Unghostly entanglement

[Lazarus]

 

I think you have massively misunderstood my objection to your claim. The details of the detector CANNOT matter. There is no horizontal vs vertical distinction. What exchange made you think that this was an issue?

 

 

There are two calculations, one Quantum and the other Classic that are being compared. The Quanum side is extremely complex but the Classic side is just High School Math so it should be resolvable to everyones satisfaction.

 

The question is still "What is the justifcation for the rotated detector's wrong way detections matching the angle?".

 

Here are some of the earlier posts.

 

Post 25 Swansont

I'm not seeing what the length of the horizontal line across the target area has to do with this. It's the angle that's being measured.

 

Post 28 Lazurus

The length of the pin is less than the long dimension of the rectangle and greater than the width of it. With the rectangle in the long direction vertical, a vertical pin will always go through. A horizontal pin will always hit the side of the rectangle. When the rectangle is rotated a bit the horizontal distance becomes greater and a horizontal pin has a better chance of making it through without hitting the side.

 

Post 31 Lazurus

Regardless of whether or not the Bowling Ball model is a valid demonstration of the failure of the assumption that doubling the angle of rotation of a measuring device can’t more than double the misses, what justifies Bell’s assumption that it is impossible for a physical situation to more than double the number of misses.

 

Post 31 Swansont

I don't think you've read that right, or didn't understand what's going on. As you change the angle of the detector, you start getting wrong answers. Classically it depends on the sine of the angle. For small angles, doubling the angle doubles the sine. But QM gives a different answer, which is how we know the classical analysis is wrong.

[swansont]

Right. It's not horizontal or vertical that's the issue. It's the actual angle vs a poorly measured angle from a flawed detector. If the bowling pin is at 10º to some axis, your detector won't measure this. The theory only cares that the angle is 10º, not that you measure it to be some other value. The details of how the detector works can't be included in the discussion.

 

A measurement that depends on cos (the bowling pin) will not vary the same as one that depends on cos^2 (polarization). Notice that the construction details of the detector are completely absent from that statement.

[Lazarus]

Right. It's not horizontal or vertical that's the issue. It's the actual angle vs a poorly measured angle from a flawed detector. If the bowling pin is at 10º to some axis, your detector won't measure this. The theory only cares that the angle is 10º, not that you measure it to be some other value. The details of how the detector works can't be included in the discussion.

 

A measurement that depends on cos (the bowling pin) will not vary the same as one that depends on cos^2 (polarization). Notice that the construction details of the detector are completely absent from that statement.

 

What is the justification for the cos detemining the number of "wrong way detections"?

[swansont]

What is the justification for the cos detemining the number of "wrong way detections"?

Because you're measuring the projection of the spin.

[Lazarus]

Because you're measuring the projection of the spin.

 

We are on the classic side of the fence, so how does spin relate to anything?

[swansont]

 

We are on the classic side of the fence, so how does spin relate to anything?

 

You've repeatedly cited an example that's measuring a spin, and you've been critiquing the analysis. To all of the sudden claim that spin isn't involved is preposterous.

[Lazarus]

 

You've repeatedly cited an example that's measuring a spin, and you've been critiquing the analysis. To all of the sudden claim that spin isn't involved is preposterous.

 

 

Spin is usually concerned with a condition of a particle that resolves into two distinct choices, 0 or 1, red or blue, up or down, horizontal of vertical, etc. So what you mean by “projection of the spin” must be the projection of the polarized photon or bowing pin. The problem still remains “How does that justify the cosine of the angle of rotation of the measuring device matching the number of wrong way detections?”.

[swansont]

 

 

Spin is usually concerned with a condition of a particle that resolves into two distinct choices, 0 or 1, red or blue, up or down, horizontal of vertical, etc. So what you mean by “projection of the spin” must be the projection of the polarized photon or bowing pin. The problem still remains “How does that justify the cosine of the angle of rotation of the measuring device matching the number of wrong way detections?”.

 

Trigonometry

[Lazarus]

 

Trigonometry

 

In Post 41 Swansont said:

You double the angle (according to the small angle approximation) and you double the counts in the orthogonal axis.

 

The length of the orthogonal part varies as sin(x). That's basic trig. sin(2x) = ~2sin(x) for small values of x

 

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Two plus two is four. Therefore, the moon is made of green cheese.

 

For small angles the cosine is almost linear. Therefore, the cosine of the rotation of the measuring device matches the wrong way detections.

 

That’s a hard sell.

[uncool]

In Post 41 Swansont said:

You double the angle (according to the small angle approximation) and you double the counts in the orthogonal axis.

 

The length of the orthogonal part varies as sin(x). That's basic trig. sin(2x) = ~2sin(x) for small values of x

 

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Two plus two is four. Therefore, the moon is made of green cheese.

 

For small angles the cosine is almost linear. Therefore, the cosine of the rotation of the measuring device matches the wrong way detections.

 

That’s a hard sell.

Let's count the errors in this post.

 

First error in the first three words; the quote is from post 43, not post 41.

 

Second error: the cosine is not almost linear. That's not what was said. What was said is that the sine is almost linear.

 

Third error: The reasoning is not "almost linear, therefore that's wrong way detections". The reasoning is: "This is how wrong way detections work, therefore linearity happens at small angles".

 

Three errors in 4 (if you only count non-quotes) mostly-vacuous lines. That's impressive.

Edited December 11, 2015 by uncool

[Lazarus]

Let's count the errors in this post.

 

First error in the first three words; the quote is from post 43, not post 41.

 

Second error: the cosine is not almost linear. That's not what was said. What was said is that the sine is almost linear.

 

Third error: The reasoning is not "almost linear, therefore that's wrong way detections". The reasoning is: "This is how wrong way detections work, therefore linearity happens at small angles".

 

Three errors in 4 (if you only count non-quotes) mostly-vacuous lines. That's impressive.

 

That's cool, uncool. That is 3 more errors than Bell's Inequality Theorem has.

 

In spite of my sloppy post, the point is that the cosine relationship has not been justified.

[uncool]

That's cool, uncool. That is 3 more errors than Bell's Inequality Theorem has.

 

In spite of my sloppy post, the point is that the cosine relationship has not been justified.

Let's be more precise, here. What, precisely, is the "cosine relationship" that you are talking about? Is it the prediction, from quantum mechanics, that the correlation in Bell's theorem should be proportional to the cosine of the angle?

[Lazarus]

Let's be more precise, here. What, precisely, is the "cosine relationship" that you are talking about? Is it the prediction, from quantum mechanics, that the correlation in Bell's theorem should be proportional to the cosine of the angle?

 

 

The assumption in Bell’s Theorem is that in the Classic calculation the number of wrong way detections is proportionate to the sine of the angle of rotation. If the assumption were that it was proportionate to the 1- cosine of the angle the Classic and Quantum results would match. The reason that sine rather than 1- cosine was chosen is the question.

Edited December 11, 2015 by Lazarus

[uncool]

The assumption in Bell’s Theorem is that in the Classic calculation the number of wrong way detections is proportionate to the sine of the angle of rotation.

Do you have a source for that being a relevant assumption? It seems unlikely, especially because it claims a negative number of wrong way detections (if you go beyond 180 degrees).

 

ETA: To be clear, I am suggesting that you want the absolute value of the sine.

Edited December 11, 2015 by uncool

[swansont]

It's sin or cos depending on which axis you reference. Because that's how trig works.

[uncool]

I know; my more relevant point is that both go negative, and that shouldn't be possible when counting a "number of detections".

[Lazarus]

Do you have a source for that being a relevant assumption? It seems unlikely, especially because it claims a negative number of wrong way detections (if you go beyond 180 degrees).

 

ETA: To be clear, I am suggesting that you want the absolute value of the sine.

 

 

Yes, it goes negative at 180 degrees but that is easy to fix. As you say, just put absolute bars around the 1 – cosine.

 

Here is something from Wikipedia that shows the way the Classic calculation is being made with the wrong way detections proportionate to the angle. It seems consistent with other articles on the internet.

 

Bell’s Theorem From Wikipedia

 

By the mismatch argument, the chance of a mismatch at two degrees can't be more than twice the chance of a mismatch at one degree: it cannot be more than 2f.

 

 

The best possible local realist imitation (red) for the quantum correlation of two spins in the singlet state (blue), insisting on perfect anti-correlation at zero degrees, perfect correlation at 180 degrees. Many other possibilities exist for the classical correlation subject to these side conditions, but all are characterized by sharp peaks (and valleys) at 0, 180, 360 degrees, and none has more extreme values (±0.5) at 45, 135, 225, 315 degrees. These values are marked by stars in the graph, and are the values measured in a standard Bell-CHSH type experiment: QM allows ± 1/2^.5 = ± 0,7071, local realism predicts ±0.5 or less.

[uncool]

Yes, it goes negative at 180 degrees but that is easy to fix. As you say, just put absolute bars around the 1 – cosine.

(1 - cos) doesn't go negative. It does go above 1, which I think would also be a problem, as it seems you are trying to deal with the proportion of electrons determined to spin the "wrong" way.

Here is something from Wikipedia that shows the way the Classic calculation is being made with the wrong way detections proportionate to the angle. It seems consistent with other articles on the internet.

 

Bell’s Theorem From Wikipedia

 

By the mismatch argument, the chance of a mismatch at two degrees can't be more than twice the chance of a mismatch at one degree: it cannot be more than 2f.

 

graph.JPG

 

The best possible local realist imitation (red) for the quantum correlation of two spins in the singlet state (blue), insisting on perfect anti-correlation at zero degrees, perfect correlation at 180 degrees. Many other possibilities exist for the classical correlation subject to these side conditions, but all are characterized by sharp peaks (and valleys) at 0, 180, 360 degrees, and none has more extreme values (±0.5) at 45, 135, 225, 315 degrees. These values are marked by stars in the graph, and are the values measured in a standard Bell-CHSH type experiment: QM allows ± 1/2^.5 = ± 0,7071, local realism predicts ±0.5 or less.

That graphic is exactly one of the reasons I asked you to provide a source.

 

 

Do you understand the mismatch argument, which is what tells you that this is the "perfect" classical detector?

[Lazarus]

(1 - cos) doesn't go negative. It does go above 1, which I think would also be a problem, as it seems you are trying to deal with the proportion of electrons determined to spin the "wrong" way.

 

That graphic is exactly one of the reasons I asked you to provide a source.

 

 

Do you understand the mismatch argument, which is what tells you that this is the "perfect" classical detector?

 

 

Mismatched Argument from Wikipedia

 

Consider three (highly correlated, and possibly biased) coin-flips X, Y, and Z, with the property that:

1. X and Y give the same outcome (both heads or both tails) 99% of the time
2. Y and Z also give the same outcome 99% of the time,

then X and Z must also yield the same outcome at least 98% of the time. The number of mismatches between X and Y (1/100) plus the number of mismatches between Y and Z (1/100) are together the maximum possible number of mismatches between X and Z (a simple Boole–Fréchet inequality).

 

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That is solid logic but doesn’t apply to the mismatches of the 1 degree rotation of the detectors in opposite directions. It applies to the “wrong way” detections but not to the mismatches.

When each detector shows 1 “wrong way” detection so there is no mismatch between the detectors, certainly not 2.

[uncool]

 

 

Mismatched Argument from Wikipedia

 

Consider three (highly correlated, and possibly biased) coin-flips X, Y, and Z, with the property that:

1. X and Y give the same outcome (both heads or both tails) 99% of the time
2. Y and Z also give the same outcome 99% of the time,

then X and Z must also yield the same outcome at least 98% of the time. The number of mismatches between X and Y (1/100) plus the number of mismatches between Y and Z (1/100) are together the maximum possible number of mismatches between X and Z (a simple Boole–Fréchet inequality).

 

-----------------------------

 

That is solid logic but doesn’t apply to the mismatches of the 1 degree rotation of the detectors in opposite directions. It applies to the “wrong way” detections but not to the mismatches.

When each detector shows 1 “wrong way” detection so there is no mismatch between the detectors, certainly not 2.

The mismatch isn't the difference in the number of detections of each type. The mismatch is the number of times the two detectors differ. If in one case, you see the first detector say "right way" and the second detector says "wrong way", while in another case you have the first say "wrong way" while the second says "right way", then that's two mismatches, no 0.

[Lazarus]

The mismatch isn't the difference in the number of detections of each type. The mismatch is the number of times the two detectors differ. If in one case, you see the first detector say "right way" and the second detector says "wrong way", while in another case you have the first say "wrong way" while the second says "right way", then that's two mismatches, no 0.

 

To made it easier to communicate, let’s set things up so when the detectors have the same orientation that both of the get the same result. When one detects the other one will, too. For convenience, start with them both vertical and just consider the vertically oriented particles. Turning either detector 1 degree will get some ”wrong way” detections. Now turn both detectors 1 degree in opposite directions. Each pair of vertical particles will fail to be detected by both. The result is that none of those pairs will cause a mismatch.

[swansont]

Now turn both detectors 1 degree in opposite directions. Each pair of vertical particles will fail to be detected by both.

 

Why?

[Lazarus]

 

Why?

 

Cause both detectors are off 1 degree from perfect alignment with their particle so both will detect the same number of "wrong way" particles. That means they will match.

[uncool]

 

Cause both detectors are off 1 degree from perfect alignment with their particle so both will detect the same number of "wrong way" particles. That means they will match.

No, it doesn't. As I said: The mismatch isn't the difference in the number of detections of each type.

 

There are times when one will record a "wrong way" when the other won't, and vice versa.

[Lazarus]

No, it doesn't. As I said: The mismatch isn't the difference in the number of detections of each type.

 

There are times when one will record a "wrong way" when the other won't, and vice versa.

 

 

If you divide everything up into 1 degree increments there are 46,656,000 possibilities with the orientation of the 2 detectors and the pairs. If we hold one of the detectors still that cuts it down to a mere 129,600 possibilities. We are talking about 1 of them.

 

In this case, when one detector accepts a wrong way particle the other will accept its partner and so no mismatch. That demonstrates that the application of the logic given does not apply to mismatched.

 

The experiments are statistical and we have 129,599 other possibilities to consider. Regardless of the other possibilities, this one case shows that there is a bad assumption in Bell’s Theorem.