Suppose all wavefunctions encode some constant, sub-unity fraction of the information about the ‘true state’ - that all wavefunctions are equally specific. Then we should be able to tease out more of that information with some very basic experiments (edited to clarify: by measuring in multiple ways—not that the new state would be intrinsically better constrained). This contradicts the results of the many many instances of these experiments.
So you can escape by supposing that it’s possible to prepare a wavefunction that has more or less information about the ‘true state’.
It’s nice to have yet another very strong constraint to put on global hidden variables, but nothing could ever be total proof.
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edited to add: But if you pull that escape route, then it’s trivial to perform (by which I mean, they have already been done zillions of times) additional experiments showing that quantum states with different distributions of ‘real’ states (as we just allowed by the escape route) actually have identical dynamics.
The more I think about this, the less wiggle room I see.
The idea is:
Suppose all wavefunctions encode some constant, sub-unity fraction of the information about the ‘true state’ - that all wavefunctions are equally specific. Then we should be able to tease out more of that information with some very basic experiments (edited to clarify: by measuring in multiple ways—not that the new state would be intrinsically better constrained). This contradicts the results of the many many instances of these experiments.
So you can escape by supposing that it’s possible to prepare a wavefunction that has more or less information about the ‘true state’.
It’s nice to have yet another very strong constraint to put on global hidden variables, but nothing could ever be total proof.
~~~~ edited to add: But if you pull that escape route, then it’s trivial to perform (by which I mean, they have already been done zillions of times) additional experiments showing that quantum states with different distributions of ‘real’ states (as we just allowed by the escape route) actually have identical dynamics.
The more I think about this, the less wiggle room I see.