Sweat The Small Stuff

Let’s talk about science! Literally, here I am talking about science, the quantum world, scientists, and answering audience questions from a kindly bunch at Pint of Science this May in Dublin. There is also a bit of a surprise in the middle.

Quantum Worldview

I have always loved the kind of science fiction where you think about a world that is largely like our own, but in some fundamental way different. What if we all lived underwater, or if the force of gravity was lower, or if the sun were a weaker star? To me, that’s what the world of quantum physics is like: in a lot of ways it’s similar to our own world, in fact it’s the basis of our world! But it’s also crazy and strange. So what would it be like if we were quantum creatures, if we could actually see how everything around us is quantized?

Well first, there’s what it means to be quantum. A quantum of anything is a piece that can’t be subdivided any further, the smallest possible unit. But this implies a sort of graininess, where rather than a continuous stream of, say, light, we start to see at the small scale that light is actually composed of little chunks, quanta of light. Imagine being able to see how everything around you is made of discrete pieces, from light to sound to matter. When the sun came up, you’d see it getting lighter in jumps. When you turn up your music, you’d hear each step of higher volume. And as your hair grew, you’d see it lengthening in little blips.

And at the quantum scale, the wave nature of everything becomes indisputably clear. We normally think of waves as something that emerges from a lot of individual objects acting together, like the water molecules in the sea, or people in a crowd. But if you look at quanta, you actually find that those indivisible packets of light or sound or matter are also waves, waves in different fields of reality. That’s hard to get your head around, but think of it this way: as a quantum wave, if you passed right by a corner, you could actually bend around the back of it a little the way that ripples going around a rock in water do. Things like electrons and photons of light actually do this, so for example the pattern below is made by light going through a circular hole, and the wave diffraction is clearly visible.

Amazingly, as a wave, you could actually have a slight overlap with the person next to you. This gets at something that’s key to quantumness: the probabilistic nature of it. Say I thought you were nearby, and I wanted to measure your position somehow to see how close you were to me. I’d need to get a quantum of something else to interact with you, but because it would be a similar size to you, it would slightly change your position, or your speed. We don’t notice the recoil when sound waves bounce off us in the macroscale world, but if we were very small we would! So there is actually a built in uncertainty when dealing with quantum objects, but we can say there’s a probability that they are in one place or another. So as a quantum creature, you can think of yourself as a little wave of probability, that collapses to a point when measured but then expands out again after. When I’m not measuring you, where are you really? Well I can’t say physically, and this is why you can have a little wave overlap with your neighbour without violating the principle that you can’t both be in the same place at the same time.

And imagine that you’re next to a wall. As a wave you may have a little overlap of probability with that wall. And if the wall is thin enough, as a quantum object there is actually some chance that you’ll pass through the wall entirely! This is called quantum tunnelling, and actually it’s happening all the time in the electronics inside your phone. Modern microelectronics work in part because we can use effects from the quantum world in our own, larger world!

It’s difficult to imagine a world where everything happens in discrete chunks, where I can see myself as a wave, where I don’t know where I am until someone else interacts with me. But this is the world at the quantum scale, and it’s not science fiction!

The Universe Is Made Of…

Since we have been digging pretty deep lately I thought a step back might be in order. One of my favorite inspirational series is the Symphony of Science videos, musical versions of popular science content like the Cosmos series with Carl Sagan. Many of the videos are beautiful and thought-provoking, and describe the amazing things you can see by looking at the world through the lens of science, but most pertinent for what we have been talking about is the one about the quantum world. Enjoy!

What is an atom?

Much of the interesting science in modern electronics stems from the properties of quantum-size objects, at very small scales. So the most sensible place to start is at the bottom, with atoms.

There are many different kinds of matter, but most of the matter on Earth that humans interact with is made from atoms. What makes atoms non-intuitive for many people is their size, which is so small that we are able to get through day-to-day life never having to think about the atomic nature of matter. An atom like hydrogen is so small that you could line up ten million of them in a millimeter. In the same way that the universe is made of trillions of stars, in differing arrangements made up of differing materials, our bodies are made of trillions upon trillions of atoms.

A helium atom. The inset shows a detail of the nucleus, which has two protons and two neutrons. The entire atom is about an angstrom in size, which is less than a billionth of a meter.

Atoms were originally proposed as indivisible units of matter, hence the name which comes from a Greek word meaning indivisible or unable to be cut. However, what we now call atoms do have smaller objects inside them. Atoms are comprised of a central ball of protons and neutrons, called a nucleus, surrounded by a cloud of electrons. The nucleus is very heavy compared to the electron cloud, because protons and neutrons are approximately 2,000 times heavier than electrons. This means that in a collection of atoms, there are many dense nuclei, and the disperse electron clouds around them. Much of what we perceive as solid matter is actually made up of empty space, because of the low density of electron clouds. Nothing on Earth as dense as a nucleus is big enough to see by eye.

Within an atom, there can be different numbers of protons, neutrons, and electrons. What name we give to an atom is depends on the number of protons in its nucleus. The number of protons and the number of neutrons affect the size of the atomic nucleus. So if we compare a nucleus with one proton and no neutrons, which is a kind of hydrogen, with a nucleus that has eight protons and eight neutrons, which is a kind of oxygen, we find that the oxygen nucleus is physically larger than the hydrogen nucleus.

The number of electrons in an atom has a large effect on how the atom interacts with other atoms and with its surroundings. The numbers of protons and electrons impact each other as well, which we’ll get into when we go deeper into the quantum nature of atoms. But the numbers of protons, neutrons, and electrons give us many types of atoms, also called atomic species, which can be used as building blocks for matter.

But, from here we can begin to talk about what makes materials different, which largely depends on atomic properties and interactions. Even though many people don’t think about atoms when they go out into the world, much of our lives does stem from happenings in the world of atoms.

The Weird Quantum World

One of the first and most effective tricks of teaching any subject is making analogies. A concept that initially doesn’t click may make more sense when compared to a common experience or narrative. In the sciences this can come up a lot, where the mechanical motion of balls can be compared to things we’ve seen in sports, or laws of heat transfer compared to experiences cooking food. Scientific inquiry is, among other things, an inquiry into the rules of the world around us, so it makes sense that while exploring those rules, we try to place them in the context of that world.

But as we examine the world at a smaller and smaller scale, looking at components much tinier than we have any normal experience thinking about, the rules begin to change. As you approach the scale at which the constituents of matter become indivisible, the behavior of these constituents is nothing like what we are used to at our scale, the macro scale, with bouncing balls and boiling water. This is the quantum world, so-called because many aspects of reality are quantized and discrete rather than continuously variable . And the trouble with learning about the quantum world is that there are very few analogies to the world we know, even though the quantum world is what underlies our own!

One example of weirdness in the quantum world is particle-wave duality. This terms stems from the history of research on light: from the 17^th century through the early 20^th, many of the best scientific minds were divided on whether light was a particle or a wave. Initially light was assumed to be an indivisible particle, observed to travel along straight lines. But the way that light can bend, or refract, around corners seemed more similar to the behavior of a wave. An experiment was devised to test which theory was true, with two narrow slits cut into a thin plate, in front of a screen. Classical particles would be expected to form an image of the two slits on the screen, whereas a wave traveling through the two slits would form a complicated interference pattern on the screen due to overlapping wavefronts. When light is sent through the double slit, the interference pattern is seen, implying that light is a wave. But, if you set up a detector to determine which slit each light particle is passing through, then the screen shows an image of the two slits. Thus light has both a particle and a wave nature, and in fact this is true for many other “particles” such as the components of atoms: protons, neutrons, and electrons. Each of these particles has wave properties as well.

But something about the double slit experiment may have struck you as even stranger than light being both a particle and a wave. It appears that whether we see evidence for the wave or the particle nature of light depends on the measurement we do: if we measure which slit the light passes through, we see particles, and if we do not, we see waves. It turns out that another example of strange quantum behavior is the importance of measurement.

Within quantum mechanics, the mathematical system devised to describe quantum behavior, it turns out that in addition to discrete quantum states, it is possible to have superpositions of states. So, in addition to having an atom aligned to the left or to the right, we can have a state which is “left plus right”, that is not just zero. There is no analogue for this idea in the macro world, and the whole strange setup leads to the question: If we measure the state “left plus right” for alignment, what do we get? Left or right? It turns out that we have an equal probability of measuring either one, but what’s even stranger is that before we perform the measurement, the system is not really in either state. It is in both, and neither. The measurement itself causes a fundamental physical property of the system to change, meaning that the traditional scientific idea of observing a physical system without affecting it must be discarded!

Both of these ideas, particle-wave duality and the importance of measurement, have a lot of tricky implications and can be explored in much more detail than I’ve given so far. And they take awhile to wrap your head around! For many people, their first reaction to these concepts is a creeping unease, an inability to place these in any “real world” context and a sense that something must be wrong. To me, that is precisely what is so fascinating about the quantum world. It’s completely unlike anything that we have practical experience with, and yet it has been verified by experiment after experiment that the quantum world is a reality that underlies everything we see, a bizarro-land hidden behind all the things with which we are familiar. What a place to explore!