Why exactly does light move at varying speeds in different media?

Sounds pretty hand-wavey. Can you put it in particle terms?

You're wrong, light is absorbed and emitted again. Unless you have some new theory that surpasses QED in which case you should publish immediately.

light particle goes in
light particle bounces around in a matrix of crystalline atoms and as a result it takes more time for it to leave the crystal on the other side
and its trajectory is altered by a certain amount
it can also become polarized
it can also become trapped in the material forever and become heat, (probably)

Nice
Why though do different photon energies result in varying angles?

To fully appreciate the physics, you must understand the math. I cannot explain it to you in any simpler form, for the phenomena do not exist as such. Any deviation or analogy from what is actually happening will be ultimately unsatisfactory.

the light beam got lensed
and it just so happens that mathematics is unreasonably effective at describing how much it gets lensed by, in terms of angles
angles aren't real though
that's a complex number joke

But say I want rather an explanation than a description, what does the math have to offer?

Something that would make all that work obsolete will probably be very welcome, you think?

You want a "why" answer, that is the problem.
youtu.be/36GT2zI8lVA

It will only be welcomed by brainlets.

I think this video rather misleadingly confuses our current ignorance of a satisfactory explanation with the absence of one,

...

Because the media is liberal and liberals are slow

no, that's a myth
the real explanation is waay more complicated:

youtube.com/watch?v=CiHN0ZWE5bk

the best mathematical model available to describe how light works is one where light enters a medium and loses energy by losing velocity. Because light moves at a constant speed, its trajectory changes by an amount that we can calculate, based on other calculations that we made about various media that light can travel through.

All the math offers is a ruler by which to measure a change that is happening. There might not be an underlying 'why' and if there is one, it's happening on a scale so small and so fast that all we'd ever be able to do is calculate it, unless you think you can find a way to build a really really fast camera that is also a microscope

there are so many misconceptions here you'll probably manage to make someone confused. well played!

i think you're the one that's confused

do you think math is a thing that exists?

Hecht, page 67 and onward.

Hang on, would it be remiss of me to think that if we can't even solve the three body problem then we can't positively say that it isn't just the photon bouncing around in a vibrating mess of some insane number of electrons?

that's what's happening, though
what do you think stuff is made of?

I thought everything was just probability densities and non-physical at the deebest levels of consideration, as contrasted to the rather classical view

If that was happening, then why, after all that random bouncing, does a laser beam passing through glass refract but not spread? It would be an awful coincidence if the chaotic bouncing passed every single photon through in the same direction.

>we can't even solve the three body problem
We did

>can't solve three body problem

We can solve it to any level of practical usefulness, we just can't express it's solution in (previously) well known terms. But that may be because we haven't come up with a clever enough definition yet which makes the solution expressible. Before anyone discovered exponential functions you could argue differential equations were not possible to solve. But in reality we just didn't have the language established to express the solution in any practical way!

Three body problem is completely solved, it's just chaotic.

the three body problem has too many factors to be solved

there are no general solutions for a^n+b^n=c^n for n greater than 2

>It would be an awful coincidence if the chaotic bouncing passed every single photon through in the same direction.
Could just be simple conservation of momentum

You forgot to mention a,b,c,n all need to be integer. That is example of an equation that does not have any solutions. The three body problem must have a solution. If it doesn't, then it basically means we need to improve the language of expressing it.

That's a difference between a physical problem and a mathematical. If it is a mathematical problem we first put up the definitions and start investigating "what if these things were true". In physics it's the other way around. We get observations and then we try and find a flavour of mathematics ( a set up of numbers and rules ) would make it make sense

By solving maxwell's equations, you can find that the speed of propagation of an EM wave (light) is [math] c^2=\frac{1}{\epsilon * \mu}[/math]. We should note [math]\epsilon=(1 + \chi) \epsilon_0[/math], where [math]\chi[/math] describes how well an electric field will polarize the material. For vacuum, there is nothing to polarize, but for any other medium, there are atoms that can shift their electrons orbits, so [math]\epsilon[/math] will increase, which leads to a lower speed of propagation.

Hopefully this helps!

For the same reason it even reaches our eyeballs. The light needs to land on things, and that includes the slightly opaqueness of the glass.

So how can one see how much of the slow down is due to polarization of the media and which is due to the photons being absorbed and re-emitted or are those two the same process?

That doesn't actually explain what is happening on a fundamental level. It doesn't explain why the permittivity of the materiel is different to that of the vacuum.
The real explanation is that the photon field couples to the phonon field - a phonon is essentially the quantum of vibration in the same way a photon is the quantum of the EM field - so when the photon enters the medium you don't have a pure light wave any more, but a superposition of photon and phonon coupled together. This new type of wave, a mixture of photon and phonon, is called a polariton and is massive. Its mass means it moves at a lower speed, and the mass depends on the material which is why different things have different refractive indices.
In this description there's no absorption and emission, which explains why you don't have very particular wavelengths being slowed down a lot, while nearby wavelengths carry on unaffected.
The fact that the polariton has a mass answers OP's question - different wavelengths of light move at different speeds because the photon has effectively become massive, and for massive particles more energy implies higher speed.

There is more to it than that, like how polaritons can also be a mix of a photon and an exciton, but the point is that the photon field changes to a massive field by coupling to some other (quantum) field. Most properties of materials come from bulk effects, and here we see the photon isn't absorbed by any particular atom, instead interacting with the whole lot of them at all at once.

/x/ here

So how does this relate to Ronald Mallet's work on time travel?

What research?

Apparently he's realised that slowing light down won't actually help him - he needed light to have more of an effect on spacetime and thought that lowering the speed of light would make that easier, but that is untrue. The curvature of spacetime depends on the speed of light in the vacuum, not the the refractive index. Otherwise gravity would grow 40% stronger when you're underwater...
So, to answer your question, nothing.

You can't solve it analytically. But you can solve it numerically.

So where is the numerical simulation of a double slit down to the subatomic level?