One of the original questions was: A basic rule of logic is that something cannot contradict itself. It is impossible for P to be true and not true. Doesn’t Schrödinger’s cat violate this law and therefore invalidate logic?
Physicist: The resolution to this comes from a careful look at what is meant by the “state” of something. Turns out, logic is safe from Lil’ Schrödinger’s claws.
There’s a big difference between “reasonable” and “logical”. To see the difference, find a calm, reasonable person and talk to them, and then (this is more difficult) find a professional logician and try to talk to them.
It’s pretty reasonable to say that a single thing must be in one state or another, especially if those states are mutually exclusive. It’s obvious. It’s common sense. In fact, it’s so reasonable/obvious/sensible that disagreeing with it would be a good way of being laughed out of every fancy science salon of the 19th century (or at least the occasional salon with sober members). Logic, on the other hand, has nothing to do with physical reality (neither does being reasonable for that matter).
Logicians start with a big bucket of postulates and symbols and statements, and then run with them. None of it needs to be “physically motivated” or even remotely intuitive.
The statement that things must be one way or another (specifically, that each state is mutually exclusive of the others), is a whole new logical statement on its own. The statement even has a name: “counterfactual definiteness“. Overly-complicated terms like that are just made up so that people will think that physicists are wizards-of-smartness. A better term for things needing to be in a definite state is “realism”. While realism is “obviously true”, is isn’t necessarily true (not “logically true”), and point of fact: isn’t true.
There’s a famous no-go theorem in quantum physics called “Bell’s theorem” that says that, given the results of a variety of experiments involving entanglement, “local realism” is impossible. This means that things always being in single states requires the exchange of some kind of faster-than-light signals. Or conversely, if no effects can travel faster than light, then things must be allowed to be in multiple states.
It’s pretty natural to jump to the conclusion that things are communicating faster than light. Losing realism is philosophically, even mathematically, a bitter pill to swallow. Unfortunately, there are a lot of problems with faster than light stuff (like this one!).
It turns out that the universe doesn’t seem to have any problem dropping realism. Things are perfectly happy being in multiple states at the same time: particles being in multiple positions or energy states, single events happening at multiple times, or (admittedly reaching a little past our grasp) being in multiple states of living and dead. The last of course has never been observed in the lab (and probably never will be), but this is a well-studied property otherwise. We’ve seen multiple-stated-ness in every physical system we’re capable of measuring the effect in. So far, there doesn’t seem to be any limit to the scale at which quantum weirdness shows up.
In short, it does make sense to say that things must be in a single state or another, but it isn’t necessarily “logical”. The universe couldn’t care less about what makes sense.
Answer gravy: This bit threatened to derail the flow of the post.
Realism is technically a statement that limits the exact nature of what kind of states are allowed. For example, only the states and are allowed. When the cat is both living and dead it’s technically just in multiple states in certain “measurement bases”. So the cat could be in the single state .
We see this all the time in the polarization of light, for example. A diagonally polarized photon is in a single state, . But, if you insist on looking at it (measuring it) in terms of horizontal and vertical polarizations, then you find that it must be in multiple states, . This moves the problem from being a purely philosophical/logical problem, to one of defining what is meant in detail by the word “state”.
The answer to whether Schrödinger’s cat is in multiple states becomes a resounding “Yes! Unless some very specific measurement is set up, in which case: no!”.