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.

Could "Chaos" have been Implied in the Quantum Harmonic Oscillator, as Supersymmetry?

See:Quantum Harmonic Oscillators


Fortunately being the junior here in knowledge comprehension, the benefits, as of my having wrongly thought a certain way, allows "fantasy a great journey." I have wondered, could I have ever attained such insights that would awaken even the most determined individual to the quest of, to finally rest easy and a warm satisfaction?

Let's hold the Trigger in suspension. What is it's potential, had such symmetrical realizations made the axis of this process move according to some plan not seen? Are There methods seen in the matrices, that revolve around this "i" that woud have given the photon dispersement some relevance to a interactive phase within context? How about gluon perceptions? Tipler's lightcones also comes to mind here, as such a process?

I am so afraid to trip on my tongue, that such words listed, would have provided the necessary crackpot label. I wondered whether I should continue. But a motivation is borne of it's own accord, I couldn't help see some relevance to the "uncertainty in langrange points."

Although chaotic planetary motion had not been observed, experimentalists had encountered turbulence in fluid motion and nonperiodic oscillation in radio circuits without the benefit of a theory to explain what they were seeing.

Could have exemplified such unequilibrium, that at first, it made no sense to me that such points could have ever accomplished anything. Was there a lesson from lorentz and his model butterfly that such models had found the transfer from one state to another, could reveal such supersymmetrical acts of consideration in having found the anti- anything, and soon learnt, that it was the other side of the equation? The 720 degree turn, that brought the history of this action into a complete whole, and accord.



I would like to say this is nice to see that Lee Smolin has taken the time to help set things straight. This caught my eye.

This is linked to a Post written by Peter Woit called, " Why No New "Einstein"?

Lee Smolin:

6) With regard to the non-standard quantization, in which holonomies, but not local field operators are well defined, it is of course true that when applied to standard systems this leads to inequivalent results. “This apparently leads to unphysical consequences, such as an unbounded spectrum for the harmonic oscillator.” But, give me a break, do you really think someone is proposing to replace the standard quantization of the harmonic oscillator with the alternative one? What is being proposed is that the quantization used in LQG is well suited to the quantization of diffeo invariant gauge theories.

In case it is not obvious, let me emphasize that harmonic oscillators are not relevent here, and can play no role in a background independent quantum theory, precisely because the division of a field into harmonic modes requires a fixed background metric. Thus, the physics of the problem REQUIRES an alternative quantization.

I have to read things over quite a few times before it seems to sink in, but reference to three sphere and the understanding of Poincare's model did not reduce my interest in seeing such correlations in how we saw such langrange points develope into this suspended state for the trigger to make itself known?

Many physicists find extra dimensions a distasteful notion. In remarks to an American Physical Society newsletter, physicist Frank Wilczek of MIT called the black hole study a sound way to test an unattractive idea.

"There's no question that the Auger observatory will be sensitive to this signal, if it exists," says Penn State's Stéphane Coutu, a member of the international Auger Observatory team. "We'll definitely look."

All of us are on the same wavelenght right? Blackhole determinations, set the stage, for what we hope to percieve is, "the basis of this trigger?"

How wonderful this rubber band that is slipped over the sphere, and as it expands from this point, "the loop" now becomes a exemplifier of all those things manifested from the spherical gaze of the harmonics?

What image is given from the blackhole to realize, that the gravitonic messager sent from the daisy of Taylor, would have found the penduluminaric thoughts in Greg's Egans's "animations of Lissajous" and a coordinated frame?

Coulomb Interactions, Thomson Scatterings

I think most people understand this stuff, and that experiment is the most efficient way of dealing with this issue. Even if we understand the matrix developemental view it's shortcoming are well expressed by others in that field of quantum grvaity. That could have easily helped orientate further constructive processes in that same respect.

John Ellis:

To my mind, one of the most plausible extensions of the Standard Model is supersymmetry (just look at the subjects of my research papers!), so could the minimal supersymmetric extension of the Standard Model have created the matter in the Universe?

John Ellis and the views about the supersymmetrical are really more in depth then the suttle words listed and spoken about by some. String Theorists knew how far this went?:)

Peter Woit said,

Certainly some people should be working on quantum gravity, especially if they are doing it in a non-overhyped way, trying to really seriously understand the technical issues involved. The LQG community appears to be doing this. But, personally, I don't have any ideas about how to start from thinking about quantum gravity and get to particle physics, whereas I do see some hope that if one better understands the structure of the standard model, one may be able to get to quantum gravity from there.

Posted by Peter Woit at May 30, 2005 05:22 PM

While some people are looking for consistant means of determinations, others apply "conceptual situations" and bring forth comprehension of a kind. Now to this degree, that "gluonic perception is being adjusted" to see these values. The Smolins and others understood well the limitation of these views? Are there any?

It becomes extremely difficult, as reductionistic processes are further detailed. So how far will this informtaion take us in terms of early universe understanding? Througha comsic interactive theme in the expeirments lead by situation in particle interaction in our atmosphere we can direct same particle interaction?

The calorimeter design for GLAST produces flashes of light that are used to determine how much energy is in each gamma-ray. A calorimeter ("calorie-meter") is a device that measures the energy (heat: calor) of a particle when it is totally absorbed.

What will glast do for this comprehension, understanding well the Calorimetric view of information given to us about those early universe situations?

Remember that the age is determined by the dark matter density. Mathematically, the length is roughly the geometric mean of the mean free path and the distance light can travel without obstruction (the horizon scale).

A recipe for making strings in the lab

All you educated people must forgive me here. I do not have the benefit, of the student and teacher relationship, yet I rely heavily on my intuitive processes. I cannot say whether for sure these are always right. IN this sense, I would not have been liked to call a Liar, or one who had ventured forth to spread illusionary tactics to screw up society.

On the contrary, my ideal is set in front of my mind, and all things seem to gather around it most appropriately. A place and time, where good educators have watched out for the spread and disemmination, that could lead society away from, good science? I will give credit to Peter Woit in this sense. Lubos Motl for staying the course. As to those who excell these views for us as well. We are your distant cousins in need of education and for those, in the backwoods of isolation.

Fixations on Objective Design

This is far from the truth of my goal, and "fixations on objective design" of reality, are not what I was hoping to reveal. More, the understandng, that to get there, there are some considerations to think about.

The idealization in theoretcial developement should show this. The physics must accompany the development of this lineage of mathematics, as well as the lineage of physics must lead mathematics? What is the true lineage? Could any mathematican tell me or are they limited to the branches they deal with in physics?

Now back to the topic of this thread.

When I was a kid, I liked to take buttons and place a thread through them. Watching Mom, while I prep the button, she got ready to sew. I would take both ends of the thread and pull it tightly. I liked the way the button could spin/thread depending on how hard I pull the thread.



Now for some of you who don't know, the pythagorean string tension was arrived at by placing gourds of water on strings, to dictated the harmonical value, "according to weight?"

It is said that the Greek philosopher and religious teacher Pythagoras (c. 550 BC) created a seven-tone scale from a series of consecutive 3:2 perfect fifths. The Pythagorean cult's preference for proportions involving whole numbers is evident in this scale's construction, as all of its tones may be derived from interval frequency ratios based on the first three counting numbers: 1, 2, and 3. This scale has historically been referred to as the Pythagorean scale, however, from the point of view of modern tuning theory, it is perhaps convenient to think of it as an alternative tuning system for our modern diatonic scale.

So we see the nature spoken too, in a much different way?

KakuIf strings are to be the harmony then what music do such laws of chemistry sing? What is the mind of God? Kaku saids,"According to this picture, the mind of God is Music resonanting through ten- or eleven dimensional hyperspace which of course begs the question, If the Universe is a symphony, then is there a composer to the symphony."

Simply put, superstring theory says all particles amf forces are manifestations of different resonances of tiny one dimenisonal strings(or possibly membranes) vibrating in ten dimensions.


Artist's impression of the setup.

The disks represent the bosonic condensate density and the blue balls in the vortex core represent the fermionic density. The black line is a guide to the eye to see the wiggling of the vortex line that corresponds to a so-called Kelvin mode, which provides the bosonic part of the superstring

(image and text: )arXiv.org/abs/cond-mat/0505055.

Now I will tell you why this elementary experiment is very good for fixing the mind around some potential idea? Now, when I look at it, and look at the ball placings on each disk ( are they in the same spot....hmmm yes this could be a problem), each disk will automatically spin according to the placement of the ball, in relation to it's edge. Now when you place this in line, like a one dimensional string, as if you see this string vibrate, imagine how you would get these waves to exemplify themself and the disk placement acccordingly.

Now it is most important that you see the tension of this string vibrate, in relation to how we see the disks spin. Pull tightly on the string and you get a wonderful view of a oscillatory nature, that is dictated by the respective placement of the balls on the disk. Good stuff!

In brackets above, the exploration of artistic rendition is very good, because it allows you to further play with this model and exhaust it's potential. Would it be incorrect to say, that ball placement and vibratory placement can be related to string harmonics? In this case, how would KK tower and circle allocation to disk identify this string, but to have some signature in the way these disks spin,,individually and as a whole(one string)

The link below was 2000 but it is effective in orientating thoughts?

To find extra dimensions of the type studied by the CERN group, experimenters are on the alert for what they call Kaluza-Klein towers, which are associated with carriers of the nongravitational forces, such as the photon of electromagnetism and the Z boson of the weak force. Excitations of energy within the extra dimensions would turn each of these carriers into a family of increasingly massive clones of the original particle—analogous to the harmonics of a musical note.

For me, nodal impressions at spots, serve me well to see the vibratory nature of the reality that we live in. Balloons with dyes spread around it, and sound application help us see where such nodal point considerations would settle themself to these distinctive notes. You take the sum(it harmical value, in order to distinctively classify the partcle/object?

Maybe we can have experts describe this in a most genaral way, where I might have complicated the picture:?) What I did want to say about artistic rendition, is like the work of Penrose. It is very important it culminates the vision, to real things? As I showed in Monte Carlo effect. Or, John Baez's view of Plato's God?

Ultracold Superstrings byMichiel Snoek, Masudul Haque, S. Vandoren, H.T.C. Stoof

Supersymmetric string theory is widely believed to be the most promising candidate for a "theory of everything", i.e., a unified theory describing all existing particles and their interactions. Physically, superstring theory describes all particles as excitations of a single line-like object. Moreover, the bosonic and fermionic excitations are related by supersymmetry. A persistent problem of string theories is the lack of opportunity to study them experimentally. In this Letter, we propose and analyze a realistic condensed-matter system in which we can create a non-relativistic Green-Schwarz superstring in four space-time dimensions. To achieve this, we make use of the amazing tunability that is now possible with ultracold trapped atomic gases. In particular, for the creation of the superstring we consider a fermionic atomic gas that is trapped in the core of a vortex in a Bose-Einstein condensate. We explain the tuning of experimental parameters that is required to achieve supersymmetry between the fermionic atoms and the bosonic modes describing the oscillations in the vortex position.

Now what is very interesting to me is the way such harmonical value can be seen in in relation to particle identification. It is not always easy to see how such disks and toys could exemplify this for us, but I am trying. If we wanted to see the new toy and the relations that I will show how would this all relate to the disk and the ball on it?



I wanted to look at what you were saying to "try," and understand.

One of the most exciting predictions of Einstein's theory of general relativity is the existence of a new type of wave, known as a gravitational wave. Just as in electromagnetism, where accelerating charged particles emit electromagnetic radiation, so in general relativity accelerating masses can emit gravitational radiation. General relativity regards gravity as a curvature of spacetime, rather than as a force, so that these gravitational waves are sometimes described as `ripples in the curvature of spacetime'.

This mode is characteristic of a spin-2 massless graviton (the particle that mediates the force of gravity). This is one of the most attractive features of string theory. It naturally and inevitably includes gravity as one of the fundamental interactions.

By looking at the quantum mechanics of the relativistic string normal modes, one can deduce that the quantum modes of the string look just like the particles we see in spacetime, with mass that depends on the spin according to the formula

Remember that boundary conditions are important for string behavior. Strings can be open, with ends that travel at the speed of light, or closed, with their ends joined in a ring.

See:

Quantum Harmonic Oscillators

Distinctions of Holographical Sound

Without Gravitational Waves, Spacetime is Flat?

I know it is very difficult for some people to understand this translation to harmonical expressions(any horizon and what is to lie beyond?) and the way in which we would percieve this dynamcial nature, using the expressions of non-Euclidean geometries?



We understood this creation of positive and negtaive in context of each other did we?

Riemannian Geometry, also known as elliptical geometry, is the geometry of the surface of a sphere. It replaces Euclid's Parallel Postulate with, "Through any point in the plane, there exists no line parallel to a given line." A line in this geometry is a great circle. The sum of the angles of a triangle in Riemannian Geometry is > 180°.



It is a strange thing to wonder how the heck one get's to translating harmonical oscillations in context of what we see expounded by Taylor and Hulse. To understand that at some point, the rotation around each other in distance, will decrease in time, and the oscillations will increase? What does this signal?:)



You do not discard thnking about the cosmological nature, methods, that have been used to orientate the world view in such a way, where all of a sudden the complexity of this dynamical nature has moved your thinking to strength and weakness of those same gravitational wave explanations.

Working closely with the experimental group, we use astrophysical, particle physics and superstring theory combined with observations to study gravitation and the origin and evolution of our universe.

The beautiful consistency of the cosmological tests with the Lambda CDM theory for structure formation maybe is particularly impressive to me because I spent so much of the last 15 years studying alternatives; you can trace through astro-ph my history of proposals that were viable when submitted but soon ruled out by advances in measurements of the angular distribution of the 3K thermal background radiation. But the constraints from the cosmological tests are not yet much more numerous than the assumptions in Lambda CDM and related models; it's too soon to declare closure of the cosmological tests.

Supersymmetry

There is no branch of mathematics, however abstract, which may not some day be applied to phenomena of the real world.

— Nikolai Lobachevsky


John Ellis:

Extensions of the Standard Model often contain more discriminatory parameters, and this is certainly true of supersymmetry, my personal favourite candidate for new physics beyond the Standard Model. One of the possibilities suggested by supersymmetry is that Higgs bosons might distinguish couple differently to matter

Without consideration of that early universe, the quantum interpretation doesn't make sense unless you include it in something whole?



Lubos said,

There are also many other, indirect ways how can we "go" back in time. This is what evolution, cosmology, and other fields of science are all about.

   Unsymmetrical-cooling-gravity weaker
              Expanding
            \            /
             \          /
              \        /
              _\      /___
             /  \    /    /
            /    \  /    /
           /      \/    /  --------300,000 years
          /            /          Gravity strong
          -------------           Symmetrical
                ^
                I
            seedlike
           
                    
     Q-------------Quark measure is stronger
            \        /
             \      /
              \    /
               \  /
               Q--Q
                                     

Symbolically how do you create a inclusive system, but to look at alien and foreign ways in which this logic might force you to consider the interactivity of a theory of everything? Greater quark distance, greater energy, higher gravitational field generation. The field around this distance, and supersymmetrical realization bring us closer to the source of the energy creation, closer to the source of the universe's beginnings

....to consider such eneregies within the sphere of M, at a quantum level, as well at such cosmological scales."

The Bubble Universe / Andre Linde's Self Creating Universe

These are the theories discussed in class. The bubble universe concept involves creation of universes from the quantum foam of a "parent universe." On very small scales, the foam is frothing due to energy fluctuations. These fluctuations may create tiny bubbles and wormholes. If the energy fluctuation is not very large, a tiny bubble universe may form, experience some expansion like an inflating balloon, and then contract and disappear from existence. However, if the energy fluctuation is greater than a particular critical value, a tiny bubble universe forms from the parent universe, experiences long-term expansion, and allows matter and large-scale galactic structures to form.

The "self-creating" in Andre Linde's self-creating universe theory stems from the concept that each bubble or inflationary universe will sprout other bubble universes, which in turn, sprout more bubble universes. The universe we live in has a set of physical constants that seem tailor-made for the evolution of living things.

It is very difficult sometimes to bring another individuals view in line with the vast resources that could point the mind to consider the whole thing?



If you did not have a encompassing philosophy, and I know this word is dirty to some, but without pointing to a basis for which the universe sprang, then such topological features would never make sense.

So you direct the thinking to what the early universe looked like(?), and it's potential for expression. A lot of things are going on that are not considered geometrically/topologically unfolding, which hide within the basis of expression. So you have to use analogies to nudge the mind into possible structural considerations, with evidence of graviton production?

Notes on Hyperspace Saul-Paul Sirag

The rule is that for n hidden dimensions the gravitational force falls off with the inverse (n + 2 ) power of the distance R. This implies that as we look at smaller and smaller distances (by banging protons together in particle accelerators) the force of gravity should look stronger and stronger. How much stronger depends on the number of hidden dimensions (and how big they are). There may be enough hidden dimensions to unify the all the forces (including gravity) at an energy level of around 1 TeV (1012 eV), corresponding to around 10-19 meters. This would be a solution to the hierarchy problem of the vast difference in energy scale between the three standard gauge forces and gravity. This is already partly solved by supersymmetry (as mentioned previously); but this new idea would be a more definitive solution--if it were the right solution!

The Arrow of Time

Rudolf Julius Emanuel Clausius

There is but one kind of entropy change. Entropy change is due to energy dispersal to, from, or within a system (as a function of temperature.), measured by microstate change: S = k_B ln [microstates _final / microstates _initial ].

I should back up here and mentioned that Peter Woit seems to be coming out in the open and explaining somethings that have been not so clear before?

Perter Woit:

Penrose also carefully lays out areas in which his point of view differs from the general consensus of most theoretical physicists. An example is his emphasis on the importance for cosmology of understanding why the universe had such low entropy at the Big Bang

What is strange today that with this thought on the subject of entropy.

Lubos Motl:

This is what allows the early gas to clump (and seemingly create a more order state) without violating the 2nd law of thermodynamics: the gravitational entropy overcomensates the decrease of the entropy.

OK, so why was the beginning of the Universe a low-entropy state? The best explanation we have is inflation. It simply explodes the size of the Universe. During inflation, the total entropy of the Universe grows, but much more slowly than how it would grow otherwise, without inflation.

if one did not understand the early universe consideration here, and the idealization of supersymmetry, could we have found a association to low orders of entropy since this early time would have been very topologically considered and part of a continuum?

Entropy and the second law of thermodynamics

Entropy is no mystery or complicated idea. Entropy is merely the way to measure the energy that spreads out in a process (as a function of temperature). What's complicated about that? Entropy change, S, measures how much energy is spread out in a system, or how spread out is the energy of a system (both always involving T). The first example in our text was melting ice to water at 273 K where S = q/T. So, in that equation, it's easy to see that q (the enthalpy of fusion) is how much "heat" energy was spread out in the ice to change it to water. What's the big deal?

Update: Reading Peter Woit's blog today he linked Sean Carroll's "Arrow of Time article," so I thought it most apropriate to link it from here as well, since I am on the topic.


Sean Carroll:

Jennie and I do the following thought experiment -- if it weren't for inflation, what would be a "natural" state for the universe to be in? Different people have addressed this question, with different answers; Roger Penrose, for example, has suggested that it would be a lumpy universe full of black holes. Our answer is almost exactly the opposite -- the only natural state is empty space. This is basically because gravity makes everything unstable, and the entropy of any given configuration can always be increased by just expanding the universe by a huge factor. Sure, black holes will form, but they will ultimately evaporate away. If you let the universe evolve forever, it will ultimately get emptier and emptier (generically).

Is Everyone Declaring their Position Clearly?

"Most string theorists are very arrogant," says Seiberg with a smile. "If there is something [beyond string theory], we will call it string theory."

I am going to comment on Peter Woit's reference to the article called String Fellows he has highlight from the Guardian.

Here's what Nathan Seiberg mentions and points to the difficulty of finding the means to describe the microstates of quantum geometry. I wanted to place his statement, in context of a poem earlier written. So I'll post his comment, and then link to the appropriate source for consideration. It's getting a little worn out already, without us constantly being reminded:)

Nathan Seiberg, a colleague of Witten's at the IAS, uses the analogy of blind men examining an elephant to explain the course of string theory until 1995. "One describes touching a leg, one describes touching a trunk, another describes the ears," he says. "They come up with different descriptions but they don't see the big picture. There is only one elephant and they describe different parts of it."The Guardian

Now I most definitely see there is a great wish to eliminate any familiarity with dimensional anaylsis in regards to Peter Woit, that I find many others now, all of a sudden clarfying for us the model distinctions that are being used, and I think Peter Woit understands this?

Model Building

I am not like the kind of people who would like to eliminate (and often they DO eliminate) every piece of data that is inconvenient to them. And moreover I think that John Ellis is an interesting person with inspiring ideas, and I have absolutely no reason to try to verbally eliminate him from some group---Posted by Luboš Motl at January 20, 2005 08:32 AM

.

In delving into the issue of dimenisons it has become pretty clear there are intelligent people who have paved the roads for us to count to the fourth dimension for sure and we have also heard, there is no such things as dimensions? So what the heck does this mean.

Maybe a expanded version of dimension is needed? But if you do this, you might go beyond string theory?:) Which of course brings me to the issue, that if dimension is to be used to the fourth, then anything that goes beyond the fourth if not a dimension has to be something else? Of course giving room to grow being expounded here, tells us what is beyond string theory, to have said, we are going beyond the standard model?


THOMAS BANCHOFF has been a professor of mathematics at Brown University in Providence, Rhode Island, since 1967. He has written two books and fifty articles on geometric topics, frequently incorporating interactive computer graphics techniques in the study of phenomena in the fourth and higher dimensions

With John Ellis' reference to what took place at Cern in 2003 brings to a head the idea of dimension, as it has been expounded by Thomas in regards to computer screens?

Today, however, we do have the opportunity not only to observe phenomena in four and higher dimensions, but we can also interact with them. The medium for such interaction is computer graphics. Computer graphic devices produce images on two-dimensional screens. Each point on the screen has two real numbers as coordinates, and the computer stores the locations of points and lists of pairs of points which are to be connected by line segments or more complicated curves. In this way a diagram of great complexity can be developed on the screen and saved for later viewing or further manipulation

As a reality greatly expanded from what the internet used to be, refering to the Cern Article. If you accept the conceptualization of higher dimension then indeed the work that Thomas moved into, was mind expanding and thought provoking in regards to the animations and reality in front of you with this two dimensional screen?

So has this computer screen okayed the analogy to the fifth dimension?

So What is this Dimenisonal Archetecture Built On?

3-d: no hidden dimensions 1/R2 in F = G(m1 x m2)(1/R2)
4-d: one “ “ 1/R3 replaces 1/R2
5-d: two “ “ 1/R4 “
6-d: three “ “ 1/R5 “

and so on.

The rule is that for n hidden dimensions the gravitational force falls off with the inverse (n + 2 ) power of the distance R. This implies that as we look at smaller and smaller distances (by banging protons together in particle accelerators) the force of gravity should look stronger and stronger. How much stronger depends on the number of hidden dimensions (and how big they are). There may be enough hidden dimensions to unify the all the forces (including gravity) at an energy level of around 1 TeV (1012 eV), corresponding to around 10-19 meters. This would be a solution to the hierarchy problem of the vast difference in energy scale between the three standard gauge forces and gravity. This is already partly solved by supersymmetry (as mentioned previously); but this new idea would be a more definitive solution--if it were the right solution!

New Non-geometrical Generalization of the Principles of CFT Found?

There is always a certain expectancy, when it comes having formulated the theoretical work, that further developement along these lines presenst the opportunities for such things to exist.


A new non-geometrical generalization of the principles of CFT will be found, and it will allow to extend the success of S-matrices etc. to the non-perturbative realm. A geometry-like original of dualities - such as E_k in supergravity - will be clarified. Non-perturbative physics on general backgrounds will become calculable, and supersymmetry breaking will be shown to be very different in details than previously anticipated. Realistic N=1 4D vacua with SUSY breaking will be connected and the potential will pick up a rather small number of priviliged points - close to the "heterotic strings on Calabi-Yau three-folds" and/or "M-theory on G2 manifolds" and/or "intersecting brane models with some warping". Two years after the beginning of the revolution, the people will calculate the masses of the heaviest quarks, the (small) QCD theta-angle, and other things, and they will predict the first new physics beyond the SM, which will be only confirmed several years later experimentally.

Meanwhile, the structure of M-theory in 11D will be solved exactly, and the position of poles of the scattering amplitudes in 11D will be known more or less exactly.

Alternatively, theorists won't be that fast, and the revolution will start experimentally in 2007, most likely with the LHC. A rather simple pattern of masses of superpartners will be found, together with supersymmetry, and it will match one of the popular SUSY scenarios within string theory. Alternatively, small black holes or excited strings are gonna be seen, and their precise patterns will be used to reversely engineer the shape of branes and hidden dimensions.

Longitudinal and Transverse Information about the Energy Deposition Pattern

The calorimeter design for GLAST produces flashes of light that are used to determine how much energy is in each gamma-ray. A calorimeter ("calorie-meter") is a device that measures the energy (heat: calor) of a particle when it is totally absorbed. CsI(Tl) bars, arranged in a segmented manner, give both longitudinal and transverse information about the energy deposition pattern. Once a gamma ray penetrates through the anticoincidence shield, the silicon-strip tracker and lead converter planes, it then passes into the cesium-iodide calorimeters. This causes a scintillation reaction in the cesium-iodide, and the resultant light flash is photoelectrically converted to a voltage. This voltage is then digitized, recorded and relayed to earth by the spacecraft's onboard computer and telemetry antenna. Cesium-iodide blocks are arranged in two perpendicular directions, to provide additional positional information about the shower.

I am enamoured by the ideas of Nature, that such sublteness could have been defined in the cosmo with this exchange of information. That we are now looking at these events in the cosmo with some understanding, using measurements, where previously held comments about what we had understood in that same cosmo, had not shown to be of any use?

For the well informed, and those who venture into the Blog of Petter Woit, we find, that even Sean Carrol must caution Peter and thus I do the same, here, not just in regards to supersymmetry( my previous posts in early historical journey laid out in the question of Gerard t'Hooft), the ways in which interpret and map these dynamical situations?



A question is left in my mind as Gerard postulates that same universe. How would the fundamentals of quantum mechanics speak to what we had understood here.

Without some guidance and tutorial thoughts for introspection one would have to wonder about the artistic interpretation we assign the energy of this dynamical universe?