How Can Light Carry Energy Without Mass?

[backtoearth]

Hi everyone(:
I was reading the other day and I read that the photons don't have the mass. If a light is a flow of photons, how can a light carry an energy or momentum?
I have learned that if the matter was to carry the energy or have momentum, it needs a mass. How can this happen for light?

I was very curious about it and it would be nice to know! Thanks,

 

[G01]

The problem is that the standard formula for kinetic energy from Newtonian mechanics,$E=\frac{1}{2}mv^2$does not apply in relativistic mechanics, which governs photons.

In special relativity, the kinetic energy of a particle is given by,

$$E=\sqrt{p^2c^2+m^2c^4}$$

For a photon, m=0, therefore

$$E=pc$$

And from quantum mechanics a photon has a momentum proportional to the inverse of its wavelength(the deBroglie formula): $p=\frac{h}{\lambda}$

Thus, a photon has energy:

$$E=\frac{hc}{\lambda}=hf$$

 

[backtoearth]

Thanks! But what do you mean by light as being a part of relativistic mechanics?

 

[HallsofIvy]

Anything that travels a a relatively high fraction of the speed of light is relativistic. And light travels at the speed of light!