Unghostly entanglement

[swansont]

If the results depend on the measurement design, then you have a poor design.

[Lazarus]

Hooray! We finally agree on something.

[swansont]

Hooray! We finally agree on something.

Since the Bell example does not depend on any convoluted detection scheme, it describes the underlying physics

[Lazarus]

The reason we have not been able to reach agreement is that not all the possibilities are being discussed. Using David Mermin’s explanation, which follows. a black and white distinction can be made.

 

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“Original Bell’s inequality

The inequality that Bell derived can be written as:^[4]

 

p(a,c ) - p(b,a) - p(b,c) < or = 1

 

where ρ is the correlation between measurements of the spins of the pair of particles and a, b and c refer to three arbitrary settings of the two analysers. This inequality is however restricted in its application to the rather special case in which the outcomes on both sides of the experiment are always exactly anticorrelated whenever the analysers are parallel. The advantage of restricting attention to this special case is the resulting simplicity of the derivation. In experimental work the inequality is not very useful because it is hard, if not impossible, to create perfect anti-correlation.

This simple form does have the virtue of being quite intuitive. It is easily seen to be equivalent to the following elementary result from probability theory. 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).

 

Imagine a pair of particles that can be measured at distant locations. Suppose that the measurement devices have settings, which are angles—e.g., the devices measure something called spin in some direction. The experimenter chooses the directions, one for each particle, separately. Suppose the measurement outcome is binary (e.g., spin up, spin down). Suppose the two particles are perfectly anti-correlated—in the sense that whenever both measured in the same direction, one gets identically opposite outcomes, when both measured in opposite directions they always give the same outcome. The only way to imagine how this works is that both particles leave their common source with, somehow, the outcomes they will deliver when measured in any possible direction. (How else could particle 1 know how to deliver the same answer as particle 2 when measured in the same direction? They don't know in advance how they are going to be measured...). The measurement on particle 2 (after switching its sign) can be thought of as telling us what the same measurement on particle 1 would have given.

 

Start with one setting exactly opposite to the other. All the pairs of particles give the same outcome (each pair is either both spin up or both spin down). Now shift Alice's setting by one degree relative to Bob's. They are now one degree off being exactly opposite to one another. A small fraction of the pairs, say f, now give different outcomes. If instead we had left Alice's setting unchanged but shifted Bob's by one degree (in the opposite direction), then again a fraction f of the pairs of particles turns out to give different outcomes. Finally consider what happens when both shifts are implemented at the same time: the two settings are now exactly two degrees away from being opposite to one another. 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.

 

Compare this with the predictions from quantum mechanics for the singlet state. For a small angle θ, measured in radians, the chance of a different outcome is approximately f = θ^2/2 as explained by small-angle approximation. At two times this small angle, the chance of a mismatch is therefore about 4 times larger, since 2^2 =4. But we just argued that it cannot be more than 2 times as large.

This intuitive formulation is due to David Mermin. The small-angle limit is discussed in Bell's original article, and therefore goes right back to the origin of the Bell inequalities.”

 

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We can agree that Quantum Theory predicts that the chance of a different outcome is approximately f = θ^2/2 and that experimental results have agreed with it.

 

A 2 degree rotation should agree with the f = θ^2/2 number. However, Two 1 degree rotations should just add because they are independent.

 

The question is “Were the experiments performed with a 2 degree rotation of one measuring device or 1 degree rotations of each measuring device?”.

[TJ McCaustland]

This isn't technically entanglement at all because you cannot define the result of either an up pin or a down pin by a single state because they are unentanglable, even if you had a situation where you had both an up pin and a down pin it still couldn't be defined by a single state because you're basically trying to define matter and antimatter by a single quantum state, it just doesn't work. You should research quantum entanglement and defining things with quantum states.

[Lazarus]

This isn't technically entanglement at all because you cannot define the result of either an up pin or a down pin by a single state because they are unentanglable, even if you had a situation where you had both an up pin and a down pin it still couldn't be defined by a single state because you're basically trying to define matter and antimatter by a single quantum state, it just doesn't work. You should research quantum entanglement and defining things with quantum states.

 

 

The point is that creating a scenario with bowling pins that gives the same results as Quantum entanglement questions whether or not the condition of the “Quantum” particles is really indeterminate while in flight.

[Strange]

Except it doesn't (and can't) give the same results.

[swansont]

The Bell discussion does not detail the detection method; IOW the detection is assumed to have no error. Your example does not appear to me to agree with that condition.

[Lazarus]

Except it doesn't (and can't) give the same results.

 

The Bell discussion does not detail the detection method; IOW the detection is assumed to have no error. Your example does not appear to me to agree with that condition.

 

Comparing bowling pins results with photon results:

 

BOWLING PINS

Two bowling balls are loaded into the chamber of a gun at a time, one vertical and the other horizontal. The chamber is spun, making the orientation of the pins undetermined but their relation of 90 degrees is constant. At some random time the pins are fired. Now the angle of rotation is determined but is unknown and the 90 degree relationship still holds.

 

PHOTONS

Radiation is split into two photons one polarized vertical and the other horizontal. The angle of rotation is undetermined but their 90 degree relationship is constant.

 

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BOWLING PINS

The detectors are rectangular holes that consider the pin detected if the pin passes through the hole without touching the edge. The vertical dimension of the hole is 1.5 times the length of the pin. The horizontal dimension is 0.99 times the length of the pin. The arriving pins have random variation of 0.1 times the length of the pin.

 

PHOTONS

The detectors measure the angle of polarization of the photons. The arriving photons have a random variation of 0.1 times the wave length of the photon.

 

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BOWLING BALLS

When the detectors are aligned with the arriving pins, there is a 100 percent match between the detectors. When one of the detectors is rotated 90 degrees there is a zero percent match. When one of the detectors is 2 degrees from alignment the number of mismatches will be 4 times as great as when the alignment is 1 degree off. The difference the horizontal distance available for the wrong way pins to get through is 4 times as great at 2 degrees as it is for 1 degree.

 

PHOTONS

When the detectors are aligned with the arriving photons polarization, there is a 100 percent match between the detectors. When one of the detectors is rotated 90 degrees there is a zero percent match. When one of the detectors is 2 degrees from alignment the mismatches are 4 times as many as when the alignment is 1 degree off.

 

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What is the difference?

[swansont]

Comparing bowling pins results with photon results:

 

BOWLING PINS

Two bowling balls are loaded into the chamber of a gun at a time, one vertical and the other horizontal. The chamber is spun, making the orientation of the pins undetermined but their relation of 90 degrees is constant. At some random time the pins are fired. Now the angle of rotation is determined but is unknown and the 90 degree relationship still holds.

 

PHOTONS

Radiation is split into two photons one polarized vertical and the other horizontal. The angle of rotation is undetermined but their 90 degree relationship is constant.

 

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

 

BOWLING PINS

The detectors are rectangular holes that consider the pin detected if the pin passes through the hole without touching the edge. The vertical dimension of the hole is 1.5 times the length of the pin. The horizontal dimension is 0.99 times the length of the pin. The arriving pins have random variation of 0.1 times the length of the pin.

 

PHOTONS

The detectors measure the angle of polarization of the photons. The arriving photons have a random variation of 0.1 times the wave length of the photon.

 

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

 

BOWLING BALLS

When the detectors are aligned with the arriving pins, there is a 100 percent match between the detectors. When one of the detectors is rotated 90 degrees there is a zero percent match. When one of the detectors is 2 degrees from alignment the number of mismatches will be 4 times as great as when the alignment is 1 degree off. The difference the horizontal distance available for the wrong way pins to get through is 4 times as great at 2 degrees as it is for 1 degree.

 

PHOTONS

When the detectors are aligned with the arriving photons polarization, there is a 100 percent match between the detectors. When one of the detectors is rotated 90 degrees there is a zero percent match. When one of the detectors is 2 degrees from alignment the mismatches are 4 times as many as when the alignment is 1 degree off.

 

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What is the difference?

Your detector details are irrelevant. We're talking about the underlying physics, so the detection is assumed to be perfect.

 

Why will a perfect detector of bowling pin orientation measure the wrong spin the fraction of time you claim it will?

[TJ McCaustland]

Your detector details are irrelevant. We're talking about the underlying physics, so the detection is assumed to be perfect.

 

Why will a perfect detector of bowling pin orientation measure the wrong spin the fraction of time you claim it will?

You cannot have technically have perfection in physical reality just as you cannot have a perfect, neutral, temperature of perfectly and exactly 0 degrees. This isn't entanglement at all because you're dealing basically with matter and antimatter, which are unentangleable, a down pin and an up pin cannot exist at the same time so you cannot have entaglement, If you had a 2 barreled cannon THEN you could have entanglement because you would need to predict 2 results which is a "cooexistence" scenario instead of an either or "Annihilation" scenario.

[swansont]

You cannot have technically have perfection in physical reality just as you cannot have a perfect, neutral, temperature of perfectly and exactly 0 degrees. This isn't entanglement at all because you're dealing basically with matter and antimatter, which are unentangleable, a down pin and an up pin cannot exist at the same time so you cannot have entaglement, If you had a 2 barreled cannon THEN you could have entanglement because you would need to predict 2 results which is a "cooexistence" scenario instead of an either or "Annihilation" scenario.

So? We're talking about the theory, not the physical manifestation of the experiment. And nobody has brought up antimatter in this thread except you, so how is it that we're talking about it?

[TJ McCaustland]

So? We're talking about the theory, not the physical manifestation of the experiment. And nobody has brought up antimatter in this thread except you, so how is it that we're talking about it?

Because that's the scenario, it's an "Or" scenario, not an "And/or" scenario, which means that it's one again an Annihilation scenario instead of a coeexistence scenario which pertains to the realm of physics involving antimatter vs matter destruction of matter and antimatter even though it seems to not be related to the OP I'm just pointing out that entanglement cannot exist in the given scenario of the OP.

[Lazarus]

Swansont said:

Your detector details are irrelevant. We're talking about the underlying physics, so the detection is assumed to be perfect.

 

Lazarus said:

The formula f = A^2/2, where f is the number of unmatched items and A is the angle of rotation, dictates different values for f when each measuring device is rotated 1 degree in opposite directions rather than one measuring device rotated 2 degrees. That is f = 2*1^2/2 = 1 for 1 degree vs f = 2^2/2 = 4 for 2 degrees. The 2 separate rotations are independent so must add to get the total number of mismatches. Experimental or theoretical corroboration of that would weaken Bell’s Inequality Theorem. Has that experiment been performed?

 

Swansont said:
Why will a perfect detector of bowling pin orientation measure the wrong spin the fraction of time you claim it will?

 

Lazarus said:

The detectors are rectangular holes that consider the pin detected if the pin passes through the hole without touching the edge. The vertical dimension of the hole is 1.5 times the length of the pin. The horizontal dimension is 0.99 times the length of the pin. The arriving pins have random variation of 0.1 times the length of the pin.

 

 

 

 

When the rectangle is rotated the horizontal distance across it is equal to the width of the rectangle divided by the cosine of the angle of rotation. With the width = d0, the horizontal distance across with a rotation of 1 degree = d1 and with a rotation of 2 degrees = d2, d1 = d0/cosine(1) and d2 = do/cosine(2). Since d1 = d0*1.0001523 and d2 = d0*1.0006095 it follows that the increase in length of the horizontal distance across is 4 times as great for a rotation of 2 degrees as it is for a rotation of 1 degree.

[swansont]

Swansont said:

Your detector details are irrelevant. We're talking about the underlying physics, so the detection is assumed to be perfect.

 

Lazarus said:

The formula f = A^2/2, where f is the number of unmatched items and A is the angle of rotation, dictates different values for f when each measuring device is rotated 1 degree in opposite directions rather than one measuring device rotated 2 degrees. That is f = 2*1^2/2 = 1 for 1 degree vs f = 2^2/2 = 4 for 2 degrees. The 2 separate rotations are independent so must add to get the total number of mismatches. Experimental or theoretical corroboration of that would weaken Bell’s Inequality Theorem. Has that experiment been performed?

 

There's no functional difference between the cases. It's just an angle difference.

 

Swansont said:

Why will a perfect detector of bowling pin orientation measure the wrong spin the fraction of time you claim it will?

 

Lazarus said:

The detectors are rectangular holes that consider the pin detected if the pin passes through the hole without touching the edge. The vertical dimension of the hole is 1.5 times the length of the pin. The horizontal dimension is 0.99 times the length of the pin. The arriving pins have random variation of 0.1 times the length of the pin.

 

 

 

 

When the rectangle is rotated the horizontal distance across it is equal to the width of the rectangle divided by the cosine of the angle of rotation. With the width = d0, the horizontal distance across with a rotation of 1 degree = d1 and with a rotation of 2 degrees = d2, d1 = d0/cosine(1) and d2 = do/cosine(2). Since d1 = d0*1.0001523 and d2 = d0*1.0006095 it follows that the increase in length of the horizontal distance across is 4 times as great for a rotation of 2 degrees as it is for a rotation of 1 degree.

 

 

What part of not depending on the details of the detector did you not understand? The polarization explanation above did not depend on any material details of the detector. Having this rest on the detector design means the issue is with the detector, not the physics. Present an explanation that doesn't depend on how the detector actually works.

[Lazarus]

There's no functional difference between the cases. It's just an angle difference.

 

 

 

What part of not depending on the details of the detector did you not understand? The polarization explanation above did not depend on any material details of the detector. Having this rest on the detector design means the issue is with the detector, not the physics. Present an explanation that doesn't depend on how the detector actually works.

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Lazarus:

 

First, it has been claimed that no physical device could behave in the way that Quantum Theory dictates. That is what the bowling ball thing is all about..

 

Second, the above equation, f = theta squared divided by 2, shows that 2 degree rotation of one sensor gives a different result than 1 degee opposite rotation of both sensors as the sensors are independent.

 

Are you suggesting that the 2 sensors are not independent?

[swansont]

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Lazarus:

 

First, it has been claimed that no physical device could behave in the way that Quantum Theory dictates.

 

No, it's been claimed that the systems do not behave that way. Deliberately botching a detector design to give bad results is not the same thing.

"The detectors are rectangular holes that consider the pin detected if the pin passes through the hole without touching the edge. The vertical dimension of the hole is 1.5 times the length of the pin. The horizontal dimension is 0.99 times the length of the pin."

 

So if the detector is vertical and the pin is at 45 degrees to that, what happens? You detect it as vertical, even though it's not. All you've done is design a horrible detector. The photon detected with vertical polarization is actually vertically polarized.

What you've done is just an iota short of simply hardwiring perfect correlation into the detectors.

 

Second, the above equation, f = theta squared divided by 2, shows that 2 degree rotation of one sensor gives a different result than 1 degee opposite rotation of both sensors as the sensors are independent.

 

Are you suggesting that the 2 sensors are not independent?

 

The state of the particles is not independent. Moving the angle of the second detector re-defines what you would mean by zero for an entangled system. I don't think you are appreciating the details of the physics involved. You appear to be thinking about this classically.

[Lazarus]

The state of the particles is not independent. Moving the angle of the second detector re-defines what you would mean by zero for an entangled system. I don't think you are appreciating the details of the physics involved. You appear to be thinking about this classically.

 

Lazarus:

 

The rectangle hole sensor should work OK for 90 degree correlations and it is easy enough to make a 180 degree correlation but that is irrelevant because YOU ARE ABSOLUTELY CORRECT that the measuring device doesn’t matter in Bell’s Inequality Theorem.

 

What does matter is that Bell’s Theorem is based on the contention that the Quantum results cannot be matched by Classic physics but that is called into question. Here is a way to produce the same result without resorting to Quantum assumptions:

 

The assumptions are that the number of unmatched pairs are detected is proportional to the angle between the detectors between 0 to 90 degrees. From 90 to 180 degrees the matched and unmatched numbers are reversed so the results are symmetrical.

 

The conditions are that the Bob detector is stationary and the Alice detector is rotated and all the particles we are looking at are detected by the Bob detector as correct. At 1 degree the Alice detector receives 1 “wrong way” particle.

In the 1 to 2 degree range the Alice detector gets 2 wrong particles for a total of 3 particles.

 

For each 1 degree between 0 and 90 degrees all the Alice detectors wrong way particles are counted and added to a total. Since all of the Bob detectors are “right way” particles the number of unmatched pairs is equal to the Alice detectors total of wrong way particles for this degree of rotation. The total number of pairs is 8100. There are 45 pairs in each 1 degree.

 

Here are the results:

 

1 deg of Total

Deg Wrongs Wrongs Unmatched Fraction

0 0.000 0.000 0.000 0.000

1 1.000 1.000 44.000 0.000

2 2.000 3.000 88.000 0.000

3 3.000 6.000 132.000 0.001

4 4.000 10.000 176.000 0.001

5 5.000 15.000 220.000 0.002

6 6.000 21.000 264.000 0.003

7 7.000 28.000 308.000 0.003

8 8.000 36.000 352.000 0.004

9 9.000 45.000 396.000 0.006

10 10.000 55.000 440.000 0.007

11 11.000 66.000 484.000 0.008

12 12.000 78.000 528.000 0.010

 

44 44.000 990.000 1936.000 0.122

45 45.000 1035.000 1980.000 0.128

46 46.000 1081.000 2024.000 0.133

 

88 88.000 3916.000 3872.000 0.483

89 89.000 4005.000 3916.000 0.494

90 90.000 4095.000 3960.000 0.506

91 89.000 4184.000 3916.000 0.517

92 88.000 4272.000 3872.000 0.527

 

177 3.000 8097.000 132.000 1.000

178 2.000 8099.000 88.000 1.000

179 1.000 8100.000 44.000 1.000

180 0.000 8100.000 0.000 1.000

 

 

Graphs of Quantum results and Classic results:

[TJ McCaustland]

Because that's the scenario, it's an "Or" scenario, not an "And/or" scenario, which means that it's one again an Annihilation scenario instead of a coeexistence scenario which pertains to the realm of physics involving antimatter vs matter destruction of matter and antimatter even though it seems to not be related to the OP I'm just pointing out that entanglement cannot exist in the given scenario of the OP.

Well at least not quantum entanglement, now seeing he posted a second variable of "Cannon rotation" We can have entanglement because now we have both X and Y to entangle. and not just X or Z.

Edited December 6, 2015 by TJ McCaustland

[Lazarus]

Well at least not quantum entanglement, now seeing he posted a second variable of "Cannon rotation" We can have entanglement because now we have both X and Y to entangle. and not just X or Z.

 

Thank you for the comments.

[Lazarus]

The essence of this discussion is that Bell’s Inequality Theorem relies on an unwarranted assumption. It assumes that the classic calculation of the number of “wrong way” detections in one of the detectors is linearly proportionate to the angle of rotation. There is no justification for that and it gives incorrect results. If the assumption were that the number of “wrong way” detections increased as the angle increased to the maximum, the result would be correct. That assumption is implicit in the Quantum calculation. If Bell’s Theorem is flawed Spooky Entanglement does not exist.

[Strange]

The essence of this discussion is that my understanding of Bell’s Inequality Theorem relies on an unwarranted assumption.

 

Fixed it for you.

 

You seem to have latched on to one aspect of one test of Bell's theorem and then totally misinterpreted/misunderstood it. For example, the link I posted earlier does not depend on any such linear relationship.

 

 

If Bell’s Theorem is flawed Spooky Entanglement does not exist.

 

No. Bell's Theorem just limits the possible explanations for entanglement.

[swansont]

The essence of this discussion is that Bell’s Inequality Theorem relies on an unwarranted assumption. It assumes that the classic calculation of the number of “wrong way” detections in one of the detectors is linearly proportionate to the angle of rotation. There is no justification for that and it gives incorrect results. If the assumption were that the number of “wrong way” detections increased as the angle increased to the maximum, the result would be correct. That assumption is implicit in the Quantum calculation. If Bell’s Theorem is flawed Spooky Entanglement does not exist.

 

Baloney. What you've done is shown that if you build a really crappy detector, you can get results that don't have good agreement with the theory. Because the detector is crappy. I can do a similar thing by leaving the lens cap on a telescope. But that doesn't disprove astronomical observations.

[Lazarus]

 

Baloney. What you've done is shown that if you build a really crappy detector, you can get results that don't have good agreement with the theory. Because the detector is crappy. I can do a similar thing by leaving the lens cap on a telescope. But that doesn't disprove astronomical observations.

 

We discussed the reason for the assumption of the linear relationship and you wanted the vertical change to be the deciding factor and I wanted the horizontal difference to be the choise. Would you clarify why your position is better?

[swansont]

 

We discussed the reason for the assumption of the linear relationship and you wanted the vertical change to be the deciding factor and I wanted the horizontal difference to be the choise. Would you clarify why your position is better?

 

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?