Thread: The Holographic Principle with Special Relativity

I had 2 questions on the holographic principle:

1. The holographic principle was originally made to make sense of a paradox involving black holes. The holographic principle states that information is encoded on the boundary of a area. If an object was to fall into a black hole, the surface area of the black hole increases in size, allowing for more information to be encoded. Here is my question:

In special relativity, when an object approches the speed of light, its length decreases to make sure that the speed of light remains constant. Therefore, the surface area of the object must also be decreasing. So, the same amount of information is held in an area with a smaller surface area. How is this possible according to the holographic principle?

2. Does the holographic principle explain why spacetime has dimensions?

In special relativity, when an object approches the speed of light, its length decreases to make sure that the speed of light remains constant. Therefore, the surface area of the object must also be decreasing. So, the same amount of information is held in an area with a smaller surface area. How is this possible according to the holographic principle?

This effect is observer dependent. An outside observer will see a length contraction ( but only along the direction of movement ! ), but an observer moving along with the object does not notice any change in the dimensions of the object. The holographic principle applies to the surface of an object in its own frame of reference.

Does the holographic principle explain why spacetime has dimensions?

No. The holographic principle only says that the information contained within a 3-dimensional volume can be encoded on its 2-dimensional boundary, but it doesn't explain why the volume has 3 dimensions to start with.