Bell's Inequality: GTB+GTD+GLD+SLD >= GLD+GTD

[Lazarus]

Bell's Inequality (in a simple, comprehensible form anyway) states that in a group of items that possess three properties, A, B, and C, the number of items that possess property A but not B plus the number of items that possess the property B but not C is greater or equal to the number of items that possess property A but not C.

 

Assign A as Gold vs Silver, B as Large vs Tiny, C as Bright vs Dull. That leads to the trivial inequality, GTB+GTD+GLD+SLD>=GLD+GTD.

Is this wrong?

[Lazarus]

 

Let me add some more detail. Think of coins.

A not B is the number of coins that are Gold, Tiny and either Bright or Dull (GTB+GTD).

B not C is the number of coins that are Large, Dull and either Gold or Silver

(GLD + SLD).

A not C is the number of coins that are Gold, Dull and either Large or Tiny.

(GDL + GDT)

 

So GTB + GTD + GLD + SLD >= GLD + GDT

That is GLD + GTD + anything non-negative >= GLD +GTD

(GTD=GDT)

 

From http://www.techlib.com/science/bells_inequality.htm

Edited September 17, 2016 by Lazarus

[Lazarus]

Nobody has objected to the conclusion that this interpretation on Bell’s Inequality is trivial. That implies that either Bell’s Inequality is trivial or this interpretation of Bell’s is flawed. Is there a better interpretation of Bell’s proof?

[Mordred]

Probably because as posted its too difficult to follow accurately. You need to find a more detailed way to explain the above. That is easily readable. People lose patience with difficult to read posts.

 

"this post takes too much effort to translate. Let someone else worry about it"

 

The quoted section is probably the typical response...

Edited September 19, 2016 by Mordred

[Strange]

I'm sure you can come up with arbitrary examples of things that appear to match Bell's inequality (if that is what you are doing; I don't really know what your posts mean).

 

However, the important point about Bell's inequality is that classical theory predicts a different result.

[swansont]

One problem is that you have adopted a classical system that has no obvious quantum analogue, and one more complicated than typical quantum experiments, so it's not clear to me that you've applied it correctly. Also you've cited a link of someone who admittedly struggles with QM, so I'm not sure how credible their information is.

 

To me it's a lot clearer to look at QM predictions with a QM system.

[imatfaal]

I'm sure you can come up with arbitrary examples of things that appear to match Bell's inequality (if that is what you are doing; I don't really know what your posts mean).

 

However, the important point about Bell's inequality is that classical theory predicts a different result.

 

Bell's inequality (it was also formed in a different manner by Wigner) is technically pure probability and not particularly hard - Bell's Theorem is a way to test between Local Hidden Variables and Spooky Action at a Distance by using this inequality when a set of marginal probability distributions is derived from a single joint distribution.

[Strange]

You are right, of course. I think I should stop posting for a while: I keep posting things that I know are wrong!

[imatfaal]

One problem is that you have adopted a classical system that has no obvious quantum analogue, and one more complicated than typical quantum experiments, so it's not clear to me that you've applied it correctly. Also you've cited a link of someone who admittedly struggles with QM, so I'm not sure how credible their information is.

 

To me it's a lot clearer to look at QM predictions with a QM system.

 

I agree about the application - by the set up is correct and the basis of the inequality that is the foundation of Bell's work.

 

1. An object can have (or not ) three independent characteristics A, B, & C

2. We can denote these as A or A' , B or B' , C or C'

3. Each object can therefore be shown as - for example AB'C which has A, doesn't have B and has C

 

What Bell rediscovered was that various inequalities exist when you sample basis one, two or three of these characteristics

 

AB' + A'B + AC' + A'C + BC' + B'C <= 2

 

This is the important one. Which with a genius like Bells can be shown to be useful in distinguishing between two regimes of physics. If there were Hidden Variables then the measurements done by people like Aspect would be derived from a single joint distribution and MUST follow Bell's inequalities. But they do not

[Lazarus]

OK. How about a classical device that violates Bell's Inequality.

 

 

 

Here is an “impossible” classical, mechanical device, using pennies rather than photons, that emulates the CHSH devices and gets similar results. Also, it violates Bell’s Inequality.

 

 

 

The source is a device that holds 2 pennies and fires them toward the shields. The 2 pennies are parallel, which is their entangled state. The drums holding the pennies rotate. When the drums are rotating the angle of the pins is undetermined. After the pins are fired they are determined but unknown. The pairs of shields can be individually, manually rotated to any angle. Most of the pennies are deflected by the shields. A few reach the first metal plate with a slit. Some pass through the slit and hit the second metal plate, D+. Some do not pass through, D-. When both the A and B shields are rotated by the same angle, the results do not change. When the shields are at the same angle, A and B get the same results, E = 1. When the shields are perpendicular, none of the results are the same, E = -1. In between the fraction of the pennies getting through is cos^2(omega), where omega is the angle between the shields and the slit. Since changing the rotation of both shields by the same angle doesn’t affect the results, only the angle between the A and B shields needs to be considered.

 

The opening between shields is twice the width of a penny. The width of the slit is 99 % of the diameter of a penny.

 

The fraction of pennies that get through is cos^2(omega). Omega is the angle of the shields, which is the angle between the shields and the slit. The slits are always at 0 degrees

 

The only trials that are counted are those where both A and B detect something, D+ or D-. D+ will be considered a 1, D- will be considered a 0. There are 10,000 counted trials.

 

The formulae we are dealing with are:

E = (N11+N00-N10-N01) / (N11+N00+N10+N01)

S = E(a,b) - E (a’,b) + E(a,b’) + E(a’,b’)

 

E is the Correlation Coefficient.

N is the number of detections of different combinations.

a and b are angular settings of the polarizers.

S is Bell’s Inequality

 

For (a,b) the A shields set at 0 degrees and the B shields set at 22.5 degrees the number of A 1,0 counts is 10,000 times cos^2(0) = 10,000. The number of A 0,1 counts is 0. A01 = 10,000 – A10.

 

The number B 1,0 counts is 10,000 times cos^2(22,5) = 8536. B 0,1 is 1464. B01=10,000 – 8536 = 1464.

 

E = (A10+B10-A01-B01)*( A10+B10+A01+B01)

E = (10,000 + 8536 – 0 – 1464)( 10,000 + 8536 + 0 + 1464)

E = .7071

 

A deg B deg 1,1 0,0 1,0 0,1 Match E

0 22.5 8536 0 1464 0 8536 ,707

0 67.5 1464 0 8436 0 1464 -,707

45 22.5 Same as 0 22.5 .707

45 22.5 Same as 0 22.5 .707

 

S = .707 - (-.707) + .707 + .707 = 2.8

 

[swansont]

The fraction of pennies that get through is cos^2(omega). Omega is the angle of the shields, which is the angle between the shields and the slit.

It's not obvious to me why this would be true.

 

I hope this isn't just a recreation of your bowling pin example without fixing the errors it contained.

[Lazarus]

It's not obvious to me why this would be true.

 

I hope this isn't just a recreation of your bowling pin example without fixing the errors it contained.

 

As you pointed out, there were flaws in that model. This one should be more solid

as it is closer to the CHSH experiments. It is difficult to find the actual data and the

nitty gritty description of the CHSH devices but this has got to be pretty close.

 

Again. thank you for your advice and patience.

[swansont]

So when can we expect your justification for having a cos^2(omega) dependence?

[Lazarus]

So when can we expect your justification for having a cos^2(omega) dependence?

 

The reason for cos^(angle) is that Malus' Law (I =Io*cos@(angle)) seemed similar.

 

It doesn't matter because almost any reasonable choice will result in a violation

of Bell's Inequality.

 

For example: Using cos(angle) in place of cos^2(angle) produces

A at 0 degrees and B at 22.5 degrees gives an E of .8478

A at 0 degrees and B at 67.5 degrees gives an E of -..2346

S = .8478 - (-2346) + .8478 + .8478 = .2.7789

[swansont]

 

The reason for cos^(angle) is that Malus' Law (I =Io*cos@(angle)) seemed similar.

 

It doesn't matter because almost any reasonable choice will result in a violation

of Bell's Inequality.

 

For example: Using cos(angle) in place of cos^2(angle) produces

A at 0 degrees and B at 22.5 degrees gives an E of .8478

A at 0 degrees and B at 67.5 degrees gives an E of -..2346

S = .8478 - (-2346) + .8478 + .8478 = .2.7789

 

 

Malus' law is for polarization of light. You can't arbitrarily use it for a classical system.

[imatfaal]

For the second thread running you seem to be claiming that the physics following from Bell's inequality which refutes EPR is flawed; this is based on an incomplete understanding of the mathematics and a completely erroneous assertation in the physics that one can arbitrarilly use concepts (the roots of which are deep in Quantum Mechanics) in predicting the behaviour of purely classical objects.

 

Why not spend the time actually learning about basic quantum mechanics? I have a feeling there is an MITx course running at edx on QM - it will be seriously tough; bu you will come out of it actually knowing stuff

[Lazarus]

 

 

Malus' law is for polarization of light. You can't arbitrarily use it for a classical system.

 

 

You are right. Not only are the cos^2(angle) and the cos(angle) not justified, they are not correct. The correct relationship is that the fraction of 1’s = sin(angle +90).

 

Here is why. First, consider how photons passing through a polarizer work. Take the case where the wave length of the photons equals the width of the slits in the polarizer grid. When the electric component of the photons is aligned with the slits. almost none of the photons get through. When perpendicular to the slits, almost all get through. The magnetic field of the photons is aligned with the slits when the photons are getting through.

 

For the pennies to match the photon’s magnetic field, 90 degrees must be added to the 22.5 and 67.5 degrees of the tests.

 

To determine the relationship of the angle of rotation to the fraction of 1’s we can consider the coins whose centers are on one line perpendicular to the slits. Calculating the fraction of 1’s on the line (or half of the line) gives the fraction for all photons.

 

This picture shows the shields, the edge of the hole and coins at significant positions on the line.

 

 

 

 

The hole in the detector is equivalent to one slit of a polarizer. The hole’s width is = the diameter of a penny. The opening between the shields is set to equal the penny’s diameter times 1 + the sine of the test rotation. The shields would not be needed if we used multiple holes to match a polarizing grate. Coins that hit the edge of the hole are counted as 1’s. Coins that pass through the hole are counted as 0’s. 90 degrees is added to the test rotation to match the photon’s magnetic field orientation. The coins that will hit the edge of the hole are those whose center is within the sine of the test rotation angle plus 90 degrees times the size of the hole. (Size of the hole is the diameter of a penny)

 

N = sin(angle+90) * d

N is number of 1’s.

d is diameter of penny.

 

At 22.5 + 90 degrees, the fraction of 1’s is sin(112.5) = .9239. E = .8478

At 67.5 + 90 degrees, the fraction of 1’s is sin(157.5) = .3827. E = -.2346

 

S = .8478 -(-.2346) + .8478 + .8478 = 2.5434

 

S is closer to the CHSH test results around 2.4 than the Quantum prediction of 2.8.

[Lazarus]

For the second thread running you seem to be claiming that the physics following from Bell's inequality which refutes EPR is flawed; this is based on an incomplete understanding of the mathematics and a completely erroneous assertation in the physics that one can arbitrarilly use concepts (the roots of which are deep in Quantum Mechanics) in predicting the behaviour of purely classical objects.

 

Why not spend the time actually learning about basic quantum mechanics? I have a feeling there is an MITx course running at edx on QM - it will be seriously tough; bu you will come out of it actually knowing stuff

 

It is easy to change my mind. Just give me a clear logical reason and I change sides in an instant. Most of the mathematics of Quantum, Relativity and Astronomy is beyond question. The problem is in the contradictory, bizarre and sometimes just flat out wrong conclusions drawn from the math. For example: the D-Wave Quantum computer uses a Quantum DC SQUID as its Qubit. The DC SQUID is thought to be Quantum because the current flows in opposite directions at the same time in the loop with the Josephson Junctions. Mathematically, it is perfectly legitimate to describe the current as the sum or difference of 2 currents. Physically, that is not the case. All electrons are flowing in the same direction. The external magnetic field pushes some of the electron from one path to the other. Nothing Quantum there. The D-Wave computer is an updated analog computer. Your concerns are well justified. I am definitely out to destroy the ridiculous conclusions of current physics and replace them with logical, rational concepts.

[swansont]

Coins that hit the edge of the hole are counted as 1’s. Coins that pass through the hole are counted as 0’s.

All you've done here is describe a really crappy detector, which has nothing to do with the underlying science. Here you detect pennies aligned with the slit and reject anything other than a slight misalignment. A penny at 5 degrees off-axis is counted as being perpendicular. That was ridiculous when you proposed it for bowling pins and it's still ridiculous.

 

Most theory efforts describe perfect detectors and then in the experimental results one compensates for the imperfections. You have taken another tack, and incorporated a horrible detector into the theory. Why?

[Lazarus]

All you've done here is describe a really crappy detector, which has nothing to do with the underlying science. Here you detect pennies aligned with the slit and reject anything other than a slight misalignment. A penny at 5 degrees off-axis is counted as being perpendicular. That was ridiculous when you proposed it for bowling pins and it's still ridiculous.

 

Most theory efforts describe perfect detectors and then in the experimental results one compensates for the imperfections. You have taken another tack, and incorporated a horrible detector into the theory. Why?

 

 

At 5 degrees, the fraction of pennies that successfully pass through the hole and are counted as parallel is .9128 (91.28%). The fraction of pennies that hit the edge of the hole and are counted as perpendicular is .0872 (8.72%)

[swansont]

 

 

At 5 degrees, the fraction of pennies that successfully pass through the hole and are counted as parallel is .9128 (91.28%). The fraction of pennies that hit the edge of the hole and are counted as perpendicular is .0872 (8.72%)

 

 

 

How do you physically justify that? These are classical particles.

[Lazarus]

 

 

 

How do you physically justify that? These are classical particles.

 

That is the result of the calculation, the number of 1's = sin(angle+90) and also from the diagram. However that is moot because I agree with you that this device does not completely match the CHSH experiments.

 

If I can find a device that better matches, i will present it for your inspection.

 

Your help is appreciated.

[swansont]

 

That is the result of the calculation, the number of 1's = sin(angle+90) and also from the diagram. However that is moot because I agree with you that this device does not completely match the CHSH experiments.

 

 

 

That's moot if all you've done is arbitrarily write down an equation. If a penny can make it through the slit, it makes it through the slit. It's a classical object. What is your physical justification for saying that there is some probability involved?

 

If you're going to present theory, do it in a way that does not rely on how the experiment is done. The bottom line here is that you can determine the orientation of a penny to more or less arbitrary accuracy, in the context of what is required here.

[imatfaal]

 

It is easy to change my mind. Just give me a clear logical reason and I change sides in an instant. Most of the mathematics of Quantum, Relativity and Astronomy is beyond question. The problem is in the contradictory, bizarre and sometimes just flat out wrong conclusions drawn from the math. For example: the D-Wave Quantum computer uses a Quantum DC SQUID as its Qubit. The DC SQUID is thought to be Quantum because the current flows in opposite directions at the same time in the loop with the Josephson Junctions. Mathematically, it is perfectly legitimate to describe the current as the sum or difference of 2 currents. Physically, that is not the case. All electrons are flowing in the same direction. The external magnetic field pushes some of the electron from one path to the other. Nothing Quantum there. The D-Wave computer is an updated analog computer. Your concerns are well justified. I am definitely out to destroy the ridiculous conclusions of current physics and replace them with logical, rational concepts.

 

Two coins are not entangled by the fact that they are parallel. You are reproducing results because you are designing your experiments and (mis-)doing your maths in order to find these results - it would not be the case if you were to actually do it properly. And, before you ask, no I will not spend the time doing the preliminary research, the background mathematical work etc to either bear out or trash your ideas - that's your job and you are failing

 

DC Squids work on tunnelling and are by their very nomenclature quantum devices electrons do not just jump across isolators in these circumstances without the effects which you are decrying - you cannot just compare them with a couple of coins. You have to have shared states of superposition etc.

[Lazarus]

Even with the objections, if a physical device can be built using CHSH experiment rules, that violates Bell’s Inequality, there is a problem that needs to be addressed.

 

Here is an “impossible” classical, mechanical device, using pennies rather than photons, emulates the CHSH devices and gets similar results. Consequently, it violates Bell’s Inequality.

 

 

 

 

The polarizers are grates with iron bars between the slits. The slits are the diameter of a penny wide. The polarizers are manually rotated to the desired settings, 0 – 22,5, 0 – 67.5, 45 – 22.5, 45 – 67.5. Pennies are fired at the polarizers in entangled pairs with state being parallel or perpendicular. The calibration sets the A penny parallel to the A slits. Pennies that pass through the polarizer fall into the D+ bucket and are counter as 1’s. The pennies that bounce off of the bars fall into the D- bucket and are counted as 0’s.

 

A penny will bounce off of a bar and fall into the D- bucket and be counted as a 0 when the center of the penny comes closer to the bar than the radius of a penny times the square of the sine of the angle between the polarization of the penny and the direction of the bar.

 

Here are some of the results of a simulation. Each run makes 10,000 trials with the coins hitting the polarizer at random points.

 

adeg bdeg n11 n00 n10 n01 E

0.0000 22.5000 8534.0000 0.0000 1466.0000 0.0000 0.7068

0.0000 67.5000 1481.0000 0.0000 8519.0000 0.0000 -0.7038

45.0000 22.5000 8525.0000 0.0000 1475.0000 0.0000 0.7050

45.0000 67.5000 8563.0000 0.0000 1437.0000 0.0000 0.7126

S = 2.8282

 

adeg bdeg n11 n00 n10 n01 E

0.0000 22.5000 8530.0000 0.0000 1470.0000 0.0000 0.7060

0.0000 67.5000 1421.0000 0.0000 8579.0000 0.0000 -0.7158

45.0000 22.5000 8531.0000 0.0000 1469.0000 0.0000 0.7062

45.0000 67.5000 8573.0000 0.0000 1427.0000 0.0000 0.7146

S = 2.8426

 

adeg bdeg n11 n00 n10 n01 E

0.0000 22.5000 8519.0000 0.0000 1481.0000 0.0000 0.7038

0.0000 67.5000 1526.0000 0.0000 8474.0000 0.0000 -0.6948

45.0000 22.5000 8528.0000 0.0000 1472.0000 0.0000 0.7056

45.0000 67.5000 8539.0000 0.0000 1461.0000 0.0000 0.7078

S = 2.812

 

adeg bdeg n11 n00 n10 n01 E

0.0000 22.5000 8560.0000 0.0000 1440.0000 0.0000 0.7120

0.0000 67.5000 1461.0000 0.0000 8539.0000 0.0000 -0.7078

45.0000 22.5000 8566.0000 0.0000 1434.0000 0.0000 0.7132

45.0000 67.5000 8542.0000 0.0000 1458.0000 0.0000 0.7084

S = 2.8414

 

 

Here is the explanation of the range of the bounce being the radius of the penny times the square of sine of the angle between the coin and a bar.

 

The overlap of the bar from pennies with their center close to a bar is the radius of the penny times the sine of the angle. Not all of the pennies that hit a bar bounce. Some of them just clip a bar. Depending on their alignment some will experience torque and not much force to make them bounce. That is compensated for by using the square of the sine rather than just the sine.

 

 

 

 

The state of the coins is set to parallel with these numbers. Setting the state to perpendicular reverses the signs of the results.

 

This device has the same functions as CHSH experiments, gets similar results and violates Bell’s Inequality.