Way, way back in 1935, Albert Einstein looked at the emerging theory of quantum mechanics and although he said a lot of things about it at the time, and a lot of things after that too, what it really boils down to is this. As I’ve mentioned in previous articles, Einstein had a teeny-tiny (did you see what I did there?) problem with quantum mechanics. To summarise, what he was basically declaring was…

“This cannot be the whole story.”

By the mid 1930’s quantum mechanics had already become hugely and enormously successful (LOL I did it again, didn’t I!). It correctly described atoms, light, and the microscopic world. Einstein, however, being Einstein, believed wholeheartedly that it contained a profound flaw. He couldn’t accept that physical properties might not exist until they had been measured.

As far as Einstein was concerned, the Moon was still there even when nobody looked at it. Which to him meant, a particle should possess a definite state before anyone measures it. If quantum mechanics suggested otherwise, then perhaps some deeper set of hidden facts and hidden variables remained awaiting discovery.

This argument seemed destined to remain philosophical for nearly thirty years, before a quiet physicist from Northern Ireland by the name of John Bell came along.

What Bell did was ask an astonishingly simple question. He didn’t ask whether Einstein or Bohr (brilliant Danish dude, one of many things he is most famous for is developing the Bohr model of the atom) were right. He asked a much more powerful question:

If Einstein’s intuition is correct, what measurable consequences would follow?

At the time this was revolutionary. In an instant, Bell had transformed a debate about the nature of reality into a scientific hypothesis that could be tested in a laboratory.

The result of which he published in 1964, which became universally known as Bell’s Theorem.

I hear one of those questions nagging at you again. You want to know what Bell’s Theorem is, don’t you?

Well, at its heart lies a family of mathematical relationships called Bell’s Inequalities.

Let’s assume for a moment, that the Universe trots along, as it does, according to good old-fashioned common-sense.

Let’s catch up with Bob and Betty again. Imagine that two particles, born together, have then been hurled in opposite directions.

One travels to Betty and the other one travels to Bob, so now two experiments are so far apart that even a light signal cannot travel between them quickly enough to coordinate their measurements.

Now you have to ask yourself, if that’s the case, how could the particles remain correlated?

And that is when the common-sense answer comes in and seems the most obvious. They must have left the source carrying matching instructions.

Like two naughty boys, who have already agreed on their response before getting told off severely for doing something stupid (middle school, my best mate Duncan and the green houses in the garden behind the Spar next door spring to mind, but that is 100% a different story and not for now). What if the particles already know how to respond to every possible measurement?

This view, however, rests on two assumptions:

Number one: Realism. That is the properties of the particles exist before measurement, and Number two: Locality. Nothing can influence something far away faster than light.

Put them together and these two ideas form what physicists call local realism (original, huh?).

Now then, to most people, like you and old me before I learnt all this stuff, local realism sounds less like a theory and more like plain old-fashioned common-sense.

And that was Bell’s perfectly set trap!

He wondered whether pre-arranged instructions could explain every possible pattern observed in entangled particles, and he imagined particles carrying complete answer sheets.

Here’s the clever bit though: Betty and Bob don’t just get asked one question each, they can each be asked one of two different questions. So each answer sheet needs a pre-written response ready for both, not just whichever one actually gets asked.

So, if Betty chooses measurement A, the particle will give a predetermined result.

And if Bob chooses measurement B, his particle will also give a predetermined result.

What’s so unreasonable about that? Sounds very reasonable to me. I hear you say.

The thing is, Bell had discovered something quite remarkable.

He discovered that no matter how cleverly those answer sheets are designed, they can only produce correlations up to a certain mathematical limit. And that limit, folks, is a Bell Inequality!

The most famous version of which is the CHSH inequality, which predicts that a quantity called S cannot exceed 2 if local realism is true.

Nature, however, had other plans. That’s right, you’ve hit the nail firmly on the head. It’s those pesky quantum mechanics breaking the rules again, isn’t it!

And you’re right! Quantum theory predicts that entangled particles can produce correlations stronger than Bell’s limit. Not infinitely stronger. Just strong enough. Instead of stopping at 2, quantum mechanics allows values as high as:

or approximately 2.828. This maximum quantum value is called the Tsirelson bound (you’ll have to take my word on this as it’s way to complicated for me to explain simply), and to Bell, this meant something extraordinary. (If you really wanna know about Tsirelson’s bound, have a look at Wikipedia here).

If experiments ever exceeded the classical limit of 2, then no theory based on local hidden variables could fully describe reality. That was when the argument ceased to be philosophical, as reality itself would have to choose a side.

And so the experiments began. In the 1970s, physicists John Clauser and Stuart Freedman conducted the first significant tests. The results of which agreed with quantum mechanics. Although a 1973 Harvard experiment by Francis Pipkin and Richard Holt initially produced opposite results before later experiments, such as Fry and Thompson in 1976, strongly violated Bell’s Inequalities, aligning perfectly with quantum mechanics.

There were still many sceptics who remained unconvinced though.

“Perhaps the experiments contained flaws!” they shouted

“Perhaps the particles somehow communicated!” they screamed

“Perhaps the detectors introduced biases?” the shyer ones whispered to each other.

Then, in the early 1980s, a French physicist called Alain Aspect and his collaborators performed more sophisticated experiments in which detector settings changed while the particles were already in flight. And, you’ve guessed it, once again, Bell inequalities were violated. And this time the evidence was growing harder to dismiss.

For decades, physicists searched for loopholes, but every escape route was closed.

Maybe detector inefficiencies could explain the results? Nope!

Or it could be experimental effects mimicking quantum correlations? Nope!

Ah, could the measurement choices somehow be known in advance? Nope!

Researchers attacked each loophole one by one, and every time the loopholes were firmly closed.

More recently in 2015, multiple groups began reporting “loophole-free” Bell tests. However, these experiments simultaneously addressed the major known objections and still found violations of Bell Inequalities exactly where quantum mechanics predicted them. The verdict was becoming increasingly unavoidable with everything they tried. Simply put, Nature does not obey local realism.

So, what did Bell actually prove?

We often hear popular science accounts say that “Particles communicate faster than light.”

Bell did not prove that. Nor did he prove that information travels instantaneously. Nor did he show that relativity is wrong. What he proved was way, way subtler.

Basically, Bell was saying that the world cannot be explained by a picture in which distant objects merely carry pre-existing local instructions, and that something about our classical understanding of reality must give way.

And so, the great mystery remains.

The awkward truth of the matter is that physicists still disagree about exactly what Bell’s theorem means, with some interpretations abandoning realism, and others abandoning locality.

Other physicists have attempted to rethink the measurement altogether.

But all serious interpretations must confront Bell’s result.  The experimental facts may no longer be in doubt, but the philosophical meaning remains fiercely debated.

And that leads us to why Bell matters. While many scientific discoveries tell us how the universe behaves, Bell’s theorem is fundamentally different. It tells us how the universe cannot behave.

It places a permanent limit on any explanation that can be built from everyday intuitions about objects carrying definite properties which are interacting only through local causes.

For centuries, philosophers wondered whether reality existed independently of observation. Bell found a way to ask the question experimentally.

The answer appears to be that the microscopic world is stranger than even Einstein imagined. And perhaps the most astonishing part of all is that a debate that began around blackboards and thought experiments ended with photons, detectors, laboratory equipment, and reality itself casting the deciding vote.

Hopefully, with my explanation of Bell’s Inequalities, my previous two articles will make a bit more sense now.

It’s mind-bogglingly amazing that with all the mind-bogglingly stuff all the clever physicists and quantum dudes have learned and discovered and now understand, that we have been going around in circles with this one for nearly a century. And that, my friends, is one of the many reasons I love physics!