Eistein-Podolski-Rosen paradox, non-commuting operator, complete wavefunction and entanglement

TL;DR

This paper analyzes the EPR paradox, identifies a hidden assumption behind it, and clarifies that entanglement between separated particles requires proper measurement to be confirmed, reinforcing quantum theory.

Contribution

The paper reveals a hidden assumption in the EPR paradox and clarifies the conditions under which entanglement can be experimentally verified.

Findings

EPR paradox arises from a hidden assumption

Proper measurement is essential to confirm entanglement

Reinforces the correctness of quantum theory

Abstract

Einstein, Podolski and Rosen (EPR) have shown that any wave function (subject to the Schr\"odinger equation) can describe the physical reality completely, and any two observables associated to two non-commuting operators can have simultaneous reality. In contrast, quantum theory claims that the wave function can capture the physical reality completely, and the physical quantities associated to two non-commuting operators cannot have simultaneous reality. The above contradiction is known as the EPR paradox. Here, we unambiguously expose that there is a hidden assumption made by EPR, which gives rise to this famous paradox. Putting the assumption right this time leads us not to the paradox, but only reinforces the correctness of the quantum theory. However, it is shown here that the entanglement phenomenon between two physically separated particles (they were entangled prior to separation) can only be proven to exist with a "proper" measurement.