“II. AGAINST NONLOCALITY
There is no nonlocality in quantum theory; there are only some nonlocal interpretations of quantum mechanics. ….
.. QBism makes sense of quantum mechanics by taking an unfamiliar perspective on scientific theories and the scientists who use them. QBist quantum mechanics is local because its entire purpose is to enable any single agent to organize her own degrees of belief about the contents of her own personal experience. No agent can move faster than light: the space-time trajectory of any agent is necessarily time- like. Her personal experience takes place along that trajectory.
Therefore when any agent uses quantum mechanics to calculate “[cor]relations between the manifold aspects of [her] experience”, those experiences cannot be space-like separated. Quantum correlations, by their very nature, refer only to time-like separated events: the acquisition of experiences by any single agent. Quantum mechanics, in the QBist interpre- tation, cannot assign correlations, spooky or otherwise, to space-like separated events, since they cannot be experienced by any single agent. Quantum mechanics is thus explicitly local in the QBist interpretation. And that’s all there is to it.”
What Henson did was to point out that one can replace ‘Quantum theory” or “quantum mechanics” in the above Qbism argument with a hypothetical nonlocal theory called “NL Theory” or “NL mechanics.” That is, NL is an explicitly nonlocal theory that allows violations of relativity such as controllable superluminal signaling (although it prohibits observers themselves from moving faster than light). This gives the following (with the replacement highlighted in red):
“There is no nonlocality in NL theory; there are only some nonlocal interpretations of NL mechanics. ….
.. QBism makes sense of NL mechanics by taking an unfamiliar perspective on scientific theories and the scientists who use them. QBist NL mechanics is local because its entire purpose is to enable any single agent to organize her own degrees of belief about the contents of her own personal experience. No agent can move faster than light: the space-time trajectory of any agent is necessarily time- like. Her personal experience takes place along that trajectory.
Therefore when any agent uses NL mechanics to calculate “[cor]relations between the manifold aspects of [her] experience”, those experiences cannot be space-like separated. NL correlations, by their very nature, refer only to time-like separated events: the acquisition of experiences by any single agent. NL mechanics, in the QBist interpretation, cannot assign correlations, spooky or otherwise, to space-like separated events, since they cannot be experienced by any single agent. NL mechanics is thus explicitly local in the QBist interpretation. And that’s all there is to it.”
Thus, the Qbism ‘against nonlocality’ argument regarding QM also must also deny the nonlocality of an explicitly nonlocal theory as long as that theory doesn’t allow agents themselves to travel faster than light. This is a reductio ad absurdum; i.e., it demonstrates that the Qbism argument for locality leads to the self-contradictory conclusion that a nonlocal theory is local.
Another way to see the problem with the Qbism argument is to consider a medical test for the existence of some disease. Suppose Mr. X has a symptom, such as shortness of breath, and he goes in for tests to determine the cause. Unfortunately, Mr. X has lung cancer, but the test fails to disclose it. (All medical tests have some fallibility in this way, but good tests have a very small chance of this sort of error.) This is called a ‘false negative’: Mr. X really does have a disease, but the test for the disease yields the wrong answer: it says he lacks the disease when in fact he has it. (A false positive would say that someone has the disease when in fact he does not).
The Qbism test for nonlocality is whether an agent will experience spacelike separated correlations. But since a timelike-restricted agent can never encounter spacelike separated events, this ‘test’ trivially yields a negative result for nonlocality. It is thus guaranteed to find ‘no nonlocality’ in all theories in which observers are restricted to timelike paths, whether the theory itself is local or not. So it will yield a false negative for a theory that is explicitly nonlocal, as long as that theory does not allow agents themselves to move faster than light. This is like a test for a disease that is guaranteed to yield the result ‘no disease’ whether or not the disease is present (provided there is some condition, analogous to a timelike-restricted observer, that masks the disease).
Would it help Qbists to argue that there could be no theory such as NL that would allow controllable superluminal signaling while restricting observers to timelike trajectories? No, since there is no logical necessity for a theory to describe observers by the same laws as it describes physical objects or events. Moreover, it is certainly conceivable to have a theory that would allow superluminal behavior on the part of some objects but not to observers, as defined by the theory. So it’s important to note that one cannot escape this conclusion by noting that such a theory would not be realistic, or correct, and/or would not apply to our world. The issue, raised by Qbists themselves, is not whether a theory (such a quantum mechanics) is correct or true or not, but whether or not it is local. And they are forced by their own criterion to say ‘yes’ even for a hypothetical nonlocal theory that has explicitly relativity-violating controllable signaling, whether or not such a theory could ever be true. This contradiction is what reveals the Qbism locality ‘test’ as having no real informative content about whether any theory (whether or not it’s a good theory) is local.
If we don’t want to subject Mr. X to a test guaranteed to say that there are no cancer cells even when there are (given a loophole analogous to the timelike-restricted observer), then we should probably be leery of an interpretive criterion guaranteed to say that a theory is ‘local’ even when, like ‘NL’, it allows explicitly superluminal nonlocal signaling between events.
A final remark regarding what is meant by ‘about the world’ in the title of this post: I can imagine a self-described Qbist as objecting and saying that Qbism is ‘about the world’ and that the Qbist approach is an enlightened view on what it means for a theory to be about the world–in that ‘world’ can only mean ‘the subjective experiencing of an agent’. Such a view denies that the theoretical quantities of quantum theory (such as quantum states) refer to specific definable entities beyond the observer’s perceptions. In essence, Qbism assumes that we are moving through unspeakable ‘quantum stuff’ and that we can (and should) say nothing more about it than that. But in fact it is perfectly possible and reasonable to suppose that quantum theory is indeed saying something about this ‘quantum stuff’: i.e., that quantum states really do describe constituents of reality and their nature. It’s just that their nature is highly non-classical, and that is evidenced by their nonlocality.
Thus, many researchers still think of quantum nonlocality as a kind of disease that needs to be eliminated, denied, or explained away in order for the theory to ‘make sense’. An alternative approach is to admit that maybe the theory is indeed telling us that Nature has a certain kind of hidden nonlocality. For a way to make sense of quantum theory without denying its essential nature, I invite the reader to consider this book. It is certainly true that what we perceive is contextual in some sense, but quantum theory has much more to tell us about the nature of this contextuality than the usual instrumentalist assumption, as in Qbism, that we cannot know anything about the nature of the interaction between observers and the quantum ‘stuff’ and therefore must treat everything external to our perceptions as an unknowable ‘black box’. The transactional picture allows us to understand at least something about the nature of our interaction with the unseen aspects of reality that we describe by quantum states and forces (see the above book link for that account, and stay tuned for my 2019 followup book, pictured below.)