Eli5 Simulation Theory vs Holographic Principle?

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Can someone explain in very basic terms the difference between these two?

In: Physics

The holographic principle is a principle in quantum physics which tells you about how to think about the information contained in a particular volume of space. It *basically* says that the whole internal volume can be encoded as information on the surface of that volume. It’s a pretty cool thing for laypeople to think about, but the real, practical implications of the holographic principle are pretty much beyond the reach of ordinary laypeople to understand. You have to know a *lot* of physics. It’s hard science.

The simulation theory is an idea which doesn’t really depend on or have much to do with physics directly. It’s more an idea of metaphysics. The simulation hypothesis suggests that the world we experience, and all the physical interactions that happen in it, all the atoms bouncing around which make *us*, are actually taking place in something like a computer, the same way we might simulate the bouncing of billiard balls in a video game. And the computer-or-whatever which is running the simulation, in turn, would exist in some more “real”, more “physical” world than the world we live in. This theory is sometimes supported by some kind of probabilistic, “what fraction of all possible worlds” type of argument, but those generally aren’t very rigorous. Questions like how such a computer-or-whatever should come to exist in whatever world it’s in, who would design it and why, and what this all is a simulation *of*, are raised but not really answered by the theory.

The Holographic Principle considers the idea that we can store three-dimensional information in a two-dimensional space, like a hologram. Because we can do this with data, the idea states, we need to consider the possibility that our reality may be structured the same way. What we perceive as three-dimensional space might actually emerge from a two-dimensional structure: for example, perturbations in the surface of an ultra-massive black hole. The visible universe *can* be argued to have an event horizon, so the theory speculates that our 3D space could be projected inside of it by fluctuations on the surface.

Simulationism is essentially pseudoscientific window-dressing for the question “Wouldn’t it be cool if we lived in The Matrix”?

The holographic principle is a statement about the structure of spacetime. Simulation theory, whatever you have in mind, most likely doesn’t tell you anything you don’t already know about spacetime. However, I think this question points to an interesting analogy that’s actually driven a lot of progress in AdS/CFT in recent years.

The analogy you might be thinking of might be something along the following lines. In the framework of holography, the geometry and dynamics of spacetime is fully encoded by the physics of a system on the boundary. One might say that in this sense, the boundary theory “simulates” the bulk system – the bulk is the program/software/simulation, the boundary the computer. This turned out surprisingly to be a really useful perspective, which I‘ll try to explain a bit now.

A basic observation is that the **boundary theory encodes information like a computer does**. Say you‘re interested in an apple you’re holding in your hand. In bulk theory your apple describes a little clump of energy localized near your hand. In the corresponding boundary description however, the information of your apple gets scrambled and smeared everywhere. This is like when you stare at an image of an apple on your screen, that image is localized as a clump of pixels at the center your screen but the instruction for producing that image is encoded in bits in your compute in an essentially incomprehensible way.

More generally, the bulk theory is something that (ideally) resembles the real world – much like how an image on your screen resembles the real world. The boundary theory on the other hand looks like a much simpler physical system in a lab – like switches and circuits in a compute that generate your image. And indeed it turned out to be useful in physics to ask questions about the *information theory* of the system on the boundary – as if it‘s a computational device encoding the data of the bulk it‘s “simulating”.