What is the physical significance of Bell's math?

[edguy99]

Sorry I don't see it. If there was no wobble wouldn't you get the expected number of matches?

Using expected was unclear. To clarify, with no wobble you get the "calculated" graph in post #48, ie. it does not match the reality of QM. With a wobble, you match the "experimental", ie. it matches the reality of QM.

 

[N88]

I gave what I consider a coherent definition of locality. The experiment could either be classical or quantum and could include EPR.
You might prefer: nielsen and chuang p.111

? Is p.111 meant to be included in the linked material (which appears to end at p.20)?

 

[Zafa Pi]

? Is p.111 meant to be included in the linked material (which appears to end at p.20)?

Indeed. That's why I didn't link directly to the pdf. It is just a different Bell Inequality, CHSH, but I really like the they write. Their book is great for me since it requires minimal physics.

If you like the "Jabberwocky" you may also like http://www.askamathematician.com/2009/12/q-howwhy-are-quantum-mechanics-and-relativity-incompatible/
then scroll down till you get to the posts of Stephen Tuck. It's like what a lot of physics sounds like to me.

 

[edguy99]

This has plenty of experimental errors, but can still disprove the Bell Equality (in this case). That is all that's necessary.
https://vcq.quantum.at/fileadmin/Publications/2002-12.pdf

You can go on line and find many with good accuracy.

Page 231: "A correlation circuit extracts only those events where all four detectors registered a photon
within a small time window of a few ns."

This condition will exclude all mismatched entangled pairs and can be modeled by a photon with a "wobble". ie. if you model the setup with a photon with a wobble, mis-matches will not be counted and you end up with the same statistics as QM.

 

[N88]

Indeed. That's why I didn't link directly to the pdf. It is just a different Bell Inequality, CHSH, but I really like the they write. Their book is great for me since it requires minimal physics.

If you like the "Jabberwocky" you may also like http://www.askamathematician.com/2009/12/q-howwhy-are-quantum-mechanics-and-relativity-incompatible/
then scroll down till you get to the posts of Stephen Tuck. It's like what a lot of physics sounds like to me.

Let me try it another way. Please: Do you mean that the material your refer to is in pp.111-117?

 

[Zafa Pi]

Page 231: "A correlation circuit extracts only those events where all four detectors registered a photon
within a small time window of a few ns."

This condition will exclude all mismatched entangled pairs and can be modeled by a photon with a "wobble". ie. if you model the setup with a photon with a wobble, mis-matches will not be counted and you end up with the same statistics as QM.

I think what they are doing is making sure that the photon that was sent was the the one received. It's not about noise. It's like I'm testing the weight of frogs and I exclude a fish that got into my sample. If you think I'm wrong (highly possible here) can you talk to me like I've been talking here. I don't follow what your wobble is about.

 

[Zafa Pi]

Let me try it another way. Please: Do you mean that the material your refer to is in pp.111-117?

Yes.

 

[N88]

I think what they are doing is making sure that the photon that was sent was the the one received. It's not about noise. It's like I'm testing the weight of frogs and I exclude a fish that got into my sample. If you think I'm wrong (highly possible here) can you talk to me like I've been talking here. I don't follow what your wobble is about.

Zafa Pi and edguy99: It's my impression that the photons (in the cited example) do NOT wobble. Rather: the detectors (in the cited example) are such [sic] that they collect widely-differing input-polarizations and direct them to a single output. I have yet to see where this idea breaches Bell's theorem.

 

[edguy99]

I think what they are doing is making sure that the photon that was sent was the the one received. It's not about noise. It's like I'm testing the weight of frogs and I exclude a fish that got into my sample. If you think I'm wrong (highly possible here) can you talk to me like I've been talking here. I don't follow what your wobble is about.

Absolutely I agree on the reason they do it. But.. by doing this they are assuming the the photon obeys the Bell assumption that entangled photons will match no matter the angle they are measured at. Assume that the polarization is represented by the normalized Jones vector.

By introducing a "wobble", we can make some sense out of the QM fact that these polarization are only the "best guess" (amplitude of probability if you like) of what you will measure the polarization as. QM tells us that if you create a vertical photon, you will alway detect a vertical photon if measured vertical. But if you create a vertical photon and measure it an a different angle (say 45 degrees), the result is probabilistic, as if there was a wobble in the orientation. The point is that a photon with a wobble, will not match the starting conditions of a Bell Test since Bob and Alice are not guaranteed to get matches when photons are measured off of their basis vectors. But a photon with a wobble will match QM if we do not use the entangled pairs that do not match at weird angles as many experiments do.

 

[Zafa Pi]

Zafa Pi and edguy99: It's my impression that the photons (in the cited example) do NOT wobble. Rather: the detectors (in the cited example) are such [sic] that they collect widely-differing input-polarizations and direct them to a single output. I have yet to see where this idea breaches Bell's theorem.

The Bell Theorem in this case is the GHZ Theorem, and the purpose of the paper is to refute the equality in the theorem in the lab as does QM in theory (which I do understand).
If you believe they failed talk it over with edguy99. it is really out of my realm.

 

[Zafa Pi]

Absolutely I agree on the reason they do it. But.. by doing this they are assuming the the photon obeys the Bell assumption that entangled photons will match no matter the angle they are measured at. Assume that the polarization is represented by the normalized Jones vector.

By introducing a "wobble", we can make some sense out of the QM fact that these polarization are only the "best guess" (amplitude of probability if you like) of what you will measure the polarization as. QM tells us that if you create a vertical photon, you will alway detect a vertical photon if measured vertical. But if you create a vertical photon and measure it an a different angle (say 45 degrees), the result is probabilistic, as if there was a wobble in the orientation. The point is that a photon with a wobble, will not match the starting conditions of a Bell Test since Bob and Alice are not guaranteed to get matches when photons are measured off of their basis vectors. But a photon with a wobble will match QM if we do not use the entangled pairs that do not match at weird angles as many experiments do.

I'm having difficulty following, but I think I can get it with some more thought.
I don't understand the ket notation a1 + a2i|x>: a1 is a number, a2i|x> is a vector, how do you add the two?

 

[N88]

The Bell Theorem in this case is the GHZ Theorem, and the purpose of the paper is to refute the equality in the theorem in the lab as does QM in theory (which I do understand).
If you believe they failed talk it over with edguy99. it is really out of my realm.

I was talking about edguy99's model, with its "wobbling" photons; not your case.

To be clear: In which case are we talking about GHZ?

Do you mean in the example given by your math without the equation numbers?

PS: Re GHZ, I have no problems under QM or experiment. But I do hold the view (in agreement with you, I take it), that the related "Bell theorem" departs from reality: ie, there are hypotheses in the math theorem which are validly violated via experiments, etc.

 

[edguy99]

I'm having difficulty following, but I think I can get it with some more thought.
I don't understand the ket notation a1 + a2i|x>: a1 is a number, a2i|x> is a vector, how do you add the two?

You don't really add them. The notation symbolizes that a1/a2 are on the x-axis and b1/b2 are on the y axis. There are a set of rules on how these are manipulated, but think of it as an axis of a spinning ball. The real numbers (a1,b1) are where you would detect the axis of spin or polarization (subject to this only being an amplitude of probability), if you were to measure it. (a2,b2) in front of the imaginary number i represents the "spin" of the photon (ie. where the axis of spin is going). The photon is a spin 1 particle, so that spin axis has 3 states, spinning left, spinning right or at a specific angle.

 

[stevendaryl]

I gave what I consider a coherent definition of locality. The experiment could either be classical or quantum and could include EPR.

The big assumption that EPR violates is Bell's notion of locality.

Basically: the probability of Bob getting a particular result can only depend on facts about Bob and his detector and the particle being measured by the detector.

The predictions of QM for EPR, in contrast, say that the probability of Bob's result can depend on Alice's result. That's what makes it nonlocal, in Bell's sense. Bob's result doesn't depend on Alice's choice, so EPR doesn't allow FTL communication, but it does depend on Alice's result.

We can picture it this way:

This picture represents regions of spacetime relevant for a single "round" of an EPR-type experiment. Region 1 is where (and when) Alice performs her measurement, and Region 2 is where Bob performs his measurement. Regions 3 and 5 are in the causal past of Alice (her "backwards lightcone"), and Regions 4 and 5 are in the causal past of Bob.

Locality in the sense of Bell says that Bob's result, in Region 2, can only depend on facts about his causal past, which means facts about regions 4 & 5. If Alice's result in Region 1 reveals information about Bob's result in Region 2, and that information is unavailable in Regions 4 & 5, then that means that the information is nonlocal in the sense of Bell.

That's exactly what EPR does. In the anti-correlated spin-1/2 version of EPR, if Alice in region 1 measures spin-up for her particle along axis \vec{\alpha}, then she immediately knows something about Bob's result in region 2: She knows that he did not (or will not, if it hasn't happened yet) measure spin-up along that axis. So this is definite information about Bob's result. And it is nonlocal in the sense that no amount of information about conditions in regions 4 and 5 can tell you this fact.

For comparison purposes, we can consider a classical analog of EPR: In Region 5, somebody (call him Charlie) takes a pair of shoes, takes two identical white shoe boxes, and puts one shoe in each box. Then he mixes up the boxes and sends one box to Alice and another box to Bob. Later, in region 1, Alice opens her box, and finds a left shoe. She immediately knows that Bob found (or will find, if it hasn't happened yet) a right shoe. So that's seemingly similar nonlocal information. However, in the classical case, it's not true that "no amount of information about conditions in regions 4 and 5 can tell you this fact". If you had a video of Charlie putting the shoes into boxes and shuffling them, then you could slow the video down. By paying close attention, you could figure out at each moment which box contained the left shoe and which box contained the right shoe. Then you could see which box was sent to Alice and which was sent to Bob. That would allow you to predict what result Bob would get, based only on facts about region 5.

The quantum version does not allow the prediction of Bob's result based on information about Region 5.

 

[DrChinese]

By introducing a "wobble", we can make some sense out of the QM fact that these polarization are only the "best guess" (amplitude of probability if you like) of what you will measure the polarization as. QM tells us that if you create a vertical photon, you will alway detect a vertical photon if measured vertical. But if you create a vertical photon and measure it an a different angle (say 45 degrees), the result is probabilistic, as if there was a wobble in the orientation. The point is that a photon with a wobble, will not match the starting conditions of a Bell Test since Bob and Alice are not guaranteed to get matches when photons are measured off of their basis vectors. But a photon with a wobble will match QM if we do not use the entangled pairs that do not match at weird angles as many experiments do.

1. There is no photon "wobble" and the idea is obviously in contradiction to observation. This is someone's personal theory.

2. There is no exclusion of entangled pairs that don't "match". All pairs meeting a pre-specified criteria are included, and it would not be scientific to do otherwise. What you have interpreted relates to another part of the apparatus (i.e. part of that pre-specified criteria), not the outcomes of the measured pairs themselves. Whether that criteria is reasonable or not is another question entirely.

At any rate, this has little to do with this thread. If you want to discuss a specific referenced experiment, we should really do that in another thread. I would be happy to add my 2 cents there.

 

[Zafa Pi]

The notation symbolizes that a1/a2 are on the x-axis and b1/b2 are on the y axis.

Now that I understand Jones vectors the problem is that the ket notation in post #69 is just wrong.
What is a1/a2. I hope you won't tell me that "/" is fake division, like + was fake sum.
In spite of what DrChinese said in post #75 I would like to know what your posts were trying show (in english). E.g. were you trying to show that Zeilinger et. al. were wrong, they didn't violate the GHZ identity? Are you trying to simulate QM classically? What? (don't use wobble)

 

[Zafa Pi]

The quantum version does not allow the prediction of Bob's result based on information about Region 5.

I'm not buying your post. Suppose back in region 5 someone created a pair of particles (maybe a positron and an electron) but can't tell which is which until measured, one always measures "up" and the other "down". So in particular that happens when when they are measured along the same axis as is only required in your post. Thus Bob's result cannot be predicted based on information about Region 5. No classicist would have a problem with that, the particles were born that way, hidden variables. The particles are like tiny shoes for atoms, too small to video, but cute nevertheless. All is local.

What EPR suggested was more complicated (as I'm sure you know). If A measured hers at 0 degrees and B measured at 90 degrees, she would know what B's measurement would have been if he measured at 0, and thus we would know what the values of B's particle at both measurements contradicting Heisenberg's Uncertainty Principle. There were hidden variables that allowed for this that QM didn't allow for and was thus incomplete. All was deterministic and local in their minds. Bohr disagreed, but nothing was settled until Bell & Aspect. At that point in heaven Bohr asked Einstein what he thought and E replied "God why have you forsaken me."

Now with respect to the measurements made on entangled particles in the Bell experiments, it appears to me that there are still physicists arguing both ways in regards to to locality. How does one go about proving non-locality if realism (= CFD) is denied?

 

[edguy99]

Now that I understand Jones vectors the problem is that the ket notation in post #69 is just wrong.
What is a1/a2. I hope you won't tell me that "/" is fake division, like + was fake sum.
In spite of what DrChinese said in post #75 I would like to know what your posts were trying show (in english). E.g. were you trying to show that Zeilinger et. al. were wrong, they didn't violate the GHZ identity? Are you trying to simulate QM classically? What? (don't use wobble)

The notation schemes can be quite confusing. This is a great video that can help you understand how it works:

 

[Zafa Pi]

The notation schemes can be quite confusing. This is a great video that can help you understand how it works:

You didn't answer my question, but instead gave me a trivial video that I thought was garbage.

 

[Boing3000]

You didn't answer my question, but instead gave me a trivial video that I thought was garbage.

Why do you think that video is garbage ? It actually answers your question about notations

then scroll down till you get to the posts of Stephen Tuck. It's like what a lot of physics sounds like to me.

Really ? Your example for what Physics sounds like to you is someone getting a perfect score on this ?

Beside your question have been answered many times. Bell's show that no theory using local feature (as perfectly explained by Stevendaryl) can match the result of quantum experiments.

 

[Nugatory]

I'm not buying your post. Suppose back in region 5 someone created a pair of particles (maybe a positron and an electron) but can't tell which is which until measured, one always measures "up" and the other "down". So in particular that happens when when they are measured along the same axis as is only required in your post. Thus Bob's result cannot be predicted based on information about Region 5. No classicist would have a problem with that, the particles were born that way, hidden variables. The particles are like tiny shoes for atoms, too small to video, but cute nevertheless. All is local.

You are misunderstanding Stevendaryl's point (which you will find made in more detail in one of Bell's essays in "Speakable and Unspeakable"). Locality is not a matter of what information we have about regions 4 and 5, but rather what information is in principle available about those regions - that is, a complete specification of the physical state. Classically, that would include the spin that hasn't yet been measured.

How does one go about proving non-locality if realism (= CFD) is denied?

You don't, at least as far as Bell's inequality is concerned. A violation of the inequality shows that at least one of the two assumptions is wrong, but not which one.

 

[stevendaryl]

I'm not buying your post. Suppose back in region 5 someone created a pair of particles (maybe a positron and an electron) but can't tell which is which until measured, one always measures "up" and the other "down". So in particular that happens when when they are measured along the same axis as is only required in your post.

It doesn't matter whether someone "can't tell". The question is whether the information exists. If in Region 5, there is a difference between positrons and electrons, then that is information available in Region 5. You could imagine that there IS no difference between electrons and positrons until you measure them. That's the approach that some people take to QM (not about electron versus positron, but about other properties.)

Thus Bob's result cannot be predicted based on information about Region 5.

It doesn't matter whether Bob can know the information. The point is that the information is a fact about Region 5. It might be that Bob doesn't learn the information until later, and has to retrodict that the particle had a particular property in Region 5. That's the really the whole point of Bell's analysis, to be able to take into account "hidden" properties that we don't know how to measure, but that affect future measurements.

No classicist would have a problem with that, the particles were born that way, hidden variables. The particles are like tiny shoes for atoms, too small to video, but cute nevertheless. All is local.

Yes, and the diagram proves that it's local. The important property has a value in Region 5, even if it's not observable.

What EPR suggested was more complicated (as I'm sure you know). If A measured hers at 0 degrees and B measured at 90 degrees, she would know what B's measurement would have been if he measured at 0, and thus we would know what the values of B's particle at both measurements contradicting Heisenberg's Uncertainty Principle.

I don't agree that that is a more complicated case. I hate it when people talk about counterfactual definiteness, because to me that sends people off onto a philosophical and meaningless discussion about whether counterfactual definiteness is a desirable property, or what it means, and whether nondeterministic theories are counterfactually definite. It's a mess that doesn't make any difference. It's a red herring.

To say that Alice knows what value Bob would have gotten if he had measured along a different axis is just to say that Alice something about Bob's situation: You know that a certain combination of Bob's detector setting and Bob's result did NOT happen. So forget about counterfactual definiteness---Alice knows something about Bob that was not available in the region 5. It's nonlocal information.

Look, this way of describing things is not new with me--it's Bell's "Theory of nonlocal beables", which was his attempt at explaining the idea behind his inequality.

 

[Zafa Pi]

Why do you think that video is garbage ? It actually answers your question about notations

If you look at post #71 where I asked about notation. I was asking about the ket notation in post #69 that read: a1 + a2i|x> + b1 + b2i|y>. After reading the definition of a Jones vector it became immediately apparent that the notation was flawed, it had a glaring typo. That neither you or edguy99 could see that I find telling.

Why I find the video insulting and garbage is off topic. Try a new thread.

The question I asked edguy99 that wasn't answered was at the bottom of post #76. But that's ok I am no longer interested.

 

[edguy99]

If you look at post #71 where I asked about notation. I was asking about the ket notation in post #69 that read: a1 + a2i|x> + b1 + b2i|y>. After reading the definition of a Jones vector it became immediately apparent that the notation was flawed, it had a glaring typo. That neither you or edguy99 could see that I find telling.

Why I find the video insulting and garbage is off topic. Try a new thread.

The question I asked edguy99 that wasn't answered was at the bottom of post #76. But that's ok I am no longer interested.

There is no error. a1+a2i is a complex number as is b1+b2i.

 

[Nugatory]

There is no error. a1+a2i is a complex number as is b1+b2i.

So we're supposed to read it as $(a_1+ia_2)|x\rangle$?

 

[edguy99]

So we're supposed to read it as $(a_1+ia_2)|x\rangle$?

Absolutely.

 

[Zafa Pi]

So we're supposed to read it as $(a_1+ia_2)|x\rangle$?

Thank you.

 

[Zafa Pi]

Really ? Your example for what Physics sounds like to you is someone getting a perfect score on this ?

Thanks for referencing Baez's Crackpot Test, it's apt and funny. Indeed Tuck would get a perfect score.

Beside your question have been answered many times. Bell's show that no theory using local feature (as perfectly explained by Stevendaryl) can match the result of quantum experiments.

Your grammar is a bit dicey, but if I understand it correctly then I disagree. Eventually I'll discuss why.

 

[Zafa Pi]

Alice knows something about Bob that was not available in the region 5. It's nonlocal information.

The quantum version does not allow the prediction of Bob's result based on information about Region 5.

1) I take you post #74 as a stand alone statement. If it needs to be augment by "Speakable and Unspeakable" (suggested by Nugatory) or something else then perhaps we should start a new thread.

2) When I use the term measure I mean along the axisα, the only one employed in your post. (I think this a problem)

3) In this item I will narrate as I think a classical physicist, say E, would address your post.
All the information is available in region 5 under any circumstance. If, for example, two electrons are produced there with opposite up and down, then Bob's, as an element of reality, will either be up or down. I can measure Bob's to find out, and we will know what each will get in regions 1 & 2. It's just like looking in the shoe box to see which shoe Bob will get. Hence there is no non-local phenomena going on.

4) Bell says in the paper cited by OP, "It is the requirement of locality, or more precisely that the result of a measurement on one system be unaffected by operations on a distant system with which it has interacted in the past, that creates the essential difficulty . " However, all I see him do is assume locality then show QM and hidden variables are incompatible. It is the same as in post #54, answered in #60.
At the bottom of post #81 Nugatory indicates one cannot prove non-locality as far as Bell's inequality is concerned. And I have said that many times as well.

So I hope my issues are laid out in a clearer fashion and I look forward to some clear criticism.

 

[stevendaryl]

1) I take you post #74 as a stand alone statement. If it needs to be augment by "Speakable and Unspeakable" (suggested by Nugatory) or something else then perhaps we should start a new thread.

I was paraphrasing it to make it stand-alone. I only brought up Bell because the notion of "local" I'm talking about IS Bell's notion.

3) In this item I will narrate as I think a classical physicist, say E, would address your post.
All the information is available in region 5 under any circumstance.

Yes, that's what a classical physicist would say, and it's what Bell proved is not true.

If, for example, two electrons are produced there with opposite up and down, then Bob's, as an element of reality, will either be up or down. I can measure Bob's to find out, and we will know what each will get in regions 1 & 2. It's just like looking in the shoe box to see which shoe Bob will get. Hence there is no non-local phenomena going on.

You know that that's not true of EPR, though. Bob is free to change his detector settings after the particles have left Region 5. Alice is free to change her detector settings after the particles have left Region 5. But regardless of when they choose their detector settings, if Alice measures spin-up along axis \vec{a} Alice finds out something about Bob's measurement that was not available in Region 5: that Bob did not (or will not) measure spin-up along axis \vec{a}.

At the bottom of post #81 Nugatory indicates one cannot prove non-locality as far as Bell's inequality is concerned. And I have said that many times as well.

I'm just saying that I think you're wrong. If nonlocality is defined in Bell's terms, then QM is either nonlocal, or one of the weird acausal interpretations (superdeterminism, back-in-time causality) must be true.

The issue, as I said, is: Does Alice's measurement in Region 1 give information about Region 2 that was unavailable in Region 5? It appears to, in the case of EPR, unless both Bob's future measurement and his future measurement result are determined in Region 5. That's a possibility, but that's the superdeterminism loophole.