What is the holographic principle? Does it mean that "our universe is a hologram"?

JOSEPH WANG
Ph.D. Astrophysics

 That "our universe is a hologram" is perhaps one of the greatest physics-related misconceptions of recent years. Let me write a clarification in bold so that it will be absolutely clear:

No, our universe is NOT a hologram! It's just a metaphor used to describe some property we think the universe might have. It has absolutely nothing to do with actual holograms, or with "living in a simulation".

Okay, now that we've got this covered, let me explain what the holographic principle actually means.

The Holographic Principle

The entropy of a black hole is given by the area of its horizon, divided by 4. Now, imagine that you have some volume of space with some matter in it, not necessary a black hole. Is there a similar limit to the total entropy in that volume?

Well, let's think about it. Intuitively, you can put more and more matter inside that volume of space, thus increasing the entropy within it. But at some point there will be so much matter inside that it will inevitably collapse into a black hole!

In other words, we cannot increase the entropy of a volume of space indefinitely; we can only increase it until it is equal to the surface area of the volume, divided by 4.

Now, entropy is a measure of information; the more information you have, the more entropy you'll get. So it appears that there is a principle, the holographic principle, which roughly says that the total amount of information inside a volume of space cannot be larger than the amount of information that can be encoded on the boundary of that volume.

The word "principle" here means that it is a principle that you must follow when you try to formulate a theory of quantum gravity. This means that any potential theory of quantum gravity must either be shown to follow this principle, or have a very good reason to violate it, otherwise it is not compatible with the intuitive picture I gave above.

Note that the holographic principle is just a principle with which to formulate certain scientific theories, and not a scientific theory by itself, so it does not have any predictions that can be tested experimentally. So the mere existence of the principle doesn't mean that "our universe is a hologram" or that our universe actually obeys the holographic principle.

To be perfectly clear: whether our universe obeys the holographic principle or not is a statement that must be tested empirically, but it cannot be tested until we have an actual theory of quantum gravity, which we do not have.

So if someone tells you that "the universe is a hologram", you can be sure they don't know what they're talking about.

The AdS/CFT Conjecture: Holography In An Imaginary, Unrealistic Universe

The misleading and incorrect articles that frequently appear in the media citing "evidence" that "the universe is a hologram" are usually talking about something called the AdS/CFT conjecture. Let me first make another very important clarification in bold:

The AdS/CFT conjecture suggests a purely mathematical relation between two completely unrealistic theories, one on the "AdS" side and one on the "CFT" side, and it says absolutely nothing whatsoever about the real universe that we live in.

Why do we need AdS/CFT? The holographic principle described above is just words. But words are not precise and you cannot use them to calculate stuff. We physicists like to write things down as precise mathematical equations so that they can be analyzed quantitatively as well as qualitatively.

The AdS/CFT conjecture gives a mathematical model in which the holographic principle seems to work. As I said above, this mathematical model is not a realistic one, and it has nothing to do with our own universe.

Why do we study it if it's not realistic? There is a concept called a "toy theory". A toy theory is a theory that we know is not realistic in any way, but we study it mainly for two reasons:

It is a very simple model, so we can perform calculations on it that we can't do in more realistic models; and/or
We have no realistic model, so we make do with what we have.Okay, now, what does the AdS/CFT conjecture actually say? Without going too much into the technical details, it basically talks about some object described by string theory called a D3-brane (but the name doesn't matter).

You can look at this brane from two different "perspectives". From one perspective it looks like a theory of (quantum) gravity in 5 dimensions ("AdS"), and from the other perspective it looks like a theory without gravity in 4 dimensions ("CFT").

But the brane is still a brane, and it should act the same way no matter from which perspective you look at it. In other words, we can perform calculations either in the 5-dimensional theory or in the 4-dimensional theory and we'll get the same results.

This duality of two different descriptions is extremely useful for doing calculations. This is because if something is too hard to calculate from the gravity perspective you can calculate it from the non-gravity one, or vice versa.

In addition, and more relevantly to the present context, this duality provides a concrete, if unrealistic, model in which the holographic actually works. This is because the 5-dimensional theory "encodes the same information" as the 4-dimensional theory!

I say AdS/CFT is a conjecture because it has not actually been proven. There are many pieces of evidence that the conjecture might be true. These basically come from calculating the same thing from both perspectives and checking that the results agree. But there is still no proof that the results always agree.

So whenever you read an article saying that "physicists found evidence that our universe is a hologram", what it actually means is that physicists did some more calculations and found that they agree with the AdS/CFT conjecture. But it doesn't say anything about our universe, only about a very unrealistic model.

Why is the model unrealistic? For many reasons:

The model is built using string theory. Despite the impression you might get from popular media, string theory is really a "toy theory"; it doesn't actually describe our own universe. It describes an imaginary universe which turns out to be similar to our own universe in some ways, but very different from it in other ways.
The perspective of a theory with gravity is called AdS because it describes a universe which has a special geometry called "Anti de Sitter". However, our universe does not have this geometry. In fact, it is (asymptotically) described by the exact opposite of Anti de Sitter, which is called "de Sitter". So the AdS perspective definitely does not describe anything even remotely close to our universe.
The perspective of a theory without gravity is called CFT because it describes a universe which has a special symmetry called "conformal symmetry". So the theory is called a Conformal Field Theory. However, our universe does include gravity, and does not have conformal symmetry. So the CFT perspective also definitely does not describe anything even remotely close to our universe.
In conclusion, AdS/CFT is a conjecture offering a model of an imaginary, unrealistic universe which is certainly not our universe, in which the holographic principle is mathematically realized. It's a very important conjecture and has many applications, but it says absolutely nothing about our own universe, which is neither AdS nor CFT.

However, unlike the specific unrealistic model of AdS/CFT, the holographic principle as a general principle is something that we think should apply to the real universe that we live in.

As I mentioned above, the validity of the holographic principle in our universe is something that must ultimately be determined empirically once we have a working theory of quantum gravity.

ANAΔΗΜΟΣΙΕΥΣΗ ΑΠΟ ΤΟ QUORA 20/6/2017