光子：光既是粒子又是波

Introduction and Warm-Up

Alright, so today's lesson is about photons which have this odd, yet awesome, application of being able to show how light has both the properties of a particle and wave. Before we start, a few questions to warm up our minds a little bit.

If you were thinking of the last option, you are right! Photon is a word that is derived from the root word "photo" in Latin which means light. However, we aren't here for a language lesson, let's talk about the star of our lesson!

Definition

Alright, so now that we have a sense of what we are talking about, let's dive into the lesson and talk about what is so special about photons!

Simple Explanation (a.k.a. not quantum-mechanics heavy)

As the title states, photons explain how light is both a particle...and a wave! How is this possible? Issac Newton explains throughout his lifetime how light has the properties of particles, and thus should be defined as such. This idea lasted throughout the 18th century until we find a man named Thomas Young (There were explanations and theories of light being a wave by people like Rene Descartes, Robert Hooke, and Christian Huygens. However, most people belived the idea of light being a particle).

Young brought forth his "double-slit experiment" which shows that if you shoot light (or an electron as well) through one screen with two slits, and a second screen with no slits. Then the second screen will show the interference pattern of that light. Incidentally, the intereference pattern for light is that of a wave! (For a more elaborate explanation, check out my lesson on the Double-Slit Experiment!) Eventually, by the work that followed Young's by August Fresnel, James Clark, James Maxwell, and Heinrich Hertz, the idea of light having wave-like properties was accepted. Thus light has a property called "wave-particle duality" (also called the dual nature of light).

Quantum Mechanics Explanation

Here is an even more developed explanation for those who know quantum mechanics. We define the mass of a photon as 0, as if any physical entity moves at the speed of light then its mass is non-existent and instead becomes energy. However, that is not where the physical property comes from (the physical property will be shown in a moment).

In an empty space, a photon moves at $c$ (the speed of light) while its energy and momentum are related through the equation $E = pc$, where p is the magnitude of the momentum vector p. This derives from the following relativistic relation, with $m = 0$

$E^{2}=p^{2} c^{2} + m^{2} c^{4}$ The energy and momentum of a photon depend only on its frequency ($\nu$) or inversely, its wavelength ($\lambda$):

$E=\hbar\omega=h\nu=\frac{hc}{\lambda} \boldsymbol{p}=\hbar\boldsymbol{k}$, where $k$ is the wave vector (where the wave number $k$ is defined by $k = |k| = 2\pi\lambda$, $\omega = 2\pi\nu$ is the angular frequency, and $\hbar = h/2\pi$ is the reduced Planck constant.)

Now is when the physical property comes in. Since p points in the direction of the photon's propagation, the magnitude of momentum can be defined through the equation

$p=\hbar k=\frac{h\nu}{c}=\frac{h}{\lambda}$.

Concluding Remarks

So now you may ask, what does this mean? Here is how we can "see" this (partially). If we shine a light to a specific point onto a wall, while it moves as a wave (its energy is also detected through its "wavelength") the moment it hits the wall, there is a specific spot that the light hits (as if you through a tiny ball to the wall and it leaves a mark that shows the specific point of impact).

Therefore, light has both particle-like and wave-like properties. Hopefully you understood and enjoyed the lesson!

Photons are packets of electromagnetic energy that have energy related to the frequency of the wave.