I Is the model presented in the thread consistent with QM?

[msumm21]

TL;DR Summary

Seems that a model in a recent paper is not consistent with QM, this post includes an example case and questions how it can be consistent.

I started another thread on this but it went off into other topics. Hoping to focus on the math here, specifically whether or not the model presented in here is consistent with QM.

Let's measure the polarization at the same angle $\alpha = \beta = \pi/3$ ($\varphi_1=0, \varphi_2=\pi/2$). Now $\delta_1=\pi/3,\delta_2=-\pi/6$ and hence we have $A=1$ when $\lambda <= 1/4$ and $B=-1$ when $\lambda <= 3/4$ so that the A,B measurement results matching or not is not guaranteed, but varies with $\lambda$ which is inconsistent with QM.

Even more odd, changing the measurement direction to say $\alpha=\beta=0$ changes this conclusion as if there's a preferred direction in space. Or did I miss another exception?

 

[PeterDonis]

Moderator's note: This thread is a reopen of a previous thread. Please keep discussion in this thread exclusively focused on the consistency of the referenced mathematical model with QM.

 

[Demystifier]

Then I will repeat what I already said. I think the model is in fact nonlocal, so it has a potential to be consistent with QM. This is seen in the paragraph around Eq. (9). In particular, before (9) it says that it uses
$$\delta = \alpha +\pi/2 -\beta$$
It's not clear to me how exactly did he get this formula, but this formula is nonlocal. It is nonlocal because $\alpha$ is a property of one apparatus, while $\beta$ is a property of the other apparatus. Or if the author still claims that this formula has a local origin, it would help if he could better explain how did he obtain this formula, because to me it's not clear from the paper.

 

[msumm21]

It's not clear to me how exactly did he get this formula, but this formula is nonlocal

Looks like he's considering the special case where the 2nd polarizer is set at $\alpha + \pi/2$ so that the equation gives the angle $\delta$ between $\varphi_2$ and the polarizer. I'm unconfident because this is reusing the same symbol in different ways: using $\beta$ here to be what was originally defined to be $\varphi_2$.

This may be the source of another error, because it looks like equation 9 is later used as if $\beta$ is the polarizer setting again (whereas it was really $\varphi_2$ in this equation) and then using this equation for general polarizer settings whereas the equation was made for 90deg offset polarizers.