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Hidden-variable models aim to reproduce the results of quantum theory and tosatisfy our classical intuition. Their refutation is usually based on derivingpredictions that are different from those of quantum mechanics. Here instead westudy the mutual compatibility of apparently reasonable classical assumptions.We analyze a version of the delayed-choice experiment which ostensibly combinesdeterminism, independence of hidden variables on the conducted experiments, andwave-particle objectivity (the assertion that quantum systems are, at anymoment, either particles or waves, but not both). These three ideas areincompatible with any theory, not only with quantum mechanics.

Determinism, independence and objectivity are incompatible