Does the momentum of a photon change in a medium with varying speeds of light?

[bob012345]

Here’s a question I’ve always wondered. Is it possible to slow light within some gaseous medium and thus increase its momentum? Imagine creating a region around a ship where c=1 m/s and then using a beam where P=E.

 

[Vitro]

Here’s a question I’ve always wondered. Is it possible to slow light within some gaseous medium and thus increase its momentum? Imagine creating a region around a ship where c=1 m/s and then using a beam where P=E.

Try applying conservation of momentum to your question, if the light is increasing its momentum then something else would have to increase its momentum in the opposite direction to keep the total constant. What would that be and how?

 

[bob012345]

Try applying conservation of momentum to your question, if the light is increasing its momentum then something else would have to increase its momentum in the opposite direction to keep the total constant. What would that be and how?

I know, that would be both the ship and the medium the light is slowed in if light could actually be slowed. The gaseous medium would carry the momentum away that the ship gains as the light passes out of the medium and returns to normal. The question is if light can actually be slowed in a way that increases it's momentum greatly? I've read where light can be slowed to meters per second in certain vapors but don't know about the momentum of such light. I've heard that light actually does have a bigger kick inside glass but don't have a good reference.

 

[jartsa]

Here’s a question I’ve always wondered. Is it possible to slow light within some gaseous medium and thus increase its momentum? Imagine creating a region around a ship where c=1 m/s and then using a beam where P=E.

Imagine creating a region around a ship where c=0.00000001 m/s, or slower if needed, so that we will say that light becomes trapped in the region.

How do light traps behave? For example a mirror lined box with a door which is closed after some light has entered.

 

[bob012345]

Imagine creating a region around a ship where c=0.00000001 m/s, or slower if needed, so that we will say that light becomes trapped in the region.

How do light traps behave? For example a mirror lined box with a door which is closed after some light has entered.

I don't know about 'light traps'. Please enlighten me. Thanks.

 

[jartsa]

I don't know about 'light traps'. Please enlighten me. Thanks.

Two examples of "light traps":

Trap 1: Vertical light beam enters a box, then the light beam bounces inside the box horizontally. First the light had vertical momentum, then it has no vertical momentum, vertical momentum must be conserved, so the box must now have the vertical momentum that the light had.

Trap 2: An atom absorbs a photon, momentum of the photon becomes momentum of the atom.

Some mathematics:

Energy-momentum relation:
E²=p²c²+m²c⁴

So massless energy E has momentum: E/c

And energy that has some mass has momentum: Less than E/c

So E/c is the maximum momentum of energy E.

So massless constant energy can not gain more momentum by changing its propagation speed. It can lose momentum by gaining mass and slowing down its propagation speed.

For example: A system consisting of two parallel light beams collides with a lens, which collision causes the beams to become less parallel. After the collision the system has a rest mass that is moving at some speed lower than c, and the system has less momentum than originally, and the lens has absorbed some momentum.

 

[bob012345]

Two examples of "light traps":

Trap 1: Vertical light beam enters a box, then the light beam bounces inside the box horizontally. First the light had vertical momentum, then it has no vertical momentum, vertical momentum must be conserved, so the box must now have the vertical momentum that the light had.

Trap 2: An atom absorbs a photon, momentum of the photon becomes momentum of the atom.

Some mathematics:

Energy-momentum relation:
E²=p²c²+m²c⁴

So massless energy E has momentum: E/c

And energy that has some mass has momentum: Less than E/c

So E/c is the maximum momentum of energy E.

So massless constant energy can not gain more momentum by changing its propagation speed. It can lose momentum by gaining mass and slowing down its propagation speed.

For example: A system consisting of two parallel light beams collides with a lens, which collision causes the beams to become less parallel. After the collision the system has a rest mass that is moving at some speed lower than c, and the system has less momentum than originally, and the lens has absorbed some momentum.

Thanks. The question was what happens when c is smaller, like 1 m/s like in a BEC that envelops the ship. Experimental results are hard to come by and theoretical results are contradictory. There has been a over a century of controversy concerning the momentum of a photon in a medium. I just read a paper that claimed to prove the momentum is the same no matter what the speed of light in any medium. Any thoughts here?

P.S. Photon recycling allows one to use the momentum of a photon over and over as long as there is something close to bounce it back. It's been done in the lab with thousands of bounces, moving kg scale objects with typical lab lasers.