On Fri, Oct 17, 2014 at 7:35 AM, Richard Ruquist <[email protected]> wrote:
>> In 1972 Bekenstein discovered that the maximum amount of information you >> can put inside a sphere is proportional not to it's volume as you might >> expect but to it's surface area, and it's 2PI*R*E/h*c*ln2 where R is the >> radius of the sphere, E is the mass-energy inside the sphere h is Planck's >> constant and c is the speed of light. >> > > > Here is something I do not understand. The Bekenstein formula for max > information is proportional to the radius of the sphere and not its area. > Only when you put in a black-hole's mass-energy dependence on the radius > of the event horizon does one get a dependence on surface area > The formula I gave was for the amount of information you can pack inside a sphere and it's I = 2PI*R*E/h*c*ln2; we can see that and the more mass-energy inside that sphere (the E term in the above formula) the more information it can hold. However you can't make E arbitrarily large, put too much in and a Black Hole forms and you can't put more mass-energy inside the sphere after that without increasing the size of the sphere. The maximum mass-energy you can put inside a fixed size sphere before a Black Hole forms is E= R*c^2/2*G where c is the speed of light and G is the gravitational constant. So plug that equation for E into the formula for I and we get a formula for the maximum information you can put inside a sphere and its I= PI *R^2 *c/G*h*ln2. As you can see the maximum information of any sphere is proportional to the square of the radius (the area) not the cube of the radius (volume) as you might expect. There is another way to do this. String Theorists say that for Quantum Mechanical reasons it takes 4 Planck Areas (1.6* 10^-69 square meters) to encode one bit of information, so figure out how many Planck Areas it would take to tile a entire Black Hole event horizon, divide by 4, and then you've got the number of bits in a Black Hole, or rather the number of bits on the surface of a Black Hole. John K Clark -- You received this message because you are subscribed to the Google Groups "Everything List" group. To unsubscribe from this group and stop receiving emails from it, send an email to [email protected]. To post to this group, send email to [email protected]. Visit this group at http://groups.google.com/group/everything-list. For more options, visit https://groups.google.com/d/optout.
