What is the paradox in the EPR paradox?

[bksree]

Hi
Which of these understandings is correct ?
A stationary particle separates into 2 particles A & B
Is it that :
(a) One can independently measure accurately to the desired accuracy the momentum of A and the position of B and thus obtain both position AND momentum of either particle thus violating Heisenberg's uncertainty principle (Is this really a violation of Heisenberg's uncertainty principle since no simultaneous measurement of momentum and position is done here?)
OR is it that
(a) one can measure accurately to the desired accuracy the momentum or position of particle A and deduce instantaneously the value of the corresponding property of B (even though B is several light years away).
What is the need to assume instantaneous transmission of information because from the principle of conservation of momentum if pA is measured, then pB is known)TIA

 

[PeroK]

The "paradox" is that QM says that the observables do not have defined values until they are measured. The question is then how nature correlates distant outcomes.

 

[vanhees71]

There is no paradox, if you accept quantum theory in its (minimal) statistical interpretation. In the original EPR example the momenta of the decayed particles are entangled due to momentum conservation in the particle decay. The total momentum $p_1+p_2$ and the relative position $x_1-x_2$ are compatible observables and there's no contradiction to the uncertainty relations between the single-particle momenta and positions whatsoever. Of course one has to work with normalizable states, i.e., wave packets. Neither momentum nor position (generalized) eigenvectors are representing proper (pure) states.

The same holds for Bohm's version of the paradox using entangled spins of partilces. The only difference is that it is a bit simpler to formulate, because the spin eigenstates are proper (pure) states, i.e., angular momenta have only discrete spectra.