# I Does light contain kinetic energy?

1. Feb 9, 2017

### Ingrid Eldevj

Does light contain kinetic energy as it moves, or does it require mass.

2. Feb 9, 2017

### Staff: Mentor

It has kinetic energy, equal to its total energy because it has no mass.

3. Feb 9, 2017

### Leesa Johnson

Yes, light has kinetic energy and the photon is a massless particle so the light has no mass.

4. Feb 9, 2017

### hilbert2

This is interesting.. If I make a Fourier series or integral to represent an electromagnetic wave traveling in vacuum, the individual plane wave components act similarly to harmonic oscillators, don't they? Then the individual modes should have Hamiltonian functions that consist of terms that are equivalent to the kinetic and potential energies in $H = \frac{p^2}{2m}+\frac{1}{2}kx^2$... Does the total amount of "kinetic energy", as defined by this equivalence, have some actual name and physical significance?

5. Feb 9, 2017

### Staff: Mentor

The concepts are not completely unrelated, but I'm not sure if we can call that "similarly".

The amount of kinetic energy of a beam of light is just its energy. It doesn't need an additional special name because "energy" is a good name already.

6. Feb 9, 2017

7. Feb 9, 2017

### DrStupid

It has kinetic energy, equal to its total energy if it has no mass. Light can have mass and that's not limited to exotic objects like a geon. Almost all light you see in everyday life (e.g. sunlight) has mass. Even single photons can have mass (e.g. a single photon bessel beam).

8. Feb 9, 2017

### Drakkith

Staff Emeritus
Mind elaborating on this?

9. Feb 9, 2017

### DrStupid

I'm afraid my English is not good enough for this phrase.

10. Feb 9, 2017

### Drakkith

Staff Emeritus
Would you mind elaborating about your previous post? Would you explain it in more detail?

11. Feb 9, 2017

### DrStupid

In case of the geon it is quite easy to understand (even though it is was the most complicate example). It consists of light only but has enough mass to contain itself by its own gravity. The mass of normal light is not as easy to explain. Let's try it with the very simple case of two plane light waves in vacuum, superimposing each other with the angle $\alpha$. That means for the momentums

$\frac{{p_1 \cdot p_2 }}{{\left| {p_1 } \right| \cdot \left| {p_2 } \right|}} = \cos \left( \alpha \right)$

If every wave has the energy E/2 then we also have

$\left| {p_1 } \right| = \left| {p_2 } \right| = \frac{E}{{2 \cdot c}}$

That results in the total momentum

$p^2 = \left( {p_1 + p_2 } \right)^2 = \left[ {1 + \cos \left( \alpha \right)} \right] \cdot \frac{{E^2 }}{{2 \cdot c^2 }}$

and therefore in the mass

$m = \sqrt {\frac{{E^2 }}{{c^4 }} - \frac{{p^2 }}{{c^2 }}} = \frac{E}{{c^2 }} \cdot \sin \left( {\frac{\alpha }{2}} \right)$

of the resulting light wave which travels with the speed

$\left| v \right| = \frac{{\left| p \right| \cdot c^2 }}{E} = c \cdot \cos \left( {\frac{\alpha }{2}} \right)$

along the bisecting line between the original waves. Of course normal light and Bessel beams are much more complex but the principle is the same. Plane parallel light waves (e.g. lasers) are exceptional cases in everyday life.