Quantum geometry differs in substantial ways from the classical geometry underlying general relativity. For instance, topology change (the "tearing" of space) is a sensible feature of quantum geometry even though, from a classical perspective, it involves singularities. As another example, two different classical spacetime geometries can give rise to identical physical implications, again at odds with conclusions based on classical general relativity.Brian Greene

Is there not some way presented by Susskind which can help one approach understanding of what is going on in the blackhole by incorporating his "thought experiment" in relation to the entanglement process?

So of course questions about "the horizon" are interesting.

Consider any physical system, made of anything at all- let us call it, The Thing. We require only that The Thing can be enclosed within a finite boundary, which we shall call the Screen(Figure39). We would like to know as much as possible about The Thing. But we cannot touch it directly-we are restricted to making measurements of it on The Screen. We may send any kind of radiation we like through The Screen, and record what ever changes result The Screen. The Bekenstein bound says that there is a general limit to how many yes/no questions we can answer about The Thing by making observations through The Screen that surrounds it. The number must be less then one quarter the area of The Screen, in Planck units. What if we ask more questions? The principle tells us that either of two things must happen. Either the area of the screen will increase, as a result of doing an experiment that ask questions beyond the limit; or the experiments we do that go beyond the limit will erase or invalidate, the answers to some of the previous questions. At no time can we know more about The thing than the limit, imposed by the area of the Screen. Page 171 and 172 0f,Three Roads to Quantum Gravity, by Lee Smolin

TWO UNIVERSES of different dimension and obeying disparate physical laws are rendered completely equivalent by the holographic principle. Theorists have demonstrated this principle mathematically for a specific type of five-dimensional spacetime ("anti–de Sitter") and its four-dimensional boundary. In effect, the 5-D universe is recorded like a hologram on the 4-D surface at its periphery. Superstring theory rules in the 5-D spacetime, but a so-called conformal field theory of point particles operates on the 4-D hologram. A black hole in the 5-D spacetime is equivalent to hot radiation on the hologram--for example, the hole and the radiation have the same entropy even though the physical origin of the entropy is completely different for each case. Although these two descriptions of the universe seem utterly unalike, no experiment could distinguish between them, even in principle. by Jacob D. Bekenstein

The old version of string theory, pre-1995, had these first two features. It includes quantum mechanics and gravity, but the kinds of things we could calculate were pretty limited. All of a sudden in 1995, we learned how to calculate things when the interactions are strong. Suddenly we understood a lot about the theory. And so figuring out how to compute the entropy of black holes became a really obvious challenge. I, for one, felt it was incumbent upon the theory to give us a solution to the problem of computing the entropy, or it wasn't the right theory. Of course we were all gratified that it did. Black Holes and Beyond: Harvard's Andrew Strominger on String Theory

So we have these diagrams and thought processes developed from individuals like Jacob D. Bekenstein to help us visualize what is taking place. Gives us key indicators of the valuation needed, in order to determine what maths are going to be used? In this case the subject of Conformal Field Theory makes itself known, for the thought process?

Holography encodes the information in a region of space onto a surface one dimension lower. It sees to be the property of gravity, as is shown by the fact that the area of th event horizon measures the number of internal states of a blackhole, holography would be a one-to-one correspondence between states in our four dimensional world and states in higher dimensions. From a positivist viewpoint, one cannot distinguish which description is more fundamental.Pg 198, The Universe in Nutshell, by Stephen Hawking

So we are given the label in which to speak about the holographic notions of what is being talked about in the case of the blackhole's horizon.

Campbell's Soup Can by Andy Warhol Exhibited in New York (USA), Leo Castelli Gallery

Spacetime in String Theory-Dr. Gary Horowitz, UCSB-Apr 20, 2005

This year marks the hundredth anniversary of Einstein's "miraculous year", 1905, when he formulated special relativity, and explained the origin of the black body spectrum and Brownian motion. In honor of this occasion, I will describe the modern view of spacetime. After reviewing the properties of spacetime in general relativity, I will provide an overview of the nature of spacetime emerging from string theory. This is radically different from relativity. At a perturbative level, the spacetime metric appears as ``coupling constants" in a two-dimensional quantum field theory. Nonperturbatively (with certain boundary conditions), spacetime is not fundamental but must be reconstructed from a holographic, dual theory. I will conclude with some recent ideas about the big bang arising from string theory.

The purpose of this note is to provide a possible answer to this question. Rather than the radical modification of quantum mechanics required for pure states to evolve into mixed states, we adopt a more mild modification. We propose that at the black hole singularity one needs to impose a unique final state boundary condition. More precisely, we have a unique final wavefunction for the interior of the black hole. Modifications of quantum mechanics where one imposes final state boundary conditions were considered in [6,7,8,9]. Here we are putting a final state boundary condition on part of the system, the interior of the black hole. This final boundary condition makes sure that no information is “absorbed” by the singularity.Gary T. Horowitz and Juan Maldacena,

See: Stringy Geometry

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