Dilation and the Cosmic String

One such field, called the dilaton, is the master key to string theory; it determines the overall strength of all interactions. The dilaton fascinates string theorists because its value can be reinterpreted as the size of an extra dimension of space, giving a grand total of 11 spacetime dimensions

According to T-duality, universes with small scale factors are equivalent to ones with large scale factors. No such symmetry is present in Einstein's equations; it emerges from the unification that string theory embodies, with the dilaton playing a central role.

Gabriele Veneziano


According to Einstein's theory of general relativity, the sun's gravity causes starlight to bend, shifting the apparent position of stars in the sky.

Time will also pass more slowly in a strong gravitational field than in a weak one? So what effect would this have if we consider the gravitational lensing, that had been talked about in previous post?:)

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

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

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



Where spacetime is flat, there is no gravity, hence light will travel unabated. If we move this consideration in contrast to the non-euclidean realms, what have we learnt of gravity? What have we learnt of dimensions?



Mass, Photons, Gravity Dr. Lev Okun, ITEP, Russia

Warped Field Creates Lensing

The statement of this post, is distilled from the collaboration of some of the images to follow.



In cosmic string developement there are these three points to consider.

1. Cosmological expansion

2. Intercommuting and Loop Production

3. Radiation

I am always looking for this imagery that helps define further what gravitational lensing might have signified in our perception of these distances in space. How the cosmic string might have exemplified itself in some determination, as we find Lubos has done in the calculation of the mass and size of this early event. This image to follow explains all three developemental points.



Bashing Branes by Gabriele Veneziano
String theory suggests that the big bang was not the origin of the universe but simply the outcome of a preexisting state

The pre–big bang and ekpyrotic scenarios share some common features. Both begin with a large, cold, nearly empty universe, and both share the difficult (and unresolved) problem of making the transition between the pre- and the post-bang phase. Mathematically, the main difference between the scenarios is the behavior of the dilaton field. In the pre–big bang, the dilaton begins with a low value--so that the forces of nature are weak--and steadily gains strength. The opposite is true for the ekpyrotic scenario, in which the collision occurs when forces are at their weakest.

The developers of the ekpyrotic theory initially hoped that the weakness of the forces would allow the bounce to be analyzed more easily, but they were still confronted with a difficult high-curvature situation, so the jury is out on whether the scenario truly avoids a singularity. Also, the ekpyrotic scenario must entail very special conditions to solve the usual cosmological puzzles. For instance, the about-to-collide branes must have been almost exactly parallel to one another, or else the collision could not have given rise to a sufficiently homogeneous bang. The cyclic version may be able to take care of this problem, because successive collisions would allow the branes to straighten themselves.

The most strongest image that brought this together for me was in understanding what Neil Turok and Paul Steinhardt developed for us. It was watching the animation of the colliding branes that I saw the issue clarify itself. But before this image deeply helped, I saw the issue clearly in another way as well.

The processes of intercommuting and loop production.

It was very important from a matter distinction, to understand the clumping mechanism that reveals itself, after this resulting images of the galaxy formation recedes in the colliding brane scenrio viewing. If such clumping is to take place, we needed a way in which to interpret this.




Branes Reform Big Bang By Atalie Young

Catch a Wave From Space

Imagine the journey it took for us to have come to the developement of the methods to discern the nature of the Universe, and what Einstein has done for us in terms of General Relativity. A statement, about Gravity.




Imagine these great distances in space, and no way in which to speak about them other then in what LIGO will translate? That any extention of this prevailing thought could not have found relevance in the connection, from that event to now, and we have found ourselves limited in this view, with bold statements in regards to Redshifting perspectives?



Without a conceptual framework in which to look at the gravitational differences within the cosmo, how the heck would any of this variation make sense, if you did not have some model in which to regulate distances traversed, in the space that must be travelled?

Albert Einstein discovered long ago that we are adrift in a universe filled with waves from space. Colliding black holes, collapsing stars, and spinning pulsars create ripples in the fabric of space and time that subtly distort the world around us. These gravitational waves have eluded scientists for nearly a century. Exciting new experiments will let them catch the waves in action and open a whole new window on the universe - but they need your help to do it!

Cosmic strings are associated with models in which the set of minima are not simply-connected, that is, the vacuum manifold has `holes' in it. The minimum energy states on the left form a circle and the string corresponds to a non-trivial winding around this.

3 Sphere

What would mathemaics be without artistic expression, trying out it's hand at how such geometrical visions continue to form? Did Escher Gauss and Reimann, see above 3 sphere?

An expression of Salvador Dali perhaps in some religious context, who then redeems himself, as a man and author of artistic expression?

A sphere is, roughly speaking, a ball-shaped object. In mathematics, a sphere comprises only the surface of the ball, and is therefore hollow. In non-mathematical usage a sphere is often considered to be solid (which mathematicians call ball).

More precisely, a sphere is the set of points in 3-dimensional Euclidean space which are at distance r from a fixed point of that space, where r is a positive real number called the radius of the sphere. The fixed point is called the center or centre, and is not part of the sphere itself. The special case of r = 1 is called a unit sphere.



Spheres can be generalized to higher dimensions. For any natural number n, an n-sphere is the set of points in (n+1)-dimensional Euclidean space which are at distance r from a fixed point of that space, where r is, as before, a positive real number. Here, the choice of number reflects the dimension of the sphere as a manifold.

a 0-sphere is a pair of points
a 1-sphere is a circle
a 2-sphere is an ordinary sphere
a 3-sphere is a sphere in 4-dimensional Euclidean space

Spheres for n ¡Ý 3 are sometimes called hyperspheres. The n-sphere of unit radius centred at the origin is denoted Sn and is often referred to as "the" n-sphere. The notation Sn is also often used to denote any set with a given structure (topological space, topological manifold, smooth manifold, etc.) identical (homeomorphic, diffeomorphic, etc.) to the structure of Sn above.

An n-sphere is an example of a compact n-manifold.

So in looking for this mathematical expression what does Gabriele Veneziano allude too in our understanding of what could have come before now and after, in the expression of this universe, that it is no longer a puzzle of what mathematics likes express of itself, now a conceptual value that has encapsulated this math.



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


In mathematics, a 3-sphere is a higher-dimensional analogue of a sphere. A regular sphere, or 2-sphere, consists of all points equidistant from a single point in ordinary 3-dimensional Euclidean space, R3. A 3-sphere consists of all points equidistant from a single point in R4. Whereas a 2-sphere is a smooth 2-dimensional surface, a 3-sphere is an object with three dimensions, also known as 3-manifold.

In an entirely analogous manner one can define higher-dimensional spheres called hyperspheres or n-spheres. Such objects are n-dimensional manifolds.

Some people refer to a 3-sphere as a glome from the Latin word glomus meaning ball.

So as if beginning from some other euclidean systemic pathway of expression, how in spherical considerations could topolgical formation consider Genus figures, if it did not identify the smooth continue reference to cosmoogical events? Where would you test this mathematics if it cannot be used and applicable to larger forms of expression, that might also help to identfy microstates?

The initial process of particle acceleration is presumed to occur in the vicinity of a super-massive black hole at the center of the blazar; however, we know very little about the origin of the jet. Yet it is precisely the region where the most important physics occurs: the formation of a collimated jet of charged particles, the flow of these particle in a narrow cone, and the acceleration of the flow to relativistic velocities.


So in looking at these spheres and their devlopement, one might have missed the inference to it's origination, it's continued expression, and the nice and neat gravitational collpase that signals the new birth of a process? Can it be so simple?

Would it be so simple in the colliders looking for those same blackholes?

Curvature Parameters

How does get this intuitive feeling embedded within thinking if it has not grokked the significance on a cosmological scale?



When one first begins to comprehend the intuitive possibilities the universe can move through, I was was struck, by the coordination of how we could see in terms of non-euclidean prospectives, and find correlation, with what was happening on a cosmological scale.



AS I looked at the the Friedmann Equation the connection to this dynamical movement in the cosmos, revealed itself, when you accepted the move to Reimannian understanding?



It was important that the connections and links to teachers be recognized. For what Gauss himself imparted, was also demonstrated in the work of Einstein, to bring Gaussian curvature along into the dynamical world gravity would reveal of itself when Einstein was completed.

But the Euclidean model stops working when gravity becomes strong

Once it came to understanding the metric and the distance function, between two points a new world was revealed. It became very interesting to see how non-euclidean was lead too, and how the work of GR blended together in a new perspective about the reality we live in. It no longer made sense to think of that space between those two points other then in the mathematical ideas of NCG.

Virtual interactions make the electron charge depend on the distance scale at which is it measured.



How would not derive some sense of this fluctuation if we did not understand the dynamical nature that has been revealed to us? On large scales it seems so easy, while in these micro states, it's all spread out and fuzzy. So at planck length, how would we describe the motions we understand of the spacetime fabric if we change the quantum mechanical description of it?

dS²=c² dT²-dX²

The amount of dark matter and energy in the universe plays a crucial role in determining the geometry of space. If the density of matter and energy in the universe is less than the critical density, then space is open and negatively curved like the surface of a saddle

Lagrange Points

How would clumping been drived from anything if such a supersymmetrical reality did not exist at some point?




Without someview that would be consistent through out the cosmo, how would such points be of value, if we could not see this variation ? In order for this view to be scalable it had to have begun in some other way, that we could sufficely say that it was strong once and all pervasive, but now?



Sun-Earth Lagrange Point forces affect spacecraft orbits.


Some would have trashed the cosmological view and the understanding of the quantum perspective that is developing with those short distances, that if they did not include this realization, what value would they hold for cosmology?

This is the golden age of cosmology. Once a data-starved science, cosmology has burgeoned as ground and space-based astronomical observations supply a wealth of unprecedently precise cosmological measurements. Questions that were recently the stuff of speculation can now be analyzed in the context of rigorous, predictive theoretical frameworks whose viability is determined by observational data. Finally, cosmological theory is being confronted by cosmological fact. The most surprising and exciting feature of cosmology's entrance into the realm of data-driven science is its deep reliance on theoretical developments in elementary particle physics. At the energy scales characteristic of the universe's earliest moments, one can no longer approximate matter and energy using an ideal gas formulation; instead, one must use quantum field theory, and at the highest of energies, one must invoke a theory of quantum gravity, such as string theory. Cosmology is thus the pre-eminent arena in which our theories of the ultra-small will flex their muscles as we trace their role in the evolution of the universe.

What is the Ultimate Theory of Physics?

It is always very interesting for me to try and understand how such short distances could have begun to have some visual world possibilities? When mathematics begins to develope a method to describing that same small world.

Shahn Majid's research explores the world of quantum geometry, on the frontier between pure mathematics and the foundations of theoretical physics. He uses mathematical structures from algebra and category theory to develop ideas concerning the structure of space and time. His research philosophy drives a search for the right mathematical language for a unified expression for the ideas of quantum physics, founded on the notion of non-commutative geometry

It is not always clear to me what would have arisen out of the possibilties of what could possibly lies beneath, but any emergent principal wuld have to be able to describe its origination(the geometry)?



If we thought for a moment that there was a guiding principal in the higg's field, how would we have perceptably explained this in conglomerations of students who would gather around their professors? In a strange sense, one could intuitively feel this gathering consequence, as a consolidation of dominante principles, around which the matter states could easily have resigned themselves?


Braided independence is another of the conceptual ideas going into the modern approach to quantum geometry. When electrons pass each other either in physical space or lexicographically during a calculation, their exchange involves an additional -1 factor. Building on this idea, one is led to a kind of braided mathematics in which the outputs of calculations are `wired' into the inputs of further calculations much like the way information flows inside a computer. Only now, when wires cross each other there is a nontrivial operator, in fact a different one for when one wire goes under the other and when it goes over. Here is a typical calculation in braided-mathematics

Noncommutative Geometry, Monday July 24th 2006 - Friday December 22nd 2006

Noncommutative geometry aims to carry over geometrical concepts to a a new class of spaces whose algebras of functions are no longer commutative. The central idea goes back to quantum mechanics, where classical observables such as position and momenta no longer commute. In recent years it has become appreciated that such noncommutative spaces retain a rich topology and geometry expressed first of all in K-theory and K-homology, as well as in finer aspects of the theory. The subject has also been approached from a more algebraic side with the advent of quantum groups and their quantum homogeneous spaces.

The subject in its modern form has also been connected with developments in several different fields of both pure mathematics and mathematical physics. In mathematics these include fruitful interactions with analysis, number theory, category theory and representation theory. In mathematical physics, developments include the quantum Hall effect, applications to the standard model in particle physics and to renormalization in quantum field theory, models of spacetimes with noncommuting coordinates. Noncommutative geometry also appears naturally in string/M-theory. The programme will be devoted to bringing together these different streams and instances of noncommutative geometry, as well as identifying new emerging directions.

THE ANTHROPIC PRINCIPLE

The String Theory Landscape, by Raphael Bousso and Joseph Polchinski

Given the success of replacing the gravitational force with the dynamics of space and time, why not seek a geometric explanation for the other forces of nature and even for the spectrum of elementary particles? Indeed, this quest occupied Einstein for much of his life. He was particularly attracted to work by German Theodor Kaluza and Swede Oskar Klein, which proposed that whereas gravity reflects the shape of the four familiar spacetime dimensions, electromagnetism arises from the geometry of an additional fifth dimension that is too small to see directly (at least so far). Einstein's search for a unified theory is often remembered as a failure. In fact, it was premature: physicists first had to understand the nuclear forces and the crucial role of quantum field theory in describing physics--an understanding that was only achieved in the 1970s.

.



Previous, a discussion took place there in Peter's Blog on Susskind and Smolin. I would like to know if Peter supports Smolin's position?

I had mention to Lubos about the fact that strings/M theory had changed the concept of the quantum mechanical discription of the spacetime fabric. Part of this question, was based on how Smolin and LQGists would be limited in there perceptions, if acceptance of GR, does not go through any revision? Compton scattering amplitudes would have pointed to Glast determinations and support of Smolin in his valuation. But what was deeper in my mind, was the question of what graviton intersection might have implied, if such a unity would have been established, based on KK theory and unification of electromagnetism and gravity?

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

In para 3, he writes,

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

NATHAN MYHRVOLD

I found the email debate between Smolin and Susskind to be quite interesting. Unfortunately, it mixes several issues. The Anthropic Principle (AP) gets mixed up with their other agendas. Smolin advocates his CNS, and less explicitly loop quantum gravity. Susskind is an advocate of eternal inflation and string theory. These biases are completely natural, but in the process the purported question of the value of the AP gets somewhat lost in the shuffle. I would have liked more discussion of the AP directly

The thing I like about the oppositon of minds who embrace the Solvay attitude, is that it forces another to bring forward a history that few of us would have seen. So outside of the comments of opposing views what kind of harmony could have been produced?


SMOLIN VS. SUSSKIND: THE ANTHROPIC PRINCIPLE



Leonnard Susskind and Lee Smolin

While this is a conversation written by physicists for physicists, it should nonetheless be of interest for Edge readers as it's in the context of previous Edge features with the authors, it's instructive as to how science is done, and it's a debate that clarifies, not detracts.

Quantum Geometry

Mathematics is not the rigid and rigidity-producing schema that the layman thinks it is; rather, in it we find ourselves at that meeting point of constraint and freedom that is the very essence of human nature.

- Hermann Weyl

I know I said I would post the discussion between Susskind and Smolin again for refreshing but I wanted to post the issue of Quantum Geometry first and then move there.

My area of research is superstring theory, a theory that purports to give us a quantum theory of gravity as well as a unified theory of all forces and all matter. As such, superstring theory has the potential to realize Einstein's long sought dream of a single, all encompassing, theory of the universe. One of the strangest features of superstring theory is that it requires the universe to have more than three spatial dimensions. Much of my research has focused on the physical implications and mathematical properties of these extra dimensions --- studies that collectively go under the heading "quantum geometry".

Quantum geometry differs in substantial ways from the classical geometry underlying general relativity. For instance, topology change (the ``tearing" of space) is a sensible feature of quantum geometry even though, from a classical perspective, it involves singularities. As another example, two different classical spacetime geometries can give rise to identical physical implications, again at odds with conclusions based on classical general relativity.

If one did not understand where this geometry will begin, then it does not make much sense for a person to consider the mathematics that will arise from this situation?

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

"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 mathetical core of genral 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."

So I have shown I thnk the importance of the math involved and how it might address the quantum nature of the world in small things. We find, we can be quite comfortable in looking at the achievemets of Einstein, in leading us to a good perception about things on a cosmological scale. But moving back to the "quantum geometry," what are we describing here?

Quantum gravity is perhaps the most important open problem in fundamental physics. It is the problem of merging quantum mechanics and general relativity, the two great conceptual revolutions in the physics of the twentieth century. The loop and spinfoam approach, presented in this book, is one of the leading research programs in the field. The first part of the book discusses the reformulation of the basis of classical and quantum Hamiltonian physics required by general relativity. The second part covers the basic technical research directions. Appendices include a detailed history of the subject of quantum gravity, hard-to-find mathematical material, and a discussion of some philosophical issues raised by the subject. This fascinating text is ideal for graduate students entering the field, as well as researchers already working in quantum gravity. It will also appeal to philosophers and other scholars interested in the nature of space and time.

The same vigor with which string theory/M theory is attack for is fundamental points about the nature of the geometric world is no less important then what achivements and attempts are made by Rovelli. Each aspect of the societal influence theoretists and physics people engage in, is part and parcel of the individuals who are, hands on with the Elephant.


Edward Witten

Reflections on the Fate of Spacetime

Compton and Graviton Scatterings?

Sometimes it is very difficult to express what you want to say when you have so much information in your head. That you know it has to be expressed most carefully in order for one to get the jest of what is being implied when making statements. It is indeed a struggle for me to be clear in this regard, but hopefully, recogizing the requirements of the physicist and the theoretician, that such scholar attributes can be waivered for the commoner?






Compton scattering detector

Compton scattering happens when a photon interacts with an electron - the photon leaves the interaction with a lower energy and the electron has a higher energy. The energies of the outgoing photon and electron along with the angle at which these two leave the interaction allow determination of the energy and direction of the original photon.






What the heck is a Graviton

1. A quantizied gravitational wave...........
2. They travel at the speed of light
3. They have never been experimentally proven to exist.
4. They have been theoretically proven?
5. They permeate all dimensions.

Particle Physics Probes Of Extra Spacetime
Dimensions


The exact expression may be found in (15,17). It is important to note that due to integrating over the effective density of states, the radiated graviton appears to have a continuous mass distribution; this corresponds to the probability of emitting gravitons with different extra dimensional momenta. The observables for graviton production, such as the γ/Z angular and energy distributions in e+e− collisions

Visiting Scientist Sends Physics World Spinning

This summer, Afshar, Flores and Knoesel are conducting follow-up experiments in Rowan's state-of-the-art Science Hall to determine whether they can validate Afshar’s initial findings for single photons. In the experiment at Rowan, the team is using a single photon source instead of a beam. Some critics have pointed out that the results of the experiment with a laser beam could be explained in terms of classical physics. Thus, the use of single particles is critical and would be able to finally determine the validity of Afshar’s claims.

If the next round of experiments does support Afshar’s findings, this can mean a whole new way of looking at quantum theory among physicists, who have long-accepted the opinion of Einstein's rival on the subject, Danish scientist Niels Bohr. And that can have meaning for the lay community as well.

Flores noted, "It is likely that the interpretation problems of quantum mechanics are a hint that there is something new to learn about our physical world. There might be either a new force or a new physical property to be discovered. The problems of quantum mechanics will not be resolved unless they are exposed and studied. Thus, doing this experiment at Rowan is an exciting prospect."

The ideas presenting the way in whch we have percieved the quantum mechanical spacetime fabric, I am asking, that if applied to string considerations we have indeedd changed the language attributes of the same field that is understood in Compton scattering?


Dying to Know, by Max Tegmark



Three quarks indicated by red, green and blue spheres (lower left) are localized by the gluon field.

A quark-antiquark pair created from the gluon field is illustrated by the green-antigreen (magenta) quark pair on the right. These quark pairs give rise to a meson cloud around the proton.

The masses of the quarks illustrated in this diagram account for only 3% of the proton mass. The gluon field is responsible for the remaining 97% of the proton's mass and is the origin of mass in most everything around us.

Experimentalists probe the structure of the proton by scattering electrons (white line) off quarks which interact by exchanging a quantum of light (wavy line) known as a photon.