The wave-function as a true ensemble

[bohm2]

"We argue that the ψ-ontic/epistemic distinction fails to properly identify ensemble interpretations and propose a more useful definition. We then show that all ψ-ensemble interpretations which reproduce quantum mechanics violate Statistical Independence."

https://arxiv.org/abs/2109.02676

 

[Morbert]

"Suppose you have a theory that isn’t ontic because two of the hidden variables map to the same wave-function. Well, then you can just declare the wave-function to be part of the hidden variables, so that the new hidden variables – now including the wave-function – will always map to only one wave-function. Such an easily malleable definition of ‘ontic’ is not what one wants to base theorems on."

This is an interesting point. If I have a quantum state $\psi$, I can always define an observable $$\hat{O} = \lambda_\psi|\psi\rangle\langle\psi| + \lambda_{\not\psi}(\hat{I} - |\psi\rangle\langle\psi|)$$ We have a property $\lambda_\psi$ resolvable (in principle) by experiment, that $\psi$ predicts with certainty. All other pure states will predict $\lambda_{\not\psi}$ with certainty. Make this variable a real hidden variable and voila, your wavefunction uniquely characterises the physical state of the system.

 

[PeterDonis]

"All other pure states will predict $\lambda_{\not\psi}$ with certainty.

No, they won't. Only pure states orthogonal to $\psi$ will.

 

[Morbert]

Oops stupid mistake