Impossible to exclude hidden variables without entanglement?

[greypilgrim]

Hi.

In most articles on Bell's inequalities, both the reality and locality assumptions are thrown at the reader from the beginning. DrChinese however starts with only the reality assumption and shows that it doesn't comply with QM IF it were possible to measure two non-commuting observables simultaneously on the same particle.

Since this is experimentally impossible, Bell assumed entangled particles that allow to make two simultaneous measurement. However, the price to pay is the addition of a second assumption, namely locality.

So it seems to me that the locality assumption is merely needed to make Bell's results experimentally verifiable. Can it be proven that there is no other way to do so than using entangled particles and assuming locality?

 

[.Scott]

The original Bell article was published in Scientific American in 1979. As long as you are willing to spend a little time with the arithmetic, it's not a bad read: https://www.scientificamerican.com/media/pdf/197911_0158.pdf

The point of the article was to describe an experiment where the QM-predicted result would be inconsistent with any model that was based on information (hidden values) carried at light speed or less (locality) and reflecting reproducible results based on universal physical laws (reality).

It's important because, in our daily lives, we presume a cause and effect and a "local" connection leading from the cause to the effect.
The QM prediction (which has since been demonstrated as correct) describes a system where there is no cause/effect direction between the two measurements.

 

[Doc Al]

The original Bell article was published in Scientific American in 1979. As long as you are willing to spend a little time with the arithmetic, it's not a bad read: https://www.scientificamerican.com/media/pdf/197911_0158.pdf

FYI, that's not the original Bell paper, it's a popular article by Bernard d'Espagnat (with a silly subtitle, in my opinion). Bell's original paper ("On the Einstein Podolsky Rosen paradox") was published in 1964.

 

[Nugatory]

FYI, that's not the original Bell paper, it's a popular article by Bernard d'Espagnat (with a silly subtitle, in my opinion). Bell's original paper ("On the Einstein Podolsky Rosen paradox") was published in 1964.

Yep, and it's time to put in another plug for the website maintained by our own @DrChinese at http://www.drchinese.com/Bells_Theorem.htm which has copies of some of the most important papers and a bunch more besides. The d'Espagnat article was written in 1979 because the first experimental confirmations of Bell Inequality violations were hitting the news.

 

[greypilgrim]

Well you're sort of not answering my question... I'll try to reformulate:
From DrChinese's article, I read that

1. for showing that QM does not comply with the reality assumption, we actually don't need to assume locality. We only have to assume that it is possible to measure two non-commuting observables simultaneously on the same particle.
2. since this is EXPERIMENTALLY impossible, we'll use two different particles that are highly correlated, namely entangled. Here's where the locality assumption comes in.

In Bell's original paper, uses both the reality and locality assumptions from the beginning, as it is the case for virtually every article or paper I read on this matter EXCEPT DrChinese's article. Reading the latter, my impression was that the locality assumption is used only such that we can work with entangled particles to make the argument about QM not complying with the reality assumption experimentally testable.

My question is: Is this the only way to go or can we make this argument about QM not complying with the reality assumption experimentally testable WITHOUT using entangled particles? We'd probably still need a second assumption, but are there other possibilities than locality?

In his original article, Bell says in the introduction
"It is the requirement of locality, or more precisely that the result of a measurement on one system be unaffected by operations on a distant system with which it has interacted in the past, that creates the essential difficulty. There have been attempts [3] to show that even without such a separability or locality requirement no "hidden variable" interpretation of quantum mechanics is possible. These attempts have been examined elsewhere [4] and found wanting. Moreover, a hidden variable interpretation of elementary quantum theory [5] has been explicitly constructed. That particular interpretation has indeed a grossly nonlocal structure. This is characteristic, according to the result to be proved here, of any such theory which reproduces exactly the quantum mechanical predictions."

[3] J. VON NEUMANN, Mathematishe Grundlagen der Quanten-mechanik. Verlag Julius-Springer, Berlin (1932), [English translation: Princeton University Press (1955)]; J.M. JAUCH and C. PIRON, Helv. Phys. Acta 36, 827 (1963).
[4] J. S. BELL, to be published.
[5] D. BOHM, Phys. Rev. 85, 166 and 180 (1952).

So apparently von Neumann worked on this matter (showing no hidden variable interpretation of QM is possible without requiring locality), but Bell found his results to be "wanting". Did he publish his concerns later?

Also, I can't see Bell's logic in deducing from his results in the paper that ANY hidden variable interpretation of QM "characteristically" needs to be nonlocal, as the example of Bohmian mechanics happens to be. As all his results are derived from the reality and locality assumptions which Bell uses right from the start, I can't see how this qualifies to make statements about theories that don't use the locality assumption.

 

[DrChinese]

Well you're sort of not answering my question... In Bell's original paper, uses both the reality and locality assumptions from the beginning, as it is the case for virtually every article or paper I read on this matter EXCEPT DrChinese's article. Reading the latter, my impression was that the locality assumption is used only such that we can work with entangled particles to make the argument about QM not complying with the reality assumption experimentally testable.

My question is: Is this the only way to go or can we make this argument about QM not complying with the reality assumption experimentally testable WITHOUT using entangled particles? We'd probably still need a second assumption, but are there other possibilities than locality?

In his original article, Bell says in the introduction
"It is the requirement of locality, or more precisely that the result of a measurement on one system be unaffected by operations on a distant system with which it has interacted in the past, that creates the essential difficulty. There have been attempts [3] to show that even without such a separability or locality requirement no "hidden variable" interpretation of quantum mechanics is possible. These attempts have been examined elsewhere [4] and found wanting. Moreover, a hidden variable interpretation of elementary quantum theory [5] has been explicitly constructed. That particular interpretation has indeed a grossly nonlocal structure. This is characteristic, according to the result to be proved here, of any such theory which reproduces exactly the quantum mechanical predictions."

If you look at the math, there is really no difference in my approach and anyone else's - including Bell. Just different words to describe. Certainly, EPR was an attack on the Heisenberg Uncertainty Principle. EPR didn't really bother to question locality.

Bell himself points out (bolded above) that separated particles (that interacted in the past) should not be affected affected by operations on the other. Of course, in QM these are a single quantum system. Which is what the separability assumption (Bell's [2]) is meant to question, a la EPR.

Please note that in QM, the component particles (of an entangled system) do not need to have interacted in the past anyway (as we now know). Or even ever exist in a common light cone.

-DrC