# Binney's interpretation of Violation of Bell Inequalities

## Main Question or Discussion Point

Although he is primarily an astrophysicist, Dirac medal-winning Oxford Professor James Binney has taught a Quantum Physics course to second-year students at the university for years. A series of 27 of his lectures for the course is featured on the university's official website. Binney's take on the violation of Bell inequalities and Quantum Physics in general seems unorthodox though. He takes an "instrumentalist" approach which views the Copenhagen Interpretation of quantum theory as a useful epistemological "roadmap" to getting results about an underlying reality that it does not accurately represent. Wavefunction collapse is simply seen as a caricature of measurement that is convenient for calculations but has no relation to a microscopic reality which has many definite physical values and of which non-locality is not a feature.

Binney refuses to admit that the violation of Bell inequalities has important ontological implications.

Here is how he accounts for it:

" Many discussions of the EPR experiment generate needless confusion by supposing that after Alice has measured +1/2 for the component of the electron's spin parallel to a, the spin is aligned with a. The electron has half a unit of angular momentum in each of the x, y and z directions, although the signs of the x and y components are unknown when we know the value of Sz.
Hence the most Alice can know about the orientation of the spin vector is that it lies in a particular hemisphere. Whatever hemisphere Alice determines, she can argue that the positron's spin lies in the opposite hemisphere. So if Alice finds the electron's spin to lie in the northern hemisphere, she concludes that the positron's spin lies in the southern hemisphere. This knowledge excludes only one result from the myriad of possibilities open to Bob: namely he cannot find Sz = +1/2. He is unlikely to find +1/2 if he measures the component of spin along a vector b that lies close to the z axis because the hemisphere associated with this result has a small overlap with the southern hemisphere, but since there is an overlap, the result +1/2 is not excluded.
Contrary to the claims of EPR, the results of Bob's measurement are consistent with the hemisphere containing the positron's spin being fixed at the outset and being unaffected by Alice's measurement."

Binney draws the underwhelming conclusion that

"The experimental demonstration that Bell inequalities are violated establishes that quantum mechanics will not be superseded by a theory in which the spin vector has a definite direction."

He adds that "Macroscopic objects only appear to have well-defined orientations because they are not in states of well-defined spin. That is, the idea that a vector points in a well-defined direction is a classical notion and not applicable to objects such as electrons that do have a definite spin."

This is not an interpretation of the violation of Bell's inequalities about which I have heard much.
Nonlocality is not even entertained as a possibility!
It is hard to find discussions of Binney's view online. I hope someone here can provide a critique of it - many students here in Oxford are being blithely taught that there is nothing important or surprising about these famous experimental results. I doubt that's true!

Looking forward to learning more,
Thanks,
Pat

Related Quantum Interpretations and Foundations News on Phys.org
Yes, it is fairly easy to find special cases where a correlation can be explained by local variables, but AFAIK, the overall dependency of the correlation against b is not explicable this way. That is the reason why Aspect's et al experiments with photons, not electrons used odd multiples of 22.5 degrees where Bell's inequality is maximally violated. A vague fuzz of polarization would account for the special cases of parallel beamsplitters (full correlation) and might be stretched to the 45 degree case (no correlation).

I do not understand how Blinney can agree that Bell's Inequality is violated and yet you say he does not entertain the idea of non-locality. Violation implies that local realism is impossible. It is a theorem. Not negotiable.

Blinney appears to interpret the spin state as being fuzzy or undefined. Nothing wrong with that but it would mean the hemispheric representation was a local, if hidden, variable. Bell's Theorem applies to *any* local variables. Any idea like this must be tested for consistency with the cos^2(b) rule (photons). But b is not a fixed angle in space, it is the angle against the angle chosen by Alice. It should be written as b-a. That alone tells us it is impossible for this rule to be local, though in special cases it can be.

Yes, in his lecture and his book, "The Physics of Quantum Mechanics" by James Binney and David Skinner (available as a free PDF online) he explicitly acknowledges that experiments have shown that
"The quantum-mechanical result is inconsistent with Bell's inequality and is therefore inconsistent with the existence of hidden variables."

Notably he doesn't bother saying "local hidden variables"-it's taken for granted that they would be. He than adds that similar results are gained with entangled photons, concluding
"Consequently, these experiments rule out the possibility that hidden variables exist."

I think what he is saying about spin is that it is well-defined in the case of the electron, but that it is a mistake to think that the vector points in a well-defined direction. So he's claiming it's impossible to measure spin with enough accuracy to draw any conclusions, even though the spin of an electron or photon does have definite values that, if we could measure them, would show that the inequalities aren't violated when the two particles are spatially separated. But then if that's what he thinks, why does he agree that hidden variables are ruled out?

Furthermore, wouldn't the inaccuracies he cites as resulting from the vector not pointing in a well-defined direction cancel themselves out? How can they explain the results' consistent violations of the inequalities? I would have thought a simple statistical analysis would rule this out as a an explanation, but I'm no expert.

The last ten minutes of this lecture outline his position: www.youtube.com/watch?v=uef_qN7VFuY

I think what he is saying about spin is that it is well-defined in the case of the electron, but that it is a mistake to think that the vector points in a well-defined direction. So he's claiming it's impossible to measure spin with enough accuracy to draw any conclusions, even though the spin of an electron or photon does have definite values that, if we could measure them, would show that the inequalities aren't violated when the two particles are spatially separated.
Furthermore, wouldn't the inaccuracies he cites as resulting from the vector not pointing in a well-defined direction cancel themselves out? How can they explain the results' consistent violations of the inequalities? I would have thought a simple statistical analysis would rule this out as a an explanation, but I'm no expert.
Not sure I fully follow you but I don't think he means there is any inaccuracy, just quantum uncertainty when we insist on measuring spin as if it were a direction. He's right to say that spin states are not vectors and do not in general correspond to spatial directions/vectors. I can't see any way round Bell's theorem though - and yes, the important bit of Bell's theorem is undoubtedly the statistical part, so it doesn't matter whether you get your two tables of results from pairs of entangled electrons or from Mystic Meg's crystal ball, if the correlations violate Bell's theorem, the system can't be locally real.

Mind you, I did like this: Macroscopic objects only appear to have well-defined orientations because they are not in states of well-defined spin. That is, the idea that a vector points in a well-defined direction is a classical notion and not applicable to objects such as electrons that do have a definite spin. That's turning things upside down a bit but it might be quite a useful conceptual step. Perhaps.

I can't really say anything more. Nothing useful anyway

Mystic Meg enters the quantum arena...'twas written thus.
I like your analogy - it drives home the key point well. As you say, "If the correlations violate Bell's theorem, the system can't be locally real." It's non-negotiable.
But then I think, "Can someone as accomplished as Binney be foolish enough not to see that?" If, as seems clear, that's all there is to it, then he should be called out on it.

You're right, he's not talking about inaccuracy. But for Binney "quantum uncertainty" is just a convenient representation of the "common-sense" uncertainty inevitably involved in the act of measurement, which suggests he is unaware of Kennard's proven formulation of the uncertainty principle in terms of unavoidable uncertainty caused by quantum fluctuations, whether a measurement is made or not.
And come to think of it, pertinently for this discussion in 2012 Yuji Hasegawa et al experimentally proved that Heisenberg's "measurement" uncertainty and Kennard's "fluctuation" uncertainty are two distinct and different things through the simultaneous "indirect" measurement of two components of spin for each of a stream of neutrons! This measurement violated Heisenberg's "error-disturbance" inequality- either error or disturbance could be reduced while the other remained finite-but Kennard's formulation continued to hold. T
The technology they used would be useful for further testing of Bell's theorem...

Nugatory
Mentor
Binney draws the underwhelming conclusion that

"The experimental demonstration that Bell inequalities are violated establishes that quantum mechanics will not be superseded by a theory in which the spin vector has a definite direction."
That's not an "underwhelming" conclusion - it's the whole point of the exercise, and a fair case can be made that it is the one of the most important philosophical discoveries of the twentieth century.

I'd have to think about it more, but when I read "Many discussions of the EPR experiment generate needless confusion by supposing that after Alice has measured +1/2 for the component of the electron's spin parallel to a, the spin is aligned with a" I'm hearing a rejection of EPR reality; that's a reasonable position as Bell's theorem tells us that we cannot have both locality and EPR reality.

That sounds interesting, I'll look it up. (neutron/fluctuation stuff I mean)

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Nugatory, in Binney's case it is underwhelming because the spin vector not having a definite direction is just seen as a feature particular to spin, rather than having anything to do with local realism. I'll repeat the important quote as far as local realism is concerned from my first post:

"Contrary to the claims of EPR, the results of Bob's measurement are consistent with the hemisphere containing the positron's spin being fixed at the outset and being unaffected by Alice's measurement."

You can get more of a flavour of his views by viewing his lecture entitled "Demystifying Quantum Mechanics," in which he dimisses the "pundits" who think that entanglement involves anything more than mundane correlation: www.youtube.com/watch?v=LfBPzVzkdOo

That sounds interesting, I'll look it up. (neutron/fluctuation stuff I mean)
In 2003 Ozawa developed a new formulation of the uncertainty principle which separated it into "measurement" and "fluctuation" components. Hazegawa's experiment (arxiv.org/abs/1305.7251) confirmed that the "measurement" component alone does not satisfy Heisenberg's inequality except in special cases. I don't think the "fluctuation" component alone satisfies it either, but the important thing is that an intrinsic uncertainty exists whether or not measurement is involved.

"The results demonstrate that Heisenberg's error-disturbance relation can always be violated for a non-vanishing lower limit. In contrast, Ozawa's inequality always holds. Furthermore, we conclude that increasing error does not always lead to increasing disturbance and vice versa in spin measurements. Such a reciprocal behaviour occurs only in certain areas and along certain directions. Thus, our results give an experimental demonstration that the generalized form of Heisenberg's error-disturbance relation has to be abandoned."

I think I have to stop at the level of the Sci Am article here.

The intrinsic uncertainty is a theorem so it's not going to be violated.

According to the Sci Am article, Heisenberg thought in terms of actually disturbing the system so maybe it's not so surprising if this can be minimised at the expense of uncertainty in the measurement (so-called fluctuations).

But I need to chew on the Ozawa inequality: ε(q)η(p) + σ(q)η(p) + σ(p)ε(q) ≥ h/4π to see what it really means. Some time.

But I need to chew on the Ozawa inequality: ε(q)η(p) + σ(q)η(p) + σ(p)ε(q) ≥ h/4π to see what it really means. Some time.
It looks to be in a superposition of being quite straightforward and fiendishly complicated!

Derek Potter
Binney on entanglement:

"In quantum mechanics being correlated is the same thing as being entangled, and there are these chattering pundits in philosophy and even in physics departments who will tell you that there is something mysterious about entanglement. There is nothing mysterious about entanglement, it is merely the development of correlation."

"When 2 systems are dynamically coupled, where the first system evolves to depends on the initial state and evolution of the 2nd system. In quantum mechanics they call this correlation 'entanglement' and claim it's mysterious."

Non local entanglement is not entertained as an option because Binney considers any form of instantaneous or superluminal correlation to violate special relativity, questions of whether they actually involve the communication of information notwithstanding. Long-distance experiments such as Aspect's, Zeilinger's and Gisin's, which refute this view unless we abandon realism, are dismissed because their results interpret spin as being directed along an axis. In fact we can apparently only tell what hemisphere the spin is in, so given that Alice and Bob don't make measurements along identical axes, the hemispheres of these axes will overlap, meaning that for example a result apparently indicating that Bob's positron's spin is in the opposite hemisphere to Alice's electron's spin is unreliable - they could actually be in the same hemisphere without us knowing. Binney claims that this unreliability creates a loophole allowing the results of Bob's measurement to be consistent with the hemisphere containing the positron's spin being fixed at the outset and being unaffected by Alice's measurement, as is required by his adherence to refusal to accept non locality - in conjunction with his adherence to realism.

Realism is preserved from his perspective by viewing a correlated system holistically and saying that the physical world that we perceive is real, but that position,momentum, energy etc are not intrinsic properties of a physical system (I think I misunderstood his take on this earlier in the thread). Each time a measurement is made on one of the particles, it will be disturbed by the measuring instrument and yield a value, and the particle with which it is entangled will yield a correlated value, but not instantaneously-the "message" cannot travel from the electron to the positron at superluminal speed. With this proviso, entanglement is seen by Binney as mundane (although why I don't know. Leaving aside the question of whether or not these properties are intrinsic, how a very distant, even if not spatially separated, pair of entangled particles could react to each other's measurements still seems mysterious, even if the equations tell us to treat them holistically).

But if we accept his take on realism (or the part of realism unconcerned with locality/non locality), the fact remains that his "hemispheres" argument against non locality just doesn't seem to matter. When measurements are made of a large collection of data, unreliability in those measurements is not statistically capable of producing the way-above-chance levels of correlation that have been repeatedly recorded, because it cuts both ways - non-correlations will be recorded as correlations, and correlations will be recorded as non-correlations. For every overlapping hemisphere that leads to an incorrect recording of a correlation, there will be an "underlapping" hemisphere that produces an incorrect recording of a non-correlation. Therefore, thanks to a large body of experimental evidence, we have proof of correlations arising between Alice's and Bob's results either instantaneously or at superluminal speed, and that's what's important.

So as far as I can see Binney's local, realistic account of the violation of Bell's inequalities fails. Can someone tell me if I'm going wrong somewhere?

maline
If you're reporting him correctly then you're perfectly right and he's simply wrong.

Bell's inequality, or the more general CHSH, is statistics - quite simple statistics at that, not physics. It cannot be violated if the assumptions of local realism are true. Bell's theorem shows that QM would violate it. So: if QM then violation; if violation then no local realism. Therefore if QM then no local realism. It doesn't really get any simpler.

It certainly doesn't depend on QM being true, let alone on the physical model of spin being correct. In fact QM could be a load of rubbish served up to us by a malicious lizard-mathematician who enjoys tormenting his pet brains in a vat. However it does mean that QM cannot be locally real. (I think I just said that.)

If you're reporting him correctly then you're perfectly right and he's simply wrong.

Bell's inequality, or the more general CHSH, is statistics - quite simple statistics at that, not physics. It cannot be violated if the assumptions of local realism are true. Bell's theorem shows that QM would violate it. So: if QM then violation; if violation then no local realism. Therefore if QM then no local realism. It doesn't really get any simpler.

It certainly doesn't depend on QM being true, let alone on the physical model of spin being correct. In fact QM could be a load of rubbish served up to us by a malicious lizard-mathematician who enjoys tormenting his pet brains in a vat. However it does mean that QM cannot be locally real. (I think I just said that.)
Thanks Derek. I suppose it's a question of whether I'm reporting him correctly then! I think I am. The quotes I used are verbatim. If you or anyone else wants to check the video clips I linked to earlier in the thread, maybe we can achieve further clarity.

stevendaryl
Staff Emeritus
I may have missed something subtle, but it sounds to me that Binney's "hemisphere" explanation of EPR correlations is exactly the type of explanation that Bell proves doesn't work.

Derek Potter
What's confusing is that he's an eminent figure who has taught quantum mechanics to Oxford University undergraduates for years. Can he be making an error this crass? I know that his true field of expertise is astrophysics but still...Then again, I suppose the last 100 years is littered with examples of prominent scientists who have been undone by quantum theory. Maybe he's unwilling to give up certain religious/philosophical beliefs with which QM is incompatible. I don't know if you looked at the video links, but in them he does concede that it is a deep mystery why only in QM is probability calculated using the squares of the amplitudes, which are of course complex numbers. Apart from that, all other "mysteries" are summarily dismissed.

jambaugh
Gold Member
He's more "right" than some IMNSHO. He's correct in that it has nothing to do with locality as such which is what too many others have focused on. He is correct that entanglement is nothing more complicated that correlation. So I would hardly call his error "crass".

The issue is the change of paradigm from classical theory which is ontological to quantum theory which is phenomenological. Bell inequality violation is on par with, say, the twin paradox of relativity. You, in the twin paradox case, retain an intuitive notion of absolute time while considering the predictions of a theory that has dropped this notion. You get a contradiction which indicates your incorrect implicit assumption. So too with Bell inequality violation. The phenomenological theory of QM makes predictions by dropping assumptions about states of absolute objective reality (classical models) and fixating on the empirical phenomena (one's algebra of observables and dynamical actions). You then get a contradiction when you reassert the objective reality in the form of Bell inequality vs quantum prediction.

With relativity one might have abandoned the assumption of absolute time only to see it emerge again as the observed case. But one has opened the door to other possibilities when one fails to assume it a priori an lo and behold time turns out to be relative in fact! Many had a hard time accepting that and many still do.

With QM "lather, rinse, repeat" but what's relativized here is (objective) reality itself.

The thing is, Binney doesn't accommodate locality by loosening his adherence to objective reality. Yes, he emphasizes that the spin vector does not have a definite direction, but this is seen as a particular feature of spin, which he still views as having a definite hemisphere once the measurement has been made. He views quantum theory as a handy guide to a microscopic world which is "mundanely" real but that we can't measure properly for practical reasons.

Here he gets a bit heated debating Simon Saunders, an Oxford philosopher of physics who advocates the Many Worlds Interpretation (he speaks after Saunders and then they have a discussion): www.youtube.com/watch?v=NKPI_wurNIo

stevendaryl
Staff Emeritus
He's more "right" than some IMNSHO. He's correct in that it has nothing to do with locality as such which is what too many others have focused on. He is correct that entanglement is nothing more complicated that correlation. So I would hardly call his error "crass".
Well, I would say just the opposite, that he's mistaken about both points. Entanglement is not the same as correlation, and the violation of Bell's theorem does have something to do with locality.

An "entangled" quantum state of two subsystems is a composite pure state $|\psi\rangle$ that cannot be written as a product of two component states. So, for a pair of spin-1/2 particles, the state $\frac{1}{\sqrt{2}} (|U\rangle |D\rangle - |D\rangle |U\rangle)$ cannot be written as a product state. Entanglement is a fact about pure states.

A "correlated" state of two subsystems is a mixed state such that knowing something about one subsystem tells you something about the other subsystem. If the two subsystems are entangled, then they are correlated, but the other way around is not true. The following mixed state shows correlation, but does not involve entanglement:

Letting $|\psi_1\rangle = |U\rangle |D\rangle$ and $|\psi_2\rangle = |D\rangle |U\rangle$, then the mixed state corresponding to density matrix $\rho$ defined below shows perfect correlation:

$\rho = p |\psi_1\rangle \langle\psi_1| + (1-p) |\psi_2\rangle\langle \psi_2 |$

But $\rho$ does not show entanglement, since it can be decomposed into an incoherent mixture of product states.

As to locality. Bell's theorem doesn't have anything necessarily to do with locality, except that the application of his theorem to an EPR-like experiment requires the assumption that a measurement on one particle can have no effect on another measurement taking place at a spacelike separation (too far away for light-speed influences to propagate from one measurement event to the other).

So, yes, as far as I understand them, his errors seem "crass" to me.

Pat71 and Derek Potter
With QM "lather, rinse, repeat" but what's relativized here is (objective) reality itself.
Hmm. Relative reality means the same in QM as it does in relativity: we see things from our own perspective whether through boosts in "absolutely real" Minkovski spacetime or through entanglements within one "absolutely real" superposition.

There is no non-locality in quantum Bell Inequality violation in a superposition-based (many worlds) model any more than there is a contradiction when the Twins Paradox is analysed correctly in SR. We don't need to abandon objective reality, we just need to abandon our belief that we see it directly.

State reduction, however, does run into problems. Non-locality remains spooky action at a distance, no matter how we dress it up, if we introduce state reduction. So, in that case, reality has to go. (Which is ironic considering that state reduction is only there to avoid having to think dangerous thoughts like "what happens to the other cat?")

Anyway, back to Binney. He may teach at Oxford but so do many others who would disagree with him and they can't all be right - well maybe they can in quantum logic where reality is optional.

Pat71
I think it's one thing to disagree but see the logic of your opponent's position, and another to be unable to see how their argument holds together. Binney seems to want to have his common-sense reality cake and eat it. I think maybe he pines for the Newtonian era. Here's a quote:

"The idea that a vector points in a well-defined direction is a classical notion and not applicable to objects such as electrons that do have a definite spin. This idea is an old friend from which we part company as sadly as after studying relativity we parted company with the concept of universal time. The world we grew accustomed to in playgroup is not the real world, but an approximation to it that is useful on macroscopic scales. The study of physics forces one to move on and let childish things go"

The irony is that he seems to be using this feature of spin to avoid giving up a much more important concept he got used to in playgroup - local realism!
Having reluctantly swallowed relativity, maybe he finds that QM is too much.

DrChinese
Gold Member
One issue with those who dismiss quantum correlations as relating to some "common cause" such as Binney's "the results of Bob's measurement are consistent with the hemisphere containing the positron's spin being fixed at the outset and being unaffected by Alice's measurement.":

Entangled Alice and Bob do NOT need to have ever interacted in the past for this to be true. They do not need to have ever existed in either's light cones. They do not even need to have existed at the same time. And they can be entangled after they are observed. How does any of this fit in with the dismissal above? The point being that entanglement is a far cry from simply saying that our knowledge is all that is being updated on measurement. How can you explain perfect correlation at any angle setting in this situation without invoking quantum non-locality?

Pat71
I was wondering how Binney would account for Gisin et al's recent quantum teleportation results, in which the teleportation between two photons that had never been in contact outperformed the classical benchmark over 25km.

One issue with those who dismiss quantum correlations as relating to some "common cause" such as Binney's "the results of Bob's measurement are consistent with the hemisphere containing the positron's spin being fixed at the outset and being unaffected by Alice's measurement.":

Entangled Alice and Bob do NOT need to have ever interacted in the past for this to be true. They do not need to have ever existed in either's light cones. They do not even need to have existed at the same time. And they can be entangled after they are observed. How does any of this fit in with the dismissal above? The point being that entanglement is a far cry from simply saying that our knowledge is all that is being updated on measurement. How can you explain perfect correlation at any angle setting in this situation without invoking quantum non-locality?
Thanks again for this powerful argument Dr Chinese.

Here is how he accounts for it:
" Many discussions of the EPR experiment generate needless confusion by supposing that after Alice has measured +1/2 for the component of the electron's spin parallel to a, the spin is aligned with a. The electron has half a unit of angular momentum in each of the x, y and z directions, although the signs of the x and y components are unknown when we know the value of Sz.
Hence the most Alice can know about the orientation of the spin vector is that it lies in a particular hemisphere.
And therein lies Binney's confusion. The hemisphere's axis - as defined by Binney right here - is a, not the z axis.
Whatever hemisphere Alice determines, she can argue that the positron's spin lies in the opposite hemisphere. So if Alice finds the electron's spin to lie in the northern hemisphere, she concludes that the positron's spin lies in the southern hemisphere.
This knowledge excludes only one result from the myriad of possibilities open to Bob: namely he cannot find Sz = +1/2.
He is unlikely to find +1/2 if he measures the component of spin along a vector b that lies close to the z axis
He should have said "that lies close to the a vector".
because the hemisphere associated with this result has a small overlap with the southern hemisphere, but since there is an overlap, the result +1/2 is not excluded.
Indeed so. But that means the correlation depends on b-a not on bz-z
Contrary to the claims of EPR, the results of Bob's measurement are consistent with the hemisphere containing the positron's spin being fixed at the outset and being unaffected by Alice's measurement."
Unaffected, yes, but the hemisphere's axis is defined by her measurement so it can't be pre-defined and can't affect Bob's measurement.

Perhaps one should interpret Binney's hemisphere that it does not literally contain a spin vector, but is actually the complete representation of the spin. But in this case, the two hemispheres arrive ready-made at Alice and at Bob. This would give some correlations but they would not be the right ones. After all, Bell's theorem is applied to specifically quantum systems, it does not work with the canonical "red and black ball in a sack" correlation and would not apply to, say, the charges on the particles either. It is easy to show that Binney's correlations would actually be linear in b-a.

Construct a plane through a and b. Draw a circle and split it for the two "given" hemispheres. Choose a direction for a. This determines Alice's hemisphere and thus her result. Choose a direction for b, pointing the other way. Obviously b goes into the other hemisphere. Now allow b to swing round to some other angle. Recall that the electron spins are evenly distributed around 360 degrees. So the probabilty of a and b both lying in the same semicircle is proportional to the angle between them. No trigonometrical functions involved. Hence the anti-correlation will follow a linear rule, not the required cos^((b-a)/2) rule.

See the Wikipedia image below. The text there merely asserts that the triangular (linear) correlation is the best possible one under classical assumptions, which are exactly what Binney makes.