Whenever we talk about Quantum Mechanics, one of the first questions would be, “What about the cat?” This question, wirklich, is about the interpretations of Quantum Mechanics. The standard interpretation, die so genannte Kopenhagener Interpretation, leads to the famous Schrodinger’s cat.
Why do we need an interpretation for Quantum Mechanics? Schließlich, we don’t look for any interpretations when we learn classical physics. The reason is that the semantic context of QM (which is a fancy way of saying what the heck it means) is not clear, while in classical physics, es ist offensichtlich. Classical physics is merely a mathematical description of whatever we can see and sense directly. Earlier, I said Quantum Mechanics was a mathematical formulation that mapped the unknowable reality of particles to the macro effects around us. I thought it was an interpretation-free way of looking at it, but I was wrong. It turns out that even this minimalist perspective with a very low expectation of the semantics in QM is still an interpretation – called the instrumentalist interpretation.
The Copenhagen interpretation tries to go further. It tries to answer the question what the state of a system is, when all we know is its wave function. Wenn, when we make a measurement on the system, we may one of a few possible values, does it mean that the system was in that particular state (with that particular value) before we made the measurement? The Copenhagen interpretation says that system was in all possible states at the same time, in a kind of superposition of states. Here is where the cat comes in.
Given that the state of any system is probabilistic at a fundamental level, why don’t we see randomness of that kind in our daily life? Why do the probabilistic laws of Quantum Mechanics give rise to an almost perfectly deterministic world around us?
It happens through a magical property of probabilities, technically called the central limit theorem. Let me illustrate it this way. You know that if you throw a die, you may get any number from one through six with equal probability. What happens if you throw two dice and look at the sum? It turns out that the probability of the possible numbers (two through 12) is not equal any more. A sum of seven is more likely than the rest, because there are more ways in which you can make seven than any other number. There is only one combination (one and one) that makes the sum two, oder 12 (six and six). But you can make a seven by having one and six, two and five, or three and four, and it is three times more likely.
When you have a larger number of dice, the probability of getting an average of 3.5 per die becomes larger. If you throw a thousand dice, it would be really foolish to expect to see a sum less than 3200 or more than 3800, die würde ein Fünf-Sigma-Ereignis, or has a probability of less than one in a few million. And when you have trillions and trillions of atoms acting like dice as prescribed by QM, the macro behavior, though probabilistic, is fairly indistinguishable from a deterministic behavior.
Tatsächlich, this determinism out of probabilistic behavior is similar to the emergence of an arrow of time from the laws of physics that are time-reversible.