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I try to understand quantum entanglement and especially what it’s called « Action at a distance »

from my understanding, if you have a pair of entangled photon, after measuring the polarization of one photon you will find a correlation between his polarisation and the polarisation of the other photon even if they are very far away from each other.

From there i fail to see the difference between an entangled pair of photon and two magnets in a box (if there are any) , let me explain. What if, we use round magnets in a non-transparent box instead of photons... and use magnetic polarity instead of photon polarization and then perform that experiment :

we place a magnet in two boxes and shake them in a way that there polarity is random an unknown. Then we make a pair of « entangled » magnet by  approaching the boxes sufficiently. after “measuring” the polarity (just opening the box and see in which side the magnet is) of one box you will find a correlation between his polarity and the polarity of the magnet in the other box even if they are very far away from each other. (because the two magnets moved in their boxes thanks to the magnetic force when there were close at the ‘entanglement’ step)

The real question is: So is there any difference between my two ‘entangled’ magnet box, and two entangled photons?

As a second question : I suppose, like my magnet box example, that the polarisation (or any quantum property)of two entangled photons is fixed at the entanglement state (still in a random position but correlated), and no real superposition or any 'action at a distance' occurs. Can this statement be false ? Is there any proof or experiment that invalidate this?

Ps : I’ve very limited physic and quantum physic knowledge, and English is not my native language, so some paper may be hard to understand and i apologize for my bad English..

Qmechanic
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E.Brandonn
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    Possible duplicate of Why is quantum entanglement considered to be an active link between particles? – Norbert Schuch May 19 '19 at 19:53
  • "So is there any difference between my two ‘entangled’ magnet box, and two entangled photons?" 1. One is magnets; the other is photons. 2. The photons are entangled; the magnets aren't. This means, in particular, that the outcomes of various measurements you could make on the photons have no joint probability distribution, whereas the outcomes of any measurements you could make on the magnets do have a joint probability distribution. – WillO May 19 '19 at 19:57
  • @E.Brandonn in your fourth paragraph you describe shaking two magnets to create random polarities but creating two photons with correlated polarities takes great care. It is not an easy process and is far from random shaking. Now if you placed two magnet in separate boxes with their pole vertically alligned they would be correlated or so called entangled and you would always know what the other one was. – Bill Alsept May 19 '19 at 22:44
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    If you want to have any hope of understanding this material, please do not read the postings of Bill Alsept. When you place magnets in separate boxes and then measure their alignments, there is a perfectly good probability distribution that describes the joint outcomes of the various measurements you could make. That is the very definition of being unentangled. – WillO May 19 '19 at 23:23
  • @WillO That is also the very definition of being correlated. I am only trying to make the point that sometime entanglement is mistakenly taken as some kind of connection between the two. – Bill Alsept May 19 '19 at 23:34
  • @WillO also I forgot to say, if you place two magnets in separate boxes without correlating their polarizations then what’s the point of measuring anything? Correlation is what you’re trying to achieve. – Bill Alsept May 19 '19 at 23:48
  • @WillO correlation can easily be explained. Can you explain entanglement? – Bill Alsept May 19 '19 at 23:50
  • @BillAlsept: There are a million places to read about entanglement. This is not the place for me to compose a textbook chapter for you. But in brief: It's an easy exercise in algebra to see that if $V$ and $W$ are vector spaces of dimension at least 2, then $V\otimes 1$ and $1\otimes W$ do not span $V\otimes W$. That forces most (pure) states to be entangled. – WillO May 20 '19 at 00:32
  • @WillO I don’t expect a text book answer but could you explain that a little clearer? For me and the OP. Specifically what entanglement is IF NOT correlated polarizations. – Bill Alsept May 20 '19 at 01:17
  • @billalsept: an entangled state is one that is not of the form $u\otimes v$. The existence of such states, and the implications for the outcomes of measurements, all follow from simple algebra. You'll learn more if you work this all out yourself, but if you prefer to be lazy, you can read a book! In view of the admonition to avoid extended chats, this will be my last comment here. – WillO May 20 '19 at 01:31
  • Good thoughts. Perhaps an answer https://physics.stackexchange.com/a/469654/46708 – HolgerFiedler May 20 '19 at 19:34
  • @HolgerFiedler My point is that particles are correlated and do not form some spooky connection called entanglement. There is still a physical explanation that describes the correlated pairs. Is Bell’s so called inequality the only reason causality/realism was thrown out the window? I can physically correlate pairs so that when tested later at random angles The measurements will match cos2theta and all QM predictions. – Bill Alsept Jun 02 '19 at 17:20
  • @BillAlsept I’m with you about the correlation, https://physics.stackexchange.com/questions/469143/sending-information-with-entangled-particles/469654#469654 – HolgerFiedler Jun 02 '19 at 17:50
  • @HolgerFiedler I thought you agreed. Bell said No physical theory can ever reproduce all the predictions of quantum mechanics. So what does it mean if two objects can be set up to give the results of cos2theta? – Bill Alsept Jun 02 '19 at 18:28

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One can have an even simpler classical entanglement conceptual set up. Bob and Bill are twins working for the same company , one in London the other in Paris. If you see Bob in London you immediately know that Bill is in Paris.

The only difference with the classical entanglement examples lies in quantum mechanics, which is a probabilistic theory.

Take the decay of the $π^0 \rightarrow γ γ$ where $γ$ is a photon. Because the $π^0$ has spin zero, the two photons must come out with their spin opposite to each other. Because of the probabilistic nature of quantum mechanics the spin is unknown until measurement, but due to conservation of angular momentum if you measure the spin of one photon, the spin of the other is immediately known.

It is the probabilities that make the difference. In the case of Bob and Bill they are in classical reality, it is the knowledge that is probed. In the case of the $π^0$ there is no absolute knowledge, just a probability for the state of spin of each photon.

With your magnet example you imitate the probability distribution of quantum mechanics so it is an equivalent entanglement, except that in principle, because one is dealing with macroscopic classical mechanics the "shakes" and their effect could in principle be determined, whereas in quantum mechanics there is no determinism underneath.

As the $π^0$ example shows there is not action at a distance.

anna v
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  • Good answer and partly the point I was trying to make. That correlation is different from what is sometimes meant by entanglement. As for probabilities, I believe two particles can be correlated to produce the predictions of quantum mechanics. In every experiment I’ve studied only one variable is ever considered (usually polarization). With two variables pairs of particles or any objects can be correlated to produce all the probabilities of quantum mechanics. – Bill Alsept May 20 '19 at 06:43
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    This makes it sound like the measurement outcomes are fixed probabilistically prior to measurement. – Norbert Schuch May 20 '19 at 08:44
  • @NorbertSchuch ??? Probability by definition means nothing is fixed within the phase space where it applies. In the case of photon spins there are only two states to the phase space. – anna v May 20 '19 at 09:19
  • Photons can not be described by probability distributions over a classical "phase space" with only two states. For instance, how would you describe photons with different polarizations (horizontal, vertical, circular, diagonal, ...)? And this gets even worse once you consider entangled states. – Norbert Schuch May 20 '19 at 13:58
  • @NorbertSchuch it is not a classical phase space, photons are quantum mechanical entities. For the specific example of the pi0 there is a restricted phase space. It is an example of simple entanglement induced by angular momentum conservation, not a treatise on the photon. – anna v May 20 '19 at 14:02
  • Yet, quantum mechanics cannot be explained by probability distributions over any kind of (reasonable) phase space - that's exactly the point of Bell inequalities. – Norbert Schuch May 21 '19 at 09:51
  • E.Brandonn Isn’t this the more intuitive answer? – HolgerFiedler May 25 '19 at 03:43
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Brandonn, welcome to SE! Here is an attempt at a not-too-technical answer:

One simple way to see the difference is that, although the magnets' orientations may indeed be aligned (or antialigned) after some interaction between them, this correlation is specific to a particular axis of measurement, namely, the shared direction along which they are both aligned. So if you check the directions of the magnets along this axis, you will indeed find that they are correlated. But their alignments along any other axis are not well-defined.

However, in the case of the photons, if their states are entangled, then you will find that the measurement results you obtain will be correlated no matter what axis you measure along. This is possible first of all because for either photon individually, you can measure the polarization along any axis (perpendicular to the trajectory) and obtain a single, well-defined result that is parallel to the measurement axis. Given that this is true, the fact that when you measure both photons along any axis (the same for both photons) you will obtain correlated results is a qualitative difference from the case of the magnets.

As pointed out in the comments on this answer, the description I have given is not a complete picture of the non-classical properties of an entangled system. There is more to the story, but in my opinion the details go beyond the scope of the question.

Will
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    That's not the point of entanglement; this can also be captured by a local hidden variable model. – Norbert Schuch May 20 '19 at 08:43
  • I'm aware -- but I wasn't trying to describe Bell inequalities or contextuality. The OP asked if there is any difference between his magnets and a pair of entangled photons, so I described in as qualitative terms as I could the simplest difference (in my opinion). You are correct that I have not fully described the non-classical properties of entanglement, I just didn't think the question justified a full-blown description, especially since as you had already pointed out in the comments, such already exists elsewhere. – Will May 20 '19 at 12:27
  • @NorbertSchuch I think you are right, though, that I should have noted that there is more to the story, so I'll update my answer. Thanks for the feedback! – Will May 20 '19 at 12:28