I Uncovering the Conceptual Catch in EPR Proposal for Non-Commutative Variables

[DrChinese]

The right shoe left shoe analogy was contributed by Einstein as part of his criticism of "spooky action at a distance".

That example was reasonable, prior to Bell (1965). Einstein did not live to see his wonderful paper.

But it is no longer a good example, and is misleading. Bell himself wrote about some mismatched socks later on:

https://cds.cern.ch/record/142461/files/198009299.pdf

 

[ProfChuck]

Thank you for the link. That is an excellent paper. I knew Feynman while at grad school and remember something he said, "If you think you understand quantum physics it is certain that you don't because nobody does". The issue of hidden variables brings to mind Hawking's observation, "God not only throws dice he throws then into a dark corner where you can never see them." QED is the most accurate theory in scientific history and nobody knows why. That is truly spooky. It is very difficult to abandon the classical view of reality but quantum physics reveals that it is only an illusion.

 

[bhobba]

"If you think you understand quantum physics it is certain that you don't because nobody does".

Yes he did say that, and in the intended context is 100% true. The context however is in terms of classical pictures. Plenty of people, including Feynman when he was was alive, understand it only too well.

We now know a LOT more about the foundations of QM. Its simply the most reasonable probability model that allows continuous transformations between pure states and entanglement:
http://arxiv.org/pdf/quant-ph/0101012.pdf
https://arxiv.org/abs/0911.0695

It is very difficult to abandon the classical view of reality but quantum physics reveals that it is only an illusion.

That is true without any caveat due to context etc etc. It is the essence of the real issue with QM. It's this. QM is a theory about observations that appear in an assumed common sense classical world. How does a theory that assumes such in the first place explain it? A lot of progress has been made doing that, but a few issues still remain:
http://www.fisica.ufmg.br/~dsoares/cosmos/10/weinberg-einsteinsmistakes.pdf

THE textbook giving the modern detail is by Schlosshauer
https://www.amazon.com/dp/3540357734/?tag=pfamazon01-20

Thanks
Bill

 

[stevendaryl]

I understood that EPR ruled out the possibility of having the Rules of Quantum Mechanics consistent with the Criterion of Reality (COR) as they defined, because if it is consistent, a contradictory will ensue, therefore they concluded that quantum mechanics can not be complete. So long as this combination leads to a contradiction, then the hypothesis of consistency between the quantum mechanics and COR must be false and then it should not be used to deduce anything from it.
However, trying to find ways to explain the result that perfect prediction of one particle state after measuring its entan gled particle indicates that they, EPR, indirectly admitted that both perfect prediction and measurement, with resultant collapse of the wavefunction to a definite state, can be possible altogether. But they already ruled out that possibility in their paper. So on what logical base did they postulate the existence of hidden variables to explain something which is logical invalid?

I'm thinking that Einstein, et al, thought of it in terms of the right shoe, left shoe analogy. They thought that the values for measurements were predetermined, and that QM only gives statistical predictions. They didn't know that hidden variables were inconsistent with QM

 

[Adel Makram]

I think it was impeccable reasoning, but was never-the-less proved false by Bell's inequality. How flawless reasoning can be empirically refuted is one of those big mysteries of the universe.

Now I come to understand this statement in the following way.
1) EPR showed that the Rules of Quantum Mechanics and the criterion of reality can not be both true which implies that quantum mechanics is not complete theory.
2) Bell`s type experiments confirmed that the Rules of Quantum Mechanics and the criterion of reality is physically real (because Alice`s particle is collapsed to a particular eigen state which means the quantum mechanics is correct and the Bob`s particle turns instantaneously into the opposite eigen state which means that Bob`s particle state is an element of reality that can be predicted with absolute certainty by Alice once she measures her particle).
As long as the physical reality represented by (2) does not match the logic represented by (1), we can then say that the physical reality is not logically sound. Or "we live in a real but false world".
But also, there is another point, if Bell`s type experiments showed that the quantum mechanics rules and the criterion of reality are both true, then there must be a simultaneous reality of two non-commuting variables which is again against the rules of the quantum mechanics.
Also I am not sure whether any kind of experiments have been performed to show this!

 

[DrChinese]

EPR: No one really disputed that there are elements of reality. The question, as you mention, is whether they have simultaneous reality.

Bell: He showed that for QM to be correct in its predictions, there could not be such simultaneous reality - at least not without non-local influences.

Today: Of course, virtually any experiment with a Bell inequality defined is testing whether there can be simultaneous reality of non-commuting observables. All suitable tests fail in this regard, so there is NOT simultaneous reality of non-commuting observables.

 

[Adel Makram]

EPR: No one really disputed that there are elements of reality. The question, as you mention, is whether they have simultaneous reality.

Bell: He showed that for QM to be correct in its predictions, there could not be such simultaneous reality - at least not without non-local influences.

Today: Of course, virtually any experiment with a Bell inequality defined is testing whether there can be simultaneous reality of non-commuting observables. All suitable tests fail in this regard, so there is NOT simultaneous reality of non-commuting observables.

But where in Bell`s inequality, a simultaneous reality of non-commuting observables is measured? My understanding is; Bell`s-like experiments only test whether an objective reality with particles have a predefined physical values before the measurement determined by the hidden variables exists or no! So if they do exit, Bell`s inequality should hold, if the opposite then BI should be violated.

 

[RUTA]

But where in Bell`s inequality, a simultaneous reality of non-commuting observables is measured? My understanding is; Bell`s-like experiments only test whether an objective reality with particles have a predefined physical values before the measurement determined by the hidden variables exists or no! So if they do exit, Bell`s inequality should hold, if the opposite then BI should be violated.

Read this Mermin version of the BI http://users.etown.edu/s/stuckeym/MerminAJP1981.pdf or here https://www.physicsforums.com/insights/quantum-liar-experiment-instantiation-mermin-device/

 

[bhobba]

EPR showed that the Rules of Quantum Mechanics and the criterion of reality can not be both true which implies that quantum mechanics is not complete theory.

EPR showed that counterfactual definiteness and locality are not possible in QM - it actually had nothing to do with the completeness of QM although Einstein thought it did - but he was wrong.

Thanks
Bill

 

[DrChinese]

But where in Bell`s inequality, a simultaneous reality of non-commuting observables is measured? My understanding is; Bell`s-like experiments only test whether an objective reality with particles have a predefined physical values before the measurement determined by the hidden variables exists or no! So if they do exit, Bell`s inequality should hold, if the opposite then BI should be violated.

The inequality expresses the test by considering the relationship of outcomes at all permutations of 3 angle settings. Only 2 at any time are observed, a third is counterfactual. The inequality compares the averages of the permutations. If there is complete and total independence between Alice and Bob, that should be OK.