An abstract long-distance correlation experiment

[A. Neumaier]

But are you saying that, because there is a description in terms of fields, the Geiger counter clicks at Alice and Bob are correlated in a nonlocal way?

Because of the description by means of quantum fields, the answer must of course be yes, since it is known that this produces results in accordance with the standard quantum mechanical calculations.

But the general reason is indepedent of quantum fields, namely the one given in https://www.physicsforums.com/posts/5364662 (post #132), that Bell inequality derivations assume more than just Lorentz invariance. They assume a very strong form of causality that doesn't follow from relativity. That the inequality is violated in experiments proves that a causality assumption of this form is far too strong.

A deterministic universe can be based on Lorentz invariant laws, and of course implies superdeterminism. But again, one doesn't have to assume superdeterminism to have doubts that your 3-way classification is complete.

 

[morrobay]

Because of the description by means of quantum fields, the answer must of course be yes, since it is known that this produces results in accordance with the standard quantum mechanical calculations.

But the general reason is indepedent of quantum fields, namely the one given in https://www.physicsforums.com/posts/5364662 (post #132), that Bell inequality derivations assume more than just Lorentz invariance. They assume a very strong form of causality that doesn't follow from relativity. That the inequality is violated in experiments proves that a causality assumption of this form is far too strong.

A deterministic universe can be based on Lorentz invariant laws, and of course implies superdeterminism. But again, one doesn't have to assume superdeterminism to have doubts that your 3-way classification is complete.

From post # 132 referenced above : Quote, 1 . Given locality and space like separation Alice's detector setting and measurement result have no effect on Bob's measurement result
Reply: This form of locality is not realized in nature.

Then what are the examples in nature where this form of locality does not apply and how
can this produce Bell inequality violations ?

 

[strangerep]

Yes, special relativity encompasses the Poincare group, but relativity as such doesn't, as field theory in curved spaces (where the translation group is explictly broken but the local Lorentz groups are still intact) shows.

Both special and general relativity give a light (bi-)cone structure on spacetime -- which is the important thing for causality analysis in Bell-type scenarios. I'd argue that light cone structure is implied by relativity, via the constraint that relative speed between 2 (co-located) observers is limited by $c$: there is at least an infinitesimal light cone structure associated with each observer.

The more complicated light cone structure in GR is essentially just a way to knit many infinitesimal light cones together in a continuous manner.

 

[A. Neumaier]

what are the examples in nature where this form of locality does not apply and how can this produce Bell inequality violations ?

Long distance entanglement combined with sufficient shielding from decoherence. This creates a coherent system extended over a considerable amount of space, for which our simplifying intuition of pointwise causality is misleading and (as proved by the experiments) indeed fails completely.

 

[A. Neumaier]

Both special and general relativity give a light (bi-)cone structure on spacetime -- which is the important thing for causality analysis in Bell-type scenarios. I'd argue that light cone structure is implied by relativity, via the constraint that relative speed between 2 (co-located) observers is limited by $c$: there is at least an infinitesimal light cone structure associated with each observer.

Yes, but the light cone structure is an expression of local Lorentz invariance and not of Poincare invariance. On a curved manifold you don't have a consistent notion of translation, hence no Poincare group.

Moreover, for the analysis of Bell-type scanarios one must figure out what precisely is implied by local Lorentz invariance. The very strong form implied by malines post #130 and confirmed in his post #136 to be much stronger than Lorentz invariance is a hidden assumption that impairs the argument!

Note that von Neumann had proved the nonexistence of hidden varible theories by at the time very plausible arguments, regarded to be conclusivve until Bohm discovered his deterministic pilot wave model. Only then it was noticed that his arguments were based on assumptions that are not impeccable and could be violated by sensible models.

In general, a theoretical no-go theorem only applies to situations where its assumptions are satisfied. Thus if the assumptions are stronger than warranted, it does not exclude any situation where the strong assumptions are violated. This also applies to Bell-type reasoning. Since the first two points in maline's synopsis are argued by handwaving only, and since maline conceded that they make stronger assumptions than what is required from the relativity principle, Bell's theorem and its relatives say nothing about general deterministic settings satisfying the relativity principle, as long as they violate the strong form of causality assumed.

One can restate the current state of affairs by saying: Bell's arguments together with the experimental fact that Bell inequalities are violated in Nature implies that Bell's assumptions are too strong and don't apply to Nature. One possibility is to conclude that Nature is necessarily nondeterministic and has properties seemingly violating the principle of relativity. But a much more natural possibility is to conclude that Nature doesn't honor the strong assumptions implicit in steps 1 and 2 of maline's synopsis. They are simply too strong, and not justified by the relativity principle in the form we can be sure about at the present stage of our knowledge - which is just local Lorentz invariance. One day, soneone will perhaps find a deterministic and relativistic model showing this explicitly.

To close this gap in Bell's argument one would have to prove by a formal, conclusive argument (rather than the usual handwaving) that local Lorentz invariance alone implies Bell's locality assumption. I don't think this is possible.

 

[maline]

Since the first two points in maline's synopsis are argued by handwaving only, and since maline conceded that they make stronger assumptions than what is required from the relativity principle

Please don't attribute this specifically to me. I merely repeated what is explicit in every account of Bell's Theorem, including Bell's own.
Here is one that elaborates on the concept: (from wle's post above)
CERN-TH-2053 (1975)

 

[A. Neumaier]

Please don't attribute this specifically to me.
CERN-TH-2053 (1975)

This is just for easy reference. The present discussion is about physical contents, not about historical accuracy. I also do not mean to attack you, but just point out problems with the traditional argumentation.

 

[stevendaryl]

Because of the description by means of quantum fields, the answer must of course be yes, since it is known that this produces results in accordance with the standard quantum mechanical calculations.

But the general reason is indepedent of quantum fields, namely the one given in https://www.physicsforums.com/posts/5364662 (post #132), that Bell inequality derivations assume more than just Lorentz invariance. They assume a very strong form of causality that doesn't follow from relativity. That the inequality is violated in experiments proves that a causality assumption of this form is far too strong.

Well, if the point is to figure out what's weird about QM, then I think this issue is exactly what is weird about QM.

Classically, we can reason about variants of the universe: Alice announces that she will flip a coin, and decide what to do based on the coin result. We can reason about two variants of the actual universe: A universe in which the coin lands "heads-up", and a universe in which the coin lands "tails-up". The two universes would be exactly identical except for (presumably tiny) differences affecting the result of the coin tosses. Far away, Bob is also flipping coins. We assume that these two events are independent, in that we can come up with 4 variants of the universe that only differ near Alice and Bob: One where they both get "heads", one where they both get "tails", and two where they get different results.

A deterministic universe can be based on Lorentz invariant laws, and of course implies superdeterminism.

Superdeterminism is stronger than determinism. Newtonian mechanics is not superdeterministic, but it is deterministic.

Going back to my coin tosses above. It might be that the result of Alice's coin toss is deterministic, and so is the result of Bob's coin toss. The results in both cases are functions of the initial conditions of the universe. However, those initial conditions have enough leeway that the results can be treated as independent, for all practical purposes. Superdeterminism would say that there are no independent choices.

 

[stevendaryl]

I think that the direction of this discussion has changed from "Quantum mechanics is not weird" to "There is no conclusive proof that it is weird". The latter is a much weaker statement, and I guess I would agree with it.

 

[A. Neumaier]

those initial conditions have enough leeway that the results can be treated as independent, for all practical purposes. Superdeterminism would say that there are no independent choices.

Well, who knows? What is the argument for the first sentence, assuming a classical, Newtonian universe, and Alice and Bob being many-particle subsystems?

 

[stevendaryl]

Well, who knows? What is the argument for the first sentence, assuming a classical, Newtonian universe, and Alice and Bob being many-particle subsystems?

I think it's an assumption. It would be very difficult to derive it, but you could certainly test it by having Alice and Bob flip coins a bunch of times, and check for correlations.

 

[ddd123]

Could someone recap the argument for me? What is Bell's assumption that is supposedly too strong and the more sensible Lorentz invariance assumption that could escape it? I got lost in quote hopping. Thanks.

 

[stevendaryl]

Could someone recap the argument for me? What is Bell's assumption that is supposedly too strong and the more sensible Lorentz invariance assumption that could escape it? I got lost in quote hopping. Thanks.

What Bell assumed is that if there are two separate measurements done far apart (too far apart for information to travel from one to affect the other), then they are only correlated through the intersection of their backwards lightcones. So Alice and Bob each perform some measurement, and Alice gets result A and Bob gets result B. Let \alpha be a description of the state of affairs near Alice, and let \beta be a description of the state of affairs near Bob, and let \lambda be the state of affairs in their common backward lightcone (that is, \lambda includes everything that could have affected both Bob and Alice, under the assumption that influences travel at lightspeed or slower). Then Bell assumes that

P(A \& B | \alpha, \beta, \lambda) = P(A | \alpha, \lambda) P(B | \beta, \lambda)

Another way of saying this is that probabilities for distant events are independent, once you've taken into account all the causal factors that might be affecting them. This is definitely not the same as Lorentz Invariance.

 

[stevendaryl]

What Bell assumed is that if there are two separate measurements done far apart (too far apart for information to travel from one to affect the other), then they are only correlated through the intersection of their backwards lightcones. So Alice and Bob each perform some measurement, and Alice gets result A and Bob gets result B. Let \alpha be a description of the state of affairs near Alice, and let \beta be a description of the state of affairs near Bob, and let \lambda be the state of affairs in their common backward lightcone (that is, \lambda includes everything that could have affected both Bob and Alice, under the assumption that influences travel at lightspeed or slower). Then Bell assumes that

P(A \& B | \alpha, \beta, \lambda) = P(A | \alpha, \lambda) P(B | \beta, \lambda)

Another way of saying this is that probabilities for distant events are independent, once you've taken into account all the causal factors that might be affecting them. This is definitely not the same as Lorentz Invariance.

Yet another way to put Bell's assumption is that correlation between events implies that one event influences the other, or that some third thing influences both of them. Plus the assumption that influences travel at lightspeed or slower.

 

[zonde]

that some third thing influences both of them.

You can include that third thing in $\lambda$ if does not influence $\alpha$ and $\beta$ directly.

 

[ddd123]

Yet another way to put Bell's assumption is that correlation between events implies that one event influences the other, or that some third thing influences both of them. Plus the assumption that influences travel at lightspeed or slower.

Thanks. But isn't this just the assumption that superdeterminism is to be ruled out?

 

[A. Neumaier]

Let me attempt to refocus on stage 3 (begun at post #119), and invite again comments.

I want to add some comments on the following:

The knowledge that Alice has feels more like what we know about an
(ideal) pendulum when its initial conditions are unknown - we know the
general structure of the possible configurations, but we don't know
anything about the configuation itself. If we take the analogy seriously
we conclude that [given Norbert's fixed signalling strategy]
Nature solves an initial-value problem with two inputs
(pointer settings) and two outputs (color of response) - that on Alice's
side and that on Bob's side. The joint output depends on both inputs.

Let us consider in a bit more detail the role of knowledge in classical predictions. In a classical dynamical system, the output is not yet determined if only half the initial conditions are known. Thus our quantum system is not extraordinary in this respect. However, in our experiment the output is not even determined when also half of the output is known. This seems a bit unnatural in a classical system, if we just count the number of degrees of freedom needed. But even in classical situations, knowing half the input and half the output of a dynamical system (leading to a boundary-value problem) doesn't always determine the state of the system. examples are resonances in a linear oscillating system, and many nonlinear systems where the boundary value problem has multiple solutions.

One such system is a long and thin bar under ingoing opposite forces at both ends, which has a symmetric solution (bar under tension) and a continuum of asymmetric solutions (the buckled bar). To pick the right solution, one needs additional information. Thus that what Alice knows still leaves room for activities of Bob also has a classical analogue. Of course, all details are different, but the purpose of my remark is that most of what we find in the quantum experiment is qualitatively not too far from classical behavior.

 

[maline]

Of course, all details are different, but the purpose of my remark is that most of what we find in the quantum experiment is qualitatively not too far from classical behavior.

I'm afraid I don't see the point of focusing on the aspects of QM that are not weird. How will that help us to come to terms with the parts that are? But go on...

 

[A. Neumaier]

I'm afraid I don't see the point of focusing on the aspects of QM that are not weird. How will that help us to come to terms with the parts that are? But go on...

The goal is understanding weirdness, thereby making it less weird. Looking at both the weird and the non-weird stuff clarifies the yardsticks that can be put on the arguments. Also, I want to know how convincing my arguments are. At the end, I want to write an Insight article summarizing my position as it developed after all these long threads, and I want to use there the most effective descriptions. Thus your critique now will help me to write a better final report...

 

[wle]

To close this gap in Bell's argument one would have to prove by a formal, conclusive argument (rather than the usual handwaving) that local Lorentz invariance alone implies Bell's locality assumption. I don't think this is possible.

You've misconstrued Bell's argument. The claim was that relativistic causality, or the idea that causal influences shouldn't propagate faster than light, contradicts predictions made by quantum physics (that have since been confirmed experimentally). Among other things, Bell, quoting Einstein, says in the nouvelle cuisine essay I referenced earlier:

In 1907 he [Einstein] pointed out that if an effect followed its cause sooner than light could propagate from the one place to the other, then in some other inertial frames of reference the 'effect' would come before the 'cause'! He wrote

...in my opinion, regarded as pure logic...it contains no contradictions; however it absolutely clashes with the character of our total experience, and in this way is proved the impossibility of the hypothesis...​

of a causal chain going faster than light.

And two paragraphs later, after an example involving a hypothetical murder with a tachyon gun (emphasis added):

What we have to do then is to add to the laws of relativity some responsible causal structure. To avoid causal chains going backward in time in some frames of reference, we require them to go slower than light in any frame of reference.

This is not a hidden assumption or handwaving or a misunderstanding of relativity. Bell is quite open that he is assuming something more than Lorentz invariance only.

 

[strangerep]

Yes, but the light cone structure is an expression of local Lorentz invariance and not of Poincare invariance. On a curved manifold you don't have a consistent notion of translation, hence no Poincare group.

Let's rewind a little bit. I originally thought this thread was in the context of SR (since that's usually the case for Bell-type analyses). That's why I mentioned the Poincare group. But then, in post #147, you mentioned curved spaces, so I generalized to light cone structure. Of course, I meant generalized light "cone" structures as applicable in a curved spacetime, constructed by producing null geodesics from a given point.

But is such an enlargement of this discussion to encompass curved spacetime really necessary? Bell-type experiments are usually performed in the absence of strong gravitational fields, and certainly without any singularities nearby.
Can we therefore restrict this discussion to SR for the sake of minimizing any red herring digressions?

Moreover, for the analysis of Bell-type scanarios one must figure out what precisely is implied by local Lorentz invariance. The very strong form implied by malines post #130 and confirmed in his post #136 to be much stronger than Lorentz invariance is a hidden assumption that impairs the argument!

To keep this subdiscussion self-contained, I'll summarize. Maline wrote:

1.Given locality, and spacelike separation, Alice's detector settings and measurement result have no effect on Bob's measurement result.

2.Therefore, Bob's results depend only on the signal in Bob's region, and his settings.

which are essentially just the usual Bell criteria, as Maline said.

Maline then also said:

[...] Yes, Bell locality is intended as a stronger assumption than "relativity holds". It is justified (for me) by:

1.The intuition that causation occurs from past to present to future, in an objective sense. Since relativity does not define regions outside the light-cone as "past" or "future", causation should be confined to this cone.

2.FTL signalling would imply a possibility of sending messages to the past, and I see no fundamental reason why signals should differ from other forms of influence.

Then,

Since the first two points in maline's synopsis are argued by handwaving only, and since maline conceded that they make stronger assumptions than what is required from the relativity principle, Bell's theorem and its relatives say nothing about general deterministic settings satisfying the relativity principle, as long as they violate the strong form of causality assumed.

The first point concerns how "past" is different from "future", specifically, that an observer can only send (resp. receive) signals to (resp. from) his/her forward (resp. backward) light cone.
The second point is about an observer not being able to send or receive signals at all from outside his/her light bicone.

(The 1st first point is usually made plausible by the lack of tourists from the future, and variations on that theme.)

(I think the 2nd point does indeed follow from special relativity and is not merely "hand-waving", but I'll have to write a more extensive post to explain why.)

Which point do you think is too strong? And how do you propose to weaken it/them?

 

[stevendaryl]

Thanks. But isn't this just the assumption that superdeterminism is to be ruled out?

Yes, it definitely rules out superdeterminism, but I'm not sure that it's equivalent to ruling out superdeterminism.

 

[A. Neumaier]

This is the second and final part of my interpretation of weirdness in the present experimental setting. Its discussion will end Stage 3, and also Stage 2. Stage 4 will then address the implications for causality and relativity of what we did so far.

In our setting, assume for the moment that the nature of Norbert's signals are known to everyone, and are of the kind consistent with quantum mechanics but inconsistent with Bell-type assumptions.
Assume also that there is a human Alice behind the dumb machine Alice.

Under these conditions I want to discuss what the human Alice knows about Bob's results after she has completed her experiments.

My claim is that she knows nothing definite at all.

For the results Bob gets depend on what he is doing, and she is not informed about the latter. At best she can draw conditional inferences ''If Bob's pointer position was set to ... then his results were ...''.

Since there was no complaint about the above, it is perhaps common ground between the participants of this discussion.

How can Alice know this conditional knowledge? Only by believing the predictions of quantum mechanics. If she believes instead in a local hidden variable theory, she would have a different conditional knowledge about Bob's results. This makes it clear that what in this context is conventionally referred to as knowledge is in fact only subjective belief.

How can she believe in the predictions of quantum mechanics? Only if she has been exposed to sufficient indoctrination of the official doctrine through teaching or reading, or because in the past she had done many of these experiments herself.

But then how can she find it weird if she has seen it often enough as being real or as being convincingly conveyed to her as real? Only by an irrational act that

• (i) declares understanding based on reasoning from classical mechanics to be normal but understanding based on reasoning from quantum mechanics or from experience to be weird, while
  
• (ii) it declares predicting from classical mechanics as inappropriate but predicting from quantum mechanics or experience as trustworthy.

Thus the weirdness is in the contradictory mental attitude, not in the experimental setting or in the results obtained. It is like the weirdness in optical illusions that we have accepted as being amusing but not really weird.

 

[maline]

But then how can she find it weird if she has seen it often enough as being real or as being convincingly conveyed to her as real? Only by an irrational act that

• (i) declares understanding based on reasoning from classical mechanics to be normal but understanding based on reasoning from quantum mechanics or from experience to be weird, while
  
• (ii) it declares predicting from classical mechanics as inappropriate but predicting from quantum mechanics or experience as trustworthy.

Thus the weirdness is in the contradictory mental attitude, not in the experimental setting or in the results obtained.

In other words, "QM is correct, ergo it is not weird". Do you think that is helpful?

 

[A. Neumaier]

In other words, "QM is correct, ergo it is not weird". Do you think that is helpful?

These are your words, not mine.

I do not negate that some people find the results of bell-type experiments weird. I just explain it.

Note that my goal in this discussion is not to prove or disprove local realism in the conventional form, but (in line with the originating thread) to investigate weirdness in quantum mechanics and its dependence on the language chosen, using this specific experimental arrangement.

I said (less explicitly from the beginning, but now explicitly and substantiated) that weirdness comes from applying contradictory schemes to prediction and interpretation. This has nothing to do with correctness - whenever one applies contradictory schemes to the same situation it is likely to result in inconsistencies and the associated weirdness.

Indeed, perceived weirdness and the underlying contradictions are a sure sign of having applied somewhere something in an irrational way. It is the basis for discovering misunderstandings, and overcoming them through their analysis - not only in quantum mechanics but everywhere in science and in ordinary life.

We enjoy optical illusions because they appear weird to our senses and at the same time we understand how they come about. Therefore they don't appear weird to our intellect.

My analysis given above shows that something similar happens in certain quantum mechanical long-distance experiments. As in the case of optical illusions, one needs careful preparation of the situation in order to obtain the effect, since in the usual case (i.e., unless special efforts are made to suppress decoherence), entanglement ceases at macroscopically large distances. Our senses are trained on the latter only.

Therefore we feel irritated when confronted with special effects due to extraordinary preparation. Just as in the case of optical illusions - as you can readily verify by following the link. Enjoy!

 

[stevendaryl]

Under these conditions I want to discuss what the human Alice
knows about Bob's results after she has completed her experiments.

My claim is that she knows nothing definite at all.

For the results Bob gets depend on what he is doing, and she is not
informed about the latter. At best she can draw conditional inferences
''If Bob's pointer position was set to ... then his results were ...''.

Okay, but consider the case in which Alice and Bob agree ahead of time what their detector settings will be. For example, they decide to measure spins (or polarizations--I can't remember which one) along the same axis. In that case, Alice's measurement tells her exactly (modulo detection loopholes) what Bob's measurement result will be.

So then we're in the situation where, it seems to me, there are two possibilities:

1. Either Bob's measurement result was fixed before Alice did her measurement (that is, her measurement just informed her about a pre-existing situation), or
2. Alice's measurement affected Bob; it made his situation go from some superposition or mixed state of possibilities to a definite, single possibility.

I think both possibilities are weird and implausible, given everything else that we know about QM and relativity. You seem to be claiming that quantum field theory alone allows us to say that future measurement results are determined now, by the detailed state of the entire universe, and that the probabilities only reflect our lack of knowledge about these details. That seems wildly improbable to me.

If I have a single electron that is in the state "spin-up in the z-direction", then does quantum mechanics have a definite answer to the question "Will it be spin-up or spin-down in the x-direction 10 seconds from now?" It definitely does not. It only gives probabilistic answers. I don't see a difference in principle if you let the system become more complex, to include measuring devices and human scientists, and you let the question change from "Will the electron be spin-up in the x-direction?" to "Will the macroscopic system be such that there is a record of measuring spin-up in the x-direction?"

I understand that classically, systems with a huge number of degrees of freedom can be in metastable state, and that small perturbations can push it over into a discrete number of more stable "pointer states". But I don't think it is at all appropriate to borrow results from classical mechanics here. There is a huge difference between the classical and the quantum state in that superpositions don't exist, classically. So if I delicately balance a coin on its edge, and I perturb it, it will either land on "heads" or it will land on "tails". There is no state corresponding to "a superposition of heads and tails". In quantum mechanics, there is such a state. So the argument that the metastable system will end up in one or the other state just doesn't go through, quantum mechanically.

So I think it's wildly improbable that QM can be made deterministic through the use of metastable states.

 

[ddd123]

Or suppose that Alice and Bob are machines set up by the experimenter. At that point there's no talk about assuming unseen phenomena, the experimenter looks at the correlator results later on and finds them weird.

 

[A. Neumaier]

but consider the case in which Alice and Bob agree ahead of time what their detector settings will be. For example, they decide to measure spins (or polarizations--I can't remember which one) along the same axis. In that case, Alice's measurement tells her exactly (modulo detection loopholes) what Bob's measurement result will be.

... if he keeps the agreement and the detectors work properly. Alice cannot know whether this will be the case. Thus her knowledge is still conditional. But causality is only about what actually happens, not about what happens if...

Or suppose that Alice and Bob are machines set up by the experimenter. At that point there's no talk about assuming unseen phenomena, the experimenter looks at the correlator results later on and finds them weird.

The experimenter doesn't even have to look at the correlated results.

By the same assumptions that allow Alice to know what will happen on Bob's side, Norbert knows already all future correlations - against all causality understood in a naive way.

But suppose that we grant that there is no causal barrier for Norbert to know the correlations that the results of Alice and Bob will have. In this case, what is good for Norbert will even more be good for Alice, who is in the future cone of Norbert. Therefore, in this case there is no causal barrier for her to know of Bob's results. What remains of the weirdness?

The conclusion is that anything seemingly acausal in the class of experiments considered is not due to the material aspects of Nature but to the intelligence of an observer.

But the nonlocal nature of intelligence is familiar from ordinary experience: The use of models and their predictions do not respect causality. We can model and predict what happens in the interior of a black hole although no information is supposed to escape from there. We can model and predict the interior of the sun at any time although we'll never receive direct signals from there. We can model and predict collision or noncollision of comets with the Earth in the far future, although it is not in our past light cone. We can predict the correct local clock time of our twin light years away in his accelerated relativistic journey.

 

[ddd123]

But suppose that we grant that there is no causal barrier for Norbert to know the correlations that the results of Alice and Bob will have. In this case, what is good for Norbert will even more be good for Alice, who is in the future cone of Norbert. Therefore, in this case there is no causal barrier for her to know of Bob's results. What remains of the weirdness?

Keeping the optical illusion analogy, the point is that there's no illusion, it's really happening. That's like saying that Norbert walks up the stairs in Escher's ladder:

He then gets back where he started. But since he's done that already, he knew that was going to happen. So he should find that non-weird.

I don't think so...

 

[A. Neumaier]

it seems to me, there are two possibilities:

1. Either Bob's measurement result was fixed before Alice did her measurement (that is, her measurement just informed her about a pre-existing situation), or
2. Alice's measurement affected Bob; it made his situation go from some superposition or mixed state of possibilities to a definite, single possibility.

In a deterministic universe, the first is the case. The conditions of the density matrix of the universe at any given time determines everything at any later time. Nobody found anything weird in this at the time of Laplace, where in place of the density matrix we had the positions and momenta of all atoms in the universe. Now we have a far more realistic theory, but whatever let Laplace conclude that a deterministic universe is rational and not weird is applicable in the same way to the density matrix of the universe, which, according to orthodox (shut up and calculate) quantum mechanics, evolves in a deterministic way.

 

[stevendaryl]

... if he keeps the agreement and the detectors work properly. Alice cannot know whether this will be the case. Thus her knowledge is still conditional. But causality is only about what actually happens, not about what happens if...

You can certainly reason about the case where Alice and Bob are not humans, but are machines, programmed to perform particular measurements at a particular time. You are saying in that case that Alice's and Bob's results are determined ahead of time. That does not seem plausible to me. It also doesn't seem to really address the issue of quantum weirdness. As I said, in the case of a single electron in the state of being spin-up in the z-direction, QM does not in any way support the idea that it has a definite (but unknown) spin in the x-direction. It says the opposite. As the systems under consideration become more and more complex, it becomes more and more difficult to see them as superpositions of possibilities, and so, for practical matters, we go to density matrix descriptions. These descriptions can be interpreted via classical probability, that the system is actually in this state or that one, but we just don't know which, and the density matrix reflects our lack of knowledge. But looking back, you can see that you introduced density matrices as a practical matter of dealing with very large, complex systems. There is nothing essentially different between the case of a single electron and the case of a detector, other than complexity. So an interpretation that treats the two as fundamentally different (in the electron case, certain questions have no definite answers--it can be in a superposition of possibilities, in the detector case, we say that all macroscopic questions have definite answers--we just don't know what they are ahead of time) seems like cheating to me.

I would say that this effort to show that QM is not weird really amounts to the fact that we have ad hoc rules for dealing with it, and they pretty much work. It doesn't actually make the weirdness go away, or explain it. It just says you don't have to worry about it.

 

[stevendaryl]

In a deterministic universe, the first is the case. The conditions of the density matrix of the universe at any given time determines everything at any later time. Nobody found anything weird in this at the time of Laplace,

That's because in classical mechanics, dynamical variables have definite values at all times, and we can understand statistical phenomena as being due to our lack of knowledge about the precise state of the universe. That interpretation doesn't work in quantum mechanics. If an electron is in the state of being spin-up in the z-direction, then it's not the case that it has a definite (but unknown) spin in the x-direction.

So the comparison with non-weird classical mechanics just heightens how weird QM is. It doesn't lessen it.

 

[A. Neumaier]

That interpretation doesn't work in quantum mechanics.

But it works in quantum field theory. I'll start a new thread about it; please continue any discussion of a deterministic universe there. It has no direct relations with what we are discussing here.

In this thread, the topic is solely the experiment depicted in the initial post, and a discussion of why, or the extend to which, it is weird (independent of any particular explanation of the quantum result).

 

[stevendaryl]

But it works in quantum field theory.

I don't believe it. Quantum field theory certainly can be used to describe a single electron in a state with a definite spin-up in the z-direction, can't it? In that case, is it, or is it not true that the spin in the x-direction is indeterminate?

 

[A. Neumaier]

Quantum field theory certainly can be used to describe a single electron in a state with a definite spin-up in the z-direction, can't it?

Please continue this part of the discussion (relating to quantum field theory) not here but in the following thread:
https://www.physicsforums.com/threads/particles-in-quantum-field-theory.855770/

 

[A. Neumaier]

OK, since no more comments on Stage 2 or 3 are coming in, I declare their discussion closed. My conclusion of the two stages is that the weirdness in the present experimental setting has two sources:

• inappropriate use of relativistic thinking in an otherwise nonrelativistic context (simultaneity) - see post #119
• contradictory assumptions in the theoretical inference of knowledge (which uses quantum mechanical reasoning) and of weirdness (which uses classical reasoning) - see post #173.

The main concern that creates the weirdness seems to be the apparent conflict with causality. This is the topic of the final Stage 4, which begins with the next post #187.

 

[A. Neumaier]

What I did in the leading post #2 to stevendaryl's blueprint is the following:

• I made the language fully precise.
• I removed from the basic setting any model-dependent features.
• I separated all anthropomorphic language from the physics.

The result is a fully local description of how Nature appears to any particular non-intelligent observer in the sense that everything visible to an observer (Norbert, Alice, Bob, Yvonne, or you) was caused in the past light cone of this observer.

Indeed, Alice knows her results (which follow causally from Norbert's signals) and has uncheckable beliefs about Bob's results. Symmetrically, Bob knows his results (which follow causally from Norbert's signals) and has uncheckable beliefs about Alice's results. Yvonne has access in her past light cone to a bigger quantum system (consisting of both Alice's and Bob's results) and hence finds that her correlation analysis satisfy causality, too.

The conclusion is that anything nonlocal in this class of experiments is not due to the material aspects of Nature but to the intelligence of an observer - which generates beliefs about unseen results far away.

But the nonlocal nature of intelligence is familiar from ordinary experience: The use of models and their predictions do not respect causality. We can model and predict what happens in the interior of a black hole although no information is supposed to escape from there. We can model and predict the interior of the sun at any time although we'll never receive direct signals from there. We can model and predict collision or noncollision of comets with the Earth in the far future, although it is not in our past light cone. We can predict the correct local clock time of our twin light years away in his accelerated relativistic journey.

Closer to our everyday experience, we can know the time our bus goes tomorrow morning, although this is an event not in today's past light cone. Of course, we cannot be 100% sure, since the bus might be delayed due to an accident, say. But by the same token, the intelligent Alice behind the dumb robot Alice - cannot know Bobs's measurement for sure since perhaps he is unable to measure anything due to a power outage, a defect transistor, or the limited efficiency of his detector.

If we look closer of what kind of knowledge Alice can infer we find no true knowledge but only conditional knowledge of the form ''if the detector was working properly and Bob did this or that then his results are this or that''. But for lack of knowledge of whether the hypothesis holds she knows nothing about the actual observations - the color of Bob's light (if any).

On the other hand, even Norbert has conditional knowledge about the future. He knows that if Alice and Bob choose the same settings there will (given the particular signals Norbert is sending) be coincident lights of opposite color. Again, he knows nothing definite since Norbert knows neither the color nor whether or not Alice and Bob will (or can) really choose the same setting.

Given that Norbert's action is known, an intelligent Alice at spacetime position $x$ can infer conditional knowledge about what Bob observes at spacetime position $y$ under the assumption that Bob's preparation satisfies a property $p$ only when she has a theory that predicts Bob's observation from information in Alice's past light cone together with property $p$. This is the proper form causality takes for the potential local knowledge at any space-time position $x$, and it is valid for each agent in this experiment, if assumed intelligent.

If this theory is quantum mechanics Alice gets exactly the quantum mechanical (and in practice observed) predictions, and hence true conditional knowledge. If Alice uses instead a classical theory with local hidden variables she gets predictions (and hence ''apparent knowledge'') that contradict Bob's observation - as you as analyzer find out after the completed experiment that includes the comparison of the results of Alice and Bob. There is no way to distinguish inferred true knowledge from inferred apparent knowledge except by

• either waiting till material causality allows one to compare the data,
• or inconclusive plausibility reasoning that leads to endless debates.

Taken together there is nothing intrinsically strange or acausal about the results of Bell-type experiments. For every local observer, the correlations are nonlocal in the sense of relativity theory only as long as they are inferred by intelligent reasoning rather than known by measurement. The extent to which this intelligent reasoning produces true knowledge depends on the extent to which the underlying theory on which the reasoning is based reflects the true properties of Nature.

Therefore the weirdness perceived in certain interpretations of quantum mechanical experiments is fully explained by the futility to assess the weirdness by classical mechanics although it is already well-known that one needs quantum mechanics to be consistent with experiment. Indeed, quantum mechanical experience is already silently assumed in the traditional interpretations of Bell-type experiments, since without it Alice cannot infer anything conditionally about Bob's experiments (except perhaps fake knowledge obtained from local hidden variable theories.)

 

[stevendaryl]

Indeed, Alice knows her results (which follow causally from Norbert's signals) and has uncheckable beliefs about Bob's results.

I don't find this very satisfying. Instead of human Bob, and human Alice, we could program a robot Bob and a robot Alice to choose a particular detector setting at a particular time. Then if the programs are such that robot Alice chooses the same detector setting as robot Bob, she will know exactly what result robot-Bob will get. What kind of knowledge is that? Is that knowledge about the value of a predetermined result? Maybe. But that seems pretty weird. What if their instructions were encrypted, so that it takes up until the moment right before the measurements to figure out what setting to choose?

I don't find this attempt to show why QM is not weird to be at all effective. It seems to me that it amounts to: Let's ignore some of the details that make QM different from non-weird theories. Then it doesn't look so weird, does it? That's right. It's the details that make it weird, that make non-weird ways of understanding what's going on implausible (if not impossible).

 

[A. Neumaier]

she will know exactly what result robot-Bob will get

She is a robot, how can she know anything?

You can program her of course in any way you like and pretend that certain facts represented in the program represent knowledge. But she has no way to check whether her knowledge conforms to reality. This can only be checked by Yvonne.

Checking whether conjectured knowledge is correct is possible only in a causal way. A rational understanding of Nature only needs this much. Nature has facts but no conjectured knowledge, hence need not be causal about the latter. It is only (human or artificial) intelligence that can form well-informed conjectures about things that happen at causally unreachable locations in spacetime.

 

[A. Neumaier]

I don't find this attempt to show why QM is not weird to be at all effective.

At this stage I am not trying to show why QM isn't weird, just why it isn't acausal.

I had already explained the weirdness in Stage 3 - it is due to measuring with double standards. This produces true weirdness, not only in the quantum domain but also in the classical domain whenever in a complex situation the double standards are not clearly recognized and eliminated.

 

[stevendaryl]

She is a robot, how can she know anything?

Well, what does it mean to "know" something, and can machines be said to know things, and are humans a kind of machine, or not? Those are philosophical issues that I would hope do not need to be resolved in order to understand quantum mechanics.

 

[A. Neumaier]

Well, what does it mean to "know" something, and can machines be said to know things, and are humans a kind of machine, or not? Those are philosophical issues that I would hope do not need to be resolved in order to understand quantum mechanics.

Well, if you use these terms in an argument about robots, you better clarify the terms. I deliberately avoided the need to do that by making sure my experimental setting only involved dumb robots without any trace of artificial intelligence. My arguments only used the informal concept of knowledge every educated human is acquainted with.

 

[stevendaryl]

Well, if you use these terms in an argument about robots, you better clarify the terms.

You were using such terms:

Indeed, Alice knows her results (which follow causally from Norbert's signals) and has uncheckable beliefs about Bob's results.

I was questioning why you considered her information about Bob to be "uncheckable beliefs", rather than "knowledge". Is that an important distinction? I brought up robot-Bob only because in that case, Bob's detector settings are predetermined, so are as "knowable" as anything else. Is it important that Alice's beliefs about Bob are uncheckable?

 

[stevendaryl]

I know that this thread was prompted partly by me, but I am not finding it at all enlightening. It seems that the questions that I most want answers to are being dismissed and/or ignored, rather than answered. That's fine--if they don't have good answers that are easily explainable, then so be it. But then, what, exactly is the point of the thread? I thought it was to address the various lingering qualms about the foundations of quantum mechanics.

I am dropping out of this discussion.

 

[A. Neumaier]

I brought up robot-Bob only because in that case, Bob's detector settings are predetermined, so are as "knowable" as anything else.

They are indirectly knowable (by an intelligent Alice behind the dumb robot Alice, as I had mentioned when I started to talk about knowledge) by inference, not by observation. They are not truly knowable: If a power outage causes Bob's preprogrammed detector not to respond during the whole experiment, Alice ''knows'' nonexistent results.

I am dropping out of this discussion.

Maybe you can look at just one more response (to be written; it takes a bit more preparation) where I relate everything to Lorentz invariance (points 1 and 2 in maline's summary of Bell's reasoning). I wouldn't have invested a lot of time in this discussion without having something definite to contribute that I learned during the discussion, and that makes a real difference (in my opinion). After that I'll have said what can be said from my point of view, and the thread can be abandoned or closed.

 

[A. Neumaier]

Bell locality is intended as a stronger assumption than "relativity holds". It is justified (for me) by:
1.The intuition that causation occurs from past to present to future, in an objective sense. Since relativity does not define regions outside the light-cone as "past" or "future", causation should be confined to this cone.
2.FTL signalling would imply a possibility of sending messages to the past, and I see no fundamental reason why signals should differ from other forms of influence.
Therefore, to me, the violation of locality is weird.

Too strong assumptions in a no-go theorem considerably weaken the relevance of the conclusion. Once upon a time, von Neumann had disproved the existence of all hidden variable theories to the satisfaction of everyone. His seemingly innocent assumptions were proved to be ridiculously narrow only when Bohm discovered his hidden variable theory.

If you say that the assumptions are deliberately too strong, it means that there might be sensible causally impeccable hidden variable theories deliberately excluded by this too strong assumptions.

 

[A. Neumaier]

To be able to discuss why I find the assumptions of Bell far too strong, let me distinguish two kinds of causality: extended causality and separable causality. Both kinds of causality are manifestly local Lorentz invariant and imply a signal speed bounded by the speed of light. Here a signal is defined as a dependence of measured results at one spacetime point caused by a preparation at another spacetime point.

Separable causality is what is assumed in Bell-type theorems, and is thereby excluded by the standard experiments (assuming that all other conditions used in the derivation of such theorems hold in Nature). On the other hand, extended causality is far less demanding, and therefore is not excluded by the standard arguments.

To define these two kinds of causality I use the following terminology. A point object has, at any given time in any observer's frame, properties only at a single point, namely the point in the intersection of its world line and the spacelike hyperplane orthogonal to the observer's 4-momentum at the time (in the observer frame) under discussion. An extended object has properties that, in some observer frames at some time depend on more than one space-time position. A joint property is a property that explicitly depends on more than one space-time location within the space-time region swept out by the extended object in the course of time.

Both kinds of causality agree on the causality properties of point objects (''point causality'') but differ on the causality properties of extended objects. Extended causality takes into account what was known almost from the outset of modern quantum mechanics - that quantum objects are intrinsically extended and must be treated as whole. This is explicitly expressed in Bohr's writing (N. Bohr, On the notions of causality and complementarity, Dialectica 2 (1948), 312. Reprinted in Science, New Ser. 111 (1950), 51-54.):

Phrases often found in the physical literature as 'disturbance of phenomena by observation' or 'creation of physical attributes of objects by measurements' represent a use of words like 'phenomena' and 'observation' as well as 'attribute' and 'measurement' which is hardly compatible with common usage and practical definition and, therefore, is apt to cause confusion. As a more appropriate way of expression, one may strongly advocate limitation of the use of the word phenomenon to refer exclusively to observations obtained under specified circumstances, including an account of the whole experiment.

(Thanks to Danu for locating this quote!)

Here are the definitions:

• Point causality: Properties of a point object depend only on its closed past cones, and can influence only its closed future cones.
• Extended causality: Joint properties of an extended object depend only on the union of the closed past cones of their constituent parts, and can influence only the union of the closed future cones of their constituent parts.
• Separable causality: Joint properties of an extended object consist of the combination of properties of their constituent points.

I believe that only extended causality is realized in Nature. It can probably be derived from relativistic quantum field theory. If this is true, there is nothing acausal in Nature. In any case, causality in this weaker, much more natural form is not ruled out by current experiments.

 

[ddd123]

Suppose that extended causality is correct. This seems to be related with your abandoning the particle picture. Then we treat these quantum objects as fields: but the fields we know propagate at the speed of light in vacuum, at most. It is so in QFT. So to account for Bell pairs phenomenology with the fields-only picture, you need to hypotesize an instantaneous field: is it an extra field, kind of like the Higgs field? Or should we extend the behavior of the fields we currently use to somehow instantaneously jump in certain cases?

 

[A. Neumaier]

the fields we know propagate at the speed of light in vacuum, at most. It is so in QFT.

Do you really know QFT well enough to be able to claim this?

Quantum field theory is the theory underlying QED, so it agrees with the quantum mechanical predictions about photons and electrons, if the latter are derived consistent with QED (which they should, to be reliable). Hence the QFT predictions violate separable causality (because of the Bell experiments). One desn't need additional fields for this - just standard QED, together with a thorough understanding of quantum correlation functions.

Relativistic classical fields propagate at the speed of light in vacuum, yes, but quantum fields are different.

If you want to discuss this further, please do it, citing this post, in the corresponding thread on QFT - after you have read and understood which measurable information is obtainable from QFT.

 

[Mentz114]

To be able to discuss why I find the assumptions of Bell far too strong, let me distinguish two kinds of causality: extended causality and separable causality.
..
..
I believe that only extended causality is realized in Nature. It can probably be derived from relativistic quantum field theory. If this is true, there is nothing acausal in Nature. In any case, causality in this weaker, much more natural form is not ruled out by current experiments.

I find this argument very believable.

I venture that extended causality does not require changing of properties at a distance but only changing probability (ie interference) 'at a distance'.

Given that phase is unobservable but a phase change can change probability, why can't the change propagate at phase velocity ?