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>Ah yeah, I went to skim the Pitowsky reference. I forgot that people call (what I was taught as) Bonferroni inequalities Boole's inequalities. Bonferroni ineq

>Ah yeah, I went to skim the Pitowsky reference. I forgot that people call (what I was taught as) Bonferroni inequalities Boole's inequalities. Bonferroni inequalities are also on the wikipedia page of the Boole's inequality https://en.wikipedia.org/wiki/Boole%27s_inequality https://en.wikipedia.org/wiki/Boole%27s_inequality >I'm still not sure what probability distribution (or measure) you want to be defined in that paper. Experimentalists generally don't assume any probability distribution in advance, I am not sure why they would need to in this case. That's the thing, if you try to model it correctly you realize that what you were doing was not the thing to do, and that there is just nothing to see here, apart from yourself asking the wrong question. Take a zone of space (the detector volume), and define the discrete event "blip" as 1 if somewhere inside the detector volume at instant t0 the field value is greater than 1, or zero elsewhere. That's all you need : this mean you just expressed an event as a conditional probability. Therefore when you have multiple such events, you are expected to encounter some Boole's/Bell type inegalities (provided that there is information conservation in your model). Experimentalists are doing circular reasoning. By not assuming an underlying model, they don't realize that the answer they get is due to implicitly defining events as conditional probabilities which don't span a consistent Filtration_(probability_theory), then they try to ask the wrong question, getting an answer which confirm their biases. QM is a not a model of the world, but a model of what we can observe from the world based on what we observe from the world. Bell's inequalities tell nothing about how the world works but only tell you that your way of observing the world is wrong.

eigenket 5y ago
You're missing something I think (or we're talking past each other) because I can write down probability distributions which explicitly break Bell's inequalities, whereas I can't write down probability distributions which break Boole's inequalities. This is because Boole-type inequalities are derived just by assuming the basic rules of probability distributions, while Bell-type inequalities are derived by assuming some local hidden variable model (or similar locality assumption). Consider the Popescu-Rorhlich (PR) box probability distribution where P(a,b | x,y) equals 1/2 if x*y = a xor b and zero otherwise. This probability distribution explicitly breaks Bell's inequality, but it does not break any of the Bonferroni / Boole inequalities. This is precisely because although it obeys all of the axioms of probability distributions (which are the assumptions required for Bonferroni / Boole) it does not obey the extra axioms of locality that Bell's inequality requires. I'm still not sure what your issue is with the experimental papers. You acknowledge I think that the real detectors they have in the lab actually do "blip", right? And you can take these observed "blips" and use them to compute a CHSH value?
- GistNoesis 5y ago
  Violations of Boole's inequalities only happen when you do something bad with probabilities, you just need to be a little creative. Experimenters observe CHSH > 2 because they are likely doing something bad with probabilities : the same bad things with probabilities you need to do to violate Boole's inequalities. The measurement process of the pairs by the detectors implicitly do some additional filtering on the hidden_state. Typically when you define what your detection threshold for registering a blip is, or what you consider is a coincident pair by filtering based upon the time of measurement. When you try to apply Boole's inequality to something like P( anything | measurement1, measurement2, 0< hidden_state < 1), P( anything | measurement1, 0< hidden_state < 1), P( anything | measurement2, 0< hidden_state < 1) The chain rule doesn't apply the same way. Because hidden_state is not a specific value but a range of values : The joint probability is not factoring as a product of conditionals anymore. You have some incompatible sets of events and you can observe CHSH type violation for your Boole's inequalities.
  - eigenket 5y ago
    > Violations of Boole's inequalities only happen when you do something bad with probabilities. I sort of agree with this, if by "something bad" you mean not obeying the axioms of probabilities. > Experimenters observe CHSH > 2 because they are likely doing something bad with probabilities. I disagree with this completely. Note that the probability distribution I gave just now (which is an honest probability distribution) violates CHSH. It obtains a CHSH score of 4, indeed. I am not doing anything "bad" with my probabilities to obtain this score, I'm just providing a probability distribution that does not obey Bell's additional locality assumption. I ask you specifically, what is "bad" about the distribution P(a,b| x,y) = 1/2 if ab = x xor y and zero otherwise which makes it obtain a CHSH score of 4?
    - GistNoesis 5y ago
      I think you are missing the point I'm trying to make. You can violate CHSH by giving a non-local distribution (That's what happening with the distribution you provide). But there is more than one way to skin a cat. You can also violate them using the mathematical trick as I suggested above. This trick to replicate the result seems a lot more plausible than non-locality. > not obeying the axioms of probabilities. That's exactly what I blame the experimenters for. By ignoring that they are conditioning on the hidden variable, they are treating what is a "conditional probability" exactly the same way as it if was a "standard probability". Which is a big no-no from the math standpoint.

eigenket 5y ago

You're missing something I think (or we're talking past each other) because I can write down probability distributions which explicitly break Bell's inequalities, whereas I can't write down probability distributions which break Boole's inequalities. This is because Boole-type inequalities are derived just by assuming the basic rules of probability distributions, while Bell-type inequalities are derived by assuming some local hidden variable model (or similar locality assumption). Consider the Popescu-Rorhlich (PR) box probability distribution where P(a,b | x,y) equals 1/2 if x*y = a xor b and zero otherwise. This probability distribution explicitly breaks Bell's inequality, but it does not break any of the Bonferroni / Boole inequalities. This is precisely because although it obeys all of the axioms of probability distributions (which are the assumptions required for Bonferroni / Boole) it does not obey the extra axioms of locality that Bell's inequality requires. I'm still not sure what your issue is with the experimental papers. You acknowledge I think that the real detectors they have in the lab actually do "blip", right? And you can take these observed "blips" and use them to compute a CHSH value?

GistNoesis 5y ago
Violations of Boole's inequalities only happen when you do something bad with probabilities, you just need to be a little creative. Experimenters observe CHSH > 2 because they are likely doing something bad with probabilities : the same bad things with probabilities you need to do to violate Boole's inequalities. The measurement process of the pairs by the detectors implicitly do some additional filtering on the hidden_state. Typically when you define what your detection threshold for registering a blip is, or what you consider is a coincident pair by filtering based upon the time of measurement. When you try to apply Boole's inequality to something like P( anything | measurement1, measurement2, 0< hidden_state < 1), P( anything | measurement1, 0< hidden_state < 1), P( anything | measurement2, 0< hidden_state < 1) The chain rule doesn't apply the same way. Because hidden_state is not a specific value but a range of values : The joint probability is not factoring as a product of conditionals anymore. You have some incompatible sets of events and you can observe CHSH type violation for your Boole's inequalities.
- eigenket 5y ago
  > Violations of Boole's inequalities only happen when you do something bad with probabilities. I sort of agree with this, if by "something bad" you mean not obeying the axioms of probabilities. > Experimenters observe CHSH > 2 because they are likely doing something bad with probabilities. I disagree with this completely. Note that the probability distribution I gave just now (which is an honest probability distribution) violates CHSH. It obtains a CHSH score of 4, indeed. I am not doing anything "bad" with my probabilities to obtain this score, I'm just providing a probability distribution that does not obey Bell's additional locality assumption. I ask you specifically, what is "bad" about the distribution P(a,b| x,y) = 1/2 if ab = x xor y and zero otherwise which makes it obtain a CHSH score of 4?
  - GistNoesis 5y ago
    I think you are missing the point I'm trying to make. You can violate CHSH by giving a non-local distribution (That's what happening with the distribution you provide). But there is more than one way to skin a cat. You can also violate them using the mathematical trick as I suggested above. This trick to replicate the result seems a lot more plausible than non-locality. > not obeying the axioms of probabilities. That's exactly what I blame the experimenters for. By ignoring that they are conditioning on the hidden variable, they are treating what is a "conditional probability" exactly the same way as it if was a "standard probability". Which is a big no-no from the math standpoint.