# Does photon lose its momentum?

1. Apr 4, 2013

### 2sin54

Hello. I know that light exerts pressure. My question is how can light exert some kind of a force? If it exerts a force, it means that there has to be a change in momentum but light clearly can't go slower and it doesn't change its wave length after the bounce. If it is able to move a solar sail, it means the light has to lose some energy to do the necessary work. What am I missing here?

2. Apr 4, 2013

### Staff: Mentor

If light bounces off an object, it reverses its direction and therefore its direction of momentum. This leads to a momentum transfer on the mirror.
It does change its wavelength in systems where the mirror is moving.
Solar sails can absorb a part of the photons, which gives momentum (and energy) as well.

3. Apr 4, 2013

### Darwin123

Momentum is a vector, not a scalar. Momentum has a direction in addition to a magnitude.

The magnitude of momentum is Planck's constant divided by wavelength. If the wavelength doesn't change, then the magnitude of momentum doesn't change. However, the direction of momentum can change.

In an elastic reflection, the magnitude of photon momentum does not change. However, the direction of the photons changes.

In this particular way, quantum mechanics is the same as Newtonian mechanics. A photon bouncing off a mirror is no different in terms of momentum than a rubber ball bouncing off a brick wall. The magnitude of momentum doesn't change, but the direction of momentum changes.

The case of the solar sail is different because the solar sail can move. The wavelength of the light does change after bouncing off the solar sail due to Doppler shift. In the inertial frame of the sun, the light bouncing off the moving sail decreases in frequency due to Doppler shift and increases in wavelength.

The reflection off of the solar sail is not elastic in the inertial frame of the sun. Because the wavelength of light increases, the magnitude of momentum of the light decreases. Because the frequency decreases, the energy of the light wave decreases.

The photon bouncing off of the solar sail is like a pool ball bouncing off of another pool ball. The magnitude of the first pool ball decreases because the second pool ball starts moving.

Last edited: Apr 4, 2013
4. Apr 4, 2013

### Staff: Mentor

Better: a ping-pong ball bouncing off a bowling ball.

5. Apr 4, 2013

### ZapperZ

Staff Emeritus
The fatal flaw in your reasoning here is to associate light's momentum with "speed". Nowhere in the definition of momentum for light was this ever defined that way. One may write light's momentum as

p = h/lambda

where lambda is the wavelength. So simply showing a change in wavelength of light (without changing its speed) is sufficient to show a change in momentum. An example of this is in Compton scattering.

Zz.

6. Apr 5, 2013

### 2sin54

Thank you all.