# Einstein’s Nightmare

/I hope people enjoyed the first part of my BBC series, The Secrets of Quantum Physics. Since part two doesn’t really follow on from where I left off (more on that in my next blog coming shortly) I thought I would try and clarify my views here.

In the first film, called ‘Einstein’s Nightmare’, I think I went as far as anyone has on a TV programme for the general viewer, arriving at some pretty advanced ideas in quantum mechanics: the EPR paradox and Bell’s inequality, which provides a mathematical test of whether the world of the very small exists when we are not observing it or whether it just has a fuzzy potential for existence until we look, conjuring it into solidity.

The equation I had on the white board towards the end of the programme was, I said, due to John Bell and it would prove whether Einstein or Bohr was right about the nature of quantum reality. The sharp eyed among you may have noticed a CGI equation appearing on the screen a little earlier with the right hand side of the ‘inequality’ being ≤ 1. Now, it had suddenly become ≤2. Also, there are four rather than three terms on the left hand side.

The difference is that the whiteboard formula is actually called the Clauser-Horne-Shimony-Holt inequality, not the Bell inequality, and it is a slightly more sophisticated version, concocted by the four physicists it is named after, five years after Bell’s original work.

Anyway, these are subtleties. What bothered many people (well the handful who tweeted me about it anyway) was the third quantity, which was negative. Why did I then proceed to add it rather than subtract it?

To recap, I had four numbers to add together. If the total came to under 2, then Einstein’s version of quantum reality was correct and the world is deterministic, rather than probabilistic, with quantum entities existing prior to being observed. But if the total came to over 2, then Niels Bohr was right and there is no objective reality out there in the absence of measurement and the subatomic world is ruled by chance and probability.

The first two numbers were 0.56 and 0.82. The third was –0.59, so it seems I would have to take this way from the running total. The fourth number, another 0.56, should then have left me with a total of 1.35 and victory for Einstein.

That’s not what I showed.

In fact, the subtlety is that the third term, the one that had a negative value, was already negative. The inequality read:

P(a,b) + P(a,b’) – P(a’,b’) + P(a’,b) ≤ 2,

So, plugging all the numbers, this looks like:

0.56 + 0.82 – (–0.59) + 0.56

= 0.56 + 0.82 + 0.59 + 0.56 = 2.53

So, sorry Einstein, victory goes to Bohr instead.

But this seems a little ‘convenient’ you might argue. Why subtract just that third term. Well, you’re welcome to go through the derivation of the maths. It’s not easy for the uninitiated, and it can be even found on Wikipedia. But I certainly didn’t have the time to go into the details. I mean, I can get into considerable depth on BBC4 programmes (and I am very grateful to them for that). But at the end of the day, this is a one-hour TV film for non-scientists, NOT a physics lecture course, so I am not bound by the same constraints of thoroughness like I am when I teach my students at university. Those who think I am should maybe take a course on quantum mechanics.

Before I end, I should say one thing. I did give the impression in the film that I sided with Bohr on this issue. After all, that was the whole point of that experiment, right? Well, actually, if push comes to shove, I am closer to Einstein than Bohr when it comes to the interpretation of quantum mechanics.

You see Einstein was arguing for a deterministic explanation of quantum theory, suggesting that what we see as indeterministic, probabilistic quantum laws are simply because quantum mechanics is incomplete and that there are what are referred to as ‘hidden variables’ that, once revealed, would give a more common-sense picture of the quantum world – one based on objective reality, a reality that exists even when we aren’t looking. The truth is that Bell’s theorem, and his inequality that is broken, doesn’t mean Einstein was wrong about all of this, only that the most basic version is ruled out: what is called ‘local hidden variables’.

As it happens, there is another way of explaining all the weirdness of quantum mechanics, developed first by Louis de Broglie in the mid-20s, called pilot wave theory, and later made more sophisticated in 1952 by David Bohm (yes another quantum physicist with a four-letter name starting with B, along with Bohr, Born, Bell and Bose). This interpretation, called Bohmian Mechanics never really picked up many followers, mainly because of the hegemony of the Copenhagen view.

Bohmian mechanics says the electron does indeed only go through one or other slit, but it is carried along by a wave or field (called the quantum potential) and it is this wave that goes through both slits, interferes and guides the electron to the points on the screen that build up the usual interference pattern. You can learn a little more about how this idea is being explored at the moment here.

Basically, while the mathematical construct that is quantum mechanics is not much in doubt these days, what it MEANS (the interpretation of the theory) is still up for grabs. There’s the Copenhagen view, Bohmian mechanics, the Multiverse interpretation, the Transactional theory, spontaneous wave function collapse theory…) We don’t know which of these is right. Many physicists don’t care, as long as the theory works and is useful. But that is not how physics should be. Quantum mechanics is the only theory in the whole of science that gets away with having multiple interpretations of what the mathematics means. So many quantum physicists decide early on in their research careers that if they want to make progress then they simply label such issues as metaphysics and leave the debate to the philosophers.

But to my mind, what it comes down to is more than just philosophical taste as to what is going on in the quantum world. And I happen to be convinced that there is an objective reality out there. Our scientific theories are not epistemological. Here I would say Bohr was wrong, as are all his Copenhagenist desciples. Nature does thing a certain way and it is our job as physicists to figure out how it does it. We may not like it, it may be counterintuitive, but tough luck. And we may fail to ever find the ‘right’ interpretation.

What we shouldn’t do is ‘shut up and calculate’.

Right, off my chest. Now stand by for a quick preview of this Tuesday’s second part of my BBC series.