Down with Quantum Woo!

Despite the best efforts of science communicators everywhere, quantum woo is still prevalent, mostly peddled by annoying snake oil sellers and very much even on the fringes of pseudoscience. In that regard it's less harmful than, say, anti-vaccination propaganda or GMO scaremongering - which both have a far bigger platform.

Unfortunately, its supporters are no less rabid. To them, quantum mechanics is a mystical tool which can allow you to do anything, and if you don't believe them, you're a fed.

Yes, every practising physicist is now a fed. I was quite surprised by this as well.

Quantum mechanics is actually fairly old and has its roots in the 19th century. Even what we think of as modern quantum mechanics was actually born in the 1920s and is at this point nearly a century old. Still, classical electromagnetism, which is about 150 years old, doesn't really have any accompanying woo (even if electricity and magnetism can be conceptually very difficult until you're confident with vector calculus). So how do we explain this?

1) Quantum mechanics is legitimately weird. This is probably the best starting point. Other established theories also have weird or counterintuitive elements; for example, Newtonian mechanics predicts that in the absence of friction, an object set in motion will keep moving forever. This clearly goes against our everyday experience, but nobody tries to sell Newtonian mechanics as something mystical and deeply profound.

The difference lies in the foundations of quantum mechanics. Unlike other theories, which are relatively neat and logical, the foundations of quantum mechanics are a mess of educated guesses (Ansätze) which fly in the face of previous assumptions about the world and predict incredibly strange things. The practical applications aren't much better; because the Schrodinger equation, which predicts the evolution of the quantum state of a quantum system over time, cannot be solved analytically for anything more complicated than a hydrogen atom, we use elaborate systems of approximations. Still, they work reasonably well: these elaborate systems of approximation govern the insides of your computer or phone and are allowing you to read this right now. Not bad, huh?

In fact, quantum mechanics is so weird that quantum mysticism was seriously entertained by leading physicists like Erwin Schrodinger and Werner Heisenberg up until about the second half of the twentieth century. However, current quantum woo has very little to do with older quantum mysticism.

2) Quantum mechanics is hard. I can't stress this enough. Not only is it conceptually difficult, but even introductory quantum mechanics requires knowledge of linear partial differential equations, integration by parts, classical mechanics and electromagnetism. The mathematics alone is beyond the grasp of people who haven't spent years in continuous study and practice. This is incredibly unfortunate, because we as physics students use the maths as a sort of shortcut to understanding the concepts. In fact, it's probably one of the only ways to understand the concepts without getting caught in the woo.

So what do we as science communicators do?

We've been doing our best, I suppose. It's not an easy topic to explain at all and the fact that it's gotten so popular has a lot to do with the talent and enthusiasm of science writers and scientists themselves. Even the woo-mongers helped to keep quantum physics alive and in the public eye, so for that at least we owe you one.

I suppose the first step now is to challenge the misconceptions. This in itself is not going to be easy, because most misconceptions run on "I don't understand quantum mechanics and I want magic to exist, so quantum mechanics is magic". I suppose what I'm trying to say is that the misconceptions are extremely broad in scope. Happily, they all have one major flaw: all misconceptions operate at macroscopic scales, because that's what people are familiar with.

On a macroscopic scale, particles interact, wavefunctions collapse incredibly easily, and the energies we deal with are huge compared to the energies you might encounter in quantum mechanics. The larger the energy of a particle, the smaller its wavelength and the less likely it will be able to pass through barriers, for example. This is why people cannot diffract through walls and why I am at negligible risk of quantum tunnelling through my bed.

Personally, I find it easier to think of quantum mechanics in terms of what you're not allowed to do rather than what you're allowed to do. Contrary to what woo-peddlers want you to think, quantum mechanics is very restrictive. Instead of energy being allowed to take continuous values, energies are discrete (quantised) and associated with certain eigenvalues (special values which satisfy the particular form of the Schrodinger equation). It is these restrictions which underpin most of physics (and why you don't fall through the floor).

Now, this all makes sense to me but might not necessarily make sense to the average reader. This is because I have something relatively few people do: maths. Lots and lots of maths.

I don't think we're going to get anywhere combatting quantum woo unless we start teaching maths. I suspect most people would agree with me, but in this country most people stop after they take their GCSEs. The most complex mathematics most people in England will ever encounter is quadratic equations with real roots, basic trigonometry and vector arithmetic.

While you need to learn to run before you can walk, there's no calculus in there. Calculus is everywhere in basic quantum mechanics.

I started learning differentiation and integration of real functions when I was 14 or 15. I am now 20 and recently finished a course in complex analysis, including contour integration, finding residues and line integrals of complex functions a few months ago. I am also doing more linear algebra in my spare time, I will have to learn tensor calculus at some point, and there's so much more maths out there I haven't even touched. The point I'm trying to make is that this stuff takes years to learn and there's simply no way to teach it all in a book or an hour-long lecture for the public. At the same time, quantum mechanics relies on it in fundamental ways.

I propose a compromise: take one equation and explain it step by step.
When I was a first-year student, my lecturer drew this on the visualiser and explained that it was the source of all quantum "bullshit". To this day that's probably the only useful thing Brian Cox has ever taught me. (Don't believe the lies. He's a shit lecturer.)

At the same time, this involves expectation values, improper integrals, and complex conjugates. So...still kind of outside GCSE maths territory. But it's one of the simplest "useful" equations in basic quantum mechanics.

So what does it all mean?

Starting from the left, the <x> is the expected position of the particle - the place where you expect it to end up on average. (There are ways to calculate the probability of the expected position, but I'm not going to get into that.)

The integral going from minus infinity to infinity is called an improper integral. What it's telling you is that to find the expected position of the particle, you have to sum up all the infinitesimals over dx from minus infinity to infinity, or everywhere in the universe. That's right - this particle could be everywhere in the universe all at once until something interacts with the universe (say, a photon) and the wavefunction collapses.

Speaking of wavefunctions, ψ(x,t) is the symbol for a wavefunction and describes the quantum state of a system. Fair enough - but what's this ψ*(x,t)?

That's the complex conjugate. Strictly speaking, wavefunctions are complex functions - they involve i. The complex conjugate takes the part with i in it and changes the sign.

That's all very well and good, but why would we need both? Turns out that conjugates are really neat: when you multiply a complex number by its conjugate, you get a real number. This means that we can do real integrals, rather than messing around with the integration of complex functions. (Mostly, it's a pain. You will spend hours drawing squiggles. In general, integrating real functions is much nicer.)

And why is there an x squashed in the middle? Well, in classical mechanics, things like position (x) and momentum (p) are observables which can be determined by a series of physical operations. In quantum mechanics, we replace these with operators which act on the wavefunction in some way. The position operator is nice because it's just x, but other operators involve differentiation, so the order does matter.

To take a step back and stop getting bogged down by all the maths, what this equation basically tells you is that this particle could be anywhere in the universe at all until it interacts with the universe somehow and the wavefunction collapses. The expected value tells you where it's likely to end up on average.

Don't get me wrong, it's still profound and it's still beautiful, but it's also very plain. Everything adheres rigidly to the maths. You will find no quantum woo here, only austere calculus. It's not magic - it's something far better.

I have no doubt that if we step people through the maths, we can drive out quantum woo.