How do particles become entangled?

[alexepascual]

Eye_in_the_Sky:
Going back to your post #16:

Now, suppose that the interaction between these two particles is such that
|ψ>|φ> → Σk ak|ψk>|φk> ,
where each ak ≠ 0, and there are at least two distinct values for k (and, of course, the |ψk> (|φk>) are linearly independent).

I would like to look at this in more detail. How do we go from |ψ>|φ> to Σk ak|ψk>|φk> ?
The k seems a little confusing to me. What basis are you using? Shouldn't we define a new basis in the product Hilbert space? If k refers to that basis, shouldn't we write the state as Σk a_k|ψ>|φ>_k?
If H1 is n-dimmensional and H2 is m-dimmensional, k would run from 1 to nxm right? Would the ak be determined by the particular interaction? What about time evolution? Can we arbitrarily use either the Schodringer picture or the Heisenberg picture?

I have read somewhere else that the state |ψ>|φ> is "not the most general one". But I don't understand why or what they mean by "general". If you would like to look at the source, I can post a link or copy the paragraph here.

In my post #17 I expressed my puzzlement at how a composite state of two non-interacting particles is described. I understand you choose some basis for each of the particles and then make a tensor product of these single-particle base states. But what do you do with the complex coefficients? If you were to multiply them together, wouldn't you loose information about each individual particle?. Maybe my questions don't make sense, but in any case, I think you might be able to give me some orientation. Thanks in advance.

 

[alexepascual]

Today I went to the library and tried to find information about my questions in the previous post. I looked at Sakurai and Shankar but I didn't find any info on composite Hilbert spaces, interacting and non-interacting particles, etc. Maybe I didn't look in the right chapter.
Anyway, I have been doing some thinking. If we start with the state vectors for the two (non-interacting) particles (in some basis) at a particular time, and do the tensor product of them, we get a complex amplitude for each element in the tensor. It makes sense that the probability to find a particular produc-state will be proportional to the products of the probabilities for each of the components in the product state. So I guess it makes sense to multiply the amplitudes of the individual-particle state vectors.
But I realize that the states in H1 might have different energy than those in H2, therefore their phases would change at different speeds. If we had the time dependence of the phase encoded in the state vectors, then we would not have a single number for the amplitude of each of the product states but a pair of complex functions of time.
I guess another way of doing this would be to leave the state vectors alone and to plug the time dependence into the operators. (Heisenberg picture).
But all this is just my speculation. I would like to see a good explanation of these topics in a book or article or get it from someone who knows it very well. I can imagine that this topic is very elementary for those who understand quantum mechanics well. For me it is still confusing.
I'll appreciate any help.

 

[DrChinese]

1) Suppose that the value obtained in a measurement is 'determined' at the time of the measurement and not before.

Then, clearly, for a pair of spin-entangled particles far apart in space, the joint 'collapse' which ensues on account of a spin-component measurement of only one of the particles implies nonlocality. //

2) On the other hand, suppose that the value obtained in a measurement is 'determined' before the time of the measurement. That is, this value – prior to measurement – is "definite but unknown".

Then, assume locality and derive a "Bell inequality". Such an inequality, however, contradicts the QM formalism. //[/color]

Putting 1) and 2) together leads to the inescapable conclusion that quantum correlations imply nonlocality.

This argument is not correct in the context of Bell. In 1) above you essentially assume that which you want to prove.

In Bell, the argument is that locality and reality cannot both be true and still yield results consistent with QM. Locality can hold if "realistic" assumptions are abandoned. By failing to acknowledge this possibility in your argument, you naturally conclude it is locality which fails. That doesn't fly.

 

[Caroline Thompson]

Experimental facts

I am primarily an experimentalist ... In the Bell experiment he chose angles that were not 0 or 90 degrees thus confusing me beyond help. Isn't there a simpler experiment out now with simpler equations?
I have a real problem with these Alice and Bob experiments because none of the instruments in my lab are named Alice or Bob.
I have found it very hard to corner an expert and ask questions.

If you look at the real experiments you will find that most have been done using light and assuming it to come in "photons". If you want to see the logic really intuitively, though, it's easiest to look at a model of the Bohm-type idea that uses the spins of two particles. The "local realist" logic, and in particular that relevant to the "detection loophole", is covered by my Chaotic Ball model (see http://arxiv.org/abs/quant-ph/0210150 ). You might look at this first then try and follow what I'm on about in my discussions of real optical experiments and their various other loopholes in http://arxiv.org/abs/quant-ph/9903066. Alternatively, you might start by looking at the pages I contributed last summer to wikipedia (hoping someone else has not edited them out of recognition!). The key page is http://en.wikipedia.org/wiki/Bell's_Theorem, from which you can follow links to pages on the actual experiments and on the loopholes.

As you may have gathered, I'm a local realist and am firmly convinced that, once you allow for the actual experimental conditions, all the results can be explained by local realist models. An important feature of these models that you will not find in popular books on EPR is that the hidden variables set at the source do not completely determine (in conjunction with the detector settings) the outcomes. They determine only their probabilities.

This kind of model is described in Clauser and Horne's 1974 paper (Physical Review D, 10, 526-35 (1974)), which is much less widely read than it deserves. It presents versions of Bell's inequality that apply to the real conditions, in which detectors are not anywhere near 100% efficient. You will find here that they state quite categorically that the usual CHSH test cannot be used unless you know the number of pairs emitted and use this as denominator in the estimate of the quantum correlation. Though they do not, iirc, use the term "fair sampling", what they mean is what I and others have realized: that you cannot assume it. To do so will almost inevitably bias the test.

But please read some of my work and get back to me if this does not make sense!

If what you want is to understand quantum theory then you've come to the wrong place, since my studies have indicated that the QT formula is in fact wrong! The logic has to be the local realist one. That this is so could, I believe, be shown experimentally if, instead of publishing just one "Bell test statistic" each time, experimenters were to publish actual counts for a range of settings of parameters such as the efficiencies of the detectors.

Caroline

 

[Eye_in_the_Sky]

to Richard, back in post #60

Non-local hidden variable interpretation- why that's Bohmian mechanics. Is that a dirty word that cannot be said?

... Not in the least!

In using the expression "nonlocal hidden-variable interpretation of QM", I was only trying to be as general as possible.

 

[Eye_in_the_Sky]

to Alex

... I would like to look at this in more detail. How do we go from |ψ>|φ> to Σk ak|ψk>|φk> ?

By means of Schrödinger-evolution of the joint interacting system.
__________

Would the ak be determined by the particular interaction?

Yes.
__________

The k seems a little confusing to me. What basis are you using? Shouldn't we define a new basis in the product Hilbert space? If k refers to that basis, shouldn't we write the state as Σk a_k|ψ>|φ>_k?

In the above, the vectors |ψ_k> and |φ_k> do not refer to any particular basis. Indeed, in saying what I said back in post #16,

Now, suppose that the interaction between these two particles is such that

|ψ>|φ> → Σ_k a_k|ψ_k>|φ_k> ,

where each a_k ≠ 0, and there are at least two distinct values for k (and, of course, the |ψ_k> (|φ_k>) are linearly independent).

... my point was only to make clear that, on account of the interaction, the joint system can no longer be written as a "simple (tensor) product" of one element from H₁ with one element from H₂.
__________

I have read somewhere else that the state |ψ>|φ> is "not the most general one".

I think the intention of such a remark is along the lines of what I just said above:

An arbitrary vector in the tensor-product space cannot in general be written as a "simple (tensor) product" of one vector from H₁ with one vector from H₂.

For example, consider a Hilbert space H spanned by {|1>,|2>} and construct the tensor-product space H' of H with itself. Consider the vector

|1>|2> + |2>|1> Є H' .

Can you find vectors |ψ> and |φ> in H such that

|1>|2> + |2>|1> = |ψ>|φ> ?

... Good luck!
__________

What about time evolution? Can we arbitrarily use either the Schodringer picture or the Heisenberg picture?

Either picture can be used. In the above, where I wrote

|ψ>|φ> → Σ_k a_k|ψ_k>|φ_k> ,

I was working in the Schrödinger picture. The left-hand-side is at some initial time t_o, and the right-hand-side is at later time t.
__________

In my post #17 I expressed my puzzlement at how a composite state of two non-interacting particles is described. I understand you choose some basis for each of the particles and then make a tensor product of these single-particle base states. But what do you do with the complex coefficients? If you were to multiply them together, wouldn't you loose information about each individual particle?

No, you don't lose any information. It sounds to me like you are trying to "read off" the amplitude for measuring particle 1 in some eigenstate in a measurement where "you don't care" what happens to particle 2. But you can't just do that. You have to combine all the cases where particle 1 is in the prescribed eigenstate and particle 2 can be in "anything".

On the other hand, if you wish to measure each particle in some eigenstate, then you can merely "read off" the amplitude (... if you get what I mean). This part, it appears to me, you have subsequently understood, because, as you write:

Anyway, I have been doing some thinking. If we start with the state vectors for the two (non-interacting) particles (in some basis) at a particular time, and do the tensor product of them, we get a complex amplitude for each element in the tensor. It makes sense that the probability to find a particular produc-state will be proportional to the products of the probabilities for each of the components in the product state. So I guess it makes sense to multiply the amplitudes of the individual-particle state vectors.

Correct. ... But, then, you go back to the earlier confusion:

But I realize that the states in H1 might have different energy than those in H2, therefore their phases would change at different speeds. If we had the time dependence of the phase encoded in the state vectors, then we would not have a single number for the amplitude of each of the product states but a pair of complex functions of time.

There is no problem here.

Write the state of the joint, non-interacting, non-entangled system as

|ζ(t)> = |ψ(t)>|φ(t)> ,

and say that

|ψ(t)> = ∑_i a_i(t)|ψ_i>

and

|φ(t)> = ∑_j b_j(t)|φ_j>

(where, of course, {|ψ_i>} and {|φ_j>} are each orthonormal sets).

Thus,

|ζ(t)> = |ψ(t)>|φ(t)>

= ∑_ij a_i(t)b_j(t) |ψ_i>|φ_j> .

Now ... let's find the probability that particle 1 is in the state |ψ_n>. The associated projection operator is just

|ψ_n><ψ_n| (x) 1 ,

and therefore the required probability is given by

<ζ(t)| |ψ_n><ψ_n| (x) 1 |ζ(t)>

= <ψ(t)|ψ_n><ψ_n|ψ(t)> ∙ <φ(t)|φ(t)>

= |a_n(t)|² .

... Does this clear up the confusion?

 

[Eye_in_the_Sky]

to DrChinese

Back in post #59 of this thread, I wrote (among other things):

That quantum correlations imply nonlocality can be seen from the following argument:

1) Suppose that the value obtained in a measurement is 'determined' at the time of the measurement and not before.

Then, clearly, for a pair of spin-entangled particles far apart in space, the joint 'collapse' which ensues on account of a spin-component measurement of only one of the particles implies nonlocality. //

2) On the other hand, suppose that the value obtained in a measurement is 'determined' before the time of the measurement. That is, this value – prior to measurement – is "definite but unknown".

Then, assume locality and derive a "Bell inequality". Such an inequality, however, contradicts the QM formalism. //[/color]

Putting 1) and 2) together leads to the inescapable conclusion that quantum correlations imply nonlocality.

However, DrChinese has suggested some point(s) of error on my part in the above. Specifically,

This argument is not correct in the context of Bell. In 1) above you essentially assume that which you want to prove.

In Bell, the argument is that locality and reality cannot both be true and still yield results consistent with QM. Locality can hold if "realistic" assumptions are abandoned. By failing to acknowledge this possibility in your argument, you naturally conclude it is locality which fails. That doesn't fly.

Let me try to understand what you are saying here. In (a hopefully understandable) shorthand, my argument above can be summarized as:

---------
1) (QM & not 'pre-determined') → nonlocality ;

2) (QM & 'pre-determined') → nonlocality ;[/color]

therefore: QM → nonlocality .
---------

Now, let's see if I have understood you correctly.

With regard to 1), basically you are saying that the argument is "trivial".
... If so, I agree.

With regard to 2), you are saying that it omits the mention of an implicit assumption, namely, that of "realistic-ness". If we include this assumption explicitly in 2), then that argument becomes:

2') ("realistic-ness" & QM & 'pre-determined') → nonlocality .[/color]

... DrChinese, have I understood you correctly?

 

[DrChinese]

However, DrChinese has suggested some point(s) of error on my part in the above. Specifically,
Let me try to understand what you are saying here. In (a hopefully understandable) shorthand, my argument above can be summarized as:

---------
1) (QM & not 'pre-determined') → nonlocality ;

2) (QM & 'pre-determined') → nonlocality ;[/color]

therefore: QM → nonlocality .
---------

... DrChinese, have I understood you correctly?

Eye,

I am not saying your arguments are trivial, and I don't think we disagree on the basic science. I do think that your argument embodies a reformulated version of Bell which ends up losing a little something in the process.

The real alternatives from Bell are:

1) QM & Locality Fails (which does imply non-locality); this is more or less the case you call "determined at time of measurement" and therefore "not predetermined". (Locality=Bell's condition that the result of a measurement at one place does not affect the result of a measurement at another.)

2) QM & Reality Fails (which does NOT imply non-locality) which you can see does not quite match your 2) "pre-determined" alternative. (Reality=Bell's condition that the chance of an outcome is within the range of 0 to 1.)

It always comes back to your view of what is reality. If you think the measurement "caused" the photon spins to take on a definite value, then the question becomes: which measurement? The one on the "left" causing the one on the "right" (arbitrary assignments of left and right)? Or vice versa? Or perhaps, you might say this is an example of the future influencing the past.

The ultimate problem is that our concepts of reality do not readily correspond to the mathematical formalism. All you can conclude from the Bell side is that the relative angle between the non-local polarizers acts AS IF it is the fundamentally real variable being measured. This is true of many experimental setups in QM, such as demonstrations of photon self-interference. You have been tempted to conclude that non-locality is demonstrated. But this is not correct because no causal effect propagated at a speed faster than light (after all, we don't even know the direction of the travel, much less what the actual effect is).

Unless, of course, you define it that way. QED. There is still a light cone which limits everything that has happened, which is just as strong as a counter-argument to your definition of non-locality.

 

[alexepascual]

Eye_in_the_Sky:
Again you have given me a lot of material to chew on. I hope this time I won't take as long to respond as I have more time available.

Caroline:
Thanks for your contribution to the thread. I guess many of us here are just trying to gain a better understanding of QM as it has been formulated and generally accepted. I understand the value of questioning the accepted dogma, but at least in my case I think I'll benefit more from gaining full understanting of the subject as presently understood and not to venture into concepts that deffy the commonly accepted theory. (at least not yet)
From all I know, and as Dr.Chinese clearly states, it appears that the tests (which you question) of Bell's inequalities sucessfully prove that locality or reality must give way. Your position is at odds with the accepted theory, and that must be the reason you didn't get a response. You might get better results by initiating a thread just on your proposal. Good luck.

 

[CarstenDierks]

"Two particlees must have interacted."
Can you give me an example of how two particles could interact to become entangled? A simple (if possible) step by step process where two particles start off not entangled and become entangled.

Hi Donk,
Jurgen was not so bad with his example in post #4. Alain Aspects experiment shows how photons become entangled: The 2 photons are sent off in opposite directions with opposite spins.

Maybe someone should ask the physicists at Innsbruck University, Austria, how they produce entangled particles. Their research is very advanced and they should be able to say how their particles become entangled.

http://www.sciam.com/article.cfm?articleID=00014CBD-7633-1C76-9B81809EC588EF21

Or does anybody here know how they did it?

Carsten

 

[Eye_in_the_Sky]

I do think that your argument embodies a reformulated version of Bell which ends up losing a little something in the process.

I agree that my argument does not follow the structure of that given by Bell. (In my argument, I used as the "starting point": 'pre-determined' or not 'pre-determined'. Bell's "starting point" is simply 'locality' (according to Einstein's definition). Originally, I had specific reasons for choosing the "starting point" as I did, but now I am not so sure that that was entirely necessary. Moreover, I am now suspecting that the first part of my argument (labeled "1)", i.e. not 'pre-determined') is less trivial than I thought it to be.)

Let us therefore consider Bell's argument exactly as he originally presented it. You are saying that in that formulation there is a "reality", or a "realistic-ness", assumption of some kind being made. You have also indicated one implication of such an assumption:

Reality=Bell's condition that the chance of an outcome is within the range of 0 to 1.

On the face of it, to negate such a proposition is absurd ... isn't it?

Tell me, is this the only assumption of Bell which physicists consider negating on account of a not-"reality" proposal?

 

[DrChinese]

Let us therefore consider Bell's argument exactly as he originally presented it. You are saying that in that formulation there is a "reality", or a "realistic-ness", assumption of some kind being made. You have also indicated one implication of such an assumption:

Reality=Bell's condition that the chance of an outcome is within the range of 0 to 1.

On the face of it, to negate such a proposition is absurd ... isn't it?

Tell me, is this the only assumption of Bell which physicists consider negating on account of a not-"reality" proposal?

I agree that on the face of it, the proposition is absurd. But further investigation shows it is far from absurd, and that is part of what makes QM so powerful (as you know).

If you look at the outcomes, you will see that certain combinations are actually predicted (by QM) to have negative probabilities, flying in the face of the "obviously reasonable" counter-position of reality shown above. QM makes plenty of similar counter-intuitive predictions, all of which have so far been pretty well verified. Aspect verified this particular one in his famous experiments.

The "loophole" from Bell's Theorem was that a non-local theory could also account for the observed behavior. So there is your option, and you are free to choose it if you prefer.

But there are other tests of QM which show similar negative probabilities. For example, take the reflection of light off a mirror from a source to an intensity detector. There are many paths to the detector that provide negative intensity, in violation of common sense. If you prevent the light from taking those paths (such as via etching the mirror in appropriate spots), the detected intensity increases. This is because the "negative" probability cases are being excluded, which cause the sum of the various path intensities to the detector to increase.

So ultimately, what is "reasonable" to one person may not be reasonable to another. Is non-locaity more reasonable than negative probabilities?

You can also map the hidden variable concept to the negative probabilities in the Bell paper. It is the manipulation of the local hidden variable (your "predetermined") outcomes that directly leads to the negative probabilities in the first place. Another way to say it is that certain combinations are suppressed. The difficulties lie in the words used to describe it more than the actual underlying formalism.

 

[Caroline Thompson]

"Negative probabilities" don't happen either

If you look at the outcomes, you will see that certain combinations are actually predicted (by QM) to have negative probabilities, flying in the face of the "obviously reasonable" counter-position of reality shown above. QM makes plenty of similar counter-intuitive predictions, all of which have so far been pretty well verified. Aspect verified this particular one in his famous experiments.

"Pretty well" is, in this instance, surely not good enough! We're talking about a claim that something happens that is not merely (in my view) "counterintuitive" but actually "impossible". If such a thing is to be believed we need incontrovertible evidence, not experiments whose interpretation only backs the belief if you also accept a number of assumptions that are, to a local realist, simply not reasonable.

The "loophole" from Bell's Theorem was that a non-local theory could also account for the observed behavior. So there is your option, and you are free to choose it if you prefer.

Quite! [Perhaps I should have read a little further before reacting.]

But there are other tests of QM which show similar negative probabilities. For example, take the reflection of light off a mirror from a source to an intensity detector. There are many paths to the detector that provide negative intensity, in violation of common sense. If you prevent the light from taking those paths (such as via etching the mirror in appropriate spots), the detected intensity increases. This is because the "negative" probability cases are being excluded, which cause the sum of the various path intensities to the detector to increase.

I guess you've been reading Feynman's QED? But all the above is only a matter of interpretation, conducted by someone who is determined to believe that light consists of photons. Allow it to be pure waves and take account of the way interference works and these apparently negative intensities simply cease to exist. I wonder if you've read Mach's "Principles of Physical Optics"? It was first published around 1926 but has recently been re-published. It is written totally without any reference to photons or quantum theory and describes some quite amazing phenomena, all of which it explains using wave theory.

Caroline

 

[reilly]

Re Neg. Probs. (Dr. Chinese)

I agree that on the face of it, the proposition is absurd. But further investigation shows it is far from absurd, and that is part of what makes QM so powerful (as you know).

If you look at the outcomes, you will see that certain combinations are actually predicted (by QM) to have negative probabilities, flying in the face of the "obviously reasonable" counter-position of reality shown above. QM makes plenty of similar counter-intuitive predictions, all of which have so far been pretty well verified. Aspect verified this particular one in his famous experiments.

*************************************

I have a problem with negative probabilities. So, I'd be most grateful if you could provide details and chapter and verse on this idea. Thank you.

Regards,
Reilly Atkinson

 

[Caroline Thompson]

Caroline:
Thanks for your contribution to the thread. I guess many of us here are just trying to gain a better understanding of QM as it has been formulated and generally accepted. I understand the value of questioning the accepted dogma, but at least in my case I think I'll benefit more from gaining full understanting of the subject as presently understood and not to venture into concepts that deffy the commonly accepted theory. (at least not yet)
From all I know, and as Dr.Chinese clearly states, it appears that the tests (which you question) of Bell's inequalities sucessfully prove that locality or reality must give way. Your position is at odds with the accepted theory, and that must be the reason you didn't get a response. You might get better results by initiating a thread just on your proposal. Good luck.

Thanks. I may do some day (I'm not sure I'm allowed to at present) but for the time being will just carry on trying to make sure that people know what they are doing. It is entirely possible that there is no future in "entanglement" and hence no benefit (other than passing exams and/or impressing your friends) in trying to gain a "better understanding" of it.

I maintain that the future of physics lies in a return to the experimental evidence and intuitive approaches. This is as true of Einstein's theories as it is of quantum theory. I think the era in which we are content with mathematical algorithms that give us the right answer but leave us unsatisfied as regards understanding is drawing to a close. We can carry on using the algorithms but we need a new fundamental theory. So far as the experiments are concerned, there is no reason that this should not be entirely intuitive. It need not necessarily produce quantatitive predictions. Its sole purpose is to give us understanding of our universe, with local causes for everything.

Of two things I'm quite certain: the "true" physics of the future will model light as pure waves, with no "photons", and will not involve entanglement. All actual experiments can be explained using ordinary classical correlations, once you allow for the imperfections and the use of inappropriate versions of the Bell test.

Incidentally, unless allowance is made for the fact that real experiments have hidden variables that are "stochastic", only accounting for the probabilities of outcomes and not the outcomes themselves, rational interpretation of the results is impossible. Surely we all agree that when it comes to interpreting real experiments we need to use a model that covers what is actually done, not just an ideal situation dreamt up by theorists? Do have a look at my wikipedia pages (which DrChinese thinks should be somehow made to vanish!). Start with http://en.wikipedia.org/wiki/Bell's_Theorem and follow links to pages on the actual experiments and their loopholes.

Caroline
http://freespace.virgin.net/ch.thompson1/

 

[DrChinese]

Do have a look at my wikipedia pages (which DrChinese thinks should be somehow made to vanish!). Start with http://en.wikipedia.org/wiki/Bell's_Theorem and follow links to pages on the actual experiments and their loopholes.

Caroline
http://freespace.virgin.net/ch.thompson1/

Not vanish, just move to a page called Caroline's Theorem! :)

 

[alexepascual]

Caroline:
I can understand that DrChinese and you don't get along too well. On the other hand, from reading the posts it appears you might find some compatibility with Reilly's ideas. He also has expressed the opinion that quantum correlations are no different than classical correlations.
For the moment I'll accept the standard theory and try to find my own intuitive framework to make sense of it. With respect to the need for intuitive understanding, I see some compatibility between your position and mine. I think that quantum theory still needs to be modified or complemented until it becomes a better explanatory system. (I don't accept the Copenhagen interpretation) But given its success in predicting results (which you may question) , I would not question the validity of the equations.
But when it comes to finding a particular intuitive structure that makes the theory easier to make sense of, there is where you and I take different routes. I understand you are a local realist, which makes you reject anything that departs from classical thinking. I would say you are a conservative person in this respect, although being a conservative may appear as being a rebel nowadays when most people have accepted the revolutionary ideas and these don't appear revolutionary anymore.
I, on the other hand feel more confortable with an explanation that seems absurd to many people, and it is the "many worlds" interpretation. There is an apparent problem with this interpretation (there may be other problems too) and it is the proliferation of worlds. But I think perhaps a new version of this interpretation could turn out to eliminate that proliferation.
Paradoxically, I think in the end the "many worlds" interpretation is also a realist interpretation. Except that "reality" is not constrined to a 4-dimensional space-time but includes all possible outcomes. In this sense, I would say the many worlds interpretation is "super-realist" (that's my own idea).
But I can understand that such interpretation would be repulsive to you, because you are a positivist and would not accept the existence of other "worlds" which cannot be detected or measured directly.
I think Mach's ideas had an important role in the philosophy of science but are not always beneficial when taken to extremes. Remember that Mach didn't believe in the existence of atoms.
I think that some times it is advantageous to consider elements which are not directly measurable but which serve to organize the results of measurement in a more elegant way. Being the fact that nature appears to (most of the time) turn out to be pretty elegant, these non-observable constructs stand a chance of eventually becoming observable or at least so pervasive and necessary that could be considered as part of reality.
On the other hand, I think the original purpose of this thread was to explore the process of entanglement (whose existence you denny. For that reason, I think we continue to debate this controversial topic in the wrong place. You say you are not sure you can create a thread. As far as I know anybody who is a subscriber to the forum can create threads. You should have a button visible in your screen (when you are looking at the list of threads) that says "create new thread" or something similar.

 

[DrChinese]

I have a problem with negative probabilities. So, I'd be most grateful if you could provide details and chapter and verse on this idea. Thank you.

Regards,
Reilly Atkinson

It will probably take me a day or two :) to present it fully, but here is the starting point so you can see where I will be going:

a. 2 single channel detectors I will call Left and Right. The Left is set at angle A=67.5 degrees. The Right alternates between B=22.5 degrees and C=0 degrees. The selection of the angles is done to allow some sleight of hand with the math later. I will call it + if there is a detection, and a - if there is no detection. Efficiencies and actual experimental requirements are ignored as I am just trying to show the concepts involved.

b. In the Realistic case (the assumption of Realism, that the variables exist and have values independent of their observation), you could imagine that both B and C exist at the same time. Therefore, there are 8 combinations that must total to 100%. They are:

[1] A+ B+ C+
[2] A+ B+ C-
[3] A+ B- C+
[4] A+ B- C-
[5] A- B+ C+
[6] A- B+ C-
[7] A- B- C+
[8] A- B- C-

c. In the quantum world, 2 of the above cases are suppressed: [3] and [6]. The reason is that they don't actually exist as possibilities. B is the angle between A and C in my example, and B must always yield the same +/- value as either A or C. In these two cases, B is opposite to A and C. So in the Realistic scenario, [3]>=0 and [6]>=0 (and the sum of all 8 cases=1).

d. So what I have to do is to demonstrate that the quantum mechanical predictions for these 2 cases is actually less than zero. If I can do this, it will demonstrate a big conflict. The difficulty is that I have to do it using terms involving measurements of B or C, but not both at the same time. Can I do it? To be continued...

-DrC

 

[Caroline Thompson]

[1] A+ B+ C+
[2] A+ B+ C-
[3] A+ B- C+
[4] A+ B- C-
[5] A- B+ C+
[6] A- B+ C-
[7] A- B- C+
[8] A- B- C-

This setup looks very similar to the one used in http://en.wikipedia.org/wiki/Sakurai%27s_Bell_inequality
The page covers my interpretation of the Wigner-d'Espagnat inequality, which is alternatively covered by a quantum theorist at http://en.wikipedia.org/wiki/Wigner-d%27Espagnat_inequality . Your idea seems subtly different, but perhaps it would make your task easier to switch to this better-known case? Since the inequality violates local realism it would be expected to also produce negative probabilities if analysed in the manner suggested by Feynman in

Feynman, R P, Simulating Physics with Computers, International Journal of Theoretical Physics 21, 467-488 (1982).​

[I read this a very long time ago and don't guarantee anything!]

Caroline

 

[Caroline Thompson]

Not vanish, just move to a page called Caroline's Theorem! :)

Now that's not fair and you know it!

I discuss Bell's theorem in the spirit originally intended, though, not in the manner to which people have become accustomed. Bell was originally a realist. When experiments were found to (apparently) back quantum theory he was saddened. He said:

"So, for me, it is a pity that Einstein's idea does not work. The reasonable thing just does not work." [P Feyerabend "Historical Comments on Realism", p 194 of A Van der Merwe, F Selleri and G Tarozzi, “Bell's Theorem and the foundations of modern physics” (World Scientific, Singapore, 1992)]​

Caroline
http://freespace.virgin.net/ch.thompson1/

 

[Caroline Thompson]

Caroline:
I can understand that DrChinese and you don't get along too well.

[Actually we understand each other quite well, I think.]

On the other hand, from reading the posts it appears you might find some compatibility with Reilly's ideas. He also has expressed the opinion that quantum correlations are no different than classical correlations.

Thanks, I'll look him up.

Re your multiworlds ideas, you are quite right: I have no place for them in my world!

On the other hand, I think the original purpose of this thread was to explore the process of entanglement (whose existence you deny. For that reason, I think we continue to debate this controversial topic in the wrong place. You say you are not sure you can create a thread. As far as I know anybody who is a subscriber to the forum can create threads. You should have a button visible in your screen (when you are looking at the list of threads) that says "create new thread" or something similar.

Thanks for the advice, but I can't find that button. I have found, though, a comforting little note that says I have the right to create new threads. Some day I'm sure I'll find out how to do so!

Caroline

 

[DrChinese]

Now that's not fair and you know it!

I discuss Bell's theorem in the spirit originally intended, though, not in the manner to which people have become accustomed. Bell was originally a realist. When experiments were found to (apparently) back quantum theory he was saddened. He said:

"So, for me, it is a pity that Einstein's idea does not work. The reasonable thing just does not work." [P Feyerabend "Historical Comments on Realism", p 194 of A Van der Merwe, F Selleri and G Tarozzi, “Bell's Theorem and the foundations of modern physics” (World Scientific, Singapore, 1992)]​

Caroline
http://freespace.virgin.net/ch.thompson1/

Sorry, but I really don't think it is all that important whether Bell believed in local realism at various points in his life or not. His theorem holds great significance and I only wish that Einstein could have lived to see it.

As to the spirit of your Wikipedia presentation of Bell's work: I think you would be disingenuous if you said you were not aware of your presentation bias. Anyone familiar with his work will recognize the hand of a highly biased author. As I have said before, your anti-establishment bias is a good thing when it is properly disclosed. It is not fair to the less educated reader to mis-characterize your stand as commonly accepted science when it is not. That statement remains true even if you are eventually shown to be correct, because then your position would itself become mainstream. That is the way of science.

 

[freep2]

There is no space or matter in the univeres. Just Energy. Light=Energy. Thought= Energy.

 

[DrChinese]

I have a problem with negative probabilities. So, I'd be most grateful if you could provide details and chapter and verse on this idea. Thank you.

Regards,
Reilly Atkinson

I have pretty well completed my post in response, Reilly. I will be creating a separate thread to discuss this, no later than tomorrow. I think the result should be as straightforward as is possible, and the math is such that anyone can easily follow. I hope I don't bungle it :)

-DrC

 

[Caroline Thompson]

Sorry, but I really don't think it is all that important whether Bell believed in local realism at various points in his life or not. His theorem holds great significance and I only wish that Einstein could have lived to see it.

As to the spirit of your Wikipedia presentation of Bell's work: I think you would be disingenuous if you said you were not aware of your presentation bias. Anyone familiar with his work will recognize the hand of a highly biased author. As I have said before, your anti-establishment bias is a good thing when it is properly disclosed. It is not fair to the less educated reader to mis-characterize your stand as commonly accepted science when it is not. That statement remains true even if you are eventually shown to be correct, because then your position would itself become mainstream. That is the way of science.

See my response to your entry http://en.wikipedia.org/wiki/Talk:B...pson.27s_POV_and_Self_Promotion_in_this_topic.

I have never disguised my bias. In my opinion, as I think you know, it is unfair on the public to be told that quantum entanglement has been confirmed experimentally when this is not the case. Why, if it had been satisfactorily proven, would people still be trying to find "loophole-free" tests?

 

[caribou]

Here's a quote from Roland Omnes' book Understanding Quantum Theory:

An entangled state is a quantum superposition of two distinct physical systems. This is a very frequent situation because any composite system whose wave function is not simply a product of the wave functions of its components is entangled. The existence of these states is proclaimed by the Pauli principle, and in that sense, it is responsible for a host of physical properties from the hardness of a stone to the laser.

I consider the hardness of stones and the existence of lasers to be experimentally confirmed.

 

[DrChinese]

1. I have never disguised my bias.

2. In my opinion, as I think you know, it is unfair on the public to be told that quantum entanglement has been confirmed experimentally when this is not the case.

3. Why, if it had been satisfactorily proven, would people still be trying to find "loophole-free" tests?

1. Your participation in public forums usually omits reference to your unorthodox views, so I would say you disguise your bias by omission.

2. My opinion, shared by most scientists, is that it has been shown. Unambiguously.

3. The "closing of loopholes" is one of the most important elements of modern science, and in no way negates existing experiements or lessens their significance. That is why ever more elaborate tests of General Relativity are being performed today - even though GR is here to stay regardless of the outcome. Refinements and improvements to theory are good, even if minor.

 

[Caroline Thompson]

Here's a quote from Roland Omnes' book Understanding Quantum Theory:

An entangled state is a quantum superposition of two distinct physical systems. This is a very frequent situation because any composite system whose wave function is not simply a product of the wave functions of its components is entangled. The existence of these states is proclaimed by the Pauli principle, and in that sense, it is responsible for a host of physical properties from the hardness of a stone to the laser.

I consider the hardness of stones and the existence of lasers to be experimentally confirmed.

OK, so that was Omnes opinion and you are happy to go along with it. You may not be surprised to know that I do not and that I have my own ideas as to why stones are hard and how a laser works. See my web site: http://freespace.virgin.net/ch.thompson1/

Caroline

 

[Caroline Thompson]

1. Your participation in public forums usually omits reference to your unorthodox views, so I would say you disguise your bias by omission.

2. My opinion, shared by most scientists, is that it has been shown. Unambiguously.

3. The "closing of loopholes" is one of the most important elements of modern science, and in no way negates existing experiements or lessens their significance. That is why ever more elaborate tests of General Relativity are being performed today - even though GR is here to stay regardless of the outcome. Refinements and improvements to theory are good, even if minor.

Surely nobody is quite so naive as to think that local realists don't exist? Surely anyone can quickly deduce that I am one?

Re (2), on what is your opinion based? Perhaps it does not depend on the Bell tests, but really there is no other known way to test for entanglement of separated particles and, as you know, there has been no loophole-free experiment. Not only that but it is possible to find perfectly straightforward local causal explanations for all experiment to date if you take account of the actual variant of Bell test used and actual conditions.

You statement (3) is misleading. The kind of revision of theory that will be needed if entanglement turns out to be not a fact is a fundamental one. It may not involve many changes in the equations that are used, but it involves a huge change in outlook. It would mark the beginning of a new era (or is it a return to an old one?) in which magic (i.e. anything not due to local realist causes) was banished from science.

Caroline

 

[Eye_in_the_Sky]

"non-reality" vs. "nonlocality"

I still do not quite see it. I am unable to convince myself that it is wrong to say "quantum correlations imply nonlocality". I acknowledge that Bell's argument as he originally presented it is not enough to establish that claim, and moreover, that my original argument way back at post #59 is inadequate in this regard. However, if I shift the terms of that argument ever so slightly, my 2) becomes:

2') hidden variables "exist" → nonlocality .

And that is fine.

What then would my 1) become? It would become:

1') hidden variables do not "exist" → state-vector description is "complete" → state-vector description gives a full account of the "real factual situation" → under appropriate conditions, the "real factual situation" in one place will change on account of an action performed at another place arbitrarily far away → nonlocality .

I suppose that the main problem with my 1') has to do with this construct of a "real factual situation". Perhaps it is not necessarily a valid one. Is that so? If we (tentatively) grant validity to that construct, can 1') be invalidated on other grounds?