system
Given the following post, respond as if you're commenting on Reddit:
human
ELI5: What is it that gives a material the ability to be polished?

I've always wondered what it is that allows you to polish metals to a mirror finish, but not wood or plastic, for example? I assume its something to do with light scattering and reflection from the internal structures of the material?
gpt
There are two things that go into why a material can have a mirror finish.  First, is whether light that hits it reflects straight back or gets scattered in many different directions.  Smooth surfaces scatter less of the reflected light, and will be shinier than rough surfaces.

Any material can be polished.*  Polishing is just making the surface smoother.  Generally, the smoother a surface, the shinier it looks.  

So the real question is, why are smooth metal surfaces extremely shiny and other materials not so shiny?

The second part of the story is that light is reflected any time it encounters a boundary between two materials with different indexes of refraction.  The bigger the difference in the index of refraction, the more light gets reflected.

For visible light, metals have very large indices of refraction.  The huge difference in the index of refraction between the metal and air can result easily in over 90% of light being reflected.

Explaining why metals have such high indices of refraction for light is a little more complicated.   Metals have lots of free electrons that can move around inside them (that's why they conduct electricity).   All these electrons interact strongly with the electric field of light.

Things like wood and plastic do not have many free electrons so they don't interact nearly as strongly with light.  For example, when travels through air and hits a glass surface, only about 4% of the light will be reflected.

* It turns out that it's a lot easier to polish a metal than it is to polish wood.