How is information preserved on the surface of a Black Hole?

Question

Is there an compression algorithm for storing the information?

1. What if there is a uniformaly complex object dropped to the black hole? Then there will be no compression of information.

2. How is there enough space on the surface (2D) to encode something which is in 3D. The planck distance is the same in the black hole as in the universe. So how can the black hole encode information about an object in 3D that is both uniformly complex and as dense as the black hole? Or is there a law that says 3D objects cannot be more dense then some level - which is sufficiently sparse so that when collapsed to a black hole all its information can be encoded on the surface of a sphere? Has this limit been found - given that a sphere has the lowest surface to volume of any object: https://en.wikipedia.org/wiki/Surface-area-to-volume_ratio ?

Edit: added '3D' to first sentence of 2. question.

Answer 1

How is information preserved on the surface of a black hole?

We have no evidence that it is. We have some claims of this nature, associated with the holographic principle. But I'd say the physics concerned is hypothetical and speculative. It isn't in the same league as general relativity, which is one of the best tested theories we've got. See Clifford M Will's paper on the confrontation between general relativity and experiment for details of that.

Is there an compression algorithm for storing the information?

Not that I know of.

What if there is a uniformly complex object dropped to the black hole? Then there will be no compression of information.

Instead there will be a gamma ray burst. Friedwardt Winterberg wrote about this. See the 2013 AMPS paper an apologia for firewalls. Tucked away in the conclusion is footnote 31, containing a reference 87 to Winterberg’s 2001 paper gamma ray bursters and Lorentzian relativity. I'm confident that Winterberg is essentially correct.

How is there enough space on the surface (2D) to encode something which is in. The planck distance is the same in the black hole as in the universe. So how can the black hole encode information about an object in 3D that is both uniformly complex and as dense as the black hole?

I don't think it can.

Or is there a law that says 3D objects cannot be more dense then some level - which is sufficiently sparse so that when collapsed to a black hole all its information can be encoded on the surface of a sphere? Has this limit been found - given that a sphere has the lowest surface to volume of any object: https://en.wikipedia.org/wiki/Surface-area-to-volume_ratio?

As far as I know there is no law or limit. And as far as I know there is no evidence to support the holographic principle. I for one do not take it seriously. But please advise if you receive any useful answers about this subject on any other website.

Answer 2

This is not something that I believe is known at this time. Rather, it's conjectural. My answer here, though, is to address your two points of doubt regarding how that this can work, as I don't feel the sole answer here is necessarily ideal:

1. With regard to your question concerning data compression, there is no need for it. The black hole is not like a hard drive or USB stick with a bounded storage capacity: it grows when it absorbs matter - meaning, the horizon gets larger, and thus there becomes more room to store the additional information. Thus, the storage capacity goes up as the black hole swallows matter, just enough to accommodate whatever you tossed in. Furthermore, a black hole is the most entropic possible configuration of matter for a given mass, so there can be no material objects that "max out" a black hole with more entropy - you can chuck another black hole at it, but guess what - the horizon areas add exactly, which means it acquired exactly enough storage capacity to hold all the information in the other black hole,

2. With regard to your question of representing a 3D object on a 2D surface - there is no problem here, either. A crude example (compared to how our world seems to be built) is a 3D computer game on a computer with a hard drive. The objects in it are ostensibly 3D (though only displayed on a 2D monitor), but all information describing them is stored on a 2D surface: the disk platters of that hard drive. Even better, given how the data on hard drives is addressed, you could say that this is actually stored in 1D. There is no contradiction between these two things. Anything of higher dimension can be represented in a space of lower dimension with enough room and with suitably clever coding - and the Universe appears to be coded very cleverly indeed, if quantum theory is any indication. Indeed, this is the reason for the name "holographic principle": a hologram is another example where that a 3D shape is stored on a 2D surface.