An abstract long-distance correlation experiment

[maline]

My "weird result" is the standard one that I assume stevendaryl intends: A and B both have 1/2 in all entries, E=[(0,1);(1,0)], F=[(3/4,1/4);(1/4,3/4)].
This is generated by transmitting pairs of entangled electrons with total spin 0, but as required, the weirdness is in the result itself.
I consider this weird for two reasons:
1. I expect a model of reality to be expressible in terms of variables- of any form-(field strength, wavefunction amplitude, particle momentum, or anything else) that are defined at each point in spacetime and that evolve, at each point, according to incoming information from the past lightcone, plus possibly some completely random changes, where the distribution depends only on such incoming information. Bell proved that no such model can predict the above outcome. This forces me to try to define & adopt some other concept of reality. As of yet I have not done so, so all I can say is "the results are weird".
2. If we assume that measurement of a quantum variable with more than one possible value is fundamentally nondeterministic (as most people seem to conclude), meaning that before the measurement, the universe does not contain the information of what the result will be, then I see the above result as showing a superluminal effect, as follows:
Let us work in a reference frame such that Alice's measurements occur before Bob's. Consider a pair of measurements that occur immediately after a change in pointer direction, such that Alice's choice of setting & Bob's measurement are spacelike separated. An observer who sees Alice's red light flash, and sees her pointer setting, can say with confidence, "if Bob has this setting, then his blue light is about to flash". If Bob does in fact have the same setting, as noted afterward by Yvonne, then his blue light will indeed flash. But before the measurement, the information (that the blue light will flash) does not exist in Bob's region! If information about a result exists in one part of the universe & not in another part, and afterward this "prediction" comes true in the second region, I don't see how to escape the conclusion that the information traveled, in this case superluminally. (this point is also stevendaryl's, from the earlier thread). Superluminal effects are weird because time order is not defined at spacelike separation. The fact that this effect cannot be used to transmit information only makes it weirder: "But I was thinking of a plan to dye my whiskers green/ And always use so large a fan that they could not be seen".

 

[ddd123]

Yes, it's as if nature chose the weirdest mathematical possibility: before we thought either you have action at a distance and thus ftl communication or not. But instead it preserves relativistic signaling while still having nonlocal influences.

My weirdness function is just Bell inequality violation. But as I said if Neumaier puts it in a perspective I haven't thought of, I might change my mind about weirdness, of course I can't predict my reaction.

 

[A. Neumaier]

My weirdness function is just Bell inequality violation.

Can you please formulate it in terms of the matrices $A,B,E,F$ and transform the amount of violation by some function that maps it into [0,1]?

 

[ddd123]

I'm not an expert, I'm afraid of making mistakes. I hope steveandaryl does it.

 

[maline]

I don't think the weirdness should be expressed as a function of particular results. What is weird is the implications of the theory for a conception of reality. As long as these problems can be demonstrated by some set of results, I give W=0.8 for the theory as a whole.

 

[A. Neumaier]

I don't think the weirdness should be expressed as a function of particular results. What is weird is the implications of the theory for a conception of reality.

But the implications are visible only through the results. I deliberately based this thread on stevendaryl's post because he focussed exclusively on results and their weirdness.

 

[zonde]

4. The degree of weirdness should be quasiconvex, i.e., $W(\lambda R+(1-\lambda)R')\le\max(W(R),W(R'))$ for $0<\lambda<1$. This is needed since if Norbert can create signals leading to the valid results $R$ and $R'$, he can always present in another experiment signals prepared in a statistical mixture of the original signals, in this way producing a signal leading to the valid result $\lambda R+(1-\lambda)R'$. Clearly, this should not increase the degree of weirdness.

I don't think my weirdness function would satisfy this. The reason is that A and B matrices are evaluated differently than E, F. Say we have result where A, B show rare statistical fluke and in another result we have the same but when we take average of A, B from two sets they are rather quite what was expected. Then initial sets would have low weirdness (I do not consider results in E, F reliable) but in averaged set E, F can be considered and they show Bell inequality violation so the weirdness is considerably higher.

 

[A. Neumaier]

result where A, B show rare statistical fluke

If you allow rare statistical flukes to count, then nothing can be considered weird since it might be an extremely rare statistical fluke - even classically, like the proverbial brick that flies upward since all random motions of its atoms happen to go upwards for sufficently long time.

Rare statistical flukes are excluded with probability arbitrarily close to 1 if you make your experiment of sufficient long duration. You may specify if you like an average signaling rate for Norbert, and a lower bound on the data collection time $\Delta t$ that reduces such a possibility to the level specified to regard reactions in CERN as conclusive proof of something real.

 

[maline]

But the implications are visible only through the results.

Of course. But once one "weird result" is experimentally detected, what we have is a weirdness about Nature. The result in question was just a demonstration of the fact. Thus I see no point in assigning a weirdness function to the space of possible results. Either we see Nature as weird or we don't.

 

[A. Neumaier]

once one "weird result" is experimentally detected, what we have is a weirdness about Nature.

Of course. But there is a continuum of results ranging from not at all weird to completely weird, and this thread is going to explore this.

The reason is the same as why brain specialists who want to understand consciousness are not content with stating that there is a fully working brain and describing its features. They learn much more from analyzing a whole spectrum of less well functioning brains since this tells them much more about the possible mechanisms bringing the function (and malfunction) about.

 

[jimgraber]

Can you please give formulas, or at least definite references, so that it is documented what you refer to?

Note that according to my setting, the degree of weirdness must be a function of the experimental results $R=(A,B,D,E)$ only, not a function of the prepared state, which we do not know if we don't have access to what precisely Norbert prepared. My degree of weirdness is about observable things only, not about the theory behind it.

You asked for references:

https://quantiki.org/wiki/entanglement-measure
Here (above) is a link to a discussion and list of entanglement measures. Any one could be taken as a basis for further work. Below is a reference for Quantum nonlocality which indicates that it is different from entanglement in at least some cases.
https://en.wikipedia.org/wiki/Quantum_nonlocality

More later.

 

[jimgraber]

Of course. But there is a continuum of results ranging from not at all weird to completely weird, and this thread is going to explore this.

The reason is the same as why brain specialists who want to understand consciousness are not content with stating that there is a fully working brain and describing its features. They learn much more from analyzing a whole spectrum of less well functioning brains since this tells them much more about the possible mechanisms bringing the function (and malfunction) about.

Four steps on the road from not at all weird to completely weird:
1.) Classical communication
2.) Quantum communication.
3.) PRBox Communication.
4.)FTL communication.

 

[maline]

Of course. But there is a continuum of results ranging from not at all weird to completely weird, and this thread is going to explore this.

The reason is the same as why brain specialists who want to understand consciousness are not content with stating that there is a fully working brain and describing its features. They learn much more from analyzing a whole spectrum of less well functioning brains since this tells them much more about the possible mechanisms bringing the function (and malfunction) about.

Weirdness is not a phenomenon. "What is bringing the weirdness about" is not a meaningful question- the weirdness is built into Nature. The relevant question is "How can we learn to think about reality & nature that will allow these results -all physically possible results- to not seem weird?"

 

[A. Neumaier]

the weirdness is built into Nature

No, definitely not. What is weird is a subjective value judgment. Otherwise everyone would agree that Nature is weird. But I am not theonly counterexample.

 

[A. Neumaier]

The relevant question is "How can we learn to think about reality & nature that will allow these results -all physically possible results- to not seem weird?"

Yes, this question is relevant to this thread, and without understanding the nature of weirdness we cannot answer this question about the seeming weirdness of Nature. Part of what I am doing here is prepare for a better understanding of the nature of weirdness in the context of the above class of experiments.

 

[A. Neumaier]

Please restrict discussion to weirdness in the context of this class of experiments, not in general. Otherwise we'll end up nowhere.

 

[Ken G]

Why does it have to be information? And even then, everything would be that way, all experimental results, all physical settings, including slower-than-light interactions. Why would you conclude that FTL should be ignored then?

I was referring to maline's quote: "But before the measurement, the information (that the blue light will flash) does not exist in Bob's region! If information about a result exists in one part of the universe & not in another part, and afterward this "prediction" comes true in the second region, I don't see how to escape the conclusion that the information traveled, in this case superluminally. (this point is also stevendaryl's, from the earlier thread)." Since the view is also attributed to stevendaryl, it is apparently a common way to view the situation. Without this concept of a meaning of information outside of an information processor, there is never any need for any FTL anything. You can put information processors everywhere you like in this experiment, and you'll never need any of them to get any information FTL, in order for them to apply the laws of physics to understand their observations.

 

[georgir]

To the OP - what is your end goal? Are you just doing this to better understand why we think QM is weird, without the goal of convincing us it is not? Or are you going to argue how some of our proposed weirdness functions are "wrong"? Are you planning to show us your own subjective weirdness function, so we understand why you say QM is not weird?

So far, I'm with ddd123 - matrixes that show bell violations would be weird to me, despite the fact they match reality. As to more precise formulation of that, I do not understand your quasiconvex requirement, and my function would not be continuous but binary or at most ternary if I add for 0.5 to mean I don't think we have enough data yet to rule out statistical flukes or experimental errors (although I am not certain where I would place the boundary).

 

[A. Neumaier]

what is your end goal? Are you just doing this to better understand why we think QM is weird, without the goal of convincing us it is not? Or are you going to argue how some of our proposed weirdness functions are "wrong"? Are you planning to show us your own subjective weirdness function, so we understand why you say QM is not weird?

I revealed already my weirdness function, it is identically zero. And I tried to explain in the originating thread why I do not find quantum mechanics weird.

My goal is to understand the true origin of any subjectively perceived weirdness. Since it is subjective, it cannot be wrong. Perhaps I can convince some readers of my point of view; it is more unlikely but not impossible that I can convince some of the participants.

I spend my time on this and the originating thread because I learn through participating in the discussion about the usually neglected language side of the matter, and because I think I can contribute something nontrivial to understanding. After the end of this discussion, I'll write an Insight article for PF in which my insights into the matter are systematically presented.

 

[A. Neumaier]

I do not understand your quasiconvex requirement, and my function would not be continuous but binary or at most ternary

1. Quasiconvexity is a consistency requirement whose origin I had explained when defining it. It is needed since Norbert is free to choose the signals he sends. He can choose in a random order the signals that lead to $R$ in a fraction $\lambda$ of all signals and the signals that lead to $R'$ in the remaining fraction $1-\lambda$ of all signals. This changes the observed statistics as stated.

2. Imagine Norbert sends more than enough signals to rule out statistical flukes with probability $1-10^{-10}$, but changes the input gradually from something that appears weird to you to something that appears ordinary to you. (He doesn't perform yet any of these infinitely many experiments.) If your weirdness function is not continuous but $\{0,1\}$-valued then at some point the weirdness drops suddenly from ''completely weird'' to ''not at all weird''. Close to this threshold there would be two sets of results whose numerical values differs only in the 10th decimal place, one of which you'd regard as weird, the other one to be ordinary. Norbert only needs to perform these two experiments. I want to exclude such bizarre proposals, since it is obvious that in this case the weirdness measure is itself too weird to be taken seriously.

To be able to argue like this I deliberately didn't want to discuss a single setting - where one cannot analyze anything except taking note that some find the result weird but others don't. Having a continuum of possibilities reveals important nuances in what the weirdness is about.

 

[ddd123]

And I tried to explain in the originating thread why I do not find quantum mechanics weird.

Again, you haven't done that in the context of EPR yet. I'm not clear on if you intend to do that later or at all.

 

[A. Neumaier]

you haven't done that in the context of EPR yet. I'm not clear on if you intend to do that later or at all.

I'll do that in the next stage. (I don't want that my interpretation influences your weirdness criteria.)

 

[ddd123]

For the record this is my weirdness function:

matrixes that show bell violations would be weird to me, despite the fact they match reality [...] and my function would not be continuous but binary

I'd say weirdness 1 for Bell violation of any kind, weirdness 0.1 for no violation (because of particle-wave duality, tunneling, HUP, and similar stuff for which however I could potentially make the weirdness function 0 with some further clarification). If it's unclear whether there's violation or not, my function is undefined because I'd wait for a settlement.

 

[maline]

If your weirdness function is not continuous but {0,1}{0,1}\{0,1\}-valued then at some point the weirdness drops suddenly from ''completely weird'' to ''not at all weird''. Close to this threshold there would be two sets of results whose numerical values differs only in the 10th decimal place, one of which you'd regard as weird, the other one to be ordinary. Norbert only needs to perform these two experiments. I want to exclude such bizarre proposals, since it is obvious that in this case the weirdness measure is itself too weird to be taken seriously.

There is nothing bizarre about such a proposal. The idea of a binary weirdness function is that we assign weirdness "1" to`any result that makes our basic conception of reality untenable, and "0" to a result that can be "explained away" in terms that make sense to us. There is a hard boundary between these sets, given by the Bell inequality. A tiny counterexample to our understanding is just as problematic as a "huge" one, unless we allow for statistical flukes, which we are discounting here.

 

[ddd123]

I would add that the weirdness function has memory. If a series of events "undoubtedly" violates Bell inequalities, then they're gradually toned down until they stop doing so, it's not like I can forget what has happened (if anything, weirdness increases).

Also the assessment is already statistical and thus must be done over a number of events.

 

[Nugatory]

A note from the mentors:
A number of off-topic posts have been removed from this thread, and will be moved to another one. Please, please, try to respect the ground rules of this thread.

 

[A. Neumaier]

There is a hard boundary between these sets, given by the Bell inequality.

This is not hard, since it assumes unrealistic perfect experimental conditions. Tiny counterexamples are statistically not significant, not even with experiments of arbitrarily long duration.

 

[maline]

Tiny counterexamples are statistically not significant, not even with experiments of arbitrarily long duration.

As far as I understand the Law of Large Numbers, as long as the deviations are averaged over all trials, any finite deviation can reach any level of significance by increasing the trials sufficiently. But anyhow, let us agree to ignore cases where the reason for non-weirdness is mere lack of statistical significance.

 

[A. Neumaier]

It seems that the task of defining a proper degree of weirdness is too difficult. I am still waiting for stevendaryl's response to this task (post #49), and then will go on to the next stage.

 

[georgir]

Ok, "too difficult" is not quite it. There are actually too many ways, and I'm not sure which will suffice for you. Heres an attempt.
1. Most trivial: Remap the degree of correlations between different-setting measurements from the range of [0.6666, 0.75] to [0, 1].
2. Account for statistical significance of the accumulated data: Produce the weighted average between the above trivial function and a constant 0.5 function, based on the number of measurements made. At close to 0 measurements, return mostly 0.5. At close to say 1000 measurements and after, return function 1.
3. Account for observed "errors" - for example ratio of mismatched results with same-settings should be close to 0, if it is more again return weighted average of above function and constant 0.5. The weight threshold here like above is a bit arbitrary, but let's say I could go with 0.05 and above leading to entirely 0.5 outputs.
This seems to me to be changing slowly enough with each next measurement to make you happy.