Sunday, 12 November 2017

Did You See That?!!

The observer, when he seems to himself to be observing a stone, is really, if physics is to be believed, observing the effects of the stone upon himself. - Bertrand Russell

In this outing, I want to address one of the most ubiquitous and egregious misrepresentations of science we encounter. It's the starting point for all manner of metaphysical bullshit, and the anchor for reams of shoddy thought and, worse, shoddy science journalism. It's an effect that manifests in all experiments dealing with quantum phenomena, and it seems to suggest that the world doesn't exist when we're not looking at it; the observer effect.

Note the operative word there: 'seems'. This word is a pernicious little beastie, and gives us no end of trouble when we think about what it means. The most famous soliloquy in all of Shakespeare's witterings, that of the eponymous Danish prince, has one interpretation that revolves around this word, the difference between seeming and being. We looked at such differences in a previous outing on semantics and the pitfalls of natural language in The Map is Not the Terrain, wherein we learned about how words can trip us up if we're not careful, and this is the core of today's topic.

First, though, let's talk about the popular misconceptions about what the observer effect is. 

As we learned in The Certainty of Uncertainty, there are some really counter-intuitive effects that arise from Heisenberg's Uncertainty Principle. The funny thing is that the observer effect really isn't one of them, once you understand what's going on. That said, the misunderstanding is an easy one to come away with if you don't have that grasp of the underlying physics, and it's one that's promulgated even by articles in popular nominally science publications such as an article published in New Scientist entitled Consciously quantum: How you make everything real

One of those counter-intuitive effects is one we've covered in various places on this blog and it goes under the name of 'wave-particle duality'. Often taken to mean that the things we think of as particles aren't only particles, but are also waves - another misconception we've dealt with previously - what it actually is is the simple principle that the things we think of as particles are neither particles nor waves, they're something else, something that can only be named by naming the entities themselves. In short, an electron, for example, is not a particle, nor a wave, nor both: it's an electron.

This highlights one of the main reasons that Quantum Mechanics is so counter-intuitive. When we want to explain something, we do so by comparing it with something we understand. In the case of so-called particles, there really isn't anything we can compare them with that will aid our understanding. They simply don't behave like localised chunks, so comparing them to chunky things is misleading. They also don't behave like distributed waves, so comparing them to waves is misleading. When we interact with them in one way, we see a behaviour that we associate with waves. When we interact with them in another way, we see a behaviour that we associate with particles.

This is, in a nutshell, the source of all the misunderstanding of the observer effect, and the real problem in there is the word "we". 

Let's have a look at what's really going on, and see if we can tease out why this view is wrong. For simplicity, from here on, I'm going to talk only about a single electron, because this will allow me to avoid all the pitfalls inherent in talking about particles and waves. Where I talk about particles or waves (which I may or may not do - simply treat this as a caveat), I'm talking about the wave-like or particulate aspects of the behaviour of our electron.

There's a set of relationships in quantum theory known as the de Broglie relations. It's worth getting the chalk out here, so that we can grasp them completely. We don't actually need them to illustrate the point, but it's useful for completeness because they will drill down to the reality of the observer effect, and because we haven't covered this in any previous outings on Quantum Mechanics. Let's start with a wave:

Every wave has associated with it a wavelength, which we denote lambda (\(\lambda\)). It also has a linear frequency nu (\(\nu\)). The latter, for us audio geeks, corresponds to Hertz (Hz). Hertz is the number of times a wave cycle completes per second but, in quantum theory, we have to deal with time and space, so we can't use time-dependent notation.

We also have an angular frequency omega (\(\omega\)), which is found by \(2\pi\nu\). The other important terms we need are the wave number \(k \), which is \(\dfrac {2\pi}{\lambda}\), and Planck's constant \(h\), which has a numerical value of \(6.626 \times 10^{-34}\; J\cdot s\) (joule-seconds; this is the dimensional integration of energy over time). Planck's constant will always be reduced from here on, because it means we don't have to keep dividing by \(2\pi\), so we use the reduced Planck constant \(\hbar\), which is \(\dfrac {h}{2\pi}\).

So, now we have our terms. There are two other terms that we'll be using, but they're very familiar to us, as we encounter them often. They are the energy \(E\) and the momentum \(p\).

Regular readers will be wondering when our old friend Einstein is going to pop up in this post, so we might as well get it out of the way.

In one of his annus mirabilis papers from 1905, Einstein gave us the first inkling of the duality of light. We already knew from Young's double-slit experiment that light behaved like a wave, because it showed the characteristic interference pattern. Einstein, in his work on the photoelectric effect that earned him the Nobel prize, showed that light must come in packets, or 'quanta'. In particular, he showed that an electron couldn't be dislodged from a photovoltaic panel unless it had a linear frequency \(\nu\) higher than a certain minimum value, no matter the intensity of the light shone on it (the number of photons thrown at it), and that linear frequency is related to energy via a proportionality constant, the aforementioned Planck constant. In other words, the energy of a photon is given by the equation \(E=h\nu\). The momentum of a photon is given by the equation \(p=\dfrac {h}{\lambda}\)

When we put all of this together, we get an interesting set of relationships that, because we have both energy and momentum, means that we have full wave-particle duality - that photons have both wave-like and particulate behaviours.

This relationship was taken a step further by French physicist Louie de Broglie, who postulated that, if these relationships hold for light, and given that light displayed wave-like and particulate behaviour, perhaps other particles might also have wavelike properties, and that therefore the energy relationship \(E=h\nu\) might hold for them. This being the case, he conjectured that the momentum relationship might also hold, which would mean that the inverse of the momentum relationship should be true, namely \(\lambda=\dfrac{h}{p}\).

Thus, rearranging all of this and using the reduced Planck constant, we get the following generalised relations for ALL particles:
\(p=\hbar k\)

Now, we really didn't need all that to get to the nitty-gritty of the observer effect, but it does put some flesh on the topic. The really important thing to take from all of this is the interdependent relationships between energy, wavelength and frequency. In summary, the greater the energy, the higher the frequency and the shorter the wavelength. This is about to become important when we look at what happens during observation.

There are lots of ways we could illustrate this, but I haven't found anything as elegant as the following. 

Let's take a little diversion, and imagine a very popular executive toy, a pinart puzzle. I'm sure this toy doesn't need any explanation, but the image on the left shows one. 

Now let's imagine trying to work out what one of these toys might be displaying by throwing things at it and registering the interactions. This might seem a bit of a strange way to go about 'seeing' it, but this is actually precisely what's happening when we see anything, namely that we register the photons bouncing off things.

Let's start with a football (being non-American, when I use the word 'football' I'm referring to a ball that you strike with your feet, as opposed to the hand-egg that Americans use the word for). Throw a football at the pinart toy and register the interaction. Yes, I'm aware that this is silly, but the silliness highlights something important. You simply wouldn't expect to get any information about what a pinart is displaying if you throw a football at it.

Let's try something smaller like a tennis ball. You might get a little information, but it isn't going to be much. You should be able to see where this is going by now. You can work your way down in scale using smaller and smaller balls, and you're going to get very little information about what the pinart is displaying until you get down toward the scale of the pins themselves. Go even smaller, and you'll resolve more and more detail until, once you get well below the scale of the pins, you can see the bevels on the edges of the individual pins. Smaller still, down to the scale of particles, and you can resolve the microscopic detail of the surface of the individual pin.

Once we grasp this, it becomes pretty obvious that there's a direct relationship between the scale of our 'observer' and the scale of the thing being observed. We simply can't resolve any detail unless the thing we're throwing at the subject is on a commensurate scale.

Let's have a look at a double slit experiment. For a complete explanation of this experiment, see The Certainty of Uncertainty. We're going to concern ourselves not with the experiment itself, but with what happens when we 'observe' what's going on. The experimental setup is exactly the same as always. The only difference is that eye, which represents a conscious observer. Which slit does the electron go through? 

The problem is clear. We can't actually resolve an electron with our eyes. We have to interact with the electron in some way in order to see which slit it went through. This is where what we learned above becomes relevant. In order to look at the electron going through the slit, we have to throw something at it. In other words, we have to inject an observer into the picture, and if we hit it with anything, we're going to impact its travel. 

Can we be really cunning and just tap it lightly? Maybe we can just give it a tiny nudge with a really low energy photon, and that will tell us which slit it went through? Let's try it.

And we can immediately see the problem. Because the wavelength is inversely proportional to the energy, any low-energy photon is going to have such a large wavelength as to make it impossible to resolve an individual electron going through an individual slit. In order to get the required resolution, we have to throw a short wavelength photon at it, which means high energy, and higher energy means giving the electron a bigger kick.

There's simply no way around this. This relationship lies at the heart of the observer effect, and underlies the vast majority of what we think of as 'quantum weirdness'. 

It's also worth noting that this is also precisely why we have to build more and more powerful particle accelerators, because we need higher energies to probe smaller and smaller scales, and all because of this inverse correlation between wavelength and energy. 

There are other ways to find out which slit a particle has gone through, but all of them eventually lead to the same problem, namely that we have to change the particle in some way in order to make it clear which slit it went through, whether that involves smacking it with a photon or forcing its spin around a particular axis. Every single way that we can get 'which path' information has ultimately the same effect. This is the observer effect. It doesn't for a second mean that an observer has to be conscious and, as we've seen here, the observer in the vast majority of cases is another particle.

Sleep easy. The world still exists when nobody's looking at it. Indeed, looking at it makes no difference whatsoever, interacting with it does. The wavefunction of every particle making up the world is collapsed by the interactions of every other particle. 

Thanks for reading.

Further reading:

Give Us a Wave! A treatment of waves, coherence and quantum theory.