# Photons travel with speed c irrespective of frame. Explain?

Jan 2, 2018

Photons have zero mass so they travel at the speed of light when observed by any observer no matter how fast they are travelling.

#### Explanation:

Photons have zero mass. This means that they always travel at the speed of light. It also means that photons don't experience the passage of time.

Special relativity explains this by the equation which describes relativistic velocities when an object is emitted at velocity $u '$ from a frame traveling at velocity $v$.

$u = \frac{u ' + v}{1 + \frac{u ' v}{c} ^ 2}$

So consider a photon emitted at the speed of light $u ' = x$ from a spaceship traveling towards an observer at half the speed of light $v = \frac{c}{2}$.

Newton would add the velocities to have the photon arrive at $1.5 c$. The relativistic equation gives a different result.

$u = \frac{c + \frac{c}{2}}{1 + \frac{{c}^{2}}{2 {c}^{2}}} = c$

So, the photon arrives at the observer at the speed of light no matter how fast the device which emitted it was travelling!