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Reference: http://en.wikipedia.org/wiki/Holographic_Principle
The principle states that the description of a volume of space should be thought of as encoded on a boundary to the region, preferably a light-like boundary like a gravitational horizon. For a black hole, the principle states that the description of all the objects which will ever fall in is entirely contained in surface fluctuations of the event horizon.
Leonard Susskind, in his book "The Black Hole War", reflects on quantum gravity whereby the total amount of information (bits) that can be stored within a spactial volume is no more than that which can reside on its spatial boundary. This would be calculated in terms of plank length.
Surface area of box, A = 2*(L.l*L.w + L.w*L.h + L.l*L.h))
Internal volume of box, V = L.l*L.w*L.h
In Euclidean space, V>A except for L.l, L.w, L.h < 6 and other trivial proportions.
Can anyone illustrate (or direct me to) the mathematics that validates the Holographic Principle?
The principle states that the description of a volume of space should be thought of as encoded on a boundary to the region, preferably a light-like boundary like a gravitational horizon. For a black hole, the principle states that the description of all the objects which will ever fall in is entirely contained in surface fluctuations of the event horizon.
Leonard Susskind, in his book "The Black Hole War", reflects on quantum gravity whereby the total amount of information (bits) that can be stored within a spactial volume is no more than that which can reside on its spatial boundary. This would be calculated in terms of plank length.
Surface area of box, A = 2*(L.l*L.w + L.w*L.h + L.l*L.h))
Internal volume of box, V = L.l*L.w*L.h
In Euclidean space, V>A except for L.l, L.w, L.h < 6 and other trivial proportions.
Can anyone illustrate (or direct me to) the mathematics that validates the Holographic Principle?