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In most of the conventional interpretations, such as the Copenhagen interpretation and the interpretation based on Consistent Histories, where the wavefunction is not assumed to physically exist in real space-time, it is local realism that is rejected.
These interpretations propose that actual definite properties of a physical system " do not exist " prior to the measurement ; and the wavefunction has a restricted interpretation, as nothing more than a mathematical tool used to calculate the probabilities of experimental outcomes, hence in agreement with positivism in philosophy as the only topic that science should discuss.

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