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!

 

[sardar]

I can provide some insight into how light can have energy. First, it's important to understand that light is not a solid object, but rather a form of energy known as electromagnetic radiation. This means that it is made up of waves of electric and magnetic fields that are constantly moving and interacting with each other.

Now, to answer your question, light can have energy because of its wave-like nature. The energy of a wave is determined by its frequency, or the number of times it cycles per second. In the case of light, the higher the frequency, the more energy it carries. This is why higher frequency light, such as ultraviolet or gamma rays, can be more dangerous than lower frequency light like radio waves.

Additionally, light can also have energy through its momentum. While photons do not have mass, they do have momentum due to their movement and the fact that they carry energy. This momentum can be transferred to other objects upon collision, which is why solar sails are able to use the momentum of photons to propel spacecraft.

Overall, the energy of light is a result of its wave-like nature and its ability to interact with other objects. I hope this helps to answer your question and satisfy your curiosity. Keep asking great questions!