Local hidden variable theories

The many-particle theories of condensed matter physics and the standard model of particle physics are not local hidden variable theories. They obey the standard axioms of quantum mechanics such as a state being a ray in a vector space, unitary evolution between measurements, and state reduction upon measurement. This is stated clearly in Weinberg's QFT text.

The standard model of particle physics is local in a different sense: it does not allow superluminal communication of classical information. The distinction between these two definitions of locality can be found in Susskind's quantum mechanics text, part of the Theoretical Minimum series.

 

The particles of QFT have the same ontological status as particles in QM. So whatever flavour of Copenhagen or Many-Worlds one uses for QM, that should also apply to QFT, which is simply QM (not entirely sure about MWI, but although it may have open problems, the transition from QM to QFT is not one of them).

The main open problem in interpretations when one passes from QM to QFT is that it is not clear whether a Bohmian picture exists for the standard model, because it is unclear whether BM can accommodate chiral fermions interacting with non-abelian gauge bosons. There are published proposals, but as far as I understand, there is not yet a consensus whether these are correct in all technical details (even at the non-rigourous physics level of argumentation.)

 

Take a look also at bhobba's remark on cluster decomposition at https://www.physicsforums.com/threa...no-spooky-no-nonlocality.792088/#post-4974680.

So relativistic QFT is local or nonlocal depending on the definition of locality one uses:
(1) no superluminal transfer of classical information (spacelike observables commute) YES
(2) cluster decomposition YES
(3) locally causal NO

 

The standard model of particle physics with electrons, photons and quarks etc is not locally causal. There is no locally causal theory that reproduces the prediction of quantum mechanics that the Bell inequalities are violated at spacelike separation. So yes, there is a disconnect between the mathematics and the simplest narratives about these particles. It is especially clear in the Schroedinger picture, where the wave function is the Schroedinger functional (I don't know if this rigourously exists, but the standard model is not rigourous). The wave function is clearly not any wave on "spacetime", but a wave on field configurations, eg. http://arxiv.org/abs/hep-lat/9312079 (see Eq 3.2).

 

A tricky question is whether if one ignores the prediction that the Bell inequalities are violated, and restricts oneself to a subset of quantum phenomena, whether a locally causal explanation exists.

An analogy is that in quantum mechanics, we always say that particles do not have trajectories with simultaneously well defined position and momentum. Interestingly, if one makes the restriction to free particles and Gaussian wave functions, a quantum mechanical particle can have simultaneously well defined position and momentum.

Or the case of Rutherford scattering where the classical calculation gives the same result as the quantum calculation - that's how Rutherford discovered the nucleus, based on Geiger and Marsden's experiments.

 

Well, in a sense they don't ignore them (or rather, it is surprising that ignoring them is as good as not ignoring them). Ok that probably didn't make any sense, but let me explain. In QFT books, especially the path integral formalism, is that one has manifest Lorentz covariance. However, the collapse of the wave function as used in predicting the violation of the Bell inequalities means that the wave function's evolution cannot be Lorentz covariant. So the requirement for covariance in the path integral - yes, it seems we need it, even though it enter a theory without covariance. And then bizarrely, although there is no Lorentz covariance, the predictions are Lorentz invariant, so all's well that ends well. But to me it seems miraculous.