# 19.25 Wave-particle duality

Before you read this, I suggest you read posts 19.23 and 19.24. In post 19.23 we saw that electromagnetic waves (post 19.9) could behave as particles, called photons, and in post 19.24 that particles, like electrons, could behave as waves. People often try to imagine what these things are “really” like and then the first sentence doesn’t seem to make sense. How can something be either like a particle or like a wave? In our macroscopic world, we might think of a particle as being a grain of sand and a wave as a wave on the sea. The first is an object with mass (post 16.13): the second is a form of motion that transmits energy (post 18.10).

The interdependence of wave and particle properties is called wave-particle duality.

The problem in making sense of wave-particle duality arises because we are forced to infer the behaviour of light, for example, from its properties. Although we can see light, we can’t see a photon or a light wave – so we have to determine the nature of light indirectly through experiments. The experiments tell us that light can behave either as a photon or as a wave.

All we do in science is to develop ideas to predict how things behave (post 16.2). And wave-particle duality is the simplest way to predict the behaviour of light and electrons. Newton’s first law of motion doesn’t tell us why objects move with a constant speed if nothing pushes or pulls them – it’s just a general statement resulting from observing how things move that enables us to predict things (post 16.2). Similarly, wave-particle duality is a statement about the behaviour of electromagnetic radiation and particles like electrons.

The picture at the beginning of this post provides an analogy, although not a very good one. If you look at the picture it may look like a black candlestick or two white faces. What you see may change with time. So, is the picture a candlestick or two faces? It’s really just an array of black and white pixels that we can see in two different ways. An electron is really just an electron but we can see it in two different ways too.

Why don’t we encounter the wave-particle duality in everyday life? In post 19.24, we saw that a particle with momentum p is associated with a wavelength of

λ = h/p

where h = 6.626 × 10-34 m2.kg.s-1, is Planck’s constant (post 19.19). Since p = mv, where m is the mass of an object and v is its speed (post 16.13), we would expect a fast object to have a long wavelength. So let’s calculate the wavelength of a bullet, mass 7.0 × 10-3 kg travelling at a speed of 1.2 × 103 m.s-1, which means that p = 8.4 kg.m.s-1. Then λ = 7.9 × 10-35 m. This is much too small to be observable. To get an idea of how small this number is, it’s about 100 000 times smaller than the mass of a grain of sand divided by the mass of the Earth.

Wave-particle duality if important for understanding photons and particles like electrons, protons and neutrons – but we don’t need to consider it when thinking about everyday objects.

Related posts