The 1935 paradox suggesting that quantum mechanics might be incomplete is the Einstein–Podolsky–Rosen (EPR) paradox. Albert Einstein, Boris Podolsky, and Nathan Rosen presented it in a paper titled “Can Quantum-Mechanical Description of Physical Reality Be Considered Complete?”
The argument examined two particles that become entangled and then move far apart. Measuring one particle can allow a prediction about the other, even across a large distance. EPR argued that if the distant particle’s property was real before measurement, quantum mechanics did not describe every element of reality. If it was not real beforehand, the theory seemed to permit an uncomfortable kind of nonlocal influence.
The EPR paradox is often confused with Bell’s theorem, but they are not the same. Bell’s theorem, published by John Bell in 1964, converted the philosophical dispute into experimentally testable inequalities. Experiments have repeatedly found violations of Bell inequalities, supporting quantum predictions over local hidden-variable theories.
The paradox also helped establish quantum entanglement as a central subject. Modern quantum information science uses entanglement in technologies such as quantum cryptography and quantum computing, although it cannot be used to send ordinary messages faster than light.