The Black Hole Final State

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.

"Lubos Motl:

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?




Lee Smolin:

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.

Liminocentric Structures: Which Circle do you Belong Too?

If conceived as a series of ever-wider experiential contexts, nested one within the other like a set of Chinese boxes, consciousness can be thought of as wrapping back around on itself in such a way that the outermost 'context' is indistinguishable from the innermost 'content' - a structure for which we coined the term 'liminocentric'.

As most know "Liminocentric structure" will have been defined here then? I like to think this goes back much further in our natures, and to recognize this pattern, much as Brian Greene might have spoken too, in article above one would have ot venture into it to understand.



Then why would I inject past historical views here to current research? It is a issue of wholeness and bringing resolution to the camps of LQG and Strings. If you look at the circle here in an expansitory view. The circle as a point, deals with particle reductionistic principals as well as dealing with General Relativity on a cosmological scale. They both deal with gravity from their respective positions. What are their strengths and weaknesses?

I will be away for about two weeks and a much needed break, so I hope people will explore this avenue, for it is the basis of my research in understanding this interchange between, depending on which circle you belong, two ends that need to come together and in this regard, LQG and String theory might have found this unification, but from which different ends?



There is no end, and it is continous by nature?

One harmonious possibility is that string enthusiasts and loop quantum gravity aficionados are actually constructing the same theory, but from vastly different starting points. That each theory involves loops-in string theory, these are string loops; in loop quantum grvaity, they're harder to describe nonmathmatically, but. roughly speaking, they'r elementray loops of space-suggests there might be a connection. This possibility is further supported by the fact that on a few problems accessible to both, sucha s blackhole entrophy, the two theroies agree fully. And on the question of spacetime's constittuents, both theories suggest that there is some kind of atomized structure. Page 490, Fabric of the Cosmos by Brian Greene

To me this connection lies in how we interpret the circle and this variation in between them, is a powerful topological structure form that is understood as we see the question of which circle is which? From which space quantum mechanically to cosmologicazlly. In terms of that atomized look, to the nature of relativity through that cosmo.

The last departing statement in Brian Greene's book sets the stage for how the string community has to orientate its view from one perspective, while LQG needs to orientate theirs. This is used, to point to ISCAP and the introduction Brian Green gives us.

Look at Page 493 of his book, and then look here.

The goal of ISCAP is to bring together theoretical physicists, astrophysicists, and observational astronomers to address key problems in particle physics and cosmology that require a broad confluence of expertise and perspective.

Even the good intention would have failed to see this connection between both camps, but I see that having it explained as such here, I hope to point to something much deeper in our psyche that warrents the orientation to mathematcial structures that underlies our consciousness. As subjective a view as it might seem to some, there are reasons that I support such views, and without hurting the purity of the direct mathematical relations, I needed to bring the article and title of this entry forward for consideration. It is a necessary part of wholeness that the dicrete natures and the wonderful views of continuity would share some relationship even in the bulk of our considerations?

Which Circle do you belong too? You are one, and the same are you not?:)



"Nothing to me would be more poetic; no outcome would be more graceful ... than for us to confirm our theories of the ultramicroscopic makeup of spacetime and matter by turning our giant telescopes skyward and gazing at the stars," Greene said.


The Elegant Universe, by Brian Greene, pg 231 and Pg 232

"But now, almost a century after Einstein's tour-de-force, string theory gives us a quantum-mechanical discription of gravity that, by necessity, modifies general relativity when distances involved become as short as the Planck length. Since Reinmannian geometry is the mathetical core of genral relativity, this means that it too must be modified in order to reflect faithfully the new short distance physics of string theory. Whereas general relativity asserts that the curved properties of the universe are described by Reinmannian geometry, string theory asserts this is true only if we examine the fabric of the universe on large enough scales. On scales as small as planck length a new kind of geometry must emerge, one that aligns with the new physics of string theory. This new geometry is called, quantum geometry."

B Field Manifestations

Ah what the heck......I'll bite....let the skeptics converge in a harmonic convergence:)

Nigel Hitching

Sylvester Surfaces and the B field?

Are you a "gold fish" or a "Ant world person?" Are you a pigeon? Have you sent your vision into the things of nature, to explore it's potential in other ways?



Figure 2. Clebsch's Diagonal Surface: Wonderful

Rupert SheldarkeThe morphic fields of mental activity are not confined to the insides of our heads. They extend far beyond our brain though intention and attention. We are already familiar with the idea of fields extending beyond the material objects in which they are rooted: for example magnetic fields extend beyond the surfaces of magnets; the earth’s gravitational field extends far beyond the surface of the earth, keeping the moon in its orbit; and the fields of a cell phone stretch out far beyond the phone itself. Likewise the fields of our minds extend far beyond our brains.

The Faraday's, the Gauss's, the Reimanns learnt to see in other ways? Does this imply some spooky valuation beyond the confines of the brain's home?

"The gravitons behave like sound in a metal sheet," says Dvali. "Hitting the sheet with a hammer creates a sound wave that travels along its surface. But the sound propagation is not exactly two-dimensional as part of the energy is lost into the surrounding air. Near the hammer, the loss of energy is small, but further away, it's more significant."

So is it just a brain thingy, or is this "field real?" Some were not so unintelligent to "refute the aether" at one time. For we now understand what exists in the real spacetime valuations, beyond what is held to the brane, and see bulk manifestation, as real and populated. AS a extension, beyond those surfaces.

The Sound of Billiard Balls

Savas Dimopoulos:

Here’s an analogy to understand this: imagine that our universe is a two-dimensional pool table, which you look down on from the third spatial dimension. When the billiard balls collide on the table, they scatter into new trajectories across the surface. But we also hear the click of sound as they impact: that’s collision energy being radiated into a third dimension above and beyond the surface. In this picture, the billiard balls are like protons and neutrons, and the sound wave behaves like the graviton.

Are we execising the brains ability to get this toposense and geoemtrical revelation beyond straight lines and distances between points?

So what is a chaldni plate?:) helps you to see how sound is of value beyond the confines Faradays magnetic field lines, as real effects of that same magnet, and resonant coupling points. Exercising the potential of banging metal, helps the mind point to other places too. Playing pool, does too?:)

Expansitory Valuation of a Circle with Gravity?

If conceived as a series of ever-wider experiential contexts, nested one within the other like a set of Chinese boxes, consciousness can be thought of as wrapping back around on itself in such a way that the outermost 'context' is indistinguishable from the innermost 'content' - a structure for which we coined the term 'liminocentric'.

Now I refer to this often, because of this connection between inner content and outer context. I know it deals with a consciousness and subjective valuation, but it seems very important when you think of what could happen between the compactification of the sun or earth and its size, once dealt to a blackhole?

In this setting of the spherical mass M, we define the value rS = 2M as the Schwarzschild radius of the mass. If the mass has a radius less than rS, then it is called a black hole. In that case, the surface r =rS is called the event horizon of the black hole.

Sometimes the determination of this value has to be seen in light of how we see the gravitational properties of the energy. Windings then, come of value in KK tower representations, and hence images of circles joining other circles can represented in a tree?

It's trunk and branches. Although this imagery is a little different, the base of the larger circle has pointed in the right direction, if we think of flat euclidean space, where no gravity potential can exist? Although we like to think there is never this abscence of harmonic oscillation, it would have to be assumed that it had always existed and can never really be zero?

Had I then complicated the ideal of this circle by recognizing this value from the ground up, had I lost sight of it's root system, and how well it is buried in the earth. How shall I explain this, but as a inverse function of growth? This is not possible. So we see where the seeding had the potential to rise from the earth in one form, and proceed to move into the air, as a phase from it's early unverse beginnings?

So where does this motivation then exist in the design?

A circle of radius r has a curvature of size 1/r. Therefore, small circles have large curvature and large circles have small curvature. The curvature of a line is 0. In general, an object with zero curvature is "flat."

See LIminocentric structure here for a deeper explanation. Greene's emphasis helps in other aspects as well. How can a six foot man exist in such a tiny circle?:)

The familiar extended dimensions, therefore, may very well also be in the shape of circles and hence subject to the R and 1/R physical identification of string theory. To put some rough numbers in, if the familiar dimensions are circular then their radii must be about as large as 15 billion light-years, which is about ten trillion trillion trillion trillion trillion (R= 1061) times the Planck length, and growing as the universe explands. If string theory is right, this is physically identical to the familiar dimensions being circular with incredibly tiny radii of about 1/R=1/1061=10-61 times the Planck length! There are our well-known familiar dimensions in an alternate description provided by string theory. [Greene's emphasis]. In fact, in the reciprocal language, these tiny circles are getting ever smaller as time goes by, since as R grows, 1/R shrinks. Now we seem to have really gone off the deep end. How can this possibly be true? How can a six-foot tall human being 'fit' inside such an unbelievably microscopic universe? How can a speck of a universe be physically identical to the great expanse we view in the heavens above? (Greene, The Elegant Universe, pages 248-249)

So in the one sense(or topo-sense) I see similarities between planes and cyliners and they are isometrically equivalent, and then ideas of topological design spoken of, in the idea of the coffee cup becoming a donut, and all of a sudden this kind of geometry had taken a turn for perspective that deals with other things then I am normally accustom too.

So on a csomological level we get this sense of curvature and here to further exploit this understanding the means to such equations supplied for this endeavor.



But taken to the tree level(potato plant):) and interactive features of windings how shall we interpret such energies, but by those same windings? That the seed of the plant held a greater design for growth, yet it is in the seed this plant and it's energy contained that it's futre is realized. I know this plant thingy is a bad analogy for how such circle and the arrow of time. Would a flower be better? How does anything loop back onto itself and replay this universe all over again?

Physics at this high energy scale describes the universe as it existed during the first moments of the Big Bang. These high energy scales are completely beyond the range which can be created in the particle accelerators we currently have (or will have in the foreseeable future.) Most of the physical theories that we use to understand the universe that we live in also break down at the Planck scale. However, string theory shows unique promise in being able to describe the physics of the Planck scale and the Big Bang.

So when you read Lubos's entry here in Nasa's Collider you have to wonder? How on a physical level, the circle implied( our universe now after the first three minutes) could have ever recieved the connotation of it's valuation in a collision as large as we see in that situation? But you have to understand this connection between Gia and the "plate he hits", or the mirror moon measures and of course, there are simultaneous question about dimensional perspectve and compacted circles that raised the undertanding beyond current standards in our everyday world. Much like understanding strong curvature in a circle. How far can this be taken?

You would not think this post here would have ever had anything to do with Lubos simple statement about Nasa'a Collider, but it does?:) I guess it depends on which circle you belong too?

Anomalistic Features of Gold Fish and Ant World?

I was reading Mark Trodden's blog called, "Orange Quark" for reading, and he pointed out the following article. In Praise of Hard Questions, by Tom Siegfried

Geometric basis underlying science? I see this tendency of many to the Halls of records, museums, and whatever you like, to keep current for all us folks outside academia.

These are important historical correlations to draw from. These are wonderful connections to the fathers/mothers of science. Distinctive historical figures who embue science with their particular inflections and bend.

Should we dismiss the motivations of those who are driven by "anomalistic behaviors"? Remember Einstein in his youth and the compass? What are we ignorant of in such a case?

We know well, that such measures, if not supported, cannot be easily removed from the memories. Can be relinguished to subjective interpretations. Should not be ruled inadmissable:)Yet, it can drive the motvation of youth in that case t hard and fsat rules of order?

Had there ever been a time where a scientist had seen something that ran contrary to everything they know? It had to be at the front line, or how would anomalistic valuation had ver been entertained? Had been seen by a reputable scientist and held in the idealization of the Einstein who at his time, "lacked comprehension" but was moved.

Here I point out David Gross's statement and context supplied by Tom Siegfried .

Science's greatest advances occur on the frontiers, at the interface between ignorance and knowledge, where the most profound questions are posed. There's no better way to assess the current condition of science than listing the questions that science cannot answer. "Science," Gross declares, "is shaped by ignorance."

Yes I think we all understand.

So indeed we see then that all the forebears of our science then had something in common as they sought to geometrically express the abstract, and in my line of thinking, runs the Wunderkammer models. These are hard and concrete models in glass cases.

Maxwell understood this in Gauss and Faraday, and Einstein, understood this in Riemann? Sachherri elucidating beyond the limits of Euclids postulates 1-4, paved the way for a new dynamcial world? So how strange indeed that Sean Carroll would give us a sixty second explanation on extra dimensions. Have we eluded to an "aspect of mind" in abstraction?

Extra dimensions sound like science fiction, but they could be part of the real world. And if so, they might help explain mysteries like why the universe is expanding faster than expected, and why gravity is weaker than the other forces of nature.
Three dimensions are all we see -- how could there be any more? Einstein's general theory of relativity tells us that space can expand, contract, and bend. If one direction were to contract down to an extremely tiny size, much smaller than an atom, it would be hidden from our view. If we could see on small enough scales, that hidden dimension might become visible.

Sean, what shall you say to Peter Woit, who might say to you. "We are not Ants?"

So this sixty second explanation now presents itself, for the "mantra induced introspection" that one wonders, what the heck might Sean be talking about? Is there a world somewhere that that exists much like "ant world" in which we take part in?

How strange indeed then that the mind has been taken to Ant World, so that we may see, the angles of perception greatly ehanced for us? Where in the real world, walking straight lines is a "balancing act" when we engage the dynamcial qualites of science, that although engineered, also speak to the dynamcial relation underlying our everyday world.

So how shall such analogies then prepare us for the hard questions of science? Can we see now where such abstractions has moved science and the road shall lead us through to the idea of KLein's Ordering of Geometeries? Have we entered a new dynamcial realm of ant world, and together with Michio Kaku, created the new animated "goldfish world" as well, who see very much different then we see from the bridge?

Who is it that now sees and send our minds into "ants and goldfish?"

String Connection?

The possibility of a connection between string theory and RHIC collisions is unexpected and exhilarating,” Dr. Orbach said. “String theory seeks to unify the two great intellectual achievements of twentieth-century physics, general relativity and quantum mechanics, and it may well have a profound impact on the physics of the twenty-first century.”

In this narrow class of theories, the hot plasma in the 4D theory corresponds to a black hole in the 10D equivalent description, which matches very well with Stephen Hawking's prediction that black holes have temperature. Moreover, there is a direct relationship between vibrations in the plasma, such as sound waves, and vibrations of the black-hole horizon. For example, when an object is dropped into the black hole in 10D, the equivalent picture in 4D is a hot, expanding region that dissolves into a plasma. Using this equivalence, various theorists, including the present author, have deduced that if such plasmas were real, they would be almost perfect liquids.

Since Maldacena's conjecture does not apply to QCD, however, the viscosity of the real quark-gluon plasma cannot be computed via string theory. This makes the RHIC announcement that the viscosity of its plasma is comparable to the values one finds from string-theory calculations even more surprising. If this is true, the quark-gluon plasma created at RHIC could be the most perfect fluid in nature. This in itself is an interesting fact, but it could also indicate that string theory has some relation to real QCD. However, we first need more quantitative evidence from RHIC, such as an upper bound on the viscosity.

Blackholes at RHIC


A statement from RHIC theoretical nuclear physicist Dmitri Kharzeev:

Alice

The existence of such a phase and its properties are key issues in QCD for the understanding of confinement and of chiral-symmetry restoration. For this purpose, we intend to carry out a comprehensive study of the hadrons, electrons, muons and photons produced in the collision of heavy nuclei. Alice will also study proton-proton collisions both as a comparison with lead-lead collisions in physics areas where Alice is competitive with other LHC experiments

Science and it's Geometries?

On the post preceding this one, although we talked about the nature of the symmetries in action, and within context of the Calabi Yau, there is a relatiosnhip that must be drawn to other quarters of our perceptions to help orientate not only this drive for understanding energy production, but it's basis in geometry as well.

The cyclical notion driving Turok and Steinhardt, had to be found in our meddling with the likes of M theory and the brane world happenings with those points? How could such a dynamcical world arise from such a point, and it leads into all kinds of wonderful journies of the abstract. What will we find those who hold tightly to the rail from seeing width and depth, as one looks over this large abyss called the Grand Canyon.

When a gas bubble in a liquid is excited by ultrasonic acoustic waves, it can emit short flashes of light suggestive of extreme temperatures inside the bubble. These flashes of light, known as 'sonoluminescence', occur as the bubble implodes, or cavitates. Now Didenko and Suslick show that chemical reactions occur during cavitation of a single, isolated bubble,and they go on to determine the yield of photons, radicals, and ions formed. (Photo credit: Kenneth S. Suslick and Kenneth J. Kolbeck)

Today's agreement to build the ITER project in Cadarache, France, is an important milestone for Europe. It is not only the energy sector that will benefit from this decision: I expect ITER to also boost widespread positive consequences in areas like nanotechnology or material research. ITER will hugely benefit our Lisbon goals, creating more jobs, more research and more global competitiveness", said today Paul Rübig MEP (A), EPP-ED spokesman in the Committee on Industry, Technology, Research and Energy (ITRE) of the European Parliament

You see it's just more then a issue about fusion? :) Any "cyclical nature" that would exemplfy not only the universe, but models of geometry used, "theoretically must be" very important from those other mathematical perspectives.

If such a exchange, as a blackhole could arise from such a collapse, no longer able to fuel it's momentum outward as the sun in expression, then how so the collapse of the blackhole now representing the fusion that drives the energy in our sun? Our universe? You see such a trait in most universal design, and in the production of energy, had to be drawn for perspective to recognize motivations to the extent this universe would turn back on itself?

How strange indeed, then that this universe rapidly expanding, might signal the inevitable collapse that we might have seen in the suns, could also point towards a deeper comprehension of our own universe in action??

Energy in/Energy out, and if you ignite the process, how would sustain it? Compression factors in blackholes, contain a lot of potential, and if you turn them inside/out, this strange speculation rises about the energy/matter relation?


The Universe as an ecosystem: Much like biologists, astronomers trace the flow of matter and energy from one form to another in order to understand the dynamics of the entire system and how it evolves. (Credit: L. Whitlock (GSFC))

Well, microstate blackholes are in production, as well as events going on in nature. So the sun is of value in other ways, that the colliders can't touch, but on a value largely reduced from the energies needed from that same sun? You see, you would need quite a large collider that could not exist here on earth?:)

There is of course a fear of the blackhole production as well, but such collapse would be significant and part of the larger understanding of what is natural in our daily lives.

Pierre Auger is very instrumental in understanding this design?:)



See:

Bubble Nucleation

Special Lagrangian geometry

Dr. Mark Haskins

On a wider class of complex manifolds - the so-called Calabi-Yau manifolds - there is also a natural notion of special Lagrangian geometry. Since the late 1980s these Calabi-Yau manifolds have played a prominent role in developments in High Energy Physics and String Theory. In the late 1990s it was realized that calibrated geometries play a fundamental role in the physical theory, and calibrated geometries have become synonymous with "Branes" and "Supersymmetry".

Special Lagrangian geometry in particular was seen to be related to another String Theory inspired phemonenon, "Mirror Symmetry". Strominger, Yau and Zaslow conjectured that mirror symmetry could be explained by studying moduli spaces arising from special Lagrangian geometry.

This conjecture stimulated much work by mathematicians, but a lot still remains to be done. A central problem is to understand what kinds of singularities can form in families of smooth special Lagrangian submanifolds. A starting point for this is to study the simplest models for singular special Lagrangian varieties, namely cones with an isolated singularity. My research in this area ([2], [4], [6]) has focused on understanding such cones especially in dimension three, which also corresponds to the most physically relevant case.

I am execising the geometrical tendencies here in how Sylvester surfaces might have revealled the interior space of a Reimann sphere( Calabi Yau rotations exemplified and complete), while these points located on the sphere's surface, brane, reveal a deeper interactive force within this sphere. Again I am learning to see here, hopefully it's right. The bloggers out there who work in this direction are most helpful, P.P Cook, Lubos Motl and others, who help point the way.

Differences in the gravitational forces speak directly to dimensional relevances In Lagrangian, by association to the energy valuations? Euclids postulate from 1-4, had to be entertained in a new way, from a non-euclidean world of higher dimensions? It was well evident that supergravity, would find solace in the four dimensional relevances of spacetime? How did Kaluza and Klein get there? Cylinders?

Yet the dynamical world of the way in which the satelitte can move through space helps one to adjust to how these dynamcial avenues can propel this satelitte through that same space. Circular orits chaotically predictable, yet quite diverse shown in the poincare model representation, shows how bizzare the ability of the Lagrangian points become. Can one see well with this new abstractual quality?

Einstein's equations connect matter and energy (the right-hand side) with the geometry of spacetime (the left-hand side). Each superscript stands for one of the 4 coordinates of spacetime; so what looks like one equation is actually 4 x 4 = 16 equations. But since some are repeated there are really 10 equations. Contrast this with the single gravitational law of Newton! That alone gives a hint of the complexity of these equations. Indeed, they are amongst the most difficult equations in science. Happily, however, some exact solutions have been found. Below we discuss one such exact solution, the first, found in 1916 by Karl Schwarzchild.

So it was important to understand how this view was developed further. The semantics of mathematical expression was a well laid out path that worked to further our views of what could have been accompished in the world of spacetime, yet well knowing, that the dynamcial revealled a even greater potential?



So now you engaged the views inside and out, about bubble natures, and from this, a idea that is driven. That while Michio Kaku sees well from perspective, the bridge stood upon, is the same greater comprehension about abstract and dynamical processes in that same geometrical world. Beyond the sphere, within the sphere, and the relationship between both worlds, upon Lagrangian perspective not limited.

Placed within the sphere, and this view from a point is a amazing unfoldment process of views that topological inferences to torus derivtives from boson expressed gravitational idealizations removed themself from the lines of circles to greater KK tower representations?

The following is a description of some of the models for the hyperbolic plane. In order to understand the descriptions, refer to the figures. They may seem a bit strange. However, a result due to Hilbert says that it is impossible to smoothly embed the hyperbolic plane in Euclidean three-space using the usual Euclidean geometry. (Technical note: In fact it is possible to have a C^1 embedding into R^3, according to a 1955 construction of Nicolaas Kuiper, but according to William Thurston, the result would be "incredibly unwieldy, and pretty much useless in the study of the surface's intrinsic geometry."[William Thurston, "Three Dimensional Geometry and Topology," Geometry Center Preprint, 1991, p.43.]) Since there is no such smooth embedding, any model of the hyperbolic plane has to use a different geometry. In other words, we must redefine words like point, line, distance, and angle in order to have a surface in which the parallel postulate fails, but which still satisfies Euclid's postulates 1-4 (stated in the previous article). Here are brief descriptions of three models:

This process had to be thought of in another way? Point, line, plane, became something else, in terms of string world? M theory had to answer to the ideas of supergravity? How so? Great Circles and such? Topological torus forms defined, inside and out? Completed, when the circle become a boson expressed? A point on a brane now becomes something larger in perspectve? Thanks Ramond.

Periodic Impingement Orbits:Interference Patterns?

Path through S0(3) Now you must know that the views of this space had association to the >ATLAS, that the paths defined are real intermsof the Calorimetric view, that such appearances are mapped from one state to another by the plate coveringa nd measures of the energy's involved. By taking this covering to symbolize this space? gap we realize how diverse the interactions can be by the implications of the energy used? So we have various idealization here about how the rotational attributes could have been defined in a greater world expression beyond the confines of those same plates

I was looking for the right image to show this rotation and quickly I find Greg Egan's for consideration here, but I had another one as well. When I find it will bring it back for consideration

Shall I call it a real world fantasy that Alice steps into the "mirror world" and we find that exultation of the story again being use to exemplify the world where things enter, and in this strange space/gap, the photon comes out on the otherside?

G -> H -> ... -> SU(3) x SU(2) x U(1) -> SU(3) x U(1). You have to realize that such emergence into the views of universal formulations, has to have some associative response from the quantum world to see that such relevance in the cosmological particpations could have ver pointed to the motivation of these universes coming into being, that it would go through a phase tranasformation relevant to each particle discription? Is this correct? This presented itself iw ay of seeing that stretches the mind imaginations tht I wonder have I indeed gone off the deep end.

Young might have been very happy with this story of Alice in Wonderland, and the wonder of the path integrals, as part of a greater comprehension and revitalization exemplified not just in the feynnmenian toy model production, but of one that enlists a wonderful non-eucldiean world set aside for each and every wonder of entrance and departure into new phase realizations?

It was realized some time ago by Glashow [5] that the orthopositronium system provides one sensitive way to search for the mirror universe. The idea is that small kinetic mixing of the ordinary and mirror photons may exist which would mix ordinary and mirror ortho positronium, leading to maximal ortho positronium - mirror orthopositronium oscillations.

In Albrecht Durer and His Magic Square, I point to what was accomplished in use of an image and artistically rewritten Melencolia II
[frontispiece of thesis, after Dürer 1514]by Prof.dr R.H. Dijkgraaf

Now for me, and I constantly have to remind people that I am junior here in my peceptions, that it would be of my greatest pleasure to expicitly speak to the undestanding of what happens, not only in how we see these lagrange points in space, but also reveal the coming into being of the photon and it's disappearance in a way that involves this complete 720 degree rotation.

I don't know how else to explain what I am seeing other then to find examples and here it would have been most fruitful in looking at what the question mark, where we find the version Melencolia II containing this fundmnantal question about what rises from the standard model and how this is dealt with.

S0 how would define this straight line and measure, but to see it's existnce as a supersymmetrical reality, and as a Calabi Yau model of expression, and find in this same rotational value complete, as a map written, as it is below.

The Photon comes into existance here




The photon is represented here.

So you see this chaos exemplified in a way that the Lorentzian butterfly comes into it's own, that such impngement would find itself relating to each other and trasnferance from state to another? Also, as we look at this, in contrast symmetreical idealization has to have another view reveal itself in the link to the image below where we see this lorentzian butterfly, also mapped in relation to the transferance from one state to another. The Planck Epoch helps here.

How would one mapped unpreditabiltiy in chaos to have seen something grow out of it into a solvable part of some symmetrical views of the gap?

I seemed to have lost the wording that popped into my mind last night. Try as I may, it is one of those times where you repeat it to yourself so that you don't loose it, but being half asleep, this solution was presented for what ever reason.



Is it quite part of what I was looking at, I am not sure. So of course I go looking to see if anything rings a bell?

Thematic Resolutions

It is of course with some concern that any scientific mind, held to the established rules of his organizational, "motto of acceptance of the stringent rules of science" would allow such room, as to embue the human being with qualities greater then, the value assigned to subjective valuations. A church of reason that finds itself distasteful to the inquiry of life, and sanction it to the discourse of valued scientific principals that those of Strings and LQG fight back and forth with.

It's okay, we won't be fooled:)

Is it a coming to terms with the features we see in our own makeup as children, that we might sight the significant memory of that same childhood. What stuck, that you would have seen this course of action, no less then what held a Einstein in the mystery of the world, to understand it is a real and wonderful world of the forces that we do not readily see, yet we know well it directs the sciences in our world.


Nuances

The Alchemy of Creativity and the Social Artist.

Briggs speaks of themata as informing the lives of many geniuses. Beginning with themata for example --what are they, what is their deeper purpose and meaning? I see them as patterns of creation for which we are specially tuned, each of us tuned differently by the special sense organs in ourselves which pick up variations on these themes throughout the world. The famous example of the child Einstein and his fascination with the magnetic operation of the compass which then influenced his entire life of looking for the electromagnetic field in the unified field of reality. Each of us then is given as our gift a kind of guiding visionary theme which recurs throughout our life, and when we attend to it as an ally and helper, it gives us unique perspectives on working with reality.

God's Equation, by Amir D. Aczel, Pg 14

From a early age, young Albert showed great interest in the world around him. When he was five years old, his father gave him a compass, and the child was enchanted by the device and intrigued by the fact the needle followed a invisible field to point always in the direction of the north pole.Reminicing in old age, Einstein mentioned this incident as one of the factors that perhaps motivated him years later to study the gravitational field.

Is there some deeper force that evades our thinking, that it could have transcended the world of science, to know that envisioning the capabilities beyond those we enlist in our psychological reasoning, has real physical results manifest. It has been the direction and question that has existed most in my mind, that the world of the discrete, had many explanations before such solidification could have ever existed in the mind of concrete things.

So while such a view is held to a space beyond the limitations of math's design, such views revealled in the Wunderkammer were realistic abilties of the mind to incorporate the envisioning abilites beyond the euclidean defintions. "Straight lines and course of measure," that there could exist other forms beyond the limitations Einstein sought to describe for us in the gravity explanation given in General relativity.

It is well understood that the adventures lead too here were very instrumental in the realization that the noneuclidena geometires were very well adpatable to the view of Faradya, Gauss and Riemann in further defining ths geometric tendency a sa basis of exploration that today we are taken inot the abstract space of mind.

So what was the motivating force and we find that the culminative effect of a life exists, for those who by name are defined. Where is this basis that we can call forth eth elemental table of Mendelev to say that al things arise and her eare the concrete constructs of mind embellsih in the material world?

The light behind, in the analogy of Plato's cave, sets up the thinking in how issues from the source[the fire]( and here it might be referred to the fifth dimension)shines in its radiation. How is form realized?

Betrayal of Images" by Rene Magritte. 1929 painting on which is written "This is not a Pipe"

The jest here recognizes, that a picture of, and the real pipe are very different indeed. How is "form" percieved from perspective. The picture of the pipe and the real pipe are different things? And yet in this comparison, there is a third aspect as the idea?

It was a attempt to define this emergent property of existance that all of it could have been derived from some basis? Background dependant/ independant and two views that enlist the funcitonabiltiy to discourse, the thoughts held?

So it is well understood that such motivations that drive the character have some motivating force beyond what we had understood in the complete individual, called a "Peter Woit" or a "Lubos Motl", to find that such forces govern one or the other in it's drive for expression. One the justice that would not milead scoiety from someintelligent design feature to have gauaged society to a standard of being, better undertsood with a greater idealism set? Or of th efire that instigates a lubos Motl to question and position and valid it no less then the "peacemaker" might have revealled in the just and reasonable society?

So we have exposed a greater potential relaization that not only is motivated from perspectve, to find the creation of the universe is no less the creative adventure of the soul in i';s own design, for fruitation. So where exists this idea who find itself of the universe, as it unfolded in it's own motivation?