Schrödinger's theory. Schrödinger's cat and his difficult fate

is a thought experiment by physicist Erwin Schrödinger, the essence of which is that the cat in the box is both alive and dead. Thus, the scientist proved the incompleteness quantum mechanics during the transition from subatomic systems to macroscopic ones.

Origin

The Austrian theoretical physicist Erwin Schrödinger proposed an experiment with a cat in a box in his article “The Current Situation in Quantum Mechanics” (Die gegenwärtige Situation in der Quantenmechanik) in the publication Naturwissenschaften in 1935.

We take the cat and put it in the box. The box contains an atomic nucleus and a container with poisonous gas. The probability of nuclear disintegration is 50%; if it occurs, the gas container will open and the cat will die. If decay does not occur, the cat is alive. According to the basics of quantum mechanics, before we open the box, the cat is in a state of quantum superposition - that is, in all states at the same time.

It turns out that in the “cat-core” system, a cat can be alive or dead with the same probability of 50%. Or he is both alive and dead at the same time.

Popularity on the Internet

The issue of Schrödinger’s cat was first discussed on the Internet in May 1990 on the Usenet’s sci.physics forum. On August 9, 2000, a poem dedicated to Schrödinger's cat was published on the Straight Dope Q&A forum.

In August 2004, the online store ThinkGeek began selling T-shirts with the words “Schrodinger's Cat Died.”

On January 4, 2006, a Schrödinger comic was released in the Xkcd comic series.

” – The last panel of this comic is funny and unfunny at the same time. Until you read it, you can't tell how it will turn out in the end.

- Crap"

On June 2, 2007, the I Can Has Cheezburger website published a picture of a cat in a box with the caption: “In your quantum box... one cat... maybe.”

The crowning glory of Schrödinger's cat's popularity was a Google Doodle dedicated to him, which appeared on August 12, 2013, the day of Erwin Schrödinger's 126th birthday.

Popular culture references

Films, TV series, books and computer games, where this experiment was mentioned. Let's give just a few examples.

In episode 16 of the sixth season of Futurama, the police detain Schrödinger and his cat.

In the second episode of the first season of “Rick and Morty,” the main characters meet Schrödinger’s cats in a parallel reality.

Sheldon Cooper in "Theory" big bang” using Schrödinger’s cat theory to explain to Penny how relationships between men and women work.

Meaning

Schrödinger's cat is not only an Internet meme, but also a hero of popular culture. The cat, which is both alive and dead, symbolizes a certain ambiguity. Schrödinger is remembered when something is both funny and not, or when something is both prohibited and permitted. For example, a traffic light with red and green lights on at the same time is a Schrödinger traffic light.

Gallery

Schrödinger's cat is the most mysterious of all the cats, cats, cats, cats that humanity adores so much. Viral cat videos spread across the World Wide Web with millions of daily views, and images of cute kittens on advertising billboards can make us buy any product. The field of popularizing science also has its own mustachioed and striped heroes. More precisely, one is Schrödinger's cat. Surely you have heard about it, even if you are not involved in quantum mechanics. So why has the famous cat haunted physicists and lyricists for almost a hundred years, and also become one of the most curious objects of modern mass culture?

Schrödinger's cat as a metaphor

As paradoxical as it may sound, the Austrian theoretical physicist and owner Nobel Prize Erwin Schrödinger is the “father” of the most mysterious cat, not the owner. After all Schrödinger's cat is a thought experiment, a theoretical paradox, and a truly amazing metaphor for describing quantum superposition.

Was there a cat?

The question “Did Schrödinger have a cat?” still remains open. Although, according to a number of sources, in one of the early editions PhysicsToday there is a photograph of the scientist with his pet cat Milton. On the other hand, in original text article in 1935, where Erwin Schrödinger described his hypothetical experiment, and it is not a cat that is listed at all, but a cat (die Katze). Why did the physicist choose a feline representative as the main character of his concept? How did the cat turn into a cat? These questions seem destined to remain rhetorical.

Schrödinger's cat is dead with a 50% chance

Designua / shutterstock.com

However, if the source of inspiration for the researcher was his personal pet, then, apparently, the reason for this was a vase broken by a cat or damaged wallpaper. Because the main thing that Schrödinger’s cat does during the experiment is to be locked in a steel box and... die. True, with a probability of 50%. More precisely, in addition to the poor animal, a special mechanism containing a radioactive core and a container with poisonous gas is placed inside the box. If the nucleus disintegrates, the mechanism is triggered, and the cat dies from the released gas. If it doesn't work, it lives. But only the observer who opens the box can know his fate. Until then, the cat is both alive and dead.

Without a cat, quantum mechanics is not the same

This whole situation, paradoxical at first glance, clearly illustrates one of the provisions of quantum mechanics. According to him, the atomic nucleus is simultaneously in all possible states: decay and non-decay. If no observation is made of the atom, then its state is described by a mixture of these two characteristics. Therefore, the cat, read - the nucleus of an atom, is both alive and dead. And this is simply impossible. This means that quantum mechanics lacks some rules that determine the conditions under which the fate of the cat is clearly clear.

Schrödingr's cat: varieties

It is not surprising that the meaning of what is happening with the mythical cat in a steel box has several interpretations.

Copenhagen variety

There is the Copenhagen interpretation of quantum mechanics, the authors of which are Niels Bohr and Werner Heisenberg. According to it, the cat remains in both states, regardless of the observer. After all, the decisive moment occurs not when the drawer opens, but when the mechanism is triggered. That is, the animal has long since died from the gas, but the box is still locked. In other words, in the Copenhagen interpretation there is no “dead-alive” state, because it is determined by a detector that reacts to the decay of the nucleus.

Everett variety

There is also a many-worlds interpretation, or the Everett interpretation. She interprets the experience with Schrödinger's cat as two separate existing world, splitting into which occurs at the moment when the box is opened. In one universe the cat is alive and well, in another he did not survive the experiment.

"quantum suicide"

One way or another, the poor cat Schrödinger was “tortured” by many physicists. Some, for example, proposed considering the situation with the cat from the point of view of the animal itself - after all, he knows better than all the physicists in the world whether he is dead or alive. Really, you can't argue with that. This approach is called “quantum suicide” and hypothetically allows you to check which of these interpretations is correct.

Everyone can breed their own variety

If you look at modern physical science, you can say with confidence that on the pages of research, Schrödinger’s long-suffering cat is more alive than anyone else alive. From time to time, scientists offer their solutions to this well-known paradox, and also develop the concept in the framework of very interesting developments.

"second box"

For example, last year, researchers at Yale University "gave" Schrödinger's cat a second box for his deadly hide and seek. Based on this approach, scientists tried to simulate the system necessary for the operation of a quantum computer. After all, as you know, one of the main difficulties in creating this type of machine is the need to correct errors. And, as it turns out, using Schrödinger’s cats is a promising way to manage excess quantum information.

"micro cat"

And just a couple of weeks ago, an international team of scientists, led by Russian experts in the field of quantum optics, managed to “breed” microscopic Schrödinger cats in order to advance in the search for the boundary between the quantum and classical worlds. This is how Schrödinger’s cat helps physicists develop quantum communication technologies and cryptography.

Schrödinger's cat is a pop culture star

Africa Studio / shutterstock.com

If the cat cannot escape from his ill-fated box, then he managed to get out of the boundaries of scientific concepts and pages of research. And how!

The character of a mysterious cat with a difficult fate appears with enviable consistency in works of popular culture. Thus, Schrödinger's cat appears in the books of Terry Pratchett, Fredrik Pohl, Douglas Adams and other world famous writers. Of course, there was a mention of the cat in popular television projects such as “The Big Bang Theory” and “Doctor Who.” Not to mention that the image of Schrödinger's cat is constantly found in video games and song lyrics. And the Internet portal ThinkGeek has already made a fortune from selling T-shirts with the inscription on one side: “Schrodinger's Cat is Alive”, and on the other - “Schrodinger's Cat is Dead.”

Cats do it better

Agree, you can observe an amazing thing: the most famous scientific cat is just a visualized model for testing a hypothesis. However, the participation of the tailed pet in it added a significant amount of poetry and charm to the experiment. Or maybe it’s just that cats do everything better? Quite possible.

And remember: as a result of Schrödinger’s experiment, not a single cat was harmed.

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As Heisenberg explained to us, due to the uncertainty principle, the description of objects in the quantum microworld is of a different nature than the usual description of objects in the Newtonian macroworld. Instead of spatial coordinates and speed, which we are used to describing mechanical movement, for example, a ball on a billiard table, in quantum mechanics objects are described by the so-called wave function. The crest of the “wave” corresponds to the maximum probability of finding a particle in space at the moment of measurement. The movement of such a wave is described by the Schrödinger equation, which tells us how the state of a quantum system changes over time.

Now about the cat. Everyone knows that cats love to hide in boxes (). Erwin Schrödinger was also in the know. Moreover, with purely Nordic fanaticism, he used this feature in a famous thought experiment. The gist of it was that there was a cat locked in a box with an infernal machine. The machine is connected through a relay to a quantum system, for example, a radioactively decaying substance. The probability of decay is known and is 50%. The infernal machine is triggered when the quantum state of the system changes (decay occurs) and the cat dies completely. If you leave the “Cat-box-hellish machine-quanta” system to itself for one hour and remember that the state of a quantum system is described in terms of probability, then it becomes clear that it will probably not be possible to find out whether the cat is alive or not at a given moment in time, just as it will not be possible to accurately predict the fall of a coin on heads or tails in advance. The paradox is very simple: the wave function that describes a quantum system mixes the two states of a cat - it is alive and dead at the same time, just as a bound electron can be located with equal probability in any place in space equidistant from the atomic nucleus. If we don't open the box, we don't know exactly how the cat is doing. Without making observations (read measurements) over atomic nucleus we can describe its state only by a superposition (mixing) of two states: a decayed and undecayed nucleus. A cat in nuclear addiction is both alive and dead at the same time. The question is: when does a system cease to exist as a mixture of two states and choose one specific one?

The Copenhagen interpretation of the experiment tells us that the system ceases to be a mixture of states and chooses one of them at the moment when an observation occurs, which is also a measurement (the box opens). That is, the very fact of measurement changes physical reality, leading to the collapse of the wave function (the cat either becomes dead or remains alive, but ceases to be a mixture of both)! Think about it, the experiment and the measurements that accompany it change the reality around us. Personally, this fact bothers my brain much more than alcohol. The well-known Steve Hawking also has a hard time experiencing this paradox, repeating that when he hears about Schrödinger’s cat, his hand reaches out to the Browning. The severity of the reaction of the outstanding theoretical physicist is due to the fact that, in his opinion, the role of the observer in the collapse of the wave function (collapsing it into one of two probabilistic) states is greatly exaggerated.

Of course, when Professor Erwin conceived his cat-mockery back in 1935, it was an ingenious way to show the imperfection of quantum mechanics. In fact, a cat cannot be alive and dead at the same time. As a result of one of the interpretations of the experiment, it became obvious that there was a contradiction between the laws of the macro-world (for example, the second law of thermodynamics - the cat is either alive or dead) and the micro-world (the cat is alive and dead at the same time).

The above is used in practice: in quantum computing and quantum cryptography. A light signal in a superposition of two states is sent through a fiber-optic cable. 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. By conducting statistical tests of light at the receiving end of the cable, it will be possible to detect whether the light is in a superposition of states or has already been observed and transmitted to another point. This makes it possible to create means of communication that exclude undetectable signal interception and eavesdropping.

Another more recent interpretation of Schrödinger's thought experiment is a story that Sheldon Cooper, the hero of the Big Bang Theory, told his less educated neighbor Penny. The point of Sheldon's story is that the concept of Schrödinger's cat can be applied to human relationships. In order to understand what is happening between a man and a woman, what kind of relationship is between them: good or bad, you just need to open the box. Until then, the relationship is both good and bad.

Yuri Gordeev
Programmer, game developer, designer, artist

"Schrödinger's Cat" is a thought experiment proposed by one of the pioneers quantum physics, to show how strange quantum effects look when applied to macroscopic systems.

I'll try to really explain in simple words: Gentlemen of physics, don’t hold me accountable. The phrase "roughly speaking" is implied further before each sentence.

On a very, very small scale, the world is made up of things that behave in very unusual ways. One of the strangest characteristics of such objects is the ability to be in two mutually exclusive states at the same time.

What is even more unusual from an intuitive point of view (some would even say creepy) is that the act of purposeful observation eliminates this uncertainty, and the object, which was just in two contradictory states at the same time, appears before the observer in only one of them, as if in nothing never happened, looks to the side and whistles innocently.

At the subatomic level, everyone has long been accustomed to these antics. Exists mathematical apparatus, which describes these processes, and knowledge about them has found a variety of applications: for example, in computers and cryptography.

At the macroscopic level, these effects are not observed: objects familiar to us are always in a single specific state.

Now for a thought experiment. We take the cat and put him in a box. We also place a flask with poisonous gas, a radioactive atom and a Geiger counter there. A radioactive atom may or may not decay at any time. If it disintegrates, the counter will detect radiation, a simple mechanism will break the flask with gas, and our cat will die. If not, the cat will remain alive.

We close the box. From this moment, from the point of view of quantum mechanics, our atom is in a state of uncertainty - it decayed with a probability of 50% and did not decay with a probability of 50%. Before we open the box and look inside (make an observation), it will be in both states at once. And since the fate of the cat directly depends on the state of this atom, it turns out that the cat is also literally alive and dead at the same time ("...smearing the living and dead cat (pardon the expression) in equal parts..." writes the author of the experiment). This is exactly how quantum theory would describe this situation.

Schrödinger could hardly have guessed how much noise his idea would make. Of course, the experiment itself, even in the original, is described extremely crudely and without any pretense of scientific accuracy: the author wanted to convey to his colleagues the idea that the theory needs to be supplemented with clearer definitions of processes such as “observation” in order to exclude scenarios with cats in boxes from its jurisdiction.

The idea of a cat was even used to “prove” the existence of God as a superintelligence, whose continuous observation makes our very existence possible. In reality, “observation” does not require a conscious observer, which takes some of the mysticism out of quantum effects. But even so, quantum physics remains today the frontier of science with many unexplained phenomena and their interpretations.

Ivan Boldin
Candidate of Physical and Mathematical Sciences, researcher, MIPT graduate

Behavior of microworld objects ( elementary particles, atoms, molecules) differs significantly from the behavior of objects with which we usually have to deal. For example, an electron can simultaneously fly through two spatially distant places or be simultaneously in several orbits in an atom. To describe these phenomena, a theory was created - quantum physics. According to this theory, for example, particles can be smeared in space, but if you want to determine where the particle is located, then you will always find the entire particle in some place, that is, it will seem to collapse from its smeared state to some specific place. That is, it is believed that until you have measured the position of a particle, it has no position at all, and physics can only predict with what probability you can find a particle in which place.

Erwin Schrödinger, one of the creators of quantum physics, wondered: what if, depending on the result of measuring the state of a microparticle, some event occurs or does not occur. For example, this could be implemented as follows: take a radioactive atom with a half-life of, say, an hour. An atom can be placed in an opaque box, a device can be placed there that, when the radioactive decay products of the atom hit it, breaks an ampoule with poisonous gas, and a cat can be placed in this box. Then you will not see from the outside whether the atom has decayed or not, that is, by quantum theory it simultaneously disintegrated and did not disintegrate, and the cat, therefore, was simultaneously alive and dead. This cat became known as Schrödinger's cat.

It may seem surprising that a cat can be alive and dead at the same time, although formally there is no contradiction here and this is not a refutation of quantum theory. However, questions may arise, for example: who can collapse an atom from a smeared state into a certain state, and who, with such an attempt, himself goes into a smeared state? How does this collapse process occur? Or how does it happen that the one who performs the collapse does not himself obey the laws of quantum physics? Whether these questions make sense and, if so, what the answers are, is still unclear.

George Panin
graduated from Russian Chemical Technical University named after. DI. Mendeleev, chief specialist of the research department (marketing research)

As Heisenberg explained to us, due to the uncertainty principle, the description of objects in the quantum microworld is of a different nature than the usual description of objects in the Newtonian macroworld. Instead of the spatial coordinates and speed that we are used to describing mechanical motion, for example, a ball on a billiard table, in quantum mechanics objects are described by the so-called wave function. The crest of the “wave” corresponds to the maximum probability of finding a particle in space at the moment of measurement. The movement of such a wave is described by the Schrödinger equation, which tells us how the state of a quantum system changes over time.

Now about the cat. Everyone knows that cats love to hide in boxes (thequestion.ru). Erwin Schrödinger was also in the know. Moreover, with purely Nordic fanaticism, he used this feature in a famous thought experiment. The gist of it was that there was a cat locked in a box with an infernal machine. The machine is connected through a relay to a quantum system, for example, a radioactively decaying substance. The probability of decay is known and is 50%. The infernal machine is triggered when the quantum state of the system changes (decay occurs) and the cat dies completely. If you leave the “Cat-box-hellish machine-quanta” system to itself for one hour and remember that the state of a quantum system is described in terms of probability, then it becomes clear that it will probably not be possible to find out whether the cat is alive or not at a given moment in time, just as it is impossible to accurately predict the fall of a coin on heads or tails in advance. The paradox is very simple: the wave function that describes a quantum system mixes the two states of a cat - it is alive and dead at the same time, just as a bound electron can be located with equal probability in any place in space equidistant from the atomic nucleus. If we don't open the box, we don't know exactly how the cat is doing. Without making observations (read measurements) of an atomic nucleus, we can describe its state only by superposition (mixing) of two states: a decayed and undecayed nucleus. A cat in nuclear addiction is both alive and dead at the same time. The question is: when does a system cease to exist as a mixture of two states and choose one specific one?

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Schrödinger managed to acquire a reputation as an eccentric even among colleagues who themselves were often out of touch with life. The scientist dressed so casually that they did not want to let him into the hotel because they took him for a tramp. Once, at an important conference, Schrödinger refused to talk about nuclear energy and gave a lecture on philosophy.

This controversial person decided to troll the scientific community and came up with a cruel experiment involving a cat and a deadly gas. Fortunately, not a single cat was harmed. And all because the experiment was mental and everything happened only in the imagination of an individual physicist.

A few words about quantum mechanics

Here's a simple example of quantum physics at work. Take 2 empty matchboxes. Place a match in one of them - this is an object of our familiar macrocosm. Now you can say that the match is only in one box, and there is nothing in the other. This is how the Newtonian physics we are familiar with works.

Everything changes if you take an electron instead of a match: it will be located simultaneously in 2 boxes. This is how the laws of quantum physics work.

In 1935, the physicist conducted his famous thought experiment. The original text is in German. Well, we translated it for you from the language of scientists into the language of ordinary people.

A cat is placed in a closed steel box.
In addition to the cat in the box, there is an infernal machine with a radioactive core and poisonous gas. The gas is contained in a sealed glass container.
Radioactive nucleus may disintegrate within 1 hour. Or maybe it won't fall apart. The probability of the event is 50%. (Note: nuclear decay is the easiest example that came to the scientist's mind, because in this case the nucleus has only 2 options. If he had taken any other variable, the results of the experiment would have been difficult to predict.)
If the nucleus disintegrates, the cat will be out of luck. Because the decay of the nucleus will be detected by a Geiger counter, the relay will work, and a special hammer will break the ampoule with toxic gas. The cat is dead.
If the nucleus does not decay, the cat remains alive.

To understand the essence of Schrödinger's experiment, you need to get acquainted with another principle of quantum mechanics - observer's paradox .

The radioactive nucleus that threatens our cat is in superposition exactly as long as we we don't observe behind the system. As soon as an observer connects to the system and tries to see what is happening in general, the nucleus (atoms, photons) is finally determined and takes a certain position.

If no one is watching the system (does not go into the box with their measuring instruments), then the nucleus decayed / did not decay at the same time.

But a cat is a completely different matter. He is absolutely alive or absolutely dead. Because the cat, i.e. the macrosystem, is not affected by quantum laws - it consists of many different particles. The radioactive nucleus is in one world, and the cat lives in the world of big things.

The cat doesn't care when you open the lid. This nucleus will/will not decay when the observer appears. And the cat will either be alive or dead whether you look at it or not.

How does the kernel “know” that it is being watched? When people or instruments begin observing or measuring, the particles experience wave (quantum) collapse: they have been in a state of uncertainty for some time (they have many options), and the measurement/observation determines the position of the nucleus in space/time. In simple words, the core from the microworld enters the macroworld. It leaves the zone of action of the laws of quantum physics and falls under the action of Newtonian physics.