*[This is a transcript of the video embedded below.]*

Do we live in a hologram? String theorists think we do. But what does that mean? How do holograms work, and how are they related to string theory? That’s what we will talk about today.

In science fiction movies, holograms are 3-dimensional, moving images. But in reality, the technology for motion holograms hasn’t caught up with imagination. At least so far, holograms are still mostly stills.

The holograms you are most likely to have seen are not like those in the movies. They are not a projection of an object into thin air – however that’s supposed to work. Instead, you normally see a three-dimensional object above or behind a flat film. Small holograms are today frequently used as a security measure on credit cards, ID cards, or even banknotes, because they are easy to see, but difficult to copy.

If you hold such a hologram into light, you will see that it seems to have depth, even though it is printed on a flat surface. That’s because in photographs, we are limited to the one perspective from which the picture was taken, and that’s why they look flat. But you can tilt holograms and observe them from different angles, as if you were examining a three-dimensional object.

Now, these holograms on your credit cards, or the ones that you find on postcards or book covers, are not “real” holograms. They are actually composed of several 2-dimensional images and depending on the angle, a different image is reflected back at you, which creates the illusion of a 3-dimensional image.

In a real hologram the image is indeed 3-dimensional. But the market for real holograms is small, so they are hard to come by, even though the technology to produce them is straightforward. A real hologram looks like this.

Real holograms actually encode a three-dimensional object on a flat surface. How is this possible? The answer is interference.

Light is electromagnetic waves, so it has crests and troughs. And a key property of waves is that they can be overlaid and then amplify or wash out each other. If two waves are overlaid so that two crests meet at the same point, that will amplify the wave. This is called constructive interference. But if a crest meets a trough, the waves will cancel. This is called destructive interference.

Now, we don’t normally see light cancelling out other light. That’s because to see interference one needs very regular light, where the crests and troughs are neatly aligned. Sunlight or LED light doesn’t have that property. But laser light has it, and so laser light can be interfered.

And this interference can be used to create holograms. For this, one first splits a laser beam in two with a semi-transparent glass or crystal, called a beam-splitter, and makes each beam broader with a diverging lens. Then, one aims one half of the beam at the object that one wants to take an image of. The light will not just bounce off the object in one single direction, but it will scatter in many different directions. And the scattered light contains information about the surface of the object. Then, one recombines the two beams and captures the intensity of the light with a light-sensitive screen.

Now, remember that laser light can interfere. This means, how large the intensity on the screen is, depends on whether the interference was destructive or constructive, which again depends on just where the object was located and how it was shaped. So, the screen has captured the full three-dimensional information. To view the hologram, one develops the film and shines light onto it at the same wavelength as the image was taken, which reproduces the 3-dimensional image.

To understand this in a little more detail, let us look at the image on the screen if one uses a very small point-like object. It looks like this. It’s called a zone plate. The intensity and width of the rings depends on the distance between the point-like object and the screen, and the wavelength of the light. But any object is basically a large number of point-like objects, so the interference image on the screen is generally an overlap of many different zone plates with these concentric rings.

The amazing thing about holograms is now this. Every part of the screen receives information from every part of the object. As a consequence, if you develop the image to get the hologram, you can take it apart into pieces, and each piece will still recreate the whole 3-dimensional object. To understand better how this works, look again at the zone plate, the one of a single point-like object. If you have only a small piece that contains part of the rings, you can infer the rest of the pattern, though it gets a little more difficult. If you have a general plate that overlaps many zone plates, this is still possible. So, at least mathematically, you can reconstruct the entire object from any part of the holographic plate. In reality, the quality of the image will go down.

So, now that you know how real holograms work, let us talk about the idea that the universe is a hologram.

When string theorists claim that our universe is a hologram, they mean the following. Our universe has a positive cosmological constant. But mathematically, universes with a negative cosmological constant are much easier to work with. So, this is what string theorists usually look at. These universes with a negative cosmological constant are called Anti-de Sitter spaces and into these Anti-de Sitter things they put supersymmetric matter. To best current knowledge, our universe is not Anti De Sitter and matter is not supersymmetric, but mathematically, you can certain do that.

For some specific examples, it has then been shown that the gravitational theory in such an Anti de Sitter universe is mathematically equivalent to a different theory on the conformal boundary of that universe. What the heck is the conformal boundary of the universe? Well, our actual universe doesn’t have one. But these Anti-De Sitter spaces do. Just exactly how they are defined isn’t all that important. You only need to know that this conformal boundary has one dimension of space less than the space it is a boundary of.

So, you have an equivalence between two theories in a different number of dimensions of space. A gravitational theory in this anti-De Sitter space with the weird matter. And a different theory on the boundary of that space, which also has weird matter. And just so you have heard the name: The theory on the boundary is what’s called a conformal field theory, and the whole thing is known as the Anti-de Sitter – Conformal Field Theory duality, or AdS/CFT for short.

This duality has been mathematically confirmed for some specific cases, but pretty much all string theorists seem to believe it is much more generally valid. In fact, a lot of them seem believe it is valid even in our universe, even though there is no evidence for that, neither observational nor mathematical. In this most general form, the duality is simply called the “holographic principle”.

If the holographic principle was correct, it would mean that the information about any volume in our universe is encoded on the boundary of that volume. That’s remarkable because naively, you’d think the amount of information you can store in a volume of space grows much faster than the information you can store on the surface. But according to the holographic principle, the information you can put into the volume somehow isn’t what we think it is. It must have more correlations than we realize. So it the holographic principle was true, that would be very interesting. I talked about this in more detail in an earlier video.

The holographic principle indeed sounds a little like optical holography. In both cases one encodes information about a volume on a surface with one dimension less. But if you look a little more closely, there are two important differences between the holographic principle and real holography:

First, an optical hologram is not actually captured in two dimensions; the holographic film has a thickness, and you need that thickness to store the information. The holographic principle, on the other hand, is a mathematical abstraction, and the encoding really occurs in one dimension less.

Second, as we saw earlier, in a real hologram, each part contains information about the whole object. But in the mathematics of the holographic universe, this is not the case. If you take only a piece of the boundary, that will not allow you to reproduce what goes on in the entire universe.

This is why I don’t think referring to this idea from string theory as holography is a good analogy. But now you know just exactly what the two types of holography do, and do not have in common.