Space seems pretty fundamental.

To build a universe,  surely you need something to build it on or in.

Many, maybe most physicists now think that the fabric of space emerges from something deeper.

And perhaps the most existentially disturbing such proposal is that our 3-D universe is just the inward projection of an infinitely distant boundary.

A hologram, or sorts.

Let’s see how that can actually work, and what the holographic principle really says about the “realness” of this universe.

You could argue that the job of physics is to drill down and find the most fundamental elements of reality.

The most basic building blocks—the “ontological primitives”--from which everything else emerges.

A little while ago we asked whether the fabric of space deserved that status.

Isaac Newton certainly thought so, but many pretty smart people have wondered if space might actually be an emergent phenomenon.

We’ve even seen some examples of this in past episodes—from the early ideas of Leibnitz to modern loop quantum gravity.

We’ve also seen how at least one dimension of space can emerge as the inward  projection from its infinitely  distant boundary.

This is the holographic principle—which we spent many episodes building towards back in the day—culminating in a pretty intense coverage of this wild idea.

Well, today we’re travelling back to the holographic boundary to try to understand better how the fabric of space can emerge this way.

This will set us up to do a couple of things in upcoming episodes: we’ll be able to understand how gravity can emerge from entropic forces on a holographic boundary, and how the fabric of space may be knit together by the quantum entanglement of entities that themselves don’t exist in our familiar spacetime.

Feel free to watch the old holographic principle stuff later if you haven’t.

I’m going to summarize the core stuff for your convenience.

So the whole argument started in a surprising place—with Steven Hawking and Jacob Bekenstein thinking about the thermodynamics of black holes.

Normally we think of thermodynamics as the study of the statistical behavior of many particles.

It’s the study of emergent properties like temperature and pressure of, say, a room full of air molecules.

These are properties that the individual particles do not have.

Another key thermodynamic property is entropy.

We can think of this as a measure of the amount of hidden information in a system—information about the stuff that makes up the system that isn’t reflected in the observable, macroscopic properties.

This ro-om full of air molecules has a high entropy because all of the particles’ locations and speeds are hidden behind just a few thermodynamic properties that I can sense like the temperature and pressure.

We wouldn’t necessarily expect an individual black hole to have thermodynamic properties.

After all, black holes are  practically particle-like.

They are the result of the ultimate gravitational collapse of matter and are surrounded b y an event horizon which prevents anything exiting the black hole from the inside.

That includes any information about what exactly collapsed to form it.

Jacob Bekenstein realized that black holes viewed from the exterior possess three properties—mass, charge, and spin—almost like an elementary particle.

But it’s that exact fact that gets us to  black hole thermodynamics,  and to emergent space.

The difference between a black hole and an elementary particle is that the former is made by the extreme clumping together of the latter.

That means we can define the entropy of a black hole—and the number is huge because black holes hide almost all of the information of the stuff that fell in.

Bekenstein and Hawking figured out the entropy of black holes.

They found that there’s around one bit of  hidden information per 4  square Planck length units on the surface.

This simple formula was really surprising—and that surprise led physicists down the path to the holographic principle.

See it’s actually  quite weird that the entropy  should be proportional to the surface area.

Intuitively we might expect the amount of information that can be hidden in any region of space is proportional to its volume—like, one bit per tiny block in that volume, rather than a bit per tiny square on its surface.

In fact, black holes represent the maximum information density of any volume of space—this is the Bekenstein bound.

And that applies to the whole universe—the information about every particle in its 3-D volume can, in principle, be encoded on its 2-D surface.

But it’s one thing to say that all the information describing a universe fits on its surface, but the holographic principle goes way further.

It suggests that we can think of our universe as really playing out on that surface.

More  precisely, that surface is  its own lower-dimensional spacetime with its own particles and fields and a different set of laws of physics.

But encoded in the patterns that play out on that lower-dimensional spacetime is an entire universe one dimension higher.

It’s as though the volume of the universe—what we call the “bulk”--emerges from the dynamics on its surface—the boundary.

The journey from black hole entropy to the Holographic Principle was led by Gerard t’Hooft and Leonard Susskind.

But it was Juan Maldacena who gave us the first concrete example of how this could work in detail with his AdS/CFT correspondence.

I talked in a lot of detail about the nature of the AdS/CFT proposal in our previous episode—including the fact AdS/CFT is valid for a negatively curved universe with a negative cosmological constant—so-called anti-de Sitter or AdS space—quite different to our own de Sitter universe with its positive cosmological constant.

But AdS/CFT is still a powerful tool for exploring holographic emergence.

And we’re going to use just one part of this proposal—the CFT part.

CFT is for conformal field theory.

It’s the laws of physics that play out on the  boundary—that encode the universe in the bulk.

A conformal field theory is one in which the laws governing the field theory don’t care about the size-scale of the objects in the theory.

So you could have little wiggles in the field that interact with each other in a particular way, or gigantic wiggles that interact in exactly the same way—as long as the wiggles are the same shape.

This conformal-ness gives us a way for the bulk to emerge from the boundary.

Imagine the boundary consists of many Planck-length squares, each able to hold a single bit—0 or 1—empty or full.

You can have small-scale patterns of these bits, where each square is independent.

Or you could have larger-scale patterns that average over many squares—they are, as we say, course-grained.

Because it’s a conformal field theory these large patterns experience the same physics as the smaller patterns.

And these patterns could appear on many scales, all behaving basically the same.

And let’s add another fact—a system of patterns on one scale only interacts with patterns of the same scale.

They don’t interact with patterns on larger or smaller scales.

It’s like having multiple sizes of ripples on a pond that just wash over or under each other.

But there is something that’s different for   the course-grained patterns vs  the fine patterns —the amount of information needed to represent them over the surface is lower.

You’re effectively lumping the Planck-length squares together.

Let’s say we’re looking at just the patterns that have twice the scale-length  of the smallest-scale  patterns.

We can represent them using averaged square sizes that each contain 4 of our original Planck-length squares.

We can also imagine a surface containing only this pattern scale—it has ¼ of the number of effective squares as our original surface.

That means we can also think of it as having an effective radius of ½ that of the original.

The larger the pattern size,  the more Planck squares you   fit into the effective pixel scale  of that pattern size, and that means the smaller the effective  radius of that scale will be.

So here's another way to represent this 2-D  surface with its many pattern scales—and as a series of nested spheres, each sphere representing one of those scales.

The spheres near the center represent the largest scales on the boundary where the patterns are so big they have relatively few effective pixels to play with.

That’s what makes the inner spheres effectively “small”, while the outer spheres are occupied by the boundary patterns that are finer or  smaller in scale—we need higher  resolution to represent them, so these spheres are made of many effective pixels,  and so are effectively large.

But because the boundary theory is a conformal field theory, the physics on each sphere is exactly the same.

And if the separation between these spheres is small enough—for example, if it's also a Planck length—then we’ve produced a 3-D space out of a 2-D one.

This is a fairly cartoonish sketch of how a non-spatial degree of freedom in a lower dimensional space can lead to an emergent space with one more dimension.

The real picture is likely to be way more complicated—for example, the emergence may not come from simple scale invariance but rather from quantum entanglement across many scales—and that’s something we’ll come back to another time.

But the story I just told is still a useful  picture to get the basic gist  of what a holographically emergent space looks like.

Because this new  degree of freedom translates  to a radial direction, that emergent space is in a sense “inside” the original space.

That’s why we can talk about the higher dimensional  space—the bulk—emerging  from its boundary.

Although really the bulk and boundary are two distinct spacetimes.

It may be that each completely contains all of the information of the other and the two evolve over time in lock-step with each other.

But they evolve by very different laws of physics.

There’s a boundary theory and a bulk theory and on the surface they look like they shouldn’t predict the same thing, yet they do; they both predict the same universe.

This is actually a recurring thing in physics.

There are a number of places where two wildly different mathematical descriptions describe the same system or phenomenon—and often the different descriptions  seem mutually incompatible.

These are called dualities, and to me they’re one of the most mysterious features of reality.

Now for a true duality, there is no preferred  side—neither of the two theories are more fundamental than the other.

For example, in quantum mechanics you can represent a particle as a sum of waves in momentum space OR in position space.

Those are equally true, so this is a true duality.

So is the holographic duality a true one?

If so then the boundary and the bulk are equivalently real—it wouldn’t be quite right to say the interior emerges from the boundary.

Instead there’s a so-called ontological democracy.

Perhaps both emerge from something more fundamental, but neither is primary to the other.

On the other hand, there are also such things as approximate dualities, in which one side really is more fundamental—one system “causes” the other system in a meaningful sense.

Now if the holographic duality is like this then it’s much more reasonable to describe one sidie as emergent—and the emergent side in this case is most likely the bulk—but only because in the most concrete version of a holographic duality—AdS/CFT—the boundary theory is currently better defined than the bulk theory.

So which is the case?

Well even if our universe possesses some sort of holographic duality, we don’t know whether it’d be a true or approximate duality.

In fact, we don’t even know which type the AdS/CFT duality is.

That’s something we’re going to have to spend a lot more time on—and I mean this show and the theoretical physicists.

Ok, so we’re up to speed on the holographic emergence of space.

In upcoming episodes we’ll see how gravity can enter the picture—first through the entropic gravity proposal of Eric Verlinde.

We’ll also see the modern thinking for the emergence of space through quantum entanglement, and what the prospects are for finding a concrete holographic description for our universe.

As a teaser, the holographic boundary may not even be at infinite distance, but rather in the far future.

And we’ll ultimately get to the big question: is our universe really emergent from a more fundamental, lower dimensional reality?

Or are we just one side of the coin of a true duality—the boundary and the bulk—each an equally real and mutually emergent spacetime.