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On consideration of Bell's inequalities and this Why is quantum entanglement considered to be an active link between particles?.

Either localism or realism has to be given up. Can't we have a non-local theory of probabilistic realism of wave function instead, where the wave function evolution is always probabilistic but actually exists even if you don't actually do an observation of the system's wave function. This might not lead to paradoxes since everything is inherently probabilistic.

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Viesr
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There exists such theory that does what you said (no localism but realism), known as Bohmian quantum mechanics. (The theory even remains local causal, which is required by relativity theory.) You may want to check out the wikipedia section (https://en.wikipedia.org/wiki/Hidden_variable_theory#Bohm.27s_hidden_variable_theory) or Plato site (http://plato.stanford.edu/entries/qm-bohm/).

cnguyen
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