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Momentum of light in glass. By Ben. I think that most people underestimate how many scientific mysteries remain, even on questions that sound basic. My favorite candidate for the most basic thing that is still unknown is the momentum carried by light, when it is in a medium, for example, a flash of light in glass or water.
If a block of glass has a refractive index of, here's a formula, then the light inside that block travels, here's a formula, times slower than the light would in vacuum. But what is the momentum of that light wave in the glass relative to the momentum it would have in vacuum? In 1908 Abraham proposed that the light's momentum would be reduced by a factor of. Here's a formula.
This makes sense on the surface. Here's a formula. Times slower means. Here's a formula. Times less momentum. This gives a single photon a momentum of. Here's a formula. For omega the angular frequency. Here's a formula. The speed of light and. Here's a formula. The reduced Planck constant.
In 1909 Minkowski proposed that actually, the momentum of the same energy worth of light in a material is increased by a factor of n relative to vacuum. This gives a single photon momentum of, here's a formula, which was right. It's still not settled. Not really.
A lot of papers will tell you that the Labraham-Minkowski controversy is now resolved, but they won't all agree on how it has been resolved. At least three mutually incompatible resolutions have been published. New papers claiming a resolution, or else knocking holes in the old resolutions, are still coming out.
In the rest of this post I'm going to sketch out why this is a complicated problem and how some of the proposed solutions work. An analogy. The runner. Why is the momentum of light in glass complicated? Consider a runner running, as is usual, on land, with some speed. Here's a formula. On their route the runner encounters a region of knee-high water.
while traveling through the water our runner travels at a reduced speed of. Here's a formula. Now, we ask, what is the momentum of the runner while they are moving through the water? There's an image here. Description.
Stick figure demonstrating leg movements on blue surface.
If we take the mass of everything inside the runner's skin and multiply it by their velocity then clearly this has fallen by a factor of, here's a formula, relative to their momentum outside the water. However, as the runner wades they will kick a parcel of water along in front of their knees.
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