B Quantum Nonlocality or Non Counterfactual Definiteness?

[morrobay]

It seems the major premise for the derivation of Bell Inequalities is Counterfactual Definiteness for both electrons and photons : For electrons the spins at x, y, z directions are expected from conservation laws. See table. And for photons the eight polarization types along three orientations interact with nine pairs of detector settings. In each case electrons , photons the inequality does not hold. Seems this could be more from non Counterfactual Definiteness rather that quantum Non Locality. Especially since the expectations are based on three values and the experiments only measure two different settings. https://chem.libretexts.org/Bookshelves/Physical_and_Theoretical_Chemistry_Textbook_Maps/Quantum_Tutorials_(Rioux)/08:_Quantum_Teleportation/8.29:_Spooky_Action_at_a_Distance-_The_EPR_Experiment_with_Photons.

 

[Demystifier]

The assumption of counterfactual definiteness is just a more technical name for the assumption of realism. There are several versions of the realism assumption in quantum mechanics, but only a very weak version of it is really necessary in the derivation of Bell inequalities, so weak that it is very hard to honestly believe that this version of realism is not true. In other words, the possibility that the world is local but counterfactual indefinite does not seem reasonable (at least to me). For more details see https://arxiv.org/abs/1501.04168

 

[Morbert]

The assumption of counterfactual definiteness is just a more technical name for the assumption of realism. There are several versions of the realism assumption in quantum mechanics, but only a very weak version of it is really necessary in the derivation of Bell inequalities, so weak that it is very hard to honestly believe that this version of realism is not true. In other words, the possibility that the world is local but counterfactual indefinite does not seem reasonable (at least to me). For more details see https://arxiv.org/abs/1501.04168

That paper is appropriate, as I'll argue it runs afoul of counterfactual definiteness. It supposes two statements (L) and (R1)

(L): If the space-time regions A and B are spacelike separated, then events in A cannot influence events in B.

(R1): Every quantum observable (or at least (a · σ) ⊗ I and I ⊗ (b · σ) for every a and b) actually has a definite value even before any attempt to measure it; the measurement reveals that value

and argues that (L) -> (R1). Hence, concerning Bell's theorem, we do not have a choice between local theories or realistic theories, as locality implies realism.

But (R1) is too strong an implication without counterfactual definiteness because it makes a statement about every osbervable having a definite value. It is interpretation dependent. Instead, I'd argue that (L) implies a much weaker, interpretationless statement:

(R0) For a given experiment with outcome Q at time t, there exists a boolean lattice with propositions Q at time t, P at time t' < t, and the material implications P -> Q, Q -> P

This weaker statement makes no interpretational commitment about realism, and so we maintain our freedom to construct local or realistic theories

 

[DrChinese]

1. It seems the major premise for the derivation of Bell Inequalities is Counterfactual Definiteness for both electrons and photons : For electrons the spins at x, y, z directions are expected from conservation laws. See table. And for photons the eight polarization types along three orientations interact with nine pairs of detector settings. In each case electrons , photons the inequality does not hold. Seems this could be more from non Counterfactual Definiteness rather that quantum Non Locality.

2. Especially since the expectations are based on three values and the experiments only measure two different settings. ...

I don't know about the "major premise" designation for counterfactual definiteness (CD) fork of the Bell argument, since locality is also part and parcel of that argument - which of course effectively refutes local realism. But sure, Bell tests cast a lot of doubt on CD.

1. There are usually 3 or 4 polarization angle settings in Bell tests, depending on the specific inequality derived. However, theory says there are also perfect correlations (anti-correlations) at all identical angle settings. That means there must be counterfactual definiteness for a large (or perhaps infinite) range of angles. If there are, what are they? There is no way to describe such an array of possible outcomes that will produce results which match the predictions of QM.

2. If there is CD, then this argument does not matter - although I do see it put forward from time to time. Either those other settings would produce a definite value independent of the partner particle (as CD claims), or there is no CD.

And in fact, in certain modern experiments, the CD argument seems to fall apart without consideration of statistical data sets. For example: In the GHZ theorem/experiment, a single run is all that is necessary to refute local realism. They use 3 or 4 photon entanglement to accomplish this (in a GHZ state).

https://arxiv.org/abs/quant-ph/9810035
"We present the experimental observation of polarization entanglement for three spatially separated photons. Such states of more than two entangled particles, known as GHZ states, play a crucial role in fundamental tests of quantum mechanics versus local realism..."

https://www.drchinese.com/David/Bell-MultiPhotonGHZ.pdf
"On the basis of measurements on three-photon entanglement, we have realized the first experimental test of quantum non-locality following from the GHZ argument. Not only does multi-particle entanglement enable various fundamental tests of quantum mechanics versus local realism..."