Can Quantum-Mechanical Description of Physical Reality be Considered Complete ?

 The Podolsk's argument

Consider a pair of particles, A and B, having entangled positions and momentum, separated by a distance. We can hence determine either the position or momentum of B by measuring the corresponding quantity of A. But note that in doing so, we could NOT have disturbed B whatsoever, because of special relativity.

Since the value of position or momentum of B can be determined without disturbing it, a concept of reality can be associated with these physical quantities. But quantum mechanics denies to attribute a definite position AND momentum to the particles prior to their measurement, and also claims that both these quantities do not coexist to arbitrary precision. Hence Quantum mechanics must be incomplete.

Bohr's reply to  The Podolsk's argument

Position and momentum are complementary quantities, and determining one destroys anything that can be said about the other. That is, these measurements are NOT non disturbing. Measuring the position of A DOES disturb B. There is a nonlocal influence in a way that no superluminal signaling is still valid.

Einstein's argument

The choice of measuring the position OR momentum of A collapses the wavefunction of B. But locality demands that such influence should not be possible. Hence, wavefunction is not true description of the 'real' state of the system, because it is not possible to influence the 'real' state of a system nonlocally.

My take

By measuring one of the EPR pair, we do end up disturbing the other particle. Nonlocal influences exist in quantum mechanics. These influences are such that a useful superluminal signal cannot be sent. Hence, measuring position of A instantaneously disturbs the state of B (in A's rest frame) in the same manner as measuring the position of B would disturb the state of B. Hence the reality claim based on non disturbance is invalid.

Einstein is wrong because when choice of measurement on particle A steers particle B's state, such superluminal influence does not transfer any information. Hence special relativity is not violated.

Einstein believed that the real state of a particle cannot be influenced by choices made at a distance. Hence wavefunction cannot be in one-to-one correspondence with the real states.

If by real state he meant all the information that can be extracted from the system, then this cannot indeed be influenced by the choices made at a distance. BUT, wavefunction gives a probabilistic description of a system, and hence can be disturbed from a distance without revealing superluminal information.

The superluminal signals are censored, inaccessible.