Comment by dreamcompiler
1 day ago
In a sense it's the inverse of what you describe. A 3D creature could easily see everything happening in a 2D space because all the information describing the 2D space fits comfortably in a mere slice of the 3D space. It's trivial because 3D space is "bigger" than 2D space.
What AdS/CFT implies is the opposite: That all the information needed to describe a 3D space can fit in a 2D space, like a hologram. This is astounding and extremely counterintuitive.
The hitch is that our universe is (probably) not AdS; it's dS. And the astounding math doesn't work for the de Sitter space we live in.
Ahh. Okay...So, this is kind of like the 2D entities trying to make sense of their 3D counterparts, and the 3D counterparts getting the sensation of someone watching them, but its the 2D beings discussing the existence of the 3D entities instead of vice versa? I know this is quite a basic comparison but it helps me grasp it a bit better. Also, is there any particular reason that it's 3D and 2D? That is, is there any other dimension number that could accommodate the correspondence? Or does the math say it's only 3D to 2D and vice versa where this works? And do we know why or why not if so? Thanks
That's the idea, but it's like the 2D creatures know everything about the 3D creatures, which the 3D creatures find quite shocking.
The actual dimensionality is 4D to 3D once you add in time. But the math basically says an nD hyperbolic conformal manifold (AdS) can be completely described by its nD-1 boundary (CFT).* So I think it works in any number of dimensions.
*Oversimplified and probably wrong, but probably close enough for this discussion.
> That all the information needed to describe a 3D space can fit in a 2D space, like a hologram.
I'm not totally certain about this but I think you skipped over something important.
It's not that 3D space can be described by 2D space, it's that _our_ "3D" space appears to fit in 2D space because every time the universe puts too much information in the 3D space we get a black hole and a black hole is a 2D surface in 3D space.
It's not quite that: The math only works in Anti de Sitter space, which is not the universe we live in.
The tiny black holes that are suggested by non renormalizability are one of the mysteries that make AdS/CFT an attractive direction in which to explore our own universe, partially because Susskind has already shown that black holes in our universe can be described by their surfaces.