That's the impression most people get from the experiment, but in the traditional Copenhagen interpretation of quantum physics, some things that you don't know actually are in multiple states at the same time until you observe them. This because there is no other way than observation to know in what state they are. Radioactive decay like other quantum phenomena, is a truly random process. This means you cannot deduce something about the particle even if you know the state of the entire universe. It simply isn't linked to anything so the result is random. This is why observation is the only way to know and we may as well suppose those things don't really have a state until they are observed.
Observation is the only way to know, yes. But the superposition is true only on a metaphysical and probabilistic level. Physical reality is different. Updating your map does not update the territory. Schrödinger proposed the thought experiment to show that it's ridiculous to apply quantum mechanical concepts (well, the standard/Copenhagen Interpretation, Many Worlds/Mangled Worlds still works) to macroscopic objects, like a cat.
What you're saying is a
reasonable view of the thought experiment, but it's not what most people mean when they go about shouting "the cat is both alive and dead!" They don't mean to say that "since we don't know, we might just as well assume the cat is neither until we see the state of the cat for ourselves, since we can't predict it either way." They mean that the cat exists in both states, and neither, at the same time, like an electron in superposition. Which makes no sense with the cat if you use the Copenhagen Interpretation of QM. For one, why would only a human eye count as an observer, and the cat itself doesn't count? Also with the standard interpretation we get a "Schrödinger's cat inside a box, inside a box, inside a box" scenario if, for example, there's someone else outside the room when you open the box. From their perspective, you found either a dead cat or a live cat, and until they walk in the room and see which one is true, and the wavefunction collapses. And from the perspective of someone in another room... and outside the building.. and outside the city... what's outside all of those boxes that's causing the wavefunction to collapse?
But all of that applies only if you believe in the Copenhagen Interpretation of QM, which is very probably
wrong. Many Worlds seems by far the most probable explanation given the evidence we have so far. Single-world versions of quantum mechanics don't work, and the rejection of MWI mostly stems from some physicists getting the probability theory of Occam's Razor wrong -- or just not plain knowing about it.
