PBS Space Time

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.

Lets 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 blocksthe 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.

Weve even seen some examples of this in past episodesfrom the early ideas of Leibnitz to modern loop quantum gravity.

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

This is the holographic principlewhich we spent many episodes building towards back in the dayculminating in a pretty intense coverage of this wild idea.

Well, today were 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: well 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 dont exist in our familiar spacetime.

Feel free to watch the old holographic principle stuff later if you havent.

Im going to summarize the core stuff for your convenience.

So the whole argument started in a surprising placewith 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.

Its 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 systeminformation about the stuff that makes up the system that isnt 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 wouldnt 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 propertiesmass, charge, and spinalmost like an elementary particle.

But its 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 holeand 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 theres around one bit of hidden information per 4 square Planck length units on the surface.

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

See its 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 volumelike, 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 spacethis is the Bekenstein bound.

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

But its 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.

Its as though the volume of the universewhat we call the bulk--emerges from the dynamics on its surfacethe boundary.

The journey from black hole entropy to the Holographic Principle was led by Gerard tHooft 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 episodeincluding the fact AdS/CFT is valid for a negatively curved universe with a negative cosmological constantso-called anti-de Sitter or AdS spacequite 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 were going to use just one part of this proposalthe CFT part.

CFT is for conformal field theory.

Its the laws of physics that play out on the boundarythat encode the universe in the bulk.

A conformal field theory is one in which the laws governing the field theory dont 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 wayas 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 bit0 or 1empty 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 squaresthey are, as we say, course-grained.

Because its 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 lets add another facta system of patterns on one scale only interacts with patterns of the same scale.

They dont interact with patterns on larger or smaller scales.

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

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

Youre effectively lumping the Planck-length squares together.

Lets say were 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 scaleit has of the number of effective squares as our original surface.

That means we can also think of it as having an effective radius of 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 scalesand 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.

Thats what makes the inner spheres effectively small, while the outer spheres are occupied by the boundary patterns that are finer or smaller in scalewe 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 enoughfor example, if it's also a Planck lengththen weve 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 complicatedfor example, the emergence may not come from simple scale invariance but rather from quantum entanglement across many scalesand thats something well 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.

Thats why we can talk about the higher dimensional spacethe bulkemerging 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.

Theres a boundary theory and a bulk theory and on the surface they look like they shouldnt 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 phenomenonand often the different descriptions seem mutually incompatible.

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

Now for a true duality, there is no preferred sideneither 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 realit wouldnt be quite right to say the interior emerges from the boundary.

Instead theres 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 fundamentalone system causes the other system in a meaningful sense.

Now if the holographic duality is like this then its much more reasonable to describe one sidie as emergentand the emergent side in this case is most likely the bulkbut only because in the most concrete version of a holographic dualityAdS/CFTthe 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 dont know whether itd be a true or approximate duality.

In fact, we dont even know which type the AdS/CFT duality is.

Thats something were going to have to spend a lot more time onand I mean this show and the theoretical physicists.

Ok, so were up to speed on the holographic emergence of space.

In upcoming episodes well see how gravity can enter the picturefirst through the entropic gravity proposal of Eric Verlinde.

Well 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 well 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 dualitythe boundary and the bulkeach an equally real and mutually emergent spacetime.