Question

why photons are massless??

Answer 1

Photon is massless hence it can travel with the speed of light. The energy of a photon is given by E = pc

Answer 2

Here is your answer:

I will give you a mathematical answer and not theoretical one.

Okay I will call:

Energy as E, mass as m and momentum as p.

Most importantly speed of light as c.

The relationship between energy and momentum in Einstein's equations are:-

$E^2=m^2c^4+p^2c^2$

$\implies m^2c^4=E^2-p^2c^2$

$\implies m^2=\frac{E^2}{c^4}-\frac{p^2}{c^2}$

When the object is at rest its momentum is zero.

So put p=0 in the equation to get:-

$\implies m^2=\frac{E^2}{c^4}$

$\implies m=\frac{E}{c^2}$

So we get mass as the energy (when it is at rest) divided by speed of light.

Now for a photon:

It can never be at rest.

So its rest energy is zero.

Hence E=0.

Putting E=0 in the equation yields:-

$m=\frac{0}{c^2}$

$\implies m=0$

We hence proved that mass of photon is zero.

Hope it helps you.