If we take bigger and bigger volumes

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Discussion Overview

The discussion revolves around the holographic principle, particularly focusing on the relationship between the volume of a sphere and the information it can contain. Participants explore the implications of increasing volume and its effect on information density, as well as the nature of information in relation to black holes and gravitational systems.

Discussion Character

  • Exploratory
  • Debate/contested
  • Technical explanation
  • Conceptual clarification

Main Points Raised

  • One participant claims that as the radius (R) of a sphere increases, the information density decreases, suggesting that chaos within appears predetermined by external conditions.
  • Another participant questions the justification for the assertion that the maximum amount of information is proportional to the surface area (R^2).
  • A reference to the holographic principle is provided, but a participant expresses skepticism about the derivation presented in the linked source, arguing that it does not adequately account for the behavior of information crossing a black hole's event horizon.
  • Concerns are raised regarding the compatibility of gravitational effects with the second law of thermodynamics, using a hypothetical scenario involving two bodies in space to illustrate the point.
  • One participant admits uncertainty about the application of the holographic principle in non-Euclidean spacetimes, particularly in the context of black holes.

Areas of Agreement / Disagreement

Participants express differing views on the validity of the holographic principle and its implications, with no consensus reached on the justification of claims or the nature of information in gravitational contexts.

Contextual Notes

Participants acknowledge limitations in their understanding of entropy and the holographic principle, particularly in relation to black holes and non-Euclidean spacetimes. There are unresolved questions regarding the derivation of information density and its implications.

Dmitry67
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(Holographic principle)

Volume of a sphere is proportional to R^3
However, max amount of information inside is proportional to it's surface, to R^2
So information density is proportional to 1/R

It means that if we take bigger volumes, the content inside appears to be correlated with the outside, so some of the chaos we see inside (and interpret as information) in fact is predetermined by the environment.

It looks logical, but...
What is bugging me, if we take R --> INF, we find that density of information = 0.
 
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Dmitry67 said:
However, max amount of information inside is proportional to it's surface, to R^2

What is the justification for this statement?
 
I'm not saying it's untrue but the derivation they have on wikipedia doesn't hold water.

In the case of the black hole anything that falls across the event horizon has an effect on the horizon as it crosses. Information about that matter is carried away from the black hole as gravity waves and hawking radiation, there is no need to suppose that the information about everything that ever crossed the event horizon is permanently encoded thereon.

In other words everything that crosses the event horizon is happening in 2 dimensions over time, the information about it is radiated away from a 2 dimensional surface over time.

As for the information contained in the matter that initialy collapsees to form the black hole... We don't need a black hole to demonstrate that gravity is incompatible with the 2'nd law of thermodynamics. Imagine 2 rigid bodies floating freely in space. There are twice as many possible configurations of that system then there would be if there were only 1 body. If gravitational attraction causes the 2 bodies to stick together then the 1'st scenario has become the 2'nd.

I admittedly don't have a perfect grasp of the behavior of entropy so if I'm typing nonsense please educate me.
 
Frankly, I don't know how Holographic principle works is non-eucledean spacetimes. Especially, BH
 

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