Quantum entanglement - human body - self-knowledge - catalog of articles - unconditional love. What is quantum entanglement? The essence in simple words

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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 specialists (and not discussants who are far from this specificity, even if they are scientists in some way) talk about the entanglement of quantum objects, they mean not 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 by a 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, having put a stick into the wheel, the reflector will stop in a certain position 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 "point of view": the electron passes through two slots simultaneously with 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, however, 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. Unlike macro statistics, in quantum statistics it is possible to preserve such correlations for objects 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 customary 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 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 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. 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 (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 a single 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) here the particle 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 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 rather 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 printed on a sheet randomly chosen by us is 1/2. Meanwhile, for sheets on which the coins are “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 equal to 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 uniquely determine the values physical quantities detected 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 model of the structure of the electron shell of an atom is called the Pauli principle, and in 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 manifest 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 every respect, and then shoot these electrons at the 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, 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 of 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 forums of the Physics Department of the FRTK-MIPT 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). Therefore, they say that "the orientation of the spin arises only during the 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 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 presented model, of course, is simplified (in quantum phenomena, spin is not exactly the real 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 only shows 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 there is no pre-existing "algorithm" in entanglement, a pre-established 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 true 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 important point: Of these nine possibilities, note that five combinations of doors - (1.1), (2.2), (3.3), (1.2) and (2.1) - lead to the result that we see how the spheres in our boxes flash with 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 general case will 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 at all the case if we are dealing with random dependencies for many experiments, but each of these randomnesses has the same form in each experiment.
In the case of electrons, when they were first paired, which ensures their completely dependent spins (mutually opposite) and scattered, this interdependence, of course, is preserved with a complete overall picture of the true probability of dropouts and in the fact that it can be said in advance how the spins of the two electrons in a pair is impossible until one of them is determined, but they "already" (if I may say so in relation to what 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 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" - 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 a 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 a 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, 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 a mathematical model of the quantum world, this curious description, according to which a quantum state evolves over 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 becomes something localized and quite definite.
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 regard both Penrose and other similar promystically minded physicists with great skepticism, in spite of their very resounding 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.
Currently, there are a lot of interpretations of different levels of sophistication, trying not only 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

quantum entanglement (entanglement) (eng. Entanglement) - a quantum mechanical phenomenon in which the quantum state of two or more objects must be described in relation to each other, even if the individual objects are separated in space. As a result, there are correlations between the observed physical properties objects. For example, it is possible to prepare two particles that are in the same quantum state so that when one particle is observed in a state with a spin directed upwards, the spin of the other turns out to be directed downwards, and vice versa, and this despite the fact that, according to quantum mechanics, it is predicted that what directions are actually obtained each time is impossible. In other words, it seems that measurements taken on one system have an instantaneous effect on the one entangled with it. However, what is meant by information in the classical sense still cannot be transmitted through entanglement faster than at the speed of light.
Previously, the original term "entanglement" was translated in the opposite sense - as entanglement, but the meaning of the word is to maintain a connection even after a complex biography of a quantum particle. So in the presence of a connection between two particles in a coil of a physical system, by “pulling” one particle, it was possible to determine the other.

Quantum entanglement is the basis of future technologies such as the quantum computer and quantum cryptography, and it has also been used in quantum teleportation experiments. In theoretical and philosophical terms, this phenomenon is 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 notions of seemingly obvious locality. real world, in which information about the state of the system can be transmitted only through its immediate environment. Different views of 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 quantum mechanics becomes a nonlocal theory due to connectivity. We know how Einstein ridiculed connectivity, calling it “nightmare action at a distance. Naturally, non-local connectivity refuted the postulate of TO about the limiting speed of light (signal transmission).

On the other hand, quantum mechanics has been excellent at predicting experimental results, and in fact even strong correlations have been observed due to the phenomenon of entanglement. There is a way that seems to be successful in explaining quantum entanglement, a "hidden variable theory" approach in which certain but unknown microscopic parameters are responsible for correlations. However, in 1964, J.S. Bell showed that it would still not be possible 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 options. 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 they are not significant.

Connectivity has 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 the two systems may be separated long distance and be entangled at the same time, convey through their connection useful information impossible, so causality is not violated by entanglement. This happens for two reasons:
1. the results of measurements in quantum mechanics are fundamentally probabilistic;
2. The quantum state cloning theorem forbids statistical verification of entangled states.

Causes of Particle Influence

In our world, there are special states of several quantum particles - entangled states in which quantum correlations are observed (in general, correlation is a relationship between events above the level of random coincidences). These correlations can be detected experimentally, which was first done 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 is the cause of 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 household analogies. Or maybe these quantum correlations are the result of some new, hitherto unknown interaction, due 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 errors). This means that if such an interaction does take place, then it must propagate in the laboratory frame of reference extremely rapidly, at superluminal speed. And from this it inevitably follows that in other frames of reference this interaction will be generally instantaneous and will even act from the future into the past (though without violating the principle of causality).

The essence of the experiment

The geometry of the experiment. Pairs of entangled photons were generated in Geneva, then the photons were sent along fiber optic cables of the same length (marked in red) into two receivers (marked with the letters APD) spaced 18 km apart. Image from the article in question in Nature

The idea of the experiment is as follows: we create two entangled photons and send them to two detectors as far apart as possible (in the described experiment, the distance between the two detectors was 18 km). In this case, we 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. So, 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 novelty of this work is only 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 distinguished frame of reference. Due to the rotation of the Earth, the laboratory reference frame moves relative to this reference frame at different speeds. This means that the time interval between two events of detection of two photons will be different for this medium all the time, depending on the time of day. In particular, there will be a moment when these two events for this environment will seem to be 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 rate of this interaction is finite (even if it is arbitrarily large), then at this moment the correlations would disappear. Therefore, continuous observation of correlations during the day would completely close this possibility. And the repetition of such an experiment at different times of the year would close this hypothesis even with infinitely fast interaction in its own, selected frame of reference.

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

Maybe...?

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

No. The hypothetical interaction described above by construction serves the only purpose - these are the “gears” that make quantum correlations “work”. But it has already been proven that with the help of 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.
Fundamentals of the Subtle World - physical vacuum and torsion fields. four.

quantum entanglement.

Translation

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

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

I

Entanglement is thought to be a phenomenon unique to quantum mechanics – but it is not. In fact, it would be more understandable (albeit an unusual approach) to start with a simple, non-quantum (classical) version of entanglement. This will allow us to separate the subtleties associated with entanglement itself from the other oddities of quantum theory.

Entanglement appears 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 denote "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 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. Conversely, the shape of the second tells us nothing about the shape of the first.

On the other hand, we say that two kaons are entangled if information about one improves our knowledge about the other. The second tablet will show us a strong entanglement. 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 will be the same. Knowing the shape of one, we can uniquely determine the shape of the other.

The quantum version of entanglement looks, in fact, 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, which we will discuss later, but the basic concept of entangled knowledge that we demonstrated for the classical case remains the same.

Although cakes cannot be considered quantum systems, entanglement in quantum systems occurs naturally - for example, after particle collisions. In practice, unentangled (independent) states can be considered rare exceptions, since correlations arise between them during the interaction of systems.

Consider, for example, molecules. They consist of subsystems - specifically, electrons and nuclei. The minimum energy state of a molecule, in which it is usually located, is a highly entangled state of electrons and a nucleus, since the arrangement of these constituent particles will by no means be independent. When the nucleus moves, the electron moves with it.

Let's go back 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 the composite system that gives you partial information. It is possible to know, 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 characteristic consequences 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 you to this principle.

Up to this point, we have imagined that kaons come in two shapes (square and round). Now 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 can exist in one of four possible states: red square, red circle, blue square, and blue circle.

But quantum cakes are quantum cakes... Or quantons... They behave quite differently. The fact that the quanton in some situations can have different form and color does not necessarily mean that it has both form and color at the same time. In fact, the common sense that Einstein demanded of physical reality does not match the experimental facts, as we shall soon see.

We can measure the shape of a quanton, but in doing so we lose all information about its color. Or we can measure a 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; one has to take into account many different and mutually exclusive pictures, each of which has its own incomplete idea of what is happening. This is the essence of the principle of complementarity, such as it was formulated by Niels Bohr.

As a result, quantum theory forces us to be careful in ascribing properties to physical reality. To avoid controversy, it must be recognized that:

There is no property if it has not been measured.
Measurement is an active process that changes the system being measured

II

We now describe two exemplary, but not classical, illustrations of the oddities of quantum theory. Both have been tested in rigorous experiments (in real experiments, people measure not the shapes and colors of cakes, but the angular momentum of electrons).

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

An EPR pair consists of two quantons, each of which can be measured in shape or color (but not both). Suppose we have many such pairs, they are all the same, and we can choose which measurements we take on their components. If we measure the shape of one of the members of the EPR-pair, we are equally likely to get a square or a circle. If we measure the color, then with the same probability we 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 always match. That is, if we find that one of them is red and then measure the color of the second, we also find 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 was a square, then the second with the same probability can be blue or red.

According to quantum theory, we will get such results even if the two systems are separated by a huge distance and the measurements are taken almost simultaneously. The choice of measurement type in one location seems to affect the state of the system elsewhere. This "frightening action at a distance," as Einstein called it, seems to require the transmission of information - in our case, information about the measurement taken - at a speed faster than the speed of light.

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

With further study, the paradox is even more destroyed. 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 will have an equal chance of getting a square or a circle. Therefore, the result of EPR is logically predetermined. This is just a retelling of the complementarity principle.

There is no paradox in the fact that distant events are correlated. After all, if we put one of the two gloves from a pair into boxes and send them to different parts of the planet, it is not surprising that by looking into one box, I can determine which hand the other glove is intended for. Similarly, in all cases, the correlation of the EPR pairs must be fixed on them when they are nearby so that they can withstand the subsequent separation as if they had a 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

Daniel Greenberger, Michael Horn and Anton Zeilinger discovered another great example of quantum entanglement. It includes three of our quantons, which are in a specially prepared entangled state (GHZ state). We distribute each of them to different remote experimenters. Each one chooses, independently and randomly, whether to measure a color or a shape and records the result. The experiment is repeated many times, but always with three quantons in the GHZ state.

Each individual experimenter receives random results. By measuring the shape of the quanton, he gets a square or a circle with equal probability; measuring the color of the quanton, he gets red or blue with equal probability. While everything is normal.

But when the experimenters get together and compare the results, the analysis reveals a surprising result. Let's say we call the square shape and the color red "kind", and the circles and Blue colour- "evil". Experimenters find that if two of them decide to measure shape and the third choose color, then either 0 or 2 measurements are "evil" (i.e., round or blue). But if all three decide to measure the color, then either 1 or 3 measurements are evil. Quantum mechanics predicts this, and that is exactly what happens.

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

The GHZ effect, as physicist Sidney Colman describes it, is "a slap in the face of quantum mechanics." It breaks the habitual, learned expectation that physical systems have predetermined properties independent of their measurement. If this were the case, 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 broadened.

IV

For now, we're talking about how entanglement prevents us from assigning unique independent states to multiple quantons. The same reasoning applies to changes in one quanton that occur over time.

We are talking about "entangled stories" when it is impossible to assign a certain state to the system at each moment of time. Just as we rule out possibilities in traditional entanglement, we can also create intricate 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 variants of entanglement described earlier.

Using a more complex protocol, we can add a little bit of additionality to this system, and describe situations that cause 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 to the quanton the property of color in the interval between two dimensions; it does not have a definite form. Such stories realize, in a limited but fully controlled and precise way, the intuition inherent in the picture of the many worlds in quantum mechanics. A certain state can split into two contradictory historical trajectories, which then reconnect.

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 "Schrödinger's cat" postulates, as you know, quantum uncertainty, brought to the level of influence on feline mortality. Before measurement, 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 explaining 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 is automatic, and the cat continues to live (or not live). But the stories describe quantons, which are Schrödinger's kittens, with intricacy. Their full description requires that we take into consideration two mutually exclusive property trajectories.

The controlled experimental realization of entangled histories is a delicate thing, since it requires the collection of partial information about quantons. Conventional quantum measurements usually collect all the information at once - for example, determine the exact shape or the exact color - instead of 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 spread of the "many worlds" concept in quantum theory, and demonstrate its reality.

Quantum entanglement, or "spooky action at a distance" as Albert Einstein called it, is a quantum mechanical phenomenon in which the quantum states of two or more objects become interdependent. This dependence is preserved even if the objects are removed from each other for many kilometers. For example, you can entangle a pair of photons, take one of them to another galaxy, and then measure the spin of the second photon - and it will be opposite to the spin of the first photon, and vice versa. They are trying to adapt quantum entanglement for instantaneous data transmission over gigantic distances, or even for teleportation.

Modern computers provide quite a lot of opportunities for modeling a variety of situations. However, any calculations will be "linear" to some extent, since they obey well-defined algorithms and cannot deviate from them. And this system does not allow simulating complex mechanisms in which randomness is an almost constant phenomenon. This is a simulation of life. And what device could allow it to make? Quantum computer! It was on one of these machines that the largest project to simulate quantum life was launched.

Translation

I

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.

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

As a result, quantum theory forces us to be careful in ascribing properties to physical reality. To avoid controversy, it must be recognized that:

There is no property if it has not been measured.
Measurement is an active process that changes the system being measured

II

III

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

IV

For now, we're talking about how entanglement prevents us from assigning unique independent states to multiple quantons. The same reasoning applies to changes in one quanton that occur over time.