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> You've got to reframe the problem so that Bell's theorem doesn't apply. When you build your theory, if you manage to define what a measurement is, so that you

> You've got to reframe the problem so that Bell's theorem doesn't apply. When you build your theory, if you manage to define what a measurement is, so that you don't satisfy the hypothesis of the Bell's theorem, you get to avoid having to have its conclusions. This (in my opinion) a bad way of explaining how the standard reasoning goes. We start with a list of assumptions, we prove this inequality which it turns out is not satisfied, we reject (at least) one of our assumptions. These is no crackpottery here, this is the norm. > by defining measurement instead as a conditional probability This sounds like it probably doesn't get you anywhere, but I'll bite - what are we conditioning on? In the standard formulation of Bell's theorem they are conditional on the "hidden variable" we are assuming exists, as well as any relevant measurement settings but it sounds like you're imagining something wilder than that.

GistNoesis 2y ago
>what are we conditioning on? The local hidden state, but you don't get to set it from inside the universe when you do an experiment (this local hidden state is unobservable). From inside the universe based on this hidden state, everything behave classically, pseudo-randomly based on the local hidden state. But because you don't get to set the local hidden state during your experiment if you want to calculate the probabilities, you have to integrate over the possible values of the unknown hidden state, and this allows you to recover the strange looking quantum correlations. Doing repeated experiment inside a universe mean picking a different initial local hidden state (because it's unobservable). [Spoiler ahead] The original idea is not from me, if you want the nitty gritty details, look at the work of Marian Kupczynski (Closing the Door on Quantum Nonlocality https://philarchive.org/archive/KUPCTDv1 https://philarchive.org/archive/KUPCTDv1 ). Or his more recent works. I have made a straight forward implementation (3 years ago) of it to convince myself with a Monte Carlo simulation : https://gist.github.com/unrealwill/2a48ea0926deac4011d26842627b69c9 https://gist.github.com/unrealwill/2a48ea0926deac4011d268426... [End Spoiler]
- eigenket 2y ago
  Everything up to the [spoiler ahead] in this comment is (as far as I can tell) exactly how things work in standard formulations of Bell's inequality. There's nothing weird or crackpot there. Your numerical code is impossible for me to read without some basic idea of what you're trying to show, but I'd like to point out that numpy has functions like np.radians, and np.deg2rad to convert from degrees to radians, you don't have to make your own.
- DebtDeflation 2y ago
  I commented awhile back on another thread that: I think, ultimately, there are only 3 possible explanations for the paradoxes of the quantum world. 1) superdeterminism (everything including our choices in quantum experiments today were fully determined at the instant of the Big Bang), 2) something "outside" our observable reality acting as a global hidden variable (whether something like the bulk in brane cosmology or whatever is running the simulation in simulation theory) or 3) emergent spacetime (if space and time are emergent phenomena then locality and causation are not fundamental). You seem to be suggesting something similar to option 2. Or am I misunderstanding?
  - GistNoesis 2y ago
    The solution I'm suggesting is that nature does it in the really boring way : classically. It's almost like option 2, but the state is local. This state is local and "inside" our universe, but we can't observe it. (A good analog for thing that are unobservable from inside the universe are seed of a pseudo-random generator). The beauty of it, is just realising that Nature's simulator can be purely local and yet not be subjected to Bell Inequalities, but still reproduce the spurious quantum correlations, if you calculate the probabilities. Violating Bell Inequalities is totally normal when you construct your theory such that Bell Inequalities don't apply.
    - eigenket 2y ago
      I guarantee you can't break (for example) the CHSH inequality [1] with such a set-up (assuming I've understood your description of what you're proposing), and encourage you to try (with similar python script). An easy formulation of the inequality is in the CHSH game section of the same article [2]. [1] https://en.wikipedia.org/wiki/CHSH_inequality https://en.wikipedia.org/wiki/CHSH_inequality [2] https://en.wikipedia.org/wiki/CHSH_inequality#CHSH_game https://en.wikipedia.org/wiki/CHSH_inequality#CHSH_game
      - GistNoesis 2y ago
        In the script I already gave you it shows an even stronger argument than CHSH inequality : Convergence (in law) towards the QM probas : It can replicate all the proba given by QM for any alpha,beta polarizer settings, up to epsilon, with epsilon that can be made vanishingly small. QM breaks CHSH inequality, this replicates the proba of QM therefore it also breaks CHSH. Of course I'm not banging against a math theorem wall, I just made some leeway to go around, based on the fact that conditional probabilities are not probabilities. Setting the problem such that measurements/observation are defined as a conditional probability (against an unobservable variable) suffice for making Bell theorem not applicable. It offers a whole class of solution to the seemingly paradoxical Bell Inequalities.
- gus_massa 2y ago
  I agree with the sibling comment by eigenket: > Everything up to the [spoiler ahead] in this comment is (as far as I can tell) exactly how things work in standard formulations of Bell's inequality. There's nothing weird or crackpot there. Moreover, to clarify, it's not necessary that the hidden variables can be measurable or that you can set them. So if a system like the one you described must follow the Bell's Inequality if all the other hypothesis are true. I read the code and it looks like an accurate implementation of the model proposed in the paper. From the paper you liked: > However, the expectation values E(X1X2), displayed in (13) contain a factor 1/2, meaning that they do not violate CHSH inequality. I agree with that part. The model should not violate the Bell's inequality or the equivalent version. > The agreement with quantum predictions is obtained only after the “photon identification procedure”, which selects, from the raw data, final data samples. The selection rule is the weird part. It's described in equations 7 and 8. x := sign(1 + cos[2(a − φ)] − 2 · r1) where r1 is a uniform random value between 0 and 1. a is the angle of the polarizer φ is the secret variable that is the angle of the photon. (QM says that this type of entangled photons have no a secret angle, this model assumes that each photon has a hidden variable that is the secret value φ.) So far so good, this calculation gives the expected result if you assume that φ is chosen from a uniform distribution between 0° and 360°. v := r2 |sin[2(a − φ)]|^d (Vmax − Vmin) − Vmax selected := (v ≤ V) where r2 is a uniform random value between 0 and 1. With the numbers in your program v := r2 |sin[2(a − φ)]|^2 (10 − 0) − 10 selected := (v ≤ -9.99) that is equivalent to selected := r2 |sin[2(a − φ)]|^2 ≤ -0.001 I've don't remember anything similar, and I can't imagine what it means experimentally. Most of the times r2 is not tiny, so most of the times this means that the sine is tiny that means that the secret angle of the photon is almost aligned or almost orthogonal to the polarizer. So this is a device that can measure the secret angle of the photon. This is not a real device, so it can't be proposed as an alternative explanation of the violation of the Bell's inequality. You may be wondering why I claim it's not a real device. If you have a detector of polarization, once you fix the angle 'a', you can't distinguish: 1) Unpolarized light, that is in particular the type of light used in a Bell's inequality test where the state is (|00> + |11>)/sqrt(2) or in other versions (|01> + |10>)/sqrt(2), where 0 is horizontal and v is vertical, or a uniform random values of φ in the model of the paper 2) Light polarized in 45° to the detector's angle, that is like a constant φ in both models. In both cases, you detect 50% of the photons. If you use the selection device of this paper, 1) with unpolarized light you will get selections when r2 is very small or when φ is almost paraller or orthogonal to the angle a. 2) with polarized light at 45° you will get selections when r2 is very small So with polarized light at 45° the number of events will be much smaller than with not polarized light. In particular if you have the source of not polarized light and the detector, adding a polarizer at 45° in the middle will reduce the number of events in the firs case to 1/4 and in the other to almost 0.

GistNoesis 2y ago

>what are we conditioning on? The local hidden state, but you don't get to set it from inside the universe when you do an experiment (this local hidden state is unobservable). From inside the universe based on this hidden state, everything behave classically, pseudo-randomly based on the local hidden state. But because you don't get to set the local hidden state during your experiment if you want to calculate the probabilities, you have to integrate over the possible values of the unknown hidden state, and this allows you to recover the strange looking quantum correlations. Doing repeated experiment inside a universe mean picking a different initial local hidden state (because it's unobservable). [Spoiler ahead] The original idea is not from me, if you want the nitty gritty details, look at the work of Marian Kupczynski (Closing the Door on Quantum Nonlocality https://philarchive.org/archive/KUPCTDv1 https://philarchive.org/archive/KUPCTDv1 ). Or his more recent works. I have made a straight forward implementation (3 years ago) of it to convince myself with a Monte Carlo simulation : https://gist.github.com/unrealwill/2a48ea0926deac4011d26842627b69c9 https://gist.github.com/unrealwill/2a48ea0926deac4011d268426... [End Spoiler]

eigenket 2y ago
Everything up to the [spoiler ahead] in this comment is (as far as I can tell) exactly how things work in standard formulations of Bell's inequality. There's nothing weird or crackpot there. Your numerical code is impossible for me to read without some basic idea of what you're trying to show, but I'd like to point out that numpy has functions like np.radians, and np.deg2rad to convert from degrees to radians, you don't have to make your own.
DebtDeflation 2y ago
I commented awhile back on another thread that: I think, ultimately, there are only 3 possible explanations for the paradoxes of the quantum world. 1) superdeterminism (everything including our choices in quantum experiments today were fully determined at the instant of the Big Bang), 2) something "outside" our observable reality acting as a global hidden variable (whether something like the bulk in brane cosmology or whatever is running the simulation in simulation theory) or 3) emergent spacetime (if space and time are emergent phenomena then locality and causation are not fundamental). You seem to be suggesting something similar to option 2. Or am I misunderstanding?
- GistNoesis 2y ago
  The solution I'm suggesting is that nature does it in the really boring way : classically. It's almost like option 2, but the state is local. This state is local and "inside" our universe, but we can't observe it. (A good analog for thing that are unobservable from inside the universe are seed of a pseudo-random generator). The beauty of it, is just realising that Nature's simulator can be purely local and yet not be subjected to Bell Inequalities, but still reproduce the spurious quantum correlations, if you calculate the probabilities. Violating Bell Inequalities is totally normal when you construct your theory such that Bell Inequalities don't apply.
  - eigenket 2y ago
    I guarantee you can't break (for example) the CHSH inequality [1] with such a set-up (assuming I've understood your description of what you're proposing), and encourage you to try (with similar python script). An easy formulation of the inequality is in the CHSH game section of the same article [2]. [1] https://en.wikipedia.org/wiki/CHSH_inequality https://en.wikipedia.org/wiki/CHSH_inequality [2] https://en.wikipedia.org/wiki/CHSH_inequality#CHSH_game https://en.wikipedia.org/wiki/CHSH_inequality#CHSH_game
    - GistNoesis 2y ago
      In the script I already gave you it shows an even stronger argument than CHSH inequality : Convergence (in law) towards the QM probas : It can replicate all the proba given by QM for any alpha,beta polarizer settings, up to epsilon, with epsilon that can be made vanishingly small. QM breaks CHSH inequality, this replicates the proba of QM therefore it also breaks CHSH. Of course I'm not banging against a math theorem wall, I just made some leeway to go around, based on the fact that conditional probabilities are not probabilities. Setting the problem such that measurements/observation are defined as a conditional probability (against an unobservable variable) suffice for making Bell theorem not applicable. It offers a whole class of solution to the seemingly paradoxical Bell Inequalities.
gus_massa 2y ago
I agree with the sibling comment by eigenket: > Everything up to the [spoiler ahead] in this comment is (as far as I can tell) exactly how things work in standard formulations of Bell's inequality. There's nothing weird or crackpot there. Moreover, to clarify, it's not necessary that the hidden variables can be measurable or that you can set them. So if a system like the one you described must follow the Bell's Inequality if all the other hypothesis are true. I read the code and it looks like an accurate implementation of the model proposed in the paper. From the paper you liked: > However, the expectation values E(X1X2), displayed in (13) contain a factor 1/2, meaning that they do not violate CHSH inequality. I agree with that part. The model should not violate the Bell's inequality or the equivalent version. > The agreement with quantum predictions is obtained only after the “photon identification procedure”, which selects, from the raw data, final data samples. The selection rule is the weird part. It's described in equations 7 and 8. x := sign(1 + cos[2(a − φ)] − 2 · r1) where r1 is a uniform random value between 0 and 1. a is the angle of the polarizer φ is the secret variable that is the angle of the photon. (QM says that this type of entangled photons have no a secret angle, this model assumes that each photon has a hidden variable that is the secret value φ.) So far so good, this calculation gives the expected result if you assume that φ is chosen from a uniform distribution between 0° and 360°. v := r2 |sin[2(a − φ)]|^d (Vmax − Vmin) − Vmax selected := (v ≤ V) where r2 is a uniform random value between 0 and 1. With the numbers in your program v := r2 |sin[2(a − φ)]|^2 (10 − 0) − 10 selected := (v ≤ -9.99) that is equivalent to selected := r2 |sin[2(a − φ)]|^2 ≤ -0.001 I've don't remember anything similar, and I can't imagine what it means experimentally. Most of the times r2 is not tiny, so most of the times this means that the sine is tiny that means that the secret angle of the photon is almost aligned or almost orthogonal to the polarizer. So this is a device that can measure the secret angle of the photon. This is not a real device, so it can't be proposed as an alternative explanation of the violation of the Bell's inequality. You may be wondering why I claim it's not a real device. If you have a detector of polarization, once you fix the angle 'a', you can't distinguish: 1) Unpolarized light, that is in particular the type of light used in a Bell's inequality test where the state is (|00> + |11>)/sqrt(2) or in other versions (|01> + |10>)/sqrt(2), where 0 is horizontal and v is vertical, or a uniform random values of φ in the model of the paper 2) Light polarized in 45° to the detector's angle, that is like a constant φ in both models. In both cases, you detect 50% of the photons. If you use the selection device of this paper, 1) with unpolarized light you will get selections when r2 is very small or when φ is almost paraller or orthogonal to the angle a. 2) with polarized light at 45° you will get selections when r2 is very small So with polarized light at 45° the number of events will be much smaller than with not polarized light. In particular if you have the source of not polarized light and the detector, adding a polarizer at 45° in the middle will reduce the number of events in the firs case to 1/4 and in the other to almost 0.