The Einstein-Podolsky-Rosen argument for the incompleteness of quantum mechanics involves two assumptions: one about locality and the other about when it is legitimate to infer the existence of an element-of-reality. Using one simple thought experiment, we argue that quantum predictions and the relativity of simultaneity require that both these assumptions fail, whether or not quantum mechanics is complete.
EPR’s (1935) argument for the incompleteness of QM turns upon the following sufficient condition:
“If, without in any way disturbing a system, we can predict with certainty (i.e., with probability equal to unity) the value of a physical quantity, then there exists an element of physical reality corresponding to this physical quantity.“
EPR apply this condition in a case where knowledge gained from measuring one quantum system allows one to predict with certainty a value for a physical quantity on another.