Minkwe replied:
Malus doesn't allow measuring one electron twice, that is impossible. The difference between Malus and Bell is just a difference between selecting on the fly and selecting after the fact. In Malus, you pass a stream of particles through one station, which selects a subset and transforms them in some way. Then you pass this new set again through a second station which again selects a subset based on their current properties. You measure the intensity of particles you have at the end and it obeys a certain relationship relative to the angle between the two stations. In other words, the relationship is telling you how the end result from the second station is related to the transformation/selection that happens on the first.
For Bell, you take two correlated streams and pass one through station A, and its sister through station B. At each station, the incoming stream is selected/transformed based on the setting. Then after the fact, you use the results of the measurements at A to match/select the results at B or vice versa in order to decide which particle at A corresponded with which particle at B and vice versa. After doing this, you end up with a relationship that is based on the angle between A and B. Bell is just a clever Malus experiment with two correlated streams, and two remote stations instead of two local ones. In the local Malus experiment, the information is carried from one station to the next by the transformed/selected particles themselves during the experiment. In the remote version (Bell), the information transfer is accomplished by the matching of individual particle results after the fact. Without the matching step, there are no results. Show me a Bell experiment that did not involve matching.
That was my sloppy language. I know that you cannot measure the same electron twice and I did not mean it literally. I meant it in the sense that I still think of myself as the same person that I was when I played rugby in my youth. I cannot do that now as all the interactions I have had since my youth have changed me too much. Also, most of one's body content is replaced after seven years.
In my mind's eye, the electron and photon are described by my preon model. A left-handed electron going into an interaction has spin -0.5 and weak isospin -0.5. After the interaction that electron has gone and has been replaced by a right-handed electron with spin +0.5 and zero 'weak isospin'. So, yes, I do not really have the same electron being measured twice, and I agree with your description of Malus. I think of it in terms of polaroid sunglasses. I could do the Malus experiment with two polaroids put in front of one initial beam. The first polaroid (say Alice's sunglasses) cut the beam intensity to 50%. The second polaroid (Bob's) cuts the 50% down even further depending on the difference between the two polarising angles alpha and beta. So Malus has two successive measurements on one initial beam.
[An aside: another problem is seeing the Feynman diagram as simply a pathway for all the particles as weak isospin is not conserved in an interaction. IMO a lowest-generation higgs is involved in the interaction where an electron emits a photon. Behind the scenes, the higgs supplies or removes the weak isospin. The higgs must be there in the more complete QFT of the interaction but I have not checked.
In my preon model, a LH electron contains preon A while the RH electron contains Preon B. The photon contains B but not A. The higgs contains both A and B. So the photon cannot add or take away the Preon A in the interaction, but the higgs can. Also the generation 1 higgs is identical to the photon but with one B replaced by an A. As the lowest-generation higgs cannot decay into smaller particles it will not turn up at CERN in the sort of searches they are conducting.]
Next on to Bell. Yes, Bell is based on simultaneous measurements on two different but correlated beams. I am only interested in a 'quarter' Bell experiment where Alice has alpha = 0 deg in two dimensions and Bob has beta = 45 deg. In my quest for the theoretical minimum, I do not bother with cases where Alice makes measurements in more than one spin direction, do not bother with randomised detector settings. And do not bother with trying to prove Bell's Theorem. IMO, my 'quarter' Bell simulation can only reach a correlation of 0.707 if exact projections are used. Integer projections can never work because the very definition of cos theta requires exact projections. And I have recently realised that 0.707 is not even obtainable under QM in a generalised context. Unfortunately I cannot follow the selection principles, especially the modern once involving entangled states. So I can see that they have scope to be used (not consciously) to hide the truth. I did once convert one of De Raedt's Fortan programs into VB in the case of time window selections but it did not really help my understanding of the physics. And although I do not disagree with you on this, I am trying to get 0.707 by a fair means.
My 2D simulations always had a random or systematic full coverage of incoming particle polarisations or vectors of hidden variables. And all were measured and entered into the correlation calculations. One cannot fairly convert that situation into a correlation of 0.707. Well, I can do it using retrocausality, which I think is what is happening in reality. But other than that it cannot be done fairly.
Esail changes an expected particle polarisation before measurement by Bob from beta to alpha. This effectively enforces a Malus angle of alpha-beta on the experiment and converts a Bell into a Malus experiment. But I like this image as it is a way to think of what QM may be doing in its spooky action at a distance. Seeing this paper came at a time when I was wrestling with how QM calculated the 0.707 correlation using generalised particle incoming polarisations.
I realised next that Susskind's solution for QM was not generalised. His proof used Alice measuring along |up> while the incoming entangled singlet was |up, down> - |down, up>. Now that is blatantly a Malus experiment context. Alice measures along up and the incoming particle is a mixture of up and down! And Bob is also measuring a particle that is a mix of up and down and is measuring it at 45 degrees offset. Pure Malus.
I won't bother to write down the QM formula for the general case but Susskind does give the details necessary to write it down. Resolving that general case into 0.707 does not look possible to me. In the same way that I cannot make a simple but generalised simulation give more than 0.5 correlation (without using retrocausality). It is not possible as it is not convertible into a 'Malus' end point.
There were some discussion online in the past where actions at the detectors were seen to be semi-mystical. I have a classical model for electron and photon spins which can find S-G outcomes. Nothing mystical about it. (I am not meaning the measurement problem here, simply finding S-G outcomes using a classical model.)
No matter what I show, you will dismiss it as not being "faithful". Once you place yourself as the gatekeeper of accepted evidence, there is no point in trying to convince you out of your entrenchment.
First you said the recent experiments (NIST, Vienna) can't be faithfully simulated. Now you've amended your goalpost to "the experiment envisioned by Bell in ...". Do you see why nobody takes this seriously?