The cat and the atom represent two entangled particles. Entangled means that they share certain characteristics or behaviors, in this case their fate within the box: decayed atom = dead cat; and undecayed atom = live cat. The two behave as one.
Imagine that instead of an entangled atom/cat in the box, you were measuring a single electron. Before you open the box to observe it, that electron exists as a wave function, which is an array of itself in all of the places it might possibly be in the box. This quantum phenomenon is called superposition: that a particle can be in all of its possible states at once.
The measurement problem arises the moment you open the box to observe the particle. When you do, the wave function appears to collapse into a single state, fixed in time and space.
Due to the quantum principles of entanglement and superposition, until you observe it, the cat must be both dead and alive, at the same time.
But the questions his thought experiment poses are interesting: At what point in time does a quantum system stop being a superposition of all possible states and become a singular, either/or state instead?
And, by extension, does the existence of a singular cat, either dead or alive, require an external observer, i.e., you? And if not you, then who? Can the cat be an observer of itself? And without an external observer, do we all just exist in an array of all possible states at once?
The many-worlds interpretation, proposed by the American physicist Hugh Everett in 1957, challenges this theory of wave function collapse, positing instead that the superposed quantum system persists and branches.
At every juncture—in every Zen moment when possibilities arise—a schism occurs, worlds branch, and multiplicity ensues.
Every instance of either/or is replaced by an and. And an and, and an and, and an and, and another and . . . adding up to an infinitely all-inclusive, and yet mutually unknowable, web of many worlds.
The paradox is that the particles exist in superposition only as long as no one is looking. The minute you observe the array of superposed particles to measure it, the wave function appears to collapse, and the particle exists in only one of its many possible locations, and only as a single particle.”
“The many collapses into one?”
“Yes, or rather, that was one theory, anyway. That there’s no single outcome until the outcome is measured or observed. Until that moment of observation, there’s only an array of possibilities, ergo, the cat exists in this so-called smeared state of being. It’s both alive and dead.”
A Tale for the Time Being by Ruth Ozeki
Bewildered Creatures 