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The Greenberger-Horne-Zeilinger~(GHZ) version of theEinstein-Podolsky-Rosen~(EPR) paradox is widely regarded as a conclusivelogical argument that rules out the possibility of describing quantum phenomenawithin the framework of a local and realistic model of hidden variables inwhich the observers are free to choose their own experimental settings. In thispaper we show, however, that the GHZ argument implicitly relies on anadditional crucial assumption, which is not required by fundamental physicalprinciples and had gone unnoticed. Namely, we note that the argument implicitlyassumes the existence of an absolute angular frame of reference with respect towhich the polarization properties of the hypothetical hidden configurations ofthe entangled particles as well as the orientation of the measurement apparatusthat test the system can be defined. We further note that such an absoluteframe of reference would not exist if the hidden configurations of theentangled particles spontaneously break the gauge rotational symmetry. Indeed,by skipping this unnecessary additional assumption we are able to build anexplicitly local and realistic model of hidden variables for the GHZ state,which complies with the 'free-will' hypothesis and reproduces the quantummechanical predictions, and thus completes the description of the system in theEPR sense.

Solving the Greenberger-Horne-Zeilinger paradox: an explicitly local and realistic model of hidden variables for the GHZ quantum state