# Photon momentum conservation

I have been trying to research this and my understanding seems to be flawed.
From what I have gathered from light sails and other sources:

1) The frequency of reflected light is the same as the incident light.
2 ) The photon imparts a kick to the reflected surface, Transfers momentum.

This seems to paint a picture of a photon reflecting between two surfaces without losing momentum/frequency while imparting momentum at every reflection. Clearly I am missing something here.

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George Jones
Staff Emeritus
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What happens when a ball bounces elastically off a wall?

The frequency of reflected light is the same as the incident light.
Who says?

It's highly likely that there is very little change in frequency - given that the sail is much more massive than the photon, but if any momentum (and energy) is transferred, there will be a change in the photon frequency.

In the limit of an infinitely heavy sail, the photo will rebound with no momentum loss and the sail won't move.

jtbell
Mentor
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.

I have been trying to research this and my understanding seems to be flawed.
From what I have gathered from light sails and other sources:

1) The frequency of reflected light is the same as the incident light.
2 ) The photon imparts a kick to the reflected surface, Transfers momentum.

This seems to paint a picture of a photon reflecting between two surfaces without losing momentum/frequency while imparting momentum at every reflection. Clearly I am missing something here.
If you take energy conservation into account, the photon frequency would have to decrease with each reflection.

If the sail is moving, the frequency of the reflected photon is different from the frequency of the incident photon due to the Doppler effect.

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.
Fine ,,this is completely consistent with my original understanding of the conservation of momentum.

As to "who says" the frequency does not change my memory of sources is terrible but this is not an idea I came up with myself but read various places and questioned at the time, hence this thread.
SO thanks all, for the clarification.

Who says?

It's highly likely that there is very little change in frequency - given that the sail is much more massive than the photon, but if any momentum (and energy) is transferred, there will be a change in the photon frequency.

In the limit of an infinitely heavy sail, the photo will rebound with no momentum loss and the sail won't move.
Having thought about your responce some more I find the first part in agreement with my original understanding but don't understand why if the mass of the sail is approaching infinite there would be no change in momentum of the photon???
The finite temporal duration of the interchange is very small , so what difference would it make to the photon if its transfered momentum had any actuall effect on the motion of the sail or not???
Thanks

phyzguy
You're missing the point that, while the magnitude of the momentum is unchanged (in the limit of infinite sail mass), the sign of the momentum changes. The photon comes in with momentum p, and leaves with momentum -p, and so transfers momentum 2p to the sail.

You're missing the point that, while the magnitude of the momentum is unchanged (in the limit of infinite sail mass), the sign of the momentum changes. The photon comes in with momentum p, and leaves with momentum -p, and so transfers momentum 2p to the sail.
This is only true in the reference frame in which the sail is immobile, though.

You're missing the point that, while the magnitude of the momentum is unchanged (in the limit of infinite sail mass), the sign of the momentum changes. The photon comes in with momentum p, and leaves with momentum -p, and so transfers momentum 2p to the sail.
Ah, infinities - you don't want to mess with infinities - they always bite you.

If the sail has infinite mass, it has infinite inertia so it cannot be moved by any non-infinite force. therefore, it's velocity after the collision is zero and the momentum transferred to it is zero.

A completely pointless, meaningless argument of course.

However, your analysis suggest to me that if we were to take two (heavy) mirrors, fixed face to face, we could set a photon bouncing between them. At each bounce, the photon would transfer 2p momentum to the mirrors, which we could then use to power a star drive perhaps?

Errr... to anyone with little sense of humour out there - that's a joke.

Ah, infinities - you don't want to mess with infinities - they always bite you.

If the sail has infinite mass, it has infinite inertia so it cannot be moved by any non-infinite force. therefore, it's velocity after the collision is zero and the momentum transferred to it is zero.
What if the velocity of the sail before the collision was non-zero?

What if the velocity of the sail before the collision was non-zero?
You yankin' my chain?

You yankin' my chain?
Why would you think that? All inertial observers are equally right in explaining the same physical situation.

You're missing the point that, while the magnitude of the momentum is unchanged (in the limit of infinite sail mass), the sign of the momentum changes. The photon comes in with momentum p, and leaves with momentum -p, and so transfers momentum 2p to the sail.
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.

What is the change of velocity of a sail if the momentum imparted on it is 2p and its mass is infinite?

Ah, infinities - you don't want to mess with infinities - they always bite you.

If the sail has infinite mass, it has infinite inertia so it cannot be moved by any non-infinite force. therefore, it's velocity after the collision is zero and the momentum transferred to it is zero.

A completely pointless, meaningless argument of course.

However, your analysis suggest to me that if we were to take two (heavy) mirrors, fixed face to face, we could set a photon bouncing between them. At each bounce, the photon would transfer 2p momentum to the mirrors, which we could then use to power a star drive perhaps?

Errr... to anyone with little sense of humour out there - that's a joke.
Are you saying if a photon, or even a massive particle, collides with a mass too great to achieve any net motion from the collision that there would , therefore, be no propagated acceleration i.e. momentum transfer whatsoever??
Wouldn't any collision result in molecular displacement and pressure waves etc??
WHich part was the joke??? The apparent violation of conservation of momentum, implicit in the two mirror picture was my motivation for this post.

Are you saying if a photon, or even a massive particle, collides with a mass too great to achieve any net motion from the collision that there would , therefore, be no propagated acceleration i.e. momentum transfer whatsoever??
Wouldn't any collision result in molecular displacement and pressure waves etc??
WHich part was the joke??? The apparent violation of conservation of momentum, implicit in the two mirror picture was my motivation for this post.
There is no joke. But, mind you, you need to trap the photon between the mirrors from the outside, because if you generated it yourself, it would impart the oposite momentum to the system.

If the photon comes from the outside, however, then when it hits the left mirror it would bounce back, imparting an "infinitesimal" velocity to the system. Then, when it reaches the left mirror it would impart the opposite momentum making the system to stop. In this way, the system would move to the right with a periodic changes of "infinitesimal" velocity and rest.

Ah, infinities - you don't want to mess with infinities - they always bite you.

If the sail has infinite mass, it has infinite inertia so it cannot be moved by any non-infinite force. therefore, it's velocity after the collision is zero and the momentum transferred to it is zero.

A completely pointless, meaningless argument of course.
What is the momentum of object with infinite mass and zero speed ? It's:

$p=0\cdot \infty$

We can't even define momentum of such an object. So talking about conservation of momentum in this case is meaningless.

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But in case where the speed of infinite mass object is non zero (but finite), its momentum is infinite. So the conservation of momentum in this case is valid.
(i'm talking about a collision of object with infinite momentum with object with finite momentum).

Wouldn't any collision result in molecular displacement and pressure waves etc??
The conservation of momentum is valid only for CLOSED systems and if there was production of pressure waves (sound) etc. the system wouldn't be closed.

The conservation of momentum is always valid! If the system isn't isolated or closed, it simply means it exchanges momentum with the neighboring systems.

The conservation of momentum is always valid! If the system isn't isolated or closed, it simply means it exchanges momentum with the neighboring systems.
Yes of course, but we consider a system of only two objects that collides. In other case you need to consider the momentum of molecules of air and so on...

The conservation of momentum is valid only for CLOSED systems and if there was production of pressure waves (sound) etc. the system wouldn't be closed.
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
The system does not instantly move simply because momentum enters the system , true???

There is no joke. But, mind you, you need to trap the photon between the mirrors from the outside, because if you generated it yourself, it would impart the oposite momentum to the system.

If the photon comes from the outside, however, then when it hits the left mirror it would bounce back, imparting an "infinitesimal" velocity to the system. Then, when it reaches the left mirror it would impart the opposite momentum making the system to stop. In this way, the system would move to the right with a periodic changes of "infinitesimal" velocity and rest.
So in this picture does the photon decrease in frequency with every ocillation and eventually redshift out of visability??