I've been reading Leonard Susskind's book "The Black Hole War" and trying to wrap my head around this mind-bending concept he presents called the Holographic Principle.

Roughly, the idea is built from the properties of entropy and temperature surrounding black hole physics. There is a curious result that a black hole's entropy is proportional to the area of its event horizon rather than the enclosed volume. Susskind goes on to explain that this is effectively as though all the possible information about the inside of the black hole were written on it's surface in Planck area sized quanta. So this is a little surprising, but you expect that with black holes. What's really weird is that this ends up letting you describe any volume of space with a 2D encoding of the surface. Is the 3D universe just a projection of this 2D encoded surface? Weird!

Ok, not so weird... I mean, I'm a programmer, I'm very comfortable with transformations between 2D and 3D. Most of the ones we use in computer graphics are called "information losing" transformations, because once we've rendered a scene, you can't "walk around" it from the back or sides. However there are "information preserving" transforms that tell you how to encode exactly the same amount of information in a lower dimension, so this isn't too strange for me to grasp.

Another paradox?

All this has physicists wondering if the underlying nature of reality is really a 2D surface off at the edge of the universe. While I could see that transform springing out of the math involved (not that I've done any of it, mind you), I have a problem with literally believing this is the structure of things.

What is hard for me to grasp is that a literal interpretation would seem to imply that information can propagate faster than light in some cases, which is another paradox! Think of the following thought experiment: say I'm playing billiards with Susskind and I sink 5 balls in one shot. Apart from having to be an amazing billiard player (I'm not), all these balls would have physical interactions. According to Susskind, these interactions are really happening at the bounding surface of the universe in a sophisticated 2D "holographic" encoding and we just might think it was happening in 3D here. Fine.

But wait, how do you know that the interactions are all happening locally on that distant surface? If one billiard ball is represented by bits on one part of the sphere and another billiard ball is represented by bits on the opposite side of the sphere... how do they interact in a short amount of time? You might be talking about interaction effects on the surface that might be vast numbers of parsecs apart.

The interactions in our notion of space are also very fast... fractions of a sec. How can interactions happen so quickly if the underlying "real" medium was so extended? Does the underlying information travel faster than light when it interacts? (i.e. "Spooky" action at a distance?)

This is potential paradox. The only ways out seem to be 1) saying that the speed of light doesn't apply to propagation (interactions) in the underlying 2D surface, or 2) all information is encoded such that it's spread is somehow constrained locally with respect to the surface.

This tends to make me think that the Holographic Principle is a mathematical relationship more than representing any underlying nature of reality. But then again I'm basing that off of naive assumptions of how optical holograms work and simple 2D and 3D projections -- perhaps there is nothing so simple about the nature of the projections Susskind is talking about?

What do physicists think of this? Is it a real problem?

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