# Photon momentum conservation

You mean strictly valid in closed systems but whether or not the system allows photon dissapation of heat,
momentum is still propagated through the system through phonon transmission i.e. sound waves

Even if the energy is not conserved the momentum can be conserved. But, if there are air then the system of two colliding objects is not closed because the momentum is transfered to the air molecules (air resistance, Newtons third law). If the system is isolated and the collision is inelastic, the energy is not conserved (heat production etc.) but the momentum is conserved.

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Dale
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For any finite reflector mass (and who really cares about infinite masses) in the center of momentum frame the photon energy is the same before and after reflection. In any frame where the center of momentum is going towards the photon the photon is blueshifted and in any frame where the center of momentum is going away from the photon the photon is redshifted on reflection. The amount of redshift and blueshift decreases with increasing reflector mass. In all frames momentum and energy are conserved.

phyzguy
You lost me here. Wrt a photon p is simply frequency so a minus sign is simply a vector directional indicator as a negative frequency/energy makes no sense that I can understand.
As far as the 2p transfered to the sail what is the meaning of this??? Are you saying that there would be twice the initial momentum of the photon propagating through the structure of the sail???
If this is the case then perhaps my understanding of conservation is lacking.

Yes, if the mass of the sail is large compared to the photon, a momentum of 2p gets transferred to the sail. As George Jones pointed out in post #2, this is no different than an elastic rubber ball collision. Consider a basketball that hits the Earth with momentum p (pointing downward). After rebounding upward, it now has a momentum -p. Since momentum is conserved, a momentum of 2p has been transferred to the Earth. Your solar sail is basically the same.

On your first question, of course the energy and frequency are always positive.

For any finite reflector mass (and who really cares about infinite masses) in the center of momentum frame the photon energy is the same before and after reflection. In any frame where the center of momentum is going towards the photon the photon is blueshifted and in any frame where the center of momentum is going away from the photon the photon is redshifted on reflection. The amount of redshift and blueshift decreases with increasing reflector mass. In all frames momentum and energy are conserved.

Hi DaleSpam Could you explain the dependence of frequency shift on reflector mass???

It seems like, for visable light the time of the interaction would be vanishingly small compared to sound speed propagation in the reflector so how would the photon "know" how much mass was in the reflector???
Thanks

Going the other way, if the photon scatters off a very light object, say a single free electron, the loss in photon energy (and the corresponding change in wavelength) is easy to detect. We call it Compton scattering or the Compton effect.

Hi jt thanks for the link. I read it but found it unclear as to whether it dealt with free electrons or simply outer shells. Does carbon have free electrons???
Also regarding the angle of scattering. I can see how the x-ray divergence could be measured but not the electron vector.
Thanks again I will do more searching.