Does Quantum Entanglement Imply Faster-Than-Light Interaction?

[afstgl]

Hi there, I've recently read some material on QM and entanglement in particular, and even thou I managed to understand the material I felt like it didn't contain the answer to one fairly simple question...

When an entangled pair is produced, conservation of energy laws cause the members of the pair to be anti-correlated, member A is always complimentary or opposite of member B, be that spin, position of whatever. According to the entanglement theory, measuring the property of A immediately sets the property of B, which implies a change in B occurs upon measurement of A, but I don't really see it this way - since A and B have been produced anti-correlated, measurement of A doesn't change B in any way, it just indirectly defines B as the opposite of A, nothing really changes in B, it has been the same from the moment of production, the only thing that changes is that initial state of B is now known through the measurement of A.

In the same logic, I can take a white and black lab mice, put them in identical boxes, shuffle the boxes to the point it is unknown which box holds the while and which box holds the black one, send one to China, the second to the US, opening either of the boxes and inspecting its content will immediately define the content of the other box, no matter the distance in between, but does that mean the two mice are entangled? I don't think so...

My question is: What exactly suggests any FTL interaction between entangled particles or change if any of them takes place upon measurement?

 

[SpectraCat]

Hi there, I've recently read some material on QM and entanglement in particular, and even thou I managed to understand the material I felt like it didn't contain the answer to one fairly simple question...

When an entangled pair is produced, conservation of energy laws cause the members of the pair to be anti-correlated, member A is always complimentary or opposite of member B, be that spin, position of whatever. According to the entanglement theory, measuring the property of A immediately sets the property of B, which implies a change in B occurs upon measurement of A, but I don't really see it this way - since A and B have been produced anti-correlated, measurement of A doesn't change B in any way, it just indirectly defines B as the opposite of A, nothing really changes in B, it has been the same from the moment of production, the only thing that changes is that initial state of B is now known through the measurement of A.

In the same logic, I can take a white and black lab mice, put them in identical boxes, shuffle the boxes to the point it is unknown which box holds the while and which box holds the black one, send one to China, the second to the US, opening either of the boxes and inspecting its content will immediately define the content of the other box, no matter the distance in between, but does that mean the two mice are entangled? I don't think so...

My question is: What exactly suggests any FTL interaction between entangled particles or change if any of them takes place upon measurement?

First of all, entangled states do not have to be anti-correlated .. they can also be correlated. The correlation (or anti-correlation) between the entangled properties has nothing to do with conservation of energy.

Second, you made (at least) one other incorrect statement in your description ... namely, the statement

nothing really changes in B, it has been the same from the moment of production

This is not true. If A & B are in an entangled state, then you cannot say anything about the states of the individual particles, you can only describe the overall entangled state. Only after the entangled state has been measured do the individual particles assume well-defined states. This is the prediction of QM, and it has been verified many times in experimental contexts. Your phrasing of the problem is equivalent to a "local hidden variables" theory, which has been ruled out via a series of really neat experiments. You can learn more about this from the links on Dr. Chinese's website (www.DrChinese.com).

Anyway, if you read about those experiments, and about Bell's Theorem, you should be able to understand why the case of entanglement is NOT the same as the mouse example you posted.

 

[afstgl]

Sorry, it is poor English skills, I used anti-correlated as a synonym of complimentary, but I see now it wasn't appropriate...
Why can't I say anything about the states of the individual particles? All in all, there is a 50/50 chance of any of them being in a given state with the other being the oposite, just because WE DON'T know doesn't mean the particles are undetermined from the moment of their creation, or does it?

This is what I fail to understand, why does entanglement theory assumes particle B is in an undetermined state and only gets determined upon measurement of A? Again, just because we don't know the state of B doesn't mean B itself doesn't know its state and decides AND assumes that state the moment A is measured in some FTL interaction. B is NEVER undetermined, it is ALWAYS complimentary to A from the moment it is "born", it is only US as observers that aren't unaware of the states of individual particles until we measure one.

This goes back to Schrödinger's cat - just because an observer is obstructed from observing doesn't really put the cat in a state of superposition, it is never both dead and alive, it is EITHER dead or alive, no matter of the uncertainty of an observer. Also the cat itself is an observer to begin with, logically Schrödinger's cat example is never in a state of superposition since the cat collapses it, since it knows whether it is alive...

I guess what I am trying to say the view of superposition is not an objective property, it is subjective to an observer, but in the objective sense there is no superposition, even if we refuse to individually concern ourselves with particles A and B, the particles have their fixed states all along in what we conceive as entanglement and view as a composite state of superposition...

I don't think A and B are stateless just because we don't know their states, that is all... A and B always have their complimentary states. I fear this is more of a philosophical rather than a scientific matter, I understand the actual experiments being performed, their statistical results and such... The results make perfect sense and all, but I just don't see any evidence of any process taking place in the moment of observation of A that induces a response in B over distance

you made (at least) one other incorrect statement in your description ... namely, the statement

nothing really changes in B, it has been the same from the moment of production

Well, considering the question I asked was referring to that same statement, it shouldn't really be conceived as a statement, but a question without a question mark, I mean the answer to my question is what would make this statement incorrect, and that was what I was hoping to get - what makes TRUE the statement that any objective change in B occurs in the moment of disentanglement, in order to differentiate B from the state it assumed in the moment of its production?

You make it sound like individually, A and B do not physically exist prior to observation, like it is not two entangled particles BUT a sole entanglement, which morphs into two particles upon measurement, which is purely conceptual and subjective view, especially since experiments involve separating A from B we do have two individual particles with their appropriate states all along, those are just unknown prior to measurement.

All in all, entanglement is presented to be some link, one that cannot transfer information and "disappears" upon any attempt to verify it... which is kind of counter-intuitive, I could just as easily have an imaginary friend, one that can't talk and disappears every time someone tries to look at him...

Let's say we measure A and it is spin up, which logically makes B spin down, how do we know B "became" spin down in the moment of measurement of A and wasn't spin down prior to it, especially since we have only one measurement allowed?

I don't claim anything, nor try to redefine anything, I just hope things get explained to me, I have read quite a lot prior to asking those questions and I still see an inconsistency, a gaps filled by what seems like an assumption (represented by all BOLD text), and I doubt I am that stupid I failed to get it, but who knows...

 

[SpectraCat]

Sorry, it is poor English skills, I used anti-correlated as a synonym of complimentary, but I see now it wasn't appropriate...



Why can't I say anything about the states of the individual particles? All in all, there is a 50/50 chance of any of them being in a given state with the other being the oposite, just because WE DON'T know doesn't mean the particles are undetermined from the moment of their creation, or does it?

This is what I fail to understand, why does entanglement theory assumes particle B is in an undetermined state and only gets determined upon measurement of A? Again, just because we don't know the state of B doesn't mean B itself doesn't know its state and decides AND assumes that state the moment A is measured in some FTL interaction. B is NEVER undetermined, it is ALWAYS complimentary to A from the moment it is "born", it is only US as observers that aren't unaware of the states of individual particles until we measure one.

This goes back to Schrödinger's cat - just because an observer is obstructed from observing doesn't really put the cat in a state of superposition, it is never both dead and alive, it is EITHER dead or alive, no matter of the uncertainty of an observer. Also the cat itself is an observer to begin with, logically Schrödinger's cat example is never in a state of superposition since the cat collapses it, since it knows whether it is alive...

I guess what I am trying to say the view of superposition is not an objective property, it is subjective to an observer, but in the objective sense there is no superposition, even if we refuse to individually concern ourselves with particles A and B, the particles have their fixed states all along in what we conceive as entanglement and view as a composite state of superposition...

I don't think A and B are stateless just because we don't know their states, that is all... A and B always have their complimentary states. I fear this is more of a philosophical rather than a scientific matter, I understand the actual experiments being performed, their statistical results and such... The results make perfect sense and all, but I just don't see any evidence of any process taking place in the moment of observation of A that induces a response in B over distance



Well, considering the question I asked was referring to that same statement, it shouldn't really be conceived as a statement, but a question without a question mark, I mean the answer to my question is what would make this statement incorrect, and that was what I was hoping to get - what makes the statement that any objective change in B occurs in the moment of disentanglement, in order to differentiate B from the state it assumed in the moment of its production?

You make it sound like individually, A and B do not physically exist prior to observation, like it is not two entangled particles BUT a sole entanglement, which morphs into two particles upon measurement, which is purely conceptual and subjective view, especially since experiments involve separating A from B we do have two individual particles with their appropriate states all along, those are just unknown prior to measurement.

All in all, entanglement is presented to be some link, one that cannot transfer information and "disappears" upon any attempt to verify it... which is kind of counter-intuitive, I could just as easily have an imaginary friend, one that can't talk and disappears every time someone tries to look at him...

Again, I suggest you start reading about the EPR paradox and Bell's theorem, to help guide your questions. The link I gave to DrChinese's website is a great place to start.

 

[afstgl]

You seem to have quoted my entire post without even reading it, since if you did read it, you'd notice I mentioned that I have already read and understood the material you advice me to read prior to posting, including the articles of DrChinese, perhaps you could be at least helpful enough to provide more specific pointers that contain the answer I am asking for?

I particularly fail to see a major problem with a "hidden variable theory" which seems to be the issue I am addressing... we can't reach full vacuum, we can't reach absolute zero, there are always tons of factors which are way too much and too small to be accounted for, giving a certain degree of an illusion of randomness, meaning on such a small scale it would be impossible to come up with a certain result even if we know all the hidden variables, such an experiment would be unable to model within 100% accuracy, but this doesn't mean classical physics fails at small scales, it just means unaccountably small factors get too prominent

 

[SpectraCat]

You seem to have quoted my entire post without even reading it, since if you did read it, you'd notice I mentioned that I have already read and understood the material you advice me to read prior to posting, including the articles of DrChinese, perhaps you could be at least helpful enough to provide more specific pointers that contain the answer I am asking for?

Well, you may have read some of those links, but your post makes it clear that you have not yet understood them. In fact, I couldn't tell that you had read them at all from your previous post.

1) Entanglement works as I have already described .. I can't explain it any better than that. Your ideas about the "reality" of the particles in the entangled state fall under the realm of interpretations of QM, which can be instructive, but do not give conclusive answers about questions like this one. My view is, there are no known measurements (there may not even be any theoretically possible ones) we can do to ascertain the "reality" of the particles in an entangled state without destroying the entanglement, so why bother worrying about it?

2) There is no way to explain the experimental results of Aspect, or the more recent ones of Zeilinger, with a local realistic model where the properties of the particles are determined at creation. I suggest that you read those papers more carefully to understand why this is the case. Very briefly, the significant experimental result is that the coincidence statistics only depend on the *relative* angle between the polarizers used to measure A and B. If the polarization states of the particles were well-defined before the measurement, then this would define a "preferred basis" for the polarization measurements, and the coincidence statistics would show a more complicated dependence on the settings of the detectors at A and B.

I particularly fail to see a major problem with a "hidden variable theory" which seems to be the issue I am addressing... we can't reach full vacuum, we can't reach absolute zero, there are always tons of factors which are way too much and too small to be accounted for, giving a certain degree of an illusion of randomness, meaning on such a small scale it would be impossible to come up with a certain result even if we know all the hidden variables, such an experiment would be unable to model within 100% accuracy, but this doesn't mean classical physics fails at small scales, it just means unaccountably small factors get too prominent

I suggest that you read David Mermin's excellent article, "Is the moon there when nobody is looking?", which was published in Physics Today in 1985. You can find it http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.110.8947&rep=rep1&type=pdf". That should help you better understand why QM is incompatible with local hidden variable theories.

I also suggest reading the original EPR paper (you can find it on Dr C's website), or re-reading it if you have already looked at it. It gives a very clear statement of the issues related to the questions you are asking.

 

[mathal]

what makes TRUE the statement that any objective change in B occurs in the moment of disentanglement, in order to differentiate B from the state it assumed in the moment of its production?

You make it sound like individually, A and B do not physically exist prior to observation, like it is not two entangled particles BUT a sole entanglement, which morphs into two particles upon measurement, which is purely conceptual and subjective view, especially since experiments involve separating A from B we do have two individual particles with their appropriate states all along, those are just unknown prior to measurement.

All in all, entanglement is presented to be some link, one that cannot transfer information and "disappears" upon any attempt to verify it... which is kind of counter-intuitive, I could just as easily have an imaginary friend, one that can't talk and disappears every time someone tries to look at him...

Try thinking of entanglement as a 'state' that two particles share that is independant of space and independant of time. It 'exists' in each particle for a particular period of time in particular places but has only two pertinent 'points' in time/space for each particle- the entanglement and the collapse of the entanglement. In a very 'real' sense one particle is 'still' entangled until it has been measured in some way even long after the 'first' particle's state collapses to a measured condition. As long as the same entangled property of both particles is measured, the entanglement will be confirmed. It is our temporal nature to ascribe the collapse to the 'first' measurement over the 'second' collapse -but they are on an equal footing. There is no causal relationship between the two collapses. They are the same collapse occurring at two different time/space locations, that is all.

Mathal

 

[afstgl]

The thing that is troubling me is the scientific consensus is pro-entanglement without actually being able to explain its operational mechanics, it seems like a HUGE assumption to swallow, what is worse - kind of dogmatic - "no one knows why and how, but it happens". The fact it is claimed to be an FTL interaction makes things all that much worse, making it far too "far fetched" to be accepted in a dogmatic manner, without an actually explanation how does this process exactly occur.

It may be just me, but I have to know how stuff works and cannot settle for the "well, it just works" view - not only the mechanics of a process must be explained but should also be plausible and simple enough to work flawlessly - we all know the more complex the mechanic the more often it breaks - and from my experience the universe is quite stable.


Mathal - you mean partial collapse? Like for example, two entangled particles can have their Z entanglement broken, but only it and otherwise remain entangled so that those same particles can be measured along Y and having their Y entanglement broken and so on, a sort of "thread by thread" disentanglement?

 

[DrChinese]

...This is what I fail to understand, why does entanglement theory assumes particle B is in an undetermined state and only gets determined upon measurement of A? Again, just because we don't know the state of B doesn't mean B itself doesn't know its state and decides AND assumes that state the moment A is measured in some FTL interaction. B is NEVER undetermined, it is ALWAYS complimentary to A from the moment it is "born", it is only US as observers that aren't unaware of the states of individual particles until we measure one...

I don't claim anything, nor try to redefine anything, I just hope things get explained to me, I have read quite a lot prior to asking those questions and I still see an inconsistency, a gaps filled by what seems like an assumption (represented by all BOLD text), and I doubt I am that stupid I failed to get it, but who knows...

Welcome to PhysicsForums!

SpectraCat has given you some good information, perhaps I can add to that a bit. Your mice example happens to fit the same situation as entangled particles. So that is why it seems to make sense to you. Unfortunately, there are a limited number of cases it does work. Actually, there are cases in which it turns out there is no possibility your example will match the predictions of QM. That is what Bell discovered.

The Mermin example is good, and I have a variation of it on my website. If you don't follow the thinking, I will try to walk you through it. Needless to say, your concept was in fact in vogue from 1935 to 1965 before Bell came along.

But consider this: if you use measurements at 0, 120 and 240 degrees instead of 0 and 90 degrees, what would you expect with a hidden variable model? Some kind of mixture of properties, correct?

 

[San K]

In a very 'real' sense one particle is 'still' entangled until it has been measured in some way even long after the 'first' particle's state collapses to a measured condition. As long as the same entangled property of both particles is measured, the entanglement will be confirmed. It is our temporal nature to ascribe the collapse to the 'first' measurement over the 'second' collapse -but they are on an equal footing. There is no causal relationship between the two collapses. They are the same collapse occurring at two different time/space locations, that is all.

Mathal

Hi Mathal,

you got me curious

i can understand the different space part, but not the time part.

1. one version/understanding/hypothesis is:

when one of the entangled pair is measured the wave-function collapses, i.e. the other twin also assumes a definite state at the same instant in time

2. the other could be what you are saying...same collapse happening at different time/space...

3. there are more hypothesis/explanations

however right now, I am trying to understand what you mean when you say that both the particles don't collapse at the same time because to me 1 above explains the results of the delayed choice quantum eraser DCQE "completely", then why assume 2?

also why assume/state there is no casual relationship?

the way I understand is, and I am open to new logic, that this casual relationship "transcends/is outside" time-space and its instantaneous?

 

[SpectraCat]

The thing that is troubling me is the scientific consensus is pro-entanglement without actually being able to explain its operational mechanics, it seems like a HUGE assumption to swallow, what is worse - kind of dogmatic - "no one knows why and how, but it happens". The fact it is claimed to be an FTL interaction makes things all that much worse, making it far too "far fetched" to be accepted in a dogmatic manner, without an actually explanation how does this process exactly occur.

That is a mis-representation of the scientific consensus on entanglement .. it is not dogmatic at all in general .. in fact, these are some of the most oft-challenged, and experimentally tested foundational ideas in QM. The reason people accept that the QM description of entangled states is correct is because it is has been shown to be consistent with every experimental result obtained to date.

Furthermore, you should be precise when saying that there is a claim of "FTL interaction". The "speed" at which the collapse of an entangled state happens has been shown experimentally to be many orders of magnitude faster than the speed of light. Since we tend to think of interactions with measurement apparatus as happening locally, it is hard to understand how a local interaction at one end of an entangled state can "instantaneously" determine a result another spatial region containing the entangled state that is separated from the measurement region by a space-like interval.

This is why people have proposed that *something* must be transmitted FTL between the two regions of the entangled state. However we can state with certainty that any such "transmission" does not involve photons, or EM fields, or mass, or any "normal" entity that can be used to carry information between spatial locations. For example, even within the theoretical framework of QM, there is no way to use this mechanism for FTL communication, so it seems that entanglement and the collapse of entangled states does not raise a conflict between QM and special relativity.

It may be just me, but I have to know how stuff works and cannot settle for the "well, it just works" view - not only the mechanics of a process must be explained but should also be plausible and simple enough to work flawlessly - we all know the more complex the mechanic the more often it breaks - and from my experience the universe is quite stable.

Well, if you really want to know how entanglement works (and I can appreciate that sentiment), and you are not satisfied with the answers that have been turned up so far, then perhaps you could consider a career in scientific research studying these questions in more detail. The rest of that statement is your personal prejudice I am afraid... my view is that the universe is how we find it to be. I appreciate a simple mechanism as much as the next person, but sometimes things are NOT simple.

 

[afstgl]

Sure, entanglement is an experimentally verified and accepted property of nature, but I find it strange that no one seems to have even the slightest idea how exactly does it work. In this regard, does entanglement have any parallels - any other process, which takes place without any insight of its mechanics? It just doesn't seem to be in accordance with the scientific approach, for if something happens then there must be a mechanic through which it happens, otherwise it is taking it for granted, something more typical in the area of theology...

It is not even known what is that "something" which travels orders of magnitude over luminal, neither how does that "something" achieve that velocity... on the other hand, hidden variable theories may be able to explain the phenomenon without using mysterious entities, traveling in mysterious ways...



As for complexity - there are two types of it - the first is complexity of systems that are made of lots of simple components that are easy to understand on their own - like a CPU for example - a modern CPU contains billions of transistors, in numerous circuits, combined into higher and higher order circuits, the system is complex but based on transistors which are not complex at all - this same type of complexity seems to apply to everything else - physics, chemistry, biology and so forth. And then we have the "other" type of complexity, which is not due to "stacking" of numbers of less complex units, but is simply complex, such complexity that is typical to theoretical areas of science that rarely yield in any practical applications.

I am much more prone to embracing the first type of complexity, because it is plausible and practical, it works without assumptions and even thou complex is also consistent. IMO this type of complexity is a much better candidate for explaining test results, even if it employs millions or even billions of hidden variables, but with the entanglement theory it is the second type of complexity, a matter so complex no one even comes close to suggesting how it actually works, instead people just go with it, simply because experiments seem to produce a certain effect. "It works because it works" just doesn't ring a bell for me, there is nothing for logic and reason to hold on to...

 

[DrChinese]

Sure, entanglement is an experimentally verified and accepted property of nature, but I find it strange that no one seems to have even the slightest idea how exactly does it work. In this regard, does entanglement have any parallels - any other process, which takes place without any insight of its mechanics? It just doesn't seem to be in accordance with the scientific approach, for if something happens then there must be a mechanic through which it happens, otherwise it is taking it for granted, something more typical in the area of theology...

Yes there are parallels. All quantum mechanics falls into the same category. So does general relativity. No one has any idea how any of it "works" other than the mathematical formalism. We simply apply the rules and get the best answer possible for a prediction. This is science.

And before you go too far, I suggest you take a moment to learn why Bell's Theorem ruins your hypothesis (as it did Einstein's similar 1935 hypothesis). Because I don't think you want to stick your neck out too far before you get to square 2. You are currently at square 1, you have grasped the EPR argument (or at least some of it, it is actually quite sophisticated). Bell is square 2. Aspect is square 3.

I will be glad to walk you through it if that helps.

 

[unusualname]

@afstgl actually people do have suggestions for how entanglement works such as non-local pilot waves, holographic projection... but since these ideas are not experimentally testable these ideas are considered purely interpretational/speculative

What is certain scientifically is that naive realist models like you suggest have been ruled out.

(I even have suggested a simple explanation of how it works, check my home page)

 

[edpell]

What is the address of your homepage? I would like to look at it.

 

[unusualname]

if you left-click on a username it gives you various links.

 

[edpell]

afstgl, my thinking is much like yours. In the case of two photons with linear polarization along a particular axis if the "A" photon passes through a linear filter aligned with the y-axis (zero angle) then by construction the "B" photon will pass through a linear filter aligned with the y-axis (zero angle). But the problem is there are an infinite number of axes we could measure with respect to (i.e. 90 degrees, 10 degrees, 10.1 degrees, 10.11 degrees, ...). Penrose in his book "The Road To Reality" makes this point clearly. So now each photons needs a notebook with infinitely many entries one for each angle this clearly makes no sense. Maybe it is possible to specify the answer (pass or no pass) for the y-axis and the x-axis and come up with an equation to fill in the infinite number of results for the angles in between. I think this fails but it has been a long day and I am not up for thinking this through right now. You might want to look at Penrose's crack at this.

On Bell's inequality I think I understand the QM result it is the "classical" or at least no signaling result I am still trying to understand.

Gisin's paper "Can relativity be considered complete? From Newtonian nonlocality to quantum nonlocality and beyond" talks about non-signaling correlations. Also interesting, also I have not understood it yet.

 

[edpell]

unusualname, I do like your

h) No wave-function collapse or decoherence mechanism is required
(The cat is dead or alive, but we have to "look" to know which one)

That is the way I think about it. What we know is limited and best described by statistics but reality is what it is, is definite.

On the other hand I like Feynman's the particle takes every path idea. So maybe I am not so definite.

 

[unusualname]

unusualname, I do like your

h) No wave-function collapse or decoherence mechanism is required
(The cat is dead or alive, but we have to "look" to know which one)

That is the way I think about it. What we know is limited and best described by statistics but reality is what it is, is definite.

On the other hand I like Feynman's the particle takes every path idea. So maybe I am not so definite.

My model is consistent with decoherence, but decoherence is just the correct statistical explanation of the evolution of states (rather than an explanation of macroscopic non-superposition), in fact that has to be the case since decoherence "mechanism" has been observed experimentally.

(btw the most remarkable thing about my model is not simply as an explanation of QM but rather that it claims relativistic physics is due to discrete time evolution)

 

[mathal]

Hi Mathal,

you got me curious

i can understand the different space part, but not the time part.

1. one version/understanding/hypothesis is:

when one of the entangled pair is measured the wave-function collapses, i.e. the other twin also assumes a definite state at the same instant in time

2. the other could be what you are saying...same collapse happening at different time/space...

3. there are more hypothesis/explanations

however right now, I am trying to understand what you mean when you say that both the particles don't collapse at the same time because to me 1 above explains the results of the delayed choice quantum eraser DCQE "completely", then why assume 2?

also why assume/state there is no casual relationship?

the way I understand is, and I am open to new logic, that this casual relationship "transcends/is outside" time-space and its instantaneous?

When you speak of a causal relationship you are in the camp of (1.) the unmeasured particle somehow now having the attribute of the measured particle -without being measured-the key point to consider. If the unmeasured particle is measured for a different quantum property and you accept that it has this property plus the unmeasured matching property of the other particle then you've found a way around Heisenberg's uncertainty principle. I would say that by measuring a different property for the particle nothing can be said about the entangled property of this particle. This would hold true even if you had two particles totally entangled (if that is even possible). It is only the act of measuring the same property of an entangled state for both particles that will result in their being measured as 'having' this entangled property.
I prefer (2.)addendum- Clearly, my point of view is that an entangled state allows an entangled measurement to occur if it is made on both particles. The entangled state then is a clear potential for both particles, never a clear actuality unless it is measured.

Another point to consider AKA the cat problem -you measure particle A for the entangled property but in a confined unreadable box. Particle B is 'then' measured and the measurement is observed. Only then is the reading for Particle A observed and found to match. Which collapse came 'first'. In my way of thinking when the measurement is made this particular entangled particles state collapses to it's measured state whether this measurement is observed or not. The same applies for both particles.

mathal

 

[harrylin]

Hi there, I've recently read some material on QM and entanglement in particular, and even thou I managed to understand the material I felt like it didn't contain the answer to one fairly simple question...
[...]
My question is: What exactly suggests any FTL interaction between entangled particles or change if any of them takes place upon measurement?

The question is simple, but the correct answer has been the topic of intense debate until this day, in part because the issue isn't as simple as you think. The short answer: the fact that your simple model does not work suggests FTL interaction between entangled particles.

The debate is about probability calculus of possible models for realistic experiments and there are many subtleties involved.

- one introduction to Bell's theorem:

http://www4.ncsu.edu/unity/lockers/users/f/felder/public/kenny/papers/bell.html

- one objection to that theorem (starting from p.7):

http://bayes.wustl.edu/etj/articles/cmystery.pdf

In addition, see threads in this forum about Bell's Theorem.
For example:

https://www.physicsforums.com/showthread.php?t=496839

https://www.physicsforums.com/showthread.php?t=369286

https://www.physicsforums.com/showthread.php?t=499002

Harald

PS see also the physics FAQ:
http://www.desy.de/user/projects/Physics/Quantum/bells_inequality.html

 

[edpell]

The http://bayes.wustl.edu/etj/articles/cmystery.pdf paper is interesting.

Can folks suggest some good books on entanglement, EPR, Bell's theorem? I am so far from even understanding the questions that I can not post anything worthwhile yet.

 

[DrChinese]

Can folks suggest some good books on entanglement, EPR, Bell's theorem? I am so far from even understanding the questions that I can not post anything worthwhile yet.

Amir Aczel wrote a book called Entanglement which I can recommend. It is fairly readily available.

 

[harrylin]

The http://bayes.wustl.edu/etj/articles/cmystery.pdf paper is interesting.

Can folks suggest some good books on entanglement, EPR, Bell's theorem? I am so far from even understanding the questions that I can not post anything worthwhile yet.

One book that I found that gives a good overview (except for the possible objections), is Tim Maudlin's "Quantum Non-Locality and Relativity".

 

[afstgl]

Thank you everyone for your insightful assistance. It did help me to come up with insights of my own.

I have a question to whoever might be concerned with answering it: (again, some of the questions will be without question marks, counting on you to correct errors in my statements)

When entangled photons are being measured, the process involves polarizes. When A is measured along x it passes a polarizer and for example returns +x, then to confirm the entanglement B passes through a polarizer and returns -x.

At this point, only spin along x is known for B, whereas spin along any different axis is uncertain.

And here is a question mark question - if afterwards we perform a measurement of B along y, does it return a complimentary result of measuring A along the same axis? And vice versa, does a secondary measurement of A in any other axis determined the spin of B in that same axis?

 

[DrChinese]

...

At this point, only spin along x is known for B, whereas spin along any different axis is uncertain.

And here is a question mark question - if afterwards we perform a measurement of B along y, does it return a complimentary result of measuring A along the same axis? And vice versa, does a secondary measurement of A in any other axis determined the spin of B in that same axis?

No, it does not. This is a critical point, because x and y observations do not commute. Once A is measured, any subsequent non-commuting measurement will be according to the Heisenberg Uncertainty Principle and B is in no way affected (and vice versa, a subsequent measurement of B does not yield any additional information about A). Keep in mind that measuring B along x is redundant.

 

[Delta Kilo]

At this point, only spin along x is known for B, whereas spin along any different axis is uncertain.

The fact that the spin is +1 along axis x is the complete description of the spin state (up to arbitrary phase factor e^{ia} which is not essential). It says it all, there is nothing more to learn about it.

One remark: the original Bell paper is written in terms of spin 1/2 particles, that is measuring electrons with stern-gerlach apparatus, while other experiments use spin 1, i.e. photon polarization. While the principle is the same, care should be taken which one we are talking about to avoid confusion. For electrons (spin 1/2) the directions up and down any given axis are two different, orthogonal states which form a basis (eg, \left|z_+\right\rangle and \left|z_-\right\rangle). Any other spin direction can be expressed as a linear combination of these two (with complex coefficients). Eg. \left|x_\pm\right\rangle = \frac{1}{\sqrt{2}}(\left|z_+\right\rangle \pm \left|z_-\right\rangle), \left|y_\pm \right\rangle = \frac{1}{\sqrt{2}}(\left|z_+\right\rangle \pm i\left|z_-\right\rangle). Look up spinors , Pauli matrices and Bloch sphere.

And here is a question mark question - if afterwards we perform a measurement of B along y, does it return a complimentary result of measuring A along the same axis? And vice versa, does a secondary measurement of A in any other axis determined the spin of B in that same axis?

No. Once we perform a measurement on either A or B, the wavefunctions for A and B both collapse into the eigenstate corresponding to the result of measurement. The state is fully known. The entanglement disappears. Any subsequent measurement on either A or B will be according to the usual QM rules for a single particle.

 

[afstgl]

"Keep in mind that measuring B along x is redundant."
But isn't this measurement the one that verifies particles are in complimentary states? Sure it is redundant in ways that QM predictions already state it will be the opposite state of A...Pardon my eventual ignorance, but if we have a fully symmetrical pair of particles to begin with, and we apply mirror transformations to them (measuring along the same axis after polarizing the same direction) then isn't it perfectly logical to always have complimentary particles in the end. Mirror objects, subjected to mirror transformation always equals mirror objects. As for what breaks the entanglement - measuring probably upsets and breaks the mirror state of the particles, so they no longer respond identically to further transformations, and perhaps if it was possible to measure with zero disturbing it would be possible to continue applying mirror transformations and always get complimentary particles along every possible axis. Simple logic suggests the result will be the same as long as particles are in sync and transformations are mirrored, without really mattering at which angle transformations get applied, particles will always be complimentary without any mysterious entanglement in between, which was my view to begin with. At the time I didn't knew that polarization took place, but if B is polarized under the same angle to verify its state is complimentary to A, then it is pretty much self explanatory...

On a side note, I've been able to create interference pattern with a pocket laser without slits - instead of slits I simply point the laser to a needle and still get a banded pattern - I've tried to find something on the web to explain why this may happen but I failed, does anyone have an idea?

 

[DrChinese]

Pardon my eventual ignorance, but if we have a fully symmetrical pair of particles to begin with, and we apply mirror transformations to them (measuring along the same axis after polarizing the same direction) then isn't it perfectly logical to always have complimentary particles in the end. Mirror objects, subjected to mirror transformation always equals mirror objects. As for what breaks the entanglement - measuring probably upsets and breaks the mirror state of the particles, so they no longer respond identically to further transformations, and perhaps if it was possible to measure with zero disturbing it would be possible to continue applying mirror transformations and always get complimentary particles along every possible axis. Simple logic suggests the result will be the same as long as particles are in sync and transformations are mirrored, without really mattering at which angle transformations get applied, particles will always be complimentary without any mysterious entanglement in between, which was my view to begin with. At the time I didn't knew that polarization took place, but if B is polarized under the same angle to verify its state is complimentary to A, then it is pretty much self explanatory...

Yes, this was a common "classical" explanation of the situation. And again, this initially seems to work. But we now know it is not so simple, largely due to Bell's Theorem.

But even before that, there were problems. Your explanation requires that there be a large number of hidden variables so that you get the expected results at any pair of matching angle settings. Because if there weren't such, you would not get the cos^2 theta relationship. This alone severely constrains theoretical mechanisms. Run some examples and you will see why.

Bell thought this through, and realized that there were angle settings at which the hidden variables explanation did not work. A good example is hidden variable values at 0/120/240 degrees (this is for one particle of the pair). You cannot come up with a set of values for these angles that matches the quantum mechanical expectation values.

Again: without understanding Bell, you will never go any further on this subject and you will simply keep returning to your starting point (as you just did!).

 

[afstgl]

And does mr. Bell have anything to say about my "needle experiment"?

 

[SpectraCat]

And does mr. Bell have anything to say about my "needle experiment"?

Your "needle experiment" was not very clearly stated. What did you do precisely? What is the wavelength of the laser (approx is fine) ... what is the width of the needle (approx is fine)? What was the spacing of the laser and needle and the relative orientation? Did you shine the laser on the tip of the needle or further down on the shaft?

My guess is that you simply observed constructive and destructive interference due to the light diffracting around the needle, but I need some details to know if that is on the right track or not.

 

[Delta Kilo]

Sure it is redundant in ways that QM predictions already state it will be the opposite state of A...

Exactly. Besides, it is easy to explain from classical point of view, so it is just not interesting. Interesting things start to happen when you measure A and B along somewhat different axis. As you increase the angle between detectors A and B the coincidence rate will begin to drop from 100% (exact match) to 50% (completely random) according to Malus law which is slower than can be explained by any classical theory. This is the crux of Bell test. This is what makes it interesting.

...and perhaps if it was possible to measure with zero disturbing it...

Well, too bad QM postulates say it is impossible in principle.

On a side note, I've been able to create interference pattern with a pocket laser without slits - instead of slits I simply point the laser to a needle and still get a banded pattern - I've tried to find something on the web to explain why this may happen but I failed, does anyone have an idea?

Well you still have two different ways around the needle so it is pretty much the same. Also see diffraction.

 

[Brainguy]

I know you already got some great answers, but put a little more simply, the lab mice are not entangled, just like you said. But when you have a radioactive atom with no electric charge, and it decays into two other particles, you have no idea what charge the two have, measuring one of them, let's say it was positive, automatically determines the value of the second because they came from a neutral atom and need to cancel each other out.

 

[Delta Kilo]

But when you have a radioactive atom with no electric charge, and it decays into two other particles, you have no idea what charge the two have, measuring one of them, let's say it was positive, automatically determines the value of the second because they came from a neutral atom and need to cancel each other out.

Well, yes but this is not the weird bit. Weirdness starts when you try to measure non-commuting observables. It goes like that:

* You have two photons/electrons/whatever flying in opposite directions. Ok so it's just a momentum conservation, nothing weird about it.

* You measure the spin of one of them along some axis and find it to be completely random, 50/50 chance of getting +1 or -1. Ok so the particle gets random spin, nothing weird about it.

* You measure the spin of both of them along some axis and find it to be always opposite each other but still completely random. Ok so the particles always get opposite spin. So this is just angular momentum conservation, nothing weird about it.

* You measure the spin of both of them but this time at an angle. You find the coincidence rate drops as you increase the angle. Ok so the particle's spin gets projected onto the axis of measurement, or something like that, nothing weird about it.

* Finally, you plot coincidence rate vs. angle graph and find it follows \cos^2 \theta law. Then you read EPR paper and Bell's paper and realize that it cannot possibly be so, the coincidence rate is higher than can be explained by any classical theory. Then you read about Aspect's experiments and find that it is indeed so even though "no reasonable definition of reality could be expected to permit this" (the famous punchline of the Einstein-Podolsky-Rosen paper). Now this is what they call weird.

 

[afstgl]

Delta Kilo - can you provide a link to a high resolution graph plot for coincidence rate vs. angle

DrChinese - I still don't see why I need "lots of hidden variables" - all I need is a hidden in plain sight principle, found in Maxwell's views of electromagnetism

SpectraCat & Delta Kilo - it is standard red laser, so I guess somewhere around 750 nm, it is about a meter from the needle, pointed at the needle body (not tip or ear) and the pattern ends up projected on the wall about 4 meters away. Is it the same product as of the two slit experiment?

 

[DrChinese]

DrChinese - I still don't see why I need "lots of hidden variables" - all I need is a hidden in plain sight principle, found in Maxwell's views of electromagnetism

Somehow I think you have not yet read and understood Bell Theorem. It is almost pointless to discuss in absence of that, but I will explain a bit about hidden variables.

Imagine we have entangled Alice and Bob (polarizations clones of each other). If I measure both at 0 degrees I get the same answer. If I measure both at 10 degrees I get the same answer. If I measure both at 20 degrees I get the same answer. Etc.

If I measure Alice at 0 degrees and Bob and 90 degrees, I get different answers every time. If I measure Alice at 10 degrees and Bob and 100 degrees, I get different answers every time. If I measure Alice at 20 degrees and Bob and 110 degrees, I get different answers every time. Etc.

Now, obviously, if there was some simple arrangement to explain this - such as 1 set of variables to cover from 0 to 90 degrees, another from 90 to 180 - then the coincidence rate would never match the cos^2(theta) rule. You can work this out for yourself (I hope).

So perhaps there are hidden variables at every 10 degrees. Then we would need 36 sets of variables in both Alice and Bob for everything to work out. Of course, if I change the resolution to 1 degree, I need 360 sets of hidden variables.

So a lot of hidden variables.

 

[Delta Kilo]

Delta Kilo - can you provide a link to a high resolution graph plot for coincidence rate vs. angle

Yeah, sure, http://images.lmgtfy.com/?q=bell+coincidence+count"

Also this: (http://www.sciencefile.org/SciFile/forum/Foundations/164390-Alain-Aspect-EPR-Lecture" )

 

[afstgl]

Oh yeah, that cosine curve, I really expected something fancier, with multiple plots, like this one:
http://www.nature.com/nphys/journal/vaop/ncurrent/carousel/nphys1996-f2.jpg

I guess the smooth cosine curve came from ... how do you call it in English... averaging of results, similar to the point plots in the image above...

I took this one off wikipedia and did some mirroring to give a visual representation of the degree of asymmetry, with 180 degree being the center, RED is right superimposed on left, GREEN is left with mirror transformations superimposed on left.
[PLAIN]http://img64.imageshack.us/img64/5021/cosine.png[/URL]

As it is obvious, a very neat, almost perfect symmetry is observed, and the small differences probably fall well within the margin of error when averaging dot plots to a single curve.
In that case, this graph (supplied to me with the hint that I am a moron to the extent I don't know how to google) seems to be consistent with my moronic idea - we observe anti-correlation increasing with the increase of symmetry in the transformations of entangled particles and what is MORE IMPORTANT - we also observe correlation when measured at 180 degree relative, which is CRUCIAL to my idea - we start with anti-correlated particles, we apply mirror transformations to both particles and get anti-correlated particles as result, BUT measuring at 180 degree applies mirror transformation only to one of the particles, if we have two mirror particles and rotate one at 180 degree, we end up with two identical particles. And that is not all, the cosine graph shows a very neat relationship between correlation shifting at equal steps of 90 degree. It makes perfect sense to me, I can visually imagine the whole process with its logical outcome, and [B]you are telling me that I am able to grasp the mechanics of the experiment because I don't understand something, which if I DID UNDERSTOOD, I wouldn't be able to explain the mechanics of the experiment[/B]...

DrChinese - I understand your last post perfectly, it seems that it is you who cannot understand how I understand the mechanics of this experiment, perfectly logical without any hidden variables at all.

Pardon the nonconformity of my expression in regard to academic nomenclature, I am not a member of academia, not to mention not a native English speaker, that is why I feel a pictorial explanation might bridge that gap and make things clear - keep in mind this is a photochop file - no precision at all, just explaining my concepts in a visual way:

[PLAIN][PLAIN]http://img232.imageshack.us/img232/9229/entanglement.png[/URL]
Note - disregard the "transformation boundary" in the legend at the end, I accidentally forgot to delete it from a previous idea. Arrows do not represent physical direction of rotation but spin + or -, up or down or whatever.

 

[SpectraCat]

@afstgl

Look, you are really making this very difficult. You are shouting so loudly about what you think you understand (but actually don't), that you cannot hear the helpful suggestions and explanations being provided to you. That last post of yours is almost entirely non-sensical in the context of what is already known about entanglement, and how measurements are made in quantum mechanics. You probably won't take my advice, but you need to slow down, back up, review basic QM, and carefully re (or re-read) the Mermin paper I linked, which goes through the issues with what you are describing in patient detail, in a fashion that is designed to be accessible to non-academics.

Some key points you are missing:

1) entangled pairs do not have to be anti-correlated .. they can also be correlated. In other words, you can create entangled pairs such that both particles always have the same spin (or polarization) when measured at the same angle.

2) entangled pairs are quantum mechanical superpositions.

For correlated pairs you have: \Psi_I=\frac{1}{\sqrt{2}}[|U>|U> + |D>|D>]

For anticorrelated pairs you have: \Psi_II=\frac{1}{\sqrt{2}}[|U>|D> + |D>|U>]

where U and D denote up and down, and the notation |U>|D> means that particle A is up and particle B is down.

3) there is no preferred polarization angle. In other words, if you have a correlated state, and particle A is measured at 45º, and particle B is measured at 135º, you will observe zero coincidences (a coincidence being defined as both particles having the same state). If you measure particle A at 67º, and particle B at 247º, you will also observe zero coincidences. What I am saying is that the coincidence rate does not depend on the polarization angles of the photons as they come out of the source. It ONLY depends on the relative angle (\theta) between the measurements, and the dependence (as shown in the plot you posted) is given by cos^2\theta.

 

[afstgl]

So you claim that I don't understand something you don't understand yourself and last time I checked no one really does, is that right? If that is the case, I don't really think you have a case here, and if not, perhaps you will be the first one to provide a plausible explanation of the mechanics behind those "predictions"?

If anything, you obviously missed the bottom of my image, where it says "cause of "randomness" due to relative angle between (measurement of) A and B", otherwise you wouldn't repeat the statement "It ONLY depends on the relative angle (θ) between the measurements" since it was implied I am well aware of that.

My example would be equally valid with correlated "entangled" particles as well, do you really fail to understand my idea, which perfectly explains the results of the experiment in a way even a kid would probably get it right away? Why is that I feel a kind of "it cannot be that simple" attitude. Don't get me wrong, the image I made is just a very rough concept - it would take me way too long to do it all in 3D animation so that it can be perfectly clear what happens with photons upon their polarization, I think you should be able to do that in your mind fairly easy.

Again, my concept is based on the ideas of Maxwell and not really compatible with stuff like GR which came later on. But I smell a closed loop here - Einstein was clearly displeased to say the least with the very notion of FTL since it violated his theories, but it is potentially his theories which led to the very concept of entanglement due to the fundamental disability to explain the mechanics of certain processes. What if Maxwell was right and Einstein was wrong - he would be happy in his grave there is no "spooky" action at a distance, no FTL interactions to violate his theory, but in the same time this would prove his theory as wrong, since it was GR's inability to bridge the gap between classical and quantum mechanics and left QM in obscurity to the point no man can explain how it works through the prism of Einstein's scientific legacy. And just to make sure - I am not proposing pseudo science here - Maxwell is NOT a pseudo scientist, not by a long shot, I merely propose some of his "discarded" ideas were actually worth keeping, since they can easily be quantized and explain QM in a laughably simple way. That would however make about a century worth of science pretty much obsolete, which is a tough pill to swallow, especially since that science consists the academic baggage scientist base their credentials on. And sure, there is always the argument "Science could not have been wrong for over a century, look at all the technology we've come up with" - however, everything from the world electric grid through logic gates and the chips they make, radio communications, robotics and practically the very backbone of modern technology traces its origin to one, named Nikola Tesla - a person who not only denied, but heavily criticized, even ridiculed Einstein's ideas, and as famous as Einstein is, the number of his practical inventions is zero, and I for one believe science is not a popularity contest, science is about practical implications... I really do hope this doesn't get interpreted as "scientific blasphemy" as it often happens. I am just being objective.

Sure, I feel you, you - a PhD in science have a really hard time believing a nobody could get something no man of science has managed to, just as I as a Muaythai instructor have a hard time believing a 5 year old can just come and beat me up...

 

[Joncon]

afstgl,

Let's say we have two entangled, polarization correlated particles. Both pass a polarizer set at 0 degrees to the vertical.

How would you explain them giving the same results i.e both 0 or both 1?

Because the way I understand it (and I may well be wrong, I'm only starting to learn this stuff), either the polarization is undetermined, in which case each particle has a 50/50 chance of passing the polarizer, or the particles have definite unknown polarizations, in which case they should follow Malus' law.

 

[SpectraCat]

My example would be equally valid with correlated "entangled" particles as well, do you really fail to understand my idea, which perfectly explains the results of the experiment in a way even a kid would probably get it right away? Why is that I feel a kind of "it cannot be that simple" attitude.

It doesn't explain anything, for reasons that have already been explained to you several times on this thread. It starts from a premise that is known to be false, namely that the individual particles in entangled states have well-defined properties. Everything in your "model" falls apart unless you can assume that. Furthermore, you assume a mathematical relationship between the results and the measurement angles without any justification or mathematical derivation. Until you have read and appreciated Mermin and Bell, there is really nothing left to talk about.

 

[afstgl]

Joncon - Yes, particles may fail to pass the polarizer and get absorbed by it, but in case they are the right polarization to pass the filter their quantum correlation will be +1 - they should remain correlated.

In my view there isn't any entanglement to begin with. Good old electromagnetism all the way.

SpectraCat - just as well you start with the premise it is a phenomenon, making it unexplainable, I simply state it is a phenomeNOT which renders it explainable in a classical way. Also, I am not a mathematician, perhaps you or someone else could translate my simple idea in a complex language, so that smart people can get it too :)

 

[Joncon]

Joncon - Yes, particles may fail to pass the polarized and get absorbed by it, but in case they are the right polarization to pass the filter their quantum correlation will be +1 - they should remain correlated.

But they don't need to be the "right polarization" do they? As long as the difference between their polarization and the polarizer is less than 90 degrees, they have a chance of passing through. And if there is no entanglement, then the results of the measurements won't correlate 100% of the time.

 

[afstgl]

Even so, if you want to confirm the result, you will have to it to both particles, both will still be subjected to the same transformation and measured at 0 degree relative to each other, thus correlation is +1

My questions is what would happen if both particles get polarized in a different manner and still measured at the same degree, if that is even possible, and if it is, what will the correlation be, +1 or 0?

 

[Joncon]

Even so, if you want to confirm the result, you will have to it to both particles, both will still be subjected to the same transformation and measured at 0 degree relative to each other, thus correlation is +1

Which transformation is this?
Here's an example: -
Two particles, A and B, are entangled. Let's suppose they are polarized at 45 degress to the vertical. A goes to Alice, B goes to Bob. Both measure at 0 degrees (how do I do a "degrees" symbol anyway?) so each has a 50/50 chance of passing the polarizer.

So the possible results are
A B
1 1
1 0
0 1
0 0

But in experiments the results are always one of the following: -
A B
1 1
0 0

So what happened to the other possible results?

My questions is what would happen if both particles get polarized in a different manner and still measured at the same degree, if that is even possible, and if it is, what will the correlation be, +1 or 0?

Well if they had different polarizations they wouldn't be entangled would they?

 

[afstgl]

Well, as far as I am familiar with, experiments rarely use single measurement, lots of measurements are taken and summarized in a statistical way. In case any, and naturally both particles fail to pass, you get nothing or garbage data that is irrelevant, both particles have to pass through to return a result, and if both pass that result will always be quantum correlation of +1. What happens to the other possible results - well, you simply have no way to come up with a result unless both particles pass through and get detected. It is practically impossible to get correlation -1 - all those get "selected" out by the test equipment...

 

[Joncon]

Well, as far as I am familiar with, experiments rarely use single measurement, lots of measurements are taken and summarized in a statistical way. In case any, and naturally both particles fail to pass, you get nothing or garbage data that is irrelevant, both particles have to pass through to return a result, and if both pass that result will always be quantum correlation of +1. What happens to the other possible results - well, you simply have no way to come up with a result unless both particles pass through and get detected. It is practically impossible to get correlation -1 - all those get "selected" out by the test equipment...

Of course. I'm not talking about single measurements. What I'm saying is that the measurements at the same angle, regardless of how many you do, always correlate.

And it isn't always necessary that the particles pass the polarizer. Alain Aspect has done experiments using two-channel polarizers, whereby the particle goes one way or the other, so it is always detected - http://arxiv.org/ftp/quant-ph/papers/0402/0402001.pdf"

Again, the results match QM predictions.

 

[Delta Kilo]

afstgl,

You appear to be working down the list I gave previously. At the moment you are at the second-last point of it.

Yes, a classical model of it, like the one on your photoshop slide, is possible. Here is a simple example: when the particles are created one gets random polarisation and another gets the exact opposite of it. The outcome of the measurement is +1 if the angle between particle polarisation and detector is < 90 and -1 otherwise: result=sign(cos(Aparticle-Adetector)). This model will describe the process qualitatively: You get perfect correlation when the detection angles are the same, completely random results when they are at 90 degrees and something in between for all other angles.
But, as I said, this is not the weird bit.

The trouble is, this model produces linear dependency between angle and coincidence rate while QM predicts and experiments confirm cosine-squared dependency. And then Bell tells us that NO classical theory can possibly produce cosine-squared law and on the other hand Aspect puts actual experimental error bars on the graph which fit QM predictions nicely and are far away from the classical limit.

So the problem, the weird bit, is just this difference between the two curves on the graph. It may seem like a minor technical detail but it got people like Einstein all worked up.

Of course, to get to this point, it is not sufficient to just "visualize the process". One has to get their hands dirty with math to see the conflict here. On the positive side, both EPR and Bell's papers are quite readable.

 

[afstgl]

Well, that is just the thing, QM prediction are derived 100% experimentally, there is absolutely no math involved in the derivation of the cosine curve, abstract math is only used to formulate the predictions, not to derive them.

Going back to the slide shot you attached to your last post - it says "No ... theory (in the spirit of Einstein's ideas) can reproduce QM predictions..." - I put the critical aspect of it in bold - it is that potentially flawed spirit of Einsteinian ideas which suggests a linear curve. Maxwellian view of spacetime fabric and EM radiation's mechanics of mediation along it do not. In this case the nonconformity of the result is direct evidence against the validity of Einstein's work - his theory is INCOMPLETE at its foundation, experiments obviously prove the dependency is NOT linear, and if that cosine curve proves Einstein's theory wrong, well then it is only natural for that theory to fail to explain why it is a cosine curve and not a linear one. Ironically or not, but it was Einstein's work, which somehow managed to swing mainstream science away from the concept of AETHER while still partially relying on it, but starting with Newton, passing through Maxwell, Lorentz, including mr. Tesla I mentioned previously and potentially many more I don't know of - those have been incorporating the concept of AETHER, and it is a fundamental property of aether which is responsible for the non-linear curve of QM predictions. You say like you mean it, but you hardly expect a common Joe like me to prove this concept to you in academic nomenclature, it would take a large scale effort to verify my claims, and effort that for SOME reason has never been attempted the last century, again, it is blind directional belief in the rightness of the doctrine that has place only in theism is observed in the scientific community, like there is no possible way for Einstein's legacy to be wrong, in the face of the fact it fails at the quantum scale and as a result "mystifies" it. What IF people like Maxwell were on the right track and people like Einstein "accidentally" derailed science from this track for the sake of simplification or whatever? You demand of me, a non-mathematician to explain in math something mathematicians fail to do... well la-de-da :)