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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

by neals 10y ago

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'?

deleted 10y ago
[deleted]
philipov 10y ago
This is a statement of the holographic principle, which is that a projection on the surface (boundary) of a volume completely encodes the contents of that volume. You then no longer need the volume at all, you can perform all operations on the surface projection instead.
greydius 10y ago
It's an awkward sentence. The 2-dimensional surface is the boundary of the 3-dimensional surface. I think what they're saying is that they believe the 3-dimensional universe is a 'reverse-projection' from the 2-dimensional surface.
PaulAJ 10y ago
I'm familiar with the idea of coordinate transforms and projections, so I get the idea that you could project our 3D universe onto a 2D surface, and I kind of see how a hologram encodes 3D information, but I don't see how that is a useful idea. Or are there only certain kinds of 4D information that can be encoded in the 2D surface, so our 4D model of space and time gets reduced to a theory of only 2 dimensions? Are there conceivable arrangements of a 4D universe that can't be represented in this way?
- marcosdumay 10y ago
  Laymen "easy" language makes everything harder to understand. 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.
  - bsaul 10y ago
    Thanks a lot. I've just watched susskind talk on the universe as a hologram ( https://youtu.be/2DIl3Hfh9tY https://youtu.be/2DIl3Hfh9tY ), and it didn't occured to me until i read what you just said simply that the holographic principle meant you could actually push less stuff / bits in a black hole by growing it, than you first thought if you compared it to a volume growing. So that meant information was stored on its surface (r^2), and not inside it (r^3). Am i correct ?
    - marcosdumay 10y ago
      Keep in mind that IANAP. 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.)
- VLM 10y ago
  Having only read the abstract (so I might have it totally wrong) we have the 2D holographic picture from the cosmic microwave background already and we're trying to fit that data to various theories. The cool kid theory used to revolve around dark matter in some way I'm a little unclear on. If you run a bunch of simulations on imaginary 4D universes playing games with the usual cosmological parameters, sometimes with some parameter settings processing the results as a holographic projection gives better match to the pix we already have, than stuff done that relies on dark matter and things. Quantum field theory mixes into this which is interesting because that usually applies to little things not the shape of the universe size stuff. I'm working on an automobile analogy but its not easy.
btilly 10y ago
Have you ever seen a hologram? 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.
empath75 10y ago
Think about it in terms of (dramatically oversimplified) category theory: 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.

by neals 10y ago

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'?

deleted 10y ago

[deleted]

philipov 10y ago

This is a statement of the holographic principle, which is that a projection on the surface (boundary) of a volume completely encodes the contents of that volume. You then no longer need the volume at all, you can perform all operations on the surface projection instead.

greydius 10y ago

It's an awkward sentence. The 2-dimensional surface is the boundary of the 3-dimensional surface. I think what they're saying is that they believe the 3-dimensional universe is a 'reverse-projection' from the 2-dimensional surface.

PaulAJ 10y ago

I'm familiar with the idea of coordinate transforms and projections, so I get the idea that you could project our 3D universe onto a 2D surface, and I kind of see how a hologram encodes 3D information, but I don't see how that is a useful idea. Or are there only certain kinds of 4D information that can be encoded in the 2D surface, so our 4D model of space and time gets reduced to a theory of only 2 dimensions? Are there conceivable arrangements of a 4D universe that can't be represented in this way?

marcosdumay 10y ago
Laymen "easy" language makes everything harder to understand. 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.
- bsaul 10y ago
  Thanks a lot. I've just watched susskind talk on the universe as a hologram ( https://youtu.be/2DIl3Hfh9tY https://youtu.be/2DIl3Hfh9tY ), and it didn't occured to me until i read what you just said simply that the holographic principle meant you could actually push less stuff / bits in a black hole by growing it, than you first thought if you compared it to a volume growing. So that meant information was stored on its surface (r^2), and not inside it (r^3). Am i correct ?
  - marcosdumay 10y ago
    Keep in mind that IANAP. 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.)
VLM 10y ago
Having only read the abstract (so I might have it totally wrong) we have the 2D holographic picture from the cosmic microwave background already and we're trying to fit that data to various theories. The cool kid theory used to revolve around dark matter in some way I'm a little unclear on. If you run a bunch of simulations on imaginary 4D universes playing games with the usual cosmological parameters, sometimes with some parameter settings processing the results as a holographic projection gives better match to the pix we already have, than stuff done that relies on dark matter and things. Quantum field theory mixes into this which is interesting because that usually applies to little things not the shape of the universe size stuff. I'm working on an automobile analogy but its not easy.

btilly 10y ago

Have you ever seen a hologram? 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.

empath75 10y ago

Think about it in terms of (dramatically oversimplified) category theory: 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.