Radiation Pressure and Conservation of Momentum

[jbriggs444]

That brought up a question about light slowing down in a medium. Since the energy doesn't change, does this mean the momentum doesn't either?

Momentum is conserved. So the momentum cannot change. But it can be shared with the medium so that it may not make sense to ask whether the momentum resides in the medium or in the light.

 

[ProfChuck]

I thought I had a grasp on this and now I'm not so sure. A photon's momentum is a function of its energy, but it is not proportional to the velocity, which is always c.
That brought up a question about light slowing down in a medium. Since the energy doesn't change, does this mean the momentum doesn't either?

Momentum exchange occurs when the photon is generated or absorbed The energy of the photon is converted into heat and kinetic energy when it strikes an absorbing or reflecting body. That is a simple explanation of why solar sails work.

 

[ProfChuck]

The discussion of photons and momentum exchange poses an interesting question. Index of refraction is n=c/v where c is the speed of light in a vacuum and v is the speed of light in a refractive medium. Photons slow when they enter a refractive medium and return to c when they leave it. Is there a momentum exchange? In other words, does the refractive medium experience a force? If so, how is momentum conserved?

 

[Nugatory]

Is there a momentum exchange? In other words, does the refractive medium experience a force? If so, how is momentum conserved?

If there is a net force on the medium (for example, a triangular prism in which the refracted light leaves at a different angle than the incident light) then the momentum it gains will be taken from the momentum of the electromagnetic radiation. The refracted light will be very slightly red-shifted, so will carry away less momentum than the incident light delivered, and the difference ends up with the medium. It's basically the same as a reflective solar sail, except that we're refracting the incident light instead of reflecting it.

Be aware that "photons slow when they enter a refractive medium and return to c when they leave it" is a rather dubious way of describing what's going on. Light is not a stream of photons flowing by the way that a river is a stream of water molecules flowing by.

 

[ProfChuck]

If there is a net force on the medium (for example, a triangular prism in which the refracted light leaves at a different angle than the incident light) then the momentum it gains will be taken from the momentum of the electromagnetic radiation. The refracted light will be very slightly red-shifted, so will carry away less momentum than the incident light delivered, and the difference ends up with the medium. It's basically the same as a reflective solar sail, except that we're refracting the incident light instead of reflecting it.

Be aware that "photons slow when they enter a refractive medium and return to c when they leave it" is a rather dubious way of describing what's going on. Light is not a stream of photons flowing by the way that a river is a stream of water molecules flowing by.

I admit it is rather clumsy to try to describe a quantum phenomena using classical physics concepts but none the less the issue of momentum exchange without absorption and consequent termination of the photon's existence remains. If there is a momentum transfer between light and a transparent media, such as an interstellar gas, there are significant astrophysical consequences that must be resolved without opening the door to the discredited notion of "tired light".

 

[sophiecentaur]

admit it is rather clumsy to try to describe a quantum phenomena using classical physics concepts

The force on a surface, due to an incident EM wave is dealt with with classical EM theory. My ancient copy of Panofski and Philips Elec and Mag deals with the simple case. It's always best to avoid photons whenever possible and certainly to avoid 'little bullets' in an argument.

 

[Nugatory]

I admit it is rather clumsy to try to describe a quantum phenomena using classical physics concepts but none the less the issue of momentum exchange without absorption and consequent termination of the photon's existence remains.

There is no such issue because a photon is not a small object that enters the medium, slows down, and then speeds back up when it's done passing through the medium.

 

[Samson4]

If there is a net force on the medium (for example, a triangular prism in which the refracted light leaves at a different angle than the incident light) then the momentum it gains will be taken from the momentum of the electromagnetic radiation. The refracted light will be very slightly red-shifted, so will carry away less momentum than the incident light delivered, and the difference ends up with the medium. It's basically the same as a reflective solar sail, except that we're refracting the incident light instead of reflecting it.

Be aware that "photons slow when they enter a refractive medium and return to c when they leave it" is a rather dubious way of describing what's going on. Light is not a stream of photons flowing by the way that a river is a stream of water molecules flowing by.

There is no such issue because a photon is not a small object that enters the medium, slows down, and then speeds back up when it's done passing through the medium.

I thought that was exactly what it does. I thought that was the whole reason why it bends and curves through mediums.

 

[Dale]

I thought that was exactly what it does. I thought that was the whole reason why it bends and curves through mediums.

All of that is classical behavior and doesn't require the idea of photons at all

 

[sophiecentaur]

the whole reason why it bends and curves through mediums.

I'm not aware of any evidence that is what happens. The only evidence about photons is where the EM wave interacts with matter and, as far as 'curving' it would perhaps be valid to think in terms of individual photon interaction with each infinitesimal portion of the medium but, really, why bother when the classical model works so well on a macroscopic basis?
You use the word "reason" but that isn't really appropriate in Science. The best one can say is that a certain model fits observations well or badly.
You seem to be trying to fit your knowledge of the system to something that's bigger than your knowledge extends. This doesn't usually go well, particularly when QM is concerned. Photons are essentially part of QM and you can't assume they 'behave' anything like our classical intuition would suggest. Perhaps that's unsatisfactory for you but it's something we all just have to deal with - unless you start from scratch and build a brand new model of Physics that's supported by evidence better than Physics as we know it.

 

[Nugatory]

I thought that was exactly what it does. I thought that was the whole reason why it bends and curves through mediums.

Light does that, but you were talking about photons in the earlier posts and they do not.

There's a good thread here - be sure to follow the links in the first two posts.

 

[Samson4]

I found quite a bit of gathered information on this particular subject under Abraham-Minkowski controversy.

One of the things I've learned from this thread is any fluctuations in momentum of light will be conserved by accelerations of the medium it propagates through.

https://physics.aps.org/story/v22/st20#videos
This link shows a Chinese experiment showing evidence that light may indeed gain momentum as it exits a fiber optic cable.

Here is what I don't understand. Shouldn't the air accelerate and not the fiber optic cable? Or perhaps the air is responsible for the bending of the fiber. In the article they say the pulsed beam passes into air so I am assuming the fiber was not in vacuum.