3.4 ENTANGLEMENT AND THE EPR PAPER

The EPR paper is central to our search for the ontology of a quantum object so we shall describe it in some detail. It was written by the latter two authors and contained more formalism and philosophy than the first author thought necessary. We prefer therefore to use Einstein’s own words to describe the basic argument as put forth in a 1935 letter to Karl Popper:

We consider a composite system, consisting of the partial system $A$ and $B$ which interact for a short time only. We assume that we know the ψ-function of the composite system before the interaction—a collision of two free particles, for example—has taken place. Then Schrödinger’s equation will give us the ψ-function of the composite system after the interaction. Assume that now (after the interaction) an optimal measurement is carried out upon the partial system $A$ , which may be done in various ways, however, depending upon the variables which one wants to measure precisely—for example, the momentum or the position co-ordinate. Quantum mechanics will then give us the ψ-function for the partial system $B$ , and it will give us various ψ-functions that differ, according to the kind of measurement which we have chosen to carry out upon $A$ . Now it is unreasonable to assume that the physical state of $B$ may depend upon some measurement carried out upon a system $A$ which by now is separated from $B$ (so that it no longer interacts with $B$ ); and this means that two different ψ-functions belong to one and the same physical state of $B$ . Since a complete description of a physical system must necessarily be an unambiguous description, it is therefore not possible to regard the ψ-function as the complete description of the state of the system.

Concerning the inference “that two different ψ-functions belong to one and the same system”, Schrödinger employs a very plastic example to make the same point:

Yet since I can predict either the position or the momentum of system $B$ without interfering with it, and since system $B$ , like a scholar in examination, cannot possibly know which of the two questions I am going to ask it first: it seems to me that our scholar is prepared to give the right answer to the first question, anyhow. Therefore, he must know both answers; which is an amazing knowledge.
Erwin Schrödinger, Discussion of Probability Relations Between Separated Systems, (1935)

Now, writes Einstein in his Autobiographical Notes:

it appears to me that one may speak of the real state of the partial system $B$ . On one assumption we should, in my opinion, insist without qualification: the real state of the system $B$ is independent of any manipulation of the system $A$ which is spatially separated from the former.

Hence, the tension: if one takes, as Einstein clearly does, the system $B$ to be real, then the quantum mechanical description which assigns different wave functions to that system depending on how one manipulates system $A$ , cannot be complete; and if one takes, as Bohr clearly does, the description to be complete, the system thus described cannot be real, by which Einstein understands “something that is considered to be independent of its being observed”.