What is the holographic principle?

This is not what scientists mean when they ask if the universe is holographic.

Sometimes, news reports of scientific findings are oversimplified, exaggerated or just wrong. The most extreme disparity that I have seen is between the holographic principle of theoretical physics and how it is usually presented in the news. Most of the news articles on this topic include a statement about “living in a hologram” or a simulated universe, like The Matrix, which isn’t what the physicists mean at all.

The physicists are referring to a surprising relationship between gravity and quantum mechanics. Gravity is known to be a consequence of curved space-time — for example, the Earth curves nearby space and time, which bends the trajectories of tossed objects downward. However, gravity is not well understood on extremely small scales, such as the distance between subatomic particles. The quantum mechanical interactions of the other three forces are understood on small scales, but not for strong fields.

The surprise is that there is a correspondence between the mathematical theory of gravity (specifically, for space-time with an anti-de Sitter shape) and the mathematical theory of quantum fields (specifically, for field distributions that have a conformal symmetry). A correspondence means that although the theories have different interpretations, equations in one theory can be translated to the other theory by a dictionary that relates terms in one with terms in the other. This relationship is incredibly useful because hard problems in gravitational physics often translate to easy problems in quantum field theory and vice-versa, so physicists can now solve more problems.

What does this have to do with holograms? The word “holographic” is used because this dictionary translates three-dimensional gravity problems into two-dimensional field theory problems. Similarly, a hologram produces a three-dimensional image from a two-dimensional film or glass plate. The three-dimensional information in the hologram (for instance, what an object looks like from all angles) must be flattened into the two-dimensional film that is used to project it. The dictionary that relates gravity to field theory must also flatten three-dimensional information about the gravity problem into the two dimensions of the field theory problem. Thus, the phrase “holographic principle” is meant metaphorically.

This correspondence is not certain or completely understood, so experiments like Fermilab’s Holometer are looking for evidence of quantum mechanical features in space-time — specifically, fluctuations in the distance between two mirrors. Also, it’s not just a clever trick to solve more physics problems with a wider set of tools: It could explain why the information content of a black hole is related to its surface area (two-dimensional) rather than its volume (three-dimensional).

There’s nothing wrong with wondering, philosophically, whether the world as we know it is a Matrix-style simulation. It’s just a different question from the one physicists are trying to address when they investigate the holographic principle.

Jim Pivarski