I'm having some trouble understanding this sentence:
" [...] our 3-D ‘reality’ (plus time) is contained in a 2-D surface on its boundaries."
What, exactly, do they mean with 'on its boundries'?
" [...] our 3-D ‘reality’ (plus time) is contained in a 2-D surface on its boundaries."
What, exactly, do they mean with 'on its boundries'?
You can think of the rules of physics as requiring 4 parameters to specify things like position, momentum, etc -- (x,y,z,t). Imagine that you have a category of states in that space, and the physical laws are functions that take states to other states in that same category.
Now imagine you have some functor which takes those states and translates them to a new space that only requires only (x,y,t) to specify them, and translates the functions so that they now take those states to other states in that 2 spatial dimension category. And there's a one-to-one correspondence, so you can move back and forth between the two categories. So if you have states A and B in 3d and A' and B' in 2d, You can go from A to A' to B' and back to B and it's the same as going from A to B.
It turns out that the physical laws in the 3d category have gravity, and the ones in the 2d category might not. But the laws still correspond one-to-one.
The reason this is useful is that figuring out quantum gravity is really hard, and it might be easier to figure out the functor that translates 3d physics into 2d physics that lacks gravity, perform the calculations there, and then translate the result back to 3d physics.
The holographic principle means that if you take a sphere somewhere, the amount of entropy you can push there grows with r^2, and not with r^3 like you'd expect.
Am i correct ?
The information stored is proportional to the surface, not volume.
But also, the holographic principle applies to more than black holes. At any volume, the maximum information you can put there is proportional to r^2. That applies to all the volumes inside the volume you just measured... what means that a volume can not be completely full (a weird case of apparent non-locality).
An hologram is a better analogue to it than information being stored on the surface because, outside of black holes it apparently isn't all on the surface. (I guess for the black hole information loss problem, information being in the surface or in a hologram don't make much difference.)
I'm working on an automobile analogy but its not easy.
Shine lasers on a 2-D surface, and interference patterns create a 3-D image in mid-air. You see a 3-D object, but all information is actually stored in 2-D.
This is the same idea.