Nonlocal aspects of a quantum wave

Various aspects of nonlocality of a quantum wave are discussed. In particular, the question of the possibility of extracting information about the relative phase in a quantum wave is analyzed. It is argued that there is a profound difference in the nonlocal properties of the quantum wave between fermion and boson particles. The phase of the boson quantum state can be found from correlations between results of measurements in separate regions. These correlations are identical to the Einstein-Podolsky-Rosen (EPR) correlations between two entangled systems. An ensemble of results of measurements performed on fermion quantum waves does not exhibit the EPR correlations and the relative phase of fermion quantum waves cannot be found from these results. The existence of a physical variable (the relative phase) that cannot be measured locally is the nonlocality aspect of the quantum wave of a fermion.