In Quantum Mechanics this is called a wave function, and the cat is in a superposition of wave functions that represent all possible states. The wave function collapses when we make an observation.
Or it doesn't, it simply seems that way because all our instruments of observation - both natural and artificial - are specifically designed to report a cat as either alive or dead but not both. In other words, the cat doesn't stop being in superposition, but rather we enter a superposition of seeing a living cat or a dead cat. We don't notice that, of course, but someone who asked us about the status of the cat couldn't know beforehand what answer they'd get, so they'd describe us in the same terms - superposition - we described the cat. And of course the chain of correlated superpositions (I'm a honest guy, the odds of me lying about the cat are 1/10000, but this other researcher always lies) goes on potentially ad infinitum.
This line of thinking also solves the non-locality problem: no, measuring the polarization of a photon doesn't make it send a superluminal message to another, entangled photon. Rather, the wavefunctions of the measuring devices become correlated with the wavefunctions of the photons (which is the definition of observation), so since the wavefunctions of the photons interfered, so must the wavefunctions of the devices. Which we then interpret as "spooky action at distance", when all that's happening is perfectly local physics (correlating the photons at the source, correlating a measuring device to a photon x 2, summing up the wavefunctions of the devices).