A classical challenge to Bell's Theorem?

*Gordon Watson*

Quote by billschnieder

And my understanding of your position is

GW-1: No reservations re Einstein-Locaity
GW-1: Reservations re EPR elements of reality

GW-1 = Bill-1 = agreement
GW-2 ?≠? Bill-2 = either disagreement or different definitions

http://www.marxists.org/reference/su...e/einstein.htm

1. Your understanding is correct. Thanks. And good!

2. To sort out our "possible" disagreement re EPR-epr may take a while. If you think it relevant here, maybe discuss it here? I think first need for me here is to re-cap with some neatly formatted equations so that critiques can focus on the essentials.

3. This is interesting, from ttn, my emphasis (and ignoring the subsequent sentence):

"Thanks to Sheldon Goldstein (private communication) for pointing out that Tim Maudlin also stresses this point in “Space-time in the quantum world,” in Bohmian Mechan- ics and Quantum Theory: An Appraisal, edited by James T. Cushing, Arthur Fine, and Sheldon Goldstein (Kluwer Academic Publishers, 1996), p. 305. Maudlin writes that “Physicists have been tremendously resistant to any claims of non-locality, mostly on the assumption (which is not a theorem) that non-locality is inconsistent with Relativity. The calculus seems to be that one ought to be willing to pay any price – even the renunciation of pretensions to accurately describe the world – to preserve the theory of Relativity. But the only possible view that would make sense of this obsessive attachment to Relativity is a thoroughly realistic one! These physicists seem to be so certain that Relativity is the last word in space-time structure that they are willing even to forego any coherent account of the entities that inhabit space-time.”" http://arxiv.org/pdf/quant-ph/0404016v2.pdf

4. Maybe I'm a thorough-going realist? BUT let's not get off thread.

*Gordon Watson*

Quote by billschnieder

And my understanding of your position is

GW-1: No reservations re Einstein-Locaity
GW-1: Reservations re EPR elements of reality

GW-1 = Bill-1 = agreement
GW-2 ?≠? Bill-2 = either disagreement or different definitions

http://www.marxists.org/reference/su...e/einstein.htm

Please copy and paste the bits that refer to EPR-epr, or that you want discussed here because relevant to this thread. I find little to fault in Einstein's article: but EPR and their epr-definition is not so clear to me:- "corresponding" is the bug for me.

Quoting Einstein (from your cited article): "I am, in fact, firmly convinced that the essentially statistical character of contemporary quantum theory is solely to be ascribed to the fact that this [theory] operates with an incomplete description of physical systems."

billschnieder

Quote by Gordon Watson

I find little to fault in Einstein's article: but EPR and their epr-definition is not so clear to me:- "corresponding" is the bug for me.

As concerns "corresponding", here is my view, edited from a previous post in another thread:

Quote by billschnieder

Apparently not everyone understands correspondence is difference from equivalence ... As the following illustration demonstrates:

- Elements of reality = Wide spectrum wavelength photons from the sun
- Observation = DrC wears red goggles and looks at the sun
- Observable = Red Sun

- EPR: we can predict the observable with certainty, therefore there is an element of reality corresponding to that observable. That is, we can predict with certainty that if DrC wears red goggles and looks at the sun, he will see a red sun. Therefore there exists an element of reality (photons in the red-wavelength region) from the sun.

- EPR: Realism means the "elements of reality" ie, the red-wavelength photons, exist independently of the act of observation. Just because the "red-wavelength photons from the sun" exist independent of measurement, does not mean "red-sun" is an element of reality, it simply means "red-sun" corresponds to an element of reality which in this case is the "red-wavelength photons from the sun".

Looking at the EPR quote again, they say:

Quote by EPR

If, without in any way disturbing a system, we can predict with certainty (i.e., with probability equal to unity) the value of a physical quantity, then there exists an element of physical reality corresponding to this physical quantity

Note a few very important things often ignored:
1) Predict with certainty - probability 1.0 !!!
2) They did not say "then this physical quantity IS an element of physical reality", they say it corresponds to one.

So "spin-component along x" maybe a physical quantity which corresponds to "spin" which is an element of physical reality. If a theory can predict "spin-component along x" with CERTAINTY, then there exists an element of reality corresponding to it (ie, spin). Now you can predict spin-component along an infinite number of directions with certainty and still they will all correspond to just one element of reality, the spin.

Take three such "physical quantities" which we predict with certainty to be components along "x", "y", "z". Let us manipulate them together, do algebra and come up with some inequalities which for the purpose of this explanation, we call Bill's inequalities

,

xy + yz + xz ≥ V

Practically only one of "x", "y", "z" can be measured at a time on a particle, so therefore only the one which was measured now exists as an "actual outcome". The limitations of experimentation does not change the fact that the element of reality, "spin", exists. Bill's inequality is not testable because it is an expression involving terms which can not be simultaneously realized (actualized) in an experiment. Note that the inequality expresses a relationship between pairs of spin components of the same particle But some people, on the basis of statistics, naively think that if we average over a very large number of different particles, we can obtain the same relationship.

So if we take spin components from different particles and plug in Bill's inequalities, we find that it is violated. Does that mean elements of reality do not exist? Of course not. Now QM makes a prediction for what we will obtain if we measure "xy" on a large number of particles. Now we naively take the result from QM and plug it into the inequality and it is violated. Does that mean elements of reality do not exist? Of course not. Bill's inequality is valid so long as we understand the meaning of the terms in it. Our error is that we have now taken oranges from QM and oranges from experiments and we expect an inequality which was derived for apples to still be obeyed.

*Gordon Watson*

Quote by billschnieder

As concerns "corresponding", here is my view, edited from a previous post in another thread:

Looking at the EPR quote again, they say:

Note a few very important things often ignored:
1) Predict with certainty - probability 1.0 !!!
2) They did not say "then this physical quantity IS an element of physical reality", they say it corresponds to one.

So "spin-component along x" maybe a physical quantity which corresponds to "spin" which is an element of physical reality. If a theory can predict "spin-component along x" with CERTAINTY, then there exists an element of reality corresponding to it (ie, spin). Now you can predict spin-component along an infinite number of directions with certainty and still they will all correspond to just one element of reality, the spin.

Take three such "physical quantities" which we predict with certainty to be components along "x", "y", "z". Let us manipulate them together, do algebra and come up with some inequalities which for the purpose of this explanation, we call Bill's inequalities

,

xy + yz + xz ≥ V

Practically only one of "x", "y", "z" can be measured at a time on a particle, so therefore only the one which was measured now exists as an "actual outcome". The limitations of experimentation does not change the fact that the element of reality, "spin", exists. Bill's inequality is not testable because it is an expression involving terms which can not be simultaneously realized (actualized) in an experiment. Note that the inequality expresses a relationship between pairs of spin components of the same particle But some people, on the basis of statistics, naively think that if we average over a very large number of different particles, we can obtain the same relationship.

So if we take spin components from different particles and plug in Bill's inequalities, we find that it is violated. Does that mean elements of reality do not exist? Of course not. Now QM makes a prediction for what we will obtain if we measure "xy" on a large number of particles. Now we naively take the result from QM and plug it into the inequality and it is violated. Does that mean elements of reality do not exist? Of course not. Bill's inequality is valid so long as we understand the meaning of the terms in it. Our error is that we have now taken oranges from QM and oranges from experiments and we expect an inequality which was derived for apples to still be obeyed.

Bill,

Thanks for addressing a possible difference in our world views. However, it seems to me that there is so much wriggle-room in your wordage that any conclusion would be (for me) inconclusive. For example, this next bit worries me, and seems to be a stretch in the EPR context:-

"Now you can predict spin-component along an infinite number of directions with certainty and still they will all correspond to just one element of reality, the spin."

Questions: Why then bother with the prediction-without-disturbing? What relevance does "prediction" have, if things are as you say?

Possibly I'm biassed by the case that I now mount in the context of this thread:

1. Consider a number of experiments Q_i (i = 1-N), such a series forming a run: Q [itex]\in[/itex] {W, X, Y, Z}.

2. Here is my genuine prediction (no tricks); the primes indicating things in Bob's locale:

[itex]P(\delta _{b}'\lambda' \rightarrow \textbf{b}^+|Q, \;experiment \; number \; i\;selected \;by \;GW) = 1.[/itex]

3. Where, please is the EPR-epr? The one (in your words) that EPR say it corresponds to? The one (presumably) existing ["there exists"] before the selected i-th experiment is concluded?

4. Especially when I tell you that (regarding correspondence) the probability of the predicted outcome having ever occurred before (anywhere in the Cosmos) is zero:

[itex]P(\textbf{b}^+|heretofore) = 0.[/itex]

5. HOWEVER: If you say that, after that particular experiment is concluded (confirming the prediction), THEN there exists a new epr ... well, THEN we agree. Indeed we would agree that a new epr had been brought into EXISTENCE by Q. Then we might also agree that EPR's definition of an EPR-epr is not so good?

PS: The simplicity of my case is designed to make it easy for you to correct any defective perceptions I may have about EPR.

Thanks again,

GW

billschnieder

Quote by Gordon Watson

For example, this next bit worries me, and seems to be a stretch in the EPR context:-

"Now you can predict spin-component along an infinite number of directions with certainty and still they will all correspond to just one element of reality, the spin."

Questions: Why then bother with the prediction-without-disturbing? What relevance does "prediction" have, if things are as you say?

Two reasons:
1) Because it should be a theory not an experiment. A theory can predict with certainty and yet experimental limitations may not allow exact measurement.
2) Completeness: a theory which by itself, i.e. without any experiment, can not predict with certainty, is not complete. If a theory says the probability is 0.98, then there is information missing from it that would have allowed it to give a CERTAIN prediction (P=1 or 0).

Possibly I'm biassed by the case that I now mount in the context of this thread

The case you mount in this thread in my view is to show that the QM result can be obtained from a locally causal theory of hidden variables, contrary to Bell.

1. Consider a number of experiments Q_i (i = 1-N), such a series forming a run: Q [itex]\in[/itex] {W, X, Y, Z}.

2. Here is my genuine prediction (no tricks); the primes indicating things in Bob's locale:

[itex]P(\delta _{b}'\lambda' \rightarrow \textbf{b}^+|Q, \;experiment \; number \; i\;selected \;by \;GW) = 1.[/itex]

3. Where, please is the EPR-epr? The one (in your words) that EPR say it corresponds to? The one (presumably) existing ["there exists"] before the selected i-th experiment is concluded?

It is easier to see if you focus on ONE photon for a moment, not a whole series. What do you think [itex]\lambda_i[/itex] represents? [itex]1[/itex] is the physical quantity which corresponds to the element of reality [itex]\lambda_i[/itex] which belongs to the one photon under consideration. In a complete theory, by knowing [itex]\lambda_i[/itex] and the mechanism that governs interactions, [itex]\rightarrow[/itex], you may predict with certainty that the interaction [itex]\lambda_i \rightarrow b_i^+[/itex] will happen resulting in the physical quantity [itex]1[/itex]. In other words, if we can predict with certainty without in any way disturbing the system the physical quantity [itex]1[/itex], then the corresponding [itex]\lambda_i[/itex] exists.

I guess I do not quite understand your reservation to EPR's elements of reality. More later.

billschnieder

Quote by Gordon Watson

3. Where, please is the EPR-epr? The one (in your words) that EPR say it corresponds to? The one (presumably) existing ["there exists"] before the selected i-th experiment is concluded?

Imagine yourself as the i-th photon, leaving the source flying toward a device. The EPR question is, "Do you have properties [itex]\lambda_i[/itex] which exist as part of your "identity" which ultimately interact with Bob's device to result in a measurement outcome [itex]+1[/itex]?"

The EPR point of view is that if a theory can predict [itex]+1[/itex] with certainty, then the theory is complete with respect to the hidden element of reality [itex]\lambda_i[/itex] which corresponds to [itex]+1[/itex]

*Gordon Watson*

Quote by billschnieder

Imagine yourself as the i-th photon, leaving the source flying toward a device. The EPR question is, "Do you have properties [itex]\lambda_i[/itex] which exist as part of your "identity" which ultimately interact with Bob's device to result in a measurement outcome [itex]+1[/itex]?"

The EPR point of view is that if a theory can predict [itex]+1[/itex] with certainty, then the theory is complete with respect to the hidden element of reality [itex]\lambda_i[/itex] which corresponds to [itex]+1[/itex]

Bill, I'm responding to this post first, in the hope it might ease my response to #243 (see PS at foot). Or (please, Bill) it might help me avoid that need by your saying, "Ah-Ha, I see the light!" For it seems to me that this second post of yours (where it is accurate) is moving you closer to my position re EPR-eprs.

1. What you suggest above ("imagine") is exactly what I do. (Is it not?)

2. But at that level (QM-level), "reality is veiled" from us (in d'Espagnat's terminology; or h > 0).

3. But, on the classical level (where I come from), reality is unveiled.

4. So I just continue in that vein, seeking to move from the classically unveiled to unveil as much of the "veiled reality" as I can.

5. So I just use PT (here, classical Probability Theory), taking the view that a veiled reality may be represented by a probability distribution.

6. So I ("imagining, as usual") answer your good question, "Do you [dear photon i] have properties λ_i which exist as part of your "identity" which ultimately interact with Bob's device to result in a measurement outcome +1?":

Yes, of course!

7. Then, re this from you: "The EPR point of view is that if a theory can predict +1 with certainty, then the theory is complete with respect to the hidden element of reality λ_i which corresponds to +1."

7a. I suggest that this is NOT accurate at all (see PS): and may be misleading you! See how your question (to me, as photon) differs re +1? FOR I THINK this says something quite different; or maybe I'm missing something?

7b. Can you not say: λ_i is the specific HV that delivers the output +1 during the Q_i particle/device interaction?

8. Note this re your quote in #7 above, EPR say (with no mention of "theory" but with focus on existence): "If, without any way disturbing a system, we can predict with certainty, the value of a physical quantity, then there exists an epr corresponding to this physical quantity."

9. So, is it not the case that my prediction is disturbance-free wrt the subject system?

10. So does it not follow, does it not remain the case, that the epr represented by b⁺ is brought into existence by the particle-device interaction; and not otherwise? Is it not the case that λ_i, the pre-interaction HV, is transformed (during the interaction) to become the previously-non-existent (the now-post-interaction existent) b⁺?

11. In a nutshell: Does it not remain the case that EPR's "corresponding" is just plain WRONG?

Bill, this might help you rephrase #243 and I can just reply to your next post? Or else, maybe rephrase questions for #243 with this new info in mind?

PS: See this, as part of my difficulty in responding, in #243: "1 is the physical quantity*** which corresponds to the element of reality λ_i which belongs to the one photon under consideration."

In my view, 1 represents a green-light, a printed +1, a beep, ... it represents the output of the device AS IT TOO is transformed during the interaction. Yes?

*** How about: The OUTPUT +1 "corresponds to" the element of reality b⁺!!!! For both +1 (the device output) and b⁺ (the particle's new property) represent/denote/signal/tell-us of a photon linearly-polarised-parallel-wrt-the-principal-axis-of-the-device (s = 1) or of a spin-half particle spin-up-wrt-the-principal-axis-of-the-device (s = 1/2).

PPS: I am sure that we are NOT saying or implying the same thing; that it's NOT just semantics. Do you agree?

Thanks,

GW

billschnieder

Quote by Gordon Watson

6. So I ("imagining, as usual") answer your good question, "Do you [dear photon i] have properties λ_i which exist as part of your "identity" which ultimately interact with Bob's device to result in a measurement outcome +1?":

Yes, of course!

Then you have no reservations with EPR's elements of reality for that is precisely what they mean. (cf The moon is there even when you are not looking).

7. Then, re this from you: "The EPR point of view is that if a theory can predict +1 with certainty, then the theory is complete with respect to the hidden element of reality λ_i which corresponds to +1."

7a. I suggest that this is NOT accurate at all (see PS): and may be misleading you! See how your question (to me, as photon) differs re +1? FOR I THINK this says something quite different; or maybe I'm missing something?

I guess you are missing something then, though it is not yet clear to me what.

7b. Can you not say: λ_i is the specific HV that delivers the output +1 during the Q_i particle/device interaction?

Yes of course. But what in your mind is the difference between HV and "element of reality".

8. Note this re your quote in #7 above, EPR say (with no mention of "theory" but with focus on existence): "If, without any way disturbing a system, we can predict with certainty, the value of a physical quantity, then there exists an epr corresponding to this physical quantity."

Remember that the goal of the EPR paper was to discuss the completeness of a certain theory. Their objective was not to discuss existence.

9. So, is it not the case that my prediction is disturbance-free wrt the subject system?

I don't get where you are going with this. Please enlighten.

10. So does it not follow, does it not remain the case, that the epr represented by b⁺ is brought into existence by the particle-device interaction; and not otherwise? Is it not the case that λ_i, the pre-interaction HV, is transformed (during the interaction) to become the previously-non-existent (the now-post-interaction existent) b⁺?

I think you may have been misled about what EPR elements of reality are. λ_i is an element of reality.

11. In a nutshell: Does it not remain the case that EPR's "corresponding" is just plain WRONG?

No, I do not buy that. I think we need a simple analogy so you could show me clearly what you think EPR elements of reality are and why you think it is wrong. For example:

We have a tablet with two well defined chemicals X and Y (aka elements of reality). In addition we have two glasses of different liquids A and B. In addition we have a theory which predicts with certainty the following *observables*:

a) if you place the tablet into liquid A, and drink it, it will taste sweet (X interacts with A to produce the sweetness).
b) if you place the tablet into liquid B, and drink it, it will taste bitter (Y interacts with B to produce the bitterness).

It is obvious that each observable (a) or (b) above *corresponds* to an element of reality. The two elements of reality (X,Y) in the particle are simultaneously well defined even before any experiment is performed. The prediction of the *observables* are certain. This is exactly what EPR were talking about.

YET! The *observables* (a) and (b) are not, and can NEVER be simultaneously actual, simply because you can only place your tablet into one of the two liquids. Once you place your tablet, you destroy the tablet. Therefore, the fact that a realist says elements of reality are well defined even when experiments are not performed, does not mean the results of all possible *observables* which can correspond to those observables are also simultaneously actual.

*Gordon Watson*

Bill, I'm in a meeting but just wanted to say THANKS for your effort. I'll get back to you. In meantime could you comment on the BLUE bit in my post. It might help me be more succinct. (I confirm that the moon is there when you're not looking! And I'm happy that our views might be closer than I thought -- even if it's my view that changes.

) Thanks. GW

billschnieder

Quote by Gordon Watson

*** How about: The OUTPUT +1 "corresponds to" the element of reality b⁺!!!! For both +1 (the device output) and b⁺ (the particle's new property) represent/denote/signal/tell-us of a photon linearly-polarised-parallel-wrt-the-principal-axis-of-the-device (s = 1) or of a spin-half particle spin-up-wrt-the-principal-axis-of-the-device (s = 1/2).

Why in your opinion shouldn't it correspond to λ_i, isn't b⁺ simply a deterministic result of interaction of λ_i with the device? I guess I'm not getting why you insist on a strong distinction between λ_i and b⁺ as concerns EPR.

billschnieder

Quote by Gordon Watson

Bill, I'm in a meeting but just wanted to say THANKS for your effort. I'll get back to you. In meantime could you comment on the BLUE bit in my post. It might help me be more succinct. (I confirm that the moon is there when you're not looking! And I'm happy that our views might be closer than I thought -- even if it's my view that changes.

) Thanks. GW

Hi Gordon

I think our views are the same. The only difference I see is that you think your view differs from EPR and I think my view agrees with EPR. But from what you are saying, I'm more sure we agree that "our" views agree

.

*Gordon Watson*

Quote by billschnieder

Why in your opinion shouldn't it correspond to λ_i, isn't b⁺ simply a deterministic result of interaction of λ_i with the device? I guess I'm not getting why you insist on a strong distinction between λ_i and b⁺ as concerns EPR.

??? In Bell's terms, the entangled particles [with pre-test λ_i] are UNpolarised. The post-test particle with (now) b⁺ is POLARISED! BIG DIFFERENCE!

billschnieder

Quote by Gordon Watson

??? In Bell's terms, the entangled particles [with pre-test λ_i] are UNpolarised. The post-test particle with (now) b⁺ is POLARISED! BIG DIFFERENCE!

Again I remind you to focus on one particle. What does polarization mean for this one particle? Isn't it simply a direction of it's spin vector? Don't all particles have spin vectors which have direction? (Polarized or not, entangled or not) Now you have a device which re-orients the spin-vector λi of a particle passing through it into a fixed direction b⁺. Isn't b⁺ simply a value for the new direction of λi after transformation? It is still "spin-vector" after all, so the element of reality continues to be spin-vector. It's new *value* happens to be b⁺. How do you suppose this new direction came to be? Did the device flip a die and randomly pick a direction, or does it have a mechanism which maps old values of λi to one of b⁺ or b^-? Isn't it true that the outcome +1 or -1 is determined ultimately by λi, and the nature of the interaction between λi and the device. Said "nature" which must be existing independently before any such interaction ever took place. This "nature" is what EPR call "elements of reality". Particles do have'em, devices do have'em.

So to my mind, I do not see the big difference at least as far as EPR's epr is concerned.

*Gordon Watson*

Quote by billschnieder

Focussing on one particle: What does polarisation mean for this one particle? It is simply a direction of its spin vector. Don't all particles have spin vectors which have direction: polarised or not, entangled or not? Now you have a device which re-orients the spin-vector λi of a particle passing through it into a fixed direction b⁺. Isn't b⁺ simply a value for the new direction of λi after transformation? It is still a "spin-vector" after all, so the element of reality continues to be a spin-vector. Its new *value* happens to be b⁺. How do you suppose this new direction came to be? The device has a mechanism which maps old values of λi to one of b⁺ or b^-! The outcome +1 or -1 is determined ultimately by λi and the nature of the interaction between λi and the device.

Said "nature" must be existing independently before any such interaction ever took place.

This "nature" is what EPR call "elements of reality". Particles do have them, devices do have them.

So, to my mind, I do not see a big difference in our views, at least as far as EPR's eprs are concerned.

NB: EDITED and emphasised by GW.

Bill, I've edited your post (as above) to remove some typos and put it closer to what I believe we both accept: our core agreement so far being that we each accept Einstein-locality without reservation.

However, the emphasised pieces above represent a point-of-view that I suspect has never occurred to me: so I have some homework to do.

It may take a day or so due my current situation. So, anticipating that I might have to yield to your position (but still doubting it), here's some homework for you:

As your own time permits, please comment on the formatting, the physical significance, the final results, including the short-cut in (6) which you should recognise, whatever, etc. We begin with Q [itex]\in[/itex] {W, X, Y, Z} as discussed earlier in this thread; primes indicate items in Bob's locale; their removal (where appropriate) from HVs is based on the initial correlation of each particle-pair via their [itex]\lambda[/itex] and [itex]\lambda'[/itex] relations; all analysis is classical; Einstein-locality is maintained throughout.

Device/particle interactions are denoted [itex]\delta_{\textbf{b}}' \lambda[/itex], etc. Note that we retain the prime in [itex]\delta_{\textbf{b}}' [/itex] because we may sometimes need to refer to [itex]\delta_{\textbf{b}} [/itex] and [itex]\delta_{\textbf{a}}'[/itex], etc., when discussing the results for identical device settings.

The chances are that there are errors in what follows, including formatting, etc. But the gist of our discussion so far is here, for sure:

[itex]A({\textbf{a}}, \lambda)_Q = (\int d\lambda

\;(\delta_{\textbf{a}} \lambda \rightarrow \left \{{\textbf{a}}^+ , {\textbf{a}}^- \right \})\;cos[2s\cdot({\textbf{a}}, \lambda)])_Q = \pm 1.\;\;\;\;(1)[/itex]

[itex]B({\textbf{b}}, \lambda')_Q = (\int d\lambda'\;(\delta_{\textbf{b}}' \lambda' \rightarrow \left \{{\textbf{b}}^+ , {\textbf{b}}^- \right \})\;cos[2s\cdot ({\textbf{b}}, \lambda')])_Q \;\;\;\;(2)[/itex]

[itex]= ((-1)^{2s} \cdot \int d\lambda\;(\delta_{\textbf{b}}' \lambda \rightarrow \left \{{\textbf{b}}^+ , {\textbf{b}}^- \right \})\;cos[2s\cdot ({\textbf{b}}, \lambda)])_Q = \pm 1. \;\;\;\;(3)[/itex]

[itex]E(AB)_Q = (\int d\lambda\;\rho (\lambda )\;AB)_Q\;\;\;\;(4)[/itex]

[itex]= ((-1)^{2s} \cdot\int d\lambda\;\rho (\lambda )\cdot\int d\lambda\;

(\delta_{\textbf{a}} \lambda \rightarrow \left \{{\textbf{a}}^+ , {\textbf{a}}^- \right \})\;cos[2s\cdot({\textbf{a}}, \lambda)] \cdot \int d\lambda\;(\delta_{\textbf{b}}' \lambda \rightarrow \left \{{\textbf{b}}^+ , {\textbf{b}}^- \right \})\;cos[2s\cdot ({\textbf{b}}, \lambda)])_Q \;\;\;\;(5)[/itex]

[itex]= [(-1)^{2s}]_Q \cdot[ 2 \cdot P(B^+|Q,\,A^+) - 1].\;\;\;\;(6)[/itex]

[itex]E(AB)_W = (cos[2 ({\textbf{a}}, {\textbf{b}})])/2.\;\;\;\;(7)[/itex]

[itex]E(AB)_X = - ({\textbf{a}}. {\textbf{b}})/2.\;\;\;\;(8)[/itex]

[itex]E(AB)_Y = cos[2 ({\textbf{a}}, {\textbf{b}})].\;\;\;\;(9)[/itex]

[itex]E(AB)_Z = - {\textbf{a}}. {\textbf{b}}.\;\;\;\;(10)[/itex]

(E. & O. E.)

*Gordon Watson*

Quote by billschnieder

Again I remind you to focus on one particle. What does polarization mean for this one particle? Isn't it simply a direction of it's spin vector? Don't all particles have spin vectors which have direction? (Polarized or not, entangled or not) Now you have a device which re-orients the spin-vector λi of a particle passing through it into a fixed direction b⁺. Isn't b⁺ simply a value for the new direction of λi after transformation? It is still "spin-vector" after all, so the element of reality continues to be spin-vector. It's new *value* happens to be b⁺. How do you suppose this new direction came to be? Did the device flip a die and randomly pick a direction, or does it have a mechanism which maps old values of λi to one of b⁺ or b^-? Isn't it true that the outcome +1 or -1 is determined ultimately by λi, and the nature of the interaction between λi and the device. Said "nature" which must be existing independently before any such interaction ever took place. This "nature" is what EPR call "elements of reality". Particles do have'em, devices do have'em.

So to my mind, I do not see the big difference at least as far as EPR's epr is concerned.

The above is Bill's view of EPR-eprs, and I have yet to understand it in detail. However, losing sleep, I sense even more difficulties here (for me) than I did with my first reading of EPR and their eprs. At that first reading, years ago, EPR's definition of eprs jumped off the page (to me, so it may be my problem) as unsatisfactory.

EPR's definition (1935) of an EPR-epr: "If, without any way disturbing a system, we can predict with certainty (i.e., with probability equal to unity) the value of a physical quantity, then there exists an element of physical reality [an epr] corresponding to this physical quantity." (My emphasis, identifying two of my problem areas; my [.].)

I interpret "corresponding" in its conventional sense = "according, agreeing, conforming, fitting, matching, tallying."

In my view, EPR's definition of eprs relates to "inferred pre-existence": the inference that the predicted physical quantity existed PRIOR to the test interaction.

(The word "test" is used by me in place of "measurement" -- which I avoid where possible because of its tendency, imho, to mislead when compared to classical measurements. In QM a "measurement" generally perturbs the "measured" system.)

My alternative view relates to two concepts:

"Explicit local causality": "If, without any way disturbing a system p'(λ'), we can predict with certainty the result B of its test at δ_b, which may be a disturbance, then existents λ' and b locally mediate this result. That is B = B(λ', b)."

PLUS

"Explicit local determinism: "The 'prediction with certainty' implies that the new particle property, say b⁺, is determined locally by the interaction of λ' and b. The corresponding device-output B⁺ is equally locally determined."

Here p'(λ') is the particle p' that flies to Bob, its HV = λ'. δ_b is Bob's test-device, its principal axis oriented b. B is the usual test-outcome from Bell (1964), as is B = B(λ', b). B⁺ is the device-output corresponding to the particle property b⁺.

THUS in my view, the existents λ' and b (say, a field-orientation, by way of its connection with device δ), via their interaction, bring into existence the property b⁺ (say) which particle p', now designated p'(b⁺) post-test, NOW possesses ... B⁺ being the corresponding device-output.

SO my view arrives at the SAME function as Bell (1964). However, Bell's subsequent use of this function (1964, his unidentified eqn following his eqn (14)) may indicate that he had in mind EPE eprs -- which I did not; and do not.

SOS, please: critical, alternative, helpful comments invited!

billschnieder

Quote by Gordon Watson

EPR's definition (1935) of an EPR-epr: "If, without any way disturbing a system, we can predict with certainty (i.e., with probability equal to unity) the value of a physical quantity, then there exists an element of physical reality [an epr] corresponding to this physical quantity." (My emphasis, identifying two of my problem areas; my [.].)

I interpret "corresponding" in its conventional sense = "according, agreeing, conforming, fitting, matching, tallying."

In my view, EPR's definition of eprs relates to "inferred pre-existence": the inference that the predicted physical quantity existed PRIOR to the test interaction.

It is not the "physical quantity" that is inferred to pre-exist. It is the epr that is inferred to pre-exist. Purely from the plain-English parsing of the phrase, you can see that they distinguish "physical quantity" from "element of physical reality". They ascribe pre-existence only to the epr, not the physical quantity, and what is being predicted is the physical quantity not the epr. Take a step back, read the sentence again and see that this is the case, noting the use of the phrases "physical quantity" and "element of physical reality".

(The word "test" is used by me in place of "measurement" -- which I avoid where possible because of its tendency, imho, to mislead when compared to classical measurements. In QM a "measurement" generally perturbs the "measured" system.)

It doesn't matter as far as EPR is concerned, whether measurement perturbs the measured system or not because a complete theory should include in it all aspects of the perturbation if one happens.

My alternative view relates to two concepts:
...
THUS in my view, the existents λ' and b (say, a field-orientation, by way of its connection with device δ), via their interaction, bring into existence the property b⁺ (say) which particle p', now designated p'(b⁺) post-test, NOW possesses ... B⁺ being the corresponding device-output.

It sounds to me like you are just using a complicated way of saying the results are "contextual". There is no problem with that, contextual theories were well known and accepted prior to EPR (cf photoelectric effect) and EPR surely did not exclude them. Maybe you thought that EPR did not support contextual theories. But I think it is because you may have misunderstood the meaning of their "corresponding".

*Gordon Watson*

Quote by billschnieder

It is not the "physical quantity" that is inferred to pre-exist. It is the epr that is inferred to pre-exist.

EDIT: Agreed.

Quote by billschnieder

Purely from the plain-English parsing of the phrase, you can see that they distinguish "physical quantity" from "element of physical reality". They ascribe pre-existence only to the epr, not the physical quantity, and what is being predicted is the physical quantity not the epr. Take a step back, read the sentence again and see that this is the case, noting the use of the phrases "physical quantity" and "element of physical reality".

EDIT: OK; thanks.

Quote by billschnieder

It doesn't matter as far as EPR is concerned, whether measurement perturbs the measured system or not because a complete theory should include in it all aspects of the perturbation if one happens.

EDIT: I totally agree with this.

Quote by billschnieder

It sounds to me like you are just using a complicated way of saying the results are "contextual". There is no problem with that, contextual theories were well known and accepted prior to EPR (cf photoelectric effect) and EPR surely did not exclude them. Maybe you thought that EPR did not support contextual theories. But I think it is because you may have misunderstood the meaning of their "corresponding".

EDIT: I think this is the bit that you should expand for my benefit, please: contextual, corresponding: using the elements of reality (via their symbols) that I used in my posting above to make your point. Thanks.

.....

Bill, thanks! I'm again breaking my vow: again posting in a meeting. BUT your effort here looks very good ... and I'm keen to get the monkey off my back. [END OF EDITS. NO More HERE. See next post from me.] GW

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Gordon Watson	Bill, I'm in a meeting but just wanted to say THANKS for your effort. I'll get back to you. In meantime could you comment on the BLUE bit in my post. It might help me be more succinct. (I confirm that the moon is there when you're not looking! And I'm happy that our views might be closer than I thought -- even if it's my view that changes. ) Thanks. GW