I Why can't classical models explain quantum entanglement?

[SimplePrimate]

TL;DR Summary

Why are classical descriptions of particle pairs now considered inadequate?

In my messy apartment I might well find a right-hand mitten, and immediately know the left-hand state of its missing partner. A classical description works just fine for this (their opposite states were produced at the time of manufacture) and I don't need to consider my observation of one causes the state of the other.

Why is this classical view inadequate for understanding quantum paired particles?

 

[f95toli]

Google "Dr. Bertlmann's Socks"

 

[PeroK]

Why is this classical view inadequate for understanding quantum paired particles?

Your mittens have so-called "hidden variables". I.e. one is definitely a right mitten and one a left mitten. Properties of QM particles are not pre-defined, but result from measurement.

Bell's Theorem shows that (local) hidden variables cannot reproduce the results of QM.

 

[SimplePrimate]

I believe Einstein argued unsuccessfully for hidden variables. I'll have to read up on why, but was hoping I might get a primer here on the thrust of Bell's argument.

 

[PeroK]

I believe Einstein argued unsuccessfully for hidden variables. I'll have to read up on why, but was hoping I might get a primer here on the thrust of Bell's argument.

Bell's argument is statistical in nature. The simplest description is as follows:

QM uses complex probability amplitudes. Whereas, classical hidden variables use traditional probabilities. This gives QM generally more flexibility in terms of correlating data, as the complex amplitudes are able to combine in more flexible ways that classical probabilities.

Bell identified a particular experiment where QM could "beat" anything that hidden variables could do. (*) That experiment has been carried out with the results predicted by QM.

To understand Bell's theorem you have to look at the specific calculations that QM uses andd compare these with the calculations involving classical probabilities. It's not that difficult, but again it belies the idea that you can truly understand physics without putting in the hard work of study!

As an aside, the non-classical behaviour at the heart of QM underpins everything that makes our universe interesting: essentially by underpinning chemistry and sub-atomic processes.

The sad thing about Einstein's legacy, I believe, is that he didn't have a practical alternative to QM. If we didn't have QM, then we wouldn't have anything by way of an explanation for atoms and chemistry.

(*) Ironically, Bell was hoping to disprove QM by his theorem! In the end, the experiments not only vindicated QM but ended Einstein's dream.

 

[SimplePrimate]

PeroK: "To understand Bell's theorem you have to look at the specific calculations that QM uses andd compare these with the calculations involving classical probabilities. It's not that difficult, but again it belies the idea that you can truly understand physics without putting in the hard work of study!"

Lack of maths seems like a lax oversight, but some of us struggle with numbers in very much the same way dyslexic learners do with written words. But you do what you can.

I'll see if Bertlmann's socks enlighten me first up.

 

[Motore]

Perhaps this video can help you better understand violation of Bell's inequalities:

 

[Nugatory]

I believe Einstein argued unsuccessfully for hidden variables. I'll have to read up on why, but was hoping I might get a primer here on the thrust of Bell's argument.

You will find many older threads here, and two of the better starting points are this Scientific American article and the web site maintained by our own @DrChinese. There is also Louisa Gilder's book The age of entanglement which readably covers the century-long history of our attempts to understand entanglement.

The very quick summary is that entanglement is not like your mittens. If you find a left-handed glove you know its mate is right-handed because you started with a left/right pair. However, with spin-entangled quantum particles when we measure one of them spin-up it does not mean that we started with an up/down pair and the other one is down, it means that the other one is now in a state such that if we measure its spin on the same axis we will get down. Bell's theorem shows that there are subtle statistical differences between "We know it is spin down" and "We know that if we measure it on this axis we will get spin down"; these differences will show up in carefully designed experiments; the experiments have been done; they agree with quantum mechanics and not the lost mitten model.

 

[Dale]

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[gentzen]

The sad thing about Einstein's legacy, I believe, is that he didn't have a practical alternative to QM. If we didn't have QM, then we wouldn't have anything by way of an explanation for atoms and chemistry.

Not sure why this should be sad, or even have anything to do with Einstein's legacy. He never claimed to have an alternative to QM, practical or not. He invented some pretty nice paradoxes, and some of his paradoxes improved our understanding of QM.

His own approach to physics was related to paradoxes from the very beginning. Bohr always wanted Einstein to make contributions to quantum mechanics rather than focusing on relativity. So Einstein contributed the best he could contribute, and that were his paradoxes.

 

[DrChinese]

PeroK: "To understand Bell's theorem you have to look at the specific calculations that QM uses andd compare these with the calculations involving classical probabilities. It's not that difficult, but again it belies the idea that you can truly understand physics without putting in the hard work of study!"

Lack of maths seems like a lax oversight, but some of us struggle with numbers in very much the same way dyslexic learners do with written words. But you do what you can.

If you want to tackle the Bell concept using very easy math, I would point you to a page I created for this purpose: Bell's Theorem with Easy Math. It shows precisely how the "mitten model" (or Bertlmann's socks model) predicts a value in one case of at least 33%, where the Quantum Mechanical expectation is 25%. Experiment says the value is 25%, thus refuting the classical models.

http://drchinese.com/David/Bell_Theorem_Easy_Math.htm