Andrew Strominger

Any area of space.

However, we've made sense of the holographic principle for black holes.

We've made sense of the holographic principle for something which could be called anti-de Sitter space, which could be thought of as a giant, as a black hole turned into a whole universe.

And we don't really understand how to talk about the holographic principle for either flat space, which we appear to live in, or asymptotically deciduous space, which the astronomers tell us we actually live in as the universe continues to expand.

So it's one of the huge problems in physics is to

you know, apply or even formulate the holographic principle for more realistic, well, black holes are realistic, we see them, but yeah, in more general context, to give a more general statement of the holographic principle.

Okay, so for thousands of years, you know, until the last half of the 20th, well, sorry, until the 20th century, we thought space-time was flat.

Well, like the surface of this table is flat.

Let me just give an intuitive explanation.

Surface of the table is flat, but the surface of a basketball is curved.

So the universe itself is,

could be flat, like the surface of a table, or it could be curved like a basketball, which actually has a positive curvature.

And then there's another kind of curvature called the negative curvature.

And curvature can be even weirder because that kind of curvature I've just described is the curvature of space, but Einstein taught us that we really live in a space-time continuum, so we can have curvature in a way that mixes up space and time.

And that's kind of hard to visualize.

So it's hard to... You have to step a couple.

But even if you have flat space and it's expanding in time, you know, we could imagine we're sitting here, this room, good approximation, it's flat, but imagine we suddenly start getting further and further apart.

Then space is flat.

but it's expanding, which means that space-time is curved.

The three simplest space-times are flat space-time, which we call Minkowski space-time, and negatively curved space-time, anti-de Sitter space, and positively curved space-time, de Sitter space.