If we take bigger and bigger volumes

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SUMMARY

The discussion centers on the holographic principle, which posits that the volume of a sphere (R^3) contains less information than its surface area (R^2), leading to a paradox where information density approaches zero as the radius increases. Participants express skepticism regarding the derivation of this principle, particularly in relation to black holes and the transmission of information via gravity waves and Hawking radiation. The conversation highlights the incompatibility of gravity with the second law of thermodynamics, especially when considering multiple bodies in space and their configurations.

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  • Understanding of the holographic principle
  • Familiarity with black hole physics and event horizons
  • Basic knowledge of thermodynamics, particularly the second law
  • Concepts of information theory in the context of physics
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  • Research the derivation and implications of the holographic principle
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Physicists, cosmologists, and students of theoretical physics interested in the implications of the holographic principle and its relationship with black holes and thermodynamics.

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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