Mathematics is not the rigid and rigidity-producing schema that the layman thinks it is; rather, in it we find ourselves at that meeting point of constraint and freedom that is the very essence of human nature.- Hermann Weyl
It was a nice vacation and now being back, I see Lubos is clarifying some issues here for us to consider.
However, Hawking's semiclassical calculation leads to an exactly (piecewise) thermal final state. Such a mixed state in the far future violates unitarity - pure states cannot evolve into mixed states unitarily - and it destroys the initial information about the collapsed objects which is why we call it "information loss puzzle". A tension with quantum mechanics emerges.
The Gepner point demonstrates greater potential recognition of the brane world understandings and two dimensional views from a five dimenisonal developmentment for those who do not like such abstract adventures P.P. Cook helps to enlighten us on this subject.
So have I done justice to the developing perspective, that we are now ready to take what what demonstrated, and move it to a greater format for those who will lead us laymen through the world of the abstract mathematics? To help us enjoy what was mathematically unenduring for those not gifted to see the B field manifestaion, is a continuance of what we like to engage at higher dimensional perspectives. And really, it is all about imagery is it not?
It was worry about the possibility that string theory would lead to the present situation, which Susskind has so ably described in his recent papers, that led me to invent the Cosmological Natural Selection [CNS] idea and to write my first book. My motive, then as now, is to prevent a split in the community of theoretical physicists in which different groups of smart people believe different things, with no recourse to come to consensus by rational argument from the evidence.
You must understand the state of thinking and dualistic nature that continues to force minds to engage the process, and this quest for wholeness, between two thoughts that are part and parcel of the same thing? Relativity and Quantum Nature. The larger circle is RElativity, and the smaller, the quantum nature. LQG and STring work from their respective positions.
So do we select the basis for this model, and find that LQG and Strings are formulated on principals embedded in association with the blackhole topic? This throws light back again on a topic that has been shared more then once by such trends in thinking as Lubos exemplfies for us, and again directs our thoughts towards Lenny Susskind and Lee Smolin, in contrast to each other.
I see people are teaming up appropriately, such as Cosmic Variance, and this of course has already been lead by Lubos and Peter's contrast to each other. Whether some like to speculate on co-joining for such comparsions on the validity of strings, versus no strings approach, as resolutions, had already been developed while we see this new means to develope, much as Brain Greene and others in ISCAP foundations principals.
So of course onward and forward, we push the topic and the expertise for the layperson like me, that we see and continue to find, developmental processes appropriately gathering for future thoughts shared? Again too, we see Quantum Diaries has indeed served it's purpose more then once in what John Ellis and other's have shared, have open the doorway to how we see such developmental attitudes expanding in contrast to the larger circle of possibilties.
See John's latest entree and for me, hitting big objects and particle collisions still open the mind for the natural cosmic interactive processes ongoing in nature around us.
Anyway back to the title of this post. I have some thinking here to do.
Gary T. Horowitz1 and Juan Maldacena,2
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.
If indeed we started to think about the point on the brane then what kind of simplification can be drawn so that those less enclined to such abstract thinking could find a greater potential to that dimensionnal thinking?
(a) Compactifying a 3-D universe with two space dimensions and one time dimension. This is a simplification of the 5-D spacetime considered by Theodor Kaluza and Oskar Klein. (b) The Lorentz symmetry of the large dimension is broken by the compactification and all that remains is 2-D space plus the U(1) symmetry represented by the arrow. (c) On large scales we see only a 2-D universe (one space plus one time dimension) with the "internal" U(1) symmetry of electromagnetism.
Here such thoughts begin to form around the idealization of computer graphics imagery developed and leading in this idealization of this two dimensional screen. We see where the likes of Thomas Banchoff demonstrate where such new roads to the developing insight ot this imagery can be seen in Smolins views of the Bekenstein Bound, that we we now understand a greater potential exists in how we view the screen, and what is being described in the blackhole horizon?
Let me show this image again, for greater clarity of what I mean.