Information and sphere’s interior versus surface… not.

[rrw4rusty]

Hello,

 

I have heard the following from several places:

 

The amount of information that can be stored within a sphere is equal to the amount of information that can be stored on its surface.

 

This seems like a contradiction or, a self-defeating statement. It seems to instead say that a sphere can hold an infinite amount of information. For example:

 

Since the amount of information you can put within the sphere is equal to the amount you can put on its surface… just put the information on its surface… then, with the interior of the sphere empty; put a slightly smaller sphere within and put more information on its surface then repeat this process until the space within the sphere offers diminishing returns. Then, jump back to the outer most sphere and place a slightly larger sphere around that… ad infinitum.

 

I’m I cheating, missing the point, or… missing something else?

 

Cheers,

Rusty

[insane_alien]

perhaps if you could post the source of this for some context. i'd imagine it would scale with the volume over the surface area.

[rrw4rusty]

perhaps if you could post the source of this for some context. i'd imagine it would scale with the volume over the surface area.

 

Dear insame_alien,

 

Actually I assumed most people would have heard this. This claim stemmed from Bekenstein and Hawking's conjecture regarding the total amount of information held by a black hole was equal to the total area of the event horizon (loosely stated). It is also related to Holographic Universe ideas. The statements concerning a sphere I heard in an audio lecture and also read in a book but at present I am at a loss as to which lecture and which book. I will try to locate these or other sources.

 

Sorry!

Rusty

[swansont]

I hope you can see that the case where this is applied to a black hole is very different from it applying in general.

[ajb]

I hope you can see that the case where this is applied to a black hole is very different from it applying in general.

 

To stress this further, the OP is talking about the holographic principle. This seems a general feature of quantum gravity.