The Scientific Gamer

And so the blog finally drags on to the point where I have to start talking quantum again. Quantum mechanics is a hell of a thing; it’s both complex and hugely counterintuitive, and it isn’t helped by many of the popular misconceptions about it such as Schrodinger’s cat. I originally wanted to explain how quantum entanglement and the quantum eraser works because it’s one of the most head-screwy bits of physics out there, but then I realised there’s a lot of basic physics knowledge required to understand that that I can’t just take for granted. In particular you really have to know about wave-particle duality and the double slit experiment.

Wave-particle duality is exactly what it says, but a lot of people misunderstand because of the way they’re taught science in secondary school. A specific example of this is the model of the atom we present to kids, which is that it’s a collection of electrons orbiting an atomic nucleus made up of neutrons and protons in neat, regular shells of 2-8-8-8 and so on. This is a very simplified picture of what’s actually going on that is deliberately designed to be understood by teenagers with no prior experience of nuclear/particle physics; it’s one of the not-quite-lies we tell children to prepare the ground for teaching them a more complex model of the atom later on. It would be fine if we ever actually did that. Unfortunately most kids stop studying science subjects at sixteen, and even if they didn’t they wouldn’t find out what’s actually going on unless they chose to study physics at university.

So most people come out of school with this picture of electrons and other subatomic particles as… well, as point particles. We think they’re discrete physical objects orbiting an atomic nucleus just like planets orbit a sun (or at least I know that’s what I thought after doing my GCSEs). As an explanation of what’s going on inside an atom this is fifty percent right. Electrons do orbit the atomic nucleus, but they don’t do it as particles that can be found in one specific place at one specific time. Instead, your typical electron is smeared out into a collection of probability states where it could exist at a particular time, and the first counterintuitive thing about quantum physics is that until the position of the electron is measured it acts like it exists in all of them at once, simultaneously.

I went over this in the Schrodinger’s cat post linked earlier but I’ll just quickly recap: the behaviour of an electron as it orbits an atomic nucleus is governed by a mathematical expression called the electron’s wavefunction (which in turn is described by the famous Schrödinger equation). As the name implies, at this point the electron is behaving like a wave — several waves superimposed on top of each other, in fact. Each wave represents a possible quantum state that the electron can be found in, where a quantum state is a collection of quantum numbers (such as spin and energy level) that tell us when and where the electron is, and if you square the wave function you get what’s called the electron’s probability density. This is a set of probabilities corresponding to each quantum state that tells you how likely you are to find the electron in that quantum state.

Now, while the electron is made up of all these waves blurred together it’s absurd to think of it as occupying any one point in space. As an analogy, imagine taking one end of a long piece of string in each hand and jiggling one end up and down so that you got a standing wave. We can’t say that the wave is “at” any one point on the string as the string itself is constantly moving up and down to create the wave. Similarly we cannot say that an electron’s wave function describes a static point in space because that’s constantly moving and shifting as well thanks to the superposition of the waves describing the electron’s possible quantum states.

(Wikipedia’s article on wave functions has a pretty animated gif that is supposed to show what’s going on, but it’s still really hard to visualise because it involves imaginary numbers.)

This stands rather at odds with the classical interpretation of an electron, which says you can stick your instruments in and measure the position of an electron and it will be found at a discrete time and place rather than spread out over this large range of probability states. Quantum mechanics solves this inconsistency with a mechanism called wavefunction collapse. Say a quantum particle has a wave function which describes it as having four possible quantum states, A, B, C and D. The chances of the particle being found in states A and B are 20%. The chances of the particle being found in states C and D are 30%. The particle has a slightly larger probability of being found in states C and D, but until we directly measure its position we won’t know for sure. When we do this, we find that the particle is indeed in state C, one of the more likely quantum states, but if we then go on to recalculate the particle’s wave function it’ll tell us that the chance of finding the particle in state C is now 100%, while the chances of finding it in any of the other previously possible states are now zero. In other words, by the simple act of measuring the particle and finding it in one discrete quantum state we erased the other possible quantum states from existence. The quantum particle will now exhibit particle-like properties, only occupying one particular quantum state at one particular time.

This phenomenon of changing things by looking at them is known as wavefunction collapse. Any time you directly measure the state of a quantum particle you collapse its wavefunction describing many possible quantum states down to just a single definite quantum state. If you want to know what wavefunction collapse is or what it represents then you’re in good company because nobody really knows, and in fact we don’t even know if the mathematical process of wavefunction collapse is describing an actual real physical process. All we know is that the maths behind it is robust enough to describe the physical outcome of whatever happens when we look at a quantum particle.

So unmolested quantum particles will exhibit wave-like behaviour. When we measure them we collapse their wavefunction and they exhibit particle-like behaviour. This is wave-particle duality. A misconception about wave-particle duality is that it describes particles with some of the properties of waves, or waves with some of the properties of particles, and this is exacerbated by the use of terms like “particle” to describe quantum objects. Just look at wikipedia’s article on wave-particle duality:

Wave–particle duality postulates that all particles exhibit both wave and particle properties. A central concept of quantum mechanics, this duality addresses the inability of classical concepts like “particle” and “wave” to fully describe the behavior of quantum-scale objects.

So right after describing these quantum objects as particles it admits that the term particle is inadequate to describe whatever they are, but it goes ahead and does it anyway because it’s entrenched in the standard scientific lexicon now. In reality stuff we describe at the quantum scale is neither one or the other, but somewhere in between; at times they exhibit wave-like properties, and at others they exhibit particle-like properties, and smooshing together our existing physical descriptions of waves and particles is the best way we have of describing how these quantum objects work.

Anyway, there’s a neat experiment you can do to demonstrate wavefunction collapse; the double-slit experiment. This is a slight modification of Thomas Young’s original double-slit experiment designed to demonstrate light is a wave. If you project a wave front towards a small aperture or slit then the wave front will, upon passing through the aperture, diffract outwards in a circular pattern like this. In Young’s version of the experiment he projected beams of light through two slits that were next to each other. This produced two sets of diffracted waves that collided with each other and produced what’s called an interference pattern which looked like this:

When the two diffracted beams of light were projected onto the screen F, Young saw the pattern at the far right of the diagram: a neat, regular series of peaks and troughs in the intensity of the light that was exactly what you’d see if the light were made up of two overlapping wavefronts.

The quantum mechanical version of this experiment is a little bit different. Here the two slits are very close together, and the beam of light is replaced by a single coherent stream of single electrons. Each electron passes through the plate with the slits one at a time; there is no way for two electrons to pass through the plate at once and interfere with each other. Classical physics tells us that if an electron wants to pass through the plate with the slits it has to pick a slit to go through and then stick with it until it hits the screen at the far end of the experiment. Consequently you’d expect to see two thin lines projected onto the screen F made up of electrons that passed through one slit or the other, as an interference pattern of the sort produced during Young’s experiment is impossible.

This being quantum mechanics, though, that’s not what we see at all. Thanks to electrons being made up of superpositions of different quantum states, all of which exist at once, it is perfectly possible for a quantum state where the electron went through the right slit to coexist with a quantum state where the electron went through the left slit; in other words, while it’s behaving like a wave a single electron can go through both slits at once and interfere with itself, producing an interference pattern just like Young’s experiment. This demonstrates the wave-like nature of electrons, but it doesn’t stop there.

If you try to catch the electron out by putting a particle detector next to one of the slits that ticks each time an electron passes through it, you force the electron to stop messing around and pick a slit to go through. Either it passes through the slit with the detector, in which case the detector ticks, or it passes through the slit without and the detector remains inert. Either way you’ll know which slit an electron went through. The moment — the moment — you turn your particle detector on to find out which slit the electron went through the nice interference pattern produced by the wave-like electrons vanishes, to be replaced by the two thin lines you’d expect to see if the electrons were behaving like point particles. By adding the particle detector to the mix to measure which electrons go through which slits you’ve collapsed the wavefunction and forced the electrons into a particle state.

(Interestingly when the electrons hit the screen at the far end of the apparatus they always do so as discrete point particles, but when the electron buildup over time is measured it forms an interference pattern.)

That’s double slits 101. It illustrates what’s called the principle of complementarity — that quantum objects can behave either as particles or as waves, but not as both at the same time. Scientists have tried ever more ingenious variations on this experiment to see just how far this principle of complementarity goes, with some rather startling results. More on that next time.

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All diagrams sourced from Wikipedia except the one with the New Scientist watermark, which was sourced from New Scientist.