By Leonard Susskind
During the last decade the physics of black holes has been revolutionized by means of advancements that grew out of Jacob Bekenstein's recognition that black holes have entropy. Steven Hawking raised profound matters in regards to the lack of info in black gap evaporation and the consistency of quantum mechanics in an international with gravity. for 2 a long time those questions wondered theoretical physicists and at last ended in a revolution within the manner we predict approximately house, time, subject and data. This revolution has culminated in a amazing precept known as ''The Holographic Principle'', that is now an immense concentration of realization in gravitational learn, 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 options
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Additional resources for An Introduction to Black Holes, Information And The String Theory Revolution: The Holographic Universe
In nature, black holes are formed from the collapse of gravitating matter. The simpest model for black hole formation involves a collapsing thin spherical shell of massless matter. For example, a shell of photons, gravitons, or massless neutrinos with very small radial extension and total energy M provides an example. To construct the geometry, we begin with the empty space Penrose diagram with the infalling shell represented by an incoming light-like line 16 Black Holes, Information, and the String Theory Revolution t=+ 8 Future Singularity + I III r = 8 H+ II H - t=- 8 IV Past Singularity r 2 t=+ 8 Future Singularity II H or iz on r = r r 1= + t=2 t=0 r= t=-1 = t -2 III 8 t=1 on iz or H - t=- 8 IV Past Singularity Penrose diagram for Schwarzschild black hole, showing regions (top) and curves of ﬁxed radial position and constant time (bottom) Fig.
15) Thus we see that the Von Neumann entropy is a measure of the number of states which have an appreciable probability in the statistical ensemble. We may think of eS as an eﬀective dimensionality of the subspace described by ρ. The Von Neumann (or entanglement) entropy should not be confused with the thermal entropy of the second law of thermodynamics. This entropy has its origin in coarse graining. B. = e−β H . B. B. 4 Black Holes, Information, and the String Theory Revolution The Unruh Density Matrix Now let us consider the space of states describing a Lorentz invariant quantum ﬁeld theory in Minkowski space.
30) This remarkable result, discovered by William Unruh in 1976 , says that the Fidos see the vacuum as a thermal ensemble with a density matrix of the Maxwell–Boltzmann type. 31 is entirely independent of the particulars of the relativistic ﬁeld theory. It is equally correct for a free scalar quantum ﬁeld, quantum electrodynamics, or quantum chromodynamics. 5 Proper Temperature It is noteworthy that the temperature TR is dimensionless. Ordinarily, temperature has units of energy, or equivalently, inverse length.