Graduate Alternative model for counterfactual definiteness in Bohm-like EPR

[cianfa72]

TL;DR

About the existence of alternative models for Bohm-type EPR experiment other than hidden variables (HVs)

As far as I know, in the context of Bohm-type EPR experiment, Bell's inequalities are logical consequences of the following assumptions:

1. counterfactual definiteness (CFD): pairs of QM non commuting variables/observables have each a define value; even though in an experiment's run we actually measure only one variable, the (counterfactual) value of the other variable that could have been measured in that run exists and is well defined (i.e. in that run it is well defined even though is unknown)
2. principle of locality: there is no action at distance for spacelike separated events (Alice and Bob measurements)
3. measurement independence (no conspiracy): the settings of spin measurements are "free", i.e. they are uncorrelated w.r.t. the preparated physical state

In this scenario, I believe the unique let me say "implementation" of CFD is by mean of an hidden variables model. Basically there is an hidden variable $\lambda$ that may take on different values, one for each run of experiment.

Do exist other "implementation" models for the CFD ?

 

[Peter Morgan]

Concerning 3), even if there no dependencies of the controlled settings in the apparatus (which we can verify because we have a list of the binary values that were used, to which we can apply statistical tests), there will be dependencies between uncontrolled degrees of freedom of the two devices that apply that choice to the electromagnetic field.
I discuss this at some length in an article in JPhysA 2006 (though sadly not clearly enough, which is why it is not well-known.) Here's how I now talk about this, from a colloquium for NSU Dhaka on May 18th:

The diagram at upper right is from page 60 of Gregor Weihs's thesis (which gives more detail about the apparatus than the PRL from 1998, in this case with English annotations, from Gregor, personal communication.) The idealized diagram of the same apparatus at upper left is from §7.2 of an article of mine in Annals of Physics 2020.
The two devices that apply the recorded choice to the electromagnetic field are called ElectroOptic Modulators in this experiment. They switch between zero applied voltage and ~1000 Volts in less than a microsecond, so there's a lot going on inside them.
If we think of the apparatus as enclosing and conditioning the noisy electromagnetic field —to engineer the statistics of the events in the Avalanche PhotoDiodes so they violate a Bell inequality, very much nontrivially— instead of as about two particles, there are measured correlations between events in the Avalanche PhotoDiodes, so we cannot claim that there are no correlations whatsoever between the inner workings of the ElectroOptic Modulators.
To understand that in a broader perspective, perhaps try the whole talk (there's a link in the video description to a PDF of the slides, so you can try that to see whether you want to take the time to watch the whole colloquium. Slides 15-19 are about Gregor Weihs's experiment.)

To circle back to your question about CFD, I construct what I call QND Optics as a commutative subalgebra within Quantum Optics that is loosely comparable to Bohmian trajectories for a QFT, except that it is linear, Lorentz invariant, and more measurement theoretic (see slides 24-25, though the slides before that are necessary to understand the notation.) I think it's preferable to work with a sophisticated measurement theory that can accommodate multiple apparatuses and data analyses in a single mathematical structure, however I find the field theoretic mathematics of QND Optics makes me mostly unworried about CFD for particle properties.

 

[cianfa72]

Concerning 3), even if there no dependencies of the controlled settings in the apparatus (which we can verify because we have a list of the binary values that were used, to which we can apply statistical tests), there will be dependencies between uncontrolled degrees of freedom of the two devices that apply that choice to the electromagnetic field.
I discuss this at some length in an article in JPhysA 2006 (though sadly not clearly enough, which is why it is not well-known.) Here's how I now talk about this, from a colloquium for NSU Dhaka on May 18th:
View attachment 368180

Sorry, not sure to understand your apparatus/setup. Is it a Bohm-type EPR kind of experiment ? From a correlation perspective, it seems like you're actually refuting measurement independence (no conspiracy). Are you talking about a sort of superdeterminism ?

 

[Peter Morgan]

Sorry, not sure to got your apparatus/setup. Is it a Bohm-type EPR kind of experiment ? From a correlation perspective, it seems loke you're actually refuting measurement independence (no conspiracy). Are you talking about a sort of superdeterminism ?

It's Gregor Weihs's experiment from the mid-1990s, demonstrating a violation of a Bell-CHSH inequality, which is closely related to Bohm's version of EPR (except that it's for photons, not for fermions.) On arXiv, with a link there to PRL, that's "Violation of Bell's inequality under strict Einstein locality conditions", https://arxiv.org/abs/quant-ph/9810080. That was the classic experiment of its kind for over a decade, which is part of why I use it, but it is also significantly simpler in operation than more recent experiments, which typically include heralding and other subtleties.

QND Optics, being contained within Quantum Optics, considered as a Quantum Field Theory, is a statistical theory that is equivalent to Quantum Optics but admits a classical interpretation because its observables generate a commutative subalgebra of measurement operators acting on the same Hilbert space.
This is very loosely analogous to superdeterminism but it is not the same as superdeterminism because for quantum field theories measurements have variances that diverge as the measurement scale approaches zero length. That is, at all scales there is noise that 'bubbles up' from smaller scales, so despite the superficially classical structure afforded by the commutative subalgebra, nothing is determined within the theory. Another loose analogy would be a random fractal structure that is everywhere not differentiable, something like a randomized version of the Weierstrass function, so that we can't use differential equations.
Note that because this is contained within Quantum Optics, it doesn't do anything that isn't compatible with what quantum field theories do. That's to say, it looks a little like superdeterminism but it isn't superdeterminism — and if it were then QFT would also be.