Light and force

Question

We know that photons also have momentum though they do not have mass given by the equation :

$E=pc$

Then why can't we apply force to light? I mean we can apply fore and increase its momentum and thus its energy.

Also if light collides with something (which is I am not sure) than will it follow the law of conservation of momentum?

score 4 · Accepted Answer · answered Feb 13 '18 at 09:32

4

You can apply a force to light. Simply shine the light onto a mirror then move the mirror towards the incoming light:

The light that reflects off the mirror will be blue shifted to a shorter, higher energy wavelength, $\lambda_\text{out} \lt \lambda_\text{in}$, and you'll need to apply a force to the mirror to achieve this blue shift.

answered Feb 13 '18 at 09:32

John Rennie

355,118

Then does light follow the law of conservation of momentum? – Theoretical Feb 14 '18 at 04:46
@AsifIqubal: yes light obeys conservation of momentum. A photon has momentum $p = h/\lambda$. For more on this see If photons have no mass, how can they have momentum? – John Rennie Feb 14 '18 at 07:34
Suppose there's a mass in space. It is constantly being hit by photons as it is in the way of sunlight. Then wouldn't it move even a tiny bit to conserve the momentum? And follow the law of conservation of momentum. – Theoretical Feb 14 '18 at 08:06
@AsifIqubal Yes it would move in response to being hit by photons. The force due to the photons hitting the mass is called radiation pressure. – John Rennie Feb 14 '18 at 08:09
If the mirror is moved away from the light is energy removed from light? – Lambda Feb 14 '18 at 14:12
@Lambda yes, if the mirror is moved in the same direction as the light then the light will be red shifted. The energy lost is equal to the work done on the mirror. – John Rennie Feb 14 '18 at 14:23

score 0 · Answer 2 · answered Feb 13 '18 at 09:31

We can apply force to light: you can act on light with gravitation. Even though light does not have electric charge, it has some (small) sensitiveness to electromagnetic fields. This comes from loop diagrams in quantum electrodynamics. So you can act on light by EM fields.

"will it follow the law of conservation of momentum?" Of course.

Light does not have "rest mass". It has relativistic mass due to its speed. This mass has all properties of mass. Although sometimes physicists have philosophical arguments about nature of relativistic mass, by its properties the relativistic mass is a "well behaved true" mass. So if you want light has a mass: a stopped photon does not exist, an existing photon moves at with $c$ velocity and has (relativistic) mass.

Is this happens really, then why can't we see it in the nature? Suppose we have a mass in space, then it should move even a little bit due to photons' momentum and the law of conservation of momentum. Does it happen? — Theoretical, Feb 13 '18 at 15:12
Mass of an macroscopic object is much much larger then the (relativistic) mass of a photon. But yes, it happens, but the movement of a macroscopic body hit by a photon is extremely small. — F. Jatpil, Feb 14 '18 at 13:22

Light and force

2 Answers2