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Could someone please explain to me the idea that Schrödinger was trying to illustrate by the cat in his box? I understand that he was trying to introduce the notion of the cat being both alive and dead at the same time. But why was it necessary to introduce this thought experiment and what did it achieve?

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The original paper is relatively short and very readable. –  MBN Feb 10 at 11:08
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First, a historical subtlety: Schrödinger has actually stolen the idea of the cat from Einstein.

Second, both men – Einstein and Schrödinger – used the thought experiment to "explain" a point that was wrong. They thought it was absurd for quantum mechanics to say that the state $a|{\rm alive}\rangle+b|{\rm dead}\rangle$ was possible in Nature (it was claimed to be possible in quantum mechanics) because it allowed the both "incompatible" types of the cat to exist simultaneously.

Third, they were wrong because quantum mechanics does imply that such superpositions are totally allowed and must be allowed and this fact can be experimentally verified – not really with cats but with objects of a characteristic size that has been increasing. Macroscopic objects have already been put to similar "general superposition states".

The men introduced it to fight against the conventional, Copenhagen-like interpretations of quantum mechanics, and that's how most people are using the meme today, too. But the men were wrong, so from a scientifically valid viewpoint, the thought experiment shows that superpositions are indeed always allowed – it is a postulate of quantum mechanics – even if such states are counterintuitive. Similar superpositions of common-sense states are measured so that only $|a|^2$ and $|b|^2$ from the coefficients matter and may be interpreted as (more or less classical) probabilities. Due to decoherence, the relative phase is virtually unmeasurable for large, chaotic systems like cats, but in principle, even the relative phase matters.

Quite generally, the people who are wrong – who have a problem with quantum mechanics – like to say that the superposition means that the cat is alive "and" dead. But the right, quantum answer is that the addition in the wave function doesn't mean "and". Instead, it means a sort of "or", so the superposition simply says that the cat is dead or alive, with the appropriate probabilities (quantum mechanics determines not only the probabilities but also their complex phases, and those may matter for other questions).

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Reading up on Wikipedia, I presume that the theft of the idea of the cat was actually the theft of an idea that lacked a cat. –  Glen The Udderboat Feb 4 at 17:28
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The thought experiment aimed at illustrating one concept, and questioning the validity of such concept: 1/ The concept: in quantum mechanics, before an observation is made (note the cat is in a closed box, and nobody can see what is going on in the box), a system is not in a defined state, but only has a certain probability to be in any state - here the system is a cat, and the states are "dead" and "alive", and it is indeed a striking picture. With this, the goal of making eyebrows raise, and listeners question realize the significance of the concept is indeed reached.

2/ The questioning: by applying the concept of superposition to life and death issues, and also to a macroscopic object, the aim was to highlight the really revolutionary nature of the concept itself - in particular to highlight our complete ignorance of the reason why this quantum behaviour is ubiquitous at the atomic scale, but more rarely observed at the macroscopic scale (even though some manifestations do exist: superconductivity, BEC...)

So my answer is: it was not necessary, but it was a striking way to convey the concept of quantum superposition, and ask what is the defining limit between the microscopic and macroscopic laws of nature, if there is any. This question is still in debate, and is one of the goals of unification theories, with the major question of a quantum theory of gravity still unsolved.

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Schrödinger's cat is a thought experiment, sometimes described as a paradox. The scenario presents a cat that may be both alive and dead, depending on an earlier random event. Although the original "experiment" was imaginary, similar principles have been researched and used in practical applications.

The thought experiment is also often featured in theoretical discussions of the interpretations of quantum mechanics. Schrödinger wrote: One can even set up quite ridiculous cases. A cat is penned up in a steel chamber, along with the following device (which must be secured against direct interference by the cat): in a Geiger counter, there is a tiny bit of radioactive substance, so small, that perhaps in the course of the hour one of the atoms decays, but also, with equal probability, perhaps none; if it happens, the counter tube discharges and through a relay releases a hammer that shatters a small flask of hydrocyanic acid.

If one has left this entire system to itself for an hour, one would say that the cat still lives if meanwhile no atom has decayed. The psi-function of the entire system would express this by having in it the living and dead cat (pardon the expression) mixed or smeared out in equal parts.

It is typical of these cases that an indeterminacy originally restricted to the atomic domain becomes transformed into macroscopic indeterminacy, which can then be resolved by direct observation. That prevents us from so naively accepting as valid a "blurred model" for representing reality. In itself, it would not embody anything unclear or contradictory. There is a difference between a shaky or out-of-focus photograph and a snapshot of clouds and fog banks.

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This is why I think Schrodinger introduced this thought experiment. You can explain why Schrodinger developed this thought experiment by first considering the double slit experiment. You fire a photon at a double slit, and the photon goes through the double slit device and then strikes a screen. If you don’t try to determine which slit the photon has gone through, then the photon will (almost certainly) strike a spot on a screen that corresponds to the position of an interference antinode (you won’t generate an interference pattern of antinodes with just one photon, but one photon will land in one of the places that would be an antinode if you had used more light (and had sent many more photons the double slit). This tells you that the photon could not have gone through one slit or the other. If it had gone through one slit or the other, it would have traveled along one of the two possible classical paths. The photon would have traveled along a straight line from the light source to the slit that it went through and continued traveling in a straight line until it hit the screen at a point that is in-line with the slit and source. But it didn’t do this – it stuck the screen at an antinode position as if the photon were a wave and traveled through both slits at the same time. So the outcome of this experiment requires that you regard the traveling photon to exist along all possible paths (i.e. it takes all possible paths) between the source and the point where the photon eventually strikes the screen.

The lesson? When you don’t interfere with a quantum entity it evolves according to a wavefunction and is in a superposition of many states until it is observed.

Now for Schrodinger’s cat. If an atom with an unstable nucleus is not being observed, it evolves according to a wavefunction and is simultaneously in an undecayed state and a decayed state (where the value of the decayed state coefficient in the wavefunction increases as time elapses, and the coefficient of the undecayed coefficient decreases as time elapses). While you can regard the wavefunction as a means of predicting the probability that the photon strikes the screen at a particular point, you cannot regard it to describe the probability that the photon has gone through one slit or the other, because that would not be consistent with the observation that the photon struck the screen at an antinode position rather than strike a point that is in-line with a particular slit and the light source. Classically, the atom must exist in one state or the other but not both simultaneously; the classical states are mutually exclusive. But in quantum mechanics, the atom can exist in both states at the same time when it isn’t observed. Schrodinger’s thought experiment shows how ludicrous quantum reality is (but doesn’t refute it). You can imagine an experiment where the superposition of atom- states requires that a macroscopic object (the cat) is also in a superposition of mutually exclusive states (alive and dead), rather than existing in one classical state or the other.

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protected by Qmechanic Jul 13 at 18:34

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