I am so enamored with the below explanation following my two-year-long study of the mathematical version of Quantum Mechanics, as well as its philosophical foundations, that I am reprinting it in full from the Discover Magazine blog:

http://blogs.discovermagazine.com/cosmicvariance/2011/11/18/guest-post-david-wallace-on-the-physicality-of-the-quantum-state/

Matt Says:
November 18th, 2011 at 10:38 pm

I’m a practicing theoretical physicist, and I don’t understand all the confusion — please someone explain it to me.

We already have a natural object in QM with a statistical interpretation, namely, the density matrix. And density matrices are the natural generalization of classical probability distributions. In classical mechanics, the probability distribution is over classical states, and in quantum mechanics, the density matrix probability eigenvalues are a distribution over quantum state vectors.

If we take the view that a density matrice’s eigenvalues are a probability distribution over its eigenvectors, and regard those eigenvectors (which are state vectors) as real, physical possible states (just like we treat classical states underlying a classical probability distribution as real, physical possible states), then we never run into contradiction with observation. So what’s stopping us from taking that point of view?

To say that state vectors themselves are statistical objects is to say that there are two levels of probability in quantum mechanics. But why give up the parsimony of having only one level of probability in QM if it’s not needed? And it’s not!

When you make use of decoherence properly, you see that all probabilities after measurements always end up arising through density matrix eigenvalues automatically. And you automatically find that for macroscopic objects in contact with a realistic environment, the density-matrix eigenbasis is essentially always highly-classical-looking with approximately-well-defined properties for all classical observables — all this comes out automatically.
So there’s no reason to insist on regarding state vectors as statistical objects. We can regard them as being as real and physical as classical states, even though for isolated, microscopic systems, they don’t always have well-defined properties for all naive classical observables — but why should weirdness for microscopic systems be viewed as at all contradictory? And again, in particular, the probabilities end up as density-matrix eigenvalues anyway, so why bother insisting on having a second level of probability at all?

As for Schrodinger’s cat, the fact is that any realistic cat inside a reasonable-size non-vacuum environment is never going to stay in a weird macroscopic superposition of alive and dead for more than a sub-nanosecond, if that — its density matrix will rapidly decohere to classicality. The only way to maintain a cat (with its exponentially huge Hilbert space) in an alive/dead superposition for an observable amount of time is to place the cat in a near-vacuum at near-absolute zero, but then you can be sure it’s going to be dead.

What about putting it in a perfectly-sealed box in outer space? Well, even in intergalactic space, the CMB causes a dust particle to decohere to classicality in far less than a microsecond. So it just doesn’t happen in everyday life — and if that’s the case, then why are we worried that it should seem counterintuitive?

So the whole Schrodinger-cat paradox is a complete unphysical fiction and a red herring, unless you do it with an atom-sized Schrodinger-kitten — and that’s been done experimentally!