In the real world cats can't be both living and dead. So what is it that forces them to choose?
In the quantum world, measurements are what make things happen. When a measurement is made, one definite answer emerges from of a range of possibilities. Without measurements, evidently, the whole Universe would languish in a permanent fog of indeterminacy. But what on earth is a measurement? Does it require human agency or observation or (like a tree falling in a forest when no one is watching) can measurements happen in the dark? And supposing we know what a measurement is, how exactly does it make a quantum system choose between its various options and decide what definite state it should take up?
When Niels Bohr, was drawing up what has become known as the Copenhagen interpretation of quantum theory, he was well aware of the significance of these questions. But he couldn't find good answers, and didn't pretend to. Measurements are possible, he said; we know they are. After all, photon detectors detect photons. Pragmatically, he asserted that a measurement is what forces a quantum system to adopt a definite state. A rather circular definition it's true, but accept that, and all else follows. This principle is the keystone of the Copenhagen interpretation, the main point of which is not to worry further about what a measurement is.
But it's uncomfortable to have a fundamental physical theory, no matter how well it works, that depends on a principle no one even claims to understand. Particularly unhappy with this state of affairs was Erwin Schroedinger's cat. The cat finds itself inside a box along with a technical gizmo that sends a photon towards a filter and records whether the photon passes through or not. If it doesn't, nothing happens. If it does, the photon trips a device that breaks open a vial of poisonous gas, and the unfortunate cat dies. The experiment is set up so that there's a fifty-fifty chance of the photon passing through the filter. Accordingly, once you open the box and look inside, there's a fifty-fifty chance the cat will jump out.
That's all very well. The difficulty arises, as Schroedinger pointed out in 1935, when you start wondering what was happening inside the box after the photon measurement was made but before anyone lifted the lid. It's simple enough to say that the gizmo delivered a photon, the photon either passed through the filter or it didn't, the vial of poison was broken or not, and the cat died or stayed alive.
Once the photon hit the filter, a quantum measurement was made, and subsequent events ensured that after that time the box contained either a dead cat or a live cat. But that assumes that the photon striking the filter was enough to constitute a measurement. What if, on the other hand, it takes human observation to trigger the measurement? In that case, it would appear, the cat must have been in some indefinite quantum cat-state, neither dead nor alive but potentially either, until someone opened the box to see. But what can it possibly mean, if anything, for a cat to be in some undefined half-dead, half-alive state?
Bohr's response was straightforward: it doesn't matter. The only demonstrable point is that when the box is opened, the cat inside will be either dead or alive. There's no point worrying about what a half-dead, half-alive cat might mean, since no one can ever see such a thing. Any cat you'll ever see will invariably be either dead or alive.
There is a genuine physics problem here, though. Bohr's attitude amounts to saying that there are quantum objects, such as photons, that can be in uncertain quantum states. And then there are classical objects, such as cats, that can only exist in definite classical states. The snag is that a cat is made of quantum components - protons, neutrons and electrons. Quantum theory is supposed to be the fundamental basis of all physics. So how does a cat get to be a classical unequivocally dead-or-alive cat, rather than a quantum half-dead, half-alive cat?
This is another way of looking at the measurement question. Where, along the chain of events from photon to filter to detection to vial of poison to cat, does the measurement actually happen? At what point does quantum indeterminacy give way to classical definition, and how?
The central issue revolves around what it means to talk about the quantum state of a complex object such as a cat. Being dead or alive is not an intrinsic property of the elementary quantum constituents of the cat, but rather a collective attribute of the way all those constituents are put together. A quantum cat-state, properly described, would mean an exact and complete specification of the quantum state of every single particle within the cat. If a single electron flips into a different energy state, then the entire cat, collectively, flips into a different overall quantum state.
Clearly, there are (almost) countless quantum states all corresponding to the same cat. Even when the cat appears to be doing nothing at all, as cats are wont to, its internal quantum disposition is in a constant turmoil, flipping from one state to another. But all those quantum cat-states must belong to one of two categories: those corresponding to live cats, and those that represent dead cats.
Is it possible then to make a true "half-dead, half-alive" quantum cat-state? Hypothetically, yes. Take one state from the array of "dead cat" quantum states and another from the array of "live cat" states and, by standard technical means, combine these two mathematically into a single state that partakes equally of each possibility. It's the same thing, although on a much larger scale, as combining quantum states for photons with horizontal or vertical polarisations so as to represent a photon in an indeterminate state, whose polarisation has yet to be measured.
A "half-horizontal, half-vertical" photon polarisation state will stay that way. And in principle, so should a "half-dead, half-alive" quantum cat-state. But here things get complicated, because the cat's dead half and live half are free to evolve quickly into any of the myriad other dead and alive states open to them. What's more, as the dead part rattles around among all the possible dead states, and the live part does likewise, they do so independently.
To demonstrate a genuine "half-dead, half-alive" state there has to be a very particular coherence in the way the two component parts are joined together. As each side evolves, that coherence drains away, so that in practice the cat behaves not as if it were in a half-dead, half-alive state, but as if it were either dead or alive - just the way we expect a cat to be. Strictly speaking, there hasn't been any change from "dead and alive" to "dead or alive", but as a practical matter it becomes impossible to perform an experiment that will find anything except a cat that's either dead or alive. For all practical purposes, the cat is classical.
This process of "decoherence" between components of a compound quantum state illustrates how hard it is to keep complex objects in pure quantum states. This is because they are subject to innumerable random interactions and influences, both internal and external. In short, a "half-dead, half-alive" cat isn't impossible, just extraordinarily unlikely - and almost impossible to detect. Another way of thinking about the situation is to say that the constant interaction of atoms and electrons within the cat amounts to a continual "self-measurement" of the quantum state. It's not observation or detection that matters, it's the incessant interaction of all the quantum states in a cat that prevents any individual state from remaining stable. So humans or cats will inevitably fall into a meaningful and observable classical state - even though the cat's interior quantum state is incessantly changing and altogether unpredictable. Anything big, in other words, is just about guaranteed to look like a classical and not a quantum object. Just what Dr Bohr ordered!