Another locally realistic violation of Bell’s inequality ?

I am thinking about the EPR experiment. I am actually thinking about the experiment as proposed by E P and R, not the experiment as performed. There are four basic but very weird points to remember in order to understand the proposed experiment. One is that electrons spin around sort of like little globes but that the absolute value of the angular momentum is always hbar/2 no matter from which direction you look at them. This is not like, say, the earth which spins around the North-South axis so the angular momentum is less if you look down another axis. The second strange fact is that you can’t measure the angular momentum of one single electron around two different axis (one version of the Heisenberg principal). This can be understood as measuring around one axis changes the spin around another axis. This makes sense in terms of comprehensible things like macroscopic magnets because the way to measure spin is with a magnet and a magnet does change spin. The third strange fact is that sometimes you know that the spin of two electrons around any axis is opposite. This is true if the two electrons are in what is called a singlet state. This means that even if you can’t know which way (clockwise or counterclockwise) each electron is spinning around both the North South axis and the East West axis you can know that the two are spinning in opposite directions around each axis. The fourth strange fact is that, according to quantum mechanics the correlation between “spin is clockwise around the North South axis” and “Spin is clockwise around the North-East South-West axis” is greater than one !!! that is the probability both are clockwise is greater than the probability that the spin around the North South axis is clockwise and the spin around the other axis is whatever and unmeasured. I won’t be able to explain this so that it makes sense. It is clearly crazy. It is also an experimental result not just a theory. I am sure I will never understand this, so I can’t explain it. Trying to grasp this fact, and it appears to be a fact (see below) is like trying to pound a square peg into a round hole.

Now the point of EPR is that Heisenberg shmeizenberg you can use the singlet state fact to test the quantum mechanical correlation greater than one by measuring the spin around N-S of one of the electrons and the Spin NE-SW of the other. They were very sure that the experimental result would disprove quantum mechanics. After some decades the experiment was finally performed (with light not electrons) and quantum mechanics was confirmed. I gave up.

Then I heard about the work of Luigi Accardi and Massimo Regoli. They have an argument that you can reconcile the experimental result with a locally realistic theory (one that makes sense as correlations are less than or equal to one) if the singlet state is a statement about measuring spin around one magic axis (NS say). The quantum craziness comes from treating electron 2 is counterclockwise around NS as equivalent to electron 1 is clockwise around NS AND electron 2 is counterclockwise around NE-SW as equivalent to electron 1 is clockwise around NE-SW. What if the singlet state had to do only with the N-S axis ?

An objection is that the singlet state fact has been tested for many directions and always works.

I have a slightly modified version of the Accardi Regoli story (which is probably in one of their working papers which I haven’t read). Here the experiment is we have electrons that were in the signlet state flying out of a source each one through an electromagnet which can be oriented NS or NE-SW. If both electromagnets are oriented the same way, the spins are opposite. If the experimenter moves the electromagnets so they are not oriented the same way, the electrons see this and don’t act like singlet state electrons at all anymore. This means that the EPR experiment result is not equivalent to a correlation greater than one.

OK so the little electrons are spying on the experimenter. There are two things. Which way does he point the electromagnets and are both turned on (measuring) or not. If they are oriented on the same axis then the measurement of electrons going through magnet 1 does not depend on whether magnet two is turned on and the measurement of electrons going through magnet 2 is always opposite. If they are oriented in different directions, then the measurement of electrons going through magnet 1 depends on whether magnet two is turned on. This is an effect of an event which took place a long time ago (by flying electron terms) so there is nothing impossible about it.