Is Nature is Local or Nonlocal?

In quantum mechanics there are two strong points of view. On one hand the philosophers of physics insist that Bell showed us that nature is nonlocal: "What Bell Did", and on the other hand qubists and practitioners of high energy physics stress that nature is purely local and there is no "tickle at a distance". Now  last time I called this debate sterile because both sides are right as they talk about different things. Also I have yet to meet supporters of a camp not agreeing with the mathematical points of the other camp, and so it is all purely a matter of perspective. Hidden behind this seeming disagreement are the epistemic and ontic points of view. 

Let's try to disentangle the arguments and explain this local-nonlocal divide. Let's start with the case for nonlocality. This point of view starts with quantum correlations. In the words of Bell: "correlations cry out for explanations". Now only two kinds of explanations for correlations were ever found: 

1. common causes from the past
2. an event causing the other one

and neither of them are valid explanations for quantum mechanics correlations. The first kind of explanation falls under local hidden variable approach and this was disproved by Bell, while the second kind is forbidden by the special theory of relativity because spatial separated experiments were performed where there was not enough time for the signal to propagate from Alice to Bob side. The absence of a third explanation is typically stated as nonlocality. Mathematically this is expressed as violation of Bell's locality condition:

\(p(s, t | a, b) = p^1 (s|a) p^2 (t|b) \)

which is equivalent with parameter and outcome independence.

Now no qbist is denying that quantum mechanics violates parameter and outcome independence because this is a solid mathematical and experimental fact. But the local point of view starts with no-signaling, or the inability of Alice to influence the outcomes for Bob (and unsurprisingly no nonlocality supporter is denying this either). In the QBist point of view, each measurement is local and quantum mechanics is a tool which updates my personal degree of belief in order to make sense of what I observe. The Alice-Bob correlations can only be determined when the two sides come in contact and for this to happen travel at speeds lower than the speed of light is required.

To better understand this debate I encourage you to watch this meeting moderated by Brian Greene.

At 1:22:00 Rudiger Schack makes a provocative statement: quantum correlations are like Bertlmann socks. I think this is just an extravagant way of saying that quantum correlations are just correlations and no explanations are needed in general. [I cannot take Schack's Bertlmann comment at face value as this would imply he disagrees with Bell's mathematical statements from his famous Bertlmann's socks paper and that would be wrong].

Now since both sides agree on the mathematics and on experiments, but disagree on interpretation maybe there is a middle ground. Abner Shimony introduced the expression: "passion at a distance" but in the charged atmosphere of today in quantum foundations this is not a popular point of view. 

Behind the local-nonlocal debate there is a fracture of interpretation: is quantum mechanics ontic or epistemic? Jean Bricmont expresses best the ontic point of view around 4: 35 in the interview below:

"you need a theory about the world whose fundamental concepts are not expressed, the meaning is not expressed in terms of measurment". 

The opposing epistemic point of view was best expressed by late Asher Peres: "quantum mechanics while correct it is not universal, some things must remain unanalyzed".

For now the supporters of each camp do not agree at all with the opposite point of view and seems that nothing can change their minds as each position is perfectly self-consistent. But what is my position because I am neither in the epistemic nor in the ontic camp?

First, Asher Peres position is wrong because his argument is pure handwaving inspired by Godel's incompletness theorem. In Godel's proof there is this key step of arithmetization of syntax without which the proof falls apart, and this is missing from Peres' musings. More important, quantum mechanics can be reconstructed from the assumption of its universality. I believe the epistemic point of view is essentially correct, but I disagree that the Bayesian point of view gives you the complete story. In fact I predict that quantum collapse happens in nature by itself (similar with spontaneous symmetry breaking) and that there is a boundary between quantum and classical due to dynamically generated superselection rules. This implies a testable extension of the quantum formalism and I'll talk about this in future posts. The same approach which allowed me to reconstruct quantum mechanics from physical principles predicts a unique extension of quantum formalism using Grothendieck group construction. Let experiments decide if I am right or wrong. 

I also think the basic demand expressed by Jean Bricmont is perfectly valid, but I disagree that the Bohmian interpretation is the way to go. The main fault of Bohmian's approach is distinguishing the complex number formalism of quantum mechanics and splitting the wavefunction into the real and imaginary parts. The quantum harmonic oscillator can be successfully solved in phase space or in the quaternionic formalisms and one obtains the same predictions. However the actual representations are very different in mathematical terms, and who says complex wavefunctions deserves ontic status and quaternionic wavefunctions do not?

Finally, is nature local or nonlocal? Local or nonlocal are bad words lacking a precise enough meaning. Nature is pure quantum mechanical, quantum mechanics is universal, locality-independent and no-signaling.