Right, because we’re part of the one big giant superposition.
How does being “among the things being superposed” make the superposition neatly divided into separate universes?
The concept of a half life predates quantum physics. It is analogous to the theories governing the behavior of gases. We could in theory come up with a deterministic set of equations that would predict the future position of all the atoms of a gas given the current state (or so it was thought). But in practice we can’t, so we have to rely on statistical methods to approximate the state of the system.
What upset Einstein about quantum physics is when you do get down to individual atoms the probalistic maths doesn’t go away. You don’t have an equation you can use to exactly predict when the decay will happen. It’s still a probability.
But that doesn’t change the answer to the OP. Eventually you get down to a single atom and it will decay at some point, and at that point there is no more decay.
The superimposed state evolves unitarily as a function of time. The environment is “among the things being superimposed”. It has a huge number of degrees of freedom which are orthogonal to each other, enough so that, whatever superposition your “cat” system starts out in, the “alive” and “dead”, or “decayed” and “non-decayed” states couple to the environment differently and overlaps cancel each other out, exponential decay over a really short timescale.
But according to Many Worlds, every environment exists.
IIUC that is precisely what causes decoherence. The system is sensitive to environmental noise, and the environment has a whole bunch of orthogonal states.
Wikipedia mentions a couple of experiments where the process of a quantum superposition being obliterated by decoherence was quantitatively measured in the lab: Quantum decoherence - Wikipedia
An atom either decays, or it doesn’t. The cat observes the atom. The cat either observes the atom decaying, and dies, or the cat observes the atom staying intact, and lives. There is no situation where the cat observes the decay but lives, or doesn’t observe the decay but dies.
Then a human observes the cat. The human either observes the cat as dead, or as alive. In the universe where the atom decayed, the human observes the cat as dead. In the universe where the atom didn’t decay, the human observes the cat as alive. In no case does the human observe the cat in the “wrong” state.
MRS. SCHRÖDINGER: “Erwin, what have you been doing with the cat? The poor thing looks half dead.”
Have you read or heard about the two slit experiment? If not, you should find someone more knowledgeable than myself to explain it. It helped me understand Schrödinger’s Cat a little better.
The last issue of New Scientist had an article by physicist Vlatko Vedral, No space, no time, no particles: A radical vision of quantum reality. Most of it is probably behind a firewall for nonsubscribers.
Vedral’s conception is that observation is not an issue, because there are “no observers at all. What really happens is that the system and observer (just another system) become entangled.” The physics behind that is turning “all the quantities in quantum Hamiltonians into q-numbers.” Simple, right?
He proposes experiments that would test this, although nothing really backs this up right now.
Of course, New Scientist writes up a physicist’s revolutionary notion about every other issue, so take it or leave it mostly as a glimpse into the ways that cutting edge scientists are seeking to solve those basic problems.