The blog article bears no resemblance to the actual math, but the issue is the same as always: if you assume locality, you can have hidden variables. Pusey et a

The blog article bears no resemblance to the actual math, but the issue is the same as always: if you assume locality, you can have hidden variables. Pusey et al assume separability (i.e., no entanglement). Hardy does so as well. It's put in weakly and carefully, but it's still assuming locality and showing that you can have hidden variables. Everyone gets so stuck on the wave function. Look, if you assume that your physical system's state is described by a vector in a linear space, that you can project onto subspaces to describe subsets of the state, and that the space has a metric and is complete (all sequences in the space converge to something in the space) then if you impose a smooth dynamics on the space, then there will be an equivalent differential equation, because there's only one infinite dimensional Hilbert space up to isomorphism, and L2, the space of square integrable functions, happens to be one of its faces. The real questions is why the theory is formulated in a linear, complete metric space. Someone posted a lecture by Scott Aaronson a few days back that had some interesting pointers on that. Seriously, if the wave function bothers you, just don't use it.