Exploring Branes: The Evolution of Superstring Theory

[sol2]

It is not always easy for people to follow the development in thinking that helps to orientate the visualization capabilites we have from instruction?

I give a case in point I and ask you, what allowed us to develope such thinking?

So all of a sudden one accepts paradigmal changes?

I do not expect people to run, once they accept the idea expressed, as a function of turning visualization capabilties into another realm of thinking? All of a sudden you see from a different perspective?

Will this help you look at earth differently or the moon?

You combine the information into a consistent model, assuming this extra feature of visualization?

What has happened to society as it changes the way it thinks? A global perspective? A Cosmological view now within the grasp of minds thinking? It still goes further then this. With one eye it turns to the cosmo, while with the other, the nature of all energy? These are never to far apart

How can a speck of a universe be physically identical to the great expanse we view in the heavens above?

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

 

[Olias]

Moving to non euclidean perspectives, are very important features of moving from the fifth postulate of Euclid. I wonder, about those like Saccherri, Gauss and Reimann. It is a new way seeing beyond what we are accustom too, and these gentlemen are very instrumental in this process. Exploring the realm here then one can also point to Kaku and ask how could any mind project itself into the eyes of the carp and then look to the surface of the water?




So we look for other ways in which to interpret the curvature parameters and to get a feel for the dynamics in the realm of non-euclidean perspective. Looking at gaussian fields help as well as the metric fields



http://www.bun.kyoto-u.ac.jp/~suchii/RonHelmholtz.html




Non-Euclidean Geometry



Further to understanding these dynamics the ideas of this flat universe concide nicely from what I see, relevant to the CMB temperature our universe is now holding. If we look back to the temperature values of our perspective looks we soon learn to see what a supermicroscope the colliders are in helping us in undertanding the first moments of the universe and it's compacted shape.

http://physicsweb.org/objects/world/13/11/8/pw1311084.gif



http://www.faculty.fairfield.edu/jmac/sj/sacflaw/B1.GIF


It came down to the question of using the triangle on different surfaces. By adding up the degrees it was easy then to assume the shape with which these surfaces spoke of themself.

So now we see where this universe having assumed such a large spherical extension of a early expansive form, has reached the flatness of today?


You have to remember the direction the temperatures values are leading us in its cooling function. Look back to the beginning of the universe and what do you see? If particle discriptions, are becoming evident and the energy values climbing, what has been revealed?

Reductionistic views, have paved the way for extraordinary energies and what is happening in the cosmos. You have made a exchange, from a reductionsitic one, to a energy one.

Of course we are assuming that your are developing your geometry along the way much like Einstein did with help from Grossman(Where has projective geometry lead us?). Does this road end?

Of course not and why all of sudden we have this topic about Quantum geometry explaining quantum gravity.

But there is a problem with relativistic views explaining, and integrating with the small word of the colliders. You had in this exchange a realization that geometrically forced you to consider the strength of those gravitational fields?

I am of course open to corrections.

Hi Sol, Geometry invokes an inquisitive quest on all who can think in abstract arena's, Einstein was one such man who tread upon the Path of Shape and form.

I have been deluded by some intricate Geometric anomolies lately, so I needed a Teacher, more so than a preacher!...thus:http://www.Newton.cam.ac.uk/webseminars/stokes/2003/03/18/atiyah/

Look, listen and learn!

 

[sol2]

Hi Sol, Geometry invokes an inquisitive quest on all who can think in abstract arena's, Einstein was one such man who tread upon the Path of Shape and form.

I have been deluded by some intricate Geometric anomolies lately, so I needed a Teacher, more so than a preacher!...thus:http://www.Newton.cam.ac.uk/webseminars/stokes/2003/03/18/atiyah/

Look, listen and learn!

I appreciate the link.

You have to understand Olias I pulled the two links from other threads today because they did not seem appropriate there. So yes, it might indeed seem like preaching with no context.

One was hereto the first post today in this link, and the second post, to the other https://www.physicsforums.com/showthread.php?goto=newpost&t=34922

For obvious reasons I brought them back here for prepping the mind, and of course, what illusions we might be under, could indeed ask oneself what delusions of grandeur we were perpetrating?

I always ask for corrections so that mathematical minds, in regards to the geometry, can respond? IN this effort, I have gone to great lengths to see how this geometry is working.

I have found a "wall" that I will reveal to you shortly I'll post it here.

Is spacetime fundamental?​

Note that there is a complication in the relationship between strings and spacetime. String theory does not predict that the Einstein equations are obeyed exactly. String theory adds an infinite series of corrections to the theory of gravity. Under normal circumstances, if we only look at distance scales much larger than a string, then these corrections are not measurable. But as the distance scale gets smaller, these corrections become larger until the Einstein equation no longer adequately describes the result. In fact, when these correction terms become large, there is no spacetime geometry that is guaranteed to describe the result. The equations for determining the spacetime geometry become impossible to solve except under very strict symmetry conditions, such as unbroken supersymmetry, where the large correction terms can be made to vanish or cancel each other out.

This is a hint that perhaps spacetime geometry is not something fundamental in string theory, but something that emerges in the theory at large distance scales or weak coupling. This is an idea with enormous philosophical implications.

http://www.superstringtheory.com/blackh/blackh4.html

That last paragraph in bold saids quite a bit too. I think there is a constant affirmation of the brane here to consider. How shall we "see" this?

What kind of geometry?

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

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

So, there is a certain realization that goes along with accepting this new geometry called Quantum geometry. What is it that must be realized?

There is lots and I have been speaking to it in regards to the Planck epoch

More preaching here I guess eh?

 

[Olias]

Sol, when I said:so I needed a Teacher, more so than a preacher!

I was referring to the Seminar I had sought, not 'meaning' that anyone on these forums are preaching?

It was meant to reflect the feeling I had after watching/lietening to the said seminar, I had learned a lot from it.

 

[sol2]

Sol, when I said:so I needed a Teacher, more so than a preacher!

I was referring to the Seminar I had sought, not 'meaning' that anyone on these forums are preaching?

It was meant to reflect the feeling I had after watching/lietening to the said seminar, I had learned a lot from it.

I know.

This statement had some effect from what my own children would say when they were younger. I imagine, if the interest was not there and you had a professor sitting at the head of the class, the attraction would wane, because the deeper meaning would not of been there to help. For some the impatience might had some effect, when they had been far past the curriculum? Pursuing their own thing?

So we see where personal motivation, like your own would say, I had to look at what I had been seeing all the time. This is also a point I raise in regards to Smolin, where he gathers his forces(information) and brings out a modified view about the reality we are currently dealing with. I find this an admirable trait But we have too, as you acknowledge, make sure we have the right information.

Thanks for your patience to respond

 

[sol2]

Supersymmetry

http://particleadventure.org/particleadventure/images/particle_main.gif

Some physicists attempting to unify gravity with the other fundamental forces have come to a startling prediction: every fundamental matter particle should have a massive "shadow" force carrier particle, and every force carrier should have a massive "shadow" matter particle. This relationship between matter particles and force carriers is called supersymmetry. For example, for every type of quark there may be a type of particle called a "squark."

No supersymmetric particle has yet been found, but experiments are underway at CERN and Fermilab to detect supersymmetric partner particles.

http://particleadventure.org/particleadventure/frameless/supersymmetry.html

http://particleadventure.org/particleadventure/frameless/string.html"

[QUOTE][B]String Theory[/B], one of the recent proposals of modern physics, suggests that in a world with three ordinary dimensions and some additional very "small" dimensions, particles are strings and membranes. Yes, membranes in extra dimensions are weird and hard to visualize. And what are "small dimensions?"[/QUOTE]

[PLAIN]http://particleadventure.org/particleadventure/frameless/string.html"

So what does particle reduction mean in terms of the colliders?

The move to understand the cosmo has taken us on a interesting journey of venturing to the early cosmos and here, General Relativity works very nice. But if we look at the early universe where we have joined GR with the quantum world, what shall this same universe look like from a microscopic view?

So now imagine that we are looking at the cosmo with a [PLAIN]http://www-glast.sonoma.edu/index.html , and that with this glass, we are able to see the universe's history, just by standing still here on earth.

What am I saying?

http://www.its.caltech.edu/~kip/images/KipDraw2.jpg
Drawing by Glen Edwards, Utah State University, Logan, UT


For Kip Thorne, this, Window on the Universe , amounted to trying to understand the "depth" of this history, and is like a Father, along with John Wheeler, who is a Father before him, to help us shape a view, on the reality of this cosmos.

Kip Thorne's research has focused on Einstein's general theory of relativity and astrophysics, with emphasis on relativistic stars, black holes and gravitational waves. He was co-founder of the Laser Interferometer Gravitational Wave Observatory. Thorne also authored the award-winning book for non- scientists, Black Holes and Time Warps: Einstein's Outrageous Legacy, as well as the textbook, Gravitation, from which most of the present generation of scientists have learned general relativity theory.

Probing the Universe with Gravitational Waves

Gravitational waves are ripples in the fabric of space and time produced by cosmic violence, such as the the universe's big-bang creation and collisions of black holes. These waves carry information about the "dark side" of the universe that cannot be learned in any other way. The high-frequency gravitational-wave window onto the universe will be opened soon by LIGO (NSF's earth-based Laser Interferometer Gravitational Wave Observatory, which is now in operation and searching for waves). A lower-frequency window will be opened in ~2012 by LISA (the NASA/ESA Laser Interferometer Space Antenna). This lecture will describe LIGO, LISA, and what they may teach us about the universe and about warped spacetime

http://www.aaas.org/meetings/MPE_01_PlenLec.shtml#kip

One of the early recognitions on my part was the value sound might have. This does not make sense until you consider the work of this man:

Joseph Weber 1919 - 2000

Joseph Weber, the accomplished physicist and electrical engineer, has died at the age of 81. Weber's diverse research interests included microwave spectroscopy and quantum electronics, but he is probably best known for his investigations into gravitational waves.

In the late 1950s, Weber became intrigued by the relationship between gravitational theory and laboratory experiments. His book, General Relativity and Gravitational Radiation, was published in 1961, and his paper describing how to build a gravitational wave detector first appeared in 1969. Weber's first detector consisted of a freely suspended aluminium cylinder weighing a few tonnes. In the late 1960s and early 1970s, Weber announced that he had recorded simultaneous oscillations in detectors 1000 km apart, waves he believed originated from an astrophysical event. Many physicists were sceptical about the results, but these early experiments initiated research into gravitational waves that is still ongoing. Current gravitational wave experiments, such as the Laser Interferometer Gravitational Wave Observatory (LIGO) and Laser Interferometer Space Antenna (LISA), are descendants of Weber's original work.

http://physicsweb.org/article/news/4/10/4

Now it is interesting that we are presented with two different perspectives going back to the early universe, that first found it's inception in the comprehension of gravitational waves as a product of General Relativity.

The road here is well documented and further understood from understanding the oscillations created from mercuries orbit or rotation binary star systems in that spacetime fabric. Here the exploration into Taylor and Hulse is a interesting value addition to the projection of these gravitational waves.

http://wc0.worldcrossing.com/WebX?14@21.LDOQcReQxm9.12@.1de0d666

 

[sol2]

I expect that some who have known me for sometime will have a thought form in their minds as to what is coming next?

Well for sure for every Father there should be a Mother?

When you look back far enough, and come to Planck Epoch, you come to certain realizations?

The thought, that I am guessing might materialize for some , is who is this Mother? Maybe, another name for membrane? Why you ask?

If we consider that the early formation of this universe began from that Planck epoch, then you have to accept certain considerations materializing in the expansive mode of this same universe.

Who is this shadow partner? Hmmmmmm...

 

[sol2]

The Heirarchy Problem

I do not know if this will help you. Hopefully others will respond.

You have to know where the Planck epoch exists. Planck Epoch to Grand Unification?

http://www.damtp.cam.ac.uk/user/gr/public/images/bb_history.gif

What exactly is the hierarchy problem?

The gist of it is that the universe seems to have two entirely different mass scales, and we don't understand why they are so different. There's what's called the Planck scale, which is associated with gravitational interactions. It's a huge mass scale, but because gravitational forces are proportional to one over the mass squared, that means gravity is a very weak interaction. In units of GeV [billions of electron volts], which is how we measure masses, the Planck scale is 10 to the 19th GeV. Then there's the electroweak scale, which sets the masses for the W and Z bosons. These are particles that are similar to the photons of electromagnetism and which we have observed and studied well. They have a mass of about 100 GeV. So the hierarchy problem, in its simplest manifestation, is how can you have these particles be so light when the other scale is so big.

http://www.esi-topics.com/brane/interviews/DrLisaRandall.html

Theories of LEDs(large extra dimensions) are quite elegant, and in fact solve a number of problems such as the hierarchy problem. They shrink the "energy desert" between electroweak and Planck scales, making the Planck scale accessible at the high GeV / low TeV level.

https://www.physicsforums.com/showpost.php?p=193339&postcount=9

 

[sol2]

In particular if we take a path around in a loop, then the frames will twist around and perhaps will be something different when we get back! So the loop tastes something about the geometry inherent in the connection.

"Symmetry," would ask that you return to your starting point? This would retain it's particle dnature, as an energy value?

Would the ole Quark to Quark measure, as an old view, still retain some of the features of this metric field with regards to the energy consideration in its distance function?

http://cerncourier.com/objects/2000/cernnews5_3-00.gif

The Function of the Metric?

Hyperspace, by Michio Kaku Page 84 and 85,
"To see higher dimensions simplify the laws of nature, we recall that any object has length, width and depth. Since we have the freedom to rotate an object by 90 degrees, we can turn its length into width, and its width into depth. By a simple rotation, we can interchange any of the three spatial dimensions. Now if time is the fourth dimension then it is possible to make "rotations" that convert space into time, and vice versa. These four-dimensional "rotations" are precisely the distortions of space and time demanded by special relativity. In other words, space and time have mixed in a essential way, governed by relativity. The meaning of time as being the fourth dimension is that time and space can rotate into each other in a mathematical precise way. From now on, they must be treated as two aspects of the same quantity: space-time. Thus adding a higher dimension helped to unify the laws of nature."

If you move to the Planck epoch, the geometry has to change Relativity in precise ways?

If I have strayed afar it was to see what these loops were doing. Also to understand the http://oldsite.vislab.usyd.edu.au/gallery/mathematics/diffeo/diffeo.html.

http://gregegan.customer.netspace.net.au/APPLETS/21/21.html and this one as well, http://gregegan.customer.netspace.net.au/APPLETS/15/15.html

http://viswiz.imk.fraunhofer.de/~nikitin/ax_3.gif

 

[sol2]

The Green lines in picture help you to understand the nature of the gravitons, as they would extend into those extra spatial dimensions.

http://cerncourier.com/objects/2000/cernnews5_3-00.gif

Of course, if this third dimension were infinite in size, as it is in our world, then the flatlanders would see a 1/r2 force law between the charges rather than the 1/r law that they would predict for electromagnetism confined to a plane. If, on the other hand, the extra third spatial dimension is of finite size, say a circle of radius R, then for distances greater than R the flux lines are unable to spread out any more in the third dimension and the force law tends asymptotically to what a flatlander physicist would expect: 1/r. However, the initial spreading of the flux lines into the third dimension does have a significant effect: the force appears weaker to a flatlander than is fundamentally the case, just as gravity appears weak to us. Turning back to gravity, the extra-dimensions model stems from theoretical research into (mem)brane theories, the multidimensional successors to string theories (April 1999 p13). One remarkable property of these models is that they show that it is quite natural and consistent for electromagnetism, the weak force and the inter-quark force to be confined to a brane while gravity acts in a larger number of spatial dimensions."

http://cerncourier.com/main/article/40/2/6/1

 

[sol2]

What the Heck are Spherical D3 Branes

If only I could see

A. Classical stability and the gravitational back reaction
The general feature that branes of spherical geometry can exist stably in a background of some anti-symmetric tensor field strength is quite similar to the mechanism of dielectric branes discussed by Myers [7], but there is one critical difference.

In AdS, the r = 0 solution is classically stable. In Myers' analysis, r = 0 solution is classically unstable. In this appendix, we will explain that even in Myers' example, r = 0 solution is classically stable when the effect of gravitational back reaction of the stress-energy of the background Ramond-Ramond field strength is taken into account.

Myers' analysis assumes a flat space-time in a background of constant RR 4-form field strength, giving rise to a potential of the form (see [7, equation (87)].)

Figure 5: Energy of spherical brane in the background Ramond-Ramond eld neglecting the back reaction (A.1) and including the back reaction (A.6). These curves are only valid locally near r = 0. When the back reaction is taken into account, r = 0 is classically stable.

However, it does not determine if this point is a global minimum or not.
The relevant energetic consideration comes from the r3 term which has a negative coefficient, and the r4 term which has a positive coefficient. Since the leading small r ffect is negative, there is a classical instability (see figure 5).

The essential difference between Myers' flat space analysis and our analysis in AdS is that in AdS, there is a term in E(r) which grows quadratically, thereby dominating over the cubic term which is the leading contribution in Myers' analysis.

Closer examination reveals that the quadratic term arises from the r dependence of g00 which enters into the Nambu-Born-Infeld action. g00 has non-trivial r dependence because the space-time is curved in response to the stress energy generated by the cosmological constant in the AdS space

http://ej.iop.org/links/q66/kvdwXsGK6lhQfbMsUaCWjw/jhep082000051.pdf

 

[arivero]

with the additional dimension totalling 11 when Witten Unifited the 5 different versions of String Theory into M-theory the extra dimension allowed for single strings to strech to the size of an entire univerese or large creating membranes or branes for short.

I missed this. Has Witten unifyed the 5 different versions? I thought it was a -by now- long standing conjecture.

 

[sol2]

I missed this. Has Witten unifyed the 5 different versions? I thought it was a -by now- long standing conjecture.

Of course we would all would like to undertand how such models emerged.

String theory's development has come primarily because of an extremely important problem that has faced physics for almost 100 years. The problem is that general relativity, the theory developed by Albert Einstein that explains things on very large or cosmological scales, is irreconcilable with Quantum Mechanics and the Standard Model, which describe the Universe on the small subatomic scale. Additionally, there are problems with the Standard Model: it has around 20 free parameters that must be plugged in by hand, and has a large number of particles it declares fundamental (there are three copies of every particle organized in what are termed as "families" whose only difference from one another is mass). Also, because it can't be reconciled with General Relativity, it lacks a description of gravity, the most familiar of the four fundamental forces.

It turns out that using 1-dimensional objects instead of point particles solves many of these problems. The number of free parameters in the theory drops from 20 to one (a parameter that corresponds to the size of the strings), and there is hope that details of the theory will explain why the three families of particles exist. Most importantly, string theorists were delighted to find that string theory necessarily contains gravitons, the particle that causes gravity. This has led Edward Witten, the founder of M-theory, to joke that string theory does have the remarkable experimental evidence that gravity exists all around us. Thus, string theory successfully unites General Relativity with Quantum Mechanics.

http://simple.wikipedia.org/wiki/M-theory

But in leading this thinking, as one reads, how could such claims be made as something being all around us when it is hidden? Some are more adept at spotting an ssue more abstractually centered, and onced ventured into , appearances seem totally devoid of reason?

But you had pointed out "degrees of freedom" that many would question in regards to dimensional relevance. Could you expand on that point please in a general way and then tree it mathematically, so I could follow.

The parameters for this link have yet to be written, so hopefully somebody reading will move to correct this.

T-duality is probably the most easily explained of the dualities. It has to do with the size, denoted by R, of the curled up dimensions of the string theories. It was discovered that if you take a Type IIA string theory that has a size R and change the radius to 1/R then you will end up getting what is equivalent to a Type IIB theory of size R. This duality, along with the others, creates connections between all 5 (or 6, if you count supergravity) theories

http://simple.wikipedia.org/wiki/M-theory

It is therefor very important to understand how concepts emerge from the ideas of string theory.

When I raised the issue of Liminocentric structure, the conceptual framework had already been established.

Whether we consider it as significant or not, I went further to develope this concept, although from the perspective of dynamcial situations, revealled in consicousness. It is hit hard by the statement of QM. But the following post should help one realize how the abstractiveness is pushing the mind to further incoporate a view of reality containing the cosmological and quantum view together as a form of dualism. This partially answers https://www.physicsforums.com/showpost.php?p=301223&postcount=1.

We had to identify what Lubos was abstractually doing in the configurations he was using.

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

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

 

[arivero]

But you had pointed out "degrees of freedom" that many would question in regards to dimensional relevance. Could you expand on that point please in a general way and then tree it mathematically, so I could follow.

I have done it in the thread "Arun...", https://www.physicsforums.com/showthread.php?t=41376
feel free to critiquize there