Bekenstein bound

The Bekenstein - border, discovered by Jacob Bekenstein, is the entropy S of a system, and thus the information content of a sphere, an upper limit

In which

  • E is the measured energy of matter contained ( when it is moved to unlimited distance in order to include the binding energies )
  • R is the radius of the ball
  • The reduced Planck constant
  • C is the speed of light

Is.

This ratio was Gerard t ' Hooft generalized to the entropy limit in a spherical region of space with a specific surface area A:

(G: gravitational constant ).

This is the entropy, which is contained in a black hole of this size. Since the size of the black hole is proportional to its mass, the amount of information that can be included in one spatial sphere is proportional to the square of the mass contained therein.

It is unclear whether these limits be true even if you take volume as the entire universe. The holographic principle is based on the assumption that this is the case.

Swell

  • JD Bekenstein: Generalized second law of thermodynamics in black hole physics. (PDF, 1.7 MB): Physical Review D. 9/1974, pp. 3292-3300.
  • JD Bekenstein: A universal upper bound on the entropy to energy ratio for bounded systems. (PDF, 2.4 MB): Physical Review D. 23/1981, pp. 287-298.
Self-information Boltzmann constant Binding energy
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