Said cat is placed in a sealed box. Attached to the box is an apparatus containing a radioactive nucleus and a canister of poison gas. When the nucleus decays, it emits a particle that triggers the apparatus, which opens the canister and kills the cat. According to quantum mechanics, the nucleus is described as a mixture of "decayed nucleus" and "undecayed nucleus". However, when the box is opened the experimenter sees only a "decayed nucleus/dead cat" or a "undecayed nucleus/living cat." The question is when does system stop becoming a mixture of states and become one or the other? The purpose of the experiment is to illustrate that quantum mechanics is incomplete without some rules to describe when the wave function collapses and the cat becomes dead or alive instead of a mixture of both.
Contrary to popular belief, Schrödinger did not intend this thought experiment to indicate that he believed that the dead-alive cat would actually exist; rather he considered the quantum mechanical theory to be incomplete and not representative of reality in this case.
In the Copenhagen interpretation, a system stops being a mixture of states and becomes one or the other when an observation has taken place. This experiment illustrates that it is unclear what exactly an observation is. One could argue the absurd position that while the box is closed, and that the system exists in a mixed superposition of the states "decayed nucleus/dead cat" and "undecayed nucleus/living cat" and that only when the box is opened and an observation performed does the wave function collapse into one of the two states. This is absurd, and intuitively one would think that the "observation" is when a particle from the nucleus hits the detector. However (and this is the point of the thought experiment), there isn't any rule that says one way or the other, and quantum mechanics is incomplete without such rules and explanations for how such rules come to exist.
In the Everett many-worlds interpretation, which does not single out observation as a special process, both states persist, but decohere?. When an observer opens the box, he becomes entangled with the cat, so observer-states corresponding to the cat being alive and dead are formed, and each can have no interaction with the other.
Curiously, all of this has some practical use in [quantum cryptography]?. It is possible to send down a fiber optic cable, light that is in a mixture of states. If one places a wiretap in the middle of the cable which intercepts the transmission and retransmits it, one conducts an observation which causes the light to fall into one state or another. By doing statistics at the other end of the cable, one can tell if one is received light that is in a mixture of states or if the light has been already observed and retransmitted. This allows one to develop communication systems that cannot be tapped without being noticed at the other end. This experiment (which one can do) also illustrates that the "observation" in quantum mechanics has nothing to do with consciousness in that a perfectly unconscious wiretap will cause the statistics at the end of the wire to be different.
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