Bell's Theorem: The Quantum Venn Diagram Paradox

A bell inequality is a feature of quantum systems by which they break our understanding of classical probability. A good reference is here [1]. The basic idea is to imagine a Venn diagram where the sum of the parts adds up to more than 100%. Bell inequalities are nifty because they heavily imply that our classical notions of “local realism” must be incomplete. Namely, that either quantum objects experience instantaneous action-at-a-distance (locality), or they do not have actualized measurement values when they aren’t being actively measured (realism). This paper is showing a way to produce a visual image of a bell inequality and explores ways that these inequalities can be used for other visual techniques. [1] [this video]

Interestingly the page for polarization of light has a very significant mistake in it. Since the demo allows the use of more than two polarizing filters, what is missing is the quantum effect that occurs when you have 3. When the outer two are the same polarization, and the middle one is opposing, the light will show through at approximately 50% even though it seems to be "stopped" at the second lens. It's not the same as the double-slit example, but is related to it. Either way, this site is really good. Unfortunately the first thing I tried to replicate didn't work because they haven't taken quantum effects into account. Here is a video about the effect with 3 polarized lenses - it sounds crazy enough I want to add a bit of proof to avoid downvotes: [this video] And here is Action Labs demonstrating something related, where light seemingly shines through a solid ball for a slightly different, but not unrelated reason: [link]

There are reliable ways to create superposition particles: when you measure in one direction, the other direction is a superposition ( [link] ). I have no idea how to create entangled superposition particles: maybe read [link] . You can tell the particles are in a superposition because they behave differently than those in a static state: - Double-split experiment: [link] - only particles in a superposition create interference patterns - Bell's paradox: [link] , [link] - entangled particles in a superposition can be measured to make predictions with more confidence than if they were simply static particles with different states I guess a good search term would be "Polarized light and quantum mechanics" because IMO polarized light is a good example which you can even simulate yourself if you have a polarizing filter ( [this video] , [link] , [link] )

What you are describing is a "hidden variable" theory. They are disproved by the experiments of the Bell's inequality. It's more weird, much more weird. Let's continue with your experiment about the pair of red or green socks. If you and your friend measure if they are red-or-green, both will get the same results. This can be explained with a classical theory. Nobody disagree with that. The weird part is that you can measure if they are 50%red and 50%green! Can I call it yellow? This makes no sense with classical socks and colors, but it makes sense for quantum particles and other properties. But there are two ways to combine 50%red and 50%green, the technical notation is (R+G)/sqrt(2) and (R-G)/sqrt(2), one with a plus and one with a minus. Can I call them good-yellow and bad-yellow? Or you prefer yellow and blue? In one of the experiments, red means vertical and green horizontal, so one of the combinations is a 45° diagonal like this / and the other is a 45° diagonal like this \. You don't need fancy equipment to measure the combinations, it's just a polarizer rotated 45°. Can I call them yellow and backyelow? I prefer good-yellow and bad-yellow because it's more clear that something weird is happening. If you measure red-or-green and your friends measures good-yellow-or-bad-yellow, then the results will not be correlated. If you got "red", your friend has a 50% probability of getting good-yellow and a 50% probability of getting bad-yellow. There is nothing to explain here.

The concern that the article presents - that the middle filter influences the light and thus allows it to pass through the third filter - is actually addressed in popular quantum mechanics explanations that use the 3 filter experiment. They say that if we use two entangled photons and let them fly far apart, then pass one of them through two filters, and the second photon through the middle filter, the first photon will be affected - it will get a chance to pass though the pair of filters. That they say is "spooky action at distance" - the second photon will influence behaviour of the first photon at the remote site of the experiment and the "influence" is faster then the speed of light. Example here by MinutePhysics and 3Blue1Brown: [this video] Explanation about entanglement starts at around 8:50. But even with that addressed, to me personally this video is not satisfying. If the spooky action at distance can be observed so trivially - choosing a filter at one site site affects what happens at the remote site - we don't need a mathematical inequality (the Bell's inequality), it's already so obviously spooky. There are also serious problems with clarity of their explanation, as I commented in [this video] and [this video] I am not sure the real Bell experiments are really done using 3 polarizing filters and will the effect really be observed in experiment with two remote sites. My conclusion, it's problematic to rely on "pupular science" explanations, even by good channels like MinutePhysi

Yeah it is a common misconception. There is also a minutephysics video on it ( [this video] ) that portrays the effect of polarising filters in a misleading/wrong way, leading to further confusion. Polarisation is used in many books and courses as a familiar classical system, which we then use to springboard into Stern-Gerlach, which actually is an inherently quantum effect. Polarisation already appears when writing down the full solution to the classical EM wave equation. On the other hand, the similar effect seen in the Stern-Gerlach experiment with the angular momentum measurements is not: the non-commutivity of the angular momentum operator for different measurement axes is a purely quantum phenomenon.