Why is Quantum Field Theory Local?

[A. Neumaier]

So you rule out something that nobody believed in the first place.

That's the case for most theorems.

 

[A. Neumaier]

For Bohmian mechanics it's not important that the particles are exactly pointlike. If you like they can be balls of the Planck size, it doesn't change anything important.

Then they can even be football size, since they are unobservable, and only their center of mass appears in the equations.

But they are point particles in all publications on the matter.

 

[Demystifier]

But they are point particles in all publications on the matter.

So are the planets in Newtonian mechanics.

 

[A. Neumaier]

So are the planets in Newtonian mechanics.

Yes, and Newtonian mechanics has the typical resulting defects: It can be formulated only as nonrelativistic theory, and has problems with collision trajectories (see the paper by Baez). Just like Bohmian mechanics.

For more than a century we are past this state of affairs.

 

[Kolmo]

It shows such theories, as a class, allow for many features of QM, with QM perhaps the simplest

Reading this thread a while later, if you find it interesting quantum theory as a GPT (Generalized Probability Theory) can be characterized in two ways:

(a) As the most general one satisfying the Exclusion principle. Namely that if each of the pairs from a set of observables $A,B,C$ are compatible/co-measurable, then the whole set is co-measurable

(b) The most general one that permits Bayesian updating

"Most general" here means "has the broadest set of possible correlations". So in a CHSH test classical probability gives $2$ as the bound and QM gives $2\sqrt{2}$, then any theory with correlations beyond $2\sqrt{2}$ breaks both (a) and (b).

Regarding (b), all GPTs allow updating but by "Bayesian" we mean there is a unique way to update in late of data. In GPTs going beyond the Tsirelson bound $2\sqrt{2}$ there is an element of arbitrary choice in how one updates in light of data. This is what leads to a recent phrase: it's the most general GPT where one can still learn.

 

[atyy]

Regarding (b), all GPTs allow updating but by "Bayesian" we mean there is a unique way to update in late of data. In GPTs going beyond the Tsirelson bound $2\sqrt{2}$ there is an element of arbitrary choice in how one updates in light of data. This is what leads to a recent phrase: it's the most general GPT where one can still learn.

Could you give some references?

 

[Kolmo]

Could you give some references?

(b) is a corollary of (a) so it is simpler to see the proof of (a) first.

It's here:
https://journals.aps.org/pra/abstract/10.1103/PhysRevA.100.032120

Freely available here:
https://arxiv.org/abs/1801.06347

 

[Kolmo]

Could you give some references?

To be more explicit there is also also a third condition proved to be equivalent in this paper, so the full list is that the theory is obeys the following which are all equivalent:

(a) The most general theory satisfying the Exclusion principle. Namely that if each of the pairs from a set of observables $A,B,C$ are compatible/co-measurable, then the whole set is co-measurable

(b) The most general one that permits Bayesian updating.

(c) The most general one which assigns probabilities to any repeatable ideal measurements.

(a) was originally a conjecture of Ernst Specker. Cabello proved (c) implies (a) and from there proves (a) in the paper I linked. After that he later proved (b) in (PDF free access):
https://journals.aps.org/prresearch/abstract/10.1103/PhysRevResearch.2.042001.