Schrödinger's Cat

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22 Feb 2024
13


Erwin Schrödinger (1887 - 1961), who wrote the fundamental wave equation of quantum mechanics, is among those who did not accept the later interpretations... Schrödinger ultimately cooled off from the theory (to the point of saying that he regretted contributing to its development!). After this, like Einstein, he began to look for examples that would strikingly demonstrate the illogicality of the theory. The thought experiment called Schrödinger's Cat, which he put forward in 1935, is the most famous of these. In the same year, Einstein, Podolski and Rosen tried to criticize the form of quantum theory with a thought experiment called the "EPR Experiment". But time has proven the quantum theory right, not Schrödinger and Einstein. Now let's see Schrödinger's thought experiment.
Let's put a healthy cat in a breathable box. Let there be a poisonous gas bottle in the box, and the mechanism that will release this gas from the bottle is controlled by a radioactive particle with a decay half-life of 1 hour. We can only express the behavior of this microscopic particle with quantum mechanics, but now the fate of the cat, which is a macroscopic system, is now linked to the behavior of the particle. According to Schrödinger's claim, the probability of the cat being alive or dead after 1 hour is equal. The meaning of the wave function is not just describing two extreme possibilities, such as either decay occurred and the cat died, or it did not occur and the cat is alive. If Schrödinger's analysis is correct, quantum theory says that there are two states of the cat side by side (until someone looks and reduces the situation to one of these two options): Half dead and half alive. Schrödinger concludes that such a counterintuitive theory needs correction. On the other hand, many physicists (Hawking, Gell-Mann and others) believe that this problem is artificial.
First of all, the idea of ​​probability of the atomic and molecular world has been moved to the macroworld. Because unless we make observations, we cannot know whether it is dead or alive. The answer here means equal probability of being dead and alive, rather than the interpretation of "The cat is fifty percent dead, fifty percent alive".
Stephen Hawking (1942-...) says: In my view, the unspoken belief in a model-independent reality underlies the difficulties philosophers of science encounter with quantum mechanics and the uncertainty principle. There is a famous thought experiment called Schrödinger's cat.
If someone opens the box, they will find the cat either dead or alive. However, before the box is opened, the quantum state of the cat will be a mixture of the dead cat state and the state where the cat is alive. Some philosophers of science find this very difficult to accept. Just as it is not possible for a cat to be half pregnant and half unborn, it is not possible for a cat to be half pregnant.
Their difficulty arises indirectly from their use of a classical concept of reality in which an object has a single, definite history. The basis of quantum mechanics is that it has a different view of reality. In this view, an object has not just one past, but all possible histories. In most cases the possibility of having a particular past cancels out the possibility of having a slightly different past, but in certain cases the possibilities of neighboring pasts reinforce each other. What we observe as the object's history is one of these enhanced histories.
The probability of a particle going from A to B was found by adding up the waves associated with each possible path through A and B. In the everyday world, objects appear to us to follow a single path, a single trajectory, between initial and final goals. Is this compatible with Feyman's concept of multiple histories (or the sum of histories)? Yes. Because the rule of assigning numbers to each path requires that for large objects, when the contributions of the paths meet, all paths except one cancel each other. That is, only one of the infinite types of paths is important as long as the motion of macroscopic objects is considered, and this trajectory is the one that emerges from Newton's classical laws of motion.
The experiment was briefly as follows. You have a cat in a box, closed off from any outside observation. The box also contains a Geiger counter, a radioactive substance that is uncertain when it will decay, such as uranium. The box remains closed the entire time.
If an atom decays, the Geiger counter detects the radiation and triggers a hammer that breaks the poison vial, killing the cat. If the atom does not decay, the cat lives. There are no weak workarounds like listening to the cat or seeing the box move.
So is the cat alive or dead now? Since there is no possible way to tell, the cat is both alive and dead. In order to make a complete judgment about the cat's fate, it is necessary to open the box (observe). In other words, the cat has the possibility of being both dead and alive, but these possibilities can only come true through observation.
What was the Purpose of Schrödinger's Cat Experiment?
One interpretation of quantum mechanics is that small particles can exist simultaneously in situations that we usually consider to be mutually exclusive. For example, an electron can be in two places at once, or a radioactive atom can decay and not decay at the same time. However, if we want to measure a system in superposition, the superposition disappears and one of the possibilities occurs.
In 1905, Einstein proposed that light could behave like waves in some situations and like particles in others. Inspired by this behavior of light, the young French physicist Louis de Broglie took a step in this journey. He proposed that not only light but also matter would behave in wave-particle form. In this case, small building blocks of matter, such as electrons, behaved like particles in some cases and like waves in other cases.
De Broglie's idea, announced in the 1920s, was not based on empirical evidence. It stemmed mostly from theoretical ideas inspired by Einstein's theory of relativity. However, experimental evidence would soon follow. In the late 1920s, experiments involving particles scattered from a crystal confirmed the wave-like nature of electrons. One of the most famous proofs of wave-particle duality is the double-slit experiment.
De Broglie's radical ideas required a new physics. What did a wave associated with a particle look like mathematically? As a result, ordinary waves can be described mathematically. You can formulate a wave equation that describes how a particular wave varies in space and time. The solution to this equation is a wave function that describes the shape of the wave at each point in time.
As we know from experience, when we look at a particle, superposition disappears. No one has ever directly seen a single particle in more than one place at the same time. So why and how does the superposition disappear when the measurement is made? No one knows exactly the answers to these questions.

Another thing that follows directly from the mathematics of the Schrödinger equation is Heisenberg's famous uncertainty principle. The principle says that you can never measure both the position and momentum of a quantum object, such as our particle in a box, with arbitrary precision. The more specific you are about one, the less you can say about the other. It's not because your measurement tools aren't good enough. This is a fact of nature.
Position and momentum aren't the only things that can't be measured simultaneously with arbitrary accuracy. The same goes for time and energy. The more precise you are about the time period in which something occurs, the less precise you can be about its energy, and vice versa.
Another quantum oddity is entanglement. A wave function can also describe a system consisting of many particles. Sometimes it is impossible to decompose the wave function into components corresponding to individual particles. When this happens, the particles become inextricably bound together, even if they are farther apart. When something happens to one of these particles, the same thing happens to its distant partner.

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