The Holographic Principle

Mathematical relationship or physical reality? Does the difference even matter?

A particular buzzword that flies around physics articles these days is holography. When most people think of holograph it conjures images of science-fiction movies with shimmering images.  In the movies, the hologram is a 3 dimensional illusion projected from a 2 dimensional screen. The physics concept is a bit different.

In general, holography refers to some higher-dimensional phenomena (a 3D image in this case) that is ‘encoded’ somehow into a lower-dimensional form (a 2D projector).  In physics, this general idea is applied to reality itself with the holographic principle.

Black Holes at the Surface

During the early studies of black holes, it became clear that we could need to understand how they work not only in terms of their gravity, but in terms of their thermodynamics. In particular, it was important to determine the entropy of a black hole. Entropy is often referred to as the disorder of a system but it also reflects the density of information. Jacob Bekenstein developed a model where black holes contained the maximum possible entropy for anything with the same volume.

blackholeentropy.png

S here represents the entropy for the entire volume.  k and l are constants. A is the surface area of the black hole.

In the course of understanding this they found that this maximum entropy was directly proportional to the surface area of the black hole. In other words, you only needed information about the surface of a black hole in order to calculate the entropy of the entire volume. Since higher dimensional information (the entropy of a black hole) is completely defined by a lower-dimension system (the surface), this is a form of holography. This observation has inspired physicists to ask why it is holographic? what does it mean? And are other physical systems holographic?

What does holography mean in Physics?

Since the early studies of black hole physics, new theories have adopted what we call the holography principle, the idea that a volume of space can be described by a lower dimensional boundary. Black holes were are early example, but now the concept is applied to string theories, quantum gravity and more. Some theories suggest that entire universe itself is actually caused by some behavior on a two dimensional boundary.

holography.png

Where holography is concerned, The behavior on the boundary is directly linked to what occurs in the volume.

Let’s unpack this a little bit because it isn’t entirely clear what all this means. A major dispute in discussions of relationships of holography is how to interpret it. The literal interpretation is that the higher dimensional reality doesn’t actually exist and that it is illusion created by interactions on some lower-dimensional structure. This goes against our intuition that 3 dimensional structures exist as whole entities that are more than just their bounding surface.

Another interpretation is that the holography principle doesn’t tell us what dimensions really exist or not, but instead it tells us about the relationships and structure of these system. Saying that we can describe something using a bounding surface doesn’t imply that the volume isn’t real, it is just that the information in that volume is bound by certain relationships that cause the total behavior to be describable by the surface. This approach has some interesting implications for how information itself flows in our universe.

Regardless of how you interpret it, the holography principle has many applications to physics. One of the major areas of research is in what we call AdS/CFT correspondence. This is a approach to quantum gravity where two theories are able to be connected through holography. Both theories produce the same results, however one theory acts on the volume (AdS) and one theory acts on the boundary (CFT).

These kind of correspondences is called a duality. That is where different theories and approaches end up being simply two ways of describing the same thing. It seems fitting that all the varied approaches to studying the universe might lead to different perspectives on the same reality.
VIDEO: The World as a Hologram,  Leonard Susskind
A different approach that focuses on the black hole information paradox when discussing holography. A very interesting watch.

PDF: The Holographic Universe, Jean-Pierre Luminet
A very readable and accessible introduction to the approaches to holography and their implications.
https://arxiv.org/ftp/arxiv/papers/1602/1602.07258.pdf

COURSE: String Theory and Holographic Duality,  Prof. Hong Liu
A free graduate course that introduces string theory and the AdS / CFT correspondence in detail.  Includes pdf readings and videos.
https://ocw.mit.edu/courses/physics/8-821-string-theory-and-holographic-duality-fall-2014/index.htm