The argument begins by assuming that there are two systems, A and B (which might be two free particles), whose wavefunctions are known. Then, if A and B interact for a short period of time, one can determine the wavefunction which results after this interaction via the Schroedinger equation or some other Quantum Mechanical equation of state. Now, let us assume that A and B move far apart, so far apart that they can no longer interact in any fashion. In other words, A and B have moved outside of each others light cones and are therefore spacelike separated.

With this situation in mind, Einstein asked the question: what happens if one makes a measurement on system A? Say, for example, one measures the momentum value for system A. Then, using the conservation of momentum and our knowledge of the system before the interaction, one can infer the momentum of system B. Thus, by making a momentum measurement of A, one can also measure the momentum of B. Recall now that A and B are spacelike separated, and thus they can not communicate in any way. This separation means that B must have had the inferred value of momentum not only in the instant after one makes a measurement at A, but also in the few moments before the measurement was made. If,on the other hand, it were the case that the measurement at A had somehow caused B to enter into a particular momentum state, then there would need to be a way for A to signal B and tell it that a measurement took place. But, the two systems cannot communicate in any way!