Momentum of light moving through a medium

What happens to the momentum of photon when its moving through a medium with a refractive index > 1 ???

I have read that this has been heavily disputed before in the scientific community, and I am not sure if a consensus has been reached.

 

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Such as in metamaterials?

http://en.wikipedia.org/wiki/Negative_index_metamaterials

 

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Nowhere on your entire link is momentum mentioned :huh:

I challenge someone to come up with a scenario in which momentum is conserved for all cases when light is moving through a substance with refractive index > 1 .

Its weird because you can have different optical path lengths ..

 

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I don’t know. The momentum is mentioned in both of these, but I don't feel like reading them, sorry...:yawn:

http://dspace.mit.edu/handle/1721.1/40500

http://en.wikipedia.org/wiki/Cherenkov_radiation

 

Eh, its only 200 pages - ill let you know what i think when I'm done. . .



:bawl:

 

I like this part-

"others warn against the use of momentum conservation theorems all together [41]" p33
http://dspace.mit.edu/handle/1721.1/40500

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DRZion, I'm asking this because I don't have enough knowledge to have an opinion on the matter, but what's the problem? My first thought was that photons have no mass so this is a non-issue. Then I thought about solar sails and concluded that the reduction in intensity of the light passing through the medium must be imparting a net momentum effect on the medium. Either way an obvious paradox did not jump out at me.

Wait, on a second read of the OP, you ask about an individual photon. Is that even a valid question? The quantum description of light passing through a refractive medium is that photons are absorbed and emitted many times by the medium's atoms; are you considering the emitted photon as "the same one" as the absorbed one? I still don't see the problem, maybe you can point it out for me...

 

That was my first thought as well. P=mv, if m is zero, P is zero.

 

Thats right, solar sails are a good example of radiation pressure. Each photon has very very low momentum, constituted of only its energy of e=mc^2.

It doesn't necessarily have to be a singular photon, but this is an easier way of quantifying it for me.. you could also consider a beam of light with energy e, it wouldn't change the momentum problem.

Here it is-

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Its a cube with perfectly reflective mirrors as its sides. The right side of the cube has a refractive index of 3 while the left side is vacuum and has a refractive index of 1. The ns indicates how many nano seconds for it to take light to travel these distances. It will be travelling three times as long in the up direction as in the down direction and an equal amount of time left and right. Worth mentioning is that whenever a photon is reflected it imparts a momentum on the mirror to conserve the momentum of the system. At each reflection the mirror cube will gain some momentum to account for the change in the direction of the beam.

The problem is - the light beam travels three times as long in the up direction as the down direction, meaning net momentum is left in the system if an equal magnitude of momentum is imparted at each reflection. But, in a theory where momentum is imparted at the time of crossing the boundary you will run into causality problems where a signal has to be sent faster than c in vacuum.

 

DRZion, if I read your objection correctly you are predicting a net movement 'south' of the system, even with no initial momentum, due to travel time differential for the photon on the 'north-south' traversals. I think the issue is addressed if you think of this in terms of the quantum explanation of the refractive slow-down...that is, the photon never actually slows down at all, but rather is absorbed and emitted repeatedly by atoms in the refractive medium. The apparent reduction in velocity of light through the medium is due to the delay between absorption and emission, and it is during these times that the momentum would be properly counter-balanced. If you were to only "count" the actual travel time of the photon moving north and south you would find that it is equal.

Did I interpret your objection correctly, and do you agree this resolves it?

 

Yes, it does! During the time the photons are absorbed, the medium will carry their momentum. This momentum balances out with the opposite momentum of the entire system. Thus, while the photon is absorbed there will be no net movement of the entire system. Only after emission will the 'massive' portion of the system be moving in one direction, while the electromagnetic portion will be moving in the opposite direction. If the photons simply slowed down while passing through this medium there would in fact be problems with conservation of momentum, but if you look at the quantum underpinnings of the refractive index it all works out neatly.

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My guess is that the p is constant. The strict relationship is probably to frequency, which is constant. Just my S.W.A.G.

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James, there is a problem with this if you give it some thought. Give the cube zero initial momentum, and let the photon be emitted from within. There should be no net momentum change, but the time of travel differential on the right side of the cube for the photon presents problems. If you read post #10 the problem is resolved by ignoring the wave description of the photon.

Actually, as I write this...it occurs to me that possibly the wave description is still valid because the longer time of travel on the right side may be compensated for by the fact that the photon hitting the mirrors on that side has a lower momentum itself.:scratchin:

 

Can you clarify the beam entry point into the system? Here at: ^ [C](135 degrees) through a hole?

Or B >>(at 45 degrees) joining lower pass direction of i=1 (toward the i=1/i=3 transition)?

 

The beam is generated at any point along the path. The LASER is on the path of the line ... also, pretend that there is no beam divergence.

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So, when the pulse is generated the LASER and cube experience a recoil in the opposite direction.

Does wavelength in fact increase, or is this some kind of statistical/conceptual change?

When you're underwater, does the color of an outside light source change in proportion to the index of refraction of water?

The causality problem is something I ran into trying to explain momentum changing at the boundary of the low and high refractive indexes... if momentum conservation holds and momentum is permanently transferred to the medium as the beam travels through the medium, then the beam/medium will have to be able to 'know' the future to keep momentum conserved.

But, looking at the refractive index as a collection of absorption/emission events this problem disappears since the photons have a constant momentum before and during the passage through the medium.

You will run into problems very quickly assuming this. This is actually the basis for some of my favorite thought experiments. It has to do with variables and constants.

Lets say the the momentum of light bouncing off of the mirror inside the medium is in fact reduced. This means that it will be x*p (where x is <1 and is dictated by the refractive index and p is the photon's initial momentum), a constant.

This means that, in order for momentum to be conserved in this system, the medium has to carry p-(x*p) momentum, always. IE it is also a constant. The problem is that the medium prior the the mirror can be any thickness. It could be hundreds of meters, but it could be only a few wavelengths. This means that p-(x*p) should not be a constant because light will travel a variable amount of time through the medium (and it is the discrepancy in travel times that is the basis for the scenario).

I'm not sure if this is clear at all, but thats how it makes sense to me. :shrug:



Going back the the quantum explanation, it is very intriguing how momentum is exchanged between the photons and the medium during emission and absorption. If you do the calculations you will find that the accelerations during such an event should be enormous!

 

What is the problem? There is a wealth of mainstream explanations, see here

Where did you read that? On some crackpot internet site?

 

This doesn't say anything about the momentum of light travelling through various media.

I think it was the wiki - it was a debate between two prominent physicists in the early 20th century, lorentz was perhaps one of them .. ? I can't remember.

 

Sure it does but you need to read between the lines. This is connected to the explanation that JamesR just gave you, i.e. \(p=h\nu\).

Well, IF it was Lorentz the debate is 100 years old, was long settled.

 

Yes, DRZion, it's an intriguing thought experiment. There are complexities that you're not considering though.

If p of the photon is reduced to (x*p), it is only during the time that it is traveling through the medium. Be mindful PART of the impulse (specifically, that which reduces p --> (x*p) of the photon) is applied at the transition between media. This would apply a torque to the system, and actually change the angle of the mirror (which we will ignore for now but I believe would destroy the experiment). Another thing you must consider is that when the wave exits the higher-refractive medium the system will again experience a counter-torque to account for increase from (x*p) --> p of the photon. It's likely that I'm mangling the hell out of the formal description of this system and for this I apologize to any true Physicists present.

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For simplification I'm trying to reformulate things in my head in terms of a two parallel mirrors with varying percentages of the space separating them of differing refractive media...