The wave-particle duality is often loosely stated: “an electron is both a particle and a wave”. But what does that really mean? The following is an explanation of what a particle physicist means when they refer to a subatomic particle.

Particles

The best way to approach this is to follow the history of the concept of a particle. The idea of a “fundamental building block” most likely arose first around the 4th or 5th century BC. The philosophy that everything is made of discrete building blocks, known as atomism, came in contrast to the prevailing assumption that matter is continuous. You could chop a piece of string in half, then chop those two halves to get quarters, then eighths, and you could keep chopping indefinitely until you had an infinite number of string segments. The atomists believed that at some point, you would reach some kind of dead end on this venture, there would be a smallest possible unit of string.

Fast forward 15 hundred years to the 19th century. It’s my article so I can totally just do that. The 19th century was when the debate between atomists and non-atomists was finally settled. Chemists worked out that matter must be made of indivisible units, suitably called atoms. Not so long after that, it turned out atoms weren’t indivisible at all, they were totes divisible. They’re made up of smaller particles – electrons, protons and neutrons.

At this point, people imagined the electrons, protons and neutrons as little billiard balls. The balls could attract or repulse each other via forces like the electric force.

Waves

The electric force between the billiard balls could be described by a field. A field exists at every point in space, at each point it has a certain strength. The strength of the field at point x tells you how much a charged particle placed at point x would feel the electric force. The electric field is strong close to an electric charge (call it charge A). So if you put another charge (charge B) close to it, it will feel the electric force, leading it to being attracted or repulsed.

Figure 1: The electric field around a charged particle. The field is strongest in the dark areas, and weakest in the light areas.

If you were to move charge A, the electric field would also change. But it wouldn’t be a simultaneous change everywhere. Since no information can move faster than the speed of light, it takes time for the strength of the electric field far away to ‘update’ according to the motion of the charge. If you moved the charge then quickly moved it back to where it was, the field around it would have to change, then change back in quick succession. This change would move out from the charge, like a ripple on water, at the speed of light. Congratulations, you’ve just made an electromagnetic wave.

Figure 2: Ripple in electric field due to wobble of electric charge. Try out this applet to get more of a feel.

The opposite of this can also occur, a pulse moving through the electric field can hit an electron and cause it to wobble. This is the physical underpinning of radio transmission. A charge (the transmitter) is shaken to create a wave. The wave travels along and nudges another charge (the receiver). That nudge can then be translated into a message.

In the 19th century, two things made up the universe. Billiard-ball like particles (e.g. electrons), and forces they feel, described by fields (e.g. the electric field), in which waves could propagate. They were two totally separate things, that slotted together nicely to make a satisfying view of nature. Everyone was happy with this description of the universe, so no more discoveries were required. The end.

Waves that look like Particles

Then in 1905, Einstein ruined it all by explaining the photoelectric effect. It’s usually explained in a way that distracts from the central point it uncovers, getting all tied up in discussions about electron shells and the work function of materials. The main point behind it is this: remember those ripples you can send through an electric field by shaking a charge? There is a smallest possible ripple you can make.

If you tried to shake the charge half as vigorously as you did before, you would make a ripple half the size. Then half your efforts again, and you have a ripple a quarter of the original size. You would naively expect that you can keep doing this indefinitely, making smaller and smaller ripples, right? No way Jose. Einstein found that there is a lower limit to the size of a wave you can send through the electric field. Before, ripples in a field were considered to be like a continuous substance, but now it seems that all of the various wobbles and shapes that you get in the electric field are ultimately built up of indivisible packets of wobbliness. Thus, the photon was born.

The experimental setup included what was essentially a device that detected the light (a.k.a. ripples in the electric field) in a clever way. It turned out that this detector was being hit, not by a continuous stream of light, but by individual units of it. One way of looking at this could be that the detector was being bombarded by an array of little billiard balls called photons that collectively created the impression of light.

Particles that look like Waves

Around the same time this mindfuck was happening to the physics community, a problem was also found with seeing the electron as a billiard ball. The electron double slit experiment showed that a beam of electrons will behave like waves as they travel, even though when they reach the detector they are measured as individual particles.

Figure 3: Left – the double slit experiment if electrons travelled like particles. Right – if electrons travelled like waves. The dark patches on the detector represent where most of the electrons are hitting.

The experiment consisted of firing a bunch of electrons at a big detector, capable of recording exactly where an electron has hit it. Between the source and the detector was a wall with two little holes in it. If the electrons were particles, the detector would be hit with electrons around two regions just across from the holes. If you carry out this experiment however, you’ll see something different. The distribution of electrons will cover the whole detector, and build up an interference pattern, exactly what you’d expect from two sources of ripples interfering with each other. Throw two stones into a pond at the same time, and look at what happens at the edges of the pond when the two sets of ripples meet, this is an interference pattern.

So both the electron and the photon actually have basically the same properties. They both travel around like waves, but appear as individual blobs when they are detected. This lead to the reformulation of our description of the universe: electrons, along with all other types of particle, are just wobbles moving through various fields. There is a field not just for every force, but also every species of particle.

A ‘particle detector’ in some experiment is really only reacting to the changes in a field. When a particle seems to have been detected, it is due to the smallest possible wobble in the field hitting the detector.

We can describe nature consistently by moving the emphasis away from both the particle and the wave, and just refer to fields themselves. The standard model of particle physics, which is thought to be our best formulation of physics at subatomic scales to date, is basically just a list of different fields and how they interact with each other. Fields are the more fundamental way of describing nature, and one can consider a particle/wave as a phenomenon that emerges from the behaviour of the underlying field.

By changing the language we use about the constituents of nature, we get away from the paradox of particle vs wave. That’s not to say that describing the electron as a particle or a wave is useless, in many situations it’s the most efficient way of formulating a problem. But, if you want to get down to what the universe really is deep down, you’ve got to talk about the fields.

Particle or wave, it doesn’t exist anyway



I’m not saying the field is more fundamental than ‘particle’ or ‘wave’ just because it’s more elegant. There is a problem deep at the heart of the concept of indivisible blobs of anything.

This problem can be explained by appealing to general relativity, another one of Einstein’s achievements. A bit of a change of gear, but you’ll be fine. One could write a gazillion blog posts explaining what general relativity is, but for our purposes all you need to hear is this: two observers can disagree on distances and shapes.

Imagine two astronauts, Alice and Bob. Say Alice was in her spaceship, and she turned on the boosters in order to leave a vapor trail. She leaves a trail that, to her, seems perfectly straight. In the mean time, Bob is watching her from some different point in space, and since his frame of reference is different to hers, geometry works differently for him. To Bob, the vapor trail isn’t straight, it’s all curvy. Which one of them is right? Both of them.

Figure 4: The world according to Bob (left) and the world according to Alice (right). Bob has drawn three (straight according to him) axes so he can quantify positions in space. Alice has done the same. These are their frames of reference.

In general relativity, frames of reference can vary such that the shapes become subjective. This leads to a straight line in one reference frame being a curvy line in the other. The example I used here is a bit extreme, the effects of general relativity are usually a lot more subtle, but the picture is nevertheless possible according to our current laws of physics.

Ok general relativity lesson over. Now say Alice detected some particles, maybe in a cosmic ray or something like that. Say she detects an electron. Each of them are manifestations of ripples in some underlying field. But Bob detects nothing. His view of geometry is different to Alice’s, so what goes on in the underlying field is different. Alice seeing that ripple was dependent on the geometry she perceives. The geometry Bob perceives is such that it cancels out the excitation, see the figure below.

Figure 5: Top – the electron field according to Alice, there is a wave going through the field so she sees an electron. Bottom – the electron field according to Bob, the field is constant so he sees no electron.

In general, the way we define what a wave/particle is is inseparably related to one’s frame of reference. Two observers can disagree about whether a particle is present or not. One says that they have differing particle concepts, dictated by the geometry that they are experiencing.

It’s also possible, if someone’s reference frame was to change over time, that one single observer can change between different particle concepts. It can seem that particles are bursting into existence or disappearing, for no reason. This is the source of the famous phenomenon of Hawking radiation, a gas of particles that appear to radiate from black holes. These particles aren’t strictly being created by the black hole. Rather the natural way to count particles is different before and after the black hole forms, since one’s frame of reference would be warped by the black hole’s presence.

So as you can see, it isn’t really enough to explain physics with particles or waves at the end of the day. You can’t describe the state of the universe by listing all the particles/waves that it contains. If you only consider the field, you can have an objective view of the universe.

Outlook

That brings us up to what we think the universe is made out of today. Manifestations of wobbles in underlying fields, that don’t really exist if you think about it too much. There is every chance that, in the future, the field picture also turns out to be not the whole story. Maybe fields are a manifestation of something more fundamental, like strings, foam, discrete space-time points, or little rubber ducks.

more stuff to read:

The dawn of Atomism

The Photoelectric Effect

The Electron Two-Slit Experiment

General Relativity

Hawking Radiation