Science has been rarely counter-intuitive to our understanding of reality, and its elegant rationalism at every step of the way has been reassuring. This is why Bell’s theorem has been one of the strangest concepts of reality scientists have come across: it is hardly intuitive, hardly rational, and hardly reassuring.

To someone interested in the bigger picture, the theorem is the line before which quantum mechanics ends and after which classical mechanics begins. It’s the line in the sand between the Max Planck and the Albert Einstein *weltanschauungen*.

Einstein, and many others before him, worked with gravity, finding a way to explain the macrocosm and its large-scale dance of birth and destruction. Planck, and many others after him, have helped describe the world of the atom and its innards using extremely small packets of energy called particles, swimming around in a pool of exotic forces.

**At the nexus of a crisis**

Over time, however, as physicists studied the work of both men and of others, it started to become clear that the the fields were mutually exclusive, never coming together to apply to the same idea. At this tenuous nexus, the Irish physicist John Stuart Bell cleared his throat.

Bell’s theorem states, in simple terms, that for quantum mechanics to be a complete theory – applicable everywhere and always – either locality or realism must be untrue. Locality is the idea that instantaneous or superluminal communication is impossible. Realism is the idea that even if an object cannot be detected at some times, its existence cannot be disputed – like the moon in the morning.

The paradox is obvious. Classical mechanics is applicable everywhere, even with subatomic particles that are billionths of nanometers across. That it’s not is only because its dominant player, the gravitational force, is overshadowed by other stronger forces. Quantum mechanics, on the other hand, is not so straightforward with its offering. It could be applied in the macroscopic world – but its theory has trouble dealing with gravity and the strong nuclear force, both of which have something to do with mass.

This means if quantum mechanics is to have a smooth transition at some scale into a classical reality… it can’t. At that scale, one of locality or realism must snap back to life. This is why confronting the idea that one of them isn’t true is unsettling. They are both fundamental hypotheses of physics.

**The newcomer**

A few days ago, I found a paper on arXiv titled *Violation of Bell’s inequality in fluid mechanics* (May 28, 2013). Its abstract stated that “… a classical fluid mechanical system can violate Bell’s inequality because the fluid motion is correlated over very large distances”. Given that Bell stands between Planck’s individuated notion of quantum mechanics and Einstein’s waltz-like continuum of the cosmos, it was intriguing to see scientists attempting to describe a quantum mechanical phenomenon in a classical system.

The correlation that the paper’s authors talk about implies fluid flow in one region of space-time is somehow correlated with fluid flow in another region of space-time. This is a violation of locality. However, fluid mechanics has been, still is, a purely classical occurrence: its behaviour can be traced to Newton’s ideas from the 17th century. This means all flow events are, rather have to be, decidedly real*and* local.

To make their point, the authors use mathematical equations modelling fluid flow, conceived by Leonhard Euler in the 18th century, and how they could explain vortices – regions of a fluid where the flow is mostly a spinning motion about an axis.

This is a vortex. Hurt your eyes yet?

Assigning fictitious particles to different parts of the equation, the scientists demonstrate how the particles in one region of flow could continuously and instantaneously affect particles in another region of fluid flow. In quantum mechanics, this phenomenon is called entanglement. It has no classical counterpart because it violates the principle of locality.

**Coincidental correlation**

However, there is nothing quantum about fluid flow, much less about Euler’s equations. Then again, if the paper is right, would that mean flowing fluids are a quantum mechanical system? Occam’s razorcomes to the rescue: Because fluid flow is classical but still shows signs of nonlocality, there is a possibility that purely local interactions could explain quantum mechanical phenomena.

Think about it. A purely classical system also shows signs of quantum mechanical behaviour. This meant that some phenomena in the fluid could be explained by both classical and quantum mechanical models, i.e. the two models correspond.

There is a stumbling block, however. Occam’s razor only provides evidence of a classical solution for nonlocality, not a direct correspondence between micro- and macroscopic physics. In other words, it could easily be a *post hoc ergo propter hoc* inference: Because nonlocality came after application of local mathematics, local mathematics must have caused nonlocality.

“Not quite,” said Robert Brady, one of the authors on the paper. “Bell’s hypothesis is often said to be about ‘locality’, and so it is common to say that quantum mechanical systems are ‘nonlocal’ because Bell’s hypothesis does not apply to them. If you choose this description, then fluid mechanics is also ‘non-local’, since Bell’s hypothesis does not apply to them either.”

“However, in fluid mechanics it is usual to look at this from a different angle, since Bell’s hypothesis would not be thought reasonable in that field.”

Brady’s clarification brings up an important point: Even though the lines don’t exactly blur between the two domains, knowing more than choosing where to apply which model makes a large difference. If you misstep, classical fluid flow could become quantum fluid flow simply because it displays some pseudo-effects.

In fact, experiments to test Bell’s hypothesis have been riddled with such small yet nagging stumbling blocks. Even if a suitable domain of applicability has been chosen, an efficient experiment has to be designed that fully exploits the domain’s properties to arrive at a conclusion – and this has proved very difficult. Inspired by the purely theoretical EPR paradox put forth in 1935, Bell stated his theorem in 1964. It is now 2013 and no experiment has successfully been able to decide if Bell was right or wrong.

**Three musketeers**

The three most prevalent problems such experiments face are called the *failure of rotational invariance*, the *no-communication loophole*, and the *fair sampling *assumption.

In any Bell experiment, two particles are allowed to interact in some way – such as being born from a same source – and separated across a large distance. Scientists then measure the particles’ properties using detectors. This happens again and again until any patterns among paired particles can be found or denied.

Whatever properties the scientists are going to measure, the different values that that property can take must be equally likely. For example, if I have a bag filled with 200 blue balls, 300 red balls and 100 yellow balls, I shouldn’t think something quantum mechanical was at play if one in two balls pulled out was red. That’s just probability at work. And when probability can’t be completely excluded from the results, it’s called a *failure of rotational invariance*.

For the experiment to measure only the particles’ properties, the detectors must not be allowed to communicate with each other. If they were allowed to communicate, scientists wouldn’t know if a detection arose due to the particles or due to glitches in the detectors. Unfortunately, in a perfect setup, the detectors wouldn’t communicate at all and be decidedly local – putting them in no position to reveal any violation of locality! This problem is called the *no-communication loophole*.

The final problem – *fair sampling* – is a statistical issue. If an experiment involves 1,000 pairs of particles, and if only 800 pairs have been picked up by the detector and studied, the experiment cannot be counted as successful. Why? Because results from the other 200 could have distorted the results had they been picked up. There is a chance. Thus, the detectors would have to be 100 per cent efficient in a successful experiment.

In fact, the example was a gross exaggeration: detectors are only 5-30 per cent efficient.

**One (step) at a time**

Resolution for the no-communication problem came in 1998 by scientists from Austria, who also closed the rotational invariance loophole. The fair sampling assumption was resolved by a team of scientists from the USA in 2001, one of whom was David Wineland, physics Nobel Laureate, 2012. However, they used only two ions to make the measurements. A more thorough experiment’s resultswere announced just last month.

Researchers from the Institute for Quantum Optics and Quantum Communication, Austria, had used detectors called transition-edge sensors that could pick up individual photons for detection with a 98 per cent efficiency. These sensors were developed by the National Institute for Standards and Technology, Maryland, USA. In keeping with tradition, the experiment admitted the no-communication loophole.

Unfortunately, for an experiment to be a successful Bell-experiment, it must get rid of all three problems at the same time. This hasn’t been possible to date, which is why a conclusive Bell’s test, and the key to quantum mechanics’ closet of hidden phenomena, eludes us. It is as if nature uses one loophole or the other to deceive the experimenters.*****

The silver lining is that the photon has become the first particle for which all three loopholes have been closed, albeit in different experiments. We’re probably getting there, loopholes relenting. The reward, of course, could be the greatest of all: We will finally know if nature is described by quantum mechanics, with its deceptive trove of exotic phenomena, or by classical mechanics and general relativity, with its reassuring embrace of locality and realism.

(*In 1974, John Clauser and Michael Horne found a curious workaround for the fair-sampling problem that they realised could be used to look for new physics. They called this the no-enhancement problem. They had calculated that if some method was found to amplify the photons’ signals in the experiment and circumvent the low detection efficiency, the method would also become a part of the result. Therefore, if the result came out that quantum mechanics was nonlocal, then the method would be a nonlocal entity. So, using different methods, scientists distinguish between previously unknown local and nonlocal processes.)

(This blog post first appeared at The Copernican on June 15, 2013.)