Difference between an entangled pair of photon and two magnets in a box?

Question

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..

Answer 1

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.

Answer 2

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.