Dear Edward,
Thank you for your thoughtful reply. Your summary has indeed helped me better understand your argument, and it is evident to me now that whatever I did not understand before may have been because of a possible difference in how we apply the notion of causality. How do you define causality? Do you consider the apparently non-local effects, say, as confirmed by Aspect et al., as causal? My impression now is that you do.
In my view, such correlations do not rise to the level of causality (at least as usually understood). Perhaps it might seem strange to think that in these situations one could have correlation without causation (of course, elsewhere it is so common that it has become an aphorism), and I myself would probably have thought so as well, were it not for the fact that I imagine that entanglement is enforced via a particular mechanism which simply fails to fulfill a key criterion indispensable to the definition of causality.
I will attempt to keep the description of my imagined mechanism at minimum, but I will have to mention at least a little in order to convey why I believe that entanglement fails to meet a key requirement of causality.
As I understand it, we would think as two events to stand in a causal relationship when one is a consequence of the other, but what exactly do we mean by that? Although there are probably many divergent views on this, I think it is fair to summarize it broadly as follows: What we mean when we say that event two is a consequence of event one is that when the first event occurs, the "world" is changed in a certain way compared to a world in which event one did not happen, and this change can be linked (perhaps via a chain of other such changes) to the occurrence of event two.
Now, if you disagree with this way of characterizing causation, then what follows may be irrelevant, but allow me to suppose that you find this characterization reasonable.
In the case of an entangled system it is perhaps not uncommon to encounter the view that whoever performs the measurement first and reduces the wave vector, by reducing it has "caused" the other part of the system to be in a definite known state, and in a special relativistic context, this conception does not change except that for spacelike separated events who "causes" what becomes frame-dependent. A subtle assumption underlying this conception is that the arena for the transmission of any effects, the "world" in which the change due to event one leads to event two, is spacetime. This seems like such an obvious auxiliary assumption that I don't think most people are even aware of it. In particular, at present hardly anyone would question that, in whatever indefinite state the quantum objects may be prior to the first measurement, they still in some form exist in spacetime.
Since you have read my paper (thank you), you know that I interpret the wave function as the spacetime manifestation of entities that don't even exist in spacetime. A 'measurement' in my view is the name we give for the emergence of spacetime objects from such entities. If this view is correct, then, when the first measurement on an entangled two-particle system occurs, *there is no second particle to exert a causal influence on*. When the second measurement reveals a definite correlated outcome, this merely reflects the fact that there was another portion of the underlying areatime entity giving rise to the two spacetime objects which had not yet had the opportunity to emerge but now just did.
Therefore, in my mind, the causal link between the two events is broken. I am satisfied with characterizing the relation as one of a correlation without causation but if one insists on "causal" talk, then I would say that the the *second* observer "caused" the empirically observable correlation because he "caused" the second particle to exist in spacetime.
If this still doesn't seem clear, allow me to give a crude analogy. Suppose you have a green marble, and I have a red one, and we are to throw our marbles in a funnel emptying into containers 1 and 2, such that when one marble fills one container, the second marble is automatically diverted into the other container, and further let us suppose that it is truly random into which of the two empty containers a marble might fall. You throw your green marble, and let's say it lands in container 1. You now immediately now, that *once I throw my marble* the second container will contain a red marble. Immediately after filling container 1, did you "cause" the second container to contain a red marble? No, because the second container is still empty. Even after it is filled with a red marble, I would say our usual notions of causality would be more in accord with saying that I "caused" the second container to be filled with a red marble because it was I who threw the red marble into the funnel.
The big shortcoming of the marble analogy is that all events occur in the same "world", spacetime, so we can still ascribe an indirect causal influence due to your throwing of your marble first on what happens to the other container. In the case of entanglement, we don't even have that: The change in spacetime due to the first measurement does not have any causal link to the outcome of the second measurement (according to my imaginations) because there simply is no "change" in spacetime which would enforce the second measurement outcome to be correlated with the first.
If my view is correct, and the apparent non-local phenomena we have empirically confirmed fail to satisfy a key criterion for causality (namely, a link between changes in the world from event one to event two), then it would seem to me that this supports the notion that the metric structure of spacetime implied by the LT does indeed reflect a deep ontological feature (namely in this context, precluding non-local causation), particularly since the objection to this notion arose from these very correlations in the first place.
The reason I agreed with your argument up to the conclusion is that it supports my view as well as yours. I pointed out that to come to your conclusion you would have to rule out a possible metric connection between apparently non-local events because I made the implicit assumption that nature as a whole is consistent: Either it is wholly about metric structures playing deep ontological roles, or it is wholly about non-deterministic interactions giving rise to the appearance of such structures. Of course, under this assumption, for me to come to the opposite conclusion, I have the burden of showing that such metric connections are not just possible as a matter of vague speculation, but can be formulated in a concrete way to give positing such connections explanatory power for the phenomena we observe, especially with respect to showing how the deep ontological significance of spacetime is preserved in the face of apparently non-local phenomena. I tried to meet that burden at least somewhat in the above exposition of my ideas about entanglement.
Naturally, you don't need to make this consistency assumption about nature, but then, it seems to me, you end up with an argument that supports equally well two opposite conclusions. Is it then an argument at all?
Finally, I really look forward to your objections on my distinction between actual and actualizable mass. I have not had yet the privilege of sharpening my own arguments through the process of defending them against thoughtful objections.
All the best,
Armin