We address the question of whether a non-nomological (i.e., anomic) interpretation of the wavefunction is compatible with the quantum formalism. After clarifying the distinction between ontic, epistemic, nomic and anomic models we focus our attention on two famous no-go theorems due to Pusey, Barrett, and Rudolph (PBR) on the one side and Hardy on the other side which forbid the existence of anomic-epistemic models. Moreover, we demonstrate that the so called restricted ontic indifference introduced by Hardy induces new constraints. We show that after modifications the Hardy theorem actually rules out all anomic models of the wavefunction assuming only restricted ontic indifference and preparation independence.
In a recent paper, Cabbolet argues that the PBR theorem is nonreal since in the ensemble interpretation of quantum mechanics the entangled measurement used in the derivation of the PBR theorem is nonexisting. However, Cabbolet (1) doesn't provide any argument for the nonexistence of entangled measurements beyond the incompatibility of the existence of entangled measurements and the existence of
ψ-epistemic models which we already know from the PBR theorem; and (2) he doesn't show why it is more reasonable to abandon entangled measurements instead of
ψ-epistemic models. Hence, the PBR theorem remains intact.