Quantum entanglement in simple words. Miracles continue. Quantum entanglement and gravity Einstein's entanglement theory in simple words
- Translation
Quantum entanglement is one of the most complex concepts in science, but its basic principles are simple. And once understood, entanglement opens the way to a better understanding of concepts such as the many worlds in quantum theory.
An enchanting aura of mystery surrounds the concept of quantum entanglement, as well as (somehow) the related requirement of quantum theory that there must be “many worlds.” And yet, at their core, these are scientific ideas with down-to-earth meaning and specific applications. I would like to explain the concepts of entanglement and many worlds as simply and clearly as I know them.
I
Entanglement is thought to be a phenomenon unique to quantum mechanics—but it is not. In fact, it may be more understandable to begin with (although this is an unusual approach) to consider a simple, non-quantum (classical) version of entanglement. This will allow us to separate the subtleties associated with entanglement itself from other oddities of quantum theory.Entanglement occurs in situations in which we have partial information about the state of two systems. For example, two objects can become our systems – let’s call them kaons. "K" will stand for "classical" objects. But if you really want to imagine something concrete and pleasant, imagine that these are cakes.
Our kaons will have two shapes, square or round, and these shapes will indicate their possible states. Then the four possible joint states of the two kaons will be: (square, square), (square, circle), (circle, square), (circle, circle). The table shows the probability of the system being in one of the four listed states. 
We will say that kaons are “independent” if knowledge about the state of one of them does not give us information about the state of the other. And this table has such a property. If the first kaon (cake) is square, we still don't know the shape of the second one. Conversely, the form of the second tells us nothing about the form of the first.
On the other hand, we will say that two kaons are entangled if information about one of them improves our knowledge about the other. The second tablet will show us strong confusion. In this case, if the first kaon is round, we will know that the second one is also round. And if the first kaon is square, then the second one will be the same. Knowing the shape of one, we can unambiguously determine the shape of the other.
The quantum version of entanglement looks essentially the same - it is a lack of independence. In quantum theory, states are described by mathematical objects called wave functions. The rules that combine wave functions with physical possibilities give rise to very interesting complications that we will discuss later, but the basic concept of entangled knowledge that we demonstrated for the classical case remains the same.
Although brownies cannot be considered quantum systems, entanglement in quantum systems occurs naturally, such as after particle collisions. In practice, unentangled (independent) states can be considered rare exceptions, since correlations arise between them when systems interact.
Consider, for example, molecules. They consist of subsystems - specifically, electrons and nuclei. The minimum energy state of a molecule, in which it usually exists, is a highly entangled state of electrons and nucleus, since the arrangement of these constituent particles will not be independent in any way. When the nucleus moves, the electron moves with it.
Let's return to our example. If we write Φ■, Φ● as wave functions describing system 1 in its square or round states and ψ■, ψ● for wave functions describing system 2 in its square or round states, then in our working example all states can be described , How:
Independent: Φ■ ψ■ + Φ■ ψ● + Φ● ψ■ + Φ● ψ●
Entangled: Φ■ ψ■ + Φ● ψ●
The independent version can also be written as:
(Φ■ + Φ●)(ψ■ + ψ●)
Note how in the latter case the brackets clearly separate the first and second systems into independent parts.
There are many ways to create entangled states. One is to measure a composite system that gives you partial information. One can learn, for example, that two systems have agreed to be of the same form without knowing which form they have chosen. This concept will become important a little later.
The more common effects of quantum entanglement, such as the Einstein-Podolsky-Rosen (EPR) and Greenberg-Horn-Seilinger (GHZ) effects, arise from its interaction with another property of quantum theory called the complementarity principle. To discuss EPR and GHZ, let me first introduce this principle to you.
Up to this point, we have imagined that kaons come in two shapes (square and round). Now let’s imagine that they also come in two colors – red and blue. Considering classical systems such as cakes, this additional property would mean that the kaon could exist in one of four possible states: red square, red circle, blue square, and blue circle.
But quantum cakes are quantons... Or quantons... They behave completely differently. The fact that a quanton in some situations may have different shapes and colors does not necessarily mean that it simultaneously has both shape and color. In fact, the common sense that Einstein demanded of physical reality does not correspond to experimental facts, as we will soon see.
We can measure the shape of a quanton, but in doing so we will lose all information about its color. Or we can measure the color, but lose information about its shape. According to quantum theory, we cannot measure both shape and color at the same time. No one's view of quantum reality is complete; we have to take into account many different and mutually exclusive pictures, each of which has its own incomplete picture of what is happening. This is the essence of the principle of complementarity, as formulated by Niels Bohr.
As a result, quantum theory forces us to be careful in attributing properties to physical reality. To avoid contradictions, we must admit that:
A property does not exist unless it is measured.
Measurement is an active process that changes the system being measured
II
Now we will 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 momenta of electrons).Albert Einstein, Boris Podolsky and Nathan Rosen (EPR) described a surprising effect that occurs when two quantum systems become entangled. The EPR effect combines a special, experimentally achievable form of quantum entanglement with the principle of complementarity.
An EPR pair consists of two quantons, each of which can be measured in shape or color (but not both at once). Suppose we have many such pairs, all of them the same, and we can choose what measurements we make on their components. If we measure the shape of one member of an EPR pair, we are equally likely to get a square or a circle. If we measure color, we are equally likely to get red or blue.
Interesting effects that seemed paradoxical to EPR arise when we measure both members of the pair. When we measure the color of both members, or their shape, we find that the results are always the same. That is, if we discover that one of them is red and then measure the color of the second, we also discover that it is red - and so on. On the other hand, if we measure the shape of one and the color of the other, no correlation is observed. That is, if the first one was a square, then the second one could be blue or red with equal probability.
According to quantum theory, we will obtain such results even if the two systems are separated by a huge distance and the measurements are carried out almost simultaneously. The choice of measurement type at one location appears to affect the state of the system at another location. This “frightening action at a distance,” as Einstein called it, apparently requires the transmission of information—in our case, information about a measurement being made—faster than the speed of light.
But is it? Until I know what results you got, I don't know what to expect. I get useful information when I know your result, not when you take a measurement. And any message containing the result you receive must be transmitted in some physical way, slower than the speed of light.
With further study, the paradox collapses even more. Let's consider the state of the second system if the measurement of the first gave a red color. If we decide to measure the color of the second quanton, we get red. But by the principle of complementarity, if we decide to measure its shape when it is in the "red" state, we have an equal chance of getting a square or a circle. Therefore, the result of EPR is logically predetermined. This is simply a restatement of the principle of complementarity.
There is no paradox in the fact that distant events are correlated. After all, if we put one of two gloves from a pair into boxes and send them to different ends of the planet, it is not surprising that by looking in one box, I can determine which hand the other glove is intended for. Likewise, in all cases, the correlation of EPR pairs must be recorded on them when they are nearby so that they can withstand subsequent separation, as if having memory. The strangeness of the EPR paradox is not in the possibility of correlation itself, but in the possibility of its preservation in the form of additions.
III
Daniel Greenberger, Michael Horn and Anton Zeilinger discovered another beautiful 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 of them chooses, independently and randomly, whether to measure color or shape and records the result. The experiment is repeated many times, but always with three quantons in the GHZ state.Each individual experimenter obtains random results. Measuring the shape of a quanton, he obtains with equal probability a square or a circle; when measuring the color of a quanton, it is equally likely to be red or blue. So far everything is ordinary.
But when experimenters get together and compare the results, the analysis shows a surprising result. Let's say we call the square shape and red color “good”, and the circles and blue color “evil”. Experimenters find that if two of them decide to measure shape and the third decides to measure color, then either 0 or 2 of the measurements are “evil” (i.e., round or blue). But if all three decide to measure a color, then either 1 or 3 dimensions are evil. This is what quantum mechanics predicts, and this is exactly what happens.
Question: Is the amount of evil even or odd? Both possibilities are realized in different dimensions. We have to abandon this issue. It makes no sense to talk about the amount of evil in a system without relating it to how it is measured. And this leads to contradictions.
The GHZ effect, as physicist Sidney Coleman describes it, is “a slap in the face from quantum mechanics.” It breaks down the conventional, experiential expectation that physical systems have predetermined properties independent of their measurement. If this were so, then the balance of good and evil would not depend on the choice of measurement types. Once you accept the existence of the GHZ effect, you will not forget it, and your horizons will be expanded.
IV
For now, we are discussing 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 talk about “entangled histories” when it is impossible for a system to be assigned a certain state at each moment in time. Just as in traditional entanglement we rule out possibilities, we can create entangled histories by making measurements that collect partial information about past events. In the simplest entangled stories we have one quanton that we study at two different points in time. We can imagine a situation where we determine that the shape of our quanton was square both times, or round both times, but both situations remain possible. This is a temporal quantum analogy to the simplest versions of entanglement described earlier.
Using a more complex protocol, we can add a little extra detail to this system, and describe situations that trigger the "many-worlds" property of quantum theory. Our quanton can be prepared in the red state, and then measured and obtained in blue. And as in the previous examples, we cannot permanently assign a quanton the property of color in the interval between two dimensions; It does not have a specific form. Such stories realize, in a limited but completely controlled and precise way, the intuition inherent in the many-worlds picture of quantum mechanics. A certain state can be divided into two contradictory historical trajectories, which then connect again.
Erwin Schrödinger, the founder of quantum theory, who was skeptical about its correctness, emphasized that the evolution of quantum systems naturally leads to states, the measurement of which can give extremely different results. His thought experiment with "Schrodinger's cat" postulates, as we know, quantum uncertainty, taken to the level of influence on feline mortality. Before measuring, it is impossible to assign the property of life (or death) to a cat. Both, or neither, exist together in an otherworldly world of possibility.
Everyday language is ill-suited to explain quantum complementarity, in part because everyday experience does not include it. Practical cats interact with surrounding air molecules, and other objects, in completely different ways, depending on whether they are alive or dead, so in practice the measurement takes place automatically, and the cat continues to live (or not live). But the stories describe the quantons, which are Schrödinger's kittens, with confusion. Their full description requires that we consider two mutually exclusive trajectories of properties.
Controlled experimental implementation of entangled stories is a delicate thing, since it requires the collection of partial information about quantons. Conventional quantum measurements typically collect all the information at once—determining an exact shape or a precise color, for example—rather than obtaining partial information several times. But it can be done, albeit with extreme technical difficulties. In this way we can assign a certain mathematical and experimental meaning to the extension of the concept of “many worlds” in quantum theory, and demonstrate its reality.
Quantum entanglement, the most controversial phenomenon in quantum mechanics, which Albert Einstein called “spooky action at a distance,” may be even more “entangled” than current theories claim. Physicists from the universities of Washington and New York believe that this phenomenon is related to wormholes - hypothetical features of space-time that, according to modern science fiction, can provide rapid transition from one part of the Universe to another.
Quantum entanglement is the phenomenon in which the quantum states of a multi-body system become interconnected. This connection is maintained even if the objects are separated at such distances that no known interactions occur between them. Also, in the physical concept there are the concepts of short-range and long-range. According to the short-range theory, the interaction between bodies is transmitted using some third link and with a finite value of speed. For example, electromagnetic interaction using an electromagnetic field. According to the theory of long-range action, interaction between objects is transmitted without an additional element, through emptiness and to any distance. In this case, interaction occurs at an infinitely high speed. As an example, we can cite the force of universal gravitation from Newton’s theory of gravity.
As a result of quantum entanglement, a group of particles interact in ways that dictate the behavior of one particle relative to the behavior of others. For example, in a pair of entangled particles, if one particle is observed to have a certain spin, then the other particle will be observed to have the opposite spin. Einstein called this interaction ghostly precisely because entanglement persists no matter how far apart the particles are. If the behavior of one particle changes, then the behavior of the particle associated with it also changes at the same time.
A wormhole between two black holes. Source: Alan Stonebraker/American Physical Society
Recent studies have shown that the features of so-called wormholes are the same if two black holes are first entangled and then separated by a certain distance. Even if black holes were at opposite ends of the universe, a wormhole could connect them. But whether black holes are even as large as an atom or larger than our Sun (which is observed throughout the Universe), their gravity is so strong that not even light can escape its gravitational grip. If two black holes were entangled, then a person located beyond the event horizon of the first black hole would still not be able to know what was happening beyond the event horizon of the second black hole. In order to communicate with the person on the other end, both would have to enter their own black holes. Then the surrounding space will be the same.
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 encounter teleportation in science fiction films and books. Have you ever wondered why what writers came up with eventually becomes our reality? How do they manage to predict the future? I think this is not an accident. Science fiction writers often have extensive knowledge of physics and other sciences, which, combined with their intuition and extraordinary imagination, helps them construct a retrospective analysis of the past and simulate future events.
From the article you will learn:
- What is quantum entanglement?
Concept "quantum entanglement" arose from a theoretical assumption arising 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 remains, even if they are separated into different parts of the Universe
The discovery of quantum entanglement goes some way to explaining the theoretical possibility of teleportation.
In short, then spin of a quantum particle (electron, photon) is called its own angular momentum. Spin can be represented as a vector, and the quantum particle itself 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 spin values 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, he is in both states of spin at once (vector spin up/vector spin down). Introduced? OK. But as soon as an observer appears and measures its state, the electron itself determines which spin vector it should accept - up or down.
Want to know how electron spin is measured? It is placed in a magnetic field: electrons with spin opposite the direction of the field, and with spin in the direction of the field, will be deflected in different directions. Photon spins are measured by directing them into a polarizing filter. If the spin (or polarization) of the photon is “-1”, then it does not pass through the filter, and if it is “+1”, then it does.
Summary. Once you have measured the state of one electron and determined that its spin is “+1”, then the electron associated or “entangled” with it takes on a spin value of “-1”. And instantly, even if he is on Mars. Although before measuring the state of the 2nd electron, it had both spin values simultaneously (“+1” and “-1”).
This paradox, proven mathematically, did not like Einstein very much. 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 moment its state is measured, instantly (faster than the speed of light) transmits to the 2nd particle information what the spin value is her to accept. Namely: the opposite meaning.
Einstein's dispute with Bohr. Who is right?
Einstein called “quantum entanglement” SPUCKHAFTE FERWIRKLUNG (German) or frightening, ghostly, supernatural action at a distance.
Einstein did not agree with Bohr's interpretation of quantum particle entanglement. Because it contradicted his theory that information cannot be transmitted faster than the speed of light. In 1935, he published a paper describing a thought experiment. This experiment was called the “Einstein-Podolsky-Rosen Paradox.”
Einstein agreed that bound particles could exist, but came up with a different explanation for the instantaneous transfer of information between them. He said "entangled particles" rather 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 the friend receives the suitcase, he will know that the suitcase contains either a left or right glove. When he opens the suitcase and sees that there is a left glove in it, he will instantly know that there is a right glove on the Moon. And this does not mean that the friend influenced the fact that the left glove is in the suitcase and does not mean that the left glove instantly transmitted information to the right one. This 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 when he believed that bound particles transmit information to each other instantly, even if they are separated over vast distances? Or Einstein, who believed that there is no supernatural connection, and everything is predetermined long before the moment of measurement.
This debate moved into the field of philosophy for 30 years. Has the dispute been resolved since then?
Bell's theorem. Is the dispute resolved?
John Clauser, while still a graduate student at Columbia University, in 1967 found the forgotten work of Irish physicist John Bell. It was a sensation: it turns out Bell managed to break the deadlock between Bohr and Einstein.. He proposed experimentally testing both hypotheses. 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 was 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 is impossible. There was only one explanation left - an inexplicable, supernatural connection between particles.
The experimental results proved that the theoretical assumption of quantum mechanics is correct. Quantum entanglement is a reality ( Quantum entanglement Wikipedia). Quantum particles can be connected despite vast distances. Measuring 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 long-distance communication actually happens.
The question remains, is teleportation possible?
Is teleportation confirmed experimentally?
Back in 2011, Japanese scientists were the first in the world to teleport photons! A beam of light was instantly moved from point A to point B.
If you want everything you read about quantum entanglement to be sorted out in 5 minutes, watch this wonderful video.
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Refers to the “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 suitable selections, building the level of description that seems acceptable for a worldview site.
Topic of the article: Many people are close to the idea that all the fascinating quirks of entangled states could be explained this way. We mix the black and white balls, without looking, pack them into boxes and send them in different directions. We open the box on one side, look: a black ball, after which we are 100% sure that there is a white ball in the other box. That's all:)
The purpose of the article is not a strict immersion in all the features of understanding “entangled states”, but to compile a system of general ideas, with an understanding of the main principles. This is exactly how you should treat everything stated above :)
Let's immediately set the defining context. When specialists (and not debaters far from this specificity, even scientists in some ways) talk about the entanglement of quantum objects, they mean not that it forms one whole with some connection, but that one object becomes quantum characteristics exactly the same as the other (but not all, but those that allow identity in a pair according to Pauli’s law, so the spin of a mated pair is not identical, but mutually complementary). Those. This is not a connection or a process of interaction, even though it can be described by a general function. This is a characteristic of a state that can be “teleported” from one object to another (by the way, there is also a widespread misinterpretation of the word “teleport”). If you don’t decide on this right away, you can go very far into mysticism. Therefore, first of all, everyone who is interested in the issue must be clearly sure of what exactly is meant by “confusion.”
What this article was started for comes down to one question. The difference in the behavior of quantum objects from classical ones is manifested in the only so far known verification method: whether a certain verification condition is met or not - Bell’s inequality (more details below), which for “entangled” quantum objects behaves as if there is a connection between objects sent in different directions. But the connection seems to be not real, because... neither information nor energy can be transferred.
Moreover, this connection does not depend neither from distance nor from time: if two objects were “entangled”, then, regardless of the safety of each of them, the second behaves as if the connection still exists (although the presence of such a connection can only be detected by measuring both objects, such a measurement can be separated in time: first measure, then destroy one of the objects, and measure the second later. For example, see R. Penrose). It is clear that any type of “connection” becomes difficult to understand in this case and the question arises as follows: can the law of probability of the loss of the measured parameter (which is described by the wave function) be such that the inequality is not violated at each end, and with general statistics at both ends - was violated - and without any connection, naturally, except for the connection by an act of general emergence.
I’ll give the answer in advance: yes, it can, provided that these probabilities are not “classical”, but operate with complex variables to describe a “superposition of states” - as if simultaneously finding all possible states with a certain probability for each.
For quantum objects, the descriptor of their state (wave function) is exactly that. If we talk about describing the position of an electron, then the probability of finding it determines the topology of the “cloud” - the shape of the electron orbital. What is the difference between classical and quantum?
Let's imagine a rapidly rotating bicycle wheel. Somewhere on it there is a red disk for the side headlight reflector, but we only see a denser shadow of the blur in this place. The probability that by putting a stick in the wheel, the reflector will stop in a certain position from the stick is simply determined: one stick - one certain position. We put two sticks in, but only the one that is a little earlier will stop the wheel. If we try to stick our sticks completely simultaneously, ensuring that there is no time between the ends of the stick touching the wheel, then some uncertainty will appear. “There was no time” between interactions with the essence of the object - the whole essence of understanding quantum miracles :)
The speed of “rotation” of what determines the shape of the electron (polarization - the propagation of electrical disturbance) is equal to the maximum speed with which anything can propagate in nature (the speed of light in a vacuum). We know the conclusion of the theory of relativity: in this case, the time for this disturbance becomes zero: there is nothing in nature that could happen between any two points of propagation of this disturbance; time for it does not exist. This means that the disturbance is able to interact with any other “sticks” influencing it without wasting time - simultaneously. And the probability of what result will be obtained at a specific point in space during interaction must be calculated by a probability that takes into account this relativistic effect: Due to the fact that there is no time for an electron, it is not able to choose the slightest difference between two “sticks” during interaction with them and does it simultaneously from its “point of view”: an electron passes through two slits simultaneously with a different wave density in each and then interferes with itself as two superimposed waves.
Here is the difference in the descriptions of probabilities in classical and quantum: Quantum correlations are “stronger” than classical ones. If the result of a coin falling out depends on many influencing factors, but in general they are uniquely determined so that you just need to make an exact machine for throwing out coins, and they will fall the same way, randomness has “disappeared”. If you make an automaton that pokes into an electron cloud, then the result will be determined by the fact that each poke will always hit something, only with a different density of the essence of the electron in this place. There are no other factors other than the static distribution of the probability of finding the measured parameter in the electron, and this is determinism of a completely different kind than in the classics. But this is also determinism, i.e. it is always calculable, reproducible, only with a singularity described by the wave function. Moreover, such quantum determinism concerns only a holistic description of a quantum wave. But, due to the absence of its own time for the quantum, it interacts absolutely randomly, i.e. there is no criterion to predict in advance the result of measuring the totality of its parameters. In this sense, e (in the classical view) is absolutely non-deterministic.
The electron really and truly exists in the form of a static formation (and not a point rotating in orbit) - a standing wave of electric disturbance, which has another relativistic effect: perpendicular to the main plane of “propagation” (it’s clear why in quotes:) an electric field arises also a static region of polarization, which is capable of influencing the same region of another electron: magnetic moment. Electric polarization in an electron gives the effect of an electric charge, its reflection in space in the form of the possibility of influencing other electrons - in the form of a magnetic charge, which cannot exist in itself without an electric one. And if in an electrically neutral atom the electric charges are compensated by the nuclear charges, then the magnetic ones can be oriented in one direction and we get a magnet. More in-depth ideas about this are in the article .
The direction in which the magnetic moment of the electron will be directed is called spin. Those. spin is a manifestation of the method of superimposing a wave of electrical deformation on itself with the formation of a standing wave. The numerical value of the spin corresponds to the characteristic of the wave superimposing itself. For the electron: +1/2 or -1/2 (the sign symbolizes the direction of the lateral shift of polarization - the “magnetic” vector).
If there is one electron on the outer electron layer of an atom and suddenly another one joins it (the formation of a covalent bond), then they, like two magnets, immediately rise to position 69, forming a paired configuration with a bond energy that must be broken in order to again share these electrons. The total spin of such a pair is 0.
Spin is a parameter that plays an important role when considering entangled states. For a freely propagating electromagnetic quantum, the essence of the conditional parameter “spin” is still the same: the orientation of the magnetic component of the field. But it is no longer static and does not lead to the emergence of a magnetic moment. To fix it, you need not a magnet, but a polarizer slit.
To get some ideas about quantum entanglement, I suggest reading the popular and short article by Alexey Levin: Passion at a distance . Please follow the link and read before proceeding :)
So, specific measurement parameters are realized only during measurement, and before that they existed in the form of that probability distribution, which constituted the statics of the relativistic effects of the dynamics of the propagation of polarization of the microworld, visible to the macroworld. To understand the essence of what is happening in the quantum world means to penetrate into the manifestations of such relativistic effects, which in fact give a quantum object the properties of being simultaneously in different states until the moment of specific measurement.
An “entangled state” is a completely deterministic state of two particles that have such an identical dependence of the description of quantum properties that consistent correlations appear at both ends, due to the peculiarities of the essence of quantum statics, which have consistent behavior. Unlike macro statistics, in quantum statistics it is possible to preserve such correlations for objects separated in space and time and previously consistent in parameters. This is manifested in the statistics of the fulfillment of Bell's inequalities.
How is the wave function (our abstract description) of the unentangled electrons of two hydrogen atoms different (even though its parameters are generally accepted quantum numbers)? Nothing except that the spin of the unpaired electron is random without violating Bell's inequalities. In the case of the formation of a paired spherical orbital in a helium atom, or in the covalent bonds of two hydrogen atoms, with the formation of a molecular orbital generalized by two atoms, the parameters of the two electrons turn out to be mutually consistent. If entangled electrons are split and they begin to move in different directions, then a parameter appears in their wave function that describes the displacement of the probability density in space as a function of time - the trajectory. And this does not at all mean that the function is smeared in space, simply because the probability of finding an object becomes zero at some distance from it and there is nothing left behind to indicate the probability of finding an electron. This is especially obvious if the pair is separated in time. Those. two local and independent descriptors arise, moving particles in opposite directions. Although it is still possible to use one general descriptor, it is the right of the one who formalizes it :)
In addition, the environment of the particles cannot remain indifferent and is also subject to modification: the descriptors of the wave function of the particles of the environment change and participate in the resulting quantum statistics through their influence (giving rise to phenomena such as decoherence). But usually almost no one thinks of describing this as a general wave function, although this is also possible.
Many sources provide detailed information on these phenomena.
M.B. Mensky writes:
"One of the purposes of this article... is to substantiate the view that there is a formulation of quantum mechanics in which no paradoxes arise and in which all the questions that physicists usually ask can be answered. Paradoxes arise only when a researcher is not satisfied with this “physical” level of theory, when he poses questions that are not customary to pose in physics, in other words, when he takes it upon himself to try to go beyond the boundaries of physics. ...The specific features of quantum mechanics associated with entangled states were first formulated in connection with the EPR paradox, but at present they are not perceived as paradoxical. For people who work professionally with quantum mechanical formalism (i.e., for most physicists), there is nothing paradoxical either in EPR pairs or even in very complex entangled states with a large number of terms and a large number of factors in each term. The results of any experiments with such states are, in principle, easy to calculate (although technical difficulties in calculating complex entangled states are, of course, possible)."
Although, it must be said, in discussions about the role of consciousness, conscious choice in quantum mechanics, Mensky turns out to be the one who takes " take the courage to try to go beyond the boundaries of physics". This is reminiscent of attempts to approach the phenomena of the psyche. As a quantum professional, Mensky is good, but in the mechanisms of the psyche he, like Penrose, is naive.
Very briefly and conditionally (only to grasp the essence) about the use of entangled states in quantum cryptography and teleportation (since this is what amazes the imagination of grateful viewers).
So, cryptography. You need to send the sequence 1001
We use two channels. According to the first, we send an entangled particle, and according to the second, information about how to interpret the received data in the form of one bit.
Let us assume that there is an alternative to the possible state of the used quantum mechanical parameter spin in conditional states: 1 or 0. Moreover, the probability of their occurrence with each released pair of particles is truly random and does not convey any meaning.
First transfer. When measuring Here it turned out that the particle has state 1. This means that the other has state 0. So that volume At the end of receiving the required unit, we transmit bit 1. There they measure the state of the particle and, to find out what it means, add it to the transmitted 1. They get 1. At the same time, they check by white that the entanglement has not been broken, i.e. info was not intercepted.
Second gear. The result is again a state of 1. The other has a 0. We transmit the information - 0. Add it up and get the required 0.
Third gear. The state here is 0. There, that means - 1. To get 0, we transmit 0. We add, we get 0 (in the least significant digit).
Fourth. Here - 0, there - 1, it needs to be interpreted as 1. We pass the information - 0.
That's the principle. Interception of the info channel is useless due to a completely uncorrelated sequence (encryption of the state of the first particle with a key). Interception of an obfuscated channel - disrupts reception and is detected. Transmission statistics from both ends (the receiving end has all the necessary data on the transmitted end) according to Bell determines the correctness and non-interception of the transmission.
This is what teleportation is all about. There is no arbitrary imposition of a state on a particle there, but only a prediction of what this state will be after (and only after) the particle here is removed from connection by measurement. And then they say that there was a transfer of a quantum state with the destruction of the complementary state at the starting point. Having received information about the state here, you can adjust the quantum mechanical parameter in one way or another so that it turns out to be identical to the one here, but here it will no longer be, and they are talking about implementing the ban on cloning in a bound state.
It seems that there are no analogues of these phenomena in the macrocosm, no balls, apples, etc. from classical mechanics cannot serve to interpret the manifestation of this nature of quantum objects (in fact, there are no fundamental obstacles to this, which will be shown below in the final link). This is the main difficulty for those who want to receive a visible “explanation”. This does not mean that such a thing is not imaginable, as is sometimes stated. This means that you need to work quite painstakingly on relativistic concepts, which play a decisive role in the quantum world and connect the world of quantum with the macro world.
But this is not necessary either. Let us recall the main task of the representation: what should be the law of materialization of the measured parameter (which is described by the wave function) so that the inequality is not violated at each end, and with general statistics, it is violated at both ends. There are many interpretations for understanding this, using auxiliary abstractions. They talk about the same thing in different languages of such abstractions. Of these, two are the most significant in terms of the correctness shared among the bearers of ideas. I hope that after what has been said it will be clear what is meant :)
Copenhagen interpretation from an article about the Einstein-Podolsky-Rosen paradox:
" (EPR paradox) - an apparent paradox... In fact, let’s imagine that on two planets at different ends of the Galaxy there are two coins that always fall out the same way. If you record the results of all the tosses and then compare them, they will coincide. The drops themselves are random and cannot be influenced in any way. It is impossible, for example, to agree that heads are one and tails are zero, and thus transmit binary code. After all, the sequence of zeros and ones will be random at both ends of the wire and will not carry any meaning.
It turns out that there is an explanation for the paradox that is logically compatible with both the theory of relativity and quantum mechanics.
One might think that this explanation is too implausible. It's so strange that Albert Einstein never believed in a "god who plays dice." But careful experimental tests of Bell's inequalities have shown that there are non-local accidents in our world.
It is important to emphasize one already mentioned consequence of this logic: measurements over entangled states will only not violate the theory of relativity and causality if they are truly random. There should be no connection between the circumstances of measurement and the disturbance, not the slightest pattern, because otherwise the possibility of instantaneous transmission of information would arise. Thus, quantum mechanics (in the Copenhagen interpretation) and the existence of entangled states prove the presence of indeterminism in nature."
In a statistical interpretation, this is shown through the concept of “statistical ensembles” (same):
From the point of view of statistical interpretation, the real objects of study in quantum mechanics are not individual microobjects, but statistical ensembles of microobjects located in the same macroconditions. Accordingly, the phrase “a particle is in such and such a state” actually means “the particle belongs to such and such a statistical ensemble” (consisting of many similar particles). Therefore, the choice of one or another sub-ensemble in the initial ensemble significantly changes the state of the particle, even if there was no direct impact on it.
As a simple illustration, consider the following example. Let's take 1000 colored coins and throw them on 1000 sheets of paper. The probability that a “heads” imprint on a randomly selected sheet of paper is equal to 1/2. Meanwhile, for sheets on which coins lie “tails” up, the same probability is equal to 1 - that is, we have the opportunity to indirectly establish the nature of the imprint on paper, looking not at the sheet itself, but only at the coin. However, the ensemble associated with such an “indirect measurement” is completely different from the original one: it no longer contains 1000 sheets of paper, but only about 500!
Thus, a refutation of the uncertainty relationship in the EPR “paradox” would be valid only if for the original ensemble it was possible to simultaneously select a non-empty subensemble both on the basis of momentum and on the basis of spatial coordinates. However, it is precisely the impossibility of such a choice that is confirmed by the uncertainty relation! In other words, the EPR “paradox” in fact turns out to be a vicious circle: it presupposes in advance the incorrectness of the fact being refuted.
Option with a “superluminal signal” from a particle A to the particle B is also based on ignoring the fact that the probability distributions of the values of the measured quantities characterize not a specific pair of particles, but a statistical ensemble containing a huge number of such pairs. Here, as a similar one, we can consider the situation when a colored coin is thrown onto a sheet in the dark, after which the sheet is pulled out and locked in a safe. The probability that “heads” is imprinted on the sheet is a priori equal to 1/2. And the fact that it will immediately turn into 1 if we turn on the light and make sure that the coin lies “tails” up does not at all indicate the ability of our gaze to mist chemically influence items locked in the safe.
More details: A.A. Pechenkin Ensemble interpretations of quantum mechanics in the USA and USSR.
And one more interpretation from http://ru.philosophy.kiev.ua/iphras/library/phnauk5/pechen.htm:
Van Fraassen's modal interpretation assumes that the state of a physical system changes only causally, i.e. in accordance with the Schrödinger equation, however, this state does not uniquely determine the values of physical quantities detected during measurement.
Popper gives here his favorite example: a children's billiard (a board covered with needles, on which a metal ball rolls down from above, symbolizing a physical system - the billiard itself symbolizes an experimental device). When the ball is at the top of the billiard, we have one disposition, one predisposition to reach some point at the bottom of the board. If we fixed the ball somewhere in the middle of the board, we changed the specification of the experiment and received a new predisposition. Quantum mechanical indeterminism is preserved here in full: Popper stipulates that billiards are not a mechanical system. We are unable to trace the trajectory of the ball. But “wave packet reduction” is not an act of subjective observation, it is a conscious redefinition of the experimental situation, a narrowing of the conditions of experience.
Let's summarize the facts
1. Despite the absolute randomness of the loss of paramert when measuring entangled pairs of particles in the mass, consistency is manifested in each such pair: if one particle in the pair turns out to have spin 1, then the other particle in the pair has the opposite spin. This is understandable in principle: since in a paired state there cannot be two particles that have the same spin in the same energy state, then when they split, if consistency is preserved, then the spins remain consistent. As soon as the spin of one is determined, the spin of the other becomes known, despite the fact that the randomness of the spin in measurements from either side is absolute.
Let me briefly clarify the impossibility of completely identical states of two particles in one place in space-time, which in the model of the structure of the electron shell of an atom is called the Pauli principle, and in the quantum mechanical consideration of consistent states - the principle of the impossibility of cloning entangled objects.
There is something (yet unknown) that actually prevents a quantum or its corresponding particle from being in one local state with another - completely identical in quantum parameters. This is realized, for example, in the Casimir effect, when virtual quanta between the plates can have a wavelength no greater than the gap. And this is especially clearly realized in the description of an atom, when the electrons of a given atom cannot have identical parameters in all respects, which is axiomically formalized by the Pauli principle.
On the first, closest layer there can only be 2 electrons in the form of a sphere (s-electrons). If there are two of them, then they have different spins and are paired (entangled), forming a common wave with binding energy that must be applied to break this pair.
In the second, more distant and higher energy level, there can be 4 “orbitals” of two paired electrons in the form of a standing wave shaped like a volumetric figure eight (p-electrons). Those. greater energy occupies more space and allows several already connected pairs to be adjacent. The second layer differs energetically from the first layer by 1 possible discrete energy state (the more outer electrons, describing a spatially larger cloud, also have higher energy).
The third layer already spatially allows you to have 9 orbits in the shape of a quatrefoil (d-electrons), fourth - 16 orbits - 32 electrons, form which also resemble volumetric eights in different combinations ( f-electrons).
Electron cloud shapes:
a – s-electrons; b – p-electrons; c – d-electrons.
This set of discretely different states - quantum numbers - characterize the possible local states of electrons. And this is what comes of it.
When two electrons have different spinsoneenergy level (although this is not fundamentally necessary: http://www.membrana.ru/lenta/?9250) pair, a common “molecular orbital” is formed with a lower energy level due to energy and bonding. Two hydrogen atoms each sharing an unpaired electron form a common overlap of these electrons—a (simple covalent) bond. As long as it exists, truly two electrons have a common consistent dynamics - a common wave function. How long? “Temperature” or something else that can compensate for the bonding energy breaks it. The atoms fly apart with electrons no longer sharing a common wave, but still in a complementary, mutually consistent state of entanglement. But there is no connection anymore :) This is the moment when it is no longer worth talking about the general wave function, although the probabilistic characteristics in terms of quantum mechanics remain the same as if this function continued to describe the general wave. This precisely means maintaining the ability to manifest consistent correlation.
A method for producing entangled electrons through their interactions is described: http://www.scientific.ru/journal/news/n231201.html or popularly-schematically - in http://www.membrana.ru/articles/technic/2002/02/08/170200.html : " To create an "uncertainty relationship" of electrons, that is, to "confuse" them, you need to make sure that they are identical in all respects, and then shoot these electrons into a beam splitter. The mechanism “splits” each of the electrons, bringing them into a quantum state of “superposition”, as a result of which the electron is equally likely to move along one of two paths.".
2. With statistics of measurements on both sides, the mutual consistency of randomness in pairs can lead to a violation of Bell’s inequality under certain conditions. But not through the use of some special, as yet unknown quantum mechanical entity.
The following short article (based on the ideas presented by R. Pnrose) allows us to trace (show the principle, example) how this is possible: The relativity of Bell's inequalities or the New Mind of the Naked King. This is also shown in the work of A.V. Belinsky, published in Advances in Physical Sciences: Bell's theorem without the assumption of locality. Another work of A.V. Belinsky for reflection by those interested: Bell’s theorem for trichotomous observables, as well as a discussion with D.P.S., Prof., Acad. Valery Borisovich Morozov (a generally recognized luminary of the forums of the physics department of the FRTK-MIPT and the “dubinushki”), where Morozov offers for consideration both of these works by A.V. Belinsky: Experience of Aspect: a question for Morozov. And in addition to the topic about the possibility of violations of Bell's inequalities without introducing any long-range action: Modeling using Bell's inequality.
Please note that “The Relativity of Bell’s Inequalities or the New Mind of the Naked King”, as well as “Bell’s Theorem without the Assumption of Locality” in the context of this article do not pretend to describe the mechanism of quantum mechanical entanglement. The task is shown in the last sentence of the first link: “There is no reason to refer to the violation of Bell’s inequalities as an indisputable refutation of any model of local realism.” those. the limit of its use is the theorem stated at the beginning: “There may exist models of classical locality in which Bell’s inequalities will be violated.” There are additional explanations about this in the discussion.
I’ll also give you a model from myself.
“Violation of local realism” is just a relativistic effect.
Nobody (normal) argues with the fact that for a system moving at the maximum speed (the speed of light in vacuum) there is neither space nor time (the Lorentz transformation in this case gives zero time and space), i.e. for a quantum it is both here and there at once, no matter how distant it may be there.
It is clear that entangled quanta have their own starting point. And electrons are the same quanta in a state of a standing wave, i.e. existing here and there simultaneously for the entire lifetime of the electron. All properties of quanta turn out to be predetermined for us, those who perceive it from the outside, that’s why. We are ultimately made up of quanta, which are both here and there. For them, the speed of interaction propagation (maximum speed) is infinitely high. But all these infinities are different, just like the different lengths of segments, although each has an infinite number of points, but the ratio of these infinities gives the ratio of lengths. This is how time and space appear for us.
For us, local realism is violated in experiments, but for quanta it is not.
But this discrepancy does not affect reality in any way because we cannot practically take advantage of such an infinite speed. Neither information, nor, especially matter, is transmitted indefinitely quickly during “quantum teleportation.”
So all this is just jokes of relativistic effects, nothing more. They can be used in quantum cryptography or something else, but cannot be used for real long-range action.
Let's look at the essence of what Bell's inequalities show.
1. If the orientation of the meters at both ends is the same, then the spin measurement result at both ends will always be opposite.
2. If the orientation of the meters is opposite, then the result will be the same.
3. If the orientation of the left meter differs from the orientation of the right one by less than a certain angle, then point 1 will be realized and the coincidences will be within the probability predicted by Bell for independent particles.
4. If the angle exceeds, then point 2 and the coincidences will be greater than the probability predicted by Bell.
Those. at a smaller angle we will obtain predominantly opposite values of the spins, and at a larger angle we will obtain predominantly identical ones.
Why this happens with spin can be imagined, keeping in mind that the spin of an electron is a magnet, and is also measured by the orientation of the magnetic field (or in a free quantum, spin is the direction of polarization and is measured by the orientation of the gap through which the plane of rotation of the polarization should fall).
It is clear that by sending magnets that were initially linked and retained their mutual orientation when sent, we will influence them with a magnetic field during measurement (turning them in one direction or another) in the same way as happens in quantum paradoxes.
It is clear that when encountering a magnetic field (including the spin of another electron), the spin is necessarily oriented in accordance with it (mutually opposite in the case of the spin of another electron). That is why they say that “spin orientation occurs only during measurement,” but at the same time it depends on its initial position (in which direction to rotate) and the direction of influence of the meter.
It is clear that no long-range actions are required for this, just as it is not necessary to prescribe such behavior in the initial state of the particles.
I have reason to believe that so far, when measuring the spin of individual electrons, intermediate spin states are not taken into account, but only predominantly along the measuring field and against the field. Examples of methods: , . It is worth paying attention to the date of development of these methods, which is later than the experiments described above.
The given model, of course, is simplified (in quantum phenomena, spin is not exactly the material magnets, although they provide all the observed magnetic phenomena) and does not take into account many nuances. Therefore, it is not a description of a real phenomenon, but shows only a possible principle. And he also shows how bad it is to simply trust descriptive formalism (formulas) without understanding the essence of what is happening.
Moreover, Bell's theorem is correct in the formulation from Aspek's article: “it is impossible to find a theory with an additional parameter that satisfies the general description and that reproduces all the predictions of quantum mechanics.” and not at all in Penrose’s formulation: “it turns out that it is impossible to reproduce the predictions of quantum theory in this (non-quantum) way.” It is clear that in order to prove the theory according to Penrose, it is necessary to prove that it is not possible to violate Bell’s inequalities using any models other than a quantum mechanical experiment.
This is a somewhat exaggerated, one might say vulgar example of interpretation, simply to show how one can be deceived in such results. But let’s make it clear what Bell wanted to prove and what actually happens. Bell created an experiment showing that in entanglement there is no pre-existing “algorithm a”, 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 an actually random process (why is well described below).
BUT in fact they simply have the same probabilistic dependencies. What does it mean? This means that it is not at all a predetermined, given connection between the fixation of a parameter and a measurement that takes place, but such a result of fixation comes from the fact that the processes have the same (complementary) probabilistic function (which, in general, directly stems from quantum mechanical concepts), the essence which is the realization of a parameter when fixed, which was not defined due to the absence of space and time in its “reference frame” due to the maximum possible dynamics of its existence (relativistic effect formalized by Lorentz transformations, see Vacuum, quanta, matter).
This is how Brian Greene describes the methodological essence of Bell's experiment in his book The Fabric of the Cosmos. Each of the two players received many boxes, each with three doors. If the first player opens the same door as the second in a box with the same number, then it flashes with the same light: red or blue.
The first player Scully assumes that this is ensured by the flash color program embedded in each pair depending on the door, the second player Mulder believes that the flashes follow with equal probability, but are somehow connected (by non-local long-range action). According to the second player, experience decides everything: if the program - then the probability of identical colors when different doors are randomly opened should be more than 50%, contrary to the truth of random probability. He gave an example why:
Just to be specific, let's imagine that the program for the sphere in a separate box produces blue (1st door), blue (2nd door) and red (3rd door) colors. Now, since we both choose one of the three doors, there are a total of nine possible combinations of doors that we can choose to open for a given box. For example, I can choose the top door on my box, while you can choose the side door on your box; or I can choose the front door and you can choose the top door; and so on."
"Yes, sure." – Scully jumped. “If we call the top door 1, the side door 2, and the front door 3, then the nine possible door combinations are simply (1,1), (1,2), (1,3), (2,1), ( 2,2), (2,3), (3,1), (3,2) and (3,3)."
"Yes, that's right," Mulder continues. - "Now the important point: Of these nine possibilities, we note that five combinations of doors - (1,1), (2,2), (3,3), (1,2) and (2,1) - lead to The result is that we see the spheres in our boxes flashing with the same colors.
The first three door combinations are the ones in which we choose the same doors, and as we know, this always results in us seeing the same colors. The other two door combinations (1,2) and (2,1) result in the same colors, since the program dictates that the spheres will flash one color - blue - if either door 1 or door 2 is open. So, since 5 is more than half of 9, that means that for more than half—more than 50 percent—of the possible combinations of doors we can choose to open, the orbs will flash the same color."
"But wait," Scully protests. - “This is just one example of a special program: blue, blue, red. In my explanation, I assumed that boxes with different numbers can and in general will have different programs.”
"Really, it doesn't matter. The conclusion is valid for any of the possible programs.
And this is indeed true if we are dealing with a program. But this is not at all the case if we are dealing with random dependencies for many experiences, but each of these accidents has the same form in each experiment.
In the case of electrons, when they were initially bound in a pair, which ensures their completely dependent spins (mutually opposite) and scattered, this interdependence, of course, remains with a complete overall picture of the true probability of precipitation and in the fact that it is impossible to say in advance how the spins of the two turned out electrons in a pair is impossible until one of them is determined, but they “already” (if one can say so in relation to something that does not have its own metric of time and space) have a certain relative position.
Further in Brian Greene's book:
there is a way to examine whether we have inadvertently come into conflict with the STO. The common property of matter and energy is that, when transferred from place to place, they can transmit information. Photons, traveling from a radio transmitting station to your receiver, carry information. Electrons traveling through Internet cables to your computer carry information. In any situation where something—even something unidentified—is implied to be moving faster than the speed of light, the safe test is to ask whether it is, or at least can, convey information. If the answer is no, the standard reasoning goes through that nothing exceeds the speed of light and SRT remains uncontested. In practice, physicists often use this test to determine whether some subtle process violates the laws of STR. Nothing survived this test.
As for the approach of R. Penrose and so on. interpreters, then from his work Penrouz.djvu I will try to highlight that fundamental attitude (worldview) that directly leads to mystical views about nonlocality (with my comments - black tsaeta):
It was necessary to find a way that would allow one to separate truth from assumptions in mathematics - some formal procedure, using which one could say with confidence whether a given mathematical statement is true or not (objection see Aristotle's Method and Truth, criteria of truth). Until this problem is properly resolved, one can hardly seriously hope for success in solving other, much more complex problems - those that concern the nature of the forces that move the world, no matter what relationship these same forces may have with mathematical truth. The realization that the key to understanding the universe lies in irrefutable mathematics is perhaps the first of the most important breakthroughs in science in general. The ancient Egyptians and Babylonians guessed about mathematical truths of various kinds, but the first stone in the foundation of mathematical understanding...
... for the first time, people had the opportunity to formulate reliable and obviously irrefutable statements - statements whose truth is beyond doubt today, despite the fact that science has stepped far forward since then. For the first time, people discovered the truly timeless nature of mathematics.
What is this - mathematical proof? In mathematics, a proof is an impeccable reasoning that uses only the techniques of pure logic. (pure logic does not exist. Logic is an axiomatic formalization of patterns and relationships found in nature) allowing one to make an unambiguous conclusion about the validity of a particular mathematical statement based on the validity of any other mathematical statements, either established in advance in a similar way, or not requiring proof at all (special elementary statements, the truth of which, in general opinion, is self-evident, are called axioms) . The proven mathematical statement is usually called a theorem. This is where I don’t understand him: there are also theorems that are simply stated but not proven.
... Objective mathematical concepts should be thought of as timeless objects; there is no need to think that their existence begins the moment they appear in one form or another in the human imagination.
... Thus, mathematical existence differs not only from physical existence, but also from the existence that our conscious perception is capable of endowing an object with. However, it is clearly related to the last two forms of existence - i.e., physical and mental existence connection is a completely physical concept, what does Penrose mean here?- and the corresponding connections are as fundamental as they are mysterious.
Rice. 1.3. Three “worlds” - Plato’s mathematical, physical and mental - and three fundamental mysteries connecting them...
... So, according to the one shown in Fig. 1.3 diagram, the entire physical world is governed by mathematical laws. We will see in later chapters of the book that there is strong (if incomplete) evidence to support this view. If we believe this evidence, then we have to admit that everything that exists in the physical Universe, down to the smallest detail, is indeed governed by precise mathematical principles - perhaps equations. I'm just quietly goofing around here....
...If this is so, then our physical actions are completely and completely subordinated to such universal mathematical control, although this “control” still allows for a certain randomness in behavior, governed by strict probabilistic principles.
Many people begin to feel very uncomfortable from such assumptions; I myself, to admit, these thoughts cause some anxiety.
... Perhaps, in a sense, the three worlds are not separate entities at all, but only reflect various aspects of some more fundamental TRUTH (emphasis added) that describes the world as a whole - a truth about which we currently have no idea concepts. - clean Mystic....
.................
It even turns out that there are areas on the screen that are inaccessible to particles emitted by the source, despite the fact that the particles could quite successfully enter these areas when only one of the slits was open! Although the spots appear on the screen one at a time in localized positions, and although each encounter of a particle with a screen can be associated with a specific act of emission of the particle by the source, the behavior of the particle between the source and the screen, including the ambiguity associated with the presence of two slits in the barrier, is similar to the behavior of a wave in which the wave When a particle collides with the screen, it feels both slits at once. Moreover (and this is especially important for our immediate purposes), the distance between the stripes on the screen corresponds to the wavelength A of our wave-particle, related to the momentum of the particles p by the previous formula XXXX.
All this is quite possible, a sober-minded skeptic will say, but this does not force us to carry out such an absurd-looking identification of energy and impulse with some operator! Yes, that’s exactly what I want to say: an operator is just a formalism for describing a phenomenon within its certain framework, and not an identity with the phenomenon.
Of course, it doesn’t force us, but should we turn away from a miracle when it appears to us?! What is this miracle? The miracle is that this apparent absurdity of the experimental fact (waves turn out to be particles, and particles turn out to be waves) can be brought into the system with the help of a beautiful mathematical formalism, in which momentum is actually identified with “differentiation along the coordinate”, and energy with “ differentiation with respect to time."
... This is all great, but what about the state vector? What prevents us from recognizing that it represents reality? Why are physicists often extremely reluctant to accept this philosophical position? Not just physicists, but those who have everything in order with a holistic worldview and are not inclined to engage in underdetermined reasoning.
.... If you wish, you can imagine that the photon wave function leaves the source in the form of a clearly defined wave packet of small sizes, then, after meeting the beam splitter, it is divided into two parts, one of which is reflected from the splitter, and the other is transmitted through it, for example, in a perpendicular direction. In both, we forced the wavefunction to split into two parts in the first beam splitter... Axiom 1: quantum is not divisible. A person who talks about halves of a quantum outside its wavelength is perceived by me with no less skepticism than a person who creates a new universe with each change in the state of the quantum. Axiom 2: the photon does not change its trajectory, and if it has changed, then this is re-emission of the photon by the electron. Because a quantum is not an elastic particle and there is nothing from which it would bounce. For some reason, in all descriptions of such experiments, these two things are avoided to be mentioned, although they have a more basic meaning than the effects that are described. I don’t understand why Penrose says this, he cannot but know about the indivisibility of the quantum, moreover, he mentioned this in the double-slit description. In such miraculous cases, one must still try to remain within the framework of the basic axioms, and if they come into some kind of contradiction with experience, this is a reason to think more carefully about the methodology and interpretation.
Let's accept for now, at least as a mathematical model of the quantum world, this curious description, according to which a quantum state evolves for some time in the form of a wave function, usually “smeared” throughout space (but with the possibility of focusing in a more limited area), and then, when the measurement is made, this state turns into something localized and well-defined.
Those. they are seriously talking about the possibility of something being spread out over several light years with the possibility of instantaneous mutual change. This can be presented purely abstractly - as the preservation of a formalized description on each side, but not in the form of some real entity represented by the nature of the quantum. Here there is a clear continuity of the idea about the reality of the existence of mathematical formalisms.
That is why I perceive both Penrose and other similar promistically-minded physicists very skeptically, despite their very loud authority...
In S. Weinberg's book Dreams of a Final Theory:
The philosophy of quantum mechanics is so irrelevant to its real use that one begins to suspect that all deep questions about the meaning of measurement are in fact empty, generated by the imperfection of our language, which was created in a world practically governed by the laws of classical physics.
In the article What is locality and why is it not in the quantum world? , where the problem is summarized based on recent events by Alexander Lvovsky, an employee of the RCC and a professor at the University of Calgary:
Quantum nonlocality exists only within the framework of the Copenhagen interpretation of quantum mechanics. According to it, when a quantum state is measured, it collapses. If we take as a basis the many-worlds interpretation, which says that the measurement of a state only extends the superposition to the observer, then there is no nonlocality. This is just an illusion of an observer who “does not know” that he has entered an entangled state with a particle at the opposite end of the quantum line.
Some conclusions from the article and its existing discussion.
Currently, there are many interpretations of different levels of sophistication, trying not just to describe the phenomenon of entanglement and other “non-local effects”, but to describe assumptions about the nature (mechanisms) of these phenomena - i.e. hypotheses. Moreover, the prevailing opinion is that it is impossible to imagine anything in this subject area, and it is only possible to rely on certain formalizations.
However, these same formalizations, with approximately equal convincingness, can show anything the interpreter wants, right down to describing the emergence of a new universe every time at a moment of quantum uncertainty. And since such moments arise during observation, bringing consciousness is like a direct participant in quantum phenomena.
For a detailed justification - why this approach seems completely wrong - see the article Heuristics.
So, every time the next cool mathematician begins to prove something like the unity of nature of two completely different phenomena based on the similarity of their mathematical description (well, for example, this is seriously done with Coulomb’s law and Newton’s law of gravity) or “explain” quantum entanglement to special “ dimension" without representing its real embodiment (or the existence of meridians in the formalism of earthlings), I will keep it ready :)
