If we take bigger and bigger volumes

  • Thread starter Dmitry67
  • Start date
  • #1
2,471
1

Main Question or Discussion Point

(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.
 

Answers and Replies

  • #2
867
60
However, max amount of information inside is proportional to it's surface, to R^2
What is the justification for this statement?
 
  • #4
867
60
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 dimentional 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.
 
  • #5
2,471
1
Frankly, I dont know how Holographic principle works is non-eucledean spacetimes. Especially, BH
 

Related Threads for: If we take bigger and bigger volumes

  • Last Post
Replies
1
Views
2K
  • Last Post
Replies
6
Views
5K
  • Last Post
Replies
6
Views
3K
Replies
0
Views
3K
Replies
13
Views
3K
Replies
29
Views
6K
Replies
25
Views
5K
Top