Holographic Principle and/or implications of the entropy bound

[geshel]

Hi all,

First post here. I'm a casual physics enthusiast, but I've been reading and thinking a lot about this topic lately.

The thing I'm most interested in is the fact that black hole formation involves the simultaneous limits of two things: time dilation and the information bound. I find it too much of a coincidence that the per-unit information flow rate from a region slows down as the aggregate per-period quantity of information increases, and finally when it reaches a saturation point, the flow stops. To me this points pretty directly at the information bound being the actual cause of time dilation. But I have not read any mention of even speculation on this so far (or at least if I did, I didn't understand it as such), which makes me second-guess this conclusion.

The other bit that's interesting to me is exactly what information our current entropy bound calculations are referring to. Entropy is considered to be the amount which a possible state's full data could be surprising given a set of known "macro" conditions. Basically this connects to: if there are limits on information exchange between regions of space, what, if anything, is shared knowledge between said regions? For instance if we take the black hole entropy bound: we begin with "we know mass, angular momentum, and charge". So then we (via Hawking) calculate entropy based on the number of possible quantum states that can lead to those three macro values for the region. And we find this bound.

But it just has me thinking a bunch of random thoughts:

* is the information about M/J/Q somehow outside of the bound? or part of it? The latter could be true if it's essentially zero compared to the vast number of bits necessary to encode all possible quantum states. But then what's the resolution? (quantization)

* possibly a noob question, but does the set of possible microstates include orientation? To my understanding of quantum mechanics (which is slim), the answer would be "no". If it's a spherical region then no matter what quantized state limitations are imposed by QM, the absolute orientation of the entire system should be free

* so this makes me wonder if the boundary encodes the orientation, or embodies it. If the former, it would imply that there are a finite number of possible orientations.

 

[AndyW]

If the latter, it would imply that orientation is itself quantized
Thank you for sharing your thoughts and questions on black hole formation and the information bound. It's great to see such enthusiasm and interest in physics!

I can definitely see why you would make the connection between the information bound and time dilation in the context of black holes. The concept of time dilation is often associated with the slowing down of time near massive objects, such as black holes. This is because the intense gravitational pull of a black hole warps the fabric of space-time, causing time to pass slower for an observer outside the black hole compared to an observer near the event horizon. This is due to the fact that the information bound, which is essentially a limit on the amount of information that can be exchanged between two regions of space, is also affected by the intense gravitational pull of a black hole. As the black hole's mass increases, the information bound decreases, leading to a decrease in the flow of information and a corresponding slowing down of time.

In terms of the information used to calculate the entropy bound of a black hole, it is indeed based on the known macroscopic properties of the black hole, such as mass, angular momentum, and charge. This information is then used to calculate the maximum number of possible quantum states that could lead to those macroscopic values. However, as you pointed out, there may be other information about the black hole that is not taken into account in this calculation. For example, the orientation of the black hole could potentially be encoded in the information bound, but this is still an area of ongoing research and speculation.

In terms of your question about the possible microstates including orientation, it is true that the absolute orientation of the system should not be affected by quantum mechanical limitations. However, the orientation of individual particles within the system may still be quantized.

Overall, the information bound and its connection to time dilation and black hole formation is a fascinating topic that is still being explored by scientists. I encourage you to continue reading and learning about this subject, and to keep asking questions and sharing your thoughts with the scientific community. Who knows, you may even make a valuable contribution to our understanding of black holes and the universe!