Understanding the particle-wave duality of electromagnetic radiation (light) is fundamental to understanding quantum theory and other phenomena as well as the nature of light. One of the biggest scientific developments in the previous century was the discovery that very small objects did not obey the same rules as everyday objects.

In plain terms, electromagnetic waves are simply known as light, though the term light is sometimes used to specify visible light (that which can be detected by the eye), and other times is used more generally to refer to all forms of electromagnetic radiation.

To fully understand electromagnetic waves, it is important to understand the notion of a field and the relationship between electricity and magnetism. This will be explained in more detail in the next section, but in essence, electromagnetic waves (light waves) consist of an electric field wave oscillating in a plane perpendicular (at right angles) to a magnetic field wave.

If electromagnetic radiation acts as a wave, then any particular electromagnetic wave will have a frequency and wavelength associated with it. The frequency is the number of oscillations per second, measured in hertz (Hz) where 1 Hz = 1/s. The wavelength is the distance between wave crests. The product of the frequency and wavelength gives the wave speed, which for light in a vacuum is approximately 3×10⁸ m/s.

Unlike most waves (such as sound waves, for example), electromagnetic waves do not require a medium through which to propagate, and hence can traverse the vacuum of empty space, which they do at the speed of light – the fastest speed in the universe!

A field can be thought of as an invisible array of vectors, one at each point in space indicating the relative magnitude and direction of a force an object would feel if placed at that point. For example, a gravitational field near the surface of the earth would consist of a vector at each point in space pointing directly toward the center of the earth. At the same altitude, all of these vectors would have the same magnitude.

If a mass were to be placed at a given point, then the gravitational force it feels would depend on its mass and the value of the field there. Electric fields and magnetic fields work the same way, except they apply forces dependent on an object’s charge and magnetic moment respectively instead of its mass.

The electric field results directly from the existence of charges, just as the gravitational field results directly from mass. The source of magnetism, however, is from moving charge (or equivalently, changing electric fields).

In the 1860s, physicist James Clerk Maxwell developed a set of four equations that completely described the relationship between electricity and magnetism. These equations basically showed how electric fields are generated by charges, how no fundamental magnetic monopoles exist, how changing magnetic fields can generate an electric field, and how current or changing electric fields can generate magnetic fields.

Shortly after the derivation of these equations, a solution was found describing a self-propagating electromagnetic wave. This wave was predicted to move at the speed of light, and indeed turned out to actually be light!

Electromagnetic waves can come in many different wavelengths and frequencies, so long as the product of the wavelength and frequency of a given wave equals ​c​, the speed of light. The forms of electromagnetic radiation include (from longer wavelengths/low energy to shorter wavelengths/high energy):

• Radio waves (0.187 m - 600 m)
• Microwaves (1 mm - 187 mm)
• Infrared waves (750 nm - 1 mm)
• Visible light (400 nm - 750 nm; these wavelengths are detectable by the human eye and often subdivided into a visible spectrum)
• Ultraviolet light (10 nm - 400 nm)
• X-rays (10^-12 m - 10 nm)
• Gamma rays (<10^-12 m)

Photons are the name for quantized light particles or electromagnetic radiation. Albert Einstein introduced the notion of light quanta (photons) in an early 20th century paper.

Photons are massless, and they do not obey number conservation laws (meaning they can be created and destroyed). They do, however, obey energy conservation.

In fact, photons are considered to be in a class of particles that are force carriers. The photon is the mediator of the electromagnetic force and acts as a packet of energy that can be transferred from one place to another.

You are probably thinking that it’s rather strange to suddenly be speaking of electromagnetic waves as particles, since waves and particles seem like two fundamentally different constructs. Indeed, it’s just this sort of thing that makes the physics of the very small so strange. In the next few sections the notions of quantization and particle-wave duality are discussed in more detail.

Electromagnetic waves result from oscillations in electric and magnetic fields. If a charge moves back and forth along a wire, it creates a changing electric field, which in turn creates a changing magnetic field, which then self-propagates.

Atoms and molecules, which contain moving charge in the form of electron clouds, are able to interact with electromagnetic radiation in interesting ways. In an atom, the electrons are only allowed to exist in very specific quantized energy states.

If an electron wants to be in a lower energy state, it can do so by emitting a discrete packet of electromagnetic radiation to carry off the energy. Conversely, in order to jump into another energy state, that same electron must absorb a very specific discrete packet of energy as well.

The energy associated with an electromagnetic wave depends on the wave’s frequency. As such, atoms can absorb and emit only very specific frequencies of electromagnetic radiation consistent with their associated quantized energy levels. These energy packets are called ​photons​.

​Quantization​ refers to something being restricted to discrete values verses a continuous spectrum. When atoms absorb or emit a single photon, they do so at only very specific quantized energy values described by quantum mechanics. This “single photon” can really be thought of as a discrete wave “packet.”

An amount of energy can only be emitted in multiples of an elementary unit (Planck's constant ​h​). The equation that relates the energy ​E​ of a photon to its frequency is:

Where ​ν​ (the Greek letter nu) is the photon’s frequency and Planck’s constant ​h​ = 6.62607015 × 10^-34 Js.

You will hear people use the words ​photon​ and ​electromagnetic radiation​ interchangeably, even though it seems like they are different things. When speaking of photons, people are typically talking about the particle properties of this phenomenon, whereas when they are talking about electromagnetic waves or radiation, they are speaking to the wavelike properties.

Photons or electromagnetic radiation exhibit what is called particle-wave duality. In certain situations and in certain experiments, photons exhibit particle-like behavior. One example of this is in the photoelectric effect, where a light beam hitting a surface causes the release of electrons. The specifics of this effect can only be understood if light is treated as discrete packets that the electrons must absorb in order to be emitted.

In other situations and experiments, they act more like waves. A prime example of this is the interference patterns observed in single- or multiple-slit experiments. In these experiments, light travels through narrow, closely spaced slits, which act like multiple in-phase light sources, and as a result, it produces an interference pattern consistent with what you would see in a wave.

Even stranger, photons are not the only thing that exhibit this duality. Indeed, all fundamental particles, even electrons and protons, seem to behave in this way. The larger the particle, the shorter its wavelength, and the less this duality will appear. This is why you don’t notice anything like this in everyday life.