Simulation of CHSH inequality experiment in Excel

[lostinmygarden]

You don't need any code to see how far off your concept is. And the usage of the CHSH just covers up the issues by making the problems unnecessarily complicated. Some of your key hypotheses are:

i) That there is a predetermined polarization for entangled photons when they are created. (Of course, simply following the Bell argument should be enough to convince you this cannot be correct - that specific scenario is discussed.)
ii) That if a polarizer is set within 45 degrees of that value, the photon will pass through it 100% of the time (you do that to get the perfect correlations, see for example Nugatory's post #14 and your response in #15).

But hey, let's analyze this as it pertains to your specific approach.

a) Your entangled pairs produce 100% correlation at any identical angle. You satisfy this experimental requirement.
b) Photons produced by PDC pass through a polarizer if they within 45 degrees of the orientation value at creation. Oops! That is known to be false!

A single Type I PDC crystal produces pairs of entangled photons at KNOWN angles. And those photons do NOT all go through a polarizer set at any different angle, regardless of whether it is within 45 degrees or not. Instead, they pass through at the usual cos^2(theta) formula. That is completely in opposition to your b).

Note that these photons are entangled, but they are NOT polarization entangled. To get polarization entanglement, you need TWO such crystals oriented 90 degrees apart and placed very close together. By your logic, the output photons must come from one or the other of the two crystals. Either one individually ONLY produces pairs that fail your test. Keep in mind that these photons (from either crystal alone) are entangled, just not polarization entangled. So why would you need two crystals to cause them to become polarization entangled when they were already entangled on all other bases?

The answer is strictly quantum: The polarization entanglement comes from them being indistinguishable as to which of the two is the source crystal. This quantum element cannot properly be represented in any code. Your code will always produce the wrong results when you attempt to model a single Type I crystal output (making it compatible with experiment) and then attempting to model two Type I crystals as I described. Here is a link to a full description of Type I crystals (theory and experiment), which are used in about half of all entanglement experiments. (Note that Type II crystals, while seemingly avoiding this issue, actually exhibit an exactly identical problem. But explaining why is more complicated.)

Ultra-bright source of polarization-entangled photons (Kwiat et al, 1998)

If you cannot model the quantum element of indistinguishability*, which determines whether polarization entanglement occurs, your entire premise fails. Good luck modeling the real world!


*And in fact every single source of quantum entangled particles includes this critical requirement. It is actually possible to intentionally vary the amount of indistinguishability from 100% down to 0%, and the resulting spin/polarization entanglement varies precisely along with it. If your concept were correct, once the photon pair is created (from the mother photon), it already has a specific angle for each of the daughter photons.

Hi. It is important to note, I am suggesting something different to what you understand to be correct. This is the point of the simulation. What if......?

Aren't photons, that are created with entangled polarizations, correlated? So they either have the same or opposite polarization? My simulation is for same polarization.

They are randomly generated photon pairs (angles) and just a copy of each other, 1 sent to each detector for measurement.

In Clauser-Horne-Shimony-Holt (chsh) experiments, isn't polarization entanglement mostly used? And it's it mostly same polarization? This is what I have read thus far and using as a basis for this. The correlation is the important part.

With regards to the version of single photon detection I mentioned, take a look here -

https://demonstrations.wolfram.com/AModelForPhotonPolarizationAndDetection/

This relates to single photon detection with +-45 degrees from a detector polarizer angle.

And so, making the assumptions I have made, for the purpose of the simulation; Why would the simulation produce similar end results as real-world tests? It wasn't necessarily aiming to do, but it has with those two assumptions made earlier.

You raised some other items which are out of scope for my post. Hope you understand.

Thanks for your comment.

 

[Nugatory]

Hi. It is important to note, I am suggesting something different to what you understand to be correct. This is the point of the simulation. What if......?

Perhaps I have misunderstood. When I read the opening post of this thread it seemed that you had a simulation that seemed to show a hidden variable model that violated the CHSH inequality and wanted feedback on it. We all agree that the simulation has to be wrong somehow (compare with someone asking for feedback on their perpetual motion machine - the question isn't whether they've invented a PMM, it's where the mistake is).

Aren't photons, that are created with entangled polarizations, correlated?

Yes, but...

So they either have the same or opposite polarization?

No. The correlation tells us that if we measure one member of the pair on a given axis we know what the result will be if and when we measure the polarization of the other member on the same axis. Bell's Theorem and the CHSH inequality show that this is not the same thing as "them having the same or opposite polarization"; that's the whole point of the observed violations of the inequalities.

They are randomly generated photon pairs (angles) and just a copy of each other, 1 sent to each detector for measurement.

The pairs in your simulation are not randomly distributed, that is obvious from inspection of the source code (both python and excel) and was pointed out in post #47. And the fact that the plus and minus counts are not roughly the same across both detectors at both angles (the sanity test suggested in post #14 that you ignored so that I had to do it for you) shows that there is something bad wrong in the internal logic of your simulation.

In Clauser-Horne-Shimony-Holt (chsh) experiments, isn't polarization entanglement mostly used? And it's it mostly same polarization? This is what I have read thus far and using as a basis for this. The correlation is the important part.

Yes, these experiments are all based on polarization entanglement. The problem is that your simulation does not accurately model the observed behavior.
I have an old CHSH simulation somewhere back in my cyber boneyard and I'll post the code for you in a while if I can find it.

There are several reliable sources that you might want to look into. You're arguing with @DrChinese so you will want to check out his website on Bell's Theorem - read and understand(!) the linked papers. Read this Scientific American article. Try rewriting your simulation to make it accurate and see whether you can find any way of tweaking the state assignments so that the inequality is violated. Until you have done this, the thread is closed.