Hi Federico,

Thanks for the comments.

“*Regarding the first part of the quoted sentence, I would like to note that from Alice’s perspective those events observed by Charlie are not more real than hidden variables (or than Bob’s measurement choices and outcomes) until Alice become conscious of them*“.

Your comment seems to already deny one of the assumptions that go into what we call “Local Friendliness”, namely the assumption of Observer-Independent Facts (OIF): that any event that is real to one observer is real to all observers. Some theories reject that assumption, and some theories do not (but must reject one of the other assumptions in light of the violation of the LF inequalities).

I would also say that most physicists believe that they can keep that assumption–even while rejecting the existence of hidden variables more generally–and so they have something interesting to learn from our theorem.

But I gather that what you mean is that if Charlie’s observations are real, then they must be (real) hidden variables (for Alice). That may be true, but again, we do not need to make that assumption. And importantly, what we are emphasising is that we do not need to assume that *all* measurement outcomes (even those that are *not* measured by Charlie) are *predetermined* by hidden variables.

In other words, OIF is not the assumption that “unperformed experiments have predetermined results”. It is the (much weaker, and widely held) assumption that “*performed* experiments have absolute–i.e. observer-independent–results”.

“*I think that this is not a step beyond Bell’s theorem, but it’s a step back, since the existence of the information for predetermining all measurement outcomes is a consequence of EPR argument, from which Bell’s theorem starts, as remembered in my paper for this workshop*“.

The EPR argument has its own set of assumptions, which have been debated for over 80 years. Whether or not predetermination of all measurement outcomes follows from the assumptions of the EPR argument is completely irrelevant to our argument, because we do not make the assumptions that EPR did. Furthermore, our assumptions DO NOT imply predetermination. Our assumptions are weaker than those of EPR, and weaker than those of Bell, and our conclusions are therefore stronger than both of those.

It is pretty straightforward to show that our theorem has precisely one less assumption than a popular way of formulating the derivation of Bell inequalities. That is, our theorem assumes:

Observer-Independent Facts (a.k.a. Macroreality)

Locality (a.k.a. Parameter Independence)

Freedom of Choice (a.k.a. No Superdeterminism / No retrocausality)

To derive a Bell inequality one needs to make another assumption, for example, Outcome Independence. (Macroreality is not usually listed as an assumption, but it is needed, see e.g. [1] for a derivation in which it is explicitly included).

Now, Shimony argued (and that’s a widely popular view) that a resolution of Bell’s theorem that could maintain “peaceful coexistence” with relativity was to reject Outcome Independence, while maintaining all of the other assumptions above. In particular, keeping Parameter Independence allowed for maintaining “no action-at-a-distance”. On the other hand, Shimony argued that the violation of Outcome Independence–dubbed “passion at a distance”–was a mild, acceptable form of nonlocality, since it was *uncontrollable* nonlocality.

What our theorem shows is that this is no longer an option in light of violation of LF inequalities. Thus it is a strictly stronger conclusion than what can be reached via Bell’s theorem.

To emphasise this point, another research programme that attempts to resolve Bell’s theorem in the same philosophical direction as “passion at a distance” is the program of quantum causal models. All frameworks for quantum causal models to date uphold all of the three assumptions that go into our theorem, and do not provide any mechanism by which the Local Friendliness inequalities could not be violated (as is done, for example, by collapse theories). Therefore our result also introduces a problem for quantum causal models, where Bell’s theorem clearly doesn’t–indeed QCMs were designed to circumvent Bell’s theorem! Again, this demonstrates that our conclusions are strictly stronger.

“*This fact suggests that abandoning “macroreality” is not a valid option for saving locality*“.

It certainly *is* an option to save Locality (as explicitly defined in our paper) by abandoning Macroreality, or Observer-Independent Facts. This is what is done in Everett, relational QM, QBism, etc. Those are constructive examples that give the same empirical predictions as standard QM. Therefore, clearly, it can be done.

If by “locality” you mean something else (I suspect you mean something similar to Bell’s notion of Local Causality), then I agree that *that* notion cannot be maintained by abandoning Macroreality. Please mentally substitute “Parameter Independence” whenever you see the word “Locality” in our paper. If you object to the idea that one can maintain Parameter Independence while abandoning Macroreality, I’m happy to discuss. If your criticism is simply that you do not agree that we call this notion “Locality”, then I am less interested in that debate.

[1] Howard M. Wiseman, Eric G. Cavalcanti, “Causarum Investigatio and the Two Bell’s Theorems of John Bell”, https://arxiv.org/abs/1503.06413