What is the Copenhagen Interpretation? Copenhagen interpretation of quantum mechanics.

· Popper's experiment · Stern-Gerlach's experiment · Young's experiment · Verification of Bell's inequalities · Photoelectric effect · Compton effect

Wording
Schrödinger representation Heisenberg representation Interaction representation Matrix quantum mechanics Path integrals Feynman diagrams

Equations
Schrödinger equation Pauli equation Klein-Gordon equation Dirac equation Schwinger-Tomonaga equation Von Neumann equation Bloch equation Lindblad equation Heisenberg equation

Development of the theory
Quantum field theory Quantum electrodynamics Glashow-Weinberg-Salam theory Quantum chromodynamics Standard model Quantum gravity

Notable scientists
Planck Einstein Schrödinger Heisenberg Jordan Bohr Pauli Dirac Fock Born de Broglie Landau Feynman Bohm Everett

Main Ideas of the Copenhagen Interpretation

The physical world consists of quantum (small) objects and classical measuring devices.

Quantum mechanics is a statistical theory, due to the fact that the measurement of the initial conditions of a micro-object changes its state and leads to probabilistic description of the initial position of the micro-object, which is described by the wave function . The central concept of quantum mechanics is the complex wave function. It is possible to describe the change in the wave function to a new dimension. Its expected result depends probabilistically on the wave function. Physically significant is only the square of the modulus of the wave function, which means the probability of finding the studied micro-object in some place in space.

The law of causality in quantum mechanics is fulfilled in relation to the wave function, the change of which in time is completely determined by its initial conditions, and not in relation to the coordinates and velocities of particles, as in classical mechanics. Due to the fact that only the square of the modulus of the wave function has physical meaning, the initial values of the wave function cannot be completely found in principle, which leads to the uncertainty of knowledge about the initial state of the quantum system.

…the Heisenberg uncertainty relations… give a connection (inverse proportionality) between the inaccuracies of the fixation of those kinematic and dynamical variables that are admissible in quantum mechanics, which determine the state of a physical system in classical mechanics.

A serious advantage of the Copenhagen interpretation is that it does not use detailed statements about directly physically unobservable quantities and, with a minimum of prerequisites used, builds a system of concepts that exhaustively describe the experimental facts available today.

The meaning of the wave function

The Copenhagen interpretation suggests that two processes can influence the wave function:

unitary evolution according to the Schrödinger equation
measurement process

No one disagrees about the first process, and about the second there are a number of different interpretations, even within the Copenhagen interpretation itself. On the one hand, we can assume that the wave function is a real physical object and that it undergoes collapse during the second process, on the other hand, we can assume that the wave function is only an auxiliary mathematical tool (and not a real entity), the only purpose of which is it gives us the ability to calculate probabilities. Bohr emphasized that the only thing that can be predicted is the results of physical experiments, so additional questions do not belong to science, but to philosophy. Bohr shared the philosophical concept of positivism, which requires that science speak only about really measurable things.

Illustrating this, Einstein wrote to Born: " I'm convinced that God does not roll the dice", - and also exclaimed in a conversation with Abraham Pais:" Do you really think the moon only exists when you look at it?". N. Bohr answered him: "Einstein, don't tell God what to do." Erwin Schrödinger came up with the famous thought experiment about Schrödinger's cat, with which he wanted to show the incompleteness of quantum mechanics in the transition from subatomic to macroscopic systems.

Similarly, the necessary "instantaneous" collapse of the wave function in all space causes problems. Einstein's theory of relativity says that instantaneity, simultaneity, makes sense only for observers who are in the same frame of reference - there is no single time for all, so the instantaneous collapse also remains undefined.

Prevalence among scientists

An informal poll taken in 1997 at a symposium sponsored by UMBC (English)Russian, showed that the once-dominant Copenhagen interpretation was supported by less than half of the participants. In general, the votes of the poll participants were distributed as follows:

Interpretation	Votes cast
Copenhagen interpretation	13
Many Worlds Interpretation	8
Bohm's interpretation	4
Consistent stories (English)Russian	4
Modified Dynamics (GRW (English)Russian)	1
None of the above or found it difficult to answer	18

Alternatives

Many physicists lean towards the so-called "no" interpretation of quantum mechanics, succinctly expressed in David Mermin's aphorism: "Shut up and count!" (orig. English "Shut up and calculate"), often (apparently by mistake) attributed to Richard Feynman or Paul Dirac.

Criticizing this approach, E. M. Chudinov noted that

A specialist working in the field of physics often has the illusion of complete independence of his scientific activity from philosophy. This is due to the fact that he enters the already finished building of scientific theory with its inherent style of scientific thinking, and through the style of scientific thinking perceives certain philosophical principles. These philosophical premises of scientific theory are not always clearly recognized by scientists, but this does not stop them from being philosophical.

F. Engels notes a common misconception among natural scientists:

Natural scientists imagine that they are freed from philosophy when they ignore or scold it. But since they cannot move a single step without thinking, logical categories are necessary for thinking, and they uncritically borrow these categories either from the ordinary general consciousness of the so-called educated people, which is dominated by the remnants of long-dead philosophical systems, or from the crumbs heard in compulsory university courses in philosophy (which are not only fragmentary views, but also a hodgepodge of the views of people belonging to the most diverse and for the most part to the worst schools), or from uncritical and unsystematic reading of all kinds of philosophical works - then in in the end they still find themselves subordinate to philosophy, but, unfortunately, for the most part the worst, and those who most abuse philosophy are slaves of just the worst vulgarized remnants of the worst philosophical doctrines.

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Sources and used literature

Gribbin J. QIS FOR QUANTUM: An Encyclopedia of Particle Physics. - 2000. - S. 4-8. - ISBN 978-0684863153.
Heisenberg V. Development of the interpretation of quantum theory // Niels Bohr and the development of physics / Sat. ed. Pauly W.- M: IL, 1958. - S. 23-45.
Heisenberg V. Memories of the era of development of quantum mechanics // Theoretical physics of the 20th century / Sat. ed. Smorodinsky Ya. A.- M: IL, 1962. - S. 53-59.
, With. 19.
Bohr N. Discussions with Einstein about the problems of the theory of knowledge in atomic physics // Atomic physics and human knowledge - M .: IL, 1961. - p. 60
, With. twenty.
Born M. Statistical interpretation of wave mechanics // Atomic physics - M.: Mir, 1965. - pp. 172-178
Born M. Statistical interpretation of quantum mechanics // Physics in the life of my generation - M.: IL, 1963. - pp. 301-315
Born M. Atomic Physics - M.: Mir, 1965. - p. 125
, With. 226.
Bohr N.// Advances in Physical Sciences, No. 1, 1959
, With. 225.
Einstein A. Physics and reality // Collection of scientific papers, vol. IV. - M., 1966. - p. 223
Tegmark M. (1997), "The Interpretation of Quantum Mechanics: Many Worlds or Many Words?", arΧiv :
N. David Mermin(English) // Physics Today. - 2004. - Fasc. 5 . - P. 10 .
, With. 300.
* Engels F. Dialectics of nature // Sobr. cit., ed. 2, vol. 20. - M .: Politizdat, 1959. - 524 p.

Literature

Heisenberg V. Physics and Philosophy. Part and whole. - M .: Nauka, 1989. - 400 p. - ISBN 5-02-012452-9.
Chudinov E. M. Theory of Relativity and Philosophy. - M .: Politizdat, 1974. - 303 p.
Problems of Physics: Classics and Modernity / ed. G. Trader. - M .: Mir, 1982. - 328 p.

An excerpt characterizing the Copenhagen Interpretation

And Mavra Kuzminishna stood for a long time with wet eyes in front of the closed gate, shaking her head thoughtfully and feeling an unexpected surge of maternal tenderness and pity for the unknown officer.

In the unfinished house on Varvarka, at the bottom of which there was a drinking house, drunken screams and songs were heard. There were about ten factory workers sitting on benches by the tables in a small, dirty room. All of them, drunk, sweaty, with cloudy eyes, tensing up and opening their mouths wide, sang some kind of song. They sang apart, with difficulty, with an effort, obviously not because they wanted to sing, but only to prove that they were drunk and walking. One of them, a tall blond fellow in a clean blue coat, stood over them. His face, with a thin, straight nose, would have been beautiful, if not for thin, pursed, constantly moving lips and cloudy, frowning, motionless eyes. He stood over those who were singing, and, apparently imagining something, solemnly and angularly waved over their heads a white hand rolled up to the elbow, whose dirty fingers he unnaturally tried to spread out. The sleeve of his chuyka was constantly going down, and the fellow diligently rolled it up again with his left hand, as if there was something especially important in the fact that this white sinewy waving arm was always naked. In the middle of the song, shouts of a fight and blows were heard in the hallway and on the porch. The tall fellow waved his hand.
- Sabbat! he shouted commandingly. - Fight, guys! - And he, without ceasing to roll up his sleeve, went out onto the porch.
The factory workers followed him. The factory workers, who were drinking in the tavern that morning, led by a tall fellow, brought leather from the factory to the kisser, and for this they were given wine. The blacksmiths from the neighboring smithies, having heard the revelry in the tavern and believing that the tavern was broken, wanted to break into it by force. A fight broke out on the porch.
The kisser was fighting the blacksmith at the door, and while the factory workers were leaving, the blacksmith broke away from the kisser and fell face down on the pavement.
Another blacksmith rushed through the door, leaning on the kisser with his chest.
The fellow with his sleeve rolled up on the move still hit the blacksmith, who was rushing through the door, in the face and shouted wildly:
- Guys! ours are being beaten!
At this time, the first blacksmith rose from the ground and, scratching the blood on his broken face, shouted in a weeping voice:
- Guard! Killed!.. They killed a man! Brothers!..
- Oh, fathers, killed to death, killed a man! screeched the woman who came out of the next gate. A crowd of people gathered around the bloodied blacksmith.
“It wasn’t enough that you robbed the people, took off your shirts,” said a voice, turning to the kisser, “why did you kill a man? Robber!
The tall fellow, standing on the porch, with cloudy eyes led first to the kisser, then to the blacksmiths, as if thinking with whom he should now fight.
- Soulbreaker! he suddenly shouted at the kisser. - Knit it, guys!
- How, I tied one such and such! the kisser shouted, brushing aside the people who had attacked him, and tearing off his hat, he threw it on the ground. As if this action had some mysteriously menacing significance, the factory workers, who surrounded the kisser, stopped in indecision.
- I know the order, brother, very well. I'll go private. Do you think I won't? No one is ordered to rob anyone! shouted the kisser, raising his hat.
- And let's go, you go! And let's go ... oh you! the kisser and the tall fellow repeated one after another, and together they moved forward along the street. The bloodied blacksmith walked beside them. Factory workers and strangers followed them with a voice and a cry.
At the corner of Maroseyka, opposite a large house with locked shutters, on which there was a sign for a shoemaker, about twenty shoemakers, thin, weary people in dressing gowns and tattered chuikki, stood with sad faces.
"He's got the people right!" said a thin artisan with a thin beard and furrowed brows. - Well, he sucked our blood - and quit. He drove us, drove us - all week. And now he brought it to the last end, and he left.
Seeing the people and the bloody man, the artisan who spoke fell silent, and all the shoemakers joined the moving crowd with hasty curiosity.
- Where are the people going?
- It is known where, to the authorities goes.
- Well, did our strength really not take it?
- How did you think? Look what the people are saying.
There were questions and answers. The kisser, taking advantage of the increase in the crowd, lagged behind the people and returned to his tavern.
The tall fellow, not noticing the disappearance of his enemy the kisser, waving his bare hand, did not stop talking, thus drawing everyone's attention to himself. The people mainly pressed against him, assuming from him to obtain permission from all the questions that occupied them.
- He show the order, show the law, the authorities have been put on that! Is that what I say, Orthodox? said the tall fellow, smiling slightly.
- He thinks, and there are no bosses? Is it possible without a boss? And then rob it is not enough of them.
- What an empty talk! - echoed in the crowd. - Well, they will leave Moscow then! They told you to laugh, and you believed. How many of our troops are coming. So they let him in! For that boss. There, listen to what the people are doing, - they said, pointing to a tall fellow.
At the wall of China Town, another small group of people surrounded a man in a frieze overcoat, holding paper in his hands.
- Decree, decree read! Decree read! - was heard in the crowd, and the people rushed to the reader.
A man in a frieze overcoat was reading a poster dated August 31st. When the crowd surrounded him, he seemed to be embarrassed, but at the demand of the tall fellow who squeezed his way up to him, with a slight trembling in his voice, he began to read the poster from the beginning.
“Tomorrow I’m going early to the most serene prince,” he read (brightening! - solemnly, smiling with his mouth and frowning his eyebrows, repeated the tall fellow), “to talk with him, act and help the troops exterminate the villains; we will also become a spirit from them ... - the reader continued and stopped (“Did you see it?” - the small one shouted triumphantly. - He will unleash the whole distance for you ...”) ... - eradicate and send these guests to hell; I’ll come back for dinner, and we’ll get down to business, we’ll do it, we’ll finish it and finish off the villains. ”
The last words were read by the reader in perfect silence. The tall fellow lowered his head sadly. It was obvious that no one understood these last words. In particular, the words: "I'll arrive tomorrow at dinner," apparently even upset both the reader and the listeners. The understanding of the people was tuned to a high tune, and this was too simple and needlessly understandable; it was the very thing that each of them could have said, and that therefore a decree from a higher authority could not speak.
Everyone stood in gloomy silence. The tall fellow moved his lips and staggered.
“I should have asked him!.. Is that himself?.. Why, he asked! two mounted dragoons.
The police chief, who went that morning on the count's order to burn the barges and, on the occasion of this order, rescued a large sum of money that was in his pocket at that moment, seeing a crowd of people advancing towards him, ordered the coachman to stop.
- What kind of people? he shouted at the people, who were approaching the droshky, scattered and timid. - What kind of people? I'm asking you? repeated the chief of police, who received no answer.
“They, your honor,” said the clerk in a frieze overcoat, “they, your honor, at the announcement of the most illustrious count, not sparing their stomachs, wanted to serve, and not just some kind of rebellion, as it was said from the most illustrious count ...
“The count has not left, he is here, and there will be an order about you,” said the chief of police. – Went! he said to the coachman. The crowd stopped, crowding around those who had heard what the authorities said, and looking at the departing droshky.
The police chief at this time looked around in fright, said something to the coachman, and his horses went faster.
- Cheating, guys! Lead to yourself! shouted the voice of the tall fellow. - Don't let go, guys! Let him submit a report! Hold on! shouted the voices, and the people ran after the droshky.
The crowd behind the police chief with a noisy conversation headed for the Lubyanka.
“Well, gentlemen and merchants have left, and that’s why we’re disappearing?” Well, we are dogs, eh! – was heard more often in the crowd.

On the evening of September 1, after his meeting with Kutuzov, Count Rastopchin, upset and offended that he was not invited to the military council, that Kutuzov did not pay any attention to his proposal to take part in the defense of the capital, and surprised by the new look that opened to him in the camp , in which the question of the calmness of the capital and its patriotic mood turned out to be not only secondary, but completely unnecessary and insignificant - upset, offended and surprised by all this, Count Rostopchin returned to Moscow. After supper, the count, without undressing, lay down on the couch and at one o'clock was awakened by a courier who brought him a letter from Kutuzov. The letter said that since the troops were retreating to the Ryazan road beyond Moscow, would it please the count to send police officials to lead the troops through the city. This news was not news to Rostopchin. Not only from yesterday’s meeting with Kutuzov on Poklonnaya Gora, but also from the Battle of Borodino itself, when all the generals who came to Moscow unanimously said that it was impossible to give another battle, and when, with the permission of the count, state property and up to half of the inhabitants were already taken out every night. we left, - Count Rostopchin knew that Moscow would be abandoned; but nevertheless this news, reported in the form of a simple note with an order from Kutuzov and received at night, during the first dream, surprised and annoyed the count.
Subsequently, explaining his activities during this time, Count Rostopchin wrote several times in his notes that he then had two important goals: De maintenir la tranquillite a Moscou et d "en faire partir les habitants. [Keep calm in Moscow and expel from If we admit this dual purpose, any action of Rostopchin turns out to be irreproachable. Why weren’t the Moscow shrines, weapons, cartridges, gunpowder, grain supplies taken out, why were thousands of residents deceived by the fact that Moscow would not be surrendered, and ruined? in order to keep calm in the capital, answers the explanation of Count Rostopchin. Why were piles of unnecessary papers taken out of government offices and Leppich's ball and other objects? - In order to leave the city empty, the explanation of Count Rostopchin answers. One has only to assume that something threatened people's peace, and every action becomes justified.
All the horrors of terror were based only on concern for the people's peace.
What was the basis of Count Rostopchin's fear of public peace in Moscow in 1812? What reason was there to suppose a tendency to rebellion in the city? Residents were leaving, the troops, retreating, filled Moscow. Why should the people revolt as a result of this?
Not only in Moscow, but throughout Russia, when the enemy entered, there was nothing resembling indignation. On the 1st and 2nd of September, more than ten thousand people remained in Moscow, and, apart from the crowd that had gathered in the courtyard of the commander-in-chief and attracted by him, there was nothing. It is obvious that even less one should have expected unrest among the people if, after the Battle of Borodino, when the abandonment of Moscow became obvious, or at least probably, if then, instead of disturbing the people with the distribution of weapons and posters, Rostopchin took measures to the removal of all sacred things, gunpowder, charges and money, and would directly announce to the people that the city was being abandoned.
Rostopchin, an ardent, sanguine man, who always moved in the highest circles of the administration, although with a patriotic feeling, had not the slightest idea about the people he thought to rule. From the very beginning of the enemy's entry into Smolensk, Rastopchin in his imagination formed for himself the role of the leader of the people's feelings - the heart of Russia. It not only seemed to him (as it seems to every administrator) that he controlled the external actions of the inhabitants of Moscow, but it seemed to him that he directed their mood through his appeals and posters, written in that jarring language, which in its midst despises the people and whom he does not understands when he hears it from above. Rastopchin liked the beautiful role of the leader of popular feeling so much, he got used to it so much that the need to get out of this role, the need to leave Moscow without any heroic effect took him by surprise, and he suddenly lost the ground on which he stood from under his feet, in resolutely did not know what to do. Although he knew, he did not believe with all his heart until the last minute in leaving Moscow and did nothing to this end. Residents moved out against his will. If government offices were taken out, then only at the request of officials, with whom the count reluctantly agreed. He himself was busy only with the role that he had made for himself. As is often the case with people endowed with ardent imagination, he had known for a long time that Moscow would be abandoned, but he knew only by reasoning, but he did not believe in it with all his heart, he was not transported by his imagination to this new position.
All his activity, diligent and energetic (how useful it was and reflected on the people is another question), all his activity was aimed only at arousing in the inhabitants the feeling that he himself experienced - patriotic hatred for the French and confidence in itself.
But when the event took on its real, historical dimensions, when it turned out to be insufficient to express one’s hatred for the French in words alone, when it was impossible even to express this hatred in a battle, when self-confidence turned out to be useless in relation to one question of Moscow, when the entire population, as one person , throwing their property, flowed out of Moscow, showing by this negative action the full strength of their popular feeling - then the role chosen by Rostopchin suddenly turned out to be meaningless. He suddenly felt lonely, weak and ridiculous, without ground under his feet.
Upon awakening from sleep, having received a cold and commanding note from Kutuzov, Rostopchin felt the more annoyed the more he felt guilty. In Moscow, everything that was exactly entrusted to him remained, everything that was state-owned that he was supposed to take out. It was not possible to take everything out.
“Who is to blame for this, who allowed this to happen? he thought. “Of course not me. I had everything ready, I held Moscow like this! And here's what they've done! Bastards, traitors!” - he thought, not properly defining who these scoundrels and traitors were, but feeling the need to hate these traitors, who were to blame for the false and ridiculous position in which he was.
All that night, Count Rastopchin gave orders, for which people from all parts of Moscow came to him. Those close to him had never seen the count so gloomy and irritated.
“Your Excellency, they came from the patrimonial department, from the director for orders ... From the consistory, from the senate, from the university, from the orphanage, the vicar sent ... asks ... About the fire brigade, what do you order? A warden from a prison... a warden from a yellow house...” - they reported to the count all night without ceasing.
To all these questions, the count gave short and angry answers, showing that his orders were no longer needed, that all the work he had diligently prepared was now spoiled by someone and that this someone would bear full responsibility for everything that would happen now.
“Well, tell this fool,” he replied to a request from the patrimonial department, “to stay on guard for his papers. What are you asking nonsense about the fire brigade? There are horses - let them go to Vladimir. Don't leave the French.
- Your Excellency, the warden from the lunatic asylum has arrived, as you order?
- How do I order? Let everyone go, that's all ... And release the crazy in the city. When we have crazy armies in command, this is what God ordered.
When asked about the stocks who were sitting in the pit, the count angrily shouted at the caretaker:
“Well, shall I give you two battalions of an escort, which is not there?” Let them go and that's it!
- Your Excellency, there are political ones: Meshkov, Vereshchagin.
- Vereshchagin! Hasn't he been hanged yet? shouted Rostopchin. - Bring him to me.

By nine o'clock in the morning, when the troops had already moved through Moscow, no one else came to ask the count's orders. All those who could ride rode by themselves; those who remained decided for themselves what they had to do.
The count ordered the horses to be brought in to go to Sokolniki, and, frowning, yellow and silent, he sat with his hands folded in his office.
In a calm, not turbulent time, it seems to each administrator that it is only through his efforts that the entire population under his control is moving, and in this consciousness of his necessity, each administrator feels the main reward for his labors and efforts. It is clear that as long as the historical sea is calm, it should seem to the ruler-administrator, with his fragile boat resting against the ship of the people with his pole and moving himself, that the ship against which he rests is moving with his efforts. But as soon as a storm rises, the sea is agitated and the ship itself moves, then delusion is impossible. The ship moves on its own huge, independent course, the pole does not reach the moving ship, and the ruler suddenly passes from the position of a ruler, a source of strength, into an insignificant, useless and weak person.

The most important thing about the quantum principle is that it

destroys the idea of a world "existing outside" when

the observer is separated from his object by a flat glass

screen. To describe what is happening

you need to cross out the word "observer" and write

“participant". In some unforeseen sense

our universe is a participating universe.

J. Wheeler

Natural science does not simply describe and explain nature;

it is part of our interaction with it.

W. Heisenberg

The starting point of the Copenhagen interpretation is the division of the physical world into an observable system, an object: an atom, a subatomic particle, an atomic process, and an observing system: experimental equipment and observers. Here a paradox arises: observable systems are not described using the language of classical physics. Until now, there is no generally accepted language model that would correspond to quantum theory, although the mathematical model has been subjected to experimental verification many times (Heisenberg 1989: 19; Capra 1994: 110).

Quantum theory describes observable systems probabilistically . This means that we can never say exactly where the particle is, how this or that atomic process occurs when the particle decays. A probability function is calculated that describes not the course of events itself, but a trend, the possibility of an event. The statistical formulations of the laws of atomic physics do not reflect our ignorance, probability should be taken as a fundamental property of the microcosm (Heisenberg 1989: 19-20; Capra 1994: 111-112).

The explanation of quantum paradoxes was based on W. Heisenberg's uncertainty principle . Physicists repeated: the trajectory of an electron in a cloud chamber can be observed. However, it was not it that was actually observed, but discrete traces of inaccurately determined positions of the electron. After all, only individual droplets of water are visible in the cloud chamber, which are much more extended than an electron. Therefore, the correct question should be: is it possible in quantum mechanics exactly describe the behavior of an electron?

One can speak, as in Newtonian mechanics, about the coordinate and velocity of an electron. These quantities can be both observed and measured. But it is impossible to measure both these quantities simultaneously with any accuracy. It is impossible to accurately describe the behavior of an electron, it is impossible to simultaneously measure the exact values of two parameters of any microparticle .

Checking a colossal number of experiments to measure various parameters of microparticles revealed uncertainty. The uncertainty in the particle's position multiplied by the uncertainty in its momentum (speed times mass) cannot be less than Planck's constant divided by the mass of the particle. This number does not depend on the experiment and on the particle, but is a fundamental property of the world.

Δq(Е) Δр(t) ≥ h/m, where:

Δ – increment of values; q – momentum (V(velocity) m(mass)); E - energy;

p is the position of the particle; t – Вр; h is Planck's constant, equal to 6.62·10 -27.

It is impossible to simultaneously measure the parameters of a microparticle, but it is possible to indicate the probability that at a certain next moment the electron will be found at a certain point in the cloud chamber. A probabilistic model of the location of the electron in various regions of the atom is created (Capra 1994: 112-113).

In a thought experiment, W. Heisenberg showed that reality in the microcosm differs depending on whether we observe it or not. In principle, it is possible to observe an electron in its orbit, for this you need a microscope with a high resolving power. However, such a resolving power cannot be obtained in a microscope using ordinary light. For this purpose, a microscope using γ-rays with a wavelength smaller than the size of an atom will be suitable. During the observation process, at least one γ-ray quantum will pass through the microscope and collide with an electron, which will change its momentum and speed.

The event must be limited to observation. The result of the observation cannot be predicted, the probability is predicted (not a certain event, but an ensemble of possible events). A subjective element is introduced into the description of atomic processes, since the measuring device is created by the observer. We must remember that what we observe is not nature itself, but nature that appears as it is revealed through our way of asking questions.

Inside the atom, matter does not exist in certain places, but rather "can exist." Atomic phenomena do not occur in certain places, but rather “may occur”. The language of formal mathematics of quantum theory calls these possibilities probabilities and associates them with mathematical quantities appearing as waves. In fact, we can't talk about particles at all. It is expedient in many experiments to talk about waves of matter, about a standing wave around the nucleus. But these are not true three-dimensional waves, like waves on the surface of water, for example. These are probabilistic waves - abstract mathematical quantities expressing the probabilities of the existence of particles at certain points Pr at certain moments Bp. All laws of atomic physics are expressed in terms of these probabilities. We can never be sure about an atomic event, we can only say how likely it is to happen (Heisenberg 1989: 22-27; Bome 1990; Capra 1994: 59-60).

Another way to resolve the contradictions of quantum phenomena was associated with Bohr's complementarity principle. Schrödinger's picture of matter waves and the corpuscular picture contain a grain of truth. N. Bohr, based on the principle of uncertainty, resolved the corpuscular-wave paradox. According to the uncertainty principle 2, the characteristics of a particle in one experiment cannot be observed simultaneously,  , there are additional languages for describing one reality, each can only be partially true.

An electron in an atom is a wave of matter (L. de Broglie), but an electron flies out of an atom and is located somewhere, manifests itself as a particle. N. Bohr advised using both pictures as complementary, they exclude each other (at the same time, the same thing cannot be both a wave and a particle), but they also complement each other: an open recognition of the need for metaphorical thinking in science (V.V. Nalimov).

A. Einstein was not ready to recognize the fundamentally statistical nature of the new theory and did not want to admit the impossibility of knowing all the defining moments necessary for the complete determination of the processes under consideration - God does not play dice (Kuznetsov 1968, 1968; Heisenberg 1989: 203-207).

In 1982, in Paris, A. Aspek conducted a series of experiments to simultaneously measure the direction of polarization of 2 photons emitted by one atom and moving in opposite directions. The results left no doubt: Einstein was wrong, quantum uncertainty cannot be bypassed. Despite this, quantum mechanics underlies modern science and technology, at the heart of the operation of semiconductor and integrated circuits that are included in televisions, computers (Davis 1989:53-54; Hawking 1990:54).

Quantum theory has radically changed our understanding of reality.

First, it has been proven unity of object and subject . In atomic physics, a scientist cannot play the role of an outside observer, he is a part of the world he observes to such an extent that he himself influences the properties of the observed objects.

Atomic phenomena represent a more complex reality than that encountered in classical macroscopic physics. The sensitivity of the object to the intervention of devices demonstrates properties that are not observed in objects of macroscopic studies. This means that the description of the object cannot be considered, as before, “separated” from the process of observation.

At the atomic level, objects can only be understood in terms of the interaction between the processes of preparation and observation. Consciousness will always be the final link in the chain. Measurements are such interactions that give rise to certain sensations in the mind: the visual sensation of a flash of light or a dark spot on a photographic plate. The laws of atomic physics tell us how likely a micro-object will produce a certain sensation if we allow it to interact with us. A human observer is needed not only to observe the properties of an object, but also to define those properties themselves. V.V. Nalimov cites the statements of physicists about the impossibility of opposing consciousness to matter (Weisskopf 1977: 39-40; Boum 1990; Capra 1994: 60,118-119; Nalimov 1993: 36-37).

Secondly, the old idea about interconnections of all natural phenomena. The main opponent of the Copenhagen interpretation was A. Einstein, later his student D. Bohm. But they also recognized one of the main conclusions of quantum theory: the indivisible quantum unity of the entire universe is the most fundamental reality. Trying to combine quantum theory and the theory of relativity, Bohm came to the conclusion that the unity of knowledge is not in science, but in philosophy. Scientific interpretations lead to the "fragmentation" of reality, which is integral and indivisible. In any experiment, integrity is violated. The great discovery of quantum physics was the discovery of individual quantum states, each of which is an indivisible whole, until exposed to the means of observation.

Thirdly, the classical, stereotypical, unambiguous perception has been replaced by probabilistic vision of the world . What is deduced from experiments is a probability function that describes not a certain event, but a set of possible events: the transition possibility-reality takes place during the observation.

Fourth, quantum theory brought not only the idea of uncertainty, but also the idea quantization , identity, identity, accuracy objects , definitions of natural substances. In classical physics, all properties are continuous (there are no two classical systems that would be the same; out of billions of planetary systems of stars, there are no two absolutely identical). The behavior of objects depends on the initial conditions, which can take on a continuous series of values. Atomic phenomena, on the other hand, have definite forms, in contrast to the arbitrarily changing forms in classical mechanics. Within classical physics, it's hard to understand why there aren't electrons with a slightly lower charge, or with a different mass?

In quantum theory, objects are quantized, not any orbits are possible, but certain ones. The identity of atoms of one chemical element, their high mechanical stability are due to the wave nature of electrons. Standing waves can have a limited number of shapes. Two Fe or O atoms are identical, since their electron orbits are quantized, the outlines of the electron orbits are the same, and the distance between them is the same.

In classical physics - an unlimited number of options, there is no explanation for the certainty of matter. But certainty exists only up to a certain threshold, there are threshold energy levels above which atoms are destroyed, there is a threshold above which the nucleus also shatters into pieces.

And finally opened complex world of subatomic and virtual particles . Quantum theory proves the falsity of classical ideas about solids and impenetrable, mobile microparticles. I. Newton believed: atoms do not wear out, do not break into pieces, there is no force that can separate them. It turns out that atoms can be broken down into more “elementary” components. But until now, the Copenhagen interpretation of quantum theory is not generally accepted due to the denial of the possibility of an ontological interpretation of the phenomena of the microworld. Alternative explanations for the behavior of microparticles have also been put forward (Weisskopf 1977: 36-48; Heisenberg 1989:23-25; Nalimov, Drogalina 1995:16-27; Boum 1990; Bohm 1993: 7; Capra 1994: 62-63, 113-117 ).

Quantum mechanics is so non-intuitive that several "interpretations" have been devised in terms that our brains can more easily visualize. The classic is the Copenhagen Interpretation, handed down to us by the founding fathers: Werner Heisenberg, Wolfgang Pauli, Paul Dirac, Niels Bohr and others.

The main ideas of the Copenhagen Interpretation are quite simple, but at the same time abstract:

The wave function () follows a unitary time evolution described by .
The physical meaning of the wave function is probability amplitude, the square of which is the probability of detecting the system when measured in a certain state. When measured, the function "collapses", that is, it is concentrated at a point corresponding to the measurement result. All other information about the original function is lost.

There is no dispute about the first point. Unitary evolution is the most unshakable fundamental physical principle at the moment, which is not going to be abandoned in the near future. But on the second point, the disagreements still do not subside. Partly because point 2 contradicts point 1. Wave function collapse is not a unitary operation! It does not obey the Schrödinger equation. It would seem that the paradox and inconsistency of the quantum theory itself is obvious.

There is one subtle point here. As the Founding Fathers showed us, the role of the observer in quantum mechanics is extremely important. Quantum mechanics is subjective. It gives out all its predictions regarding the observer - the subject who uses it. Experimenter. You and me Let's explain with an example. Imagine that you have flipped a coin and are now going to see the result.

Before you raise your hand, the outcome can only be estimated using a probability distribution. If the coin is fair, then with a probability of 50% it will fall heads and with 50% tails. That's about all you can say about the system for now. But as soon as you raise your hand and see the result, the probability distribution "collapses" into one point - into the result that really fell out. That is, now you can say with 100% probability that heads have fallen.

This "collapse" is also valid for more complex probability distributions. For example, if you roll two dice and look at the probability of getting one or another number (the sum of the number rolled on the first and second dice is from 2 to 12), we get a Gaussian distribution (seven is most likely to come up). But when we really look at what fell out in a particular case, this distribution collapses into the actual result (let's say the number six fell out in total).

Quantum mechanics can be viewed as a generalization of probability theory, in the same way that complex numbers are a generalization of real numbers. The wave function is conditionally a kind of "square root" of the probability distribution function. In order to find the probability, the wave function must be squared. Moreover, it is complex. The probability amplitude is generally a complex number. Otherwise, the idea of "collapse" as the acquisition of new knowledge about the system and the irrelevance of previous information remains the same.

Let's take a qubit located in:

\(\displaystyle |\psi\rangle=\frac(1)(\sqrt(2))|0\rangle+\frac(1)(\sqrt(2))|1\rangle\)

When measuring, the state vector collapses and we get only one of the two terms. Either when measuring we get zero and the state vector collapses into \(\displaystyle |\psi\rangle\rightarrow |0\rangle\), or one and the vector goes into \(\displaystyle |\psi\rangle\rightarrow |1\rangle \).

The difference from classical probability theory is also that with a coin, we subconsciously know that it is already either heads or tails before we raise our hand to look at the result. In the case of quantum objects. The system acquires classical properties (characteristics) precisely at the moment of subjective measurement. It cannot be assumed that the qubit was in the \(\displaystyle |0\rangle\) or \(\displaystyle |1\rangle\) state before the measurement. He was exactly in superposition. But this superposition unobservable. Therefore the word was can only be applied conditionally. The state vector is not an objective reality, just as the probability distribution function is not in the classical case.

This is the resolution of the paradox and other so-called "paradoxes" in the framework of the Copenhagen interpretation - the cat is not alive a plus dead. It's like saying eagle a plus tails, interpreting the above distribution function.

Cat or alive or dead. We will not find anything else in the measurement. It's just that quantum mechanics forbids us to implicitly draw any conclusions before the actual measurement and describes the system as a superposition. What cannot be measured does not exist. What can be measured, but not yet measured, also does not exist objectively.

Entangled states, which so worried Einstein, are also interpreted from probabilistic positions as quantum correlations. Let the system of two spins be in :

\(\displaystyle |S\rangle=\frac(1)(\sqrt(2))(|\uparrow\downarrow\rangle-|\downarrow\uparrow\rangle)\)

When measuring, we will always find correlations: if one particle is directed upwards relative to any axis, then the spin of the second particle will necessarily be directed downwards relative to the same axis. And vice versa. We can again draw an analogy with classical probability theory. Take the red and blue pills. We mix them behind our backs and squeeze one in each fist. Without unclenching our hands, we cannot tell where the blue is and where the red is. You can build a probability distribution graph similar to that given for a coin.

But as soon as we open one fist and see that there, for example, is blue, we instantly recognize that the other fist is red. And vice versa. This acquisition of information collapses the above state vector into one of the summands. Tablets can be spaced to different ends of the Universe and still the statistical correlations will remain. It is obvious that we are not talking about the superluminal speed of information transfer, simple correlations.

The only new thing in the quantum mechanical case is the impossibility of assuming that in the right hand was blue and red on the left before measurement. or most clearly explain it. Exactly measurement given observer of some property (color in our case) makes it real (objective) for this observer.

Quantum mechanics is subjective. It gives predictions only to those who use it. Only for him there is a subjective collapse of the state vector associated with the receipt of new information. The objective world exists only in his head. For everyone else, he is the same part of the physical world and obeys the same quantum mechanical laws with superpositions, complex numbers and things like that. is a clear demonstration of this principle.

The wave function (state vector) is unobservable. This is not a classical field like temperature or electric field strength. This function is rather closer to the probability distribution function, more precisely, it can be considered as some kind of its generalization. Quantum mechanics itself can be seen as a generalization of information theory + probability theory.

Copenhagen interpretation of quantum theory

W. Heisenberg

The Copenhagen interpretation of quantum theory begins with a paradox. Every physical experiment, whether it relates to the phenomena of everyday life or to the phenomena of atomic physics, must be described in terms of classical physics. The concepts of classical physics form the language by which we describe our experiments and results. We cannot replace these concepts with anything else, and their applicability is limited by the uncertainty relation. We must keep in mind the limited applicability of classical concepts, and not try to go beyond this limitation. And in order to better understand this paradox, it is necessary to compare the interpretation of experience in classical and quantum physics.

For example, in Newtonian celestial mechanics, we start by determining the position and velocity of the planet whose motion we are going to study. The results of the observation are translated into mathematical language due to the fact that the values of the coordinates and momentum of the planet are derived from the observations. Then, from the equation of motion, using these numerical values of the coordinates and momentum for a given moment of time, the values of the coordinates or any other properties of the system for subsequent moments of time are obtained. In this way the astronomer predicts the motion of the system. For example, it can predict the exact time of a solar eclipse.

In quantum theory, things are different. Suppose we are interested in the motion of an electron in a cloud chamber, and through some observation we have determined the coordinates and speed of the electron. However, this definition may not be precise. It contains at least inaccuracies due to the uncertainty relation, and probably, in addition, will contain even greater inaccuracies due to the difficulty of the experiment. The first group of inaccuracies makes it possible to translate the result of observation into the mathematical scheme of quantum theory. The probability function describing the experimental situation at the moment of measurement is recorded taking into account possible measurement inaccuracies. This probability function is a combination of two different elements: on the one hand, the fact, on the other hand, the degree of our knowledge of the fact. This function characterizes the actually reliable, since it assigns a probability equal to one to the initial situation. It is reliable that the electron at the observed point moves with the observed speed. "Observable" here means -- observable within the limits of experimental accuracy. This function characterizes the degree of accuracy of our knowledge, since another observer, perhaps, would determine the position of the electron even more accurately. At least to some extent, experimental error or experimental inaccuracy is seen not as a property of electrons, but as a flaw in our knowledge of the electron. This lack of knowledge is also expressed using a probability function.

In classical physics, observational errors are also taken into account in the process of exact investigation. As a result, a probability distribution for the initial values of coordinates and velocities is obtained, and this has some similarities with the probability function of quantum mechanics. However, there is no specific inaccuracy due to the uncertainty relation in classical physics.

If in quantum theory the probability function for the initial moment is determined from observational data, then it is possible to calculate the probability function for any subsequent moment of time based on the laws of this theory. Thus, it is possible to determine in advance the probability that the value, when measured, will have a certain value. For example, you can specify the probability that at a certain subsequent time the electron will be found at a certain point in the cloud chamber. It should be emphasized that the probability function does not describe the course of events in time itself. It characterizes the trend of an event, the possibility of an event, or our knowledge of an event. The probability function is associated with reality only when one essential condition is met: in order to identify a certain property of the system, it is necessary to make new observations or measurements. Only in this case, the probability function allows you to calculate the probable result of the new measurement. Here again, the measurement result is given in terms of classical physics. Therefore, the theoretical interpretation includes three different stages. First, the initial experimental situation is translated into a probability function. Secondly, the change of this function over time is established. Thirdly, a new measurement is made, and its expected result is then determined from the probability function. For the first stage, a necessary condition is the feasibility of the uncertainty relation. The second stage cannot be described in terms of classical physics; one cannot specify what happens to the system between the initial measurement and subsequent ones. Only the third stage makes it possible to move from the possible to the actual.

We will explain these three steps with a simple thought experiment. It has already been noted that an atom consists of an atomic nucleus and electrons that move around the nucleus. It has also been found that the notion of an electron orbit is in some sense dubious. However, contrary to the last statement, it can be said that, at least in principle, it is possible to observe an electron in its orbit. Perhaps we would have seen the movement of an electron in orbit if we could observe an atom in a microscope with a high resolution. However, such a resolving power cannot be obtained in a microscope using ordinary light, since only a microscope using r-rays, with a wavelength smaller than the size of an atom, will be suitable for this purpose. Such a microscope has not yet been created, but technical difficulties should not deter us from discussing this thought experiment. Is it possible at the first stage to convert the results of observation into a probability function? This is possible if the uncertainty relation is satisfied after the experiment. The position of the electron is known with an accuracy determined by the wavelength of the r-rays. Let us assume that before the observation the electron is practically at rest. In the process of observation, at least one z-ray quantum will necessarily pass through the microscope and, as a result of a collision with an electron, change the direction of its motion. Therefore, the electron will also be affected by the quantum. This will change its momentum and its speed. It can be shown that the uncertainty of this change is such that the validity of the uncertainty relation after impact is guaranteed. Therefore, the first step does not contain any difficulties. At the same time, it can be easily shown that it is impossible to observe the movement of electrons around the nucleus. The second stage - a quantitative calculation of the probability function - shows that the wave packet does not move around the nucleus, but away from the nucleus, since the first light quantum already knocks the electron out of the atom. The momentum of the r-quantum is much greater than the initial momentum of the electron, provided that the wavelength of the r-rays is much smaller than the dimensions of the atom. Therefore, the first light quantum is already enough to knock an electron out of an atom. Therefore, one can never observe more than one point in the trajectory of an electron; therefore, the statement that there is no, in the usual sense, the trajectory of the electron, does not contradict experience. The next observation, the third stage, detects the electron as it flies out of the atom. It is impossible to visually describe what happens between two successive observations. Of course, one could say that the electron must be somewhere between the two observations and that it seems to be describing some semblance of a trajectory, even if it is impossible to establish this trajectory. Such reasoning makes sense from the point of view of classical physics. In quantum theory, such reasoning is an unjustified abuse of language. For the present, we can leave open the question of whether this sentence refers to the form of the statement about atomic processes or the processes themselves, that is, whether it refers to epistemology or ontology. In any case, when formulating propositions relating to the behavior of atomic particles, we must be extremely careful.

In fact, we can't talk about particles at all. It is expedient in many experiments to talk about waves of matter, for example, about a standing wave around a nucleus. Such a description would, of course, contradict another description if the limits set by the uncertainty relation are not taken into account. This restriction eliminates the contradiction. Applying the concept of "matter wave" is advisable in the case when we are talking about the radiation of an atom. Radiation, having a certain frequency and intensity, gives us information about the changing distribution of charges in the atom; in this case, the wave pattern is closer to the truth than the corpuscular one. Therefore, Bohr advised using both pictures. He called them complementary. Both pictures, of course, exclude each other, since a certain object cannot be both a particle (that is, a substance limited in a small volume) and a wave (that is, a field propagating in a large volume) at the same time. But both pictures complement each other. If we use both pictures, going from one to the other and back again, then in the end we get the correct idea of \u200b\u200bthe remarkable kind of reality that lies behind our experiments with atoms.

Bohr uses the notion of complementarity in interpreting quantum theory in various aspects. Knowing the position of a particle is in addition to knowing its velocity or momentum. If we know some quantity with great accuracy, then we cannot determine another (additional) quantity with the same accuracy without losing the accuracy of the first knowledge. But in order to describe the behavior of the system, you need to know both quantities. Spatio-temporal description of atomic processes in addition to their causal or deterministic description. Like the coordinate function in Newtonian mechanics, the probability function satisfies the equation of motion. Its change over time is completely determined by quantum mechanical equations, but it does not give any spatiotemporal description of the system. On the other hand, observation requires a space-time description. However, observation, by changing our knowledge of the system, changes the theoretically calculated behavior of the probability function.

In general, the dualism between two different descriptions of the same reality is no longer regarded as a fundamental difficulty, since it is known from the mathematical formulation of the theory that the theory does not contain contradictions. The dualism of both additional pictures is clearly revealed in the flexibility of mathematical formalism. Usually this formalism is written in such a way that it is similar to Newtonian mechanics with its equations of motion for the coordinates and velocities of particles. By a simple transformation, this formalism can be represented by a wave equation for three-dimensional waves of matter, only these waves have the character not of simple field quantities, but of matrices or operators. This explains that the possibility of using various additional pictures has its analogy in various transformations of mathematical formalism and is not associated with any difficulties in the Copenhagen interpretation. Difficulties in understanding the Copenhagen interpretation always arise when the well-known question is asked: what actually happens in the atomic process? First of all, as mentioned above, the measurement and the result of observation are always described in terms of classical physics. What is inferred from observation is a probability function. It is the mathematical expression that statements about possibility and tendency are combined with statements about our knowledge of the fact. Therefore, we cannot fully determine the result of the observation. We are unable to describe what happens between this observation and the next. First of all, it looks as if we have introduced a subjective element into the theory, that we are saying that what happens depends on how we observe it, or at least depends on the very fact that we observe it happening. Before dealing with this objection, it is necessary to clarify exactly why such difficulties are encountered when trying to describe what happens between two successive observations. In this regard, it is advisable to discuss the following thought experiment. Suppose a point source of monochromatic light is emitting light onto a black screen that has two small holes. The diameter of the hole is comparable to the wavelength of light, and the distance between the holes is much greater than the wavelength of light. At some distance behind the screen, the transmitted light falls on the photographic plate. If this experiment is described in terms of a wave pattern, then we can say that the primary wave passes through both holes. Consequently, two secondary spherical waves are formed, which, originating at the holes, interfere with each other. The interference will produce bands of strong and weak intensity on the photographic plate - the so-called interference fringes. The blackening on the plate is a chemical process caused by individual light quanta.

Therefore, it is also important to describe the experiment in terms of ideas about light quanta. If it were possible to talk about what happens to an individual light quantum in the interval between its exit from the source and hitting the photographic plate, then one could argue as follows. A separate light quantum can pass either only through the first or only through the second hole. If it has passed through the first hole, then the probability of it hitting a certain point on the photographic plate does not depend on whether the second hole is closed or open. The probability distribution on the plate will be such that only the first hole is open. If the experiment is repeated many times and covers all cases in which the light quantum passed through the first hole, then the blackening on the plate should correspond to this probability distribution. If we consider only those light quanta that have passed through the second hole, then the blackening will correspond to the probability distribution derived from the assumption that only the second hole is open. Therefore, the total blackening should be the exact sum of both blackenings, in other words, there should be no interference pattern. But we know that the experiment gives an interference pattern. Therefore, the assertion that a light quantum passes through either the first or the second hole is doubtful and leads to contradictions. This example shows that the concept of a probability function does not give a spatiotemporal description of an event occurring between two observations. Every attempt to find such a description leads to contradictions. This means that already the concept of "event" should be limited to observation. This conclusion is significant because it seems to show that observation plays a decisive role in an atomic event and that reality differs depending on whether we observe it or not. To make this statement clearer, let us analyze the process of observation.

It is appropriate to recall that in natural science we are not interested in the Universe as a whole, including ourselves, but only in a certain part of it, which we make the object of our study. In atomic physics, usually this side is an extremely small object, namely atomic particles or groups of such particles. But it's not even about size; what is essential is that most of the Universe, including ourselves, does not belong to the subject of observation. The theoretical interpretation of the experiment begins at the level of both stages, which have already been mentioned. At the first stage, a description of the experiment is given in terms of classical physics. This description is eventually associated at this stage with the first observation, and then the description is formulated using a probability function. The probability function is subject to the laws of quantum mechanics, its change over time is continuous and is calculated using the initial conditions. This is the second stage. The probability function combines objective and subjective elements. It contains statements about probability, or rather, about a tendency (potentiality in Aristotelian philosophy), and these statements are completely objective. They do not depend on any observation. In addition, the probability function contains statements about our knowledge of the system, which is subjective because it can be different for different observers. In favorable cases, the subjective element of the probability function becomes negligibly small in comparison with the objective element, then one speaks of a "pure case".

When referring to the next observation, the result of which is predicted from the theory, it is important to find out whether the object was before or at least at the time of observation in interaction with the rest of the world, for example, with an experimental setup, with a measuring device, etc. This means that the equation of motion for the probability function contains the interaction effect exerted on the system by the measuring device. This influence introduces a new element of uncertainty, since the measuring device is described in terms of classical physics. Such a description contains all the inaccuracies regarding the microscopic structure of the device, known to us from thermodynamics. In addition, since the device is connected to the rest of the world, the description actually contains inaccuracies regarding the microscopic structure of the entire world. These inaccuracies can be considered objective, because they are a simple consequence of the fact that the experiment is described in terms of classical physics, and because they do not depend in detail on the observer. They can be considered subjective because they point to our incomplete knowledge of the world. After an interaction has taken place, even if it is a "pure case", the probability function will contain an objective element of tendency or possibility and a subjective element of incomplete knowledge. It is for this reason that the result of the observation as a whole cannot be accurately predicted. Only the probability of a particular outcome of an observation is predicted, and this probability statement can be tested by repeating the experiment many times. The probability function, in contrast to the mathematical scheme of Newtonian mechanics, describes not a specific event, but, at least in the process of observation, the entire set (ensemble) of possible events. The observation itself will discontinuously change the probability function: it selects from all possible events the one that actually happened. Since our knowledge changes discontinuously under the influence of observation, the quantities included in its mathematical representation also change discontinuously, and therefore we speak of a "quantum jump". If anyone tries to build a critique of quantum theory on the basis of the old saying, "Natura non facit saltus", the answer to this can be given, that our knowledge undoubtedly changes discontinuously. It is this fact - the discontinuous change in our knowledge - that justifies the use of the term "quantum leap". Consequently, the transition from possibility to reality takes place in the process of observation. If we are to describe what happens in some atomic event, then we must assume that the word "occurs" refers only to the observation itself, and not to the situation between two observations. At the same time, it means not a psychological, but a physical process of observation, and we have the right to say that the transition from possibility to reality took place as soon as the object interacted with the measuring device, and with the help of the device, with the rest of the world. This transition is not connected with the registration of the result of observation in the mind of the observer. However, the discontinuous change of the probability function is due to the act of registration, since in this case the question concerns the discontinuous change of our knowledge. The latter at the time of observation is reflected by a discontinuous change in the probability function. To what extent have we finally arrived at an objective description of the world and especially of atomic phenomena? Classical physics was based on the assumption - or, one might say, on the illusion - that it is possible to describe the world, or at least part of the world, without talking about ourselves. Indeed, to a large extent it was possible. For example, we know that the city of London exists whether we see it or not. We can say that classical physics gives precisely the idealization of the world, with the help of which one can talk about the world or about its part, while not taking into account ourselves. Its success led to the universal ideal of an objective description of the world. Objectivity has long been the highest criterion for the value of scientific discoveries. Does the Copenhagen interpretation of quantum theory correspond to this ideal? In all probability we are justified in saying that, as far as possible, quantum theory conforms to this ideal. To be sure, quantum theory does not contain any truly subjective features, and it does not at all consider the mind or consciousness of the physicist as part of the atomic event. But she starts by dividing the world into objects and the rest of the world, and by assuming that this rest of the world is described in terms of classical physics. The division itself is somewhat arbitrary. But historically it is a direct consequence of the scientific method of past centuries. The application of classical concepts is, therefore, ultimately the result of the general spiritual development of mankind. In a way, this affects us ourselves, and therefore our description cannot be called completely objective.

It was said at the outset that the Copenhagen interpretation of quantum theory begins with a paradox. It proceeds, on the one hand, from the position that we must describe experiments in terms of classical physics, and, on the other hand, from the recognition that these concepts do not exactly correspond to nature. The inconsistency of these initial positions determines the statistical nature of quantum theory. Because of this, it was proposed to abandon the classical concepts altogether, apparently hoping that a radical change in the concepts describing the experiment would lead to a non-statistical, completely objective description of nature. However, these considerations are based on a misunderstanding. The concepts of classical physics are refined concepts of our everyday life and form the most important component of the language, which is the prerequisite for all natural science. Our actual position in natural science is such that we actually use or should use classical concepts to describe an experiment. Otherwise, we will not understand each other. The task of quantum theory is precisely to explain the experiment on this basis. It makes no sense to interpret what could be done if we were of a different nature from what we really are. In this regard, we must clearly understand, in the words of Weizsacker, that "nature was before man, but man was before natural science." The first half of the statement justifies classical physics with its ideals of complete objectivity. The second half explains why we cannot free ourselves from the paradoxes of quantum theory and from the need to apply classical concepts. At the same time, several remarks should be made about the actual method of the quantum-theoretical interpretation of atomic events. Earlier it was noted that we are always faced with the need to divide the world into objects to be studied, and the rest of the world, including ourselves. This division is somewhat arbitrary. However, this should not lead to a difference in the final results. For example, let's combine a measuring device or part of it with an object and apply the law of quantum theory to this more complex object. It can be shown that such a modification of the theoretical approach does not actually change the prediction about the result of the experiment. This mathematically follows from the fact that the laws of quantum theory for phenomena in which Planck's constant is considered to be a very small value are almost identical to the classical laws. However, it would be a mistake to assume that such an application of the laws of quantum theory can eliminate fundamental paradoxes.

Only then is the measuring device worthy of its purpose when it is in close connection with the rest of the world, when there is a physical interaction between the measuring device and the observer. Therefore, the inaccuracy regarding the microscopic behavior of the world, just as in the case of the first interpretation, penetrates into the quantum mechanical description of the world. If the measuring device were isolated from the rest of the world, it could not be described in terms of classical physics.

On this occasion, Bohr argued that, in all likelihood, it would be more correct to say differently, namely: the division of the world into objects and the rest of the world is not arbitrary. In the study of atomic processes, our goal is to understand certain phenomena and to establish how they follow from general laws. Therefore, the part of matter and radiation that takes part in the phenomenon is a natural subject of theoretical interpretation and must be separated from the device used. Thus, a subjective element is again introduced into the description of atomic processes, since the measuring instrument is created by the observer. We must remember that what we observe is not nature itself, but nature that appears as it is revealed by our way of asking questions. The scientific work of physics is to ask questions about nature in the language we use and try to get the answer in an experiment done with the means at our disposal. At the same time, Bohr's words about quantum theory are recalled: if one is looking for harmony in life, then one should never forget that in the game of life we are both spectators and participants at the same time. It is clear that in the scientific relation to nature, our own activity becomes important where we have to deal with areas of nature, into which it is possible to penetrate only thanks to the most complex technical means.

The conceptual content of quantum mechanics is far from trivial. It is not surprising, therefore, that it is interpreted in different ways. We will first have to fully plunge into the world of quantum mechanical pluralism, and then, having mastered it, draw decisive conclusions.

Copenhagen interpretation

The term "Copenhagen interpretation" was used by W. Heisenberg, clearly emphasizing the priority of N. Bohr, a resident of the Danish capital of Copenhagen. Heisenberg himself is considered Copenhagen No. 2. Neither Heisenberg nor anyone else has ever clearly defined the content of the Copenhagen interpretation. At the same time, it was known that the views of Bohr and Heisenberg did not coincide. Thus, "Copenhagen interpretation" is a term for a spectrum of views. Outstanding "Copenhageners" were J. von Neumann, P. Dirac, V. A. Fok, L. D. Landau.

1) the wave function refers to a separate quantum object;
2) the behavior of quantum objects cannot be separated from the measurement results;
3) the measurement causes the collapse of the wave function;
4) hidden options are not possible;
5) quantum mechanics provides a complete, exhaustive description of the behavior of quantum objects.

scientists argue

The pluralism of the Copenhageners' views consisted in the fact that J. von Neumann did not adhere to Bohr's belief that the results of measurements are described in a classical way, as well as his adherence to the principle of complementarity. Bohr himself was not inclined to absolutize the measurement process as decisively as W. Heisenberg did. Von Neumann also adhered to the position that the results of measurements refer to a separate object only if they are eigenvalues of the operators corresponding to them.

Another feature of the "Copenhageners" is that they avoided the spatio-temporal depiction of quantum mechanical processes. As R. Feynman showed, such an image is quite possible.

Ensemble or statistical interpretation

A. Einstein is most often considered its creator. The largest representatives of this interpretation are also our compatriot D. I. Blokhintsev and the modern Canadian physicist L. Ballenstein. In fact, it is these names that represent the three most relevant stages in the development of ensemble interpretation, which has always been recognized as an obvious alternative to the Copenhagen interpretation.

Einstein, recognizing quantum statistics, believed that even it was insufficient to express the true nature of quantum objects, the reality of which he did not doubt. Quantum mechanics is incomplete.

D. I. Blokhintsev, relying on the views of not Einstein, but von Neumann and his colleagues L. I. Mandelstam and K. V. Nikolsky, formulated a new version of the ensemble interpretation. The essence of his view is that it is not the search for hidden parameters that comes to the fore, but the density operator. In an article in which he, in fact, summed up his work related to the understanding of quantum mechanics, Blokhintsev noted that "the need to introduce the density operator into quantum mechanics, as a concept more general than the wave function, is based on the fact that in quantum the domains of measurement performed on systems described by the wave function ψ (“pure” ensemble) transform these systems into states described by a set of wave functions, i.e., into a “mixed” ensemble.

Therefore, if we want to consider the theory of quantum measurements as a chapter of quantum mechanics, then mixed ensembles, which have no analogues in classical mechanics, cannot be excluded from consideration. They are analogues of statistical mechanics. This point is the whole essence of the difference between my concept of quantum mechanics and the concept of the Copenhagen school.

N. Bohr clearly preferred to consider the situation when an atomic system is described by a wave function (ie, a pure ensemble). With this approach, the measurement process itself is completely excluded from quantum mechanical consideration and, moreover, cannot be the subject of theoretical calculation. The interpretation of measurement in this approach is limited to the understanding of measurement as a phenomenon of information change. It should be emphasized that within the framework of an analysis focused on a pure ensemble, such an interpretation of the dimension is logically consistent and the only one possible. But it excludes the actually existing possibility, on the basis of the same quantum mechanics, to investigate and calculate the phenomena of measurement. In this regard, the concept of von Neumann, based on the concept of statistical populations, seems to be a broader basis for understanding quantum mechanics than the concept based on the more limited concept of the wave function.

Quantum ensembles are just analogous to the Gibbs ensembles used in classical physics. Therefore, Blokhintsev believed that he had successfully separated classical and quantum physics in different directions. But at the same time, the question of the nature of an individual particle remained open. His main opponent V. A. Fok did not fail to note this. He accused Blokhintsev of inconsistency: the wave function is sometimes considered a characteristic of an individual particle, then a characteristic of the entire ensemble, and not a single particle. Fock is right, the adherents of the ensemble interpretation have no way of coping with individual particles. Either it is completely denied that the statistical interpretation in the spirit of M. Born refers to a single particle, or it is considered only a representative of the ensemble.

From the standpoint of the modern theory of decoherence, Blokhintsev's oversight is quite obvious. He erroneously believed that the process of quantum mechanical measurement is completely explained by means of the density operator, which, they say, does not have to be derived at all. Therefore, he put it ahead of the concept of the wave function, the relevance of which, in fact, was downplayed.

Let's move on to the characterization of Ballentine's views. Unfortunately, in his main work, he avoids the laconic characterization of his position, which is relevant in this book. But K. Aylward illustrates the main provisions of Ballentine's views in a rather effective manner. He shows that the ensemble interpretation of quantum mechanics leads to conclusions that are in no way consistent with the Copenhagen interpretation. For convenience, we number his comments.

1. One should not think that statistical results characterize an individual particle. Assume that tests are being carried out with a dice. Values are dropped from 1 to 6. The average value is, for example, 2.4. But this does not mean that the dice has a side that says 2.4.
2. Corpuscular-wave dualism is untenable. Particles are always particles. It is true that they are described not by classical but by quantum statistics. But they are not waves, like waves on water, for example, which are really real.
3. The Heisenberg uncertainty principle is a description of statistical results performed on an ensemble of particles. Contrary to Heisenberg, an individual particle does not have undefined parameter values.
4. The Schrödinger cat paradox was introduced to show the limitations of the Copenhagen interpretation of quantum mechanics. A real cat, of course, is always either dead or alive, and is not a superposition of the two.
5. On the collapse of the wave function. It is not required either by the formal apparatus of quantum mechanics or by experimental data.
6. It is stated that the same particle can be in different places. But the apparatus of quantum mechanics does not require this.
7. It is argued that the consciousness of the experimenter takes part in the construction of quantum reality. In reality, the states of quantum objects do not depend on it.

So, according to Aylward, the ensemble interpretation brings final clarity to many controversial issues in quantum mechanics, brought to life by the Copenhagen interpretation.

Portal for the student. Self-training

What is the Copenhagen Interpretation? Copenhagen interpretation of quantum mechanics.

Main Ideas of the Copenhagen Interpretation

The meaning of the wave function

Prevalence among scientists

Alternatives

see also

Write a review on the article "Copenhagen Interpretation"

Notes

Literature

An excerpt characterizing the Copenhagen Interpretation

Copenhagen interpretation of quantum theory

Copenhagen interpretation

Ensemble or statistical interpretation

Portal for the student. Self-training

Main Ideas of the Copenhagen Interpretation

The meaning of the wave function

Prevalence among scientists

Alternatives

see also

Write a review on the article "Copenhagen Interpretation"

Notes

Literature

An excerpt characterizing the Copenhagen Interpretation

Copenhagen interpretation of quantum theory

Copenhagen interpretation

Ensemble or statistical interpretation

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