Wednesday, November 27, 2013

Cosmic Bell

On the playground of quantum foundations, Bell’s theorem is the fence. This celebrated theorem – loved by some and hated by others – shows that correlations in quantum mechanics can be stronger than in theories with local hidden variables. Such local hidden variables theories are modifications of quantum mechanics which aim to stay close to the classical, realist picture, and promise to make understandable what others have argued cannot be understood. In these substitutes for quantum mechanics, the ‘hidden variables’ serve to explain the observed randomness of quantum measurement.

Experiments show however that correlations can be stronger than local hidden variables theories allow, as strong as quantum mechanics predicts. This is very clear evidence against local hidden variables, and greatly diminishes the freedom researchers have to play with the foundations of quantum mechanics.

But a fence has holes and Bell’s theorem has loopholes. These loopholes stem from assumptions that necessarily enter every mathematical proof. Closing all these loopholes by making sure the assumptions cannot be violated in the experiment is challenging: Quantum entanglement is fragile and noise is omnipresent.

One of these loopholes in Bell’s theorem is known as the ‘freedom of choice’ assumption. It assumes that the settings of the two detectors which are typically used in Bell-type experiments can be chosen ‘freely’. If the detector settings cannot be chosen independently, or are both dependent on the same hidden variables, this could mimic the observed correlations.

This loophole can be addressed by using random sources for the detector settings and putting them far away from each other. If the hidden variables are local, any correlations must have been established already when the sources were in causal contact. The farther apart the sources for the detector settings, the earlier the correlations must have been established because they cannot have spread faster than the speed of light. The earlier the correlations must have been established, the less plausible the theory, though how early is ‘too early’ is subjective. As we discussed earlier, in practice theories don’t so much get falsified as that they get implausified. Pushing back the time at which detector correlations must have been established serves to implausify local hidden variable theories.

In a neat recent paper, Jason Gallicchio, Andrew Friedman and David Kaiser studied how to use cosmic sources to set the detector, sources that have been causally disconnected since the big bang (which might or might not have been ‘forever’). While this had been suggested before, they did the actual work, thought about the details, the technological limitations, and the experimental problems. In short, they breathed the science into the idea.

    Testing Bell's Inequality with Cosmic Photons: Closing the Settings-Independence Loophole
    Jason Gallicchio, Andrew S. Friedman, David I. Kaiser
    arXiv:1310.3288 [quant-ph]

The authors look at two different types of sources: distant quasars on opposite sides of the sky, and patches of the cosmic microwave background (CMB). In both cases, photons from these sources can be used to switch the detectors, for example by using the photon’s arrival time or their polarization. The authors come to the conclusion that quasars are preferable because the CMB signal suffers more from noise, especially in Earth-based telescopes. Since this noise could originate in close-by sources, it would spoil the conclusions for the time at which correlations must have been established.

According to the authors, it is possible with presently available technology to perform a Bell-test with such distant sources, thus pushing back the limit on conspiracies that could allow hidden variable theories to deliver quantum mechanical correlations. As always with such tests, it is unlikely that any disagreement with the established theory will be found, but if a disagreement can be found, it would be very exciting indeed.

It remains to be said that closing this loophole does not constrain superdeterministic hidden variables theories, which are just boldly non-local and not even necessarily realist. I like superdeterministic hidden variable theories because they stay as close to quantum mechanics as possible while not buying into fundamental non-determinism. In this case it is the measured particle that cannot be prepared independently of the detector settings, and you already know that I do not believe in free will. This requires some non-locality but not necessarily superluminal signaling. Such superdeterministic theories cannot be tested with Bell’s theorem. You can read here about a different test that I proposed for this case.

28 comments:

Joy said...

My problem with the whole Bell orthodoxy is the definition of local-realism they implicitly assume.

One can always rule out local realty by defining it sufficiently narrowly. One can define the notion, for example, that is based only on scalar or complex numbers, when the world itself is evidently made of quaternions and octonions, which in practice provide non-commuting graded basis that include commuting scalar numbers (+1 or -1) as special or limiting cases. A local-realistic framework based on such a broad scheme of numbers does not mitigate Bell's own conception of local-reality in any way, but only makes it more local and more realistic.

I am able to reproduce *ALL* possible quantum correlations (not just EPR-Bohm correlation) in such a framework. No experiment can therefore discriminate it from quantum mechanics. And yet, there exist a simple macroscopic scenario in which Bell's local-realistic framework can be decisively tested against mine. But of course, for that to ever happen, my local-realistic framework would have to be taken seriously. Sadly, the collective will of the foundations community does not seem to be inclined to do so.

Sorry to bring up my hobbyhorse. I resisted commenting on your previous posts on Bell's so-called theorem, but I couldn't resist this time.

Phillip Helbig said...

Maybe Bee can read your stuff and offer an informed comment.

This is too far from my field to form an informed opinion, and even if I did it wouldn't matter to anyone but me. I actually haven't even met anyone who has looked at your claims in detail, but have met a couple of people who claim to know someone who has (and concluded that you haven't found anything exciting). I reserve my own judgement, but I think it is not too much to expect for, say, Bee to take a look and state her opinion.

L. Edgar Otto said...

Joy, as perhaps one inner philosopher to another I found your evaluation of Bell refreshingly confusing. This comes at a time when in these matters I have made either a deeper breakthrough or a deeper confusion which seems to be ther state of foundation theory and experiments in our day. I am not one to think. it a good thing for a poet (that my one claim to credentials, energy is to me a poetic word as in the original sense) to censor oneself to be good for society. So if you had not posted here I would not have despite (independent?) ideas and reservations which may only discourage inquirey adding to the confusion. That and my good sense to see how deep and a superior intelligence there is in her stances and work.
I find the similar ideas of stringy and loopy - foamy particle and cosmology a war of stances of lesser vision although these appear to address the foundations, especially as to as to what concept of natures background is independent or observable or not.
For me that stringers would disprove Bell would be a disproof of compaction and quantum theory itself and about every limited tools of its formalism you used to make the case.
But I can say this: that information put into only a real line is not an era as you say nor is the arguement it cannot be mapped into such three space spheres true either. In the loopy stringy landscape it is not that we confuse the map with the terrain, but the terrain with the map makers.

Sabine Hossenfelder said...

Phillip,

I looked at Joy's papers some time ago and I have not and will not post a public opinion for three reasons. First, and most important, it's outside my field of expertise. I don't know what is a good or meaningful definition of local reality and I'm not sure I even care. Second, I'm friends with Joy, I like some of this older work, and I'm clearly biased in my opinion towards supporting him. Third, I strongly dislike how ugly this discussion has been. This isn't how science should work and I want nothing to do with this. I believe that in the long run, truth with prevail. Best,

B.

Phil Warnell said...

Hi Bee,

Nice piece and I do hope someone runs the experiment, although I suspect the correlations will hold. I've often wondered what has many so disturbed that nature at its deepest level has an implicate order as David Bohm suggested some years ago, as well as the explicate one being simply emergent from it.

"In the enfolded [or implicate] order, space and time are no longer the dominant factors determining the relationships of dependence or independence of different elements. Rather, an entirely different sort of basic connection of elements is possible, from which our ordinary notions of space and time, along with those of separately existent material particles, are abstracted as forms derived from the deeper order. These ordinary notions in fact appear in what is called the "explicate" or "unfolded" order, which is a special and distinguished form contained within the general totality of all the implicate orders."

-David Bohm, "Wholeness and the Implicate Order",p. Xv

Best regards,

Phil

Plato Hagel said...

Just a question Bee so I understand what you are saying.

Two signals, from different Quasars, not Supernova event, can give rise to the understanding that any signal present in our detectors here on earth, would have trouble determining the entangled state?

Best,

Sabine Hossenfelder said...

Plato,

The two quasars are far apart. They have not had any chance to exchange information. If the quasar signals are used to chose detector settings, then one can be reasonably sure that observed correlations in the measurement do not stem from the detector settings. (If the hidden variables obey locality that is.) Best,

B.

Uncle Al said...

" you already know that I do not believe in free will" Shot noise, radioactive decay, glass (physical or spin), turbulence... A determined trajectory for every everything is unimaginable. So?

Like Yukawa potentials and epicycles, Bohm has unlimited excuses without discrete solutions. Side effects are parameterized. Cartography falsifies the Shroud of Turin. Miracle. Medieval Europe fell when postulated "all is irrevocable" was externally falsified. My bet is boson photon vacuum symmetries not being exactly fermionic matter vacuum symmetries. This is postulated to be trivially wrong, then not tested. Somebody should look. Consider the parameterized alternatives to physics being testably incomplete.

The pendulum equation is truly an infinite number of terms. It happens.

Arun said...

Dear Bee,

"The two quasars are far apart. They have not had any chance to exchange information. If the quasar signals are used to chose detector settings, then one can be reasonably sure that observed correlations in the measurement do not stem from the detector settings. (If the hidden variables obey locality that is.) "

The problem I see is that the quasar signals, which are quantum, are converted into classical detector settings by local apparatus that has been in causal contact with the whole experiment.

Best,
-Arun


Don Foster said...

Silly me, I thought this might be about the universe's inclination to resonate.

Juan F. said...

Baez and people like me love this one related stuff http://arxiv.org/abs/0803.0913

L. Edgar Otto said...

Joy et al,
From the "outside " an object appears spherical with a possible center. We can imagine the reality of an electron as the old idea of epicycles. So is the issue her how we reduce things to black and white verses say gray groups. If over an interval of infinite set measure the Bell curve encompasses the bell cosmology then all in it is superindeterminism (statistical free will) . Local and nonlocal may not be clearly distinguished as measure or scale. We seem to be close to the center of macro-cosmic and micro-cosmic scales. If we take entities black hole like such as far apart quasars how can we show such objects are not inside all of space as one great quasar? On our middle scale if information is possible in exchange and over time it returns again, as in DNA Bel gives us a measure of relatively local utility. A totally random strand or all its code endlessly determined as repeated the same is of little use to the working or emergence for our evolving biochemistry. Inside a quasar from outside the constant velocity may be or appear increased by a geometry factor of ten. Did not Einstein consider this about the view of curving light if it could be seen thru the sun?

Don Foster said...

Dr. Bee

In so far as we actually have a choice here, we are given one between superdeterminism or Bell’s theorem and the oddities of entanglement. Is that a fair statement?

Could it also be the case that Bell’s theorem is correct and entanglement is simply a signal that the underlying geometry of spacetime is more ornate than we suppose? I just checked references and I guess this is what Bohm was talking about with his implicate order and “prespace”. (well, perhaps roughly?)

Apparently though, this is still no help for the free-willers.

vmarko said...

Hi Bee,

As much as I try, I am repeatedly failing to understand even the most basic premises of superdeterminism. For example, I am again confused by your comment that uncorrelated choices of detector settings do not test for SD, and so on.

Can you please give me some references where SD is explained in enough detail?

I'd like to see an argument why SD is independent of realism, how exactly is it (non)local, how does it circumvent Bell's theorem, what are its main assumptions, in which cases it is/isn't equivalent to QM... With all the gory details! Is there some nice, clear review paper out there? Or any paper where SD is discussed in enough detail?

Thanks! :-)
Marko

Sabine Hossenfelder said...

Arun,

I see your point for the explicit example that they discuss, but in general I'm not sure I know what you mean with 'quantum' here, as everything is 'quantum'. Forget for a moment that the photon flux from distant quasars is not very high and consider it was a really bright source with time-variations in it. You could use the time-variation in the brightness to change the detector settings. Sure, there's an element of quantum uncertainty to it that comes in by the time window and uncertainty on the number, but in principle this could be arbitrarily small (relative to the full signal). Unless that is, you want to argue that the detector doesn't obey the usual Born rule in this case, which seems even more problematic than local hidden variables already are.

That having been said, I don't recall a discussion on that point in the paper. It seems that one would have to estimate how far exploiting the expected quantum uncertainty in the measurement of the quasar signal could be used to generate a correlation. Best,

B.

Sabine Hossenfelder said...

Marco,

If I knew of a good reference, I'd be happy to point you towards it, but I don't know one. In fact there seems to be some confusion about exactly what means superdeterminism. So let us forget for a moment what a general definition might be and let me just tell you what I mean. I mean a correlation between the prepared state and the detector. In the derivation of Bell's inequality one uses that these are uncorrelated, which is why you can't use the inequality if they're correlated. That's a non-local correlation, but it doesn't necessarily imply superluminal signalling.

Regarding realism. Considering that the state preparation is nonlocally correlated with the detector doesn't require you to give up complex-valued wave-functions and amplitudes (instead of probabilities and some classical ensemble interpretation). I don't expect every element of a theory to describe an observable entity because I don't believe that the theory 'is' reality to begin with. I'm in the camp of people who think about theories as calculation devices, essentially. Or maybe it's just that I don't know what reality is anyway.

That having been said, the main motivation for most people to even think about hidden variable theories seems to be to hold on to a classical, realist interpretation. My main motivation is to get around the indeterministic element of the 'quantum collapse' but I see no reason to worry about the rest of quantum theory. That's why I say it stays as close to 'standard' quantum mechanics as one can possibly be, up to the 'conspiracy' that you can't twiddle the detector knob without affecting the state preparation. Hope that clarifies it. Best,

B.

kashyap vasavada said...

I do not understand superdeterminism and whatever little I understand, I have lots of problems with that.If SD is true, don't you think the whole basis of science i.e to set up experiments to find out some truth (may be even tentative)about nature will collapse?

Unknown said...

Joy,

just out of curiosity: your focus on different definitions of "local reality" means that you now recognize that your papers didn't prove that Bell's theorem is false?

L. Edgar Otto said...

@Unknown
as philosophy your question does not reach the depth and span of these frontier issues. Does the Higgs concept exist as a phenomenon or reality? Can any proof or disproof exist now or in the futute be there by thought or experiment. We seem to agree something is there be it a question of mass or gravity. Can we define life as a composite of Higgs? Vague appeal to metalanguage aside from a Platonic view may not show in depth proof of Riemann or Poinclaire conjectures even if one seems complete. How is it, a likely fact, that a Higgs may decay into spin or half spin particles? Perhaps it is not pointless to see a distinction between infinity and half infinity. Numerical powers of 2 to the domension of a continuum. The underlying physics as symmetry at once rich or simple as singularities. If in a higher sense a disproof of Bell's theorem it would involve unseen shadow binary dimensions but Joy's arguement implies there is more than the standard theory to explore.
I would like to also mention Uncle Al's comment as an organic process would tells us a lot we centered as locality fefined this way regardless we the image or our imposing it on Universe.

But I have not been able to see links supplied I'm this article from the gracious author. I do not speak for anyone else. Thank you SH

L. Edgar Otto said...

I saw some of the links and eariler lively discussions. Surely some of us have felt in this pursuit of knowledge the wisdom initially given to us is somehow a superdtermined destiny. Consider Penrose and his term "quantanglement ". Arithmetic seems to be independent of the continuum hypothesis and the axiom of choice from an infinite set of elements. Both axioms are relavant to models here debated. How implausible are steps toward a distant theory in understanding based on each step a chance intuitive thus superindetermism of free choice? (I did not realize some common terms like natural had special use in the physics community.)

How is it that some have imagined a center of the universe 65 million years nearby? Or a cosmic axis of evil in our sky maps or the like?
I suggest our ideas on odd and evenness in equations are too strictly applied. We get ideas by Feynman diagrams and their rotation but lose concepts by such reduction. Or we swim with chaos with our actual paths in the tides we say are non linear. The vastly more complex one multidimensional superimposed "brane " is not necessarily symmetric upon such rotation. But how far such steps can go is still an open question philosophically last infinity and all that.
So we still tend to use point or unit description to say 0 to 1 equal a third state ( * ) to map infinity to that interval. But this concept can be mirrored as infinity (potential) or unity as well and so mapped. Powers of Clifford like dimentions also can be so mirrored or added on the same level like mass or cosmo constant ad hoc. We need not be constrained by our equations of exponentially. Any such constraints in the interval are discrete patterns of an arithmetic pattern variety.

vmarko said...

Hi Bee,

Thanks for the clarification! The lack of good literature on SD is really frustrating... After reading your description of SD, I am confused about SD being actually deterministic. Nonlocal correlations between the system and the detector can indeed go around Bell's inequalities, but I don't see why does that make the theory deterministic? Besides, if the theory is nonlocal to begin with, then Bell's theorem is already void (pilot-wave interpretation of QM is an example of a nonlocal realist model).

Also, I understand (non)realism in the sense that the physical system does (not) have a well-defined value of a given observable before the measurement of that observable takes place. In any deterministic theory, everything that happens has been determined beforehand, and therefore having definite (predictable) values for all observables before any measurements are performed. So I don't see how a deterministic theory can be compatible with nonrealism. Am I missing something?

Best, :-)
Marko

Sabine Hossenfelder said...

Hi Marko,

You have it backwards. Saying 'superdeterminism' doesn't make quantum mechanics deterministic. The point is that in a superdeterministic theory the conclusion that quantum mechanics (standard interpretation) is the correct description of reality can no longer be made.

Regarding realism. You can have a perfectly determined superposition of eigenstates. It's just that this superposition doesn't necessarily correspond to an observable. Best,

B.

Sabine Hossenfelder said...

kashyap,

No, I don't think that. Besides, you could make the same argument in classical mechanics already. The reason we can do experiments rests on thermodynamics and some approximate validity of locality and causality. I believe your main problem is that you have a misunderstanding of the necessity of free will. I recommend you read this earlier post to understand why free will is an entirely unnecessary construct. Best,

B.

vmarko said...

Hi Bee,

"in a superdeterministic theory the conclusion that quantum mechanics (standard interpretation) is the correct description of reality can no longer be made."

Are you saying that a SD theory must have different experimental predictions from QM? That would make SD falsifiable in principle, right?

"Regarding realism. You can have a perfectly determined superposition of eigenstates. It's just that this superposition doesn't necessarily correspond to an observable."

Ok, so if you perform a measurement on such a superposition, how do you determine the outcome, and what will it be?

Best, :-)
Marko

Sabine Hossenfelder said...

Hi Marko,

No, you can 'in principle' never falsify superdeterminism because it is possible that such a theory would perfectly mimic all the outcomes of quantum mechanics and we'd never notice because we can't measure the 'hidden variables'. That's the same as saying you can't prove that a dinosaur who you can't interact with doesn't exist. Alas, the reason for this infalsifiability is that just saying 'superdeterminism' doesn't really tell you much. Once you look at a more concrete realization (eg for the origin of the hidden variables) you can in principle distinguish the theory from quantum mechanics. (Which is the point I was trying to make in my paper.)

"Ok, so if you perform a measurement on such a superposition, how do you determine the outcome, and what will it be?"

The outcome depends on the hidden variables, that's the whole point. If you average over these, you better get Born's rule. Best,

B.

kashyap vasavada said...

Hi Bee: Thanks for your reply.I will try to understand SD little better.It reminds me of law of Karma of Hinduism!!! But even there, although your past is sealed
and you have to bear consequences, you are allowed to mend the future!!

Neil Bates said...

Bee, this may sound naive about the framing of the experiments, but it seems to me that per-instance independence of the settings is not really the issue for the free-choice concept (as meant in context.) Wouldn't it be enough just to accumulate statistics generated from a wide range of relative settings? In the proofs I see explained, that is the point. IOW, the number of same hits at 60 degrees difference etc is more than a LR theory could provide. I'm not sure what I might be missing.

Sabine Hossenfelder said...

Neil,
The conclusion you can draw from the accumulated statistics depends on the presumed independence of the detector settings. Best,
B.