5.2.5 Quantum Entanglement

Objects of experience have no memory of their previous interactions if those interactions occurred sufficiently far away in time and space. Objects of explanation, on the other hand, do. As we have argued in the ninth section of Chapter 4, such objects are not given to us but rather must be manufactured by incorporating into any subsequent observation of them the experiential contexts which they had previously explained. Consequently, the memory of any experiential situation which was explained by a given object will be retained in any subsequent situation involving that object; an object of explanation is what it is in such a manner as to remain involved with what happened during its manufacture. This state of involvement obtains both for the Being of an object of explanation as well as for the physical properties we assign that object.

Let us illustrate this conception with the ‘gedanken’ experiment put forth by Einstein in his EPR paper, where he was concerned with the physical properties assigned to atomic objects rather that with their ontology. We recall from Chapter 3:

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.

The focus of Einstein’s gedanken experiment was on the two partial systems emerging from the interaction region and its purpose was to allow us to deliberate upon the degree of their independence from each other at a time when they were no longer in causal contact. If the two partial systems were objects of experience, they would be expected to be as independent of each other after the interaction had ceased as they had been before the interaction began and whatever happened subsequently to one of the systems could no longer affect the state of the other. Einstein, who insisted that atomic systems were objects of experience, had no reason therefore to wonder about the physical properties assigned to system $B$ after measurements were performed upon system $A$ because such an object possessed its properties out right independently of its partner having been observed. Consequently, Einstein was right to question the completeness of the theory the way he did.

If, on the other hand, the two partial systems were objects of explanation, one would have to actively wonder concerning the assignment of physical properties to system $B$ because, as we had argued in the previous section, an object of explanation does not possess any of its physical properties prior to observation. Rather, the physical properties of an object of explanation are the syndotic unity of two sets of properties: those we had associated with the system at the time of manufacture and those we must associate with the system now if we wanted to account for the observed outcome. Thus, if we decided to perform a measurement upon system $A$ in order to assign to it some specific property, say its momentum, we must explicitly include into the measuring apparatus employed for that purpose the short time interaction between $A$ and $B$ which manufactured it; if we decided to measure instead some other property of system $A$ , say its location, the interaction which manufactured the system would have to be re-done but, this time, as incorporated within the experimental arrangement we would employ to assign a value to the new property.

For instance, imagine we want to measure the momentum of particle $A$ well after the interaction with particle $B$ ceased. As we have said before, the manufacturing apparatus must always be incorporated into the observational apparatus. But, in this case, the manufacture process is nothing else but the short term interaction itself. Hence, the interaction which manufactured particle $A$ must be allowed to take place anew, not in isolation as it did when we had not yet conceived of measuring anything on particle $A$ , but rather within the context of our measurement. The value which we assign to the momentum of particle $A$ through our measurement must then be given together with the momenta we had to assign to both particles $A$ and $B$ in order to explain the outcome of the short time interaction which executed the manufacture. In other words, the value assigned to the momentum of particle $A$ by our measurement of it must be given together with the momentum we had to assign to particle $B$ in order to explain its interaction with particle $A$ during the manufacturing process.

The same would of course have obtained if we decided to measure instead the location of particle $A$ : the co-ordinates we assign to particle $A$ will then have to be given together with the co-ordinates we had assigned to particle $B$ after the two systems were allowed to interact with each other as a pre-amble to the co-ordinate measurements. This interaction, however, is totally different from the one involved in the momentum measurement because it had to occur within the apparatus used to observe the location, not the apparatus used to observe the momentum, of particle $A$ . The short term interaction we use for manufacturing particle $A$ is contextual and therefore it does not stand-up on its own.

It appears then as if our arbitrary decision to measure either the momentum or the co-ordinate of particle $A$ is ‘communicated’ to particle $B$ since we end-up assigning to it either its post-interaction momentum or its post-interaction co-ordinate, as the case may be, but never both. This communication is however not directly between the systems $A$ and $B$ , but indirectly through the fact that the short time interaction which manufactures particle $A$ would have to take place in different measurement settings depending on which decision was made. To put it another way, when the systems are properly recognized as objects of explanation, system $A$ pilots system $B$ through the indirect channel of the short-time interaction between them, interaction which had manufactured both. We see therefore how, on our conception of the manner in which objects of explanation are what they are, the properties assigned to what was manufactured by having allowed two systems to interact with each other in the past, and what may then happen to those properties in future, must be given together in unity. Under the circumstances, the states of the two systems could never be torn asunder.

When however the systems are taken to be objects of experience, as they are in quantum mechanics, the indirect channel is missing and the piloting must then happen directly from $A$ to $B$ , a notion that so discomforted Schrödinger. But, system $B$ is beyond the physical reach of system $A$ when the measurements on the latter are made. Consequently, the only way in which the piloting can be conceived is to think of the two systems as pre-given objects of experience whose states remain strangely entangled with each other after the short time interaction had ceased. Specifically, the state associated with the two systems after the interaction is, to use Dirac’s words, the result of a special process of superposition applied to all the possible states which those two systems could attain if we assumed that they were independent of each other. This strange process of superposition of states is a direct consequence of trying to express the unity of the two systems of explanation in a language appropriate to objects of experience.