Well, quantum mechanics is indeed not too difficult, as long as you don't think much about it and just use it to calculate things. This "shutup-and-calculate interpretation" in fact is a good starting point to get used with the formal side.
The real difficulty starts, when you like to get an intuitive picture about nature in terms of quantum theory, and as far as we know, all of nature is described (or at least should be described) by quantum theory.
Now, with Schrödinger's cat the quibbles start. If they don't start for you, it's save to say that you haven't yet understood the full implications of quantum theory yet, and in fact a lot of popular-science accounts of quantum mechanics get this and similar topics (like entanglement) simply wrong. Many even make a kind of mystery out of quantum theory, which is contrary to the aims of natural sciences, namely to describe nature by as simple as possible and as general as possible fundamental laws. As Einstein put it, the important thing is to explain things not simpler than possible but only as simple as possible.
Concerning Schrödinger's cat, many popular-science text tell the poor readers, in the famous example by Schrödinger the cat was "dead and alive at the same time". This is plain wrong. It's just one of the common misunderstandings of quantum theory by mixing socalled "common sense" with the correct description according to quantum mechanics.
The well-known setup is the following: A cat is confined in a box, together with some radioactive atom and a device, which destroys a bottle of poison killing the cat as soon as the atom decays. This setup is more complicated than necessary, but Schrödinger has chosen it to demonstrate what he thought to be odd with quantum theory. One has to keep in mind that Schrödinger, although one of the discoverers of quantum mechanics in 1926 (in terms of wave mechanics), he could never accept the probabilitistic interpretation of the quantum mechanical states, i.e., Born's Rule.
Ironically, it's Born's rule, which makes quantum theory consistent, but of course with quite drastic implications, correcting our "common sense", which is built on our everyday experience with macroscopic objects, which behave with high accuracy according to classical physics although in fact they are of course quantum objects as anything, and such common things like the stability of the matter around as cannot be understood with quantum mechanics.
Back to Schrödinger's cat: The point is that according to quantum mechanics, we cannot know with certainty that after a certain time of putting the atom into the box, whether it is decayed or not. We only know the probability that it is decayed. Approximately the probability that it is decayed after a time [itex]t[/itex] is given by
[tex]P(t)=1-\exp(-t/\tau),[/itex]<br />
where [itex]\tau[/itex] is a parameter (the mean life time of the atom) specific for the used radioactive atom.<br />
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In turn we don't know, whether the bottle with the poison is broken and finally thus whether the cat still is alive or not. Often it's claimed that the cat is in a pure state of the kine [itex]|\psi \rangle = \sqrt{P(t)} |\text{dead} \rangle + \sqrt{1-P(t)} |\text{alive} \rangle[/itex]. This is a vast oversimplification, because it's not even clear, what the pure state for "dead" and "alive" should be, but even if you assume that this very unrealistic assertion is correct, there is no problem with common sense here.<br />
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According to Born's rule, before looking into the box and checking whether the cat is dead or alive, you don't know with certainty in which state the poor pet might be. This doesn't mean that it is both dead and alive at the same time neither that it is dead or alive for sure. According to quantum theory the observable "dead or alive" is simply undetermined, and you can give only the probability, whether the cat is dead or alive. It's simply impossible to know about the cat's state from the preparation at the previous time [itex]t=0[/itex] what its state is at the later time [itex]t>0.[/itex] That's all.<br />
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Of course, it contradicts our everyday experience about a macroscopic system like a cat, because there you can say with some certainty that the cat is for sure dead or alive, no matter whether I look at it or not. According to quantum theory that's not a priori the case, and that's what's really difficult to understand.<br />
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The real question thus is, why our everyday experience with macroscopic systems suggests a classical deterministic behavior! This is answered by decoherence. The problem with macroscopic systems (and even with some not too large objects like a "Bucky Ball molecule" (made up by 60 carbon atoms shaped like a soccer ball)) is that they are very hard to isolate from interactions with the environment. On a microscopic scale a lot of very different states with only tiny differences in energy (compared with the total energy of the macroscopic object) make up the same "macroscopic" state. The reason simply is that we cannot describe even a simple body as a billard ball in all its microscopic details: It's made up of about [itex]10^{24}[/itex] atoms, which themselves are made up finally of quarks, gluons, and electrons. It's impossible to investigate such a number of particles in detail. Fortunately for everyday experimience with billard balls, we don't need such a detailed description! Mostly it's enough to know where the center of mass of the billard ball is located, sometimes you might need it's spin state as a whole too, but that's more or less all you need to know about it. These macroscopic "collective" observables are described averages over all the intrinsic states of the microscopic constituents, and one can show that this average quantities behave classically through the interaction with the environment, which can not easily be avoided.<br />
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This is even true for pretty small objects like the Bucky Ball molecules. However, physicists nowadays can prepare those molecules very carefully and are able to demonstrate that these objects behave quantum mechanically. For that purpose the group around the Austrian physicist Zeilinger cooled down Bucky Ball molecules very close to 0K temperature. Then they could perform a double-slit experiment, demonstrating quantum-mechanical behavior by leading to wave-like interference patterns of Bucky Balls on a screen.<br />
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Now, it is very easy to excite such a large molecule. But Zeilinger's group could also heat the Bucky Balls up by a tiny amount of heat energy. This makes the Bucky Ball irradiate thermal photons ("Planck radiation"). This tiny rate of thermal-photon emission was shown to be sufficient to blur the interference pattern. At quite small temperatures due to this photon emission it is completely gone, and the Bucky Balls show a pattern after the double slit as expected for classical point-like particles.<br />
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It's of course the more difficult to perform such experiments with really large objects although even this has been made possible recently (even at room temperature):<br />
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<a href="http://physicsworld.com/cws/article/news/2011/dec/02/diamonds-entangled-at-room-temperature" target="_blank" class="link link--external" rel="nofollow ugc noopener">http://physicsworld.com/cws/article/news/2011/dec/02/diamonds-entangled-at-room-temperature</a>[/tex]
