Bell inequality test without polarisation?

[lukephysics]

TL;DR Summary

can you do the inequality test without polarisation? Polarisation is complex and weird.

Was trying to understand the inequality test. The only article ever that I've found that explains it simply is the 1981 article, Bringing home the atomic world: Quantum Mysteries For Anybody. All other explanations require trust and understanding of polarisation, which is a huge deal.

So i now fully understand why it eliminates local realism. Now I want to know if the presumtions of the 3 measurement angles are correct. I have no knowledge of how polarisation 'really' works. So in my mind maybe the experimenters don't understand polarisation because 'quantum' or some conservation of momentum stuff. who knows?

So I was wondering if there are other experiments that have been done that don't use polarisation. After all, photons are just one type of particle and one of the many properties available to measure. So has this been done in other ways that can be explained by first principles, - without complexities and complications of polarisation, to verify this result? And if not, why not?

 

[lukephysics]

I found the GHZ experiment where you can do this:

in 2000, researchers at the University of Innsbruck in Austria performed an experiment using three beryllium ions in a linear trap, which were entangled in their spin states. The researchers measured the correlation between the spins of the ions and showed that the results violated Bell's inequality. This experiment demonstrated that the violation of Bell's inequality is not limited to polarization measurements, but can also occur in other physical observables such as spin.

 

[PeterDonis]

This experiment demonstrated that the violation of Bell's inequality is not limited to polarization measurements, but can also occur in other physical observables such as spin.

Polarization is spin: spin of photons.

 

[Nugatory]

The only article ever that I've found that explains it simply is the 1981 article, Bringing home the atomic world: Quantum Mysteries For Anybody. All other explanations require trust and understanding of polarisation, which is a huge deal.

You might also try this article from Scientific American: https://static.scientificamerican.com/sciam/assets/media/pdf/197911_0158.pdf

and also the website maintained by our own @DrChinese, especially the http://drchinese.com/David/Bell_Theorem_Easy_Math.htm section.

Bell tests can be done using the spin of particles which aren't photons, and this may be a bit easier to imagine. However we still have to accept that the quantum mechanical prediction is:
1) When you measure the spin of a particle on any axis, you will always get one of two results: up or down.
2) When you measure the spins of two entangled particles on the same axis, you will always get different results: one up and one down, never both up or both down.
3) When you measure the spins of two entangled particles on different axes, you will find that the probability of getting the same result is $\sin^2 \frac{\theta}{2}$ where $\theta$ is the angle between the two axes.

And as you say, there are only two ways of accepting that proposition: Either understanding (that is, learn a whole bunch of quantum physics, takes a year or so of college physics) and trust (take the word of someone who has done that year or so).

 

[f95toli]

You can also do Bell tests without using spins or photons at all.
It has become as standard experiment and has been done using many different quantum systems

See e.g.,

https://www.nature.com/articles/s41567-019-0507-7

There are many other examples.

 

[lukephysics]

When you measure the spins of two entangled particles on different axes, you will find that the probability of getting the same result is sin2⁡θ/2 where θ is the angle between the two axes.

but why are we measuring angles anyway? angles are only about photon polarisation - edge case when we have the whole quantum world to explore.

sin2⁡θ/2 where θ is the angle between the two axes

is this an important fact? seems its just again, just about measuring angles which seems a weird obsession. can you talk about local realism (which is what bells is about), without even caring about angles?

 

[Nugatory]

but why are we measuring angles anyway? angles are only about photon polarisation - edge case when we have the whole quantum world to explore.

We aren’t measuring angles, we’re setting up two pieces of lab equipment in a particular way and then looking at the results each one registers when entangled particles pass through them. It just so happens the setup includes positioning them at an angle to one another.

is this an important fact?

That fact is inconsistent with any local realistic theory, so yes, it is important. Bell’s theorem is the proof that no local realistic theory can be consistent with that fact.

 

[DrChinese]

1. Polarisation is complex and weird. All other explanations require trust and understanding of polarisation, which is a huge deal.

2. So i now fully understand why it eliminates local realism. Now I want to know if the presumtions of the 3 measurement angles are correct. I have no knowledge of how polarisation 'really' works. So in my mind maybe the experimenters don't understand polarisation because 'quantum' or some conservation of momentum stuff. who knows?

3. So I was wondering if there are other experiments that have been done that don't use polarisation. After all, photons are just one type of particle and one of the many properties available to measure. So has this been done in other ways that can be explained by first principles, - without complexities and complications of polarisation, to verify this result? And if not, why not?

1. Photon polarization is pretty well understood. Malus' Law dates to circa 1807. The reason Bell tests use spin or polarization is precisely because it is easy to understand and follow.

2. The purpose of the 3 angles is to consider the criteria of realism. While you acknowledge you don't understand polarization, it wouldn't make sense to suppose scientific professionals don't.

3. And yes, it is possible to not only entangle many different types of quantum objects, it is also possible to entangle them without using polarization or spin. There are literally hundreds of permutations. Time/energy is one, but keep in mind these experiments are substantially more complex than polarization ones.

https://arxiv.org/abs/2110.06781

 

[f95toli]

Here is a very recent example of a loophole free Bell tests which doesn't use polarisation

https://www.nature.com/articles/s41586-023-05885-0