If we take bigger and bigger volumes

  • Thread starter Dmitry67
  • Start date
  • Tags
    Volumes
In summary, the holographic principle states that the volume of a sphere is proportional to R^3, but the maximum amount of information inside is proportional to its surface, to R^2. This means that the information density is proportional to 1/R. This principle is well known, and is based on the fact that anything that falls across an event horizon in a black hole is affected by the black hole's gravity. However, the information about things that have crossed the event horizon is not permanently encoded there.
  • #1
Dmitry67
2,567
1
(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.
 
Space news on Phys.org
  • #2
Dmitry67 said:
However, max amount of information inside is proportional to it's surface, to R^2

What is the justification for this statement?
 
  • #4
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.
 
  • #5
Frankly, I don't know how Holographic principle works is non-eucledean spacetimes. Especially, BH
 

1. What happens to the density if we take bigger and bigger volumes?

The density would decrease as the volume increases. This is because the mass remains constant while the volume increases, resulting in a lower density value.

2. How does the pressure change as we increase the volume?

According to Boyle's Law, as the volume increases, the pressure decreases. This is because there is more space for the gas molecules to move and exert less force on the container walls.

3. Will the temperature change if we take bigger and bigger volumes?

The temperature would remain constant as long as the amount of gas and the pressure also remain constant. This is known as Gay-Lussac's Law and applies to ideal gases.

4. What happens to the number of gas molecules if we increase the volume?

The number of gas molecules remains constant as the volume increases. This is known as Avogadro's Law, which states that equal volumes of gases at the same temperature and pressure contain the same number of molecules.

5. How does the volume affect the rate of diffusion?

The rate of diffusion would increase as the volume increases. This is because there is more space for the gas molecules to move and spread out, increasing the chances of collisions and mixing with other molecules.

Similar threads

Replies
5
Views
1K
Replies
7
Views
2K
  • Special and General Relativity
Replies
29
Views
1K
Replies
2
Views
1K
  • Astronomy and Astrophysics
Replies
1
Views
2K
  • Engineering and Comp Sci Homework Help
Replies
31
Views
1K
  • Quantum Interpretations and Foundations
Replies
23
Views
676
  • Special and General Relativity
Replies
23
Views
2K
  • Introductory Physics Homework Help
Replies
5
Views
3K
  • Quantum Interpretations and Foundations
Replies
3
Views
936
Back
Top