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.

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.

The Alchemist in You?

The blue image is one trajaectory of the Lorenz system with (σ, ρ, β) = (10, 28, 8/3) started from the initial point (0, 0, 1). The yellow image is for the same parameters but a different initial condition, (0, 0, 1+ε) where ε = 10-5.









While it is true that you can understand the effects on macroscale, the micro dynamics is still somewhat of a issue in our determinations?

At best, a new computerer with the ability to imput extraodinary amounts of data for a model prediction, yet there is no method to detail where all microdynamic processes will lead to other then to assume it on a classical level?

I would like to think such encapsulation would have found value in as much as we move our understanding of macrosate happenings from quantum dynamcial ones, as well?

So Thales has to arise with some basic priniple? How you map this, is important.

He recorded: 'Thales says that it is water'. 'it' is the nature, the archê, the originating principle.

Almost as important, as understanding the basis of discrete things, could manifest, "from other states of existance"?


Fool's gold?:)


Symmetry breaking realizations understand well that such a process is revealled from other phases of existance?


This is a Crucible. This is the standard model? Beyond it is the existance of dynamical world that is but one more phase transiton realized from the point symmetrical breaks into manifestation of universes, galaxies worlds, as concrete things?

Ancient alchemist understood it's significance.

Processes hidden in Platonic forms, might have been of value assigned to astrological processes, while this process, could also exist in the human form, for perfection.

So the mentality, although couched in the alchemist view and widely encompassing, understood that such a crucible would have held the alchemist to a process of refinement. Usng water, as a example in this process was significant, in that the states of matter could have "other forms" in it's expression where such "solidifications" held to discrete forms.

Kaluza and Klein's thinking was a bit beyond the normal fourth dimensional realizations. Yet could have baez said this is the way of God. Why invoke, when it is a natural part of our existence to wonder, and what value assign to concrete things? meantal or otherwise in the discrete nature of things?

Search for Extra-dimensions with ATLAS at the LHC: The Lions Den

I have often wonder whether or not my opinions about left and right aspect battling in society, are right?:) Peter Woit saids string theory is right wing financed? I hate to dread that media has been perversive enough in order to support political factions affecting science?

So I'll tell you how affected I have become too, so you can see that the greater significance and responsibility is not really about right and left, but about science's perspective about the state of affairs beyond the matters at hand?

I couldn't help think of the flavour of good scientific minds, who would rise to the challenge, and make the theoretical approach some struggle between good and evil? As some atheistic attempt, "to remove informative possibilities" from the subject that might have come from the "trigger of emergent properties"? I don't say change quantum mechanical porpityies either just that we see it in context of a new model. Is this wrong, or right?

Fancy free, and without adeu, I cast myself on what it must be like, if such a fancy was taken to the issues of "Intelligent design," that it could have ever undermined the basis of this literary conversation, to have scientists designated here and there, as a division, regardless of the virtues of scientific inquiry held to both.

So herein, begins the story.:)

"The soul that rises with us, our life's star,
Hath had elsewhere its setting,
And cometh from afar."

"Intimations of Immortality" by William Wordsworth

>"Or, if through lower lives I came--
Tho' all experience past became,
Consolidate in mind and frame--
I might forget my weaker lot;
For is not our first year forgot?
The haunts of memory echo not."

"Two Voices" by Tennyson

"As to you, Life, I reckon you are the leavings of many deaths,
No doubt I have died myself ten thousand times before."

""Leaves of Grass" by Walt Whitman



Solidus of Justinian I (r. 527–565), 538–565

Byzantine; Minted in Constantinople
Gold; Diam. 3/4 in. (1.9 cm)
Bequest of Joseph H. Durkee, 1898 (99.35.7406)
Coins connected an emperor to his subjects. Through inscriptions and images, they conveyed imperial ideals and commemorated auspicious events. The emperor paid the army and received taxes in coins, and he was responsible for maintaining their weight and purity. This coin was minted under Justinian, whose preference for a completely frontal portrait—rather than the traditional profile—would set a standard for the rest of Byzantine history.


The struggle then is something contained back in our history, to have those who will guide us through common sense to say, that the evils of society are no less the roads taken by revisionist who would try and change the path of Christianity? Be smited by, those who hold on religious tenant might have been extolled into the future of lives? Where go these "lost souls" while they converge on string theory and try and change history?:)

From A Defense of an Essay of Dramatic Poesy (1668) by John Dryden

Imagination in a man, or reasonable creature, is supposed to participate of reason, and when that governs, as it does in the belief of fiction, reason is not destroyed, but misled, or blinded: that can prescribe tot he reason, during the time of the representation, somewhat like a weak belief of what it sees and hears; and reason suffers itself to be so hoodwinked, that it may better enjoy the pleasures of the fiction: but it is never so wholly made a captive as to be drawn headlong into a persuasion of those things which are most remote from probability: 'tis in that case a free-born subject, not a slave; it will contribute willingly its assent, as far as it sees convenient, but will not be forced....Fancy and reason go hand in hand; the first cannot leave the last behind; and though fancy, when it sees the wide gulf, would venture over, as the nimbler; yet it is withheld by reason, which will refuse to take the leap, when the distance over it appears too large

Missing E_T and its uses (LHC)?

This larger font sized comment directs us in our quest to wonder what had been going with the anti-stringy camps who might have challenged the views? Is there sufficient data to back up the statements, other then to stand as "religous converts of a point of view," soley spoken by the "more advanced," might have their reasons why this approach is insufficient? Other then, to hold the roads of a predawn attempts in christianity to a societal way of thinking, contrary, to the established views written in the years of Constantinople in 538?:)

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.

In post below this one the question of extra energy was a important one in that it highlights the question of those "extra dimensions or not." For my generalized view, there is no leading explanation to the general public that would annouce how this diversion from current scientific approaches of Cern, will lead to satisfaction of the road of super string theory has taken. To understand, it is not willy nilley approach to some "Intelligent design quest" that such string theorists had been cornered too, in discription by anti-stringy voices?

From what I had understood contrary to this view of the string camp, it's only opositon was LQG and the roads that lead in that general direction. At least these were directions that operated from a basis of discrete or continuity, other then mere speculation of the sort that would dissuaade most readers from idolizing , and being drawn into the lair of lions?:)

It was as if the rhtymns of life could been entangled in minds and the quantum Harmonic osccilator embedded to language that science found in the true numerical basis of eisstance, that it could be cast in forms of shakesperean words, and hidden from the view by Francis Bacon's true discourse on history?

On constitution reform, Jefferson Davis words needed revision, to have a man like Benjamin Franklin stand up and devote a treaty on reason? It would guide the American view, to a healthy and just system of inquiry, as to the rights and freedoms shared by the American views? What lessons lie in scientific inquiry then to have those who stand at the forefront, and make it some intangible realism of the "forces of light and darkness "fighting to bring society into it's talons?

"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.


See:

ICHEP'04-Accepted Abstracts for Session 12: Beyond the standard model

The Unity of Mathematics

Alain Connes

Where a dictionary proceeds in a circular manner, defning a word by reference to another, the basic concepts of mathematics are infinitely closer to an indecomposable element", a kind of elementary particle" of thought with a minimal amount of ambiguity in their defnition.

I think what intrigues me most, is that a world can be fabricated mathematically that is carefully constructed using models of math, to get to a desired visionary culmination? One had to have some culminative effect, from such model thinking, that a vision beocmes clear. In this sense I related Lenny Susskind here, for his developement and contributions to string theory.

Now having spent time delving into parts of this world, the "tidbits" help me to see that such alignmenets of the world of physics have correlations in mathematical design. This has to have it basis set, "in the Rossetta stone you might say," about how we percieve the deveopement of those physics. The math must contrast the physics?

So to set things straight here, in case I gave the wrong link, I thought I should attribute proper link to words in case this mistake was made.



So too, information in blogs can be readily adapted too, where previous articles might have made some feel that the article not worth maintaining in their blog? That it might have been removed? I was thinking of the B-field topic that Lubos had written briefly on, that when I went to look for relevant information pertaining to this current entry, it was no where to be seen.

A VIEW OF MATHEMATICS by Alain CONNES
Most mathematicians adopt a pragmatic attitude and see themselves as the explorers of this mathematical world" whose existence they don't have any wish to question, and whose structure they uncover by a mixture of intuition, not so foreign from poetical desire", and of a great deal of rationality requiring intense periods of concentration.

Each generation builds a mental picture" of their own understanding of this world and constructs more and more penetrating mental tools to explore previously hidden aspects of that reality.

Now many would have to forgive my adventurous heart. I was somehow transported in my thoughts and converted? I don't know when, that such models of the mathematical structure had easily become discernable for me(it's result)? Not it's elemental structure(although I have seen areas of string theory design developed) from basic principals. It had it's culminative effect.

Is my vision always right? Of course not. But I see where such discriptions are necessary. Solid, and in stone, so that such progression can be made. I respect this, and I respect the physics, and it's culminative approach in theoretical developement.

Nature's Greastest Puzzle



Alain Connes refers to "poetic design," much like I see beats to music:?), and artistic adventure, as the play ground of imagination. We hope such songs shared, lyrics or otherwise, will reveal what the most secluded and private individuals might have found in their own world. To seek out, good artistic drawers like Escher? Penrose, needed his help, and the ideas brought forth, interesting results.

Now there is a reason for this post besides setting the record straight. It came up a long time ago with the question of whether mathematics was natural or created.

This may seem simplistic thought to some, but to me, it forced me to consider whether mathematics and physics were directed connected to each other.:) Now as I have said it is not easy for me to follow the matheics of such abtract individuals, but once I catch sight of the world that they allude too, it is somehow easy for me to see the structure of the bubble, or a representative drawing correlated in nodes, and features of a world that is constained in the physics.

This is why I refer back to Lubos and his B-field missing post, or I cannot simply find it. I refer to it, because I made links to mathematical design, that correlated dynkin diagram as shown above, and connects to other blog. Now it was important for me to see this correlation in the archetecture of the picture I linked to its prospective author, in relation to the dynkin diagram. Not the E11 asscoiation, but with that I had linked in image in comments to the B-field post.

My whole blog is based on visionary developement, theoretically, as well as nurturing physics association as best as I can, to show that the envelope is being pushed theoretically.



Interpretations of the magnetic field, in all its desgin is easily comprehensible once we align our thinking to hard fact and design reprsentation. Magnetic field lines on paper, is a child's toy, but easily experimetally done. Much more abstract then, that we see the field created, it's north and south, and a channel through which expression can flow?



Now even this is contained, and a Gausssian representation, highly abtract, relates curvature in away that we would understand this force that nature has created for us.

You must remember I do not have the luxury or life's abilty to move through the higher avenues that scholastic carreers have venture forth in. To preview this branch or that branch in physics, so I am bombarded with information from all angles:?)

I like to wrap the gravitational field, much like we wrap the magnetic field. It's just the way I see, and in it's greater design, that vast gravitational field that is generate through our cosmos? Bubbles become very interesting whenyou wrap somehing and the inside is moving with the outside, and in the vast vacuum of space this is stretching the very fabric itself?

I won't make the mistake of calling it the aether, yet continuity of expression seen in this abstract mode, does not see "tears" and such, so it is allocated to topological relevances. Holes, that look like swiss cheese in the cosmos? Yet I know well the events, that materialize in comsological expression, I wanted to push beyond these material things, to see the greater vision that has been moved by mathematcians.

You can say the rogue man here who speaks, is a wolf cub. Has been raised in a foreign world, without the benefits of scholastic teachers to guide me. So I had to look for them who held sacred some of the vision that I see when this math leads to a comprehensive view.

Reimann lead Einstein, and it was fortunate that Grossman was able to spot Einsteins deficiences. Help him move geoemtical principal beyond the euclidean coordinated world, to one manifested in spacetime, and a new dynamcial feature called gravity. It was beyond billiards and the sound related, and not the clasical discription that now beocmes the analogy of, that strange world we now see in gravitational thought.

Was it enough to speak about theses things and theorectically develope thoughts, to describe ways, in which such sound could ring bars, or influence the flexible arms of LIGO We measure this abstract world mathematcially created, to realize, we are now engaged in something very unique about our visions developement? Kip Thorne progeny will be the new genration that sees in way that were new to bauss and Riemann and now as we see of Einstein. This has a geometrical expression and basis to it, and it leads into projective elements topologically described.

Klein's Ordering of 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.


Klien's ordering of geometries were specifc here?

Missing Energy Events

'There comes a time when the mind takes a higher plane of knowledge but can never prove how it got there. All great discoveries have involved such a leap. The important thing is not to stop questioning.'

Albert Einstein
(1879- 1955)


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

It is not easy for me to follow so many minds involved in the deeper intricacies of a world, that abstractually was built, to concieve of other possibilties. If it fell within the mind's capabilties to allow such ventures, then such values become developed in the mind's neurological developement?

High energy particles have extremely small wavelengths and can probe subatomic distances: high energy particle accelerators serve as supermicroscopes:

To see What?

The structure of matter

(atoms/nuclei/nucleons/quarks)


Did it see tidbits of nature, and ways, in which to explain other views of the microscopic world? What "eye" was held to the microscope(particle reductionistic further refined) and then, with such endearing qualties spoken to us, takes us on a journey well concieved and observed?



For me then to view this compact world, and reveal the dimensional attributes of something that may seem so foreign and alien in it's guise, I realize that for the mind to peer into the deeper workings of the microscopic world, we had to understand the images the we could produce, as we learn to build mathematical structures for contemplation

Dvali uses the analogy of a metallic sheet submerged in water to illustrate the principle. If one hits the sheet with a hammer, shock waves will carry away the energy in all directions. "Most of the energy will travel along the two-dimensional surface. Only at a substantial distance away from the source will the energy loss to water be appreciable," he said. "According to our picture, we are in a very similar situation. We think gravity is 'normal' because we only measure it directly at relatively short distances, but cosmic acceleration indicates leakage.

"

To further expand on this idea of Dvali's I wanted to draw attention to the principals of this leakage. Bear with me as I try to find the literature that I have accumlated, for what is spoken now has triggered my memory by selection of these words.

So the process now is to remember where these views were previously spoken about and bring them back here for a wider comprehension of the leakage and the dimensional significance implied by Dvali, of where this extra energy is going?

Hopefully we wil see other minds involved in string theory speaking on this matter, to seal what they are doing and descibing where they think this extra energy is going?

Given the dearth of knowledge about gravity in the subcentimeter range, the group is looking for any kind of deviation from expectations, not just extradimensional effects, he says. Nonetheless, the excitement about extra dimensions helps spur the group on, Price says.

If the strength of gravity takes a sharp turn upward at around 1 TeV, as the Stanford-Trieste scenario implies, an opportunity opens for testing this theory also in accelerators. Collisions at such energies could produce gravitons in large numbers, and some of these particles would immediately vanish into the extra dimensions, carrying energy with them. Experimenters would look for an unusual pattern of so-called missing energy events.

This and more subtle effects of extra dimensions could show up at existing accelerators, such as LEP and the Tevatron at Fermilab, only if the dimensions have scales nearly as big as a millimeter. The powerful LHC will greatly improve the chances for detecting missing energy events and other prominent extradimension effects.

The bold highlight of the article preceding, points to the realization and values of what the gravitons appear to be able to do. How they can take this energy with them into those extra dimensions. This is a very important insight, that must be considered, and not just shelved because the mathematics seem disjoined from reality.

The basis of the capabilties of the dimenisonal significance in regards to these topological manueverings, had to have some basis to move from, and it is this essence, that string theory acknowledges? The energy of these gravitations in a world quite capable of being grviaational discribed, can now have a foundation in which we may describe this dynamcial issues at the quantum level?

We have moved the GR considerations of D>=4 to a much more dynamical recogntion of the probabilties inherent in energy determinations and also grvaitonic condensation values withinthe blackhole.

KK: Kaluza Klein Theory

What is it?

KK Tower



Now part of the problem of visualization here is what and how the cosmic string could have developed. Now, determination of the various sizing of these strings would have had to incorporate the value of the energy involved, in terms of 1r and using the KK tower, such classifcations help in this direction.

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?

Electromagnetic Calorimeter of the Phenix


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?

Here again I would point to the Glast determinations and of how we percieve these comological interactions, that continue to be built mathematically? Cosmic string developement would have shown energy valuation that would have continued to expand if we see this as a continous fucntion of particle identification? The matter states would have become distinctive inregards to the weak field manifestations represented in the comsological functions of our universe now?

We would have had to learn to map topological considerations, and the only way is how we see the calorimeter is used?

Inverse Fourth Power Law

By moving our perceptions to fifth dimenisonal views of Kaluza and KLein, I looked at methods that would help me explain that strange mathematical world that I had been lead too geometrically. If such a bulk existed, then how would we percieve scalable features of the energy distributed within the cosmo?

The angular movements needed to signal the presence of additional dimensions are incredibly small — just a millionth of a degree. In February, Adelberger and Heckel reported that they could find no evidence for extra dimensions over length scales down to 0.2 millimetres (ref. 11). But the quest goes on. The researchers are now designing an improved instrument to probe the existence of extra dimensions below 0.1 mm. Other physicists, such as John Price of the University of Colorado and Aharon Kapitulnik of Stanford University in California, are attempting to measure the gravitational influence on small test masses of tiny oscillating levers.

In previous posts I have outline the emergence and understanding of hyperdimensional realities that we were lead too. Our early forbearers(scientifically and artistic embued with vision) as they moved through the geometrical tendencies, that if followed , made me wonder about that this strange mathematical world. How would we describe it, and how would it make sense?

Our new picture is that the 3-D world is embedded in extra dimensions," says Savas Dimopoulos of Stanford University. "This gives us a totally new perspective for addressing theoretical and experimental problems.

Quantitative studies of future experiments to be carried out by LHC show that any signatures of missing energy can be used to probe the nature of gravity at small distances. The predicted effects could be accessible to the Tevatron Collider at Fermilab, but the higher energy LHC has the better chance.
These colliders are still under construction, but results also have consequences for "table-top" experiments, being carried out here at Stanford, as well as the University of Washington and the University of Colorado. Here’s the basic idea: imagine there are two extra dimensions on a scale of a millimeter. Next, take two massive particles separated by a meter, at which distance they obviously behave according to the well-known rules of 3-D space. But if you bring them very close, say closer than one millimeter, they become sensitive to the amount of extra space around. At close encounter the particles can exchange gravitons via the two extra dimensions, which changes the force law at very short distances. Instead of the Newtonian inverse square law you’ll have an inverse fourth power law. This signature is being looked for in the ongoing experiments.

As you look at the issue of two points(introduction to hyperdimensional realites of quark confinement as a example), it is well understood, by this point that such emergence had to be geometriclaly consistent on many levels. That such royal roads leading too, culminate in some realistic measure? In that mathematical realm, we had left off, and in recognition of the fifth postulate of euclid. By acceptance and creation of this extra dimension, it was well apparent, that such tendencies were developing along side with the physics as well.

But we had to determine where this mathematical realm had taken us, in terms of measure? We are quckly reminded of the place in which such measures become the constant rallying point around important questions of these views.



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

It wasn't a game anymore, that we did not suspect that reductionism might have taken us as far as the energy we could produce could take us? So we had to realize there was limitations to what we could percieve at such microscopic levels.

High energy particles have extremely small wavelengths and can probe subatomic distances: high energy particle accelerators serve as supermicroscopes:

To see What?

The structure of matter

(atoms/nuclei/nucleons/quarks)

Faced by these limitations and newly founded conceptual views based on the quantum mechanical discription of spacetime as strings, how would we be able to look at the cosmos with such expectancy? To know, that the views energetically described, would allow further developement of the theoretcial positons now faced with in those same reductionistic views?

What has happened as a result of considering the GR perspective of blackholes, that we had now assigned it relevance of views in cosmological considerations? Such joining of quantum mechanical views and GR, lead us to consider the sigificance of these same events on a cosmological scale. This view, had to be consistent, geometrically lead too?

If we discover the Planck scale near the TeV scale, this will represent the most profound discovery in physics in a century, and black hole production will be the most spectacular evidence of that new discovery

Mapping Quark Confinement and The Energy

As I moved through the thinking of those extra dimensions it became apparent to me that the conceptualization of that distance scale was a strange world indeed. How, if we had accept the move to non-euclidean views could we not of accepted the consequences of this move?




Dazzled with the amazing properties of this new mathematical realm, everything seemed a bit magical, as if, experiencing for the first time a taste that is strange indeed? How would I recognize this strange dynamical world, if I had not understood this move to include the geometry that Kaluza and Klien adopted, to gather together another reality of photon engagement with that of gravity?



Fig. 1. In quantum chromodynamics, a confining flux tube forms between distant static charges. This leads to quark confinement - the potential energy between (in this case) a quark and an antiquark increases linearly with the distance between them.

So at the same time you had this distant measure, how could we resolve what was happening between those two points?

Without some supersymmetrical reality(supergravity) how could any point emerge from the brane if it did not recognize the evolution of those dimensions?



So how does this point expand? This is a simple enough question?

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.

In the above picture Michael Duff draws our attention too, I was drawn to the same principals that Klein demonstrated in his ideas of projective geometry, as the dimensions are revealed?

IN this effort and recognition of appropriate geometry, I had wondered, that if the same consistancy with which these two had demonstrated the principals, euclidean
postulates fell in line, as a basis of this method of applicabilty? Does one now see this thread that runs through the geometry?

Having accepted the road travelled to GR we have come to recognize the royal road has lead us to a strange world indeed. First it was Reimann with Gauss looking over his shoulder, and Maxwell joining Faraday in this celebration, with Einstein bringing all the happy go lucky, into a fine example of what has been implied by the harmonious nature, structure of strings in concert?



But I am not happy yet. If one could not see what was happening between those two points, what's the use of talking any math, without the co-existance of the physics?


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. (This occurs because electromagnetism is a U(1) symmetry theory and U(1) is simply the group of rotations around a circle).

Gravity and Light in the Fifth Dimension

Theodor Franz Eduard Kaluza November 9, 1885 - January 19, 1954


In Kaku's preface of Hyperspace, page ix, we find a innocent enough statement that helps us orientate a view that previous to all understanding, is counched in the work of Kaluza.

In para 3, he writes,

Similarily, the laws of gravity and light seem totally dissimilar. They obey different physical assumptions and different mathematics. Attempts to splice these two forces have always failed. However, if we add one more dimension, a fifth dimension, to the previous four dimensions of space and time, then equations governing light and grvaity appear to merge together like two pieces of a jigsaw puzzle. Light, in fact, can be explained inthe fifth dimension. In this way, we see the laws of light and gravity become simpler in five dimensions.

Oskar Klein September 15, 1894 - February 5, 1977

Oskar Klein proposed that the fourth spatial dimension is curled up in a circle of 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. (This occurs because electromagnetism is a U(1) symmetry theory and U(1) is simply the group of rotations around a circle).

A Classical Discription of the Quantum World?

D Orbital

Orbitals are probability diagrams. Specifically, an orbital describes a region in space where there is a 90% change of finding an electron. The electron is never restricted to an orbital as in travels around a nucleus, but it seems to keep returning to this particular region even though its behavior is random. The concept of the orbital differs from Bohr's concept of the orbit. Bohr considered an orbit to be a path that the electron always followed much like a train stays on a track. The concept of the orbital was developed in Schrodinger's work to avoid violating the Heisenberg Uncertainty Principle. In the Modern Theory of Atomic Structures a picture of an orbital is also called a Probability Diagram. By agreement among chemists, the orbital is a 90% Probability Diag ram. This idea allows the electron to be found anywhere and still indicates where the electron spends most of its time.

How would one remove the uncertainty principals from the small world but to have considered the probability density distributions? Below is a link that I saw early in my investigations that I had wondered, forced me to look at what could have been happening within the cosmo with events, that would release information into the bulk?



Electron’s probability density distribution for an atom in the state; n=4, l=4, m=0.



The star Eta Carina is ejecting a pair of huge lobes that form a "propeller" shape. Jet-like structures are emanating from the center (or "waist"), where the star (quite small on this scale) is located.

If string theory, in the Kaluza Klein tower energy determinations could have discriptively spoken to the particle natures, why was it not possible to map the nature of these particles, in gravitational information released from these cosmological events?

If information in the bulk has been released, then this information has been geometrically defined in the gravity waves that we would percieve here on earth? Ligo would have performed its ability to then map the configurations that we see happening in that same cosmos. What made this visualization interesting is if photon release was specific to electromagnetic events held to the brane, then our perception of this energy, would have been left for us to consider in those same gravitational waves?

Quantum Gravity

Here is one of two methods that help explain. The next post will follow tomorrow if I have time. The complexity of the pictures involved is linked down below in Fig 15-17. This will give some generalizations that I had been looking too, to comprehend the model of strings and its geometrical discriptions.

Continuity



Topology is the branch of mathematics concerned with the ramifications of continuity. Topologist emphasize the properties of shapes that remain unchanged no matter how much the shapes are bent twisted or otherwise manipulated.

Such transformations of ideally elastic objects are subject only to the condition that, for surfaces, nearby points remain close together in the transforming process. This condition effectively outlaws transformations that involve cutting and gluing. For instance a doughnut and a coffee cup are topologically equivalent. One can be transformed continuously into the other. The hole in the doughnut will be preserved as the hole in the handle of the coffee cup.










Topology becomes an important tool in superstring when it is treated as quantum mechanical object. This branch of mathematics is concerned with smooth, gradual, continuous change of geometric shape. For example, a square can be continuously deformed into a circle by pushing in the corners and rounding the sides. The essential rule is that no new hole can be created in the new form by tearing. Some topological equivalent objects are shown in Figure 15-17.

Unfortunately I lost the link to this quote and if someone could remember seeing this, I hope you will let me know.

We expect that the divergences of quantum gravity would similarly be resolved by introducing the correct short-distance description that captures the new physics. Although years of effort have been devoted to finding such a description, only one candidate has emerged to describe the new short-distance physics: superstrings. Vibrational modes

This theory requires radically new thinking. In superstring theory, the graviton (the carrier of the force of gravity) and all other elementary particles are vibrational modes of a string (figure 1). The typical string size is the Planck length, which means that, at the length scales probed by current experiments, the string appears point-like.

The jump from conventional field theories of point-like objects to a theory of one-dimensional objects has striking implications. The vibration spectrum of the string contains a massless spin-2 particle: the graviton. Its long wavelength interactions are described by Einstein's theory of General Relativity. Thus General Relativity may be viewed as a prediction of string theory!

This highlighted print tells us a lot, about the higher dimensional values assigned to spacetime as being a result. If we were to entertain the holographical consideration of these higher spaces manifesting into the spacetime curvature, that we have come to know and love, then we have indeed not only used Klein to travel to the fifth dimension but have come back home, to what GR represents for us a sa tangible?

Is Line , Hook and Sinker, Dimensionally Leading to Soul Food?

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

I think sometimes the road begun existed before many of our own perspectives were added for considerations, so although we find that Einstein argue the simplicity and beauty of GR as it is, and rejected the quantum mechanical nature of the world, he did not reject the extensions of his thoughts to lead to other things. Some might of called this a mistake as well?

Kaluza and Klein showed in the 1920s that Maxwell's equations can be derived by extending general relativity into five dimensions. This strategy of using higher dimensions to unify different forces is an active area of research in particle physics.

General consistancy of mathematics and numerical correlation, that unite, seem very plausible tools for recognition? Even if the mathematician, has divorced himself from the real world and said, it fits? Do they not become the Lewis Carroll's and paint pretty pictures for us of a implausible world when they move into this abstract world of mathematics, without joining the physics? Einstein and Kaluza did this for us? There mathematics worked, and why not the Kaluza's consideration to extra dimensions?

Let there be light! How could we not see that if the extra dimension was added how relevant might such unification have spoken to electromagnetism and gravity?

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"

Thank you Wikipedia.

Einstein's special relativity was developed along Kant's line of thinking: things depend on the frame from which you make observations. However, there is one big difference. Instead of the absolute frame, Einstein introduced an extra dimension. Let us illustrate this using a CocaCola can. It appears like a circle if you look at it from the top, while it appears as a rectangle from the side. The real thing is a three-dimensional circular cylinder. While Kant was obsessed with the absoluteness of the real thing, Einstein was able to observe the importance of the extra dimension

Compactifying a 3-D universe with two space dimensions and one time dimension.

How do we learn to deal with these abstract spaces, but to have considered the following:





(a) Compactifying a 3-D universe with two space dimensions and one time dimension. This is a simplification of the 5-D space­time considered by Theodor Kaluza and Oskar Klein. (b) The Lorentz symmetry of the large dimension is broken by the compactification and all that remains is 2-D space plus the U(1) symmetry represented by the arrow. (c) On large scales we see only a 2-D universe (one space plus one time dimension) with the "internal" U(1) symmetry of electromagnetism.

After doing some reading I needed to support what was being expounded on here, so I found the following for consideration.

Einstein's special relativity was developed along Kant's line of thinking: things depend on the frame from which you make observations. However, there is one big difference. Instead of the absolute frame, Einstein introduced an extra dimension. Let us illustrate this using a CocaCola can. It appears like a circle if you look at it from the top, while it appears as a rectangle from the side. The real thing is a three-dimensional circular cylinder. While Kant was obsessed with the absoluteness of the real thing, Einstein was able to observe the importance of the extra dimension

Quantum Gravity

I've put together links for reference on the particular subject titled. If someone has others that they would like to add, please do. I will be placing a permanent link on the sidebar for reference. Hope its useful.

List of quantum gravity researchers

• Jan Ambjørn: Expert on dynamical triangulations who helped develop the causal dynamical triangulations approach to quantum gravity.
• Giovanni Amelino-Camelia: Physicist who developed the idea of Doubly special relativity, and founded Quantum-Gravity phenomenology.
• Abhay Ashtekar: Inventor of the Ashtekar variables, one of the founders of loop quantum gravity.
• John Baez: Mathematical physicist who introduced the notion of spin foam in loop quantum gravity (a term originally introduced by Wheeler).
• John W. Barrett: Mathematical physicist who helped develop the Barrett-Crane model of quantum gravity.
• Julian Barbour: Philosopher and author of The End of Time, Absolute or Relative Motion?: The Discovery of Dynamics.
• Martin Bojowald: Physicist who developed the application of loop quantum gravity to cosmology.
• Steve Carlip: Expert on 3-dimensional quantum gravity.
• Louis Crane: Mathematician who helped develop the Barrett-Crane model of quantum gravity.
• Fay Dowker: Physicist working on causal sets as well as the interpretation of quantum mechanics.
• David Finkelstein: Physicist who has contributed much quantum relativity and the logical foundations of QR.
• Charles Francis: Mathematician who has developed a background-independent model of physics called Relational Quantum Gravity.
• Rodolfo Gambini: Physicist who helped introduce loop quantum gravity; coauthor of Loops, Knots, Gauge Theories and Quantum Gravity.
• Gary Gibbons: Physicist who has done important work on black holes.
• Brian Greene: Physicist who is considered one of the world's foremost string theorists.
• James Hartle: Physicist who helped develop the Hartle-Hawking wavefunction for the universe.
• Stephen Hawking: Leading physicist, expert on black holes and discoverer of Hawking radiation who helped develop the Hartle-Hawking wavefunction for the universe.
• Friedrich W. Hehl: Physicist who developed the metric-affine gauge theory of gravity and published a Physics Reports review article about this subject.
• Christopher Isham: Physicist who focuses on conceptual problems in quantum gravity.
• Mark Israelit Physicist who worked on torsional Weyl-Dirac electrodynamics, quantum gravity and quantum cosmology (cosmic egg model, together with Nathan Rosen).
• Ted Jacobson: Physicist who helped develop loop quantum gravity.
• John Klauder: Physicist. Proponent of the theory called Affine Quantum Gravity.
• Renate Loll: Physicist who worked on loop quantum gravity and more recently helped develop the causal dynamical triangulations approach to quantum gravity.
• Robert B. Mann: Physicist who works on "Lineal" gravity i.e. gravity in lower dimensions and alternate theories within quantum field theory.
• Fotini Markopoulou-Kalamara: Physicist who works on loop quantum gravity and spin network models that take causality into account.
• Herman Nikolai: Physicist who works on quantum gravity and investigates Kac-Moody algebras as a candidate symmetry for supergravity theories and M-theory.
• Roger Penrose: Mathematical physicist who invented spin networks and twistor theory.
• Jorge Pullin: Physicist who helped develop loop quantum gravity, coauthor of Loops, Knots, Gauge Theories and Quantum Gravity.
• Carlo Rovelli: One of the founders and major contributors to loop quantum gravity.
• Lee Smolin: One of the founders and major contributors to loop quantum gravity.
• Rafael Sorkin: Physicist, primary proponent of the causal set approach to quantum gravity.
• Andrew Strominger: Physicist who works on string theory.
• Thomas Thiemann: Physicist who works on loop quantum gravity.
• Frank J. Tipler: Mathematical physicist who maintains in a 2005 paper^[1] published in Reports on Progress in Physics that the correct quantum gravity theory has existed since 1962, first discovered by Richard Feynman in that year, and independently discovered by others. Intrinsic to this theory of quantum gravity are certain boundary conditions, which includes an Omega Point final cosmological singularity.
• Bill Unruh: Canadian physicist engaged in the study of semiclassical gravity and responsible for the discovery of the so-called Unruh effect.
• Robert Wald: Leading physicist in the field of quantum field theory in curved spacetime.
• Anzhong Wang: Physicist, major contributor to Horava-Lifshitz gravity; String theory and applications to cosmology.
• Edward Witten: Leading mathematical physicist, does research in string theory and M-theory.
• Richard Woodard: Physicist, major contributor to canonical, perturbative, and finite infrared quantum gravity; applications to cosmology.

List of loop quantum gravity researchers

• Abhay Ashtekar, Pennsylvania State University, USA
• John Baez, University of California, Riverside, USA
• John W. Barrett, University of Nottingham, UK
• Sundance Bilson-Thompson, Perimeter Institute for Theoretical Physics, Canada
• Martin Bojowald, Pennsylvania State University, USA
• Steve Carlip, University of California, Davis, USA
• Alejandro Corichi, National Autonomous University of Mexico, Mexico
• Olaf Dreyer, MIT, USA
• Laurent Freidel, Perimeter Institute for Theoretical Physics, Canada
• Rodolfo Gambini, Universidad de Montevideo, Uruguay
• Christopher Isham, Imperial College London, UK
• Renate Loll, Utrecht University, The Netherlands
• Fotini Markopoulou-Kalamara, Perimeter Institute for Theoretical Physics, Canada
• Donald Marolf, University of California, Santa Barbara, USA
• Jorge Pullin, Louisiana State University, USA
• Carlo Rovelli, Centre de Physique Theorique, Marseille, France
• Lee Smolin, Perimeter Institute for Theoretical Physics, Canada

String Theorist People

• Mina Aganagic
• Ofer Aharony
• John Randolph Sides
• Nima Arkani-Hamed
• Michael Francis Atiyah
• Igor Bandos
• Tom Banks
• Katrin Becker
• Melanie Becker
• David Berenstein
• Gerald Cleaver
• Mirjam Cvetic
• Atish Dabholkar
• Sumit R. Das
• Erik D'Hoker
• Robbert Dijkgraaf
• Jacques Distler
• Michael Douglas
• Michael Duff
• Sergio Ferrara
• Willy Fischler
• Daniel Friedan
• Davide Gaiotto
• Ori Ganor
• E. Gava
• Rajesh Gopakumar
• Michael Green
• Brian Greene
• David Gross
• Steven Gubser
• Sergei Gukov
• Amihay Hanany
• Jeffrey Harvey
• Petr Horava
• Gary Gibbons
• Michio Kaku
• Renata Kallosh
• Theodor Kaluza
• Anton Kapustin
• Elias Kiritsis
• Igor Klebanov
• Oskar Klein
• Miao Li
• Hong Liu
• Oleg Lunin
• Juan Maldacena
• Gautam Mandal
• Donald Marolf
• Emil Martinec
• Samir Mathur
• Shiraz Minwalla
• Gregory Moore
• Lubos Motl
• Sunil Mukhi
• Robert Myers
• Asad Naqvi
• K.S. Narain
• Horatiu Nastase
• Nikita Nekrasov
• André Neveu
• Dimitri Nanopoulos
• Holger Bech Nielsen
• Peter van Nieuwenhuizen
• Hirosi Ooguri
• Joseph Polchinski
• Alexander Polyakov
• Arvind Rajaraman
• Lisa Randall
• Seifallah Randjbar-Daemi
• Leonardo Rastelli
• Martin Rocek
• John H. Schwarz
• Nathan Seiberg
• Ashoke Sen
• Samson Shatashvili
• Steve Shenker
• Warren Siegel
• Eva Silverstein
• Link Starbureiy
• Matthias Staudacher
• Andrew Strominger
• Leonard Susskind
• Paul Townsend
• Sandip Trivedi
• Cumrun Vafa
• Gabriele Veneziano
• Erik Verlinde
• Herman Verlinde
• Spenta Wadia
• Edward Witten
• Xi Yin
• Tamiaki Yoneya
• Alexander Zamolodchikov
• Alexei Zamolodchikov
• Barton Zwiebach

Quantum Gravity quote

A pessimist might say that combining string theory and loop quantum gravity is like combining epicycles and aether.

(John Baez, TWF281)

What is Quantum Gravity?

Moderator: Stephen Shenker, Panelists: Abhay Ashtekar, Juan Maldacena, Leonard Susskind, Gerard 't Hooft, Cumrun Vafa

Jan Ambjørn

Kostas  Anagnostopoulos

John Baez

Julian Barbour

Chris  Isham

Ted  Jacobson

Renate  Loll

Fotini Markopoulou Kalamara at Penn
State University and Albert
Einstein Institute

Carlo  Rovelli

CGPG: Center  for Gravitational Physics and Geometry

High-Energy Theory  Group at The Niels Bohr Institute

Imperial College  Theoretical Physics Group

The Max Planck Institute for Gravitational Physics (Albert  Einstein Institute)

Penn State Physics Department

Perimeter Institute for Theoretical Physics

String theory

Loop quantum gravity of Smolin and Rovelli

Noncommutative geometry of Alain Connes

Twistor theory of Roger Penrose

Abhay Ashtekar -- Author of Ashtekar variables, he is one of the founders of loop quantum gravity.

John Baez -- Mathematical physicist.

Julian Barbour -- Author of The End of Time, Absolute or Relative Motion? and The Discovery of Dynamics.

Martin Bojowald --

Louis Crane -- Theorist.

Rodolfo Gambini -- Author of Loops, Knots, Gauge Theories and Quantum Gravity.

Brian Greene -- Physicist who is considered one of the world's foremost string theorists.

Stephen Hawking -- Leading theoretical physicists.

Peter Higgs -- Proposed the 1960's theory of broken symmetry in electroweak theory,

Christopher Isham -- Theoretical physicist.

Michio Kaku -- Theoretical physicist with significant contribution to the string field theory.

Fotini Markopoulou-Kalamara -- Theoretical physicist interested in foundational mathematics and quantum mechanics

Roger Penrose -- Mathematical physicist and imade the invention of spin networks.

Jorge Pullin -- Theoretical physicist.

Carlo Rovelli -- Obtained, with Lee Smolin, an explicit basis of states of quantum geometry.

Lee Smolin -- Theoretical physicist who has made major contributions to loop quantum gravity.

Andrew Strominger -- Theoretical physicist who works on string theory

Thomas Thiemann -- Researcher.

Edward Witten -- Mathematical physicist who does research in M-theory

Centauro event

String theory

M-theory

Loop Quantum Gravity by Carlo Rovelli

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What is Quantum Gravity

Finally, string theory started out as a generalization of quantum field theory where instead of point particles, string-like objects propagate in a fixed spacetime background. Although string theory had its origins in the study of quark confinement and not of quantum gravity, it was soon discovered that the string spectrum contains the graviton, and that "condensation" of certain vibration modes of strings is equivalent to a modification of the original background.

LQG does not have this feature to describe point particles, where a one dimensional string includes gravity.

According to Wikipedia:

1.loop quantum gravity makes too many assumptions
2. according to the logic of the renormalization group, the Einstein-Hilbert action is just an effective description at long distances

3. loop quantum gravity is not a predictive theory

4. loop quantum gravity has not offered any non-trivial self-consistency checks

5. loop quantum gravity is isolated from particle physics

6. loop quantum gravity does not guarantee that smooth space as we know it will emerge as the correct approximation of the theory at long distances

7. loop quantum gravity violates the rules of special relativity

8. the discrete area spectrum is not a consequence, but an assumption of loop quantum gravity

9. the discrete area spectrum is not testable

10. loop quantum gravity provides us with no tools to calculate the S-matrix

11. loop quantum gravity does not really solve any UV problems

12. loop quantum gravity is not able to calculate the black hole entropy, unlike string theory

13. loop quantum gravity has no tools to answer other important questions of quantum gravity

14. the criticisms of loop quantum gravity regarding other fields of physics are completely misguided

15.loop quantum gravity calls for "background independence" are misguided

16.loop quantum gravity is not science


The numbered points are connected to deeper explanations.

Criticisms of string theory can follow in someone else's post. With the group in favor of LQG they should be able together their heads and come up with lots of things

Current theories of gravity are based on the geometric curvature of space.

Current theories of other fundamental forces in the universe are 'quantum field theories', where particles pass other particles back and forth among themselves to interact.
We know that geometric gravity theories conflict with quantum field theories, and that this conflict means that we don't know what happens under extreme conditions.

A quantum theory of gravity would involve particles passing 'gravitons' back and forth among themselves. This quantum theory would probably be a more accurate description of gravity, and might be accurate enough to describe the extreme conditions found at the center of a black hole.

David Palmer
for Ask a High-Energy Astronomer

Quantum Gravity

Quantum gravity is the field of theoretical physics attempting to unify the subjects of Quantum mechanics and General relativity.

Much of the difficulty in merging these theories comes from the radically different assumptions that these theories have on how the universe works. Quantum mechanics depends on particle fields embedded in the flat space-time of either Newtonian mechanics or special relativity. Einstein's theory of general relativity models gravity as a curvature within space-time that changes as mass moves. The most obvious ways of combining the two (such as treating gravity as simply another particle field) run quickly into what is known as the renormalization problem. Gravity particles would attract each other and if you add together all of the interactions you end up with many infinite results which can not easily be cancelled out. This is in contrast with quantum electrodynamics where the interactions do result in some infinite results, but those are few enough in number to be removable via renormalization.

Another difficulty comes from the success of both quantum mechanics and general relativity. Both have been highly successful and there are no
known phenomenon that contradict the two. The energies and conditions at which quantum gravity are likely to be important are inaccessible to laboratory experiments. The result of this is that there are no experimental
observations which would provide any hints as to how to combine the two.

The general approach taken in deriving a theory of quantum gravity is to
assume that the underlying theory will be simple and elegant and then to
look at current theories for symmetries and hints for how to combine them
elegantly into a overarching theory. One problem with this approach is
that it is not known if quantum gravity will be a simple and elegant theory.

Such a theory is required in order to understand those problems involving the combination of very large mass or energy and very small dimensions of space, such as the behaviour of black holes, and the origin of the universe.

There are a number of proposed quantum gravity theories and proto-theories, including (for example) string theory and the loop quantum gravity of Smolin and Rovelli - see http://www.livingreviews.org/Articles/Volume1/1998-1rovelli/
The Noncommutative geometry of Alain Connes, and Twistor theory, of Roger Penrose, are also theories of quantum gravity

The Quantum Gravity Concept Map is a highly experimental work: it's goals are to help the author organize his own understanding of the subject, and to test the hypothesis that html is a natural language for the construction of a concept map.

Quantum gravity is the field of theoretical physics attempting to unify the theory of quantum mechanics, which describes three of the fundamental forces of nature, with general relativity, the theory of the fourth fundamental force: gravity. The ultimate goal is a unified framework for all fundamental forces—a theory of everything


A history of the Planck values provides interesting material for reflections on timely and premature discoveries in the history of science. Today, the Planck values are more a part of physics itself than of its history. They are mentioned in connection with the cosmology of the early universe as well as in connection with particle physics. In considering certain problems associated with a unified theory (including the question of the stability of the proton), theorists discovered a characteristic mass ~ 1016mp (mpis the proton mass). To ground such a great value, one first refers to the still greater mass 1019mp. In the words of Steven Weinberg:

This is known as the Planck mass, after Max Planck, who noted in 1900 that some such mass would appear naturally in any attempt to combine his quantum theory with the theory of gravitation. The Planck mass is roughly the energy at which the gravitational force between particles becomes stronger than the electroweak or the strong forces. In order to avoid an inconsistency between quantum mechanics and general relativity, some new features must enter physics at some energy at or below 1019 proton masses. (Weinberg 1981, p. 71).

The fact that Weinberg takes such liberties with history in this quotation is evidence of the need to describe the real historical circumstances in which the Planck mass arose. As we saw, when Planck introduced the mass (ch/G)1/2 (~ 1019mp) in 1899, he did not intend to combine the theory of gravitation with quantum theory; he did not even suppose that his new constant would result in a new physical theory. The first "attempt to combine the quantum theory with the theory of gravitation," which demonstrated that "in order to avoid an inconsistency between quantum mechanics and general relativity, some new features must enter physics," was made by Bronstein in 1935. That the Planck mass may be regarded as a quantum-gravitational scale was pointed out explicitly by Klein and Wheeler twenty years later. At the same time, Landau also noted that the Planck energy (mass) corresponds to an equality of gravitational and electromagnetic interactions.

Theoretical physicists are now confident that the role of the Planck values in quantum gravity, cosmology, and elementary particle theory will emerge from a unified theory of all fundamental interactions and that the Planck scales characterize the region in which the intensities of all fundamental interactions become comparable. If these expectations come true, the present report might become useful as the historical introduction for the book that it is currently impossible to write, The Small-Scale Structure of Space-Time.

The struggle to free ourselves from background structures began long before Einstein developed general relativity, and is still not complete. The conflict between [B]Ptolemaic and Copernican cosmologies[/B], the dispute between Newton and Leibniz concerning absolute and relative motion, and the modern arguments concerning the `problem of time' in quantum gravity -- all are but chapters in the story of this struggle. I do not have room to sketch this story here, nor even to make more precise the all-important notion of `geometrical structure'. I can only point the reader towards the literature, starting perhaps with the books by Barbour [9] and Earman [15], various papers by Rovelli [25,26,27], and the many references therein.

String theory has not gone far in this direction. This theory is usually formulated with the help of a metric on spacetime, which is treated as a background structure rather than a local degree of freedom like the rest. Most string theorists recognize that this is an unsatisfactory situation, and by now many are struggling towards a background-free formulation of the theory. However, in the words of two experts [18], ``it seems that a still more radical departure from conventional ideas about space and time may be required in order to arrive at a truly background independent formulation.