No drama quantum electrodynamics? (was: Local realism ruled out?)

[glengarry]

If you are talking about my article, then I don't know how this is relevant, as I mostly consider fields, not particles.

Your paper may have "mostly" considered fields, but quantum electrodynamics is ultimately a particle-based theory of nature; ie. the nature of the interaction between electrons and photons. Further, the term "local realism" cannot be understood in any sense other than a theoretical framework consisting of causally isolated material objects.

Now, let us consider what a "field" is. "A field is a mathematical entity for which addition, subtraction, multiplication and division are well-defined", says Wikipedia. The set of integers is a field. It is, in other words, just a "domain." In order for a field to have any physical significance, "something" must exist on at least one point of a field. Preferably two.

Now, in terms of physics, we see these "somethings" move about and somehow influence one another. If each of these "somethings" do not have any necessary connection to one another at any given instant in time, then they are causally isolated. This is just to say that there are not any kinds of functions operating on the field such that the knowledge of a value of any single point essentially determines the values of all other points at a given instant. This is, after all, what a wavefunction does.

In your paper, you speak about eliminating the wavefunction of QM in order to recover the EM field of Maxwell, so that a bunch of linear equations will pop out. These equations will then be able to describe the independent evolution of the EM field, which you then say can be used in a "pilot wave" theory viz. de Broglie/Bohm. Or something like that.

If all you are really saying is that you can describe how bare EM fields evolve when nobody is looking, I don't think many in the fundamental physics community will get overly excited. After all, the entire motivation behind the genesis of QM (and also QED) was to describe the nature of the *interaction* between EM and sensible matter. Algebraically eliminating matter fields from standard equations isn't going to convince anyone that matter doesn't exist, or that matter doesn't... well... matter.

On the other hand if you are really saying that your arguments somehow invalidate Bell's theorem, I still don't think there will be much excitement just because of the general lack of interest in the physical picture as described by EPR -- that nature, at any given instant, consists of a set of perfectly causally isolated material points.

 

[DrChinese]

So how does this contradict my phrase "we cannot be sure a conclusion of a theorem is valid until all assumptions of the [Bell] theorem are satisfied, and satisfied simultaneously"? If the assumptions are not fulfilled simultaneously, we cannot be sure the inequalities hold for a local realistic theory with free will, so experiments demonstrating violations do not eliminate such theories.

There is a difference between a) the theory and b) the results of experiments looking to determine whether the theory favors QM or local realism. You obscure this difference, and you must be aware that your paper is a difficult sell in light of that. Are you denying the theorem or are you denying the results of Bell tests? Fess up!

So I am asking a simple question: What is the true rate of correlation of entangled photon pairs that would be measured IF all the "loopholes" were closed simultaneously in an experiment? Obviously, not cos^2, so what is it? If your theory is realistic, and observer independent, can you give me a sample of values that might result from a series of entangled pairs? I will specify the *3* (or more) angles, you give me a series of consistent resulting values. On the other hand, if you theory is contextual (not observer independent as EPR specifiies) then please so indicate.

 

[akhmeteli]

There is a difference between a) the theory and b) the results of experiments looking to determine whether the theory favors QM or local realism. You obscure this difference, and you must be aware that your paper is a difficult sell in light of that.

With all due respect, I don't quite see how and where I obscure the difference.

Are you denying the theorem or are you denying the results of Bell tests? Fess up!

First, about the theorem. Let me repeat that I discern two parts of the theorem. In the first part (let us call it BT1), it is proven that some inequalities hold for local realistic theories (in the following, I will not mention the free will assumption, just for simplicity). I accept this part of the theorem. In the second part (let us call it BT2), it is proven that the inequalities can be violated in standard quantum theory (SQM). I admit that one can indeed prove that using the postulates of SQM. I note, however, that both BT2 and SQM have a major deficiency: the postulates of SQM, which are in the same part the assumptions of BT2, are mutually contradictory. This is indeed a deficiency of BT2: as I said, according to formal logic, as soon as you adopt mutually contradictory assumptions, you can derive anything you want.

Second, about the experiments. As I accept BT1, I agree that Bell experiments can prove (in principle) that Nature cannot be described by any local realistic theory. To this end, the experiments must demonstrate violations of the Bell inequalities without loopholes. I have no problems with the generally accepted results of the experiments, however I note that, as of now, there has been at least one loophole in each of the experiments. As soon as there is at least one loophole, BT1 cannot guarantee the Bell inequalities for local realistic theories describing the conditions of the experiment, so the apparent violations of the Bell inequalities in the experiment cannot eliminate local realistic theories.

So I am asking a simple question: What is the true rate of correlation of entangled photon pairs that would be measured IF all the "loopholes" were closed simultaneously in an experiment? Obviously, not cos^2, so what is it? If your theory is realistic, and observer independent, can you give me a sample of values that might result from a series of entangled pairs? I will specify the *3* (or more) angles, you give me a series of consistent resulting values. On the other hand, if you theory is contextual (not observer independent as EPR specifiies) then please so indicate.

The theory is indeed contextual (but deterministic) in the sense that, for example, there are no definite values of all spin components irrespective of the measurement procedure (so I have no problems with the uncertainty relation). I don't want to use the expression "observer independent" (I am not ready to discuss such things as, e.g., consciousness), so let me say that the theory is "instrument dependent". So what does the theory predict for the correlation of entangled photon pairs? Cutting some corners, one can say that to understand this, we must construct the joint state of the photon pair and the instrument and run unitary evolution. This is a messy calculation. For example, the Allahverdyan's paper in Physics Reports, where such calculation is carried out for a simplified model of measurement, is about 200 page long. I cannot do anything of the kind for the example that you are interested in. Let me just mention one thing: the results can depend on time, as no measurement described by unitary evolution is ever final or irreversible.

 

[akhmeteli]

You Devil

Well, I did say that I am not an expert on the Bell inequalities and that I said little if anything new on this issue. I just used other people's arguments. However, the referees of my articles did not raise objections to my discussion of these issues. That does not necessarily mean that the discussion is correct, but that does mean that the deficiencies of the discussion, if any, are not obvious. So if someone raises specific objections to my discussion, I'd be happy to discuss them, but I am going to ignore any arguments ad hominem.

 

[vanhees71]

Ok, I haven't followed your arguments completely. So could you point me to the argument, why standard quantum mechanics (whatever you mean by that; for me it's the mathematical formalism + the minimal statistical interpretation for non-relativistic quantum mechanics, for other readers it might mean something different on the interpretational side) is contradictory in itself? I don't see something obvious, and the great success of quantum theory (in the sense of both relativistic and non-relativistic QT with the minimal statistical interpretaton) applied to real-world observations, including very accurate experiments about the violation of Bell's inequality in favor of standard quantum theory, makes it pretty unlikely that there is a contradiction in quantum theory.

 

[DevilsAvocado]

J.S. Bell’s Concept of Local Causality
http://arxiv.org/pdf/0707.0401.pdf

Thank you very very much bohm2! Bell-QM-SR is my favorite topic and this paper looks like a ‘gift from above’. Thanks!

Bell, in some papers, seems to argue for a return to Lorentzian view with privileged reference frame as per Bohm but does refer to it as "cheap resolution":

This is very interesting, and of course Bell has thought everything through, but just out of curiosity (haven’t had the time to read the paper) – how is HUP dealt with in this scenario? I mean, even if you introduce a privileged reference frame, we are talking about a microscopic quantum measurement and at that level the uncertainty principle rules... it would AFAIK be impossible to tell which one of A & B decohere the shared wavefunction, if the setup is designed to be exactly equivalent regarding photon travel time/length, or did I miss something?

 

[DrChinese]

The theory is indeed contextual (but deterministic) in the sense that, for example, there are no definite values of all spin components irrespective of the measurement procedure (so I have no problems with the uncertainty relation). I don't want to use the expression "observer independent" (I am not ready to discuss such things as, e.g., consciousness), so let me say that the theory is "instrument dependent". So what does the theory predict for the correlation of entangled photon pairs? Cutting some corners, one can say that to understand this, we must construct the joint state of the photon pair and the instrument and run unitary evolution. This is a messy calculation. For example, the Allahverdyan's paper in Physics Reports, where such calculation is carried out for a simplified model of measurement, is about 200 page long. I cannot do anything of the kind for the example that you are interested in. Let me just mention one thing: the results can depend on time, as no measurement described by unitary evolution is ever final or irreversible.

Glad to know you are not obscuring anything. I read the above as a shortcut to this summary: it is not local realistic, and may or may not deviate from QM.

On the other hand, current theory says to expect cos^2(theta) - at least that is how everyone else reads it - and agrees quite nicely with all existing experiments.

 

[akhmeteli]

Glad to know you are not obscuring anything. I read the above as a shortcut to this summary: it is not local realistic, and may or may not deviate from QM.

So you use such a definition of local realism that even classical electrodynamics is not local realistic under your definition. Looks weird and disagrees with the standard meaning of the word "realistic". Your "realism" is the EPR realism. I believe this is an unreasonably narrow definition.

On the other hand, current theory says to expect cos^2(theta) - at least that is how everyone else reads it - and agrees quite nicely with all existing experiments.

Thermodynamics also agrees quite nicely with experiments, however there is no fundamental irreversibility.

 

[DrChinese]

Your "realism" is the EPR realism. I believe this is an unreasonably narrow definition.

This is the accepted language on the matter. If you redefine realism and locality to be either contextual or non-local, then you might be able to construct a mechanism that doesn't run afoul of Bell.

Based on the conversations in this thread so far, I would say you have failed to present something lacking in drama. If it comes down to semantics, that is a hollow victory. I will bow out as long as the commentary doesn't go too far afield of accepted physics.

 

[akhmeteli]

This is the accepted language on the matter.

The language is popular, but this is not the only language in existence. I outlined the drawbacks of such language.

If you redefine realism and locality to be either contextual or non-local, then you might be able to construct a mechanism that doesn't run afoul of Bell.

Judging by the Bell's work quoted in post 17 in this thread, Bell did not think contextuality allowed a mechanism to circumvent his theorem. Neither do I think contextuality allows that, as the projection postulate introduces nonlocality directly. I circumvent the Bell theorem by rejecting the projection postulate.

Based on the conversations in this thread so far, I would say you have failed to present something lacking in drama. If it comes down to semantics, that is a hollow victory. I will bow out as long as the commentary doesn't go too far afield of accepted physics.

According to your definitions, classical electrodynamics and classical mechanics do not lack on drama either (e.g., cf. Santos' comment on coin tossing - post 17 of this thread), so the theories of my articles are in good company.

 

[akhmeteli]

This analogy misstates the argument around experimental evidence for Bell's theorem.

I respectfully disagree. People typically say that violations are demonstrated with loopholes closed separately and tend to make a conclusion that therefore violations will demonstrated when all loopholes are closed. However, if there is just one loophole, local realism does not imply the inequalities, so demonstrated violations cannot eliminate local realism. I believe there is full analogy with my example: if just one assumption is not fulfilled, e.g., the triangle is on a sphere, rather than on a plane, the theorem on the sum of the angles being equal to 180 degrees does not hold (as its assumptions are not satisfied simultaneously), so apparent violations of the theorem do not compromise the validity of the theorem.

No one is suggesting that Bell's theorem is false because experiments don't agree with the Bell prediction. Instead, the argument is that because experiment does not agree with the Bell prediction then either:
a) there is an error in the proof of the theorem, such that the conclusion does not follow from the premises; OR
b) the premises do not accurately describe the real world; OR
c) the premises do accurately describe the real world but the experiments do not.

Case #a is a real longshot; Bell's argument has been scrutinized for decades without any error showing up.

Case #b is the one that says that no local hidden variable theory is consistent with the QM predictions. It's the mainstream interpretation of Bell's theorem and the experimental results.

Case #c is the loophole-chaser's argument. It can never be rejected because no experiment is ever free of possible loopholes; we cannot exclude the possibility that a malicious, clever, invisible, and omnipotent fairy is manipulating our lab equipment to produce wrong but internally consistent results.

Whether you choose #b or #c to explain the experimental results is a matter of which one strains your credulity more. #b is getting better all the time, and the #c arguments are looking ever more contrived and implausible... but that doesn't make them provably wrong, just implausible.

This looks somewhat messy. If I take your alternatives literally, I guess I should accept both b) and c). As for b), I do believe that some premises do not accurately describe the real world, but it's not local realism, but the projection postulate (or some analog of it), which is used in the second part of the Bell theorem to calculate the correlations and to prove that violations can have place in standard quantum theory. I reject the postulate as it contradicts unitary evolution. I do agree that no local hidden variable theory is consistent with the predictions of standard quantum theory, but I add that this is not a problem of local hidden variable theories, as standard quantum theory is inconsistent with itself, containing both unitary evolution and the projection postulate. As for c), I do believe that in all experiments performed so far at least one of the premises did not hold, so the apparent violations do not eliminate local hidden variable theories.

EDIT: I was wrong about accepting c) - please see post 52 in this thread.

 

[akhmeteli]

Ok, I haven't followed your arguments completely. So could you point me to the argument, why standard quantum mechanics (whatever you mean by that; for me it's the mathematical formalism + the minimal statistical interpretation for non-relativistic quantum mechanics, for other readers it might mean something different on the interpretational side) is contradictory in itself? I don't see something obvious, and the great success of quantum theory (in the sense of both relativistic and non-relativistic QT with the minimal statistical interpretaton) applied to real-world observations, including very accurate experiments about the violation of Bell's inequality in favor of standard quantum theory, makes it pretty unlikely that there is a contradiction in quantum theory.

Standard quantum theory (SQT) contains both unitary evolution and the projection postulate (or some analog of it). These two components of SQT are mutually contradictory, as, e.g., unitary evolution cannot produce irreversibility or turn a pure state into a mixture, whereas the projection postulate does just that. This contradiction was known as the notorious problem of quantum measurements long before I was born, so don't blame me. Von Neumann said that unitary evolution is correct only between measurements, whereas the projection postulate is only correct during measurements, but why does not unitary evolution hold during measurements for the larger system containing the system under measurement, the instrument, and the observer, if you wish?

 

[akhmeteli]

Your paper may have "mostly" considered fields, but quantum electrodynamics is ultimately a particle-based theory of nature; ie. the nature of the interaction between electrons and photons.

In my book, it is a field-based theory of nature.

Further, the term "local realism" cannot be understood in any sense other than a theoretical framework consisting of causally isolated material objects.

But not necessarily point-like objects.

Now, let us consider what a "field" is. "A field is a mathematical entity for which addition, subtraction, multiplication and division are well-defined", says Wikipedia. The set of integers is a field. It is, in other words, just a "domain." In order for a field to have any physical significance, "something" must exist on at least one point of a field. Preferably two.

With all due respect, are you pulling my leg, by any chance? That very Wikipedia contains entries both for Field (mathematics) and Field (physics), and those are very different notions.

Perhaps I should stop here.

 

[vanhees71]

Standard quantum theory (SQT) contains both unitary evolution and the projection postulate (or some analog of it). These two components of SQT are mutually contradictory, as, e.g., unitary evolution cannot produce irreversibility or turn a pure state into a mixture, whereas the projection postulate does just that. This contradiction was known as the notorious problem of quantum measurements long before I was born, so don't blame me. Von Neumann said that unitary evolution is correct only between measurements, whereas the projection postulate is only correct during measurements, but why does not unitary evolution hold during measurements for the larger system containing the system under measurement, the instrument, and the observer, if you wish?

What do you mean by "projection postulate"? If you mean the "collapse hypothesis" of some flavors of the Copenhagen interpretation, that's part of the interpretation not the formalism. It's not needed at all to apply quantum theory correctly. For this it's sufficient to use the Minimal Statistical Interpretation, and that's how it is used in practice always.

The postulates are (no intent of mathematical rigor implied)

(1) A quantum system is discribed on (rigged) Hilbert space with a set of self-adjoint operators describing the observables of the system. The possible outcome of (ideal) measurements of an observable are given by the spectrum of the self-adjoint operators.

(2) The state of a quantum system is described by a self-adjoint positive semidefinite trace-1 operator $\hat{R}$. The expectation value of an observable, defined as ensemble averages of independently prepared systems in this state are given by
$$\langle A \rangle=\mathrm{Tr}(\hat{R} \hat{A}),$$
where $\hat{A}$ is the operator representing the observable $A$.

(3) A set of observables $A_i$ ($i \in \{1,2,\ldots,n \}$) are called compatible if all representing operators commute among each other, $[\hat{A}_i,\hat{A}_j]=0$. Such a set of compatible operators are called complete if the common (generalized) eigenspaces are one-dimensional. They are called independent, if no observable can be written as a function of the other observables.

(4) If a system is prepared in the state $\hat{R}$ and $|a_1,\ldots,a_n \rangle$ denotes the (generalized) common eigenvectors of a complete set of compatible independent operator, the probability (density) to measure the corresponding values when measuring the this set of observables is given by
$$P(a_1,\ldots,a_n|R)=\langle a_1,\ldots,a_n|\hat{R}|a_1,\ldots,a_n \rangle.$$
This is Born's Rule.

(5) There exists an self-adjoint operator $\hat{H}$, that is bounded from below and refers to the total energy as an observable. It determines the dynamical time evolution of the system in the way that if $\hat{A}$ represents a (not explicitly) time dependent observable $A$ then
$$\mathrm{D}_t \hat{A}:=\frac{1}{\hbar \mathrm{i}} [\hat{A},\hat{H}]$$
represents the time derivative $\dot{A}$ of the observable $A$.

(6) The Statistical operator is generally explicitly time dependent and obeys the von Neumann equation of motion
$$\partial_t \hat{R}+\frac{1}{\mathrm{i} \hbar} [\hat{R},\hat{H}]=0.$$

 

[DevilsAvocado]

This analogy misstates the argument around experimental evidence for Bell's theorem. No one is suggesting that Bell's theorem is false because experiments don't agree with the Bell prediction. Instead, the argument is that because experiment does not agree with the Bell prediction then either:
a) there is an error in the proof of the theorem, such that the conclusion does not follow from the premises; OR
b) the premises do not accurately describe the real world; OR
c) the premises do accurately describe the real world but the experiments do not.

If I take your alternatives literally, I guess I should accept both b) and c).

[my bolding]

This is probably the most inconsistent and entertaining statement I’ve seen on PF.

 

[DevilsAvocado]

What do you mean by "projection postulate"?

If we bring this down to layman level; akhmeteli is trying hard to convince us all is that if you setup a standard EPR-Bell test experiment, then when the photon detector ‘flash’ to indicate that a photon hit the surface – this is really not happening – due to a conflict between the projection postulate (which is mandatory in QM experiments according to akhmeteli) and unitary evolution.

In exactly the same way, akhmeteli must AFAIK also reject that the electrons hits the detector one by one in this single electron double slit wave experiment:

https://www.youtube.com/watch?v=ZJ-0PBRuthc


And also in exactly the same way, akhmeteli indirectly asserts that if you stare long enough at an omelet in the pan, it will regenerate into 4 complete eggs, and jump into your hands.

Thermodynamics also agrees quite nicely with experiments, however there is no fundamental irreversibility.

To put it short – akhmeteli rejects reality/experiments in favor of mathematics/postulates, which sometimes indeed could be a very successful methodology, but maybe not in this particular case...

 

[akhmeteli]

[my bolding]

This is probably the most inconsistent and entertaining statement I’ve seen on PF.

You are right here, and I am wrong, and I do apologize. I should have said that, strictly speaking, I accept b), but not c), as not all the premises accurately describe the real world, but still "in all experiments performed so far at least one of the premises did not hold, so the apparent violations do not eliminate local hidden variable theories."

 

[DevilsAvocado]

You are right here, and I am wrong, and I do apologize.

No worries akhmeteli, we all do mistakes sometimes – just trust a mushy avocado on this (who almost turned into guacamole once ;)

I should have said that, strictly speaking, I accept b), but not c), as not all the premises accurately describe the real world, but still "in all experiments performed so far at least one of the premises did not hold, so the apparent violations do not eliminate local hidden variable theories."

Okay, that’s great. You accept Bell’s theorem, but not EPR-Bell experiments until all loopholes are closed simultaneously, correct?

 

[Nugatory]

I believe there is full analogy with my example: if just one assumption is not fulfilled, e.g., the triangle is on a sphere, rather than on a plane, the theorem on the sum of the angles being equal to 180 degrees does not hold (as its assumptions are not satisfied simultaneously), so apparent violations of the theorem do not compromise the validity of the theorem.

We all agree that apparent violations of the theorem do not compromise the validity of the theorem, and that they tell us that the theorem does not apply in the situation in which the measurement was made. However, the important question is "Why not?". In your analogy, one reason might be that our triangle is not laid out on a plane; another might be that the angles are not being measured accurately.

The second reason can never be excluded by experiment; we cannot conclusively prove that a malicious, clever, omnipotent, and invisible fairy is not messing with our measurements so we have an unclosable loophole. Nonetheless, we can accept the measurements as experimental support for the proposition that the triangle is not laid out on a plane. It is not necessary that every loophole be closed, it is merely necessary that the remaining loopholes are a less plausible explanation of the measurements than the proposition that the triangle is not laid out on a plane.

This is, of course, generally true of all experimental methodologies.

 

[glengarry]

With all due respect, are you pulling my leg, by any chance? That very Wikipedia contains entries both for Field (mathematics) and Field (physics), and those are very different notions.

A[/PLAIN] field is a physical quantity that has a value for each point in space and time.

I should hope that the mathematical and physical definitions for fields are not wholly unrelated! I was under the impression that there are certain basic physical notions that are ultimately based upon mathematics. When I said that a mathematical field only has physical significance when there are "somethings" at the given locations, then I hope I made the proper transition to the currently accepted notion of the physical field.

We know that an EM field is just a mathematical field (ie, a set of points that constitute the dimensions of space and time) that at each point consists of an energy potential for electrically charged particles like electrons. Failing the existence of any of these particles, then the entire concept of the field is meaningless. This is the same as trying to talk about gravity fields without any massive objects to be affected by them. In other words, it is only because there are objects whose behaviours are affected (eg, through acceleration) that the concept of the field in physics attains any significance.

I think the biggest problem you might be facing in terms of getting wider acceptance is simply that you are trying to apply classical logic to what is now known as quantum logic. I'm not saying that I agree that the term "quantum logic" has any real sense. I'm just saying that there are very many people out there who enjoy the hell out of the fact that they are able to "understand" things that make most people's brains hurt. In fact, every Intro to QM lecture course I've ever seen inevitably includes some kind of joyous disclaimer that no one is supposed to understand what they are being told. They are just supposed to know how to manipulate the symbols.

I wholeheartedly agree with the idea that QM-as-we-know-it offers very little insight into the inner workings of Mother Nature. So, I guess the real question is... What are intelligent people of conscience to do? In my book, the wavefunction -- as a mathematical equation that allows us to solve for real dynamical standing waves -- is an absolute godsend. It gives us models for atomic "orbitals", and we can easily model gravity fields as well. My point is that we should start taking these "real waves" seriously rather than blindly going down the probability interpretation route.

Don't throw the baby out with the bath water. The wavefunction is a beautiful, healthy baby. QM-as-we-know-it looks like a bunch of fetid, gray bath water to me.

 

[bohm2]

I mean, even if you introduce a privileged reference frame, we are talking about a microscopic quantum measurement and at that level the uncertainty principle rules... it would AFAIK be impossible to tell which one of A & B decohere the shared wavefunction, if the setup is designed to be exactly equivalent regarding photon travel time/length, or did I miss something?

The reason that Bell argues for a privileged reference frame is to avoid backward causality. Bell writes:

The reason I want to go back to the idea of an aether here is because in these EPR experiments there is the suggestion that behind the scenes something is going faster than light. Now if all Lorentz frames are equivalent, that also means that things can go backwards in time. . . . [this] introduces great problems, paradoxes of causality, and so on. And so it is precisely to avoid these that I want to say there is a real causal sequence which is defined in the aether.

So from what I understand, Bell is arguing that if there are instantaneous connections and complete Lorenz covariance, then there exists the possibility of causal anomalies, like killing one's own grandfather, etc. If there is just one preferred frame such contradictions do not follow.

 

[akhmeteli]

What do you mean by "projection postulate"? If you mean the "collapse hypothesis" of some flavors of the Copenhagen interpretation,

That's right. The projection postulate states (and I am cutting some corners now) that immediately after a measurement of some observable, if this measurement gave as a result some eigenvalue of the relevant operator, the system is in an eigenstate of the operator with the same eigenvalue.

that's part of the interpretation not the formalism. It's not needed at all to apply quantum theory correctly.

It is needed to calculate the correlation in order to prove that the Bell inequalities can be violated in SQT.

For this it's sufficient to use the Minimal Statistical Interpretation, and that's how it is used in practice always.

The postulates are (no intent of mathematical rigor implied)

(1) A quantum system is discribed on (rigged) Hilbert space with a set of self-adjoint operators describing the observables of the system. The possible outcome of (ideal) measurements of an observable are given by the spectrum of the self-adjoint operators.

(2) The state of a quantum system is described by a self-adjoint positive semidefinite trace-1 operator $\hat{R}$. The expectation value of an observable, defined as ensemble averages of independently prepared systems in this state are given by
$$\langle A \rangle=\mathrm{Tr}(\hat{R} \hat{A}),$$
where $\hat{A}$ is the operator representing the observable $A$.

(3) A set of observables $A_i$ ($i \in \{1,2,\ldots,n \}$) are called compatible if all representing operators commute among each other, $[\hat{A}_i,\hat{A}_j]=0$. Such a set of compatible operators are called complete if the common (generalized) eigenspaces are one-dimensional. They are called independent, if no observable can be written as a function of the other observables.

(4) If a system is prepared in the state $\hat{R}$ and $|a_1,\ldots,a_n \rangle$ denotes the (generalized) common eigenvectors of a complete set of compatible independent operator, the probability (density) to measure the corresponding values when measuring the this set of observables is given by
$$P(a_1,\ldots,a_n|R)=\langle a_1,\ldots,a_n|\hat{R}|a_1,\ldots,a_n \rangle.$$
This is Born's Rule.

(5) There exists an self-adjoint operator $\hat{H}$, that is bounded from below and refers to the total energy as an observable. It determines the dynamical time evolution of the system in the way that if $\hat{A}$ represents a (not explicitly) time dependent observable $A$ then
$$\mathrm{D}_t \hat{A}:=\frac{1}{\hbar \mathrm{i}} [\hat{A},\hat{H}]$$
represents the time derivative $\dot{A}$ of the observable $A$.

(6) The Statistical operator is generally explicitly time dependent and obeys the von Neumann equation of motion
$$\partial_t \hat{R}+\frac{1}{\mathrm{i} \hbar} [\hat{R},\hat{H}]=0.$$

The postulates look quite traditional, but I am afraid there might be a problem with them. Let me ask you: do postulates 5) and 6) hold during measurements? If not, you have to add some postulate on the evolution of the system during measurements. If yes, then does the Hamiltonian take into account the instruments? If yes, then you cannot say that this is "how [the Minimal Statistical Interpretation] is used in practice always" (as typically a Hamiltonian is used where there is no trace of the instruments). If no, then measurements do not change the state of the system, so you cannot say that, after a measurement of a spin projection for one particle of a singlet yields +1/2, a measurement of the spin projection for the other particle of the singlet will yield -1/2, as the first measurement did not change the state of the system. Therefore, you won't be able to prove the second part of the Bell theorem (that the inequalities can be violated in standard quantum theory).

 

[akhmeteli]

We all agree that apparent violations of the theorem do not compromise the validity of the theorem, and that they tell us that the theorem does not apply in the situation in which the measurement was made. However, the important question is "Why not?". In your analogy, one reason might be that our triangle is not laid out on a plane; another might be that the angles are not being measured accurately.

The second reason can never be excluded by experiment; we cannot conclusively prove that a malicious, clever, omnipotent, and invisible fairy is not messing with our measurements so we have an unclosable loophole. Nonetheless, we can accept the measurements as experimental support for the proposition that the triangle is not laid out on a plane. It is not necessary that every loophole be closed, it is merely necessary that the remaining loopholes are a less plausible explanation of the measurements than the proposition that the triangle is not laid out on a plane.

This is, of course, generally true of all experimental methodologies.

The above seems quite arbitrary: who decides what is plausible and what is not? I just cannot agree with such logic: "C'mon, there are loopholes in every experiment, so you're just nit-picking." As of today, all Bell experiments have had significant deficiencies, so they cannot be accepted as evidence of violations of the true Bell inequalities. The issue is too important to accept far-reaching, extraordinary conclusions without proper proof.

 

[Ilja]

About the notions: I find the use of "local" in "local realism" very misleading.

A theory with maximum speed of information transfer c is named "local". But what about a theory with maximum speed of information transfer of 2c? Or, say, of 10000 c? All the difference is, clearly, only another maximal speed of information transfer.

If it makes sense to distinguish local theories from nonlocal theories, then the difference between the two is clearly not the maximal speed of information transfer. It seems even questionable to name a theory like Newtonian gravity nonlocal - the things which cause gravity are localized, have finite speed themself, and their influence decreases with distance, so it seems quite reasonable to name Newtonian gravity a local theory. But, even if not - to name a theory with a finite maximal speed of information transfer nonlocal is clearly nonsensical.

Moreover, it distorts the discussion. There is a strong emotional support for a theory which is named "local". Simply because nonlocal strongly suggests a theory which is completely out of control, where things far away, out of our control, can influence and distort everything.

So, naming theories with maximum speed c local, and with maximum speed 2c nonlocal, is clearly a distortion of scientific discussion, a subtle one, but nonetheless quite powerful emotionally.

What would be more appropriate notions? Einstein-local or Einstein-causal for example. Of course not simply causal, for the same reason - a theory with 2c as the maximal speed of information transfer is clearly causal. Adding the "Einstein" clearly indicates that the fundamental concepts of locality and causality are not endangered, because there are local as well as causal alternatives.

Even better would be Lorentz-symmetric. It is quite clear that symmetries are quite particular properties of particular theories, usually with no fundamental importance, because there are lots of apparent symmetries caused by ignorance of asymmetric details. So, any symmetry is clearly hypothetical.

In the discussion of "local" realism this distorting emotional influence is quite important and really misleading. Indeed, once we accept that "local" realism has to be rejected because of the violation of Bell's inequality, what to do? Reject "locality" or realism?

A question quite different from rejecting Lorentz symmetry or realism, or rejecting Einstein causality or realism. Which fool would propose to reject realism if there is such a cheap alternative as to reject a particular symmetry? As if we have never seen things which look equivalent at a first look but appear different if one looks more carefully. Or if there is such a simple alternative as to reject Einstein causality, given that all one has to do is to return to classical causality?

But rejecting locality? This is, of course, horrible. My home is my castle, I do not want to have nonlocal influences into my home. Realism or not, that doesn't matter that much.

 

[DrChinese]

The above seems quite arbitrary: who decides what is plausible and what is not? I just cannot agree with such logic: "C'mon, there are loopholes in every experiment, so you're just nit-picking." As of today, all Bell experiments have had significant deficiencies, so they cannot be accepted as evidence of violations of the true Bell inequalities. The issue is too important to accept far-reaching, extraordinary conclusions without proper proof.

Arbitrary? Then how does anyone know anything? You are entitled to your own opinion about Bell, the Big Bang, and evolution - as is anyone. But the scientific community decided shortly after Aspect's groundbreaking work to accept the results. Modern discussion of "loopholes" is more for completeness than anything. Note that experiments are currently underway which similarly test General Relativity, nearly 100 years after its advent. This was Nugatory's point.

In case you were asleep, Wineland received the Nobel prize partially for his work in the area. He was part of a team that closed the detection "loophole" over a decade ago. Apparently, even ions can be made to violate local realistic inequalities:

Local realism is the idea that objects have definite properties whether or not they are measured, and that measurements of these properties are not affected by events taking place sufficiently far away. Einstein, Podolsky and Rosen used these reasonable assumptions to conclude that quantum mechanics is incomplete. Starting in 1965, Bell and others constructed mathematical inequalities whereby experimental tests could distinguish between quantum mechanics and local realistic theories. Many experiments 1, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15 have since been done that are consistent with quantum mechanics and inconsistent with local realism. But these conclusions remain the subject of considerable interest and debate, and experiments are still being refined to overcome ‘loopholes’ that might allow a local realistic interpretation. Here we have measured correlations in the classical properties of massive entangled particles (9Be+ ions): these correlations violate a form of Bell's inequality. Our measured value of the appropriate Bell's ‘signal’ is 2.25 ± 0.03, whereas a value of 2 is the maximum allowed by local realistic theories of nature. In contrast to previous measurements with massive particles, this violation of Bell's inequality was obtained by use of a complete set of measurements. Moreover, the high detection efficiency of our apparatus eliminates the so-called ‘detection’ loophole.

Of course, perhaps this experiment has deficiencies that you are privileged to be able to provide a theoretical description of. (Such as: what kind of force or signal is occurring between Alice and Bob's measurement devices to yield the Bell inequality violation. After all, discovery of that currently unknown mechanism would be quite an astonishing breakthrough. And following that, you can explain why such mechanism is elsewhere not apparent.)

 

[DrChinese]

But rejecting locality? This is, of course, horrible. My home is my castle, I do not want to have nonlocal influences into my home. Realism or not, that doesn't matter that much.

Don't come to my home either! I live in Texas, and here we have "castle" laws for intruders. Especially if they are not locals.

 

[Nugatory]

The above seems quite arbitrary: who decides what is plausible and what is not? I just cannot agree with such logic: "C'mon, there are loopholes in every experiment, so you're just nit-picking." As of today, all Bell experiments have had significant deficiencies, so they cannot be accepted as evidence of violations of the true Bell inequalities. The issue is too important to accept far-reaching, extraordinary conclusions without proper proof.

I'm not suggesting that you're nitpicking (your word, not mine); I'm suggesting that you are displaying a basic misunderstanding of the differences between scientific proof based on experimental methods and mathematical proof based on logical methods. (A fair case could be made that we shouldn't use the word "proof" for the former, and again, it's your word not mine).

Experimental methods never prove the truth of a proposition; instead they disprove competing propositions. Therefore the observation that an experiment contains loopholes isn't especially compelling in itself; we also need a plausible (and ideally, testable) conjecture as to how the loopholes allow for some alternative proposition to hold instead.

 

[akhmeteli]

I'm not suggesting that you're nitpicking (your word, not mine); I'm suggesting that you are displaying a basic misunderstanding of the differences between scientific proof based on experimental methods and mathematical proof based on logical methods. (A fair case could be made that we shouldn't use the word "proof" for the former, and again, it's your word not mine).

Experimental methods never prove the truth of a proposition; instead they disprove competing propositions. Therefore the observation that an experiment contains loopholes isn't especially compelling in itself; we also need a plausible (and ideally, testable) conjecture as to how the loopholes allow for some alternative proposition to hold instead.

OK, so the existing experimental data is good enough for you, but not good enough for me. You believe I misunderstand something, I respectfully disagree.

 

[akhmeteli]

Arbitrary? Then how does anyone know anything? You are entitled to your own opinion about Bell, the Big Bang, and evolution - as is anyone. But the scientific community decided shortly after Aspect's groundbreaking work to accept the results. Modern discussion of "loopholes" is more for completeness than anything. Note that experiments are currently underway which similarly test General Relativity, nearly 100 years after its advent. This was Nugatory's point.

This issue cannot be decided by popular vote. Whatever scientific community believes, it agrees that there has been no loophole-free experimental evidence of violations. Belief is one thing, experimental evidence is quite a different thing. Again, Zeilinger ea believe that "The realization of an experiment that is free of all three assumptions - a so-called loophole-free Bell test - remains an important outstanding goal for the physics community". Apparently, you disagree. That does not necessarily mean that you're right and he's wrong, or vice versa.

In case you were asleep, Wineland received the Nobel prize partially for his work in the area. He was part of a team that closed the detection "loophole" over a decade ago. Apparently, even ions can be made to violate local realistic inequalities:

Local realism is the idea that objects have definite properties whether or not they are measured, and that measurements of these properties are not affected by events taking place sufficiently far away. Einstein, Podolsky and Rosen used these reasonable assumptions to conclude that quantum mechanics is incomplete. Starting in 1965, Bell and others constructed mathematical inequalities whereby experimental tests could distinguish between quantum mechanics and local realistic theories. Many experiments 1, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15 have since been done that are consistent with quantum mechanics and inconsistent with local realism. But these conclusions remain the subject of considerable interest and debate, and experiments are still being refined to overcome ‘loopholes’ that might allow a local realistic interpretation. Here we have measured correlations in the classical properties of massive entangled particles (9Be+ ions): these correlations violate a form of Bell's inequality. Our measured value of the appropriate Bell's ‘signal’ is 2.25 ± 0.03, whereas a value of 2 is the maximum allowed by local realistic theories of nature. In contrast to previous measurements with massive particles, this violation of Bell's inequality was obtained by use of a complete set of measurements. Moreover, the high detection efficiency of our apparatus eliminates the so-called ‘detection’ loophole.

Of course, perhaps this experiment has deficiencies that you are privileged to be able to provide a theoretical description of. (Such as: what kind of force or signal is occurring between Alice and Bob's measurement devices to yield the Bell inequality violation. After all, discovery of that currently unknown mechanism would be quite an astonishing breakthrough. And following that, you can explain why such mechanism is elsewhere not apparent.)

Let me just repeat that this work does not contradict the following statement: there has been no loophole-free experimental evidence of violations, sorry. As for "theoretical description"... I often say: we all do what we can, not what we want. I believe that I presented some meaningful and relevant mathematical results in my articles. I wish I could do more, but something is better than nothing. A few years ago these results were unknown.

 

[akhmeteli]

I should hope that the mathematical and physical definitions for fields are not wholly unrelated! I was under the impression that there are certain basic physical notions that are ultimately based upon mathematics. When I said that a mathematical field only has physical significance when there are "somethings" at the given locations, then I hope I made the proper transition to the currently accepted notion of the physical field.

No, sorry. Physical fields typically are not mathematical fields (as defined in your post 36 in this thread): for example, as far as I know, division cannot be reasonably defined for vector or spinor fields.

We know that an EM field is just a mathematical field (ie, a set of points that constitute the dimensions of space and time) that at each point consists of an energy potential for electrically charged particles like electrons. Failing the existence of any of these particles, then the entire concept of the field is meaningless. This is the same as trying to talk about gravity fields without any massive objects to be affected by them. In other words, it is only because there are objects whose behaviours are affected (eg, through acceleration) that the concept of the field in physics attains any significance.

Again, the objects do not have to be point-like.

 

[Charles Wilson]

A theory with maximum speed of information transfer c is named "local". But what about a theory with maximum speed of information transfer of 2c? Or, say, of 10000 c? All the difference is, clearly, only another maximal speed of information transfer.

If it makes sense to distinguish local theories from nonlocal theories, then the difference between the two is clearly not the maximal speed of information transfer.

Ilja, I think you are close to something important.

1. "All the difference is, clearly, only another maximal speed of information transfer."

A theory with a speed limit greater than c must still be mapped onto the "Reality of Speed Limit c". It may be mapped into R(c) in which case, some >R(c) members may not be found in R(c). A good Scientific Theory would in R(c) have to have evidence of something beyond c and R(c).

If I find in my travels, at regular intervals, pieces of paper that have 1, then 2, then 3 and so on, 4, 5, 6, 7, 8, 9, 10, printed on them, I may also find other pieces of paper such that where I go from 1 to 2, the other paper goes "1, 2" then "3, 4" and so on. Maybe I find pieces of paper that read, "1, 4", then "7, 10" and so on.

I may deduce that there is a "Numbers on Paper Reality" where the orders may occur in a different, maybe faster order. Maybe this faster order leaves numbers out when it gets to my R(c).

Now, suppose that I find papers that start at 10 and descend to 1. Or maybe a piece of paper that simply lists the numbers 10, 9, 8, 7, 6, 5, 4, 3, 2, 1. What to make of that?

2. "If it makes sense to distinguish local theories from nonlocal theories, then the difference between the two is clearly not the maximal speed of information transfer."

You are correct. There is, however a mistake made by some. Information Transfer occurs in R(c). "Then, that's all there is, right?"

No. The Information Transfer Protocol may be in some >R(c). There might be a type of Symmetry Break that starts with a "Handshake": "I am a Point "A" with energy X looking for a point "B" with energy - X. I desire to exchange values ". A suitable Point B responds and the values are exchanged. Or maybe it's reversed. Maybe Point B starts first. Maybe the Exchange appears instantaneous to any point residing in R(c).

At the Symmetry Break, the Information Exchange Protocol begins as before, but now information transfer is defined to be only at speed no greater than c. Information appears as a positive P filling a Hole - P. The negative location is only a possibility in a time through space. The arrival of Particle P at Point O is now only a probability. It is important to see that this is not re-establishing a type of Determinism. The screen that receives Einstein's electron ONLY offers possibilities for the electron's arrival (See: Einstein @ Solvay Conference, 1927). Since it only offered an exchange of two opposing values at the exchange, only one electron appears. The energy contract completed, another possibility arises. See Whitehead. See Stapp.

The Hole should appear to be from the future but it maps into the present as a time reversed sequence: "The electron went through both slits but when we check, it only went through one slit and the interference pattern disappeared". "Some puzzles remain. The device should detect both quasi-particles or quasiholes. Push a particle and it moves away. Push a hole and it approaches. Yet the device only detects pushes. (paraphrased from He3 Superfluids, SciAm, June 1990). This is a record in a Positive Universe, R(c). Sometimes we use "Intentional Language": "It's as if the photon knew which path to take".

Entanglement, for example, gives us evidence that there is a >R(c). Our math is almost miraculous in its development in parallel with our empirical discoveries.

Our language is ingenious in picturing possibilities (Wittgenstein) but in use serves many other functions (Later Wittgenstein).
I need to know and use more math to make sure I'm well grounded.
And maybe Zoloft.

CW

 

[Charles Wilson]

AS I went to bed after my long Post, it occurred to me that there was a loophole in my argument concerning "Multiple c's".

Ilja Stated:

"All the difference is, clearly, only another maximal speed of information transfer."
AND
"If it makes sense to distinguish local theories from nonlocal theories, then the difference between the two is clearly not the maximal speed of information transfer."

I agreed with this line of thought. What kept me awake for a half hour longer was something I had settled on some time ago:

http://en.wikipedia.org/wiki/Nyquist–Shannon_sampling_theorem

Clearly, or maybe not so clearly, if this is a sturdy case of "Information Theory", then there must be a "> c" component and it must be ≥ 2c if "Every electron in the Universe has the same attributes". So the problem is at least a compound one. There must be a "> R(c)" Universe and there must be a Wave Component in it. There may be some aspect of this that both Controls this and does not map to "R (c)" but Nyquist-Shannon is pretty much settled.

What is the missing piece? After some thought and some interestingly playful half dreams, the assumption came into my consciousness:

In R(c), information transfers in a time-reversable sequence of X => - X and - X => X at the speed of light. (There is another hidden assumption that there is ONLY a transfer in a single exchange of +/- values. So far, this is still a toy universe example. See Whitehead, "Nexus".) In the > R(c) Universe, the "Handshake" to exchange between points appears to occur "simultaneously".

There is a Logic Problem here and its not just a violation of Special Relativity Sensibilities. To go all Feynman here, consider 2 particles approaching and interacting in an exchange. As you go up the Time axis, the particles approach, approach and approach until "Suddenly a Miracle occurs!", as the old cartoon went. To use what I called "Intentional Language" above, "How did the particles know to exchange at that moment?"

This is a question about the signaling mechanism. Point "A" signals to a field that it can exchange some value and receives a signal that Point "B" can exchange an appropriate opposite value. This symmetric exchange is complex, as in "complicated". "A" must find "B" and receive from "B" AND "B" must find "A" and receive from "A". As a picture, it is not "From a center A of a Circle, construct a radius to a point on the circle and label this point B." It is "There are 2 circles of equal radius in the same plane that intersect with the center of one circle being on the circle of the other and (necessarily) vice versa."

This cannot occur at the speed of light, it must be at some speed > c, indeed, by Nyquist-Shannon, it must be > 2c. 'N if this is a Symmetry Break problem, the "Agreement to Exchange" is made in this > R(c) Universe but the value exchange is made at c.

This gives both an understanding of c but also anchors the "faster than light" statements into a Mathematizable form, without appeal to a Metaphysic. Einstein is satisfied, QM is satisfied. What's not to like?

One thing not to like is the amount of sleep I'm NOT getting. See, the Contra-Positive Problem appears here and...

CW

 

[harrylin]

As the only thread I've ever started before (https://www.physicsforums.com/showthread.php?t=369328 ) attracted a lot of interest, became one of the most viewed threads in the forum, and was closed :-), I'd like to make a short update here.

I have published a new article on the topic: "No drama quantum electrodynamics?", European Physical Journal C, (2013) 73:2371 (http://link.springer.com/content/pdf/10.1140/epjc/s10052-013-2371-4.pdf - open access).

Abstract:

This article builds on recent work (Akhmeteli in Int. J. Quantum Inf. 9(Supp01):17, 2011; J. Math. Phys. 52:082303, 2011), providing a theory that is based on spinor electrodynamics, is described by a system of partial differential equations in 3+1 dimensions, but reproduces unitary evolution of a quantum field theory in the Fock space. To this end, after introduction of a complex four-potential of electromagnetic field, which generates the same electromagnetic fields as the initial real four-potential, the spinor field is algebraically eliminated from the equations of spinor electrodynamics. It is proven that the resulting equations for electromagnetic field describe independent evolution of the latter and can be embedded into a quantum field theory using a generalized Carleman linearization procedure. The theory provides a simple and at least reasonably realistic model, valuable for interpretation of quantum theory. The issues related to the Bell theorem are discussed.

That looks very interesting, as the experimental results to date suggest to me that perhaps no experiment can be done that proves or disproves "quantum non-locality" - a bit like the original formulation of the PoR. Thanks!

 

[harrylin]

[..] if you adopt both unitary evolution and the projection postulate, you just cannot get a local realistic theory. You have to ditch one of the assumptions. Santos opined that we should ditch the theory of quantum measurements. And this is exactly what I do: I reject the theory of quantum measurements, at least as a precise theory. Then I successfully reproduce unitary evolution of a quantum field theory in a local realistic theory [..]
first, the projection postulate contradicts unitary evolution anyway, second, there is no experimental evidence of violations of the genuine Bell inequalities. [..]

OK that clarifies it a little to me. However, I remain puzzled (surely not in the least because spinors and Fock space go over my head!):

[..] This rule is a rule of the theory of quantum measurements (which, strictly speaking, contradicts unitary evolution), as it does not take into account unitary evolution of the total system including the photons and the instrument. Let me note that, strictly speaking, no measurement result is ever final (at least not in a limited volume with impenetrable walls) due to recurrence theorem, so how can your rule be precise? Let me also note that statements of the theory of quantum measurements are derived from unitary evolution in Allahverdyan’s article I quoted earlier, but as approximations, not as precise results. It turns out that there are even some subtle deviations from the Born rule! The derivation of their article was not reproduced for photons yet, but the contradiction between unitary evolution and the theory of quantum measurements exists for photons as well.

What does that mean in practice, concerning expected predictions with your model? Similarly, following DevilsAvocado simplification that "classic says 1+1=2 and QM says 1+1=3"(sic), where will the predictions of your model fit in, for a typical "non-ideal" Bell experiment? You seem to suggest in your latest paper that you expect results that are close to that of standard QM.

[..] People typically say that violations are demonstrated with loopholes closed separately and tend to make a conclusion that therefore violations will demonstrated when all loopholes are closed. However, if there is just one loophole, local realism does not imply the inequalities, so demonstrated violations cannot eliminate local realism. I believe there is full analogy with my example: if just one assumption is not fulfilled, e.g., the triangle is on a sphere, rather than on a plane, the theorem on the sum of the angles being equal to 180 degrees does not hold (as its assumptions are not satisfied simultaneously), so apparent violations of the theorem do not compromise the validity of the theorem. [..]

Let me clarify in this context my comparison with the PoR.
The null result of MMX to verify wave theory would have been interpreted to prove ballistic light theory if such had not been at odds with earlier results from other types of experiments. Then a "loophole" was found: length contraction. And later as a follow-up, the null result of KTX could again be interpreted to prove ballistic light theory, as length contraction is insufficient to compensate the expected effect. However, another "loophole" had already been found: time dilation. Is that a conspiracy of Nature to save the relativity principle? Only if one considers the conservation laws a "conspiracy".

PS: I would appreciate it if you could elaborate on the following statement:

[..] if you use the "EPR definition" of local realism, then classical electrodynamics is not local realistic. The models of my articles are similar to classical electrodynamics and are not "EPR realistic" either - the statement "there are definite values for spin components at all times" is not correct for them, but they are no less realistic than classical electrodynamics. [..]

How is classical electrodynamics not local realistic in that sense?

 

[Ilja]

then there must be a "> c" component and it must be ≥ 2c if "Every electron in the Universe has the same attributes". So the problem is at least a compound one. There must be a "> R(c)" Universe and there must be a Wave Component in it.

AFAIR Gisin has tried to find some observational limits and obtained something like a 10⁴c lower bound. For exact QT we need ∞, but this does not matter if QT is only an approximation.

There is a Logic Problem here and its not just a violation of Special Relativity Sensibilities.

Sorry but I do not see any logic problem here.

The particles are flying away. Whatever particle is measured first (in absolute time, of course) sends a message to the other one which result has been measured. If this information is transferred with high enough speed, so that it reaches the other particle before the second measurement, everything is fine and Bell's inequality can be violated.

Einstein is satisfied, QM is satisfied. What's not to like?

I have not understood your description. But with the straightforward scenario I have give Einstein is not satisfied (because Einstein causality claims <c and is violated) and QM is not satisfied too (because QM requires ∞ as the maximal speed).