I compare the 3D environment to the real world environment.

Every one know that refraction is the bending ( direction shift ) of light as it passes through a transparent, or semi transparent object. But why does the light bend? The light bends due to a change of speed that the light is traveling at.
The direction it bends depends on the optical density of the objects it is passing from then into. When light passes into a denser object it slows down and it direction changes towards the normal. When it passes into a less denser object it speeds up and bends away from the normal.
( The normal is an imaginary line, passing diagonal through the object from the entry/exit point of the light,) Refraction only occurs at the boundary of the object.

Example: When light passes from the air into a crystal ball it slows down and is bent towards the normal as it enters the crystal, then it travels in a strait line through the crystal ball, then it bends away from the normal as it exits the crystal ball and speeds back up as it enters back into the air.

That's why there is no Refraction Channel for volume materials. Because refraction is not a volume property.

The Bryce environment is set at 100 percent refraction, that's why the refraction channels 100 is called air. Any setting above 100 should bend light towards the normal, any setting below should bend light away from the normal. ( but it does not )

"Sure, the air between two non-transparent objects can have refractive properties.(but I'm not sure if you would see any difference in Bryce if you did this "

Yes the air has refractive properties, but if light is not traveling between an optical dense boundary, refraction will not occur.

" But if you stuck a sphere in there and made the refraction 1.33 and the refraction of the cube 1.33 the sphere should become invisible."

No, you just would not see any refraction because there is no optical density boundary change.

"So will taking the cube and booleaning it out hollow with another cube. Which I know it is hollow to begin with really, but the effect changes with the booleaning..."

Because you are actually having the light pass through the object, it goes in than out the thin wall of the boolean. So you are really inside an environment that is Bryce's 100 percent air. Where if you are inside a cube that is not boolean, then you are in an environment which is set to whatever the cube refraction setting is.

" An increase in the refractive setting, now the cube is casting a shadow."

Yes because you are making the optical density denser. So the cube lets less light in. and cast a shadow with the light that does not penetrate into the cube. The denser the optical properties become the less light is let in, thus the spherical shape gets small as less light travels through the cube and exits out the rear.

This effect does not work the opposite way because there can not be more light let in than the surrounding environment lets in. In other words if the air is 100 percent refraction and the cube is 0, more light can not be let into the cube, than is present in the 100 percent surrounding environment. ( But if it could wouldn't that be a great way to fake GI )

Where I see the Bryce ray tracing algorithm flawed, for refraction is. The light should shift direction depending on the optical density properties. But it does not. Sure when you set refraction lower or high than air, you will see an opposite shift change on the surface of the object. But the light passing through the object does not shift in direction. In tjohns demonstration here the shadow on the sphere stays located at the same place no matter what the refraction is set at.. Where in reality the light should be shifting direction more as the refraction gets denser. I bet if the refraction was set to 0 for the cube the shadow would still be in the same location even though it should shift because the light in the real world situation is being bent in the opposite direction.

Stephen Ray