About Schrödinger's cat in simple words. Schrödinger's cat paradox. Explanation of meaning

There was a kind of "secondary". He himself rarely dealt with a specific scientific problem. His favorite genre of work was a response to someone's scientific research, development of this work or its criticism. Despite the fact that Schrödinger himself was an individualist by nature, he always needed someone else's thought, support for further work. Despite this peculiar approach, Schrödinger managed to make many discoveries.

Biographical information

Schrödinger's theory is now known not only to students of physics and mathematics departments. It will be of interest to anyone who is interested in popular science. This theory was created famous physicist E. Schrodinger, who went down in history as one of the creators of quantum mechanics. The scientist was born on August 12, 1887 in the family of the owner of an oilcloth factory. The future scientist, who became famous all over the world for his mystery, was fond of botany and drawing as a child. His first mentor was his father. In 1906, Schrödinger began his studies at the University of Vienna, during which he began to admire physics. When the First World War came, the scientist went to serve as an artilleryman. IN free time studied the theories of Albert Einstein.

By the beginning of 1927, a dramatic situation had developed in science. E. Schrödinger believed that the idea of ​​the continuity of waves should serve as the basis for the theory of quantum processes. Heisenberg, on the contrary, believed that the concept of the discreteness of waves, as well as the idea of ​​quantum jumps, should be the foundation for this field of knowledge. Niels Bohr did not accept any of the positions.

Advances in Science

For the concept of wave mechanics in 1933, Schrödinger received the Nobel Prize. However, having been brought up in the traditions of classical physics, the scientist could not think in other categories and did not consider quantum mechanics to be a full-fledged branch of knowledge. He could not be satisfied with the dual behavior of particles, and he tried to reduce it exclusively to the wave behavior. In his discussion with N. Bohr, Schrödinger put it this way: "If we plan to keep these quantum leaps in science, then I generally regret that I connected my life with atomic physics."

Further work of the researcher

At the same time, Schrödinger was not only one of the founders of modern quantum mechanics. It was he who introduced the term "objectivity of description" into scientific use. This is the ability of scientific theories to describe reality without the participation of an observer. His further research was devoted to the theory of relativity, thermodynamic processes, Born's nonlinear electrodynamics. Also, scientists have made several attempts to create a unified field theory. In addition, E. Schrödinger spoke six languages.

The most famous riddle

Schrödinger's theory, in which the same cat appears, grew out of the scientist's criticism of quantum theory. One of its main postulates is that as long as the system is not observed, it is in a state of superposition. Namely, in two or more states that exclude the existence of each other. The state of superposition in science has the following definition: it is the ability of a quantum, which can also be an electron, a photon, or, for example, the nucleus of an atom, to be simultaneously in two states or even at two points in space at a time when no one is watching him.

Objects in different worlds

It is very difficult for an ordinary person to understand such a definition. After all, each object of the material world can be either at one point in space or at another. This phenomenon can be illustrated as follows. The observer takes two boxes and puts a tennis ball in one of them. It will be clear that it is in one box and not in the other. But if we put an electron in one of the containers, then the following statement will be true: this particle is simultaneously in two boxes, no matter how paradoxical it may seem. In the same way, an electron in an atom is not located at a strictly defined point at one time or another. It rotates around the nucleus, being located at all points of the orbit at the same time. In science, this phenomenon is called "electron cloud".

What did the scientist want to prove?

Thus, the behavior of small and large objects is implemented according to completely different rules. In the quantum world, there are some laws, and in the macrocosm - completely different. However, there is no such concept that would explain the transition from the world of material objects, familiar to people, to the microworld. Schrödinger's theory was created in order to demonstrate the insufficiency of research in the field of physics. The scientist wanted to show that there is a science whose purpose is to describe small objects, and there is a field of knowledge that studies ordinary objects. Largely due to the work of the scientist, physics was divided into two areas: quantum and classical.

Schrödinger's theory: description

The scientist described his famous thought experiment in 1935. In its implementation, Schrödinger relied on the principle of superposition. Schrödinger emphasized that as long as we do not observe the photon, it can be either a particle or a wave; both red and green; both round and square. This uncertainty principle, which directly follows from the concept of quantum dualism, was used by Schrödinger in his famous cat riddle. The meaning of the experiment in brief is as follows:

• A cat is placed in a closed box, as well as a container containing hydrocyanic acid and a radioactive substance.
• The nucleus can disintegrate within an hour. The probability of this is 50%.
• If the atomic nucleus decays, then this will be recorded by the Geiger counter. The mechanism will work and the poison box will be broken. The cat will die.
• If the decay does not occur, then Schrödinger's cat will be alive.

According to this theory, until the cat is observed, it is simultaneously in two states (dead and alive), just like the nucleus of an atom (decayed or not decayed). Of course, this is possible only according to the laws of the quantum world. In the macrocosm, a cat cannot be both alive and dead at the same time.

Observer paradox

To understand the essence of Schrödinger's theory, it is also necessary to have an understanding of the paradox of the observer. Its meaning is that the objects of the microcosm can be simultaneously in two states only when they are not observed. For example, the so-called "Experiment with 2 slits and an observer" is known in science. On an opaque plate in which two vertical slits were made, scientists directed a beam of electrons. On the screen behind the plate, the electrons painted a wave pattern. In other words, they left black and white stripes. When the researchers wanted to observe how the electrons fly through the slits, the particles displayed only two vertical stripes on the screen. They behaved like particles, not like waves.

Copenhagen explanation

The modern explanation of Schrödinger's theory is called the Copenhagen one. Based on the paradox of the observer, it sounds like this: as long as no one observes the nucleus of an atom in the system, it is simultaneously in two states - decayed and undecayed. However, the statement that the cat is alive and dead at the same time is extremely erroneous. After all, the same phenomena are never observed in the macrocosm as in the microcosm.

Therefore, we are not talking about the “cat-core” system, but about the fact that the Geiger counter and the nucleus of the atom are interconnected. The kernel can choose one or another state at the moment when the measurements are made. However, this choice does not take place at the moment when the experimenter opens the box with Schrödinger's cat. In fact, the opening of the box takes place in the macrocosm. In other words, in a system that is very far from the atomic world. Therefore, the nucleus selects its state exactly at the moment when it hits the detector of the Geiger counter. Thus, Erwin Schrödinger, in his thought experiment, did not fully describe the system.

General conclusions

Thus, it is not entirely correct to associate the macrosystem with the microscopic world. In the macrocosm, quantum laws lose their force. The nucleus of an atom can be simultaneously in two states only in the microcosm. The same cannot be said about the cat, since it is an object of the macrocosm. Therefore, only at first glance it seems that the cat passes from the superposition to one of the states at the moment of opening the box. In fact, its fate is determined at the moment when the atomic nucleus interacts with the detector. The conclusion can be drawn as follows: the state of the system in Erwin Schrödinger's riddle has nothing to do with a person. It does not depend on the experimenter, but on the detector - an object that "observes" the nucleus.

Continuation of the concept

Schrödinger theory in simple words is described as follows: while the observer does not look at the system, it can be simultaneously in two states. However, another scientist - Eugene Wigner, went further and decided to bring the concept of Schrödinger to complete absurdity. “Excuse me!” said Wigner, “what if next to the experimenter watching the cat is his colleague?” The partner does not know what exactly the experimenter himself saw at the moment when he opened the box with the cat. Schrödinger's cat leaves the state of superposition. However, not for a fellow observer. Only at the moment when the fate of the cat becomes known to the latter, the animal can finally be called alive or dead. In addition, there are billions of people on planet Earth. And the final verdict can be made only when the result of the experiment becomes the property of all living beings. Of course, all people can be told the fate of the cat and Schrödinger's theory briefly, but this is a very long and laborious process.

The principles of quantum dualism in physics were never refuted by Schrödinger's thought experiment. In a sense, every creature can be called neither alive nor dead (being in superposition) as long as there is at least one person who is not watching him.

The article describes what the Schrödinger theory is. The contribution of this great scientist to modern science, as well as a thought experiment invented by him about a cat. The area of ​​application of this kind of knowledge is briefly outlined.

Erwin Schrödinger

The notorious cat, which is neither alive nor dead, is now being used everywhere. Films are made about him, communities about physics and animals are named after him, there is even such a clothing brand. But most often people mean the paradox with the unfortunate cat. But about its creator, Erwin Schrödinger, as a rule, they forget. He was born in Vienna, which was then part of Austria-Hungary. He was the son of a highly educated and wealthy family. His father, Rudolf, produced linoleum and invested money in science as well. His mother was the daughter of a chemist, and Erwin often went to listen to his grandfather's lectures at the academy.

Since one of the scientist's grandmothers was an Englishwoman, from childhood he was interested in foreign languages and was fluent in English. Not surprisingly, at school, Schrödinger was the best in class every year, and at the university he asked difficult questions. In the science of the beginning of the twentieth century, inconsistencies between the more understandable classical physics and the behavior of particles in the micro- and nanoworld were already revealed. To resolve the emerging contradictions and threw all his strength

Contribution to science

To begin with, it is worth saying that this physicist was engaged in many areas of science. However, when we say "Schrödinger's theory", we do not mean the mathematically coherent description of color created by him, but his contribution to quantum mechanics. In those days, technology, experiment and theory went hand in hand. Photography developed, the first spectra were recorded, and the phenomenon of radioactivity was discovered. The scientists who received the results closely interacted with theorists: they agreed, complemented each other, and argued. New schools and branches of science were created. The world began to play with completely different colors, and humanity received new mysteries. Despite the complexity of the mathematical apparatus, to describe what Schrödinger's theory is, plain language Can.

The quantum world is easy!

It is now well known that the scale of the studied objects directly affects the results. Objects visible to the eye obey the concepts of classical physics. Schrödinger's theory is applicable to bodies one hundred by one hundred nanometers in size and less. And most often we are talking about individual atoms and smaller particles. So, each element of microsystems simultaneously has the properties of both a particle and a wave (particle-wave dualism). From the material world, electrons, protons, neutrons, etc. are characterized by mass and the inertia, speed, and acceleration associated with it. From the theoretical wave - parameters such as frequency and resonance. In order to understand how this is possible at the same time, and why they are inseparable from each other, scientists needed to reconsider the whole idea of ​​the structure of substances in general.

Schrödinger's theory implies that mathematically these two properties are related through a construct called the wave function. Finding mathematical description This concept earned Schrödinger the Nobel Prize. However, the physical meaning that the author attributed to it did not coincide with the ideas of Bohr, Sommerfeld, Heisenberg and Einstein, who founded the so-called Copenhagen Interpretation. This is where the cat paradox came from.

wave function

When it comes to the microworld of elementary particles, the concepts inherent in macroscales lose their meaning: mass, volume, speed, size. And unsteady probabilities come into their own. Objects of such dimensions cannot be fixed by a person - only indirect ways of studying are available to people. For example, streaks of light on a sensitive screen or on a film, the number of clicks, the thickness of the sprayed film. Everything else is the area of ​​calculations.

Schrödinger's theory is based on the equations that this scientist deduced. And their integral component is the wave function. It unambiguously describes the type and quantum properties of the particle under study. It is believed that the wave function shows the state, for example, of an electron. However, it itself, contrary to the ideas of its author, has no physical meaning. It's just a handy math tool. Since our paper presents Schrödinger's theory in simple terms, let's say that the square of the wave function describes the probability of finding a system in a predetermined state.

Cat as an example of a macro object

With this interpretation, which is called Copenhagen, the author himself did not agree until the end of his life. He was disgusted by the vagueness of the concept of probability, and he insisted on the visibility of the function itself, and not its square.

As an example of the inconsistency of such ideas, he argued that in this case the microworld would influence macroobjects. The theory says the following: if a living organism (for example, a cat) and a capsule with poisonous gas are placed in a sealed box, which opens if a certain radioactive element decays, and remains closed if decay does not occur, then before opening the box we get a paradox. According to quantum concepts, an atom of a radioactive element will decay with a certain probability over a certain period of time. Thus, before experimental discovery, the atom is both intact and not. And, according to Schrödinger's theory, by the same degree of probability, the cat is both dead and otherwise alive. Which, you see, is absurd, because, having opened the box, we will find only one state of the animal. And in a closed container, next to the deadly capsule, the cat is either dead or alive, since these indicators are discrete and do not imply intermediate options.

There is a concrete but not yet fully proven explanation for this phenomenon: in the absence of time-limiting conditions for determining the specific state of a hypothetical cat, this experiment is undoubtedly paradoxical. However, quantum mechanical rules cannot be used for macroobjects. It has not yet been possible to draw a precise line between the microcosm and the ordinary. Nevertheless, an animal the size of a cat is, without a doubt, a macro object.

Applications of quantum mechanics

As for any, even theoretical, phenomenon, the question arises of how Schrödinger's cat can be useful. The big bang theory, for example, is based precisely on the processes involved in this thought experiment. Everything that relates to ultra-high speeds, the ultra-small structure of matter, the study of the universe as such, is explained, among other things, by quantum mechanics.

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Schrödinger's Cat Paradox

"Anyone not shocked by quantum theory, does not understand it,” said Niels Bohr, the founder of quantum theory.
The basis of classical physics - the unambiguous programming of the world, otherwise Laplacian determinism, with the advent of quantum mechanics was replaced by the invasion of the world of uncertainties and probabilistic events. And here, by the way, thought experiments turned out to be for theoretical physicists. These were touchstones on which the latest ideas were tested.

Schrödinger's cat is a thought experiment, proposed by Erwin Schrödinger, with which he wanted to show the incompleteness of quantum mechanics in the transition from subatomic systems to macroscopic systems.

A cat is placed in a closed box. The box contains a mechanism containing a radioactive core and a container of poisonous gas. The probability that the nucleus will decay in 1 hour is 1/2. If the core disintegrates, it sets the mechanism in motion, it opens the gas container, and the cat dies. According to quantum mechanics, if no observation is made over the nucleus, then its state is described by a superposition (mixing) of two states - a decayed nucleus and an undecayed nucleus, therefore, the cat sitting in the box is both alive and dead at the same time. If the box is opened, then the experimenter can see only one specific state - "the nucleus has disintegrated, the cat is dead" or "the nucleus has not disintegrated, the cat is alive."

When does the system cease to exist? like mixing two states and choosing one particular one?

Purpose of the experiment- show what quantum mechanics is incomplete without some rules indicating under what conditions the wave function collapses (instantaneous change in the quantum state of an object that occurs during measurement), and the cat either becomes dead or remains alive, but ceases to be a mixture of both.

Since it is clear that the cat must necessarily be either alive or dead (there is no intermediate state between life and death), this means that this is also true for the atomic nucleus. It will necessarily be either decayed or undecayed.

Schrödinger's article "The Current Situation in Quantum Mechanics" presenting a thought experiment with a cat appeared in the German journal Natural Sciences in 1935 to discuss the EPR paradox.

The articles by Einstein-Podolsky-Rosen and Schrödinger outlined the strange nature of "quantum entanglement" (a term introduced by Schrödinger), which is characteristic of quantum states that are a superposition of the states of two systems (for example, two subatomic particles).

Interpretations of quantum mechanics

During the existence of quantum mechanics, scientists have put forward its various interpretations, but the most supported of all today are "Copenhagen" and "many worlds".

"Copenhagen Interpretation"- this interpretation of quantum mechanics was formulated by Niels Bohr and Werner Heisenberg during joint work in Copenhagen (1927). Scientists have tried to answer questions that arise as a result of the corpuscular-wave dualism inherent in quantum mechanics, in particular, the question of measurement.

In the Copenhagen interpretation, the system ceases to be a mixture of states and chooses one of them at the moment when an observation occurs. The experiment with the cat shows that in this interpretation the nature of this very observation - the measurement - is not sufficiently defined. Some believe that experience suggests that as long as the box is closed, the system is in both states at the same time, in a superposition of the states "decayed nucleus, dead cat" and "undecayed nucleus, living cat", and when the box is opened, then only then does the wave function collapse to one of the variants. Others guess that the "observation" occurs when a particle from the nucleus hits the detector; however (and this is the key point of the thought experiment) there is no clear rule in the Copenhagen interpretation that says when this happens, and therefore this interpretation is incomplete until such a rule is introduced into it, or it is not said how it can be introduced. The exact rule is this: randomness appears at the point where the classical approximation is used for the first time.

Thus, we can rely on the following approach: we do not observe quantum phenomena in macroscopic systems (except for the phenomena of superfluidity and superconductivity); so if we superimpose a macroscopic wave function on a quantum state, we must conclude from experience that the superposition collapses. And although it is not entirely clear what it means that something is "macroscopic" in general, it is known for sure about a cat that it is a macroscopic object. Thus, the Copenhagen interpretation does not consider that the cat is in a state of mixing between the living and the dead before the box is opened.

In "multi-world interpretation" of quantum mechanics, which does not consider the measurement process to be something special, both states of the cat exist, but decohere, i.e. there is a process in which a quantum mechanical system interacts with the environment and acquires the information available in the environment, or otherwise, "entangles" with the environment. And when the observer opens the box, he becomes entangled with the cat, and from this two states of the observer are formed, corresponding to a living and a dead cat, and these states do not interact with each other. The same mechanism of quantum decoherence is also important for "joint" histories. In this interpretation, only a "dead cat" or "live cat" can be in a "shared history.

In other words, when the box is opened, the universe splits into two different universes, in one of which the observer is looking at the box with the dead cat, and in the other, the observer is looking at the live cat.

The paradox of "Wigner's friend"

Wigner's friend paradox is a complicated experiment of the Schrödinger's cat paradox. Nobel Prize Laureate, American physicist Eugene Wigner introduced the "friends" category. After completing the experiment, the experimenter opens the box and sees a live cat. The state of the cat at the moment of opening the box goes into the state "the core has not disintegrated, the cat is alive." Thus, in the laboratory, the cat was recognized as alive. Outside the lab is a "friend". The friend does not yet know whether the cat is alive or dead. A friend recognizes the cat as alive only when the experimenter informs him of the outcome of the experiment. But all the other "friends" have not yet recognized the cat as alive, and they will recognize it only when they are informed of the result of the experiment. Thus, a cat can be recognized as fully alive only when all people in the universe know the result of the experiment. Up to this point in scale Big Universe the cat remains half dead and half dead at the same time.

The above is applied in practice: quantum computing and in quantum cryptography. A fiber-optic cable sends a light signal that is in a superposition of two states. If attackers connect to the cable somewhere in the middle and make a signal tap there in order to eavesdrop on the transmitted information, then this will collapse the wave function (from the point of view of the Copenhagen interpretation, an observation will be made) and the light will go into one of the states. Having carried out statistical tests of light at the receiving end of the cable, it will be possible to find out whether the light is in a superposition of states or whether it has already been observed and transmitted to another point. It does possible creation means of communication that exclude imperceptible signal interception and eavesdropping.

The experiment (which in principle can be performed, although working systems of quantum cryptography capable of transmitting large amounts of information have not yet been created) also shows that "observation" in the Copenhagen interpretation has nothing to do with the mind of the observer, since in this case the change in statistics to the end of the cable leads to a completely inanimate branch of the wire.

And in quantum computing, the “Schrödinger cat” state is a special entangled state of qubits, in which they are all in the same superposition of all zeros or ones.

("Qubit" is the smallest element for storing information in a quantum computer. It admits two eigenstates, but it can also be in their superposition. Any time you measure the state of a qubit, it randomly transitions to one of its own states.)

In reality! Small brother of "Schrödinger's cat"

It has been 75 years since the "Schrödinger's cat" appeared, but still some of the consequences of quantum physics seem to be at odds with our ordinary ideas about matter and its properties. According to the laws of quantum mechanics, it should be possible to create such a state of a “cat” when it is both alive and dead, i.e. will be in a state of quantum superposition of two states. However, in practice, the creation of a quantum superposition of such a large number of atoms has not yet been successful. The difficulty is that the more atoms there are in superposition, the less stable this state is, since external influences tend to destroy it.

Physicists from the University of Vienna (publication in the journal Nature Communications”, 2011) for the first time in the world managed to demonstrate the quantum behavior of an organic molecule consisting of 430 atoms and in a state of quantum superposition. The molecule obtained by the experimenters is more like an octopus. The size of the molecules is on the order of 60 angstroms, and the de Broglie wavelength for the molecule was only 1 picometer. Such a "molecular octopus" was able to demonstrate the properties inherent in Schrödinger's cat.

quantum suicide

Quantum suicide is a thought experiment in quantum mechanics that was proposed independently by G. Moravec and B. Marshal, and in 1998 was expanded by cosmologist Max Tegmark. This thought experiment, being a modification of the thought experiment with Schrödinger's cat, clearly shows the difference between two interpretations of quantum mechanics: the Copenhagen interpretation and Everett's many-worlds interpretation.

In fact, the experiment is an experiment with Schrödinger's cat from the cat's point of view.

In the proposed experiment, a gun is pointed at the participant, which shoots or does not shoot, depending on the decay of any radioactive atom. The probability that as a result of the experiment the gun will go off and the participant will die is 50%. If the Copenhagen interpretation is correct, then the gun will eventually go off and the contestant will die.
If the many-world interpretation of Everett is correct, then as a result of each experiment, the universe splits into two universes, in one of which the participant remains alive, and in the other dies. In worlds where a participant dies, they cease to exist. In contrast, from the point of view of the non-deceased participant, the experiment will continue without resulting in the participant's disappearance. This is because, in any branch, the participant is only able to observe the result of the experiment in the world in which he survives. And if the many-worlds interpretation is correct, then the participant may notice that they will never die in the course of the experiment.

The participant will never be able to talk about these results, since from the point of view of an outside observer, the probability of the outcome of the experiment will be the same in the many-world and Copenhagen interpretations.

quantum immortality

Quantum immortality is a thought experiment stemming from the quantum suicide thought experiment, stating that, according to the many-worlds interpretation of quantum mechanics, beings with the ability to self-aware are immortal.

Imagine that a participant in an experiment detonates a nuclear bomb near him. In almost all parallel universes, a nuclear explosion will destroy the participant. But, despite this, there should be a small set of alternative Universes in which the participant somehow survives (that is, Universes in which the development of a potential rescue scenario is possible). The idea of ​​quantum immortality is that the participant remains alive, and thus is able to perceive the surrounding reality, in at least one of the universes in the set, even if the number of such universes is extremely small compared to the number of all possible universes. Thus, over time, the participant will find that they can live forever. Some parallels with this inference can be found in the concept of the anthropic principle.

Another example stems from the idea of ​​quantum suicide. In this thought experiment, the participant points a gun at himself, which may or may not fire, depending on the result of the decay of any radioactive atom. The probability that as a result of the experiment the gun will go off and the participant will die is 50%. If the Copenhagen interpretation is correct, then the gun will eventually go off and the contestant will die.

If the many-world interpretation of Everett is correct, then as a result of each experiment, the universe splits into two universes, in one of which the participant remains alive, and in the other dies. In worlds where a participant dies, they cease to exist. On the contrary, from the point of view of the non-dead participant, the experiment will continue without leading to the participant's disappearance, since after each splitting of universes, he will be able to realize himself only in those universes where he survived. Thus, if Everett's many-world interpretation is correct, then the participant may remark that they will never die during the experiment, thereby "proving" their immortality, at least from their point of view.

Supporters of quantum immortality point out that this theory does not contradict any known laws of physics (this position is far from being unanimously recognized in scientific world). They base their reasoning on the following two controversial assumptions:
- the many-world interpretation of Everett is correct, but not the Copenhagen interpretation, since the latter denies the existence of parallel universes;
- all possible scenarios in which the participant may die during the experiment contain at least a small subset of scenarios where the participant survives.

A possible argument against the theory of quantum immortality would be that the second assumption does not necessarily follow from Everett's many-worlds interpretation, and it may conflict with the laws of physics, which are thought to apply to all possible realities. The many-worlds interpretation of quantum physics does not necessarily imply that "anything is possible." She only points out that a certain moment time the universe can be divided into a number of others, each of which will correspond to one of the many possible outcomes. For example, the second law of thermodynamics is believed to be true for all possible universes. This means that theoretically the existence of this law prevents the formation of parallel universes where it would be violated. The consequence of this may be the achievement, from the point of view of the experimenter, of such a state of reality where his further survival becomes impossible, since this would require a violation of the law of physics, which, according to the assumption made earlier, is valid for all possible realities.

For example, in the explosion of a nuclear bomb described above, it is quite difficult to describe a plausible scenario that does not violate basic biological principles in which the participant will remain alive. Living cells simply cannot exist at the temperatures reached in the center of a nuclear explosion. In order for the theory of quantum immortality to remain valid, it is necessary that either a misfire occurs (and thus does not occur a nuclear explosion), or some event occurs that would be based on as yet undiscovered or unproven laws of physics. Another argument against the theory under discussion is the presence of natural biological death in all beings, which cannot be avoided in any of the parallel Universes (at least at this stage in the development of science)

On the other hand, the second law of thermodynamics is a statistical law, and the occurrence of fluctuations does not contradict anything (for example, the appearance of a region with conditions suitable for the life of an observer in a universe that has generally reached a state of heat death; or, in principle, the possible movement of all particles resulting from nuclear explosion, so that each of them will fly past the observer), although such a fluctuation will occur only in a very small part of all possible outcomes. The argument relating to the inevitability of biological death can also be refuted on the basis of probabilistic considerations. For every living organism this moment time, there is a non-zero probability that he will be alive for the next second. Thus, the probability that it will remain alive for the next billion years is also non-zero (because it is the product of a large number of non-zero factors), although it is very small.

The problem with the idea of ​​quantum immortality is that, according to it, a self-aware being will be “forced” to experience extremely unlikely events that will occur in situations in which the participant would seem to die. Even though in many parallel universes the participant dies, the few universes that the participant is able to subjectively perceive will develop in an extremely unlikely scenario. This, in turn, may in some way cause a violation of the principle of causality, the nature of which is quantum physics is not yet clear enough.

Although the idea of ​​quantum immortality stems largely from the "quantum suicide" experiment, Tegmark argues that under any normal conditions, every thinking being before death goes through a stage (from a few seconds to several years) of a decrease in the level of self-consciousness, which has nothing to do with quantum mechanics, and there is no possibility for the participant to continue to exist by passing from one world to another, enabling him to survive.

Here, a rational observer who is conscious of himself only in a relatively small number of possible states in which he retains self-consciousness continues to remain in, so to speak, a “healthy body”. The possibility that the observer, having retained consciousness, will remain crippled, is much greater than if he remains unharmed. Any system (including a living organism) has much more opportunities to function incorrectly than to remain in perfect shape. Boltzmann's ergodic hypothesis requires that the immortal observer sooner or later go through all the states compatible with the preservation of consciousness, including those in which he will feel unbearable suffering - and there will be much more such states than the states of optimal functioning of the organism. Thus, according to the philosopher David Lewis, we should hope that the many-worlds interpretation is wrong.

· Sconce and cat · Hamiltonian · Old quantum theory

The essence of the experiment

Schrödinger's original paper describes the experiment as follows:

You can also build cases in which burlesque is enough. A certain cat is locked in a steel chamber, along with the following infernal machine (which must be protected from the direct intervention of a cat): inside a Geiger counter is a tiny amount of radioactive material, so small that only one atom can decay in an hour, but with the same probability it can and not fall apart; if this happens, the reading tube is discharged and the relay is activated, lowering the hammer, which breaks the cone of hydrocyanic acid. If we leave this whole system to itself for an hour, then we can say that the cat will be alive after this time, as long as the atom does not decay. The first decay of an atom would have poisoned the cat. The psi-function of the system as a whole will express this by mixing in itself or smearing the living and dead cat (forgive the expression) in equal proportions.

Typical in such cases is that the uncertainty, originally limited to the atomic world, is transformed into a macroscopic uncertainty that can be eliminated by direct observation. This prevents us from naively accepting the "blur model" as reflecting reality. By itself, this does not mean anything unclear or contradictory. There is a difference between a fuzzy or out-of-focus photo and a cloud or fog shot.

According to quantum mechanics, if no observation is made over the nucleus, then its state is described by a superposition (mixing) of two states - a decayed nucleus and an undecayed nucleus, therefore, the cat sitting in the box is both alive and dead at the same time. If the box is opened, then the experimenter can see only one specific state - "the nucleus has disintegrated, the cat is dead" or "the nucleus has not disintegrated, the cat is alive."

The question goes like this: when the system ceases to exist as a mixture of two states and chooses one concrete one? The purpose of the experiment is to show that quantum mechanics is incomplete without some rules that specify under what conditions the wave function collapses, and the cat either becomes dead or remains alive, but ceases to be a mixture of both.

Since it is clear that the cat must necessarily be either alive or dead (there is no state that combines life and death), this will be the same for the atomic nucleus. It must necessarily be either decayed or undecayed.

In large complex systems consisting of many billions of atoms, decoherence occurs almost instantly, and for this reason a cat cannot be both dead and alive for any measurable length of time. The decoherence process is an essential component of the experiment.

The original article appeared in 1935. The purpose of the article was to discuss the Einstein-Podolsky-Rosen (EPR) paradox published by Einstein, Podolsky and Rosen earlier that year. The articles by EPR and Schrödinger outlined the strange nature of "quantum entanglement" (German. Verschrankung, English quantum entanglement, a term introduced by Schrödinger), characteristic of quantum states that are a superposition of the states of two systems (for example, two subatomic particles).

Copenhagen interpretation

In fact, Hawking and many other physicists are of the opinion that the "Copenhagen School" of the interpretation of quantum mechanics emphasizes the role of the observer unreasonably. Final unity among physicists on this issue has not yet been achieved.

The parallelization of the worlds at each moment of time corresponds to a genuine non-deterministic automaton, in contrast to the probabilistic one, when at each step one of the possible ways according to their probability.

Wigner's paradox

This is a complicated version of the Schrödinger experiment. Eugene Wigner introduced the "friends" category. After completing the experiment, the experimenter opens the box and sees a live cat. The state vector of the cat at the moment of opening the box goes into the state “the core has not disintegrated, the cat is alive”. Thus, in the laboratory, the cat was recognized as alive. Outside the laboratory is Friend. Friend does not yet know whether the cat is alive or dead. Friend recognizes the cat as alive only when the experimenter informs him of the outcome of the experiment. But everyone else Friends the cat has not yet been recognized as alive, and they will recognize it only when they are informed of the result of the experiment. Thus, a cat can be considered completely alive (or completely dead) only when all people in the universe know the result of the experiment. Up to this point, on the scale of the Big Universe, the cat, according to Wigner, remains alive and dead at the same time in quantum cryptography. A fiber-optic cable sends a light signal that is in a superposition of two states. If attackers connect to the cable somewhere in the middle and make a signal tap there in order to eavesdrop on the transmitted information, then this will collapse the wave function (from the point of view of the Copenhagen interpretation, an observation will be made) and the light will go into one of the states. Having carried out statistical tests of light at the receiving end of the cable, it will be possible to find out whether the light is in a superposition of states or whether it has already been observed and transmitted to another point. This makes it possible to create means of communication that exclude imperceptible signal interception and eavesdropping.

The experiment (which in principle can be performed, although working systems of quantum cryptography capable of transmitting large amounts of information have not yet been created) also shows that "observation" in the Copenhagen interpretation has nothing to do with the mind of the observer, since in this case the change in statistics to the end of the cable leads to a completely inanimate branch of the wire.

In quantum computing, the Schrodinger's cat state is a special entangled state of qubits, in which they are all in the same superposition of all zeros or ones, that is 1 2 (| 00 … 0 ⟩ + | 11 … 1 ⟩) (\displaystyle (\frac (1)(\sqrt (2)))(|00\dots 0\rangle +|11\dots 1\rangle)).

Recently published on the well-known scientific portal "PostNauka" Emil Akhmedov's author's article about the causes of the famous paradox, as well as what it is not.

Physicist Emil Akhmedov on probabilistic interpretation, closed quantum systems and paradox formulation.

In my opinion, the most difficult part of quantum mechanics, both psychologically and philosophically, and in many other respects, is its probabilistic interpretation. Many people have argued with the probabilistic interpretation. For example, Einstein, along with Podolsky and Rosen, came up with a paradox that refutes the probabilistic interpretation.

In addition to them, Schrödinger also argued with the probabilistic interpretation of quantum mechanics. As a logical contradiction in the probabilistic interpretation of quantum mechanics, Schrödinger came up with the so-called Schrödinger's cat paradox. It can be formulated in different ways, for example: let's say you have a box in which a cat sits, and a cylinder of lethal gas is connected to this box. To the switch of this cylinder, which admits or does not let in lethal gas, some device is connected, which works as follows: there is a polarizing glass, and if a passing photon of the required polarization, then the cylinder turns on, the gas flows to the cat; if the photon is not of the correct polarization, then the balloon does not turn on, the key does not turn on, the balloon does not let gas into the cat.

Suppose a photon is circularly polarized, and the device responds to linear polarization. It may not be clear, but it is not very important. With some probability, the photon will be polarized in one way, with some probability - in another. Schrodinger said: it turns out such a situation that at some point, until we open the lid and see if the cat is dead or alive (and the system is closed), the cat will be alive with some probability and will be dead with some probability. Maybe I am casually formulating a paradox, but the result is a strange situation that the cat is neither alive nor dead. This is how the paradox is formulated.

In my opinion, this paradox has a perfectly clear and precise explanation. Perhaps this is my personal point of view, but I will try to explain. The main property of quantum mechanics is the following: if you describe a closed system, then quantum mechanics is nothing but wave mechanics, the mechanics of waves. This means that it is described by differential equations whose solutions are waves. Where there are waves and differential equations, there are matrices and so on. These are two equivalent descriptions: matrix description and wave description. The matrix description belongs to Heisenberg, the wave description belongs to Schrödinger, but they describe the same situation.

The following is important: while the system is closed, it is described by a wave equation, and what happens to this wave is described by some wave equation. The whole probabilistic interpretation of quantum mechanics arises after the system is opened - it is affected from the outside by some large classical, that is, non-quantum, object. At the moment of impact, it ceases to be described by this wave equation. There is a so-called reduction of the wave function and a probabilistic interpretation. Until the moment of opening, the system evolves in accordance with the wave equation.

Now we need to make a few remarks about how a large classical system differs from a small quantum one. Generally speaking, even a large classical system can be described using the wave equation, although this description is usually difficult to provide, and in reality it is completely unnecessary. These systems differ mathematically in action. The so-called object exists in quantum mechanics, in field theory. For a classical large system, the action is huge, but for a quantum small system, the action is small. Moreover, the gradient of this action - the rate of change of this action in time and space - is huge for a large classical system, and small for a small quantum one. This is the main difference between the two systems. Due to the fact that the action is very large for a classical system, it is more convenient to describe it not by some wave equations, but simply by classical laws like Newton's law and so on. For example, for this reason, the Moon does not rotate around the Earth like an electron around the nucleus of an atom, but along a certain, clearly defined orbit, along a classical orbit, trajectory. While the electron, being a small quantum system, inside the atom moves around the nucleus like a standing wave, its movement is described by standing wave, and this is the difference between the two situations.

Measurement in quantum mechanics is when you influence a small quantum system with a large classical system. After that, the reduction of the wave function occurs. In my opinion, the presence of a balloon or a cat in the Schrödinger paradox is the same as the presence of a large classical system that measures the polarization of a photon. Accordingly, the measurement takes place not at the moment when we open the lid of the box and see if the cat is alive or dead, but at the moment when the photon interacts with the polarizing glass. Thus, at this moment, the reduction of the photon wave function occurs, the balloon is in a completely definite state: either it opens or it does not open, and the cat dies or does not die. All. There are no "probabilistic cats" that he is alive with some probability, dead with some probability. When I said that the Schrodinger's cat paradox has many different formulations, I only said that there are many different ways come up with the device that kills or leaves the cat alive. In fact, the formulation of the paradox does not change.

I have heard of other attempts to explain this paradox in terms of multiple worlds and so on. In my opinion, all these explanations do not stand up to scrutiny. What I explained during this video in words can be put into mathematical form and the correctness of this statement can be verified. I emphasize once again that, in my opinion, the measurement and reduction of the wave function of a small quantum system occurs at the moment of interaction with a large classical system. Such a big classical system is a cat with a device that kills him, and not a person who opens a box with a cat and sees if the cat is alive or not. That is, the measurement occurs at the moment of interaction of this system with a quantum particle, and not at the moment of checking the cat. Such paradoxes, in my opinion, find explanations from the application of theories and common sense.

The essence of the experiment

Schrödinger's original paper describes the experiment as follows:

You can also construct cases in which burlesque is enough. A certain cat is locked in a steel chamber along with the following infernal machine (which must be protected from the direct intervention of a cat): inside a Geiger counter is a tiny amount of radioactive material, so small that only one atom can decay in an hour, but with the same probability it can and not fall apart; if this happens, the reading tube is discharged and a relay is activated, lowering the hammer, which breaks the vial of hydrocyanic acid. If we leave this whole system to itself for an hour, then we can say that the cat will be alive after this time, as long as the atom does not decay. The first decay of an atom would have poisoned the cat. The psi-function of the system as a whole will express this by mixing in itself or smearing the living and dead cat (forgive the expression) in equal proportions. Typical in such cases is that the uncertainty, originally limited to the atomic world, is transformed into a macroscopic uncertainty that can be eliminated by direct observation. This prevents us from naively accepting the "blur model" as reflecting reality. By itself, this does not mean anything unclear or contradictory. There is a difference between a fuzzy or out-of-focus photo and a cloud or fog shot. According to quantum mechanics, if no observation is made over the nucleus, then its state is described by a superposition (mixing) of two states - a decayed nucleus and an undecayed nucleus, therefore, the cat sitting in the box is both alive and dead at the same time. If the box is opened, then the experimenter can see only one specific state - "the nucleus has disintegrated, the cat is dead" or "the nucleus has not disintegrated, the cat is alive." The question is this: when does a system cease to exist as a mixture of two states and chooses one concrete one? The purpose of the experiment is to show that quantum mechanics is incomplete without some rules that specify under what conditions the wave function collapses and the cat either becomes dead or remains alive, but ceases to be a mixture of both.

Since it is clear that the cat must necessarily be either alive or dead (there is no state that combines life and death), this will be the same for the atomic nucleus. It must necessarily be either decayed or undecayed.

The original article appeared in 1935. The purpose of the article was to discuss the Einstein-Podolsky-Rosen (EPR) paradox published by Einstein, Podolsky and Rosen earlier that year.