# How does the Holographic Principle relate to 11 dimensions?

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• FallenApple
In summary, the Holographic Principle states that our 3-dimensional world can be encoded in a 2-dimensional surface, inspired by Hawking's calculation of a black hole's entropy. The remaining dimensions are also present, but are encoded differently. However, mathematical examples only exist for negatively curved space, while positively curved space may be closer to reality and may result in a timeless, 3-dimensional space. While there may be a partial version in which a space-time can be projected onto a surface, it has only been fully worked out for negatively curved space.
FallenApple
So the Holographic Principle says that our 3 dimensonal world is encoded in the 2d surface of the cosmological horizon.

What about the remaining dimensions? Are they there in the regular 3space or are they also encoded?

The holographic principle says that quantum gravity equals a quantum field theory (without gravity) in one less dimension. The inspiration was Hawking's calculation that a black hole's entropy depends on its surface area rather than on its volume.

In the mathematical examples that have been worked out, the gravitational space has e.g. 4 large space-time dimensions and 7 small (compact) dimensions, and the field-theory dual has 3 large space-time dimensions. So the remaining dimensions are there too, but they are encoded differently.

However, those mathematical examples are for a negatively curved space (anti de Sitter space). Positively curved space (de Sitter space) may be closer to reality. In that case, time itself may be the extra holographic dimension, and the dual description is a timeless, purely three-dimensional space. But that dS/CFT duality has problems compared to AdS/CFT.

In both those examples, an entire space-time has a dual description in terms of a field theory on a space or space-time of one less dimension. There is probably a partial version in which you can project part of a space-time onto a surface inside it, like your example with the cosmological horizon, but I think it is only worked out for AdS/CFT.

Spinnor

## What is the Holographic Principle?

The Holographic Principle is a theory in theoretical physics that suggests that the information describing a volume of space can be encoded on its boundary. This means that all the information in a three-dimensional space could actually be represented on a two-dimensional surface.

## What are 11 dimensions in the context of the Holographic Principle?

The Holographic Principle is based on the idea that our three-dimensional universe can be described by a two-dimensional surface. However, this theory also suggests that there may be more than just three dimensions in our universe. In fact, some versions of the theory suggest that there may be as many as 11 dimensions in total.

## How does the Holographic Principle relate to string theory?

The Holographic Principle is closely related to string theory, which is a theoretical framework that attempts to reconcile general relativity and quantum mechanics. In string theory, the fundamental building blocks of the universe are not particles, but tiny, vibrating strings. These strings exist in a higher-dimensional space and their vibrations determine the properties of the particles we observe in our three-dimensional world. The Holographic Principle provides a way to understand this higher-dimensional space in terms of a lower-dimensional boundary.

## What evidence supports the Holographic Principle?

Currently, there is no direct evidence to support the Holographic Principle. However, many scientists believe that this theory has potential to explain some of the unsolved mysteries of the universe, such as the nature of black holes and the origin of the universe. Additionally, the Holographic Principle is mathematically consistent with other theories, including string theory and quantum mechanics.

## What are the implications of the Holographic Principle for our understanding of the universe?

If the Holographic Principle is true, it would fundamentally change our understanding of the universe. It would mean that our three-dimensional reality is actually a projection of a two-dimensional surface. This would have implications for our understanding of space, time, and matter. It may also provide a new framework for understanding the fundamental laws of physics and could potentially lead to new technologies and discoveries.

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