Lazarus

It is improper to use negative numbers in Bel's Inequality, no matter where you get them

The reason for ALL experiments is that Bell's Inequality is solid as a rock for non-negative numbers. The only way to violate it is to use a negative number. Since I am banned from discussing CHSH, I will leave it up to you to nane one experiment that violates Bell's Inequality using positive numbers. The negative numbers are generated in the experiments by using Correlation Coefficients rather than probabilities or counts. Probability to Correlation Coefficients is Probability times 2 minus 1.

Why does it need a citation? It's 3rd grade arithmetic.

The Bell Inequality tests are only valid for non-negative numbers, which is reasonable because counts and probabilities cannot be negative. All the experiments that depend on the violation of Bell's Inequality use a negative number in the inequality. That invalidates the experiments. Bell's Inequality can be violated by having a negative value. For example: P(a,b) -P(a,d)+P(c,b)+P(c,d) <= 2 Which can be calculated as a+b-a-d+c+b+c+d / a+b+c+d <=2 with a=1, b=2, c=3 and d= - 4 then 1+2-1-(-4)+3+2+3+(-4) / 1+2+3+(-4) <= 2 10 /2 <= 2 5 <= 2

My math professor described what he called the Wexler mail system. With frictionless holes through the earth between cities around the world, you could drop your letter in a hole and not only would it come out on the other side of the earth, the time it takes is the same for all holes.

Lazarus: The significance is that it shows that at least one of the 4 values has to be negative to violate Bell’s inequality. With probabilities and counts that cannot happen but by using Correlation Coefficients instead, negative numbers are possible since the formula to go from Probability to Correlation Coefficients is P*2 -1 which CHSH uses. That may be acceptable. On this forum I am forbidden to say that the only reason CHSH violates Bell’s Inequality is that 3 of the 4 tests are really the same test and that is because the results depend on the angle between the polarizers, not the raw settings of them, so I won’t mention it.

Lazarus The primes make it difficult. You are right, some of them were in the wrong place. Here is the abc version with both kinds of notation. P(a,b) -P(a,b’)+P(a’,b)+P(a’,b’) <= 2 P(a,b) -P(a,d)+P(c,b)+P(c,d) <= 2 a+b-a-d+c+b+c+d ------------------------ <=2 a+b-a-d+c+b+c+d / a+b+c+d <=2 a+b+c+d b+c+b+c ----------- <=2 b+c+b+c / a+b+c+d <=2 a+b+c+d 2(b+c) ------------ <=2 2(b+c) / (b+c)+(a+d) <=2 (b+c)+(a+d) 2 ------------ <=2 2 / [1 + (a+d) / (b+c)] <=2 1 + (a+d) ------- (b+c) 1 ------------ <=1 1 / [1 + (a+d) / (b+c)] <=1 1 + (a+d) ------- (b+c) and (a+d) 0 <= ------- <= infinity 0 <= (a+d) / (b+c) <= infinity (b+c)

This is where I failed to include the primes. 2 ----------------- <=2 1 + (a+b) Correction 1 + (a+b') ------- (b+a’) 1 ----------------- <=1 1 + (a+b) Correction ! + (a+b') ------- (b+a’) and (a+b) Correction (a+b') 0 <= ---------- <= infinity (b+a’)

Lazarus: Sorry my notation confused you. Here is another try to make it clear. 2(b+a’) / [(b+a’) + (a+b’)] <= 2 2 / [(b+a’) / (b+a’) + (a+b’) / (b+a’)] <= 2 2 / [1 + (a+b’) / (b+a’)] <= 2 I have to fess up that I got sloppy and dropped some primes but that should have been pretty obvious if your eye sight is better than mine.

Bell’s Inequality Simplified P(a,b) -P(a,b’)+P(a’,b)+P(a’,b’) <= 2 a+b-a-b’+a’+b+a’+b’ ------------------------------ <=2 a+b+a’+b’ b+a’+b+a’ --------------- <=2 a+b+a’+b’ 2(b+a’) -------------------- <=2 (b+a’)+(a+b’) 2 ----------------- <=2 1 + (a+b) ------- (b+a’) 1 ----------------- <=1 1 + (a+b) ------- (b+a’) and (a+b) 0 <= ---------- <= infinity (b+a’) Therefore: 1 divided by 1 or greater is less than or equal to 1.

Swansont: How does that tell you which crystal the photons came from? Lazarus: This is from post number 128. "Lazarus: All of the evidence needed is in the experiment. The evidence is not in question, the logic of the experiment is. As for determining the polarization with the CHSH equipment, that is being done when polarizer A is set to zero degrees. Detector A1 sees vertical photons coming from one BBO and they are counted. Detector A2 sees horizontal protons coming from the other BBO and they are counted."

Swansont: I have asked you a number of times to explain how you measure the time difference. Lazarus: And I have told you a number of times that the time separation is between pairs of photons which exceeds 25ns. Swansont: They are not the same test. The angle correlation is true in QM, but not for hidden variables. Lazarus: That is strange logic. The angle that affects the results of the physical experiment is different if you are thinking about QM or hidden variables. If the CHSH experiment is invalid, it is invalid no matter how you look at it. There NEVER has been a reasonable answer to the 2 questions. I have been accused of dodging questions but these questions have been dodged may times.

We are down to the nitty gritty. It is time to either answer my 2 questions about the validity of CHSH or concede that the logic of CHSH is seriously flawed so the CHSH experiments are worthless. 1. One BBO cannot produce Quantum Entangled photons. How can 2 BBO’s close together, with time spaced photons, change the photons from known to indeterminate? Here is a clue: They can’t. 2. How can 4 tests, with 3 of them the same test, be correlated with Bell’s Inequality test? The clue is: They can’t.

Swansont: This is the opposite of true. You really need to step back and study up on some basics. QM has no hidden variables. Bell tests are a way that was devised to show this. Lazarus: Since the test involves Hidden Variables it doesn’t matter that the test is logically flawed. Swansont: Put another way, if QM is right, the answers depend only on the angle difference. If QM is wrong and some alternative theory is correct, the answers depend on something else (e.g. the actual angles used, and independent of the difference). You do the experiment and find out it relies on the angle difference. What do you conclude about the validity of the two theories? Lazarus: You should conclude that the CHSH test is wrong, because it doesn’t use the QM angles. xxxxxxxxxxx Previous Lazarus: That implies that if the result depends of the polarizer settings and not the angle between them, then QM is wrong. xxxxxxxxxx Swansont: Yes. Lazarus: That leaves you with 2 choices: 1. CHSH is correct in using the polarization settings as the Bell Inequality test, which implies QM is wrong. 2. QM is correct in the use of the angle between polarizers so 3 of the 4 tests the same, which implies CHSH is wrong. Swansont: The "standard model" you refer to was not science. Galileo challenged it with evidence. Are you going to present any? And yet you have been unable to show how the polarization can be determined in the experiment, so I'd say it's a pretty good assumption. Lazarus: All of the evidence needed is in the experiment. The evidence is not in question, the logic of the experiment is. As for determining the polarization with the CHSH equipment, that is being done when polarizer A is set to zero degrees. Detector A1 sees vertical photons coming from one BBO and they are counted. Detector A2 sees horizontal protons coming from the other BBO and they are counted.

Swansont: We're >120 posts in to the discussion, so I don't see where you've been escorted anywhere. Lazarus: True, but I am sure that some would like that. The point I was trying to make is that the attention has been on the mechanics of the CHSH test but not on the logic behind it. Swansont: But you are turning into a heckler, because you are ignoring answers, refusing to answer questions put to you and are just repeating assertions. Lazarus: The reason that I have to repeat the 2 questions as to the justification of photons from the BBO’s being indeterminate and that 3 out of 4 of the tests being the same fits the criteria for Bell’s Inequality test, is that they have not been answered. I try to answer questions no matter how unrelated they are. Swansont: Further, your characterization above is wrong. The 4 settings in the left hand, as you describe it, are the theory. The 4 settings in the right hand are the experiment. When you are trying to test a theory, you do an experiment to see if it matches the predictions, which is exactly what's happening here. Further, you are completely ignoring the fact that there is another prediction, that of hidden variables. And the experiment is inconsistent with that prediction. And that's the whole point of this. So as long as you ignore any analysis of the hidden variable aspect of the analysis, you objections to this end are pretty much worthless. Lazarus: Hidden Variables is part and parcel of the Quantum Entanglement concept. If the experiments are not logically correct nothing is proved about Hidden Variables or anything else. Swansont: Put another way, if QM is right, the answers depend only on the angle difference. If QM is wrong and some alternative theory is correct, the answers depend on something else (e.g. the actual angles used, and independent of the difference). You do the experiment and find out it relies on the angle difference. What do you conclude about the validity of the two theories? Lazarus: That implies that if the result depends of the polarizer settings and not the angle between them, then QM is wrong. Swansont: Your whole objection is that they did an experiment and it supported one model and excluded another, and you don't like that it was designed to figure out which one is valid. It's like telling Galileo that dropping two different mass balls off the tower and having them hit at the same time was rigged, because that's exactly what would happen if acceleration was independent of mass. Lazarus: It is ironic that you use Galileo in your defense of CHSH in the “Standard Model” that has been accepted for 50 years as Galileo got in big trouble for challenging the “Standard Model” of the Sun orbiting the earth that had been accepted for 100s of years by most groups in authority. Swansont: Idiot's Convention? Either that or a meeting of the Society of Completely Missing the Point. Lazarus: The point that is being missed is the tests start out by assuming that BBO photons are indeterminate and ends by fudging the tests so that 3 of the 4 of them are really the same test.

Swansont: Let me get this straight: it's sleight of hand that the predictions of QM work, when testing to see if QM is correct? The bottom line here is that the predictions of hidden variables are different. Choosing the angles that make that distinction the clearest is good procedure, not sleight of hand. Lazarus: The Mathematical Magician holds up his left hand and says: “In my left hand I hold the 4 settings of the polarizer for the CHSH test. You can see that the numbers perfectly match the Bell’s inequality test.” Then he holds up his right hand and says: “In my right hand I hold the 4 physical experiments associated with the 4 settings. I will now prove that Spooky Quantum Entanglement exists and that Einstein was wrong. Since there are no counts associated with the settings in my left hand I will uses the counts from the experiments in my right hand. Now we add up the counts in the way of Bell’s Inequality and Voila, the result is 2.4 which obviously violates the Inequality. I just proved that Spooky Quantum Entanglement exists. Look closely at the experiment to see that there are no imperfections in any of the device or that extraneous photons are coming from the particle accelerator next door to make sure there are no loopholes. Any questions?” Someone in the audience says: “But the results of the experiments are dependent on the angle between polarizer and the settings in 3 of the tests are the same.” The Mathematical Magician says: “You are distracting from the point of this proof. Someone escort this heckler to the Idiots Convention down the hall where he belongs. Any more questions?”

Swansont: They are indeterminate because you can't determine the state when you do the experiment, as the experimental results show. Feel free to try and determine the polarization of the photon within the framework of the experiment. You have yet to explain how this can happen. Lazarus: Sorry, I can’t buy that logic. i.e. An experiment is designed to test the frequency of a photon so it cannot determine the polarization of the photon. THEREFORE, the polarization of the photon is indeterminate. Swansont: The Geller lab experiment. You refuse to provide links, so I have not really bothered to try and find any others. I don't owe you that. Lazarus: I still have a problem with the huge link so I uploaded a PDF copy to the internet. The link is: http://docdro.id/Kf5G3ZM Swansont: And I find that jumping from one experiment to another just confuses things. And you need less of that, not more. Lazarus: All the CHSH type I BBO experiments are pretty similar and have the same problems. Swansont: You forget (or are not getting) that a Bell test is to disprove hidden variables, in which case the result would not just depend on the angle between the polarizers. The relationship you cite is what happens if QM is right. The experiments are trying to exclude a situation where QM is not right. Did you not understand this? Lazarus: It does not matter what CHSH set out to prove. It does not fit the criteria of the Bell Inequality with 3 of the same tests. Swansont: So once again you show that you have not read the paper you're referring to. Look below table 1. You will find that your claim here is false. Other orientations, with other differences, were used. Lazarus: Thank you for pointing that out. However, 3 of these tests are also similar and at 22.5 degrees. Below is the text from Geller that you are talking about. Here is what that boils down to: Test 1 157.5 – 135 = 22.5 Test 2 135 - 22.5 = 112.5 Test 3 157.5 - 0 = 157.5. 157.5 + 180 = 337.5. 360 -337.5 = 22.5 Test 4 22,5 = 0 = 22.5 In test 3, 157.5 degrees is the same as 337.5 for photon polarization. Again, 3 similar tests. More sleight of hand.

Swansont: And I've answered it many times. And your reply has always been that you can determine the time and the polarization of the photons, but have NEVER explained how you do that in the context of the experiment that's being done. Lazarus: The question of how photons could be indeterminate has NEVER been answered. The responses are either questions or other distractions. What happens after the photons arrive at the polarizers has no connection with whether or not the photons were indeterminate on arrival. The pairs from one BBO are always vertical and horizontal from the other. Ignoring available information does not change the information. How about answering the simple question, what is the justification for claiming the photons are indeterminate, if you can. Swansont: So once again you show that you have not read the paper you're referring to. Look below table 1. You will find that your claim here is false. Other orientations, with other differences, were used. Further, if you want to show that this would not be a valid test, show it with a derivation. Unsupported claims mean nothing. Lazarus: It is not clear what paper you are referring to. The copy of the last paper I referenced (Kwiat et all) does not have a table 1. Do you disagree that: 1 Quantum theory says that only the angle between the polarizers determines the result. 2 The physical experiment agrees with the Quantum position. 3 The 3 tests at 22.5 degrees between polarizers should all give similar results. If those 3 statements are correct, it is clear that there is no fit to Bell’s Inequality.

Swansont: Shoes are not and can't be entangled. There's no point to discussion if all you do is repeat your misunderstanding. Lazarus: What I am asking for is a reason that the photons in the CHSH experiments are indeterminate. Here is another major problem with CHSH to consider. The only reason CHSH violates Bell’s Inequality is because of mathematical sleigh of hand. This is how it works. The 4 polarizer setting appear to fit in Bell’s Inequality. P(a,b) - P(a,b’) + P(a’,b) + P(a’,b’). But the only angle of the polarizer setting that has any effect is the angle between the polarizers. The angles between polarizers for the 4 tests are: 0,22.5 is 22.5 degrees, 0,67.5 is 67.5 degrees, 45,22.5 is 22,5 degrees and 45,67.5 is 22.5 degrees. That means 3 of the tests are really the same test. Plugging in the numbers gives P(a,b) - P(a,b’) + P(a,b) + P(a,b) which is not a valid Bell’s Inequality test. Problems on both ends of CHSH.

Swansont: The first pair is not "affecting" any other pair. The two photons of the pair are entangled with each other. The coincidence window is to ensure the photons are from a single event. Subsequent pair creation events could be separated by a much longer time, and probably are. Lazarus: When you say entangled it appears that you are referring to Quantum entanglement which means the objects are in an indeterminate state. Objects can be “entangled” like a left and right shoe without being indeterminate. The output of one BBO is known. With 2 BBO’s, the pairs from one BBO are all polarized vertically. The pairs from the other BBO are all polarized horizontally. All information is known. Nothing is indeterminate. Swansont: Stop describing some other experiment, and focus on the one that entangles the photons. Do they put the detectors at 0 and 90? No. So you're not critiquing this experiment. Lazarus: The 0, 45, and 90 degrees apply to the BBO’s that do the entanglement, not the detectors. Vertical for 0 degrees and horizontal for 90 degrees might be clearer. The picture is from the Kwiat et all paper that is referenced as the way their CHSH experiment is set up. A single BBO cannot generate indeterminate photons. If it could there would be no need for 2 BBO’s. The BBO's would have to affect each other to make something indeterminate. If there is no indeterminacy, everything is classical physics. Where is the evidence of any indeterminacy?

Swansont: More than 25 ns? In 25 ns, light travels 7.5 meters. So unless the crystals are 7.5 meters thick, or spaces apart by that much, that's not the time difference between them. Lazarus: The thickness of the crystals is not the issue. If photon pairs from the 2 BBO’s leave 25ns apart the first pair will be 25 feet away before the second pair leaves the other BBO. That’s a lot of distance to say one is affecting the other. Swansont: The 25 ns is the coincidence window, which is, as you say, makes sure the two photons were created in the same event. It does not, however, tell you which crystal they came from. So I will ask yet again how you distinguish between photons created in one crystal and the other. You keep insisting it can be done. Now's the time to explain how. Lazarus: With the pump beam set at 45 degrees and the 2 BBO’s set at 0 and 90 degrees, the 0 degree BBO will ship out the proton pairs polarized at 90 degrees. The 90 degree BBO will ship its protons polarized at 0 degrees. To determine which BBO launched the photon just look at whether the photon is polarized at 0 degrees or 90 degrees. Here is a picture from the Kwiat et all paper showing that the photons polarized at 0 degrees come from one BBO and the 90 degrees ones come from the other BBO. Nothing is indeterminate. How can they become indeterminate?

Swansont: How different? How do you measure this difference? Stop telling me the question can be answered and actually answer the question. Lazarus: More than 25ns. That is a long time when dealing with photons. The CHSH experiments are designed to have time between events so that each pair of photons arrives one at a time. Measuring the time difference has no bearing on the results. A wall is a wall. The events are separated in time. There is no explanation of any cause and effect relationship between the 2 BBO’s.

Swansont: And now we're back to other unanswered questions. If the detection polarizer is at e.g. 45 degrees, and a photon is detected, which crystal generated it? Lazarus: As I said, that is just blinding the polarizer so it can’t tell whether the polarization of the photon is vertical or horizontal. The photon’s polarization is available. Swansont: And the second BBO with the input beam at 45º means the output photons are in a superposition of H and V, which is crucial for entanglement. This is explained in the paper you've pointed to. That you have missed this means you don't understand what's going on. Lazarus: The photons from the 2 polarizers arrive at different times. That is the point of my question of how the second BBO can change photons to indeterminate.

Swanson: And now we're back to other unanswered questions. If the detection polarizer is at e.g. 45 degrees, and a photon is detected, which crystal generated it? Don't dodge the question for a change. Lazarus: I have answered question after question after question, including that one. If no one can justify the second BBO changing photons to indeterminate, all of that is irrelevant. The CHSH experiment is flawed.

Swansont: You keep making claims that you can't support. You haven't shown that the time separation makes the photons distinguishable; it's just a repeated bald assertion. And the second BBO with the input beam at 45º means the output photons are in a superposition of H and V, which is crucial for entanglement. This is explained in the paper you've pointed to. That you have missed this means you don't understand what's going on. Lazarus: That is a distraction from the crucial question, how can a second BBO make the known photons indeterminate. The scenario is so simple that anyone with a passing knowledge of CHSH experiments should be able to immediately answer it, if there is an answer.