an “eagle” is imprinted on a sheet is a priori 1/2. And the fact that it immediately turns into 1 if we turn on the light and make sure that the coin is “tails” up does not at all indicate the ability of our gaze to mist to influence the objects locked in the safe in an imaginary way.

More: AA Pechenkin Ensemble Interpretations of Quantum Mechanics in the USA and the USSR.

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

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

Popper gives here his favorite example: a children's billiard (a board lined with needles, on which a metal ball, symbolizing a physical system, rolls down from above - the billiard itself symbolizes an experimental device). When the ball is at the top of the billiard, we have one disposition, one propensity 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 got a new predisposition. Quantum-mechanical indeterminism is preserved here in full: Popper stipulates that the billiard is 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.

To summarize the facts

1. Despite the absolute randomness of the loss of a parameter when measuring in a mass of entangled pairs of particles, consistency is manifested in each such pair: if one particle in a pair turns out to have spin 1, then the other particle in a 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 are split, if the consistency is preserved, then the spins are still consistent. As soon as the spin of one is determined, the spin of the other will become 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 structure model electron shell of the 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 (so far unknown) that really 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 longer 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 everything, which is axiomatically formalized by the Pauli principle.

On the first, nearest layer, only 2 electrons can be found 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 the binding energy that must be applied to break this pair.

In the second, more distant and more energetic level, there can be 4 "orbitals" of two paired electrons in the form of a standing wave with a shape like a volume eight (p-electrons). Those. higher energy i occupies more space and allows several coupled pairs to coexist. From the first layer, the second differs energetically by 1 possible discrete energy state (more external electrons, describing a spatially larger cloud, also have a higher energy).

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

Forms of electron clouds:

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

Such a set of discretely different states - quantum numbers - characterize the possible local states of electrons. And here's what comes out of it.

When two electrons with different spinsoneenergy level (although this is fundamentally not necessary: http://www.membrana.ru/lenta/?9250) pair, then a common "molecular orbital" is formed with a reduced energy level due to energy and bonding. Two hydrogen atoms, each having 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 coordinated dynamics - a common wave function. How long? "Temperature" or something else that can compensate for the energy of the bond breaks it. The atoms fly apart with electrons no longer having a common wave, but still in a complementary, mutually consistent state of entanglement. But there is no connection anymore :) Here 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 just means the preservation of the ability to display a consistent correlation.

The method of obtaining entangled electrons through their interaction 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 relation" for 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 (beam splitter). The mechanism "splits" each of the electrons, bringing them into a quantum state of "superposition", as a result of which the electron will move along one of two paths with equal probability.".

2. With measurement statistics 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, yet unknown quantum mechanical essence.

The following small article (based on the ideas set forth by R.Pnrose) allows you to trace (show the principle, an example) how this is possible: 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 Uspekhi fizicheskikh nauk: Bell's theorem without the assumption of locality. Another work by A.V. Belinsky for reflection by those who are interested: Bell's theorem for trichotomous observables, as well as a discussion with d.f.-m.s., prof., acad. Valery Borisovich Morozov (generally recognized coryphaeus of the FRTK-MIPT physics department forums and "clubs"), where Morozov proposes for consideration both of these works by A.V. Belinsky: Experience of Aspect: a question for Morozov. And in addition to the topic of the possibility of violations of Bell's inequalities without introducing any long-range action: Bell's Inequality Modeling.

I draw your attention to the fact that "Relativity of Bell's Inequalities or the New Mind of the Naked King", as well as "Bell's Theorem without Assumption of Locality" in the context of this article do not pretend to describe the mechanism of quantum mechanical entanglement. The problem 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 boundary of its use is the theorem stated at the beginning: "There may be models of classical locality in which Bell's inequalities are violated.". About this - additional explanations in the discussion.

I'll bring my own model.
"Violation of local realism" is just a relativistic effect.
No one (normal) argues with the fact that for a system moving at the limiting 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, however far away it may be there.
It is clear that entangled quanta have their own starting point. And electrons are the same quanta in the state of a standing wave, i.e. existing here and there at once for the entire lifetime of the electron. All the 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 that are here and there. For them, the speed of propagation of interaction (limiting speed) is infinitely high. But all these infinities are different, as well as in 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 to us.
For us, local realism is violated in experiments, but not for quanta.
But this discrepancy does not affect reality in any way, because we cannot use such an infinite speed in practice. Neither information, nor, especially matter, is transmitted infinitely fast during "quantum teleportation".
So all this is a joke of relativistic effects, nothing more. They can be used in quantum cryptography or whatever, nor can they be used for real long-range action.

We look visually 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 at both ends will always be the opposite.
2. If the orientation of the meters is opposite, then the result will be the same.
3. If the orientation of the left gauge differs from the orientation of the right one by less than a certain angle, then point 1 will be implemented and the coincidences will be within the probability predicted by Bell for independent particles.
4. If the angle exceeds, then - point 2 and the matches will be greater than the probability predicted by Bell.

Those. at a smaller angle, we will get predominantly opposite values ​​of the spins, and at a larger angle, predominantly coinciding ones.
Why this happens with spin can be imagined, bearing 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 polarization rotation must fall).
It is clear that by sending magnets that were initially linked and retained their mutual orientation when sent, we magnetic field when measuring, we will influence them (turning in one direction or another) in the same way as it happens in quantum paradoxes.
It is clear that when encountering a magnetic field (including the spin of another electron), the spin necessarily orients itself in accordance with it (mutually opposite in the case of the spin of another electron). That is why they say that "spin orientation arises only in the course of measurement", but 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 required 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 states of the spin are not taken into account, but only predominantly - along the measuring field and against the field. Method examples: , . It is worth paying attention to the date of development of these methods, which is later than the experiments described above.
The above model is, of course, simplified (in quantum phenomena, spin is not exactly the real magnets, although it is they that provide all the observable 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 the descriptive formalism (formulas) without understanding the essence of what is happening.
At the same time, 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 general description which 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 way (non-quantum)." models, except for the quantum mechanical experiment, violation of Bell's inequalities is not possible.

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 put a clear meaning on what Bell wanted to prove and what actually happens. Bell created an experiment showing that in entanglement there is no pre-existing "algorithm a", a predetermined 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 a really random process (why is well described below).
BUT in fact, they simply have the same probabilistic dependencies. What does it mean? This means that there is no predetermined, predetermined connection between the fixation of a parameter by a measurement, but such a result of fixation comes from the fact that the processes have the same (complementary) probability function (which, in general, directly follows from quantum mechanical concepts), is which is the realization of a parameter during fixation, 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 (the relativistic effect formalized by Lorentz transformations, see Vacuum, quanta, matter).

This is how Brian Greene describes the methodological essence of Bell's experience in his book The Fabric of the Cosmos. From him, 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 is, then the probability of the same colors when different doors are randomly opened should be more than 50%, contrary to the truth 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 this 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."
"Oh sure." Scully jumped up. “If we call the top door 1, the side door 2, and the front door 3, then the nine possible door combinations are just (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 the same colors.
The first three combinations of doors are the ones in which we choose the same doors, and as we know, this always leads to the fact that we see the same colors. The other two combinations of doors (1,2) and (2,1) result in the same colors because the program dictates that the spheres will flash the same color - blue - if either door 1 or door 2 is open. So, since 5 is greater than half of 9, this means that for more than half - more than 50 percent - of the possible combinations of doors that we can choose to open, the spheres 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 could and generally would have different programs."
"Really, it doesn't matter. The conclusion is valid for any of the possible programs.

And this is indeed the case if we are dealing with a program. But this is not the case at all if we are dealing with random dependencies for many experiments, but each of these accidents has the same form in each experiment.
In the case of electrons, when they were initially bound into a pair, which ensures their completely dependent spins (mutually opposite) and scattered, this interdependence, of course, is preserved at full big picture the true probability of falling out and in the fact that it is impossible to say in advance how the spins of two electrons in a pair have developed before determining one of them, but they "already" (if I may 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 Green's book:
there is a way to examine whether we have inadvertently come into conflict with SRT. The common property for matter and energy is that they can transfer information by moving from place to place. Photons, traveling from a radio transmitting station to your receiver, carry information. The electrons, traveling through the cables of the Internet to your computer, carry information. In any situation where something—even something unidentified—is meant to be moving faster than the speed of light, a surefire test is to ask if it transmits, or at least can transmit, information. If the answer is no, the standard reasoning passes that nothing exceeds the speed of light and SRT remains unchallenged. In practice, physicists often use this test to determine whether some subtle process violates the laws of special relativity. Nothing survived this test.

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

It was necessary to find a way that would allow us to separate truth from assumptions in mathematics - some kind of formal procedure, using which one could say with certainty whether a given mathematical statement is true or not. (objection see Aristotle's method and Truth, criteria of truth). Until this problem is properly solved, 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 irrefutable mathematics is the key to understanding the universe is perhaps the first of the most important breakthroughs in science in general. Even the ancient Egyptians and Babylonians guessed about mathematical truths of various kinds, but the first stone in the foundation of mathematical understanding ...
... people for the first time had the opportunity to formulate reliable and obviously irrefutable statements - statements, the truth of which is not in doubt even today, despite the fact that science has stepped far forward since those times. For the first time, the truly timeless nature of mathematics was revealed to people.
What is a 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 to draw an unambiguous conclusion about the validity of one or another mathematical statement on the basis of the validity of any other mathematical statements, either pre-established in a similar way, or not requiring proof at all (special elementary statements, the truth of which, in the general opinion, is self-evident, are called axioms) . A proved mathematical statement is usually called a theorem. This is where I don't understand him: after all, there are simply stated but not proven theorems.
... Objective mathematical concepts should be represented as timeless objects; one should not think that their existence begins at the moment they appear in one form or another in the human imagination.
... Thus, mathematical existence differs not only from the existence of the physical, but also from the existence that our conscious perception is able to endow the object with. Nevertheless, it is clearly connected with the last two forms of existence - i.e. with physical and mental existence. connection is quite physical concept What does Penrose mean here?- and the corresponding connections are as fundamental as they are mysterious.
Rice. 1.3. Three "worlds" - Platonic mathematical, physical and mental - and three fundamental riddles connecting them...
... So, according to the one shown in fig. 1.3 scheme, the entire physical world is controlled by mathematical laws. In later chapters of the book, we will see that there is strong (though 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 - maybe equations. Here I am just quietly basking ....
...If this is so, then our physical actions are completely and completely subordinated to such universal mathematical control, although this “control” still allows a certain randomness in behavior, controlled by strict probabilistic principles.
Many people begin to feel very uncomfortable with such assumptions; for me and for myself, I confess, these thoughts cause some anxiety.
... Perhaps, in some sense, the three worlds are not separate entities at all, but only reflect various aspects of some more fundamental TRUTH (I emphasized) that describes the world as a whole - a truth about which at present we do not have the slightest concepts. - clean Mystic....
.................
It even turns out that there are regions on the screen that are inaccessible to particles emitted by the source, despite the fact that particles could quite successfully enter these regions when only one of the slits was open! Although the spots appear on the screen one at a time at localized positions, and although each encounter of the particle with the screen can be associated with a certain 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 gaps in the barrier, is similar to the behavior of a wave, in which the wave When a particle collides with a screen, it senses both slits at once. Moreover (and this is especially important for our immediate purposes), the distance between the fringes on the screen corresponds to the wavelength L of our particle wave, related to the particle momentum p by the former formula XXXX.
All this is quite possible, a sober-minded skeptic will say, but this does not yet force us to make such an absurd-looking identification of energy-momentum with some kind of operator! Yes, that's exactly what I want to say: an operator is only a formalism for describing a phenomenon within its certain framework, and not an identity with the phenomenon.
Of course, it does not force us, but should we turn away from a miracle when it appears to us?! What is this miracle? The miracle is that this seeming 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 indeed identified with "differentiation in coordinate" and energy with " time differentiation.
... All this is fine, but what about the state vector? What prevents you from recognizing that it represents reality? Why are physicists often extremely reluctant to take such a philosophical position? Not just physicists, but those who have everything in order with a holistic worldview and are not inclined to be led to underdetermined reasoning.
.... If you wish, you can imagine that the wave function of a photon leaves the source in the form of a clearly defined wave packet of small sizes, then, after meeting with the beam splitter, it is divided into two parts, one of which is reflected from the splitter, and the other passes through it, for example, in a perpendicular direction. In both, we caused the wavefunction to split into two parts in the first beam splitter... Axiom 1: The quantum is not divisible. A person who talks about the 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 2: the photon does not change its trajectory, and if it has changed, then this is the 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 experiences, 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 must know about the indivisibility of the quantum, moreover, he mentioned it in the two-slit description. In such miraculous cases, one must still try to remain within the framework of the basic axioms, and if they come into conflict with experience, this is an occasion to think more carefully about the methodology and interpretation.
Let's accept for now, at least as mathematical model of the quantum world, this is a curious description according to which a quantum state evolves for some time in the form of a wave function, usually "smeared" over all space (but with the ability to focus in a more limited area), and then, when a measurement is made, this state turns into something localized and well defined.
Those. seriously talks about the possibility of smearing something for several light years with the possibility of instantaneous mutual change. This can be represented purely abstractly - as the preservation of a formalized description on each of the sides, but not in the form of some kind of real entity, represented by the nature of the quantum. Here is a clear continuity of the idea of ​​the reality of the existence of mathematical formalisms.

That is why I take both Penrose and other similar promystically thinking physicists very skeptically, in spite of their very loud authority ...

In S. Weinberg's book Dreams of a Final Theory:
The philosophy of quantum mechanics is so irrelevant to its actual use that one begins to suspect that all deep questions about the meaning of measurement are actually 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 on the basis of 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. In accordance with it, when measuring a quantum state, it collapses. If we take as a basis the many-world 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 "not knowing" 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 already existing discussion.
There are many interpretations at present. different levels elaboration, 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 opinion prevails that it is impossible to imagine something in this subject area, but it is only possible to rely on certain formalizations.
However, these same formalizations can show with approximately the same persuasiveness anything the interpreter wants, up to describing the emergence of a new universe every time, at the moment of quantum uncertainty. And since such moments arise during observation, then bring consciousness - as a direct participant in quantum phenomena.
For a detailed rationale - why this approach seems completely wrong - see the article Heuristics.
So whenever another cool mathematician starts 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 by special " dimension" without imagining its real embodiment (or the existence of meridians in the formalism of me earthlings), I will keep it ready:)

Quantum entanglement is a quantum mechanical phenomenon that began to be studied in practice relatively recently - in the 1970s. It consists in the following. Imagine that as a result of some event, two photons were born simultaneously. A pair of quantum-entangled photons can be obtained, for example, by shining a laser with certain characteristics on a nonlinear crystal. The generated photons in a pair can have different frequencies (and wavelengths), but the sum of their frequencies is equal to the frequency of the original excitation. They also have orthogonal polarizations in the basis crystal lattice which facilitates their spatial separation. When a pair of particles is born, conservation laws must be observed, which means that the total characteristics (polarization, frequency) of two particles have a pre-known, strictly defined value. It follows from this that, knowing the characteristics of one photon, we can definitely find out the characteristics of another. According to the principles of quantum mechanics, until the moment of measurement, the particle is in a superposition of several possible states, and during the measurement, the superposition is removed and the particle finds itself in one state. If we analyze many particles, then in each state there will be a certain percentage of particles corresponding to the probability of this state in the superposition.

But what happens to the superposition of states of entangled particles at the moment of measuring the state of one of them? The paradox and counterintuitiveness of quantum entanglement lies in the fact that the characteristic of the second photon is determined exactly at the moment when we measured the characteristic of the first. No, this is not a theoretical construction, this is the harsh truth of the surrounding world, confirmed experimentally. Yes, it implies the presence of an interaction, betraying at an infinitely high speed, exceeding even the speed of light. How to use this for the benefit of mankind is not yet very clear. There are ideas for applications for quantum computing, cryptography and communication.

Scientists from Vienna have managed to develop a completely new and extremely counterintuitive imaging technique based on the quantum nature of light. In their system, the image is formed by light that has never interacted with the object. The technology is based on the principle of quantum entanglement. An article about this was published in the journal Nature. The study involved employees of the Institute for Quantum Optics and Quantum Information (IQOQI), the Vienna Center for Quantum Science and Technology (VCQ) and the University of Vienna.

In the experiment of the Viennese scientists, one of the pair of entangled photons had a wavelength in the infrared part of the spectrum, and it was he who passed through the sample. His brother had a wavelength corresponding to red light and could be detected by the camera. The beam of light generated by the laser was divided into two halves, and the halves were directed to two non-linear crystals. The object was placed between two crystals. It was a carved silhouette of a cat - in honor of the character of Erwin Schrödinger's speculative experiment, which had already migrated to folklore. An infrared beam of photons from the first crystal was directed at it. Then these photons passed through the second crystal, where the photons that passed through the image of the cat mixed with freshly born infrared photons so that it was completely impossible to understand in which of the two crystals they were born. Moreover, the camera did not detect infrared photons at all. Both beams of red photons were combined and sent to a receiving device. It turned out that thanks to the effect of quantum entanglement, they stored all the information about the object needed to create an image.

An experiment led to similar results, in which the image was not an opaque plate with a cut out contour, but a three-dimensional silicone image that did not absorb light, but slowed down the passage of an infrared photon and created a phase difference between the photons that passed through different parts of the image. It turned out that such plasticity also affected the phase of red photons, which are in a state of quantum entanglement with infrared photons, but never passed through the image.

If you haven't been struck by miracles yet quantum physics, then after this article your thinking will certainly turn over. Today I will tell you what quantum entanglement is, but in simple words, so that anyone can understand what it is.

Entanglement as a magical connection

After the unusual effects occurring in the microcosm were discovered, scientists came to an interesting theoretical assumption. It followed precisely from the foundations of quantum theory.

In the past, I talked about how the electron behaves very strangely.

But the entanglement of quantum, elementary particles generally contrary to any common sense, beyond any understanding.

If they interacted with each other, then after separation, a magical connection remains between them, even if they are separated by any, arbitrarily large distance.

Magical in the sense that information between them is transmitted instantly.

As is known from quantum mechanics, a particle before measurement is in a superposition, that is, it has several parameters at once, is blurred in space, and does not have an exact spin value. If a measurement is made on one of a pair of previously interacting particles, that is, a wave function collapses, then the second immediately, instantly responds to this measurement. It doesn't matter how far apart they are. Fantasy, isn't it.

As is known from Einstein's theory of relativity, nothing can exceed the speed of light. In order for information to reach from one particle to the second, it is necessary at least to spend the time of passage of light. But one particle just instantly reacts to the measurement of the second. Information at the speed of light would have reached her later. All this does not fit into common sense.

If we separate a pair of elementary particles with a common spin parameter of zero, then one must have a negative spin, and the other a positive one. But before the measurement, the value of the spin is in superposition. As soon as we measured the spin of the first particle, we saw that it has a positive value, so immediately the second acquires a negative spin. If, on the contrary, the first particle acquires a negative value of the spin, then the second one acquires an instantaneously positive value.

Or such an analogy.

We have two balls. One is black, the other is white. We covered them with opaque glasses, we can’t see which one is which. We interfere as in the game of thimbles.

If you open one glass and see that there is a white ball, then the second glass is black. But at first we don't know which is which.

So it is with elementary particles. But before you look at them, they are in superposition. Before measurement, the balls are as if colorless. But having destroyed the superposition of one ball and seeing that it is white, the second immediately becomes black. And this happens instantly, whether there is at least one ball on the ground, and the second in another galaxy. For light to reach from one ball to another in our case, let's say it takes hundreds of years, and the second ball learns that a measurement was made on the second, I repeat, instantly. There is confusion between them.

It is clear that Einstein, and many other physicists, did not accept such an outcome of events, that is, quantum entanglement. He considered the conclusions of quantum physics to be incorrect, incomplete, and assumed that some hidden variables were missing.

On the contrary, Einstein's paradox described above was invented to show that the conclusions of quantum mechanics are not correct, because entanglement is contrary to common sense.

This paradox was called the Einstein-Podolsky-Rosen paradox, abbreviated as the EPR paradox.

But experiments with entanglement later by A. Aspect and other scientists showed that Einstein was wrong. Quantum entanglement exists.

And these were no longer theoretical assumptions arising from the equations, but real facts many experiments on quantum entanglement. Scientists saw this live, and Einstein died without knowing the truth.

Particles really interact instantly, restrictions on the speed of light are not a hindrance to them. The world turned out to be much more interesting and complex.

With quantum entanglement, I repeat, there is an instantaneous transfer of information, a magical connection is formed.

But how can this be?

Today's quantum physics answers this question in an elegant way. There is an instantaneous connection between the particles, not because information is transmitted very quickly, but because at a deeper level they are simply not separated, but are still together. They are in the so-called quantum entanglement.

That is, the state of confusion is such a state of the system, where, according to some parameters or values, it cannot be divided into separate, completely independent parts.

For example, electrons after interaction can be separated by a large distance in space, but their spins are still together. Therefore, during the experiments, the spins instantly agree with each other.

Do you understand where this leads?

Today's knowledge of modern quantum physics based on the theory of decoherence comes down to one thing.

There is a deeper, unmanifest reality. And what we observe as a familiar classical world is only a small part, a special case of a more fundamental quantum reality.

It does not contain space, time, any parameters of particles, but only information about them, the potential possibility of their manifestation.

It is this fact that elegantly and simply explains why the collapse of the wave function, considered in the previous article, quantum entanglement and other miracles of the microcosm occur.

Today, when talking about quantum entanglement, they remember the other world.

That is, at a more fundamental level, an elementary particle is unmanifested. It is located simultaneously at several points in space, has several values ​​of spins.

Then, according to some parameters, it can manifest itself in our classical world during the measurement. In the experiment discussed above, two particles already have a specific value for the coordinates of space, but their spins are still in quantum reality, unmanifested. There is no space and time, so the spins of the particles are locked together, despite the huge distance between them.

And when we look at the spin of a particle, that is, we make a measurement, we sort of pull the spin out of quantum reality into our ordinary world. And it seems to us that particles exchange information instantly. It's just that they were still together in one parameter, even though they were far apart. Their separation is actually an illusion.

All this seems strange, unusual, but this fact is already confirmed by many experiments. Quantum computers are based on magical entanglement.

The reality turned out to be much more complex and interesting.

The principle of quantum entanglement does not fit in with our usual view of the world.

This is how the physicist-scientist D.Bohm explains quantum entanglement.

Let's say we're watching fish in an aquarium. But due to some restrictions, we can look not at the aquarium as it is, but only at its projections, filmed by two cameras in front and on the side. That is, we watch the fish, looking at two televisions. The fish seem different to us, as we shoot it with one camera in front, the other in profile. But miraculously, their movements are clearly consistent. As soon as the fish from the first screen turns, the second one instantly also turns. We are surprised, not realizing that this is the same fish.

So in quantum experiment with two particles. Because of their limitations, it seems to us that the spins of two previously interacting particles are independent of each other, because now the particles are far from each other. But in reality they are still together, but in a quantum reality, in a non-local source. We simply do not look at reality as it really is, but with a distortion, within the framework of classical physics.

Quantum teleportation in simple terms

When scientists learned about quantum entanglement and the instantaneous transfer of information, many wondered: is teleportation possible?

It turned out to be really possible.

There have already been many experiments on teleportation.

The essence of the method can be easily understood if you understand the general principle of entanglement.

There is a particle, for example, an electron A and two pairs of entangled electrons B and C. The electron A and the pair B, C are at different points in space, no matter how far away. And now let's convert particles A and B into quantum entanglement, that is, let's combine them. Now C becomes exactly the same as A, because their general state does not change. That is, particle A is, as it were, teleported to particle C.

Today, more complex experiments on teleportation have been carried out.

Of course, all experiments are carried out so far only with elementary particles. But you have to admit, it's incredible. After all, we all consist of the same particles, scientists say that the teleportation of macro objects is theoretically no different. You just need to solve the set technical issues and it's only a matter of time. Perhaps, in its development, humanity will reach the ability to teleport large objects, and even the person himself.

quantum reality

Quantum entanglement is integrity, continuity, unity at a deeper level.

If, according to some parameters, the particles are in quantum entanglement, then according to these parameters, they simply cannot be divided into separate parts. They are interdependent. Such properties are simply fantastic from the point of view of the familiar world, transcendent, one might say otherworldly and transcendent. But this is a fact from which there is no escape. It's time to acknowledge it.

But where does all this lead?

It turns out that many spiritual teachings of mankind have long spoken about this state of affairs.

The world we see, consisting of material objects, is not the basis of reality, but only a small part of it and not the most important one. There is a transcendent reality that sets, determines everything that happens to our world, and therefore to us.

It is there that the real answers to the eternal questions about the meaning of life, the true development of a person, finding happiness and health lie.

And these are not empty words.

All this leads to rethinking life values, understanding that in addition to the senseless race for material goods, there is something more important and higher. And this reality is not somewhere out there, it surrounds us everywhere, it permeates us, it is, as they say, "at our fingertips."

But let's talk about it in the next articles.

Now watch a video about quantum entanglement.

We are moving smoothly from quantum entanglement to theory. More on this in the next article.

Many popular papers have appeared that talk about quantum entanglement. Experiments with quantum entanglement are very spectacular, but they have not been awarded prizes. Why are such interesting experiments for the layman not of interest to scientists? Popular articles talk about the amazing properties of pairs of entangled particles - impact on one leads to an instant change in the state of the second. And what is hidden behind the term "quantum teleportation", which has already begun to be said that it occurs at superluminal speed. Let's look at all this from the point of view of normal quantum mechanics.

What comes out of quantum mechanics

Quantum particles can be in two types of states, according to the classic textbook by Landau and Lifshitz - pure and mixed. If a particle does not interact with other quantum particles, it is described by a wave function that depends only on its coordinates or momenta - such a state is called pure. In this case, the wave function obeys the Schrödinger equation. Another variant is possible - the particle interacts with other quantum particles. In this case, the wave function refers already to the entire system of interacting particles and depends on all their dynamic variables. If we are only interested in one particle, then its state, as Landau showed 90 years ago, can be described by a matrix or density operator. The density matrix obeys an equation similar to the Schrödinger equation

Where is the density matrix, H is the Hamilton operator, and the brackets denote the commutator.

Landau took him out. Any physical quantities related to a given particle can be expressed in terms of the density matrix. This state is called mixed. If we have a system of interacting particles, then each of the particles is in a mixed state. If the particles have scattered over long distances and the interaction has disappeared, their state will still remain mixed. If each of several particles is in a pure state, then the wave function of such a system is the product of the wave functions of each of the particles (if the particles are different. For identical particles, bosons or fermions, you need to make a symmetric or antisymmetric combination, see, but more on that later. The identity of particles, fermions and bosons is already a relativistic quantum theory.

An entangled state of a pair of particles is a state in which there is a constant correlation between physical quantities related to different particles. A simple and most common example is to store a certain total physical quantity, such as the total spin or angular momentum of the pair. A pair of particles in this case is in a pure state, but each of the particles is in a mixed state. It may seem that a change in the state of one particle will immediately affect the state of another particle. Even if they have scattered far and do not interact, This is what is expressed in popular articles. This phenomenon has already been dubbed quantum teleportation. Some illiterate journalists even claim that the change occurs instantly, that is, it spreads faster than the speed of light.

Consider this from the point of view of quantum mechanics. Firstly, any action or measurement that changes the spin or angular momentum of only one particle immediately violates the law of conservation of the total characteristic. The corresponding operator cannot commute with total spin or total angular momentum. Thus, the initial entanglement of the state of a pair of particles is violated. The spin or moment of the second particle can no longer be uniquely related to that of the first. You can consider this problem from the other side. After the interaction between the particles has disappeared, the evolution of the density matrix of each of the particles is described by its own equation, which does not include the dynamic variables of the other particle. Therefore, the impact on one particle will not change the density matrix of the other.

There is even Eberhard's theorem, which states that the mutual influence of two particles cannot be detected by measurements. Let there be quantum system, which is described by the density matrix. And let this system consist of two subsystems A and B. Eberhard's theorem states that no measurement of observables associated only with subsystem A affects the result of measuring any observables that are associated only with subsystem B. However, the proof of the theorem uses the wave reduction hypothesis. function that has not been proven either theoretically or experimentally. But all these considerations are made within the framework of non-relativistic quantum mechanics and refer to different, not identical particles.

These arguments do not work in the relativistic theory in the case of a pair of identical particles. Let me remind you once again that the identity or indistinguishability of particles comes from relativistic quantum mechanics, where the number of particles is not conserved. However, for slow particles, we can use the simpler apparatus of nonrelativistic quantum mechanics, simply by taking into account the indistinguishability of particles. Then the wave function of the pair must be symmetric (for bosons) or antisymmetric (for fermions) with respect to the particle permutation. Such a requirement arises in relativistic theory, regardless of particle velocities. It is this requirement that leads to long-range correlations of a pair of identical particles. In principle, a proton with an electron can also be in an entangled state. However, if they diverge by several tens of angstroms, then the interaction with electromagnetic fields and other particles will destroy this state. The exchange interaction (as this phenomenon is called) acts at macroscopic distances, as experiments show. A pair of particles, even dispersed by meters, remains indistinguishable. If you are making a measurement, then you do not know exactly which particle the measured value belongs to. You are measuring a couple of particles at the same time. Therefore, all spectacular experiments were carried out with the same particles - electrons and photons. Strictly speaking, this is not quite the entangled state that is considered in the framework of nonrelativistic quantum mechanics, but something similar.

Consider the simplest case - a pair of identical non-interacting particles. If the velocities are small, we can use non-relativistic quantum mechanics, taking into account the symmetry of the wave function with respect to the permutation of particles. Let the wave function of the first particle , the second particle - , where and are the dynamic variables of the first and second particles, in the simplest case, just coordinates. Then the wave function of the pair

The + and – signs refer to bosons and fermions. Let's assume that the particles are far apart. Then they are localized in remote regions 1 and 2, respectively, that is, outside these regions they are small. Let's try to calculate the average value of some variable of the first particle, for example, coordinates. For simplicity, we can imagine that only coordinates enter into the wave functions. It turns out that the average value of the coordinates of particle 1 lies BETWEEN regions 1 and 2, and it coincides with the average value for particle 2. This is actually natural - the particles are indistinguishable, we cannot know which particle the coordinates are measured. In general, all average values ​​for particles 1 and 2 will be the same. This means that by moving the area of ​​localization of particle 1 (for example, the particle is localized inside a defect in the crystal lattice, and we move the entire crystal), we act on particle 2, although the particles do not interact in the usual sense - through an electromagnetic field, for example. This is a simple example of relativistic entanglement.

No instantaneous transfer of information occurs between the two particles due to these correlations. The apparatus of relativistic quantum theory was originally built in such a way that events located in space-time on opposite sides of the light cone cannot influence each other. Simply put, no signal, no impact or disturbance can propagate faster than light. Both particles are in fact the state of one field, for example, electron-positron. By acting on the field at one point (particle 1), we create a perturbation that propagates like waves on water. In non-relativistic quantum mechanics, the speed of light is considered to be infinitely high, which gives rise to the illusion of instantaneous change.

The situation where particles separated by large distances remain bound in pairs seems paradoxical due to classical ideas about particles. We must remember that in reality there are not particles, but fields. What we think of as particles are simply states of these fields. The classical idea of ​​particles is completely unsuitable in the microcosm. Immediately there are questions about the size, shape, material and structure of elementary particles. In fact, situations that are paradoxical for classical thinking also arise with one particle. For example, in the Stern-Gerlach experiment, a hydrogen atom flies through an inhomogeneous magnetic field directed perpendicular to the velocity. The spin of the nucleus can be neglected due to the smallness of the nuclear magneton, let the electron spin be initially directed along the velocity.

The evolution of the wave function of an atom is not difficult to calculate. The initial localized wave packet splits into two identical ones, flying symmetrically at an angle to the original direction. That is, an atom, a heavy particle, usually considered as a classical one with a classical trajectory, has split into two wave packets that can scatter over quite macroscopic distances. At the same time, I note that it follows from the calculation that even the ideal Stern-Gerlach experiment is not able to measure the particle spin.

If the detector binds a hydrogen atom, for example, chemically, then the "halves" - two scattered wave packets, are collected into one. How such a localization of a smeared particle occurs is a separately existing theory, which I do not understand. Those interested can find extensive literature on this subject.

Conclusion

The question arises - what is the meaning of numerous experiments to demonstrate correlations between particles at large distances? In addition to confirming quantum mechanics, which no normal physicist has doubted for a long time, this is a spectacular demonstration that impresses the public and amateur officials who allocate funds for science (for example, the development of quantum communication lines is sponsored by Gazprombank). For physics, these costly demonstrations do nothing, although they make it possible to develop experimental techniques.

Literature
1. Landau, L. D., Lifshits, E. M. Quantum mechanics (nonrelativistic theory). - 3rd edition, revised and enlarged. - M.: Nauka, 1974. - 752 p. - (“Theoretical Physics”, Volume III).
2. Eberhard, P.H., “Bell’s theorem and the different concepts of nonlocality”, Nuovo Cimento 46B, 392-419 (1978)