By Leonard Susskind

During the last decade the physics of black holes has been revolutionized by way of advancements that grew out of Jacob Bekenstein’s attention that black holes have entropy. Steven Hawking raised profound matters about the lack of details in black gap evaporation and the consistency of quantum mechanics in an international with gravity. for 2 a long time those questions questioned theoretical physicists and finally ended in a revolution within the means we expect approximately area, time, topic and knowledge. This revolution has culminated in a notable precept referred to as "The Holographic Principle", that's now an incredible concentration of cognizance in gravitational examine, quantum box concept and simple particle physics. Leonard Susskind, one of many co-inventors of the Holographic precept in addition to one of many founders of String concept, develops and explains those ideas.

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**Example text**

The second viewpoint involves freely falling observers (FREFOS) who follow the particle as it falls. According to the Frefos, they and the particle cross the horizon after a ﬁnite time. However, once the horizon is crossed, their observations cannot be communicated to any Fido or to a distant observer. 19. 35) where pZ and pT are the Z and T components of momentum, and m is the mass of the particle. As the particle freely falls past the horizon, the components pZ and pT may be regarded as constant or slowly varying.

7) where α and β are appropriate commuting variables for the subsystems A and B. Now suppose we are only interested in subsystem A. A complete description of all measurements of A is provided by the density matrix ρA (α, α ). 8) β Similarly, experiments performed on B are described by ρB (β, β ). 10) Density matrices have the following properties: 1) T r ρ = 1 (total probability=1) 2) ρ = ρ† (hermiticity) 3) ρj ≥ 0 (all eigenvalues are positive or zero) In the representation in which ρ is diagonal ρ1 0 0 ...

8 before the shell passes. Region B is the region outside the shell and must be modiﬁed in order to account for the gravitational ﬁeld due to the mass M. In Newtonian physics the gravitational ﬁeld exterior to a spherical mass distribution is uniquely that of a point mass located at the center of the distribution. Much the same is true in general relativity. In this case Birkoﬀ’s theorem tells us that the geometry outside the shell must be the Schwarzschild geometry. 9. Once again the particular value of Y + chosen for the trajectory is immaterial.