The thought experiment went like this: A cat is placed in a room that is separated from the outside world. A Geiger counter and a little bit of a radioactive element are in the room. Within some time, say one hour, one of the atoms of the radioactive material may decay (or break down, this is because the material is not stable), or it may not. The Geiger counter can measure that. If the material breaks down, it will release poisonous gas, which will kill the cat.
The question now is: at the end of the hour, is the cat alive or dead?
Schrödinger says that as long as the door is closed, the cat could be dead or alive. There is no way to know until the door is opened.
The problem is in that by opening the room, the person is interfering with the experiment. The person and the experiment have to be described with reference to each other. By looking at the experiment the person has influenced the experiment. A famous physics theory (the Copenhagen interpretation) said that the cat was both dead and alive until its observation proved it to be one or the other (Superposition).
The cat situation was first proposed by Schrödinger to actually demonstrate the foolishness of thinking about quantum states at macro levels. It has also been referenced many times in pop culture.
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