4 ms·

To clarify, have you actually seen any of these errors in the papers, or are you just hoping/believing/assuming they are there?

GistNoesis 5y ago
Those paper don't have rigorous mathematical definition of what "probability measure" they use. From a mathematician perspective, the error is "incompatible probability measure" for events, that's why probability laws don't apply. Bell's theorem is exactly a well known mathematical theorem "Boole's inequality" which basically tells you, you are doing the math wrong when defining your measure.
- eigenket 5y ago
  If by Boole's inequality you mean the thing that I know as the union bound, then it is far from obvious to me that it is exactly the same as Bell's theorem. In fact they seem to me to be completely different. Boole's inequality also does not tell you "you're doing the math wrong when defining your measure", it tells you that the probability that either A or B happens is not greater than the sum of the probability of A happening and the probability of B happening. I'm not sure what you mean in the first part of your comment, could you indicate specifically what probability measure is defined incorrectly (or not defined) in (e.g.) this paper? https://arxiv.org/abs/1508.05949 https://arxiv.org/abs/1508.05949
GistNoesis 5y ago
Replying here due to max comment depth tree, to explain in more detail. About the link between boole's and bell's inequalities : There are tons of paper : A quick search for example https://arxiv.org/pdf/quant-ph/0406004.pdf https://arxiv.org/pdf/quant-ph/0406004.pdf (I just skimmed it for a few seconds but it's probably talking about the right thing) In the paper you suggest https://arxiv.org/abs/1508.05949 https://arxiv.org/abs/1508.05949, there is nothing which looks like a probability definition. Assuming the world is using continuous fields, defining the probability for what register as a discrete event like a "blip" must be done carefully, it's not a trivial thing. Otherwise when you are taking joint probabilities and condition probability, it just tells you that those are questions you can't ask.
- eigenket 5y ago
  Ah yeah, I went to skim the Pitowsky reference. I forgot that people call (what I was taught as) Bonferroni inequalities Boole's inequalities. 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.
GistNoesis 5y ago
>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

Those paper don't have rigorous mathematical definition of what "probability measure" they use. From a mathematician perspective, the error is "incompatible probability measure" for events, that's why probability laws don't apply. Bell's theorem is exactly a well known mathematical theorem "Boole's inequality" which basically tells you, you are doing the math wrong when defining your measure.

eigenket 5y ago
If by Boole's inequality you mean the thing that I know as the union bound, then it is far from obvious to me that it is exactly the same as Bell's theorem. In fact they seem to me to be completely different. Boole's inequality also does not tell you "you're doing the math wrong when defining your measure", it tells you that the probability that either A or B happens is not greater than the sum of the probability of A happening and the probability of B happening. I'm not sure what you mean in the first part of your comment, could you indicate specifically what probability measure is defined incorrectly (or not defined) in (e.g.) this paper? https://arxiv.org/abs/1508.05949 https://arxiv.org/abs/1508.05949

GistNoesis 5y ago

Replying here due to max comment depth tree, to explain in more detail. About the link between boole's and bell's inequalities : There are tons of paper : A quick search for example https://arxiv.org/pdf/quant-ph/0406004.pdf https://arxiv.org/pdf/quant-ph/0406004.pdf (I just skimmed it for a few seconds but it's probably talking about the right thing) In the paper you suggest https://arxiv.org/abs/1508.05949 https://arxiv.org/abs/1508.05949, there is nothing which looks like a probability definition. Assuming the world is using continuous fields, defining the probability for what register as a discrete event like a "blip" must be done carefully, it's not a trivial thing. Otherwise when you are taking joint probabilities and condition probability, it just tells you that those are questions you can't ask.

eigenket 5y ago
Ah yeah, I went to skim the Pitowsky reference. I forgot that people call (what I was taught as) Bonferroni inequalities Boole's inequalities. 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.

GistNoesis 5y ago

>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?