By Leonard Susskind

Over the past decade the physics of black holes has been revolutionized through advancements that grew out of Jacob Bekenstein's awareness that black holes have entropy. Steven Hawking raised profound concerns about the lack of info 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 at last ended in a revolution within the method we expect approximately area, time, topic and data. This revolution has culminated in a extraordinary precept known as "The Holographic Principle", that's now an enormous concentration of consciousness in gravitational learn, quantum box idea and effortless 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 techniques.

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**Extra info for An Introduction to Black Holes, Information And The String Theory Revolution: The Holographic Universe**

**Sample text**

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. However all real observables are required to be gauge invariant. Now let us consider a classical particle falling radially into a black hole. There are two viewpoints we can adopt toward the description of the particle’s motion.

Chapter 4 Entropy of the Free Quantum Field in Rindler Space In the real world, a wide variety of diﬀerent phenomena take place at diﬀerent temperature scales. At the lowest temperatures where only massless quanta are produced by thermal ﬂuctuations, one expects to ﬁnd a very weakly interacting gas of gravitons, photons, and neutrinos. Increase the temperature to the e+ , e− threshold and electron-positron pairs are produced. The free gas is replaced by a plasma. At higher temperatures, pions are produced which eventually dissociate into quarks and gluons, and so it goes, up the scale of energies.

The entropy is also a measure of the degree of entanglement between A and B. It is therefore called the entropy of entanglement. The opposite extreme to a pure state is a completely incoherent density matrix in which all the eigenvalues are equal to N1 , where N is the dimensionality of the Hilbert space. 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.