By Leonard Susskind
Over the past decade the physics of black holes has been revolutionized via advancements that grew out of Jacob Bekenstein s consciousness that black holes have entropy. Stephen Hawking raised profound concerns about the lack of info in black gap evaporation and the consistency of quantum mechanics in a global with gravity. for 2 many years those questions questioned theoretical physicists and at last ended in a revolution within the manner we expect approximately area, time, subject and data. This revolution has culminated in a amazing precept known as The Holographic precept , that's now a tremendous concentration of cognizance in gravitational study, quantum box conception and straight forward particle physics. Leonard Susskind, one of many co-inventors of the Holographic precept in addition to one of many founders of String idea, develops and explains those options.
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Extra info for An Introduction To Black Holes Information And The String Theory
Let us suppose that the thermometer is at rest with respect to the Fido at position ρ so that it has proper acceleration ρ1 . 32) i In other words the Rindler energy level of the ith state of the thermometer is ρ i . 34) Thus each Fido experiences a thermal environment characterized by a temperature which increases as we move toward the horizon at ρ = 0. The proper temperature T (ρ) can also be expressed in terms of the proper acceleration of the Fido which is equal to ρ1 . 35) The reader may wonder about the origin of the thermal ﬂuctuations felt by the Fidos, since the system under investigation is the Minkowski space vacuum.
31 Black Holes, Information, and the String Theory Revolution 32 The evolution from one surface of constant ω to another is governed by the Rindler Hamiltonian. 1) ρ=0 where T 00 is the usual Hamiltonian density used by the Minkowski observer. 2) where Π is the canonical momentum conjugate to χ. 3) The origin of the factor ρ in the Rindler Hamiltonian density is straightforward. 1 the relation between neighboring equal Rindler-time surfaces is shown. 4) Thus, to push the ω-surface ahead requires a ρ-dependent time translation.
11) The eigenvalues ρj can be considered to be probabilities that the system is in the j th state. However, unlike the case of a coherent superposition of states, the relative phases between the states |j are random. There is one special case when the density matrix is indistinguishable from a pure state. This is the case in which only one eigenvalue ρj is Quantum Fields in Rindler Space 35 nonzero. 12) A quantitative measure of the departure from a pure state is provided by the Von Neumann entropy S = −T r ρ log ρ = − j ρj log ρj .