What Are Branes in Superstring Theory?

[sol2]

http://a799.g.akamai.net/3/799/388/3d94d6b574ec9f/www.msnbc.com/news/wld/graphics/superstring.gif

What is a Brane ?

This is a fairly simple example that I am sure can be expounded upon when given "time and ten dimensions"?

Pictures can sometimes paint a thousand words, why can't math paint you:)

(a) Compactifying a 3-D universe with two space dimensions and one time dimension. This is a simplification of the 5-D space*time 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.

http://physicsweb.org/box/world/13/11/9/pw1311091

http://www.superstringtheory.com/forum/stringboard/messages25/85.html

 

[Olias]

How so this:http://uk.arxiv.org/abs/hep-th/0405188

??;)

 

[sol2]

How so this:http://uk.arxiv.org/abs/hep-th/0405188

??;)

Type I bubbles with thin domain walls can be stabilized by the entrapment of various particle modes whose masses become much smaller inside than outside the bubble

As soon as I read this I knew what you were thinking.

For me there is great danger in the metaphorical pictures that one can use, for they have to be consistent with current mathematical constructions?

So where are we going to find such a model?

I would ask then, what about the understanding of geometrodynamics here, and the effects of sonoluminence. We have been defining this action in respect of the casimere plates, but have yet to touch upon the dynamics we see having encapsulated all those dimensions with time. Is this a safe paradigmal model apprehension that we can move forward with?

It is very difficult for me to imagine the boundary walls of the bubble in this sense without knowing that it could contain information from photon accumulation, as in the black hole.

Assuming the dynamics here might have revealled galaxies in formation, what action would allowed such centers to create new universes if we did not have this center to transform this energy into new possibilities? New suns to be born?

Calculating the amount of energy contained in such bubbles, is a interesting feature when you might apply it to the schwarzchild radius as a energy determnation, yet how would you calculate such universes but by the nature and development in time( 13.7 billion years?) is how much energy?

So you look at phonon dispersal and translation into bubble morphology(surface tension)(http://superstringtheory.com/forum/extraboard/messages12/587.html ), and wonder, okay the bubble size reached these dimensions, so why did it burst? The amount of energy contained was, and immediately such collapse signalled black hole collapse and interactive abilities, to fission? You see ?

See http://wc0.worldcrossing.com/WebX?14@77.zThGbdxA64H.3@.1dde3fed/15

All the time this bubble world is going on, what is happening outside the bubble? In sonoluminence there is a translation going on with phonon dispersal over the bubbles surface and moved inside?

ds2 = c2(1-2MG/c2r)dt2 - dr2/(1-2MG/c2r) - r2(dq2+sin2qdf2).

For me such visualizations had to contain the information of supergrvaity in the early universe, and reducing it to Einsten equations of the metric had to reveal this thinking as well. The gravity of the current universe

I have responded quckly here and will now go through the article.

 

[sol2]

Using the cosmological constant what value is Omega in terms of critical density?

I like to http://www.superstringtheory.com/forum/extraboard/messages10/321.html people's imaginations?

In the one sense, "psychologically," mass thinking can activate "counter proposals" by its very presence?

Why not a example here Peter Woit?

I hope the "humour" is well taken. If you are going to apply the terms of negative energy, then how pervasive can we intend the order of geometries but to have incorporated into life? Fully grokkkkkkkkkked it:)

 

[maddy]

Are moduli in stringscape like metrics in general relativity because both determine the shape and size of spaces?

 

[kneemo]

Branes via differential forms

I enjoyed the (indirect) superstringtheory.com approach to p-branes (http://www.superstringtheory.com/basics/basic7a.html). One can work through the Maxwell equations via differential forms, say, in Wheeler et al's Gravitation (with nice pictures of diff. forms), and then extend the process to d dimensions with the p+1 form vector potential. Through a simple co-dimensional argument we find that the sources are p-dimensional objects, the p-branes.

Of course we can't *see* the structure of the branes through this approach, but the exercise is instructive, nevertheless.

 

[Tom McCurdy]

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.

 

[sol2]

The standard Model has to arise from the brane? In strings how shall we define the issues of http://wc0.worldcrossing.com/WebX?14@118.qKIvc7nofIf.1@.1ddf4a5f/17 ?

 

[Mike2]

The question for me is how can these geometric objects (p-branes) come to be in the first place? They all are submanifolds of the background spacetime dimensions, the bulk. But what principle sustains their existence? Why don't they immediately dissipate in all directions at the speed of light and thus evaporate into nothingness?

 

[sol2]

The question for me is how can these geometric objects (p-branes) come to be in the first place? They all are submanifolds of the background spacetime dimensions, the bulk. But what principle sustains their existence? Why don't they immediately dissipate in all directions at the speed of light and thus evaporate into nothingness?

How advanced have we become in the realities of the quantum geoemtry and the relevance ot quantum gravity?

You must know the GR had to be lead too and geometriclaly defined. statistical analysis, a issue in the Probabilities? So how the heck could any geometry come out of it? So toy models were developed

We can become quite flexible when we adopt these views of theoretcial models for consideration, but they don't mean a hell of a lot, if they can not speak to the quantum nature? Think gamma rays. We reduced the nature of th ecosmos to geoemtricallly define issues of quantum natures, and at the same time revealled our thinking both classically and quantifically?

 

[Mike2]

How advanced have we become in the realities of the quantum geoemtry and the relevance ot quantum gravity?

You must know the GR had to be lead too and geometriclaly defined. statistical analysis, a issue in the Probabilities? So how the heck could any geometry come out of it? So toy models were developed

One can at least understand the emergence of the original manifold - at least that it should exist. We still have yet to understand the necessity of its geometry and number of dimensions. But nothing can be described at all without the use of a manifold of some sort. And of course it would have to start out infinitesimally small and grow at some rate. For instant everything violates the causality of its existence.

But then the issue arises as to how the particles within the original manifold came to be and what sustains their structure. It would seem that if these substructures are mere distortions of the original spacetime, then the continuity of the original manifold would require that any disturbance of these structures would dissipate in all directions like any other wave through a medium. But that does not happen, so particles are not disturbance of a medium. So I wonder if they are the places where the original spacetime is absent. That would mean that particles form a boundary of spacetime. And as I understand it, boundaries don't dissipate like disturbances.

 

[Mike2]

Here's another thought:
It would certainly seem at least that black holes are places were normal spacetime does not exist, that the event horizon is a boundary of spacetime. Now, how is it possible to combine a geometry different from that of black holes to black holes geometry, and how could that combination of differing geometries be additive like the conservation of mass entering the black hole? This suggests that particle geometry is similar to black hole geometry.

 

[Mike2]

Here's another thought:
It would certainly seem at least that black holes are places were normal spacetime does not exist, that the event horizon is a boundary of spacetime. Now, how is it possible to combine a geometry different from that of black holes to black holes geometry, and how could that combination of differing geometries be additive like the conservation of mass entering the black hole? This suggests that particle geometry is similar to black hole geometry.

Not only that, but it is said black holes evaporate; they become smaller and smaller as they shed more and more particles. I seem to remember that black holes even become the size of a few particles themselves until they shed those last few particles. If so, then this is even more suggestive that black holes share the same geometry as other particles, since you would think that it is even more unlikely that geometry can change between objects of the same order of size.

 

[sol2]

Not only that, but it is said black holes evaporate; they become smaller and smaller as they shed more and more particles. I seem to remember that black holes even become the size of a few particles themselves until they shed those last few particles. If so, then this is even more suggestive that black holes share the same geometry as other particles, since you would think that it is even more unlikely that geometry can change between objects of the same order of size.

Or maybe this that in the high energy colliders such black holes already exist?

The geometry on a classical level is speaking not only to the cosmo, but to something else as well. Why we have to choose the type of discriptions we want about quantum geometry. LQG or Strings? We know strings will allow contiuity in topological considerations while in disrcete forms thsi is only now being discussed. String have theoretically been there

 

[Mike2]

Or maybe this that in the high energy colliders such black holes already exist?

The geometry on a classical level is speaking not only to the cosmo, but to something else as well. Why we have to choose the type of discriptions we want about quantum geometry. LQG or Strings? We know strings will allow contiuity in topological considerations while in disrcete forms thsi is only now being discussed. String have theoretically been there

If we consider quantized geometry of some sort, then do we not have to consider whether those different geometries can add, interfere, interact with each other? How would a 4D spacetime interact/interfere with say a 7D spacetime in a non-arbitrary manner. 1D paths of a path integral are all the same type of object with the same dimensionality; so it is easy to understand how they can be added constructively or destructively in the path integral. But 4D is not even of the same dimensionality as 7D, so how would such differing spaces be added constructively/destructively?

I suppose a amplitude and phase can be assigned to a differing 2D objects/surfaces that wonder in differing regions and then be integrated to see how they interfere with each other, just as they do with differing paths of a path integral. But if we were going to try to get a 4D object/space to interfere with a 7D object/space, then combinatorics would tell us how many different ways each dimension of the 4D space could interact with each dimension of the 7D space, right? Would every scenario where each dimension of the 4D space is integrated with each dimension of the 7D space have to be considered? Where 2D interacts with 2D, would we have to consider how each dimension interacts with each of the other dimensions? Or is there only one way a 2D object and interfere with a 2D object?

Isn't this the essential question of M-theory where objects of differing dimensionality interact with each other?

 

[sol2]

If we consider quantized geometry of some sort, then do we not have to consider whether those different geometries can add, interfere, interact with each other? How would a 4D spacetime interact/interfere with say a 7D spacetime in a non-arbitrary manner. 1D paths of a path integral are all the same type of object with the same dimensionality; so it is easy to understand how they can be added constructively or destructively in the path integral. But 4D is not even of the same dimensionality as 7D, so how would such differing spaces be added constructively/destructively?

I suppose a amplitude and phase can be assigned to a differing 2D objects/surfaces that wonder in differing regions and then be integrated to see how they interfere with each other, just as they do with differing paths of a path integral. But if we were going to try to get a 4D object/space to interfere with a 7D object/space, then combinatorics would tell us how many different ways each dimension of the 4D space could interact with each dimension of the 7D space, right? Would every scenario where each dimension of the 4D space is integrated with each dimension of the 7D space have to be considered? Where 2D interacts with 2D, would we have to consider how each dimension interacts with each of the other dimensions? Or is there only one way a 2D object and interfere with a 2D object?

Isn't this the essential question of M-theory where objects of differing dimensionality interact with each other?

I highlighted your last statement because this is the very question of how any standard model shall arise from the brane? The topological movement has to be smooth. The supersymmetrical brane is smooth from this perspective as well.How would these http://wc0.worldcrossing.com/WebX?14@229.BuTYce3bgPj.0@.1ddf4a5f/17 ?

Well from a string perspective they've change the very foundation of our thinking? The questions of background versus non background become very important here, and this is where the grounding factors in my thinking have trouble remaining in defintion, so I needed to understand this(to concretize it). The result, is two ways in which we can percieve the nature of such geometries arising for us in discriptive features of quantum gravity.

What must be realized is that they are both based on geometrical defintions, one albeit, very different from a continuity point of view to one discrete.

After all we do like structures( we have a long history of it ). The logic that Smolin put forward for us in Three Roads was extremely helpful in helping me to orientate a view, because it was by his example, that such model in comprehension could help us undertand how three roads could now have formed a new math? If Glast in taken into consideration,this is a summation to me of Smolins goal, as well as a introdcution to a new undertanding of quantum computation.

A certain distilliation had to go on on that might be no different then integrating Venn logic from a quantum perspective into some form of probabilty discription?

If I put Hopf rings into the image of GHZ entanglement what kind of geometry shall we call this? Imagine buiding such psychological determinations from such logic? Maybe we can reassign these quantum computers in how we shall view AI possibilties But this is taking it to far, so back down to earth.

 

[Mike2]

Isn't this the essential question of M-theory where objects of differing dimensionality interact with each other?

OK, let's try this:
Could it be that M-theory IS quantum gravity? It is said that String Theory is background dependent and M-theory along with it. But it seems like only a matter of perspective between whether we are trying to quantize gravity by considering a "path" integral of every possible spacetime, or considering the interaction of every kind of dimensional brane? At the differential scale one may be no different than the other. Since all the branes at the beginning are no bigger than the universe as a whole. The interaction of all possible branes would be the interaction of all possible spacetimes, right? So the ultimate M-theory may just be a background independent quantum geometry?

 

[kneemo]

Black holes as D-branes

Not only that, but it is said black holes evaporate; they become smaller and smaller as they shed more and more particles. I seem to remember that black holes even become the size of a few particles themselves until they shed those last few particles.

Let us consider the type II superstring, where we only have closed loops of string. It is possible to have a string connecting two different black holes. When the black holes emit Hawking radiation, becoming smaller and smaller as you say, and finally decaying to their ground state, we are left with two D-branes connected by a string.


See Witten's "Black holes and quark confinement" (http://www.sns.ias.edu/~witten/papers/CurrentScienceVol81.pdf )

 

[Mike2]

OK, let's try this:
Could it be that M-theory IS quantum gravity? It is said that String Theory is background dependent and M-theory along with it. But it seems like only a matter of perspective between whether we are trying to quantize gravity by considering a "path" integral of every possible spacetime, or considering the interaction of every kind of dimensional brane?

I suppose that each dimensional type of p-brane is described as embedded in the bulk. But each could just as soon be described in "p" dimensional parameter space. And if every sort of virtual interaction must be considered, then every sort of dimensional interaction must be considered. And spacetime itself become the result of every possible interaction.

 

[Mike2]

I suppose that each dimensional type of p-brane is described as embedded in the bulk. But each could just as soon be described in "p" dimensional parameter space. And if every sort of virtual interaction must be considered, then every sort of dimensional interaction must be considered. And spacetime itself become the result of every possible interaction.

As I understand it, space is filled with a "quantum foam" where every sort of virtual particle spontaneously pops into existence and then annihilate each other. The higher the energy of those particles, the less time they spend in existence. But wouldn't those virtual particles have to include every dimensional type of brane/particle? And wouldn't such a foam have to include every type of interaction between every dimensional type of brane? Isn't this the same as saying that the quantum foam is space, and space IS the interaction of every dimension? And isn't the interaction of every type of dimension the same as quantum gravity? Thus, it would seem that M-theory is quantum gravity, right? Or has somebody already gone this route?

 

[sol2]

Quantum Geometry must include a limit( I'll post it tomorrow), so from a quantum gravity perspective how would you measure pull, and the dimensional relationship?

The branes perspectives and dimensions are developing in M theory?

Imagine this quark to quark measure, and a relationship to the energy of this http://cerncourier.com/objects/2000/cernnews5_3-00.gif.

So let's say the graviton(dimension) is now being represented in the bulk. What would this mean to the graviton, and all possible interactions with it?

SR development is going through a revision with LQG? But still the dynamcis exist in the bulk for consideration and strings has answered this question? So how shall we percieve the nature of those branes, as they develope?

A standard model approach?

It seems one has to be come quite flexible when you engage the two perspectives of LQG and M Theory.

I have been reading papers that Neried and Marcus supplied from a earlier discussion that forced me to look back on the question of Lorentz Invariance.

Those in Strings research are saying something I am not hearing as well, although it is sitting vaguely on the horizon, from what information I have read.


That tomorrow as well.

A fancier way of saying that is that in general, it's okay to model the space around us using the Euclidean metric. But the Euclidean model stops working when gravity becomes strong, as we'll see later.

http://www.theory.caltech.edu/people/patricia/sptmb.html

The complexity at Planck length

 

[sol2]

Quantum Geometry must include a limit( I'll post it tomorrow), so from a quantum gravity perspective how would you measure pull, and the dimensional relationship?


I have been reading papers that Neried and Marcus supplied from a earlier discussion that forced me to look back on the question of Lorentz Invariance.

Those in Strings research are saying something I am not hearing as well, although it is sitting vaguely on the horizon, from what information I have read.

If you check out Micho Durdevich's Introduction to Quantum Geometry, he displays the length as a universal constant, he combines them as the gravitational constant, Planck's constant, and the velocity of light, as--

A very interesting potential application of quantum geometry in physics is to provide a mathematically coherent description of the physical space-time, at all scales---in particular at the level of ultra-small distances, characterized by the Planck lenght. This length is a universal physical constant, defined as a unique combination of gravitational constant , Planck's constant and the velocity of light c. Explicitly,

http://www.matem.unam.mx/~micho/mathjpg/planck-lenght.jpg


As we can see, it is an exorbitantly small number! There are many reasons to believe that Planck's length marks a boundary for the applicability of classical concepts of space and time in physics.

http://www.matem.unam.mx/~micho/mbdiag.html

F.W. Stecker, Constraints on Lorentz Invariance Violating Quantum Gravity and Large Extra Dimensions Models using High Energy Gamma Ray Observations

arXiv:astro-ph/o3o8214 v2 21 Aug 2003

 

[Mike2]

As I understand it, space is filled with a "quantum foam" where every sort of virtual particle spontaneously pops into existence and then annihilate each other. The higher the energy of those particles, the less time they spend in existence. But wouldn't those virtual particles have to include every dimensional type of brane/particle? And wouldn't such a foam have to include every type of interaction between every dimensional type of brane? Isn't this the same as saying that the quantum foam is space, and space IS the interaction of every dimension? And isn't the interaction of every type of dimension the same as quantum gravity? Thus, it would seem that M-theory is quantum gravity, right? Or has somebody already gone this route?

It may be that the nature of the interation between branes of differing dimension in M-theory is not like the interation of differing dimensions in quantum geometry/gravity. Perhaps the nature of the interaction between different branes in M-theory is that one branes serves to fix the type of boundary conditions of the other. Whereas the nature of the interactions of different dimensions in quantum gravity is more like a path integral where each dimensional object is given its own amplitude and phase, and these mix with the amplitude and phase for objects of different dimension. Comments anyone?

 

[sol2]

Brane - Interview with Dr. Michael Duff

http://www.esi-topics.com/brane/interviews/MichaelDuff.jpg



And what's the payoff as far as making progress in string theory?

Hawking wrote down the formula for what that entropy should be. It's a famous formula that says the entropy is one-quarter the area of the event horizon of the black hole. He used a kind of macroscopic thermodynamic argument to reach this conclusion, but if what he was saying is correct, there should also be some microscopic explanation. In the subsequent 20 years, nobody could figure out what this microscopic origin of black hole entropy actually was. Using these new ideas of branes and M theory, that problem has now been solved. Another thing it does, and this may be too early to tell whether it's good or not, is M theory now offers dozens of ways of trying to do a real-world analysis to see how the standard model of particle theory fits into the scheme of things. Depending on how you look at it, that can be good or bad. Now we're left with a different kind of uniqueness problem. How does nature single out the one way of doing things? It also means we have some new avenues of exploration that we didn't think were open to us before. And then there's this large-dimension industry, which is a spin-off from M theory, as well.

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

 

[sol2]

Brane New World, by Roland Pease

Some theorists propose that our Universe exists as a slice through multidimensional space. Could this 'brane-world' concept unify gravity with nature's other fundamental forces?

http://www.nature.com/nature/journal/v411/n6841/images/411986ab.0.jpg

Weak link: a simple magnet is all that is needed to overcome the force of gravity.

"Imagine a parallel universe in which the three familiar dimensions of space and one of time are replaced by alternative dimensions beyond our experience. Now imagine that multiple universes exist as membranes, or branes, through a multidimensional hyperspace. These additional dimensions could be the size of atoms, or infinitely large. We would never be able to enter them, yet they could have profound effects on the physics of our Universe."

The leading explanation of how fundamental particles and forces behave is a theory called the standard model. Its main shortcoming is the difficulty of incorporating gravity on an equal footing with the other known forces. "It's remarkable that gravity, despite being the first to be discovered, is by far the most poorly understood force," says Nima Arkani-Hamed of Harvard University, one of the architects of brane-world physics.

The fundamental problem is that, compared with its counterparts, gravity is weak. This can be illustrated by comparing the gravitational attraction between two electrons with their mutual electrostatic repulsion — gravity is weaker by a factor of 1043. Arkani-Hamed uses a more familiar image to drive the message home: "An ordinary magnet can lift a pin off a table, even though the entire mass of the Earth is tugging down on this pin, trying to prevent it from being picked up."

http://www.nature.com/cgi-taf/DynaPage.taf?file=/nature/journal/v411/n6841/full/411986a0_r.html and the http://www.nature.com/nature/journal/v411/n6841/images/411986aa.0.jpg

http://www.benbest.com/science/standard.jpg

Strings vibrate in ten dimensions, six of which are tightly coiled in on an unmeasurably small scale and four of which are in conventional space-time. A variant known as membrane theory (M-theory, "branes" -- multi-dimensional membranes) puts gravity in an eleventh dimension and points to an infinite number of solutions -- implying (for some) an infinite number of universes.

http://www.benbest.com/science/standard.html

 

[sol2]

HyperSpace : A Scientific Odyssey

http://www.physicspost.com/imageview.php?what=getAuthorPic&authorId=23

This trick is easily extended. For example, if we generalize the theory to N dimensions, then the N dimensional gravitational field can be split-up into the following pieces (see fig. 5). Now, out pops a generalization of the electromagnetic field, called the "Yang-Mills field," which is known to describe the nuclear forces. The nuclear forces, therefore, may be viewed as vibrations of higher dimensional space. Simply put, by adding more dimensions, we are able to describe more forces. Similarly, by adding higher dimensions and further embellishing this approach (with something called "supersymmetry), we can explain the entire particle "zoo" that has been discovered over the past thirty years, with bizarre names like quarks, neutrinos, muons, gluons, etc. Although the mathematics required to extend the idea of Kaluza has reached truly breathtaking heights, startling even professional mathematicians, the basic idea behind unification remains surprisingly simple: the forces of nature can be viewed as vibrations in higher dimensional space.

http://www.physicspost.com/articles.php?articleId=140&page=8

Which of course brings us to the quantum harmonic oscillator.

 

[sol2]

Georgi Dvali

http://physics.nyu.edu/people/dvali.georgi.jpg




http://online.itp.ucsb.edu/online/susy_c99/dvali/oh/02.gif


Further extensions to the above picture here

 

[Mike2]

I have a problem with particles being lesser dimensional objects (branes) in an n-dimensional space. For it would then seem that you would have the ability to transverse the defining hypersurface of the particle and there would be a sudden instantaneous change in tension or force or something as you crossed the brane of the particle. This presents a discontinuity, doesn't it? I get the sense that nature abhors discontinuities.

I suppose the only way around such a discontinuity is for particles to be the n-1 boundary of n-dimensional space so that there is no crossing the boundary since there is no space there to travel across to. Any thoughts?

 

[sol2]

LQG is discrete and Strings are continuos.

There is no tearing in Strings.

How would you descrbe each particle if it has a energy value?

How would we ever really know if there were extra dimensions and how could we detect them if we had particle accelerators with high enough energies? From quantum mechanics we know that if a spatial dimension is periodic the momentum in that dimension is quantized, p = n / R (n=0,1,2,3,...), whereas if a spatial dimension is unconstrained the momentum can take on a continuum of values. As the radius of the compact dimension decreases (the circle becomes very small) then the gap between the allowed momentum values becomes very wide. Thus we have a Kaluza Klein tower of momentum states.

http://www.sukidog.com/jpierre/strings/extradim.htm

 

[Mike2]

I have a problem with particles being lesser dimensional objects (branes) in an n-dimensional space. For it would then seem that you would have the ability to transverse the defining hypersurface of the particle and there would be a sudden instantaneous change in tension or force or something as you crossed the brane of the particle. This presents a discontinuity, doesn't it? I get the sense that nature abhors discontinuities

In other words, such a discontinuity would violate causality, right? There would seem to be no cause for the sudden impulse experienced by transversing the brane.

 

[sol2]

LQG is discrete and Strings are continuos.

There is no tearing in Strings.

How would you descrbe each particle if it has a energy value?

No Tearing, how is this possible?

Topology is more general than geometry, being simply the study of CONNECTIONS (while geometry is the study of CONNECTED systems with specific SHAPE and SIZE). More specifically, TOPOLOGY STUDIES CLASSES OF SHAPES SUCH THAT ANY SHAPE IN A CLASS CAN BE TRANSFORMED INTO ANY OTHER SHAPE OF THAT CLASS WITHOUT TEARING OR RIPPING. (Thus, a circle can be topologically transformed into a square; a sphere into a pyramid; etc.)

http://ccins.camosun.bc.ca/~jbritton/totopology3.htm

http://ccins.camosun.bc.ca/~jbritton/animcup.gif

http://scholar.uwinnipeg.ca/courses/38/4500.6-001/cosmology/donut-coffeecup.gif

http://scholar.uwinnipeg.ca/courses/38/4500.6-001/cosmology/wormhole.jpg

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.

So now that we understand this effect of no tearing in brane theory how the heck are we ever suppose to understand the dynamics on the brane? What do fermions represent and what do bosons represent? What is held to the brane and what is allowed to roam?

If we had considered fermions held to the brane what effect would em consideration have in the world of gausssian curvatures, yet not remove it from its source? What does red or blue shifting tell us from the source and is held to the brane?

If we had understood the road develped from GR to gravitational wave production what is this wave when quantized, but to have revealled, that such graviton was a evolution that geometrically had to remain consistant through a whole host of geometrical considerations. This statement might seem contradictory inthe recognition of a variance in this evolution.



They each have to be connected. Klein's ordering of geometries is one way, but there is more to it. This I will have to find and place here for considerations. Texture(?), smooth or rough, on that supersymmetrical brane?

 

[sol2]

Stretching your Brane

Imagine that such brane worlds are hidden?

The question might be then as to why and how such a development of brane world could have ever departed from GR, yet included it, in the gravitons?

The question would be that if gravitons could go through branes and exist in the bulk, then how would we use these gravitons to describe the quantum geometry in quantum gravity? If we can scale gravitons in relation to energy released from the events, then using the quantized version of these gravitatons to describe movement in the cosmo would have to be very telling.

One thing that is clear is the use of photon interaction spoken to in Glast has run into limits in regards to TEV measures. This limit in glast is 2 to 20 TEV, but the graviton must be spoken too, at about 1? Any corrections here would be appreciated.

The hidden-dimension mystery features a cast of characters known as branes, objects that occupy the unseen extra dimensions. The term is a play on ``membrane'' -- a two-dimensional surface, or two-brane. Three-dimensional spaces -- such as the known universe -- are called three-branes. Physicists therefore refer casually to the universe as ``braneworld.''

``All the standard particles -- photons, quarks, leptons -- live on a three-dimensional subspace, a three-brane, or our brane,'' says Savas Dimopoulos of Stanford.

Branes reside in the hidden dimensions, known as ``the bulk.'' While matter and light stick to the branes, gravity traverses both branes and bulk. The hidden dimensions cannot be seen because only gravity can go there.

The current frenzy over extra dimensions began with an analysis appearing on the Internet a year ago in March. Dr. Dimopoulos and Nima Arkani-Hamed of Stanford, with Gia Dvali of the International Center for Theoretical Physics in Trieste, Italy, proposed a new explanation for why the standard unit of mass in subatomic physics is surprisingly huge (by atomic standards) -- about the mass of a speck of dust. That mass would be much smaller, they found, if some hidden dimensions were millimeter-sized.

http://fnth37.fnal.gov/lykken/dallas.html

 

[sol2]

Petr Horava

http://images.google.com/images?q=tbn:92-O1SQz5oIJ:ls.berkeley.edu/images/news/02/ps-horava.jpg

My research interests are focused on string theory, as a leading candidate for the quantum theory of gravity and unification. In recent years, string theory has been going through a revolutionary period, whose results changed our understanding of the theory and created new paradigms in other fields, ranging from pure mathematics, to quantum field theory, to particle phonomenology and cosmology.

As a result of this "string revolution" we now understand that string theory is a unique theory: all the apparently distinct string theories are manifestations of a single structure, related to each other by a web of new quantum symmetries known as dualities. These dualities also relate string theory to a new theory without strings, known as M-theory, whose structure remains somewhat mysterious.

String theory represents a systematic modification of general theory of relativity, so that it is compatible with quantum mechanics. Therefore, we can address some of the long-standing puzzles of quantum gravity in the string theoretical framework, such as the statistical interpretation of the thermodynamic Bekenstein-Hawking entropy of black holes. In a class of stringy black holes amenable to analysis, the entropy has been explained as counting of stringy states. This result further confirms that string theory is indeed on the right track to describe the microscopic physics of quantum gravity, as the correct degrees of freedom have already been identified.

The question of correct degrees of freedom for quantum gravity is related to the "holographic principle," according to which the number of degrees of freedom of any quantum gravitational system should scale as the area of the surface surrounding the system. Thus, it should be possible to completely describe the system by a finite density of states on a "holographic screen." We have indications that string theory is indeed holographic, although this fact is far from manifest -- holography is a "secret" property of string theory.

http://www.physics.berkeley.edu/research/faculty/horava.html

 

[sol2]

Brane Collisions

http://www.physics.princeton.edu/www/jh/research/Steinhardt.jpg

http://www.damtp.cam.ac.uk/user/ngt1000/branes_max.gif

make sure you let it load


I wanted to help people try and visualize what is going on and from the work of Steinhardt I like the way such visualization once incorporating some of the previous information allowed me to speculate futher, and introduce analogies that would have seemed holographical in nature.

More information from Paul Steinhardt can be gotten from http://feynman.princeton.edu/~steinh/

 

[Mike2]

I suppose the only way around such a discontinuity is for particles to be the n-1 boundary of n-dimensional space so that there is no crossing the boundary since there is no space there to travel across to. Any thoughts?

What about a particle being a vector or scalar field defined on some space? It would seem that if a field could come into existence where before it was not, then space has some sort of elastic property to allow those fields to form on that space where before it was not. This elastic ability would then seem to be the property that would cause such a change to propagate away in all directions so that the particle would immediately dissipate away in all direction. Or there would have to be something other than the fields holding the field in place and preventing it from dissipating. That something holding the field would have to be something other than space, fields, or particles, in other words, something that cannot be defined by fields. Does anyone know of any self-sustained local arrangement of fields that does not propagate away?

 

[sol2]

D1 to D5 Brane

http://www.sukidog.com/jpierre/strings/stringbh.gif

How the heck did you get to D5? You had to be able to determine the gravtion scalable feature in terms of these branes? From weak to strong. Certain particle situations then become realistic under such considerations.

From a one dimension recognition weak field gravitational measure would have satifsied the particle nature at it's minimum energy consideration? This would be distinctive?

One of the most dramatic recent results in string theory is the derivation of the Bekenstein-Hawking entropy formula for black holes obtained by counting the microscopic string states which form a black hole. Bekenstein noted that black holes obey an "area law", dM = K dA, where 'A' is the area of the event horizon and 'K' is a constant of proportionality. Since the total mass 'M' of a black hole is just its rest energy, Bekenstein realized that this is similar to the thermodynamic law for entropy, dE = T dS. Hawking later performed a semiclassical calculation to show that the temperature of a black hole is given by T = 4 k [where k is a constant called the "surface gravity"]. Therefore the entropy of a black hole should be written as S = A/4. Physicists Andrew Strominger and Cumrin Vafa, showed that this exact entropy formula can be derived microscopically (including the factor of 1/4) by counting the degeneracy of quantum states of configurations of strings and D-branes which correspond to black holes in string theory. This is compelling evidence that D-branes can provide a short distance weak coupling description of certain black holes! For example, the class of black holes studied by Strominger and Vafa are described by 5-branes, 1-branes and open strings traveling down the 1-brane all wrapped on a 5-dimensional torus, which gives an effective one dimensional object -- a black hole.
http://www.sukidog.com/jpierre/strings/bholes.htm

D5 considerations would have asked us to consider four of space and one of time?

 

[sol2]

http://www.space.com/images/h_space_membranes_010412_02.gif

"The [Ekpyrotic] scenario is that our current universe is [a] four-dimensional membrane embedded in a five-dimensional 'bulk' space, something like a sheet of paper in ordinary three-dimensional space," Turok told SPACE.com. "The idea then is that another membrane collided with ours, releasing energy and heat and leading to the expansion of our universe."

http://www.space.com/scienceastronomy/astronomy/bigbang_alternative_010413-1.html

Branes reside in the hidden dimensions, known as ``the bulk.'' While matter and light stick to the branes, gravity traverses both branes and bulk. The hidden dimensions cannot be seen because only gravity can go there

.

 

[sol2]

Are Brane Intersection UNiversal?

This question was once asked?

Intersection is a strange word if you do not consider it in light of the photon?

The finding announced today supports a theory of gamma-ray production posed by Prof. Avi Loeb of Harvard University and Prof. Eli Waxman of the Weizmann Institute in Rehovot, Israel. Not unlike a black hole, the sheer mass of a cluster serves as a gravitational drain, drawing in matter at speeds of up to a thousand miles per second. Electrons in this flow are accelerated, with an additional boost from magnetic fields, to near light speed and collide with microwave light, the afterglow from the big bang known as the cosmic microwave background.

These microwave light particles, or photons, are bumped up to the gamma-ray photon energy level. The gamma rays form a halo around the galaxy clusters. Other scientists, however, have suggested that the bulk of the gamma-ray background is produced not by this mechanism but by quasar-type galaxies, called blazars, each powered by a supermassive black hole. This background was discovered by NASA's second Small Astronomy Satellite (SAS-2) in the early 1970s.

Scharf and Mukherjee's new research compared a catalog of 2,469 galaxy clusters with the Compton database. Using sophisticated statistical techniques, they showed that the sky surrounding the most massive clusters was systematically brighter in gamma rays than other regions.

"The more massive the cluster (and greater the gravitational potential), the brighter the gamma-ray halo," said Mukherjee. "The enhancement observed was very similar to that predicted by the Loeb-Waxman theory."

The result announced today also supports the theory of the cosmic web. Scientists say that matter in the Universe forms a cosmic web, in which galaxies are formed along filaments of ordinary matter and dark matter like pearls on a string. Clusters form at the intersection of these filaments. The electrons that fuel the gamma-ray production rush into clusters along these rivers or filaments of matter connecting galaxies and clusters. Thus, gamma rays serve as probes to the early structure-forming epoch of the Universe.

Gamma ray halos around clusters also provides a means to measure intergalactic magnetic fields. Two of the three variables to measure magnetic fields are known: the mass of galaxy clusters and the distribution of the microwave background. The third variable is electron efficiency, which can now be measured by virtue of gamma-ray production.

The Gamma-ray Large Area Space Telescope (GLAST), scheduled for launch in 2006, should resolve gamma-ray haloes around galaxies with unprecedented clarity. GLAST could measure intergalactic magnetic fields and watch the formation of structure in the universe through its gamma-ray eyes, the scientists said.

For more information, go to:

http://www-glast.sonoma.edu/news/08_13_02.html

So what if this energy is all spread out in the CMB at a early stage?

How would you tell and not consider the significance of the spaces inbetween as we look? So there is no supersymmetry?

Heaven forbid, what shall we cal this http://www-glast.sonoma.edu/index.html WE all know very well we had been taking a serious look at describing how the formation of the universe from then to now, and look how wonderfull we have built this view of reality. Imagine, it's all wrong?

 

[sol2]

I needed it to be a little clearer so I went for a definition.


Special relativity and Lorentz invariance

In order to account for the structure of space and time at the Planck scale, LQG breaks Lorentz invariance and posits that certain well known effects of special relativity such as length contraction and time dilation cannot occur below the threshold of the Planck scale. It also predicts that the speed of photon propagation in vacuum may be dependent on the photon's wavelength, and not constant as demanded by special relativity (where it is denoted by c). It is not clear whether an approximate Lorentz invariance can be recovered in LQG at long distances and whether LQG can explain the plethora of successful experimental tests of special theory of relativity. LQG proposes a privileged reference frame associated with the spin foam, and therefore it is natural to expect that it may suffer from the usual problems of the old-fashioned theories of luminiferous aether. Nevertheless, LQG is formally a local gauge theory of the self-dual subgroup of the Lorentz group.

Time

Additionally, in LQG, time is not infinitely continuous but discrete and quantized, just as space is: there is a minimum moment of time, Planck time, which is on the order of 10−43 seconds, and shorter intervals of time have no physical meaning. This carries the physical implication that relativity's prediction of time dilation due to accelerating speed or gravitational field, must be quantized, and must consist of multiples of Planck time units. (This helps resolve the time zero singularity problem: see subsection "Big Bang")

http://www.wordiq.com/definition/Loop_quantum_gravity

 

[sol2]

Brane World and the House of Cards

A couple of things popped into my mind about the issue of time and space.

In LQG Time is counted as discrete and space is counted a discrete also. I understand that LQG is doing work in speical relativity, and see where the Glast work might be of sigificance.

At the same time M theory has moved past SR to GR and accepted these measures in a cosmological way, and further have accepted features of time that allow this continuous nature to be expressed.

So we see the differences here, about how we can interpret the nature of reality from discreteness and from a continuous point of view in M theory, that if you accept the graviton nature of quantization of those gravity waves, you accept certain features about brane world.

I have looked at Glast and see where the potential exists now, and it is pretty clear, but we had not ventured into Brane world, and further attempts a dismantling brane world theories would have to speak to supersymmetry as it has been attacked here in this forum and other places.

We would have to have a responsible discussion, in light of the features Smolin points out that can falsify the brane world logic, so how shall we do this to save us all from delusional states

So what is the nature of the geometry in brane world? Will such intersection points allow us to speak to the theoretical graviton as we do with the issue of gamma ray radiation?

Are there such intersections in brane world that would have spoken to the holographical reality? It might be easier for some to visualize these hidden dimensins and such points arising from a intersection point?

Warped Geometry of Brane WorldGary N. Felder, Andrei Frolov, Lev Kofman

We study the dynamical equations for extra-dimensional dependence of a warp factor and a bulk scalar in 5d brane world scenarios with induced brane metric of constant curvature. These equations are similar to those for the time dependence of the scale factor and a scalar field in 4d cosmology, but with the sign of the scalar field potential reversed. Based on this analogy, we introduce novel methods for studying the warped geometry. We construct the full phase portraits of the warp factor/scalar system for several examples of the bulk potential. This allows us to view the global properties of the warped geometry. For flat branes, the phase portrait is two dimensional. Moving along typical phase trajectories, the warp factor is initially increasing and finally decreasing. All trajectories have timelike gradient-dominated singularities at one or both of their ends, which are reachable in a finite distance and must be screened by the branes. For curved branes, the phase portrait is three dimensional. However, as the warp factor increases the phase trajectories tend towards the two dimensional surface corresponding to flat branes. We discuss this property as a mechanism that may stretch the curved brane to be almost flat, with a small cosmological constant. Finally, we describe the embedding of branes in the 5d bulk using the phase space geometric methods developed here. In this language the boundary conditions at the branes can be described as a 1d curve in the phase space. We discuss the naturalness of tuning the brane potential to stabilize the brane world system.

http://arxiv.org/abs/hep-th/0112165

 

[sol2]

Brane World Interactions and Hyperspace

Brane World Cosmology Comes Down to Earth

How many dimensions are there? That’s not easy. Sure, we have three spatial dimensions plus time. And the physics of the four-dimensional framework of space-time is all encapsulated in Einstein’s general theory of relativity, a hugely successful paradigm. But cosmology raises many questions that go beyond the textbook presentation of general relativity. For example, when we run the universe backwards we reach a state of extreme matter and energy density right after the big bang. What theory can we use to describe the universe at the earliest times, when gravity needs folding into quantum theory? And at low energies, when the universe has expanded dramatically due to inflation, how can we account for the puzzles of dark energy and dark matter that weigh in at 97% of the rest mass of the universe?

In the low-energy limit these correspond to the textbook Einstein equations. Coauthor Misao Sasaki (Osaka University) had this comment for Science Watch: "We’ve derived the gravitational equations as seen by an observer on the brane. They look like the Einstein equations but they have two additional terms, which arise from the fifth dimension. One of these terms contains all the information on five-dimensional gravity, and that’s what has excited the interest of the researchers who are citing our work. If this term could be proved experimentally it will give us clear evidence that we are living in a brane-world.

http://www.sciencewatch.com/july-aug2002/sw_july-aug2002_page6.htm

 

[sol2]

Two...Two Branes Are Better then One

Additional spatial dimensions may seem like a wild and crazy idea at first, but there are powerful reasons to believe that there really are extra dimensions of space. One reason resides in string theory, in which it is postulated that the particles are not themselves fundamental but are oscillation modes of a fundamental string.

http://www.edge.org/3rd_culture/randall03/images/randall200.jpg

In cosmology, for instance. Alan Guth's mechanism whereby exponential expansion smooths out the universe works very well, but another possibility has been suggested: a cyclic universe, Paul Steinhardt's idea, wherein a smaller amount of exponential expansion happens many times. Such a theory prompts you to ask questions. First of all, is it really consistent with what we see? The jury's out on that. Does it really have a new mechanism in it? In some sense, the cyclic idea still uses inflation to smooth out the universe. Sometimes it's almost too easy to come up with theories. What grounds your theories? What ties them down? What restricts you from just doing anything? Is there really a new idea there? Do we really have a new mechanism at work? Does it connect to some other, more fundamental theoretical idea? Does it help make that work? Recently I have been exploring the implications of extra dimensions for cosmology. It seems that inflation with extra dimensions works even better than without! What's so nice about this theory is that one can reliably calculate the effect of the extra dimension; no ad hoc assumptions are required. Furthermore, the theory has definite implications for cosmology experiments. All along, I've been emphasizing what we actually see. It's my hope that time and experiments will distinguish among the possibilities.

http://www.edge.org/3rd_culture/randall03/randall03_p6.html

 

[Mike2]

As I understand it, space is filled with a "quantum foam" where every sort of virtual particle spontaneously pops into existence and then annihilate each other. The higher the energy of those particles, the less time they spend in existence. But wouldn't those virtual particles have to include every dimensional type of brane/particle? And wouldn't such a foam have to include every type of interaction between every dimensional type of brane? Isn't this the same as saying that the quantum foam is space, and space IS the interaction of every dimension? And isn't the interaction of every type of dimension the same as quantum geometry? Thus, it would seem that M-theory is quantum geometry, right? Or has somebody already gone this route?

Originally Posted by Mike2

It may be that the nature of the interation between branes of differing dimension in M-theory is not like the interation of differing dimensions in quantum geometry/gravity. Perhaps the nature of the interaction between different branes in M-theory is that one branes serves to fix the type of boundary conditions of the other. Whereas the nature of the interactions of different dimensions in quantum geometry/gravity is more like a path integral where each dimensional object is given its own amplitude and phase, and these mix with the amplitude and phase for objects of different dimension. Comments anyone?

But now that I thing of it, as I recall, it is the boundary conditions that create the quantum levels. So the intersection of branes serving to set boundary conditions for other branes may be equivalent to to the interaction of differing dimensions as in quantum geometry. So M-theory may still be equivalent to other approaches to quantum geometry.

 

[sol2]

Look

deeper...

...deeper...

...deeper...

I wanted to make sure I did not confuse the name of Andrey Krasnov with Kirrill Krasnov that Baez is related to in literature.

Why I wanted to add this here has to do with above posted, and how the intersection of photons held in regard to LQG's attempt at discribing the issues of Glast. from the SRian approach.

http://wc0.worldcrossing.com/WebX?14@92.YyIIcXeLrlD.0@.1ddf4a5f/57

http://www.sandlotscience.com/Moire/images/moire_intro.gif​

I wanted to add this animation to help people recognzie the similarity that has made me aware of how this intersection is a vital recognition of how we can see the evolution of the early universe to now.

We talk about cosmic strings here in the animation as a way of seeing the consolidation of event and structure in that universe. What was important for me was to recognize how supersymmetry might arisen from brane realizations, and again, the moire effect was most strange if we had considered this "intersection," of the graviton, as if the photon was to travel through these waves.

to here and touch the smile.

down...

the way...

all...

Look

 

[pelastration]

Intersections (like cutting properties) is imo the main problem. Ask yourself: Why would there be a Universal Sissor cutting everything in pieces?
A unifying approach needs to be: Unifying! Not separating.

If you are interested you can download my powerpoint presentations at ANPA (Cambridge UK). There were two presentations.
1. 3.6 Mb: [PLAIN]http://www.mu6.com/ANPA/pelastration1.ppt[/URL]
2. 1.2 Mb: [PLAIN]http://www.mu6.com/ANPA/pelastration2.ppt[/URL]

 

[sol2]

Intersections (like cutting properties) is imo the main problem. Ask yourself: Why would there be a Universal Sissor cutting everything in pieces?
A unifying approach needs to be: Unifying! Not separating.

If you are interested you can download my powerpoint presentations at ANPA (Cambridge UK). There were two presentations.
1. 3.6 Mb: [PLAIN]http://www.mu6.com/ANPA/pelastration1.ppt[/URL]
2. 1.2 Mb: [PLAIN]http://www.mu6.com/ANPA/pelastration2.ppt[/URL][/QUOTE]


I will be looking at your presentations. Can you put links to site presenting these two ppt presentations, as they did not download for me

I am bringing you to the very top post of this thread. Would you not agree that such scissors would have meant discrete pieces?

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.

Imagine the membranes doing all kinds of things but never tearing.The bubbles should be able to do this in bubble eversions?
http://oldsite.vislab.usyd.edu.au/gallery/mathematics/diffeo/diffeo.html

Greg Egan is very helpful here As well, Helicoid visualizations.

From the Planck epoch to now the standard model has to assume that such a path(model) would materialize? What do two complete rotations mean?

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

http://wc0.worldcrossing.com/WebX?14@208.lWSbctOOtqi.20@.1ddf4a5f/69

 

[pelastration]

I will be looking at your presentations. Can you put links to site presenting these two ppt presentations, as they did not download for me

Sol, I put them as webpages.
Here are the links (images contain some black dots):

First day: http://www.mu6.com/ANPA/pelastration1.htm

Second day: http://www.mu6.com/ANPA/2/pelastration2.htm. Here some pages are repeated + reactions added on questions during the first presentation. Some images (i.e. QM box eperiments) were explained verbally and not eplained on the slide. For the Alain Aspect experiment I had not the time to make an image.

 

[pelastration]

I am bringing you to the very top post of this thread. Would you not agree that such scissors would have meant discrete pieces?

Imagine the membranes doing all kinds of things but never tearing.The bubbles should be able to do this in bubble eversions?
http://oldsite.vislab.usyd.edu.au/gallery/mathematics/diffeo/diffeo.html

Greg Egan is very helpful here As well, Helicoid visualizations.

From the Planck epoch to now the standard model has to assume that such a path(model) would materialize? What do two complete rotations mean?

Thanks for the links.

Sure, Universal Scissors would create discrete pieces but they would loose history. If cut what would connect them gravitational?
Don't you think conservation of history (information) is essential?

Yes the 720° belt trick can be done with pelastrated holons. Lou Kauffmann showed the trick during the ANPA meeting. Fun. Lou looks into a special algebra for pelastrations.

 

[sol2]

Thanks for the links.

Sure, Universal Scissors would create discrete pieces but they would loose history. If cut what would connect them gravitational?
Don't you think conservation of history (information) is essential?

Yes the 720° belt trick can be done with pelastrated holons. Lou Kauffmann showed the trick during the ANPA meeting. Fun. Lou looks into a special algebra for pelastrations.

If cut what would connect them gravitational? Don't you think conservation of history (information) is essential?

The information is always there in the bulk. You never lose it. It just gathers in spots, sometimes stronger then other locations, and we see where all these holes start to look like swiss cheese universe.

Might Lou looked at math of topos theory?

 

[sol2]

Sol, I put them as webpages.
Here are the links (images contain some black dots):

First day: http://www.mu6.com/ANPA/pelastration1.htm

Second day: http://www.mu6.com/ANPA/2/pelastration2.htm. Here some pages are repeated + reactions added on questions during the first presentation. Some images (i.e. QM box eperiments) were explained verbally and not eplained on the slide. For the Alain Aspect experiment I had not the time to make an image.

You work very quickly and thank you for putting into html pages.

Your mention of Alain Aspect is a good sign to me that you are headed in the right direction. My little story will bring together a lot of what you are doing and seeing. Your framework will be complete as far as I see it, once you incorporate the final information.

From light to dark, and back again, and what begins and ends is very interrelated and contain seeds of each other. If you have a shadow and light and inbetween, a line, how shall we describe this line? For you, I know the image will materialize Good work. Maybe, you can give the image a complete rotation?