Erwin Schrödinger was one of the people who researched quantum mechanics. Like his colleagues, he thought quantum mechanics had very big philosophical consequences. But they did not agree with each other what this consequences would be like. So he proposed an experiment to enlighten the consequences, but actually this experiment has further mystified the consequences of quantum mechanics to the public:
We need a box which can be closed. In this box we put one radioactive atom, which has a probability of 1/2 to break during our experimentation time, for example one hour.
We also need a detector which can notice when the atom is broken.
This detector is connected with a mechanic device, so it can set some poison free.
If the atom breaks, the poison is set free. There is enough poision to kill the cat. Now we put the cat in the box and close the box.
Common sense tells us, the cat will be either alive or dead after
one hour, each with a probability of 50%.
But if you take the arguments of some physicist literally, the cat
must be in a state that is neither alive nor dead, but something
completely different. Unfortunately, they also say you can not open
the box to see this strange state, because when you open the box the
state disappears (so you should not experiment with your neighbours
cat).
To enlight why somebody in his right mind might insist on such a
strange opinion, we have to look at some of the results of quantum
mechanics:
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