An abstract long-distance correlation experiment

[edguy99]

Hi There. I am in the process of building an animation to match your parameters in post #2. The steps for a given event are:

1. Generate a photon with a random polarization angle between 0 and 360
2. Split the photon with a BBO crystal and point at Bob and Alice
3. Set a random polarization angle of 0, 120 or 240 to each of Bob and Alices's detector
4. Record if a photon is detected and send a 2 x 3 matrix of numbers to Yvonne

For the detection event, at this time I am using the classical description of the photon used by Dehlinger and Mitchell in http://arxiv.org/PS_cache/quant-ph/pdf/0205/0205171v1.pdf. When a photon meets a polarizer set to an angle γ , it will always register as Vγ if λ is closer to γ than to γ + π/2, i.e.,

• if |γ − λ| ≤ π/4 then vertical
• if |γ − λ| > 3π/4 then vertical
• horizontal otherwise.

At this point I am not sure what to put in the matrix? You can see an example of a run below where a 272° photon is shot, Bob sets his detector to 120° and is hit, likewise Alice sets her detector to 240° and is hit. What should their respective matrices they send to Yvonne look like?

Animation at: http://www.animatedphysics.com/games/photon_longdistance_nonlocality.htm

The NEXT button (not done yet) will generate a continuous stream of these events.

Thanks.

 

[edguy99]

I always go for three, because it's the easiest to see the weirdness of quantum statistics. Three was also used by Dr. Chinese in his essay here:
http://drchinese.com/David/Bell_Theorem_Easy_Math.htm
... With three choices, you can show that no hidden variable theory works, but not with just two.

Great post, I agree on your two choice assessment, but I disagree on your assessment of three choices. Here is why I feel that way. The quoted essay, is making the assumption that a split photon will measure the same on both Bob and Alice's detectors if Bob and Alice both have the same settings no matter what the original angle of the photon was. Ie. he assumes that if both Bob and Alice have an angle of 120° set on their detectors, the result of a 100° photon hit will be the same for each. This is wrong as a photon only has a certain probability of being detected if measured off of its basis vectors, hence Bob and Alice may or may not measure the photon the same.

Another way to put this, The only things certain about a vertically polarized photon is that it has a 100% chance of going through a vertical filter, and a 0% chance of getting through a horizontal filter. If Bob and Alice measure photons at 45°, each has a 50% chance of detecting them, but the ones Bob detects may or may not be the same ones that Alice detects. The essay is ignoring the fact that at smaller angles, say for example 22.5°, both Bob and Alice have a greater then 75% chance each of detecting the photons (predicted by classical models, quantum mechanics predicts a higher number). There is nothing "weird" about this that cannot be resolved if you take into account the statistical nature of photon polarization. The quoted essay does not do this.

 

[wle]

Because he created the picture during the discussion that gave rise to the present thread, and because his description was complete but didn't refer to Bell's theorem or to particles or to knowledge or to entanglement but just to observable stuff, postulating a particular outcome. If there are earlier such descriptions in the literature it matters for the history, but not for the present discussion.

Concerning loopholes, I don't think this is very relevant for this thread. We are not going to prove that no local realist explanation is possible. The concern of this thread is about weirdness and how it is caused by language, not about nonlocal correlations and how they cannot be caused by local hidden variables.

OK. Fair enough, if this is mainly a discussion between you and stevendaryl rather than about locality.

I don't think the results of nonlocality experiments would be less weird if it were impossible to close all loopholes. At least, 15 years ago, I already thought that Aspect's experiment (together with the fact that QM proved to be the right description of all microscopic phenomena) was proof enough for establishing nonlocal correlations.

Fair enough again, but then aren't the steps concerning postselection a bit unnecessary? Why not just assume that the devices always output clean results (one and only one of the lights goes on) at regular time intervals?

As I allowed for supplementary material, the remaining information, while informative, doesn't affect the basic setting. It didn't mention the specific limitations of PRL.

I already deleted the part of my post on PRL length limits before you replied since I decided it was an unnecessary distraction.

its quite common to start by imagining

whereas I deliberately eliminated any human imagination from my basic setting.

This is taking what I said out of context.

 

[maline]

The only things certain about a vertical photon is that it has a 100% chance of going through a vertical filter, and a 0% chance of getting through a horizontal filter. If Bob and Alice measure photons at 45°, each has a 50% chance of detecting them, but the ones Bob detects may or may not be the same ones that Alice detects.

This is precisely the natural assumption that QM rejects. There are no "vertical photons". As long as the detector angles are the same, we get perfect correlation.

 

[zonde]

Concerning loopholes, I don't think this is very relevant for this thread. We are not going to prove that no local realist explanation is possible.

If it's not relevant then why you changed stevendaryl's version into another one that allows double detections at one side and unpaired detections?

Each time the source sends its signals, exactly one of Alice's LEDs light up, and exactly one of Bob's LED's light up.

Detection loophole can be eliminated if we count discarded events and set a limit that say there can be no more than 10% of discarded events from total events (and if there are more we do not consider result).
And communication loophole should be eliminated too. You gave exact number for minimum distance between Alice, Bob and Norbert (1km). So let's set maximum value for $\Delta t$ to $3 \mu s$.

 

[edguy99]

What about photons that have passed through a vertical filter? These photons will pass through a second vertical filter 100% of the time and will never get through a horizontal filter. All other angles have an element of randomness.

After some thought, perhaps a clarification. I mean a vertical photon with a Jones Vector labeled vertical in the diagram below.

 

[A. Neumaier]

This is wrong as a photon only has a certain probability of being detected if measured off of its basis vectors, hence Bob and Alice may or may not measure the photon the same.

But if they are only counted when both measure it, they'll get the stated results. This is why I added an appropriate postselection to guarantee this with very high probability in spite of detector inefficiency.

What should their respective matrices they send to Yvonne look like?

$E=0$, $F$ will have 3 zeros and a 1 in the position corresponding to the color of the lights seen.

In a continuous run you start with all matrices initialized with zeros, and (assuming for simplicity that all events are valid and paired) after each such event add a 1 to the correct entry in both $A$ and $B$, and a 1 to the correct entry in either $E$ or $B$, depending on the pointer settings. You also count the number of valid pair events. After the experiment is completed you divide all matrices by this number. This is the final result. (If there are errant photons and/or detector inefficiencies you need a more sophisticated updating procedure, as you need to make sure that each matrix only counts the valid signals. In this case you need to make three counts, one for Alice alone, one for Bob alone, and one for Yvonne (who analyzes the complete results), and update the matrices only after enough time has passes so that one knows whether the signal was valid or spurious. Also, note that Yvonne's criteria for validity are more restrictive than those for Alice and Bob.

 

[A. Neumaier]

aren't the steps concerning postselection a bit unnecessary?

why you changed stevendaryl's version into another one that allows double detections at one side and unpaired detections?

I added it because I wanted the experiment to be realistic. One cannot realize stevendaryl's results in practice without postselection for errant photons and for missed photons - which could create the items you mentioned. I wanted to both keep his results as a valid possibility and have an experimental setting that produces it.

I don't care about the loophole since if they were the cause of the nonclassical correlations, Nature would in my eyes even be weirder than quantum mechanics ever was before I found the view I presented in the other thread!

Detection loophole can be eliminated if we count discarded events and set a limit that say there can be no more than 10% of discarded events from total events (and if there are more we do not consider result).
And communication loophole should be eliminated too. You gave exact number for minimum distance between Alice, Bob and Norbert (1km). So let's set maximum value for $\Delta t$ to $3 \mu s$.

OK, I added this to the basic setting; see the updated points 1 and 6 in post #2.

 

[zonde]

OK, ill add this to the basic setting.

Ok, no more comments from me.

 

[A. Neumaier]

photons that have passed through a vertical filter?

Your language is inviting misunderstanding.
If a photon goes through a polarizer producing vertically polarized light, the result is not a vertical photon but a vertically polarized photon.

 

[edguy99]

Your language is inviting misunderstanding.
If a photon goes through a polarizer producing vertically polarized light, the result is not a vertical photon but a vertically polarized photon.

Thank you for the clarification, I will amend my comments.

 

[maline]

This is precisely the natural assumption that QM rejects. There are no "vertical photons". As long as the detector angles are the same, we get perfect correlation.

What about photons that have passed through a vertical filter? These photons will pass through a second vertical filter 100% of the time and will never get through a horizontal filter. All other angles have an element of randomness.

My point was simply that in the EPR scenario only the entanglement of the particles is part of the state before detection, not the individual spins. That's how QM describes the experimental fact that equal detector angles give perfect correlation, no matter what the shared angle is.

 

[A. Neumaier]

OK, consensus has been established about the basic setting. Thus it will be frozen, and is not open to discussion anymore.
I'll soon begin with stage two.

 

[A. Neumaier]

In the second stage of our interactive specification, I want to augment the basic model by adding some information about you, the analyzer - a quantum-mechanical system much more complex than a detector.

As we reduced the detector description to its essential degrees of freedom (a 3-valued input and two 2-valued outputs), so I'll reduce the description of you (with your help) to one essential degree of freedom - essential just for the purposes described in the updated initial post of this thread: a single [0,1]-valued variable $W$ called the degree of weirdness. It is a function $W(A,B,D,E)$ of the matrices we assumed that you'd publish about the experiment if the outcome is interesting enough. For simplicity we refer to a list $R:=(A,B,E,F)$ as a valid result if if it has the form specified in the basic setting and satisfies the trivial conditions for relative frequencies (entries are in [0,1]; sums of relative frequencies have the same value if their meaning is the same). For any valid result $R$, $W(R)\in[0,1]$ is supposed to be a sensible approximation to the degree of weirdness that you assign to the statistical situation described by $R$.

Since weirdness is in the eyes of the beholders, each single you is likely to have a different weirdness function. However, they should have the following in common:

1. All situations that correspond to common experience should have $W=0$ since they are not weird at all.
2. All situations that you personally find really weird should have $W=1$.
3. If you believe that quantum mechanics is intrinsically weird, you should exhibit at least one valid result $R$ (of your choice) for which $W(R)=1$, and outline, in agreement with quantum mechanics, how Norbert can generate signals and which local detector response is required to obtain the valid result $R$. Please justify in words and references to other discussion or the literature why you consider the result to be weird.
   
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.
5. Small perturbations $R'$ of valid results $R$ with $W(R)=0$ should have $W(R')\approx 0$, and small perturbations $R'$ of valid results $R$ with $W(R)=1$ should have $W(R')\approx 1$. This is to account both for the well-known fact that relative frequencies are not precisely predictable, and for imperfections in the experiment itself, since a signal might be distorted on the way from Norbert to Alice or Bob, and since the devices might be so sensitive that they occasionally respond to a signal not caused by Norbert. (The postprocessing tries to reduce the likelihood of this but cannot suppress it completely.)

My personal weirdness function is very easy to state. Since I no longer find anything weird in quantum mechanics (except for the endless discussions about it), the personal degree of weirdness is given by $W(R)=0$ for all valid results $R$.

On the other hand, I cannot guess the degree of weirdness assigned by any of you who believe that quantum mechanics is intrinsically weird.
Therefore I invite those of you who don't share my judgment about quantum weirdness to observe yourself sufficiently well to be able to come up with a deterministic approximation $W(R)$ to your subjective judgment of the degree of weirdness of any valid result $R$, having the properties mentioned. (You may learn in this way something new about yourself, or about the experimental setting, or both.)

If you find it too difficult to define a degree of weirdness satisfying all conditions, please specify at least a weak degree of weirdness which is a lower bound to the full degree of weirdness. Then property 4 (quasiconvexity) is not needed, and property 2 is relaxed - you only need to guarantee that there is at least one $R$ where $W(R)=1$.

If you are not sure about yourself, you could alternatively work out a choice for the degree of weirdness that, in your opinion, would encode a sensible approximation to the judgment of a hypothetical rational local realist. Note, however, that my goal in this discussion is not to prove or disprove local realism in the conventional form, but to investigate weirdness in quantum mechanics and its dependence on the language chosen.

Whatever you specify will count as a possible weirdness measure for subsequent discussion. Initially we'll discuss whether the above scheme needs amendment, as well as a few checks on whether you actually meant what you proposed, and you can change your proposal until it remains stable.

Then all surviving proposals for the degree of weirdness will be frozen and we'll go on to stage four. (Stage three starts at post #119 and ends at post #186, and discusses an important part of my reasoning about the weirdness of the present setting. Stage 4 starts at post #187, and discusses implications for relativistic causality.)

 

[Ken G]

I would modify your weirdness function like this. Any outcome predicted by quantum mechanics gets W=0, and any outcome that contradicts a quantum mechanics prediction gets W=1. This reflects the idea that I have learned to strongly favor the predictions of quantum mechanics over any other expectations I might have formed by living my daily life. Also, it allows me to avoid assuming that the QM prediction must always be the same thing as the outcome of the experiment. I presume this approach is functionally equivalent to yours, in the sense that it relaxes the idea that "weirdness" means "disobeys preconception", and embraces the idea that weirdness means "doesn't conform to a well-tested theory we should have expected to work based on all our prior knowledge, including knowledge of quantum mechanics." Basically, it means that we learn what to call "weird." I think most people who argue for a different concept of weirdness in quantum mechanics use a different meaning of "weird", more along the lines of "surprising that it is true, even after you have come to expect it to be true."

 

[A. Neumaier]

Any outcome predicted by quantum mechanics gets W=0, and any outcome that contradicts a quantum mechanics prediction gets W=1.

If you do this your concept loses contact with those mentioned in the last sentence of your post. But this thread arose through discussions with proponents of the widespread view that quantum mechanics has to be intrinsically weird; so it is appropriate to use their notion of weirdness.

 

[Ken G]

That's kind of my point-- how weird we view the situation depends more on our personal relationship with the concept of weird than on the experimental outcomes. There are experiments that surprise us, are they all weird? Most people were surprised that there was length contraction and time dilation, are they as weird as quantum mechanics? Looking back into history, most people were surprised that the laws of motion can only tell you accelerations, you need to know the current velocity to get the motion going forward, so is that as weird as quantum mechanics? I'd say that all of physics was pretty surprising at one point or another, so if we define "weird" to mean "surprising to anyone", then all of physics is equally weird, and if we define "weird" as "surprising to me", then what is weird is a function of the knowledge of that person, not anything in the physics itself.

 

[A. Neumaier]

if we define "weird" as "surprising to me", then what is weird is a function of the knowledge of that person,

This is what I am investigating in this second stage, trying to give it at least some precision so that one can afterwards make some objective statements about the models of the subjective degree of weirdness.

 

[ddd123]

There are experiments that surprise us, are they all weird? Most people were surprised that there was length contraction and time dilation, are they as weird as quantum mechanics? Looking back into history, most people were surprised that the laws of motion can only tell you accelerations, you need to know the current velocity to get the motion going forward, so is that as weird as quantum mechanics? I'd say that all of physics was pretty surprising at one point or another, so if we define "weird" to mean "surprising to anyone", then all of physics is equally weird, and if we define "weird" as "surprising to me", then what is weird is a function of the knowledge of that person, not anything in the physics itself.

The main difference between QM and all your other examples is that, once, say, SR was established, the debate virtually stopped and all physicists agreed about length contraction from then onwards. QM is the only case in which there is no agreement: foundations is a thorny subject with a lot of, often colorful, disagreements, even some 100 years after QM started being investigated.

 

[jimgraber]

OK, let me suggest two candidates for degree of weirdness.

Candidate number one is the degree of entanglement. I believe there are serious papers in the literature tdefining a degree of entanglement. I think they should be transformable into your form fairly readily.Candidate number two is the degree of nonlocality. Maybe some function from Bell or CHSH can be adapted to your form.A third possible candidate which I do not advance is the degree of nonreality. First of all, every theory of nonreality gets an automatic weirdnesss rating of one, if not infinity from me. Second of all, I am not aware of a serious attempt to measure the degree of nonreality, similar to nonlocality or entanglement.

I am willing to learn more about nonreality, but so far, I think that like Oakland, “there is no there there.”

Best.

Jim Graber

 

[Ken G]

The main difference between QM and all your other examples is that, once, say, SR was established, the debate virtually stopped and all physicists agreed about length contraction from then onwards. QM is the only case in which there is no agreement: foundations is a thorny subject with a lot of, often colorful, disagreements, even some 100 years after QM started being investigated.

There is some value in that approach to "weirdness", it is a rather different one but perhaps the most useful. It sounds like you are saying we should not regard "weird" as equal to "surprising to us", and certainly not "surprising to someone who does not know physics", but instead "still exhibiting a remarkable variation in foundational concepts among practicing physicists." That makes weirdness not a personal issue any more, but rather something that can be observed across a community of scientists, which is what I think is good about it. Still, to play devil's advocate to that version of "weirdness", I would point out that classical mechanics supports many different interpretations as well-- is it forces, is it a principle of least action, or is it just the macroscopic correspondence of quantum mechanics? Notice that if we take that last view, then even something as simple as rolling a die inherits all the same interpretations as quantum mechanics does, and always did-- it's just that few took those other possible interpretations seriously before.

 

[jimgraber]

PS I'm assuming that something similar to these three proposals would be the "mainstream response" of many other physicists.

 

[A. Neumaier]

Candidate number one is the degree of entanglement. I believe there are serious papers in the literature defining a degree of entanglement. I think they should be transformable into your form fairly readily.
Candidate number two is the degree of nonlocality.

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.

 

[ddd123]

.

I answered in the other thread to keep things tidy.

 

[edguy99]

... In a continuous run you start with all matrices initialized with zeros, and (assuming for simplicity that all events are valid and paired) after each such event add a 1 to the correct entry in both $A$ and $B$, and a 1 to the correct entry in either $E$ or $F$, depending on the pointer settings...

Animation at: http://www.animatedphysics.com/games/photon_longdistance_nonlocality.htm

Thank you for your assistance, I believe the animation matches the specifications. It stops between each photon to show what each of the people is recording and it allows you to shoot additional photons to verify proper operation and build up a data set (continuous operation will come with the NEXT button, not yet done). Looking forward to use of the data to study "wierdness". At this point, I am still using the classical description of the photon used by Dehlinger and Mitchell in http://arxiv.org/PS_cache/quant-ph/pdf/0205/0205171v1.pdf. When a photon meets a polarizer set to an angle γ, it will always register as Vγ if λ is closer to γ than to γ + π/2, i.e.,

• if |γ − λ| ≤ π/4 then vertical
• if |γ − λ| > 3π/4 then vertical
• horizontal otherwise.

A sample run is shown below after 4 photon shots.

 

[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.