Perspective of the Theoretical Scientist

Most people think of "seeing" and "observing" directly with their senses. But for physicists, these words refer to much more indirect measurements involving a train of theoretical logic by which we can interpret what is "seen."- Lisa Randall

There are certain advantages to the theoretical perspective that can best portray the concepts of the world they live in with what appears, however abstract, with the minds value of image solicitor impressionism which helps the minds state of acceptance. So it had to be explained first.

Cubist art revolted against the restrictions that perspective imposed. Picasso's art shows a clear rejection of the perspective, with women's faces viewed simultaneously from several angles. Picasso's paintings show multiple perspectives, as though they were painted by someone from the 4th dimension, able to see all perspectives simultaneously.

Cubist Art: Picasso's painting 'Portrait of Dora Maar'

P. Picasso Portrait of Ambrose Vollard (1910)

 M. Duchamp Nude Descending a Staircase, No. 2 (1912)

J. Metzinger Le Gouter/Teatime (1911)

The appearance of figures in cubist art --- which are often viewed from several direction simultaneously --- has been linked to ideas concerning extra dimensions:

As if, looking at it from a larger perspective. If you stand outside of the image and see that it is capable of illuminating many angles of perspective. This helped us to see that it is derived from a much larger understanding then what is solidified to the everyday we live in.

For the artist it was a bold move to understanding that perspective could help us see Mona Lisa's smile as moving with us as we move around. So that was the challenge then was to appreciate the value of this artistic push into how we see as to understanding the road non- euclidean took was meet by people as well to culminate in a geometrical transitional form


Hyperspace: A Scientific Odyssey

A look at the higher dimensionsBy Michio Kaku

"Why must art be clinically “realistic?” This Cubist “revolt against perspective” seized the fourth dimension because it touched the third dimension from all possible perspectives. Simply put, Cubist art embraced the fourth dimension. Picasso's paintings are a splendid example, showing a clear rejection of three dimensional perspective, with women's faces viewed simultaneously from several angles. Instead of a single point-of-view, Picasso's paintings show multiple perspectives, as if they were painted by a being from the fourth dimension, able to see all perspectives simultaneously. As art historian Linda Henderson has written, “the fourth dimension and non-Euclidean geometry emerge as among the most important themes unifying much of modern art and theory."

Posted by Plato at Thursday, March 24, 2005 

Then, it quickly comes home to mind that maybe what is given,  lets say in context of Lee Smolin's road to Quantum Gravity of the thing will help us quickly see the value of describing "the space of an interior" with what is happening on the screen/label.

Spacetime in String Theory

More then just a Bekenstein imagery to illustrate a conformal approach to describing what are the contends of the tomato soup can from it's label.



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

It was necessary to see that the geometric used here were helping to shape perspective around not only "time travel" but a means to an end to use mathematical perspective to actually mean something in relation to understanding our world. A way to describe abstract concepts that were correlated with the progression of those mathematics. Klein's ordering of geometries then take on a new meaning as we move deep into the world we all know and love.

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 .

I quickly divert the attention to the world of Thomas Banchoff because it is an extraordinary move from all that we know is safe. It is not lost to some computer animator world that one engages loses the self in the process? It is also to show that what Lee Smolin tried to distance himself from, was in fact seeking to find itself understood in this way. Concurrent agreement that theoretics was trying to arrive at a consensus of different approaches saying the same thing?

Monte Carlo methods are a class of computational algorithms that rely on repeated random sampling to compute their results. Monte Carlo methods are often used in simulating physical and mathematical systems. Because of their reliance on repeated computation of random or pseudo-random numbers, these methods are most suited to calculation by a computer and tend to be used when it is unfeasible or impossible to compute an exact result with a deterministic algorithm.^[1]

Monte Carlo simulation methods are especially useful in studying systems with a large number of coupled degrees of freedom, such as fluids, disordered materials, strongly coupled solids, and cellular structures (see cellular Potts model). More broadly, Monte Carlo methods are useful for modeling phenomena with significant uncertainty in inputs, such as the calculation of riskdefinite integrals, particularly multidimensional integrals with complicated boundary conditions. It is a widely successful method in risk analysis when compared with alternative methods or human intuition. When Monte Carlo simulations have been applied in space exploration and oil exploration, actual observations of failures, cost overruns and schedule overruns are routinely better predicted by the simulations than by human intuition or alternative "soft" methods.^[2]

For me it had to make some sense such transference from that artistic impressionism help to direct the mind to the ways and means of understanding quantum gravity was being inspected in terms of Monte Carlo methods to understanding. These had a surface value in my mind to an accumulate acceptance of the geometry and methods used to model this understanding.




So you understand now how we arrived at an interpretation of the value of lets say Dyson's opinion about how we might view Riemann's Hypothesis?

Dyson, one of the most highly-regarded scientists of his time, poignantly informed the young man that his findings into the distribution of prime numbers corresponded with the spacing and distribution of energy levels of a higher-ordered quantum state. Mathematics Problem That Remains Elusive —And Beautiful By Raymond Petersen

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DNA Computing

DNA computing is a form of computing which uses DNA, biochemistry and molecular biology, instead of the traditional silicon-based computer technologies. DNA computing, or, more generally, molecular computing, is a fast developing interdisciplinary area. Research and development in this area concerns theory, experiments and applications of DNA computing See:DNA computing

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Clifford of Asymptotia is hosting a guest post by Len Adleman: Quantum Mechanics and Mathematical Logic.

Today I’m pleased to announce that we have a guest post from a very distinguished colleague of mine, Len Adleman. Len is best known as the “A” in RSA and the inventor of DNA-computing. He is a Turing Award laureate. However, he considers himself “a rank amateur” (his words!) as a physicist.

Len Adleman-For a long time, physicists have struggled with perplexing “meta-questions” (my phrase): Does God play dice with the universe? Does a theory of everything exist? Do parallel universes exist? As the physics community is acutely aware, these are extremely difficult questions and one may despair of ever finding meaningful answers. The mathematical community has had its own meta-questions that are no less daunting: What is “truth”? Do infinitesimals exist? Is there a single set of axioms from which all of mathematics can be derived? In what many consider to be on the short list of great intellectual achievements, Frege, Russell, Tarski, Turing, Godel, and other logicians were able to clear away the fog and sort these questions out. The framework they created, mathematical logic, has put a foundation under mathematics, provided great insights and profound results. After many years of consideration, I have come to believe that mathematical logic, suitably extended and modified (perhaps to include complexity theoretic ideas), has the potential to provide the same benefits to physics. In the following remarks, I will explore this possibility.

So what about the Missing Energy?

"Death, so called, is but older matter dressed
In some new form. And in a varied vest,
From tenement to tenement though tossed,
The soul is still the same, the figure only lost." Poem on Pythagoras, Dryden's Ovid.

It is unfortunate to have endured the constant flutter of disbelief(cry of pseudoscience) as to what is possible in a given space, that we can say that we do not really have all the facts to it's understanding, yet, to know that in this region, new physics will be produced.

It is also unfortunate to have observed a whole generation of string theorists who have undergone this constant rebuttal and berating over and over again while standing strong to the "educative values" undermined by those who saw no benefit too. You maintained the perseverance of a "thought domain that cover regions within the valleys" to be speaking about a time just after the big bang. How would the normal population of scientists know this?

Thanks to the high collision energy and luminosity of the LHC, the ATLAS detector will be capable of revealing the existence of extra spatial dimensions in some substantial region of parameter space. The talk will summarize recent studies from the collaboration on different possible signals predicted by models where the dimensions are "large", where they are of size ~TeV^-1 or where they are "warped". These signals include direct emission of Kaluza-Klein states of gravitons, virtual effects of graviton exchange and gauge boson excitations. We shall also discuss the possibilities of observing black holes. mini review for search of eXTRA Dimentions

Now this question is an important one to me, because it is based on the amount of energy used in the collision process, and what is to come out of that collision process as tracks, adds up to so much energy. If these two numbers do not equal in parity then where has that extra energy gone?

This has always been a fundamental question to me of where I thought "new physics was to be found" and to have Tammaso Dorigo confirm this is quite a statement indeed of what is leading perspective in terms of what is to be measured and what is going to be measured in the proposed LHC experiments.

Missing Energy Kicks New Physics Models Off The Board

The signature of large missing energy and jets is arguably one of the most important avenues for the study of potential new physics signatures at today's hadron colliders.

The above concept marks an interesting turn of events: the years of the glorification of charged leptons as the single most important tools for the discovery of rare production processes appears behind us. The W and Z discovery in 1983 by UA1 at CERN, or the top quark discovery by CDF and DZERO in 1995 at Fermilab, would have been impossible without the precise and clean detection of electrons and muons. However, with time we have understood that missing energy may be a more powerful tool for new discoveries.

Missing energy arises when a violent collision between the projectiles -protons against antiprotons at the Tevatron collider, or protons against protons at the world's most powerful accelerator, the LHC- produces an asymmetric flow of energetic bodies out of the collision point in the plane orthogonal to the beams: a transverse imbalance. This is a clear signal that something is leaving the detector unseen. And it turns out that there is a host of new physics signals which can do precisely that.

A large amount of missing transverse energy may be the result of the decay of a leptoquarks into jets and neutrinos, when the latter leave undetected; or from the silent escape of a supersymmetric neutral particle -the neutralino- produced in the chain of decays following the production of squarks and gluinos; or it may even be due to the escape of particles in a fourth dimension of space -an alternative dubbed "large extra dimensions". see more in linked title above)

Now this is the thing that has troubled me most about scientists who are working and in the know, had not realized the necessity of pushing perspective back to a time to the first moments of the big bang(not just Steven Weinberg's first three minutes but of the microseconds just after the big bang) in order to understand what we are working on in terms of unification, and of where the products of this missing energy will spring forth from, as we move forward in the experiments to come.

The understanding then has always been in what is in that missing energy, to determine what new physics shall be, that such understanding was already there for the string theorist in their considerations. The contact point has already been defined for them, and reached two extremes. There is a reason why the missing energy escapes.

You had to know already where and what this "contact point meant" and what was to come out of it to know that dynamical qualities could exist in the big bang and where this big bang resides in the cosmos. That such energies can be reached there now. This required us to know that local events in the cosmos could contribute to the very nature of the cosmos and the state of the cosmos in the now. Like some cosmological constant "hidden and growing" in Omega.

To know that the dissipative results from micro collisions decaying fast too, did not mean we would be running short of the elements of this new physics either. It left it's remnants all around us to know that what can come out of such a collision point is not the story of the FLashForward scenario, but of things that travel through the earth to meet Gran Sasso and the likes. It was a whole plethora of particle disseminations that left missing energy around for us to explore in potential as some fictional substrate of the reality of nature that had not been seen before.

Heralded from the 21st Century: String Theory

I know not how, may find their way to the minds of humanity in Some Dimensionality, and may stir up a race of rebels who shall refuse to be confined to limited Dimensionality." from Flatland, by E. A. Abbott

It is sometimes important to know what race of rebels had been raised to realize that such a revolution in the making had started from a place of thinking that many others
began to think about as well?

Cycle of Birth, Life, and Death-Origin, Indentity, and Destiny by Gabriele Veneziano

In one form or another, the issue of the ultimate beginning has engaged philosophers and theologians in nearly every culture. It is entwined with a grand set of concerns, one famously encapsulated in an 1897 painting by Paul Gauguin: D'ou venons-nous? Que sommes-nous? Ou allons-nous? "Where do we come from? What are we? Where are we going?"

See here for more information.

It is important to know where such models began to influence the idea to generate theoretical model for an apprehension of how we view this universe? Given the study at hand here are the following people for consideration.

Whence began this journey and revolution?

LEONARD SUSSKIND:

And I fiddled with it, I monkeyed with it. I sat in my attic, I think for two months on and off. But the first thing I could see in it, it was describing some kind of particles which had internal structure which could vibrate, which could do things, which wasn't just a point particle. And I began to realize that what was being described here was a string, an elastic string, like a rubber band, or like a rubber band cut in half. And this rubber band could not only stretch and contract, but wiggle. And marvel of marvels, it exactly agreed with this formula.
I was pretty sure at that time that I was the only one in the world who knew this.

So we have to take stock of the movements that change democratic societies. To have found such governments will change and fall according to the plight of it's citizens in science. As it goes with "theoretical positions?"

Working to understand the development of the model in consideration was needed in order for one to understand why Lee Smolin methodology to work science from a historical perspective is one I favour as well. It is sometimes necessary to list these developmental phases in order to get to a position to speak with authority. Find that "with certainty" we can make certain comments? Find, we must be confronted again, to say, any progress will go from There.

The Revolution that Didn't Happen by Steven Weinberg

I first read Thomas Kuhn's famous book The Structure of Scientific Revolutions a quarter-century ago, soon after the publication of the second edition. I had known Kuhn only slightly when we had been together on the faculty at Berkeley in the early 1960s, but I came to like and admire him later, when he came to MIT. His book I found exciting.

Evidently others felt the same. Structure has had a wider influence than any other book on the history of science. Soon after Kuhn's death in 1996, the sociologist Clifford Geertz remarked that Kuhn's book had "opened the door to the eruption of the sociology of knowledge" into the study of the sciences. Kuhn's ideas have been invoked again and again in the recent conflict over the relation of science and culture known as the science wars.

So we know where the idea of science wars began do we not? What instigates conflict as a healthy perspective to progress of the sciences. We will see the story unfold within this blog.

For some reason people might of thought my views were just held to Lee Smolin and the work that I had been accumulating with regards to his views of the Universe. While I had shown the cover of his book countless times, I would like to say that I have accumulated "other books," like those of Brian Greene as well.

Does this make me an expert on the subject in question or what ever Lee Smolin has written? Of course not.

But the work I have been doing, has not been limited to what the authors themself have given to the public in their outreach writing books. I have been at this a few years now, so I would like people to think this is not just a jaunt of journalism, that has been given to the public in it's books but has been a labour of love to understand my place in the universe.

The Elegant Universe: Superstrings, Hidden Dimensions, and the Quest for the Ultimate Theory

The Elegant Universe: Superstrings, Hidden Dimensions, and the Quest for the Ultimate Theory (ISBN 0-375-70811-1) is a book by Brian Greene published in 2000 which introduces string theory and provides a comprehensive though non-technical assessment of the theory and some of its shortcomings.

Beginning with a brief consideration of classical physics, which concentrates on the major conflicts in physics, Greene establishes an historical context for string theory as a necessary means of integrating the probabilistic world of the standard model of particle physics and the deterministic Newtonian physics of the macroscopic world. Greene discusses the essential problem facing modern physics: unification of Einstein's theory of General Relativity and Quantum Mechanics. Greene suggests that string theory is the solution to these two conflicting approaches. Greene uses frequent analogies and mental experiments to provide a means for the layman to come to terms with the theory which has the potential to create a unified theory of physics.

The Elegant Universe was adapted for a three hour program in two parts for television broadcast in late 2003 on the PBS series NOVA.

Thanks Q9 for the link to "Elegant physicist makes string theory sexy." I was going to posted it the day when you gave it to me, but instead seeing that Clifford of Asymptotia had it (same day), I thought I wouldn't. But as fate has it I must.

The Fabric of the Cosmos: Space, Time, and the Texture of Reality (2004) is the second book on theoretical physics, cosmology and string theory written by Brian Greene, professor and co-director of Columbia's Institute for Strings, Cosmology, and Astroparticle Physics (ISCAP).[1]

Greene begins with the key question: What is reality? Or more specifically: What is spacetime? He sets out to describe the features he finds both exciting and essential to forming a full picture of the reality painted by modern science. In almost every chapter, Greene introduces its basic concepts and then slowly builds to a climax, which is usually a scientific breakthrough. Greene then attempts to connect with his reader by posing simple analogies to help explain the meaning of a scientific concept without oversimplifying the theory behind it.

In the preface, Greene acknowledges that some parts of the book are controversial among scientists. Greene discusses the leading viewpoints in the main text, and points of contention in the end notes. Greene has striven for balanced treatment of the controversial topics. In the end notes, the diligent reader will find more complete explanations relevant to points he has simplified in the main text.

Once you get this view of the gravitational connection between everything, the form of graviton, you get this preview of the bulk and what lensing may mean. It is hard not to think of "dimensional perspectives in relation to the energy" describing the particles of science in some way. Witten below in his "Strings Unravel" lets you know what string theory has accomplished.

Warped Passages is a book by Lisa Randall, published in 2005, about particle physics in general and additional dimensions of space (cf. Kaluza-Klein theory) in particular. The book has made it to top 50 at amazon.com, making it the world's first successful book on theoretical physics by a female author. See Where are my keys?

It's alway nice having one's own blog and nice that I can retained my dignity under the name of Plato. It keeps my personal life from being treated with disrespect at the whim of the stroke of a delete key. Of course I am willing to take my lumps understanding such a role as "older student." After being expose to the exchange between people in the tribe, it's thinking can do all kinds of damage to each other? But I would like to think that all sides remain cool to positions they hold in society

A Different Universe: Reinventing Physics from the Bottom Down by Robert B. LaughlinFrom the Publisher:

Why everything we think about fundamental physical laws needs to change, and why the greatest mysteries of physics are not at the ends of the universe but as close as the nearest ice cube or grain of salt.

Not since Richard Feynman has a Nobel Prize-winning physicist written with as much panache as Robert Laughlin does in this revelatory and essential book. Laughlin proposes nothing less than a new way of understanding fundamental laws of science. In this age of superstring theories and Big-Bang cosmology, we're used to thinking of the unknown as being impossibly distant from our everyday lives. The edges of science, we're told, lie in the first nanofraction of a second of the Universe's existence, or else in realms so small that they can't be glimpsed even by the most sophisticated experimental techniques. But we haven't reached the end of science, Laughlin argues-only the end of reductionist thinking. If we consider the world of emergent properties instead, suddenly the deepest mysteries are as close as the nearest ice cube or grain of salt. And he goes farther: the most fundamental laws of physics-such as Newton's laws of motion and quantum mechanics -are in fact emergent. They are properties of large assemblages of matter, and when their exactness is examined too closely, it vanishes into nothing.

See Laughlin, Reductionism, Emergence

Out of all this uncertainty that exists at the level with which we think about in "those dimensions" what value any constructive diagram if it did not lead you to the understanding of the building blocks that a condense matter theorist may describe as manifesting in our reality?

The Year is 2020 and that's our Eyesight

Columbia physicist Brian Greene inhabits a multiple-perspective landscape modeled after M.C. Escher's artwork in a scene from "The Elegant Universe," a public-TV documentary based on Greene's book.

Q: Hawking has said that there could be a “theory of everything” produced in the next 20 years, or by 2020. Do you get that same sense? Or will there ever be a theory of everything?

A: Well, I always find it difficult to make predictions that are tied to a specific time frame, because as we all know, one of the exciting things about science is that you don’t know when the big break is going to happen. It could happen tomorrow, it could happen 10 years from now, it could happen a century from now. So you just keep pressing on, making progress, and hope that you reach these major milestones — ideally in your own lifetime, but who knows? So I don’t know if 2020 is the right number to say. But I would say that string theory has a chance of being that unified theory, and we are learning more and more about it. Every day, every week, every month there are fantastically interesting developments.

Will it all come together by 2020, where we can actually have experimental proof and the theory develops to the point that it really makes definitive statements that can be tested? I don’t know. I hope so. But hope is not the thing that determines what will actually happen. It’s the hard work of scientists around the world.

But anyway onto what I wanted to say and "being censored" I couldn't.

Clifford is defending his position on how Lee Smolin and Peter Woit have assigned a "perspective view" to string theory as a modelled approach. As a theoretical discovery of science, Clifford from my view, had to show that this process is still unfolding and that any quick decision as to giving String theory such a final vote of opinion from Lee Smolin was premature. I have supported Clifford in this view because of where we had been historically in the past years that the formulation of string theory has been given.

D-Branes by Clifford V. Johnson

D-branes represent a key theoretical tool in the understanding of strongly coupled superstring theory and M-theory. They have led to many striking discoveries, including the precise microphysics underlying the thermodynamic behaviour of certain black holes, and remarkable holographic dualities between large-N gauge theories and gravity. This book provides a self-contained introduction to the technology of D-branes, presenting the recent developments and ideas in a pedagogical manner. It is suitable for use as a textbook in graduate courses on modern string theory and theoretical particle physics, and will also be an indispensable reference for seasoned practitioners. The introductory material is developed by first starting with the main features of string theory needed to get rapidly to grips with D-branes, uncovering further aspects while actually working with D-branes. Many advanced applications are covered, with discussions of open problems which could form the basis for new avenues of research.

While Clifford's book I do not have, I understand that the "second revolution" was necessary to help us move to consider where string theory was to take us. It was progressing in the theoretics as a model to help us see science assuming the ways in which such models adjust us to possible new views in science. Clifford may not of liked the implication of a Grokking of a kind that would refer to consuming model approaches and then becoming what you eat?

Clifford:

I’ve found that different people have different takes on what it means to have a “theory of everything”. There is a popular idea (perhaps the most common) that this somehow means that this theory will describe (at least in principle) all known basic physical phenomena (constituents and their interactions, if you like) once and for all. Others mean something less ambitious, a theory that consistently describes the four fundamental forces and the things that interact with them, achieving a unification of all the forces and phenomena that we currently understand. I personally think that the first idea of a theory of everything is rather naive, and my personal hunch (and bias from what I’ve learned about the history of science) is that there is simply no such thing.

So of course entertaining the idea of a "theory of everything" leaves a bad taste in some peoples mouth, and having them to reason that it is the naivity of such a thought, that I immediately felt insulted. Clifford saids,"this theory will describe (at least in principle) all known basic physical phenomena (constituents and their interactions, if you like) once and for all" and may have been the case for those less then spending the time and effort, would have probably been insulted as I was. I of course came to recognize the positive aspect of the second position Clifford assumes.

Bench Marks of theoretical Progress

Anyway there are positions that we can take when we look back and reassess everything that we have been doing in reading the public outreach, like so called "bench marks" to see if such progressions still have have a evolutionary way to go.

Edward Witten-Reflections on the Fate of Spacetime

Unravelling String Theory

But what is string theory? It may well be the only way to reconcile gravity and quantum mechanics, but what is the core idea behind it? Einstein understood the central concepts of general relativity years before he developed the detailed equations. By contrast, string theory has been discovered in bits and pieces — over a period that has stretched for nearly four decades — without anyone really understanding what is behind it. As a result, every bit that is unearthed comes as a surprise. We still don’t know where all these ideas are coming from — or heading to

See more here



So what shall we use to measure what had first seem so abstract in Susskind's mind as a "rubber band," or the start of Veneziano views on such strings at inception? We've come a long way.

Something that I perceived back in 2004 help to "shape my views on the way I speak" "today" allows for us to consider that strings take it's rightful place within the building blocks of matter, that following Robert Laughlins lead, it was that we shifted our times from the first three seconds of Steven Weinberg, to the "First three Microseconds" of strings within the process of the unfolding universe.

The resulting collisions between pairs of these atomic nuclei generate exceedingly hot, dense bursts of matter and energy to simulate what happened during the first few microseconds of the big bang. These brief "mini bangs" give physicists a ringside seat on some of the earliest moments of creation.

See How Particles Came to be?

While Laughlin may have not seen the continued relevance of particle reductionism it was leading to some amazing insights. I now wonder now, if held to the comparisons of this superfluid, how it would have appealed to him? I think Witten in last plate above recognized what had to be done.

What is the Observer's Reality?

"Death, so called, is but older matter dressed
In some new form. And in a varied vest,
From tenement to tenement though tossed,
The soul is still the same, the figure only lost." Poem on Pythagoras, Dryden's Ovid.

When your given a certain amount of energy to work with and all of it is accountable except for a some, what conlcusion are you to draw? Sensibly the mapping is done as to the tragetories of all particles, yet it just didn't add up at the end.

Oskar Klein (left) proposed in the 1920s that hidden spatial dimensions might influence observed physics. He poses with physicists George Uhlenbeck (middle) and Samuel Goudsmit in 1926 at the University of Leiden, the Netherlands. AIP Emilio Segrè Visual Archives

Mini Review on Search for Extra Dimensions With Atlas, by S. Ferrag

Thanks to the high collision energy and luminosity of the LHC, the ATLAS detector will be capable of revealing the existence of extra spatial dimensions in some substantial region of parameter space. The talk will summarize recent studies from the collaboration on different possible signals predicted by models where the dimensions are "large", where they are of size ~TeV^-1 or where they are "warped". These signals include direct emission of Kaluza-Klein states of gravitons, virtual effects of graviton exchange and gauge boson excitations. We shall also discuss the possibilities of observing black holes.

There is no doubt in my mind that the leanings towards mysticism should not have entered the picture when dealing with the science, as you say Sean. Through Education, working with the tangible, there will no doubt people who refuse this on a ideological grounds, as to it's misleadings to a better understanding.

If the concepts of GR are ever moved as they were in the perspective of Einstein's thought Experiment, I would think it would have had it's basis on a solid foundation, yet, it drew a conclusive results in the way we now deal with how we can look at the world?



While this may have appeared confusing, and misleading to people, without a deeper comprehension, it is not without some basis some of us would think about these things, and agree with Einstein.

So let's say that if such a basis was given to thethought experiment shown here, is thought of, would the thinking as to the substance of our very thoughts ever been considered in context of the way in which I had been thinking about these things?




If one had never followed the logic and geometry would it have made sense, that the analogy of Einstein's thought experiment, about a hot stove and pretty girl, would seem less then a viable concept, had Einstein never extended his thoughts from a basis, and foundation of GR? Gravity.

On the Effects of External Sensory Input on Time Dilation." A. Einstein, Institute for Advanced Study, Princeton, N.J.

Abstract: When a man sits with a pretty girl for an hour, it seems like a minute. But let him sit on a hot stove for a minute and it's longer than any hour. That's relativity.

As the observer's reference frame is crucial to the observer's perception of the flow of time, the state of mind of the observer may be an additional factor in that perception. I therefore endeavored to study the apparent flow of time under two distinct sets of mental states.

Methods: I sought to acquire a hot stove and a pretty girl. Unfortunately, getting a hot stove was prohibitive, as the woman who cooks for me has forbidden me from getting anywhere near the kitchen. However, I did manage to surreptitiously obtain a 1924 Manning-Bowman and Co. chrome waffle iron, which is a reasonable equivalent of a hot stove for this experiment, as it can attain a temperature of a very high degree. Finding the pretty girl presented more of a problem, as I now live in New Jersey. I know Charlie Chaplin, having attended the opening of his 1931 film City Lights in his company, and so I requested that he set up a meeting with his wife, movie star Paulette Goddard, the possessor of a shayna punim, or pretty face, of a very high degree.

Discussion: I took the train to New York City to meet with Miss Goddard at the Oyster Bar in Grand Central Terminal. She was radiant and delightful. When it felt to me as if a minute had passed, I checked my watch to discover that a full 57 minutes had actually transpired, which I rounded up to one hour. Upon returning to my home, I plugged in the waffle iron and allowed it to heat up. I then sat on it, wearing trousers and a long white shirt, untucked. When it seemed that over an hour had gone by, I stood up and checked my watch to discover that less than one second had in fact passed. To maintain unit consistency for the descriptions of the two circumstances, I rounded up to one minute, after which I called a physician.

Conclusion: *The state of mind of the observer plays a crucial role in the perception of time.*

Same with how GR is reduced from a "larger frame of reference(a quantum microscopic view)," how is it, the probability of any action could have been this one, as I write, or if some thought held to some systemic relation would have found relevance in the weight of our decisions, our choices? I used a scale then, heart and feather and if one associated the gravity of the situation to our thought patterns, how would this pan out in the thinking of emotive thoughts. The discoloration of pure colors, in our expression and emotively realized?

Einstein:Since there exist in this four dimensional structure [space-time] no longer any sections which represent "now" objectively, the concepts of happening and becoming are indeed not completely suspended, but yet complicated. It appears therefore more natural to think of physical reality as a four dimensional existence, instead of, as hitherto, the evolution of a three dimensional existence.

Fanciful, Yet working with Reason



You may not take your body with you but you will take the emotive realizations, and they can color our views for a time. If we knew how to take control of the positve expression and change our attitudes, I think this is what allows the circumstance to change(our future), if we only let the reactions govern our existance, nothing changes.

We are thinking beings then, making choices, about the way we will react in the future. Following such reactions to the source and continuing to distill them we will possibly find the truer core of the reactionary base with which to consult. What future changes we will take hold of. It doesn't all have to be negative. We don't have to surround ourselves with such paling colors.

Concepts of the Fifth Dimension

"Yet I exist in the hope that these memoirs, in some manner, I know not how, may find their way to the minds of humanity in Some Dimensionality, and may stir up a race of rebels who shall refuse to be confined to limited Dimensionality." from Flatland, by E. A. Abbott

Oskar Klein September 15, 1894 - February 5, 1977

Dealing With a 5D World

A black hole is an object so massive that even light cannot escape from it. This requires the idea of a gravitational mass for a photon, which then allows the calculation of an escape energy for an object of that mass. When the escape energy is equal to the photon energy, the implication is that the object is a "black hole."

Herein, I also make the assumption:

The Spacetime Fabric, "is" the Fifth dimension.

Now of course, how do such assumptions make their way into my thinking and visualizations that I do? The seeing, of what mathematics and it's symbology had done for those who might see the geometry of expression, as a very vital way of thinking in the abstract world of mind, analogous, to the computer screen in front of us?


Juan Maldacena:

The strings move in a five-dimensional curved space-time with a boundary. The boundary corresponds to the usual four dimensions, and the fifth dimension describes the motion away from this boundary into the interior of the curved space-time. In this five-dimensional space-time, there is a strong gravitational field pulling objects away from the boundary, and as a result time flows more slowly far away from the boundary than close to it. This also implies that an object that has a fixed proper size in the interior can appear to have a different size when viewed from the boundary (Fig. 1). Strings existing in the five-dimensional space-time can even look point-like when they are close to the boundary. Polchinski and Strassler1 show that when an energetic four-dimensional particle (such as an electron) is scattered from these strings (describing protons), the main contribution comes from a string that is close to the boundary and it is therefore seen as a point-like object. So a string-like interpretation of a proton is not at odds with the observation that there are point-like objects inside it.

(Wikipedia 23 April 2006)

Similarly, in general relativity, the fourth dimension is manifested in observable three dimensions as the curvature of path of a moving infinitesimal (test) particle. 't Hooft has speculated that the fifth dimension is really the spacetime fabric.

Linked paragraph above was pointed out to a link you to further thoughts on this. It was a strange revelation of sorts to think that such a process could lead you to such thinking, as well, as leading one to understand how General Relativity becomes a result of of String theory.

It just made so much sense as I watched this developement take place in this geometrical extension of thought, that to a beginning, from a point to a line to a plane, was raised in mind, as a short cut to the brane world understandings. I really do not undertsand how I made this jump, but never the less, it took me to a fifth dimensional referencing.



The work of Banchoff helped in this understanding. In using image production, our 2d computer screens, as example, shows the work we are doing in the abstract space of mind.

While I am still ever the student, such thinking moved from the ideas of General Relativity, and it's geoemtrical nature, moves one into the dynamical regions of thought. Held, in regards to those curvatures. I just tend to see them in this way after understanding the "geometrical nature." So too, the undertanding of General Relativity means, and in this assumption, "gravity" becomes the terminology that I see in the dynamcis of that universe.

Can I help seeing the thought of humanity so capable in the mind, to relate choices to the heart and the feather weighting truth, that I also had come to see the gravity of that situation? IN such thoughts, Einsteins analogy of the Pretty girl always come to mind. It was a conceptual leap of sorts, as well as beautifully laid out model of GR as to our understanding in terms of what gravity means.

From strong to weak, and all the understanding of the place, where a flat plane of which no gravity exists, is a place where such transitions take place in my mind. Is this true or not? The very thinking of brane developement lead me to think in a 2 dimensional framework, yet I am well aware of the fifth dimensional views that this framework supplies. Is it wrong? I would have to rely on competent readers of the Brane world to have them say ye or nay, as to the thoughts being portrayed here.

(Wikipedia 23 April 2006)

In physics and mathematics, a sequence of N numbers can be understood to represent a location in an N-dimensional space. When N=5, one of these numbers is sometimes colloquially called the fifth dimension. This usage may occur in casual discussions about the fourth dimension, which, in the context of physics, refers to time, coming after the first three spatial dimensions (up/down, left/right and forwards/backwards). Abstract five-dimensional space occurs frequently in mathematics, and is a perfectly legitimate construct. Whether or not the real universe in which we live is somehow five-dimensional is a topic that is debated and explored in several branches of physics, including astrophysics and particle physics.

Lisa Randall:

My most recent research is about extra dimensions of space. Remarkably, we can potentially "see" or "observe" evidence of extra dimensions. But we won't reach out and touch those dimensions with our fingertips or see them with our eyes. The evidence will consist of heavy particles known as Kaluza-Klein modes that travel in extra-dimensional space. If our theories correctly describe the world, there will be a precise enough link between such particles (which will be experimentally observed) and extra dimensions to establish the existence of extra dimensions. Dangling Particles,By LISA RANDALL, Published: September 18, 2005 New York Yimes

The extensions beyond what we had always taken for meaning as "seeing," is the undertanding that all 3 space coordinated directions with time, are embedded in some "design" beyond that frame of reference held to General Relativity. If it wasn't, how could anything working beyond this, be found as a coordinated result?

(Wikipedia 23 April 2006)











Figure 2. Clebsch's Diagonal Surface: Wonderful

Spacetime 101

Here's some basic background covering how mathematical models of space and time have evolved since ancient times, from the Pythagorean Rule to Newtonian mechanics, Special Relativity and General Relativity.

For the roads leading to one's view of the strange world of non-euclidean views had to offer, I of course needed some model from which to work. As I looked at the model above and the transfer of higher dimensional thinking, the very idea and contrast to the lower image represented, how would you associate gravity in the diagram but watch the circle valution along side of gravity that emegres from the 2d discription as a energy valution, and relationship to gravity, evolving from mass, energy interconnectivity. I have to apologize as I was developing and am developing.



I do not know if this is right to assign my view above, while one did not know the evaluation of 1R as I watch DRL assessment of what can no longer be considered as valid, I have to wonder why such observations are not thought about more intricately as the valuation of that circle is considered. The comparison was drawn between the two pictures of the spacetime fabric above here, and below.

Let's now start analysing a 2D case, that of the classic Flatland example, in which a person lives in a 2D universe and is only aware of two dimensions (shown as the blue grid), or plane, say in the x and y direction. Such a person can never conceive the meaning of height in the z direction, he cannot look up or down, and can see other 2D persons as shapes on the flat surface he lives in.

So if you follow the dimensional analysis, there is a systemic procedure that one has to follow, that does not have to be held in context of KK interpretation to this point, but it does help if you think about the very basis of this graduation that certain statements make themself known.

Degrees of freedom(Wiki 24 Jan 2006)

Zero dimensions
Point
Zero-dimensional space
One dimension
Line
Two dimensions
2D geometric models
2D computer graphics
Three dimensions
3D computer graphics
3-D films and video
Stereoscopy (3-D imaging)
Four dimensions
Time (4th dimension)
Fourth spatial dimension
Tesseract (four dimensional shapes)
Five dimensions
Kaluza-Klein theory
Fifth dimension
Ten, eleven or twenty-six dimensions
String theory
M-theory
Why 10 dimensions?
Calabi-Yau spaces
Infinitely many dimensions
Banach space (only some have infinitely many dimensions)
Special relativity
General relativity

Would you dimiss a comment by Greene because of the speculation you have felt about him that you might not recognize, what is being said as you watch that circle develope alongside of the sphere, as it moves through the 2d discription? Here's what mean, as I had focused on Brian Greene's words.

Angular momentum can twist light cones and even make time travel possible in theory if not in practice.

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?

( Brian Greene, The Elegant Universe, pages 248-249)

Fifth dimension(wiki 24 Jan 2006)

Abstract, five dimensional space occurs frequently in mathematics, and is a perfectly legitimate construct. Whether or not the real universe in which we live is somehow five-dimensional is a topic that is debated and explored in several branches of physics, including astrophysics and particle physics.

Five dimensions in physics(Wiki 24 Jan 2006)

In physics, the fifth dimension is a hypothetical dimension which would exist at a right angle to the fourth dimension

KK Tower

Like many people who devote their time to understanding the nature of the cosmo and the micro perspective of the world around us, these things have their own motivational packages which move to further rquired comprehensions. In that, one needs to further educateas to what they are talking about.

It's definitiely not easy, but I am trying, and devote a lot of time to this regardless of what schooling is required, it is not my intent to send people down the wrong paths, or, no paths at all, before I have investigated the terrain as best I can.

Mountains can give persepctive where sitting in the valleys circumspect what the greater can be?

KK Tower

What is it?



Kaluza-Klein theory(Wiki 4 Jan 2006)

A splitting of five-dimensional spacetime into the Einstein equations and Maxwell equations in four dimensions was first discovered by Gunnar Nordström in 1914, in the context of his theory of gravity, but subsequently forgotten. In 1926, Oskar Klein proposed that the fourth spatial dimension is curled up in a circle of very small radius, so that a particle moving a short distance along that axis would return to where it began. The distance a particle can travel before reaching its initial position is said to be the size of the dimension. This extra dimension is a compact set, and the phenomenon of having a space-time with compact dimensions is referred to as compactification.

Kaluza-Klein theory is a model which unifies classical gravity and electromagnetism. It was discovered by the mathematician Theodor Kaluza that if general relativity is extended to a five-dimensional spacetime, the equations can be separated out into ordinary four-dimensional gravitation plus an extra set, which is equivalent to Maxwell's equations for the electromagnetic field, plus an extra scalar field known as the "dilaton". Oskar Klein proposed that the fourth spatial dimension is curled up with a very small radius, i.e. that a particle moving a short distance along that axis would return to where it began. The distance a particle can travel before reaching its initial position is said to be the size of the dimension. This, in fact, also gives rise to quantization of charge, as waves directed along a finite axis can only occupy discrete frequencies.

Kaluza-Klein theory can be extended to cover the other fundamental forces - namely, the weak and strong nuclear forces - but a straightforward approach, if done using an odd dimensional manifold runs into difficulties involving chirality. The problem is that all neutrinos appear to be left-handed, meaning that they are spinning in the direction of the fingers of the left hand when they are moving in the direction of the thumb. All anti-neutrinos appear to be right-handed. Somehow particle reactions are asymmetric when it comes to spin and it is not straightforward to build this into a Kaluza-Klein theory since the extra dimensions of physical space are symmetric with respect to left-hand spinning and r-hand spinning particles.

So in order to get to the summation, views of hidden dimenisons had to be mathematically described for us, so a generalization here would suffice in the following diagram.



Now, not having the room to explain, and having linked previous information on extension of KK theory, I wondered about the following. If we understood well, the leading perspective that lead us through to the dynamical realizations, then the road Gauss and Reimann lead us to would help us to understand the visualization materializing by the calorimeter disciptions of each energy placement harmonically describing each particle's value? Even in a empty space, there seems to be something of a harmonical consideration?


If one understood well enough about the direction of discernation of early universe consideration and microstates, then such questions would have been of value in the ideas of topological considerations?

Poincare Conjecture

I am a little bit sad right now?

I accidently deleted a lot of what I would have said about assumption of Sklar's position in relation to discrete and continuous functions. In relation to the value of S-Matrix as a discrete measure and how we might see the gravitational lensing as a continous function using abstract topological understandings.

Moshe:

If string thoery describes the world and it has a compact circle, there are no measurements that will distinguish a small circle from a large one. Since I am only interested in results of measurments there is no reason for me to choose.

Moshe is leaving me hanging on a limb now that he moves into the fighting reality while the poor clod like me is trying to live in the world created by scientists/ theorists.

Now, have to work our way back to reality? :( Now the assunption I have adopted is a fifth dimensional perspective as most know when talking about the horizon and the inner workings of the black hole. Inner workings, really?

Fyodor:

Let me explain. If you look at the history [say 1930] of Kaluza Klein theory, you will find that there were two schools of thought. One said that the 5th dimension was real, the other that it was just a mathematical formalism. Of course, nobody disputed that the KK equations were *exactly equivalent* mathematically to the Einstein-Maxwell system, but nobody assumed that *exact mathematical equivalence* was the same thing as “equally real”. Similarly, string theorists circa 1985 surely knew that a purely formal interpretation of Calabi-Yau compactifications was possible, but evidently nobody felt moved to attach any importance to this observation.

Who would have disputed Smolin's position about responsibility and the S-matrix stance needed to assess this reality? I certainly don't have a probem and the general consensus I am sure would find that all would be in agreement here? A testable and functionable recognizion of dicrete measure?

Now I am left in a state where I cannot distinquish between the inner/outer and of course to think that I am on the surface of a Klein bottle would be very strange to someone who saids it's oks from a distance. I have to say, "holy crap, look what you have done?"

So it is not so easy to think of the Skalr's psotion and the abstract world as ending the conversation as such, pushes me to the wonderment of continuous functions, has me now scratching my head.

Lenny's rubber bands, or sliding rubber bands over apples versus donuts. Now you guys have really done it? Is reality smooth, or discrete? The quandrum of Poincare hold the light of Sklars position in my head, as tohow I should approach the discriptin of that blackhole interior even when the consistancy of the geoemrty expression had come from some real world measure cosmolgically turned inside/out?

Explain to me the jets of the Bose Nova then as anti-matter creations if such a gravitational collapse is not held in view, and the propensity of that action written in a continous mode?

Who would have known that the very idea of the colliders would have taken on abstract proportions, and moved the very thinking to hyperdimensional status. While the few might have restraint themselves to the step by step discrete measure?

Did this move to the abstract say abandon all reason? Or move from the reality of such man made creations and see where the views are taking us into those extra dimensions. Was reason abandon?

Point--> Line-->Plane <---> Point<-- String<-- Brane

Under the heading of Klein`s Ordering of the Geometries :

A theorem which is valid for a geometry in this sequence is automatically valid for the ones that follow. The theorems of projective geometry are automatically valid theorems of Euclidean geometry. We say that topological geometry is more abstract than projective geometry which is turn is more abstract than Euclidean geometry.

Now the usual thinking here has been placed under intense thinking by the introduction of a new way in which to look at "geometry" that has gone through a "revision" in thinking.

New trigonometry is a sign of the times

Lubos Motl introduces this topic and link in his blog entry and from this this has caused great consternation in how I am seeing. I see Lisa Randall might counter this in terms of what the brain is capable of, in line with this revisionary seeing, and comparative examples of this geometry Lubos links.

Dangling Particles,By LISA RANDALL
Published: September 18, 2005 New York Yimes

Lisa Randall:

Most people think of "seeing" and "observing" directly with their senses. But for physicists, these words refer to much more indirect measurements involving a train of theoretical logic by which we can interpret what is "seen." I do theoretical research on string theory and particle physics and try to focus on aspects of those theories we might experimentally test. My most recent research is about extra dimensions of space. Remarkably, we can potentially "see" or "observe" evidence of extra dimensions. But we won't reach out and touch those dimensions with our fingertips or see them with our eyes. The evidence will consist of heavy particles known as Kaluza-Klein modes that travel in extra-dimensional space. If our theories correctly describe the world, there will be a precise enough link between such particles (which will be experimentally observed) and extra dimensions to establish the existence of extra dimensions.

But first before I get to the essence of the title of my blog entry, I like to prep the mind for what is seemingly a consistent move towards geometry that has it's basis in applicabilty to physics, and move through GR to a vast new comprehsnsion in non-euclidean geometries. Must we now move backwards that we had gained in insight, or was it recognition of the "length scales" that we now say, how could such a dynamcial view ever be assigned to the eucildean discription under the guise of brane world recognitions?

Moving Backwards?

What exactly do I mean here?

Well the idea is that if you move to fifth dimensional views, and there are ways to wrap this within our "Brains":) We then see the dynamcial nature of our neurons have found acceptable ways in which to see this brane feature. As well as, approaches in use of new processes in geometerical considerations as those linked by Lubos.

Dealing with 5D world



Thomas Banchoff is instrumental here is showing us that fifth dimensional views can be utilized in our computer screens, and such comparisons, reduce to a two dimensional frame, makes it very easy to accept this new way in which to attack the dynamcial nature of reality.

How indeed now could our computer screen act a liason with the reality of our world, when see from screen imagery effects, that all the rules of order have been safely applied for inspection and consistancy in physics approaches.

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?:)

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.