A Discussion on the Einstein–Podolski–Rosen (EPR) Effect^* in a Unique Wavefunction Quantum Mechanical Framework

Abstract

A unique wavefunction, constructed according to the original Einstein–Podolski–Rosen (EPR) description, is used here to analyze the behavior of two equal non-interacting quantum systems: S(1) and S(2).The results show that the EPR paradox, which will be referred as EPR effect in this work, always appears in this theoretical context. When the expectation value of a Hermitian operator is sought, it can yield two different values, when measured on S(1) or S(2). However, the EPR effect disappears if the wavefunction is chosen symmetric or antisymmetric by interchanging the S(1) and S(2) coordinates. The same EPR effect appears when the expectation value of a state selector projection operator is computed on S(1) or S(2), but it disappears within a symmetric or antisymmetric EPR wavefunction form. On the other hand, the action of the selectors over the EPR wavefunction provide images on EPR system S(1) or S(2) which could be different, so the EPR effect persists except if, similarly as in the statistical case, a wavefunction constructed with a symmetric or antisymmetric superposition with respect the EPR system coordinates is used. Thus, with appropriate wavefunction choices, in statistical expectation value measures and non-statistical selector images as well, the EPR effect could not persist.