CFT and the Tomato Soup Can

As always, the layman trying to develope the mathematical views?:)

Greg Kuperberg on Sep 15th, 2005 at 12:11 pm

Conformal maps of the Earth are a great introduction to complex analysis. If you identify the Earth with the Riemann sphere, then the Mercator map is exp(i*z), while the quincuncial projection is a Weierstrass elliptic function. Or you could view it as a 2-to-1 conformal projection from a torus to a sphere with four ramified points. I imagine that it is relevant to one-loop calculations in string theory in that guise.

At what level has this map then progressed if we held such views to the "horizon and boundary conditions." That is now replaces what we talk about of earth, and now relay the mass consideration to events in the gravitational field? Has the mathematic hypothesized now, gone through a revision, and needed support of mathematical views?


Campbell's Soup Can A. Warhol

What mathematics would move our perception to the gravitational views seen there? Gary Horowitz relays the outside label of a can of a soup as the conformal surface, while the soup, the spacetime fabric?

On planet Earth, we tend to think of the gravitational effect as being the same no matter where we are on the planet. We certainly don't see variations anywhere near as dramatic as those between the Earth and the Moon. But the truth is, the Earth's topography is highly variable with mountains, valleys, plains, and deep ocean trenches. As a consequence of this variable topography, the density of Earth's surface varies. These fluctuations in density cause slight variations in the gravity field, which, remarkably, GRACE can detect from space.

So one would look at topography as something much different then what is laid out on this globe as "hills and valleys"?

So now this map, has this extra feature to it.

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 correspondance between states in our four dimensional world and states in higher dimensions. From a positivist viewpoint, one cannot distinquish which discription is more fundamental.

Pg 198, The Universe in Nutshell, by Stephen Hawking

While on this topic it behooves me to think of the "horizon" and the mathematical construct that has taken us there. While we see to explain the nature of the effect in a fifth dimensional view, it had been reduced to "temperature" as a relation of this conformal view?

"D-branes provide the fundamental quantum microstates of a black hole that underlie black hole thermodynamics"

As much as one would try and ignore this position, you cannot get away from the mathematics or the approach and what this has culminated too.

I like Peter and his no nonsense views, but he has gone to far in rejecting the basis of "mathematical dialogue" in face of what D brane issue had been taken too?

Why would he reject mathematics on the one hand demonstrative of a particular point of view to which it has developed, then, ignore what position it had taken both string theory and Lee Smolins attempts at the disciption of the blackhole dynamics, from the views of that horizon?

With regards to the conformal field theory approach. While I am in my infancy, I recognize the views of Bekenstein Bound, and the hologrpahical approach. One must first learn to crawl, then walk I know, but how indeed does one get to the vision held, when he himself(who ever you like) cannot explain how such a mathematics like string theory, arose to help with our views of reality?

In 1919, Kaluza sent Albert Einstein a preprint --- later published in 1921 --- that considered the extension of general relativity to five dimensions. He assumed that the 5-dimensional field equations were simply the higher-dimensional version of the vacuum Einstein equation, and that all the metric components were independent of the fifth coordinate. The later assumption came to be known as the cylinder condition. This resulted in something remarkable: the fifteen higher-dimension field equations naturally broke into a set of ten formulae governing a tensor field representing gravity, four describing a vector field representing electromagnetism, and one wave equation for a scalar field. Furthermore, if the scalar field was constant, the vector field equations were just Maxwell's equations in vacuo, and the tensor field equations were the 4-dimensional Einstein field equations sourced by an EM field. In one fell swoop, Kaluza had written down a single covariant field theory in five dimensions that yielded the four dimensional theories of general relativity and electromagnetism. Naturally, Einstein was very interested in this preprint .

While one may use sites to give indicative values ot the information, can we ignore these assumptions mathematically driven. It paved the way for how we view things that we did not see before. Go ahead reject it then:)

Are we not looking for the Trigger?:)

Atlas and Proton-proton Collisions

Depth of Perception

I am responding to the link here on Cosmic Variance and the related article, Cosmic Violence. I do not want to tie up their space, so my "further response" is being given here.

I speak of Glast in the context of that "Window on the Universe" view. This helps to orientate our deeping recognition of those events, but does not include the realization of where high energy considerations are taking us as well.:)

What is happening at the beginning of our Universe? High energy implications and lower energy determinations reveal prospective views about that same universe? How is it such a view created by such particle collisions could not be drawn to a certain time in our universe?

By getting to the "high energy times", we are also getting to the circle (think the planck epoch to now) valuation of that early universe? There are always results of energy dissipaton of these early cosmological events, so it needed a consistant way in which to look at this?

The machine, dubbed ATLAS (A Toroidal LHC ApparatuS), is one of four facilities to be located at a powerful accelerator, the Large Hadron Collider (LHC), now under construction near Geneva, in Switzerland.

If we were to accept the circle and strong curvature as evident from our early universe considerations, (think of the circle and the planck epoch diagram as a blackhole?), then what happens when our views have been taken to suspersymmetrical points of view and the whole picture becomes locked within the model computation that Andrey Kravtsov does for us. The relaization is that this circle when taken down to planck has extremely strng gravitational considerations, and when and how do we reach this level of consideration on the time and birth of this universe?

IN Regards to Mathematical Constructs

Such an article presented by Peter Woit (How Much Mathematics Does A Theoretical Physicist Need To Know?), had me thinking in terms of what the quoted italicized statement below might mean in terms of the consistancy of mathematics developed?

http://www.math.columbia.edu/~woit/wordpress/?p=256#comment-4918(my comment below)Click on post and you now see the numbered posts alignment. What's the point?

Plato said:

If the Horizon exists as a mathematical construct, would we dissallow any mathematical counterpart that would lead from this, to incorporate other perspectives?

"D-branes provide the fundamental quantum microstates of a black hole that underlie black hole thermodynamics"

Developement of the mathematics would have been consistent then in how strng theory had developed?

So we know getting to the depth of perception necessary, had to include physics views here in order to develope the framework. High energy consideration could not have done it on it's own, so the topic is masked in theoretical definitions that we are not to accustomed too?:)

Yet it deals with a specific time frame in the developement of the early universe that is below Planck length. Below the "Planck epoch" (this holds a measureable time frame just after the beginning of the universe?)is the realization and "time valuation" that we assign this new perspective view, when we take physics in hand and abstract mathematics to it's fruitation?

While the link has been maintained to Peter Woits Blog, the post has not. It had been supplemented by Dickt's post.

This won't deter the documents and valuation of what string theory had to offer, and refused acknowledgement by Peter Woit to the progress, such developements might have taken string theory too?:)Tricky post like I wrote, acknowledges not only string theories position but Lee Smolins pursuate as well:)

So, Where was I?

Looking at the horizon as a "mathematical construct" we certainly take our abtract issues seriouly don't we?


Black Hole in Search of a Home

A team of European astronomers has used two of the most powerful astronomical facilities available, NASA's Hubble Space Telescope and the European Southern Observatory's (ESO) Very Large Telescope (VLT) at Cerro Paranal, to find a bright quasar without a massive host galaxy. Quasars are powerful and typically very distant sources of prodigious amounts of radiation. They are commonly associated with galaxies containing an active central black hole.

The team conducted a detailed study of 20 relatively nearby quasars. For 19 of them, they found, as expected, that these supermassive black holes are surrounded by a host galaxy. But when they studied the bright quasar HE0450-2958, located some 5 billion light-years away, they could not find evidence for a host galaxy. This, the astronomers suggest, may indicate a rare case of collision between a seemingly normal spiral galaxy and a much more exotic object harboring a very massive black hole.

The paper on HE0450-2958 will be published in the Sept. 15, 2005 issue of Nature.





Static, Uncharged - Schwarzschild Black Holes.

RS = 2MG/C²


M: mass of the black hole

G: 6.67 x 10^-11

C: 3 x 108

(When an object is compressed below its Schwarzschild radius (RS), it becomes a black hole.)

Static, Charged - Reissner-Nordström Black Holes





Rotating (Kerr) Black Holes, Charged and Uncharged







So:



Curvature:

From Strings to Cosmic Web

From November 30 to December 2 a conference will be held in Groningen about the origins and structure of the Universe. Astrophysicists will meet theoretical physicists, whereby astrophysical evidence for the fundamental parameters describing the Universe will be confronted with current ideas on fundamental physical laws.

Types of Blackholes

Now the statement below is important from one perspective that is not to my mind explained very good. I mean, taken from the public views, how is it such a thing like the blackhole could exist, and what scientific validations do we have for it.

This is an important question, as we learn from the statement below that this is all a mathematical construct, yet it has moved many avenues of research to build upon what we know in terms of issues about what is emitted from the horizon.

Thus far, all that we know of a black hole and its properties are mathematical deductions. The event horizon, for instance, is purely a mathematical constructProject Members from CCSP02 Semester 2, 2000-2001

How advance then our mathematical constructs become, if such realities have been merged in the mathematics, to have it detail a world in cosmology, that enlists what could happen in a geometrical valuation system. What would implore K values determined in the Friedmann equations, in the determination of our universe? Such universal implications detail further insight to determinations of curvatures parameters, that leads the mind to incorporate something much more dynamical in the geometrical nature of those same collapsing stars.

As the star is of a finite mass, there comes a time when its nuclear fuel is exhausted and as a result, the outward pressure due to radiation decreases, allowing the gravitational force to compress the star inward. The contraction of the core results in an increase in temperature which allows the remaining nuclear material to be used as fuel and thus yet again increasing the outward pressure such that hydrostatic equilibrium is once again established. The star is thus saved from further collapsed but only for a while.

This idea and nature of the "corner of the room", had me wonder how could such a thing quiver the nature of the spacetime fabric, if we did not realize that this vacuum had some truer nature to the implication of events that happen so far away in our early times. That we could have found such evidence in the here and now.

So of course such extravaganze, is in our measures of what LIGO can do or LIsa in all it's glory had been the theoretcial approach of the Wheeler's and Kip Thornes of our day, that we now implore the quest for such infomration.

Then why not too the idea that such a vacuum reveallled in our measure could have left evidence in how this spacetime will stretch with regards to that gravitational measure? So we look for these deviation in what might have been implied in those extra dimensions?

Now true to it all this mathematical construct has produced an amazing set of circumstance as show here that leads humanity to develope and proceed along some schedule as to becoming aware of the nature of our reality?

Quark Gluon Plasma

So how far back to the beginning, and if we had thought supersymmetry could exist, would it be in the most perfect fluid?

This form of matter is called quark-gluon plasma or QGP. Like its name suggests, QGP is a "soup", or plasma, of quarks and gluons.

(see physics primer)

RHIC Scientists Serve Up “Perfect” Liquid

“The truly stunning finding at RHIC that the new state of matter created in the collisions of gold ions is more like a liquid than a gas gives us a profound insight into the earliest moments of the universe,” said Dr. Raymond L. Orbach, Director of the DOE Office of Science.

Also of great interest to many following progress at RHIC is the emerging connection between the collider’s results and calculations using the methods of string theory, an approach that attempts to explain fundamental properties of the universe using 10 dimensions instead of the usual three spatial dimensions plus time.

Dr. Raymond L. Orbach
“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.”

So the issue is which blackholes would help point towards this supersymmetrical view that I jest in the Ipod post and the ipod that forms the perfect fluid? So this idea then about which blackhole has to have found some value in what I assign the new Ipod technology, that takes back to a time near the beginning of the universe.

Some say if you have to explain the joke then it sort of devalues the joke. Not in this case if you move forward with it, and see what the latest is in research. Sort of "sets the stage" as I allude too, in this other article of cosmic variance's.

A simple jesture is the question of course (Clifford reminds us here) and without it, how can you move perception forward? It's kind of hard to do that on your own, limited by the current knowledge one might have. So you in essence look forward to those areas that help direct this knowledge. For those who want to rehash the ID debate, only add fuel to the fire for the believers. Better to let it die it's own death and watch for the merits of scientific valuation that is brought forth through media. Speak directly to this only, and the refutation will be it's measure by it's own design.



What conditions would have allowed such a scene to be developed in supersymmetrical view, that I had wondered, could such a perfect fluid be the example needed? What blackholes hole would allow such a view to be carried down to this level in gold ion collisions, that we might see the results of string theory, as a useful analogy in the discernation of what can now be brought forward for inspection. As to the credibility of what string/M-Theory proposes?

Give value to string theory where previous comments on the nature of experimental research has lacked luster for this approach? The name choosen for the new Ipod model was specific, as it provided for the idea that we can take this supersymmetrical reality closer to the beginning of this universe and use the BPS blackhole nature for this conisdertaion and resulting fliud nature realized?

What conditions would provide for such a reality?

So of course by incinuation what is the nature of this BPS Blackhole that I am refering. That will be the issue on the next post created.

Mission Impossible?

Tom Cruise tackles the new world of Mission's Impossible III. What kind of recording system will he use? You got it, the illustrous Ipod? :)

Plato said:

Hey I got one for you. You remember mission impossible. Well in this case, your only able to use the ipod once, then it turns into a super liquid.

It wouldn't be right to give a older paper for inspection of Gerard's and not to include current present day assessment on the issues here. Ipodmanship has run it's course, so we'll have to wait for Clifford to update:)

But in the mean time, Bps blackhole sets up the idea of supersymmetrical valuation?

Plato said:

It’s called a “BPS Ipod”. This would surely be a “hotty and a smoothy”?

Gerard t' Hooft:

In particular the gravitational interactions are responsible for the unitarity of the scattering against the horizon, as dictated by the holographic principle, but the Standard Model interactions also contribute, and understanding their effects is an important first step towards a complete understanding of the horizon’s dynamics. The relation between in- and outgoing states is described in terms of an operator algebra. In this paper, the first of a series, we describe the algebra induced on the horizon by U(1) vector fields and scalar fields, including the case of an Englert-Brout-Higgs mechanism, and a more careful consideration of the transverse vector field components.

New Conceptualization: The Distance on the Brain:)

Now again before you jump to conclusions and say what a crackpot I am, listen to what I have to say about how I see in the coordinates assigned to the corner of the room. I give explicit idealizations in terms of measure, yet in these same quadrants, something much more had to be realized.

I accept the theoretical position of what the vacuum might mean from the beginning of time (?), or that it has always existed, and that events, are recognized from it's quivering in the very nature of that space-time fabric. But more then this the example below, asks not that you focus on the membrane that is demonstrated but of what causes this membrane to act as it does.

You see this is what sort of transfixes me to such views, where such distances are connected, even though there are problems with this view. Elasticity of a kind stretches far beyond our imaginations, to have gravity explain itself in what the bulk might represent in the space of all things. Bubble nucleation takes on new meaning here, all the while discrete things attract our attention in this world, there is something happening beyond the seen here, to understand what is not seen is very much real too.

Stretching the Brain

Quantum Gravity: The Blackhole

Drawing Plane and Coordinate Systems More information is given here in Wiki.

There is no "distance" separating cosmological events, from the cubic centimeter in the corner of the room? I have to tell you why I see this, and what lead me to conclude such a thing. As I relay at bottom of page, this will be the subject of the next posted thread.

Imagine spreading such malicious comments as those in bold below?:)

Brian Greene

Sure. One of the strangest features of string theory is that it requires more than the three spatial dimensions that we see directly in the world around us. That sounds like science fiction, but it is an indisputable outcome of the mathematics of string theory. So the question is, where are these extra dimensions? One suggestion is that they're all around us, but they're small relative to the dimensions that we directly see and therefore are more difficult to detect.

I guess the link to source is good enough sometimes but not the page with which the url exists?:)

Sometimes all it takes is a concept to fuel the direction with which we might presume to deal with this world of the spacetime fabric. Brian Greene surmizes, and in a synoptic mode aligns our view for consideration, or a Lee Smolin, in developing Three roads, previews quantum gravity approaches for consideration. This "lineage", is developed in this sense.

The Fabric of the Cosmo, by Brian Greene, is a good source for inspiration, on my "The Fifth Dimension, is the Spacetime Fabric." I am gone in a whisper, and advancement is placed for those who will exceed our limitation in how we percieve the world. This is the way it has always been. On and upward.:)

Good people like Gerard t'Hooft help direct our attention in a most appropriate way, even amidst the ramble of rejection of any theoretical position. Once the comment is established, then indeed we move ahead to wonder and draw the conclusions we do, with a whole page of such reasoning. This whole blog is filled with this central idea.

Imagine molecules in the corner cubic centimeter of the room( nice visulaization for a strting point), and all that exists in this space is contained, all, the information of the universe at large? Would I have triggered ideas in the notion that Pierre Auger seen something unusual in cosmic interactive features of our current earth, as a playing field for particle reductionism? In face of LHC and all the wonderful toys that have been produced to extend vision in a reductionistic world? You have to remember John Ellis here, is how I ascent to views in these two different ways.

Gerard t' Hooft:

The predominant force controlling large scale events in the Universe is the gravitational one. The physical and the mathematical nature of this force were put in an entirely new perspective by Albert Einstein. He noted that gravitation is rooted in geometric properties of space and time themselves. The equations he wrote down for this force show a remarkable resemblance with the gauge forces that control the sub-nuclear world as described in the previous paragraph, but there is one essential difference: if we investigate how individual sub-atomic particles would affect one another gravitationally, we find that the infinities are much worse, and renormalization fails here. Under normal circumstances, the gravitational force between sub-atomic particles is so weak that these difficulties are insignificant, but at extremely tiny distance scales, of the order of 10-33 cm, this force will become strong. We are tempted to believe that, at these tiny distance scales, the fabric of space and time is affected by quantum mechanical phenomena, but exactly how this happens is still very mysterious. One approach to this problem is to ask: under which circumstance is the gravitational force as strong as it ever can be? The answer to this is clear: at the horizon of a black hole. If we could understand the peculiar physical phenomena that one expects at the horizon of a black hole, and if we could find a meaningful description of its quantum mechanical laws, then perhaps this would open up new perspectives.

Smolins interpretive stance of the blackhole horizon( glast determnations fuel this venture into recognition of a discrete approach to measure,) in what is emitted on a cosmological scale. Others who paved the way for this horizon problem, take us back, Hawking, to the pre-established roads to wonder, where today does subject sit? How well in minds has this conclusion played out, that we have ventured forth in a wonderful way to approach this in such a theoretical fashion. That only "pure thought", mathematics, could have paved the way of where physics will continued on in physical interpretation.

I will introduce the idea of this "membrane analogy in the cubic centimentor:)" for further consideration, shortly after I attend to getting wood fuel for the winter months today.

Looking Under The Lamp Post