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


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

In science fiction films, holograms are three-dimensional, moving images. In reality, however, motion hologram technology has not caught up with the imagination. At least so far, holograms are mostly still images.

The holograms you are most likely to have seen aren’t like they are in the movies. You’re not a projection of an object in air – but that’s supposed to work. Instead, you usually see a three-dimensional object above or behind a flat film. Small holograms are widely used these days as a security measure for credit cards, ID cards, or even banknotes because they are easy to see but difficult to copy.

If you hold such a hologram up to the light, you will notice that it appears to have depth, even though it is printed on a flat surface. That’s because we’re limiting ourselves to photos from the one perspective the picture was taken, and that’s why they look flat. However, you can tilt holograms and view them from different angles as if you were examining a three-dimensional object.

Well, those holograms on your credit cards or those you find on postcards or book covers are not “real” holograms. They actually consist of several two-dimensional images. Depending on the angle, a different image is thrown back on you, creating the illusion of a three-dimensional image.

In a real hologram, the image is actually three-dimensional. However, the market for true holograms is small, making them difficult to come by, although the technology to make them is straightforward. This is what a real hologram looks like.

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

Light is electromagnetic waves, so it has ridges and valleys. And a key property of waves is that they can be superimposed and then reinforce or wash out one another. When two waves are superposed so that two ridges meet at the same point, the wave is amplified. This is called constructive interference. But when a coat of arms meets a trough, the waves will cancel out. This is known as destructive interference.

Now we don’t usually see any light that cancels out other light. This is because, to see interference, you need very regular light with the ridges and valleys neatly aligned. Sunlight or LED light do not have this property. But laser light has it and so laser light can be disturbed.

And this interference can be used to create holograms. To do this, you first split a laser beam into two parts with a semi-transparent glass or crystal, a so-called beam splitter, and make each beam wider with a diverging lens. Then aim half of the beam at the object you want to take a picture of. The light is not only reflected from the object in one direction, but is also scattered in many different directions. And the scattered light contains information about the surface of the object. Then you combine the two beams again and record the intensity of the light with a light-sensitive screen.

Now remember that laser light can interfere. This means how great the intensity on the screen depends on whether the interference was destructive or constructive, which in turn depends on where the object was and how it was shaped. The screen has captured the complete three-dimensional information. In order to view the hologram, the film is developed and irradiated at the same wavelength as the image was taken, thereby reproducing the three-dimensional image.

To understand this a little more closely, let’s look at the image on the screen when a very small point-like object is used. It looks like that. It’s called the zone plate. The intensity and width of the rings depend on the distance between the point-like object and the screen and on the wavelength of the light. But every 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 now is this. Every part of the screen receives information from every part of the object. When you develop the image to get the hologram, you can break it into pieces and each piece will still create the entire three-dimensional object. To better understand how this works, look again at the zone plate, which corresponds to a single point object. If you only have a small piece that contains part of the rings, you can infer the rest of the pattern, although it gets a little more difficult. If you have a general plate that overlaps many zone plates, you can still do so. So, at least mathematically, you can reconstruct the entire object from every part of the holographic plate. In reality, the quality of the picture will go down.

Now that you know how real holograms work, let’s talk about the idea that the universe is a hologram.

When string theorists say our universe is a hologram, they mean this. Our universe has a positive cosmological constant. But mathematically, it is much easier to work with universes with a negative cosmological constant. So this is what string theorists usually look at. These universes with a negative cosmological constant are called anti-de-sitter spaces and insert supersymmetric matter into these anti-de-sitter things. To the best of our knowledge, our universe is not an anti-de-sitter and matter is not supersymmetric, but mathematically speaking, you can certainly do that.

For some specific examples it was then shown that the theory of gravity in such an anti-de-sitter universe corresponds mathematically to another theory at the conforming boundary of this universe. What the hell is the Universe’s conformal limit? Well, our actual universe doesn’t have one. But these anti-de-sitter rooms do. Just exactly how they are defined doesn’t really matter. You just need to know that this conformal boundary is one space dimension less than the space whose boundary it is.

So you have an equivalence between two theories in a different number of spatial dimensions. A theory of gravity in this anti-de-sitter space with strange matter. And another theory on the border of this space that has strange matter too. And just so you’ve heard the name: The theory at the border is a so-called conformal field theory, and the whole thing is known as the anti-de-sitter duality of conformal field theory or AdS / CFT for short.

This duality has been mathematically confirmed for a few specific cases, but pretty much all string theorists seem to believe that it is much more general. In fact, many of them seem to believe that it is valid even in our universe, although there is no evidence of it, either observationally or mathematically. In this most general form, the duality is simply referred to as the “holographic principle”.

If the holographic principle were correct, it would mean that the information about any volume in our universe is encoded on the boundary of that volume. This is remarkable because you would naively think that 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 on the holographic principle, the information that you can put on the tape is not what we think it is. It must have more correlations than we realize. So the holographic principle was true, that would be very interesting. I talked about this in more detail in a previous video.

The holographic principle actually sounds a bit like optical holography. In both cases, one encodes information about a volume on a surface with one dimension less. However, if you take a closer look, there are two important differences between the holographic principle and real holography:

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

Second, as we saw earlier, in a real hologram, each part contains information about the entire object. However, this is not the case in the mathematics of the holographic universe. If you take only part of the limit, you will not be able to reproduce what is going on in the entire universe.

Because of this, I don’t think it’s a good analogy to refer to this string theory idea as holography. But now you know exactly what the two types of holography do and what they don’t have in common.



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