Relativity, Anomalies and Objectivity Loophole in Recent Tests of Local Realism

Local realism is in conflict with special quantum Bell-type models. Recently, several experiments have demonstrated violation of local realism if we trust their setup assuming special relativity valid. In this paper we question the assumption of relativity, point out not commented anomalies and show that the experiments have not closed objectivity loophole because clonability of the result has not been demonstrated. We propose several improvements in further experimental tests of local realism make the violation more convincing.