By Leonard Susskind
Over the past decade the physics of black holes has been revolutionized through advancements that grew out of Jacob Bekenstein s recognition that black holes have entropy. Stephen Hawking raised profound concerns in regards to the lack of details in black gap evaporation and the consistency of quantum mechanics in an international with gravity. for 2 many years those questions questioned theoretical physicists and finally resulted in a revolution within the method we expect approximately area, time, topic and knowledge. This revolution has culminated in a amazing precept referred to as The Holographic precept , that is now a massive concentration of awareness in gravitational study, quantum box idea and uncomplicated particle physics. Leonard Susskind, one of many co-inventors of the Holographic precept in addition to one of many founders of String thought, develops and explains those innovations.
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Additional resources for An Introduction To Black Holes Information And The String Theory
A much more singular quantity which will be of great concern in future lectures is the entropy of the vacuum state. 17 to obtain the entropy. 14 can be thought of as both entanglement and thermal entropy in the special case of the Rindler space density matrix. 30. Thus the computation of the entropy of Rindler space is reduced to ordinary thermodynamic methods. For the present case of free ﬁelds the entropy is additive over the modes and can be estimated from the formula for the thermodynamics of a free 1+1 dimensional scalar ﬁeld.
Quantum mechanically we have a dilemma if we try to imagine the Fidos as real. If they are extrememly light their locations will necessarily suﬀer large quantum ﬂuctuations, and they will not be useful as ﬁxed anchors labeling spacetime points. If they are massive they will inﬂuence the gravitational ﬁeld that we wish to describe. Quantum mechanically, physical Fidos must be replaced by a more abstract concept called gauge fixing. The concept of gauge ﬁxing in gravitation theory implies a mathematical restriction on the choice of coordinates.
37) 4M G Thus we ﬁnd the momentum of an infalling particle as seen by a Fido grows exponentially with time! 38) ρ(t) ≈ ρ(0)exp(− 4M G Locally the relation between the coordinates of the Frefos and Fidos is a time dependent boost along the radial direction. The hyperbolic boost angle is the dimensionless time ω. Eventually, during the lifetime of the black hole this boost becomes so large that the momentum of an infalling particle (as seen by a Fido) quickly exceeds the entire mass of the universe.
An Introduction To Black Holes Information And The String Theory by Leonard Susskind