# How does light have momentum , even if they don't have mass ?

Nov 28, 2017

A photon has energy which also means that it has momentum.

#### Explanation:

Light can behave like a wave, it can also behave like a stream of particles called photons.

Einstein's theories of relativity explain properties such as mass, momentum and energy. The actual equations are complex and hard to understand. Fortunately relativity can be explained without hard mathematics.

First of all Einstein showed that mass and energy are equivalent with his famous equation.

$E = m {c}^{2}$

This means that mass and energy are interchangeable. When an electron meets its antiparticle the position they annihilate each other. This means that two particles with mass combine to for two photons which have no mass. The process can also happen in reverse.

Now, in any interaction both energy and momentum must be conserved. Let's examine the case of the electron and the positron meeting. Energy must be conserved, so the combined energy of the resulting photons must equal the combined mass energy of the electron and positron plus their combined kinetic energy. It also means that the combined momentum of the electron and positron must have been transferred to the resulting photons!

OK, so photons have momentum. So, how do we explain it? Well if a photon has a frequency $\nu$, then its energy $E$ is:

$E = h \nu$

Where $h$ is Planck's constant.

Momentum $p$ can be calculated from energy.

$p = \frac{E}{c} = \frac{h \nu}{c}$

Where $c$ is the speed of light.

So, momentum is normally associated with mass as Newton described. This is not the full story. Objects with mass have a rest mass. Relativity show that the faster an object travels the more massive it gets. This means that the object's kinetic energy gives it extra mass - relatavistic mass. The object's momentum includes the relatavistic mass!

So, massless particles, like the photon, have energy. Therefore they also have momentum!