Catch a Wave From Space

Posted on December 17, 2004 by PlatoHagel

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.

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3 Sphere

Posted on December 15, 2004 by PlatoHagel

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?

Dialogos of Eide
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Curvature Parameters

Posted on December 14, 2004 by PlatoHagel

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

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Lagrange Points

Posted on December 13, 2004 by PlatoHagel

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.

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What is the Ultimate Theory of Physics?

Posted on December 13, 2004 by PlatoHagel

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.

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THE ANTHROPIC PRINCIPLE

Posted on December 9, 2004 by PlatoHagel

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.

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Posted in Dimension, Einstein, geometries, Glast, Graviton, Gravity, Kaluza, Landscape, M Theory, Mathematics, Particles, Quantum Gravity, Raphael Bousso, Smolin, String Theory, Susskind | Tagged , , , , , , , , , , , , , , , | Leave a comment

Quantum Geometry

Posted on December 9, 2004 by PlatoHagel

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

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Compton and Graviton Scatterings?

Posted on December 9, 2004 by PlatoHagel

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.

Dialogos of Eide
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Quantum Mechanical Discription of the Spacetime Fabric

Posted on December 8, 2004 by PlatoHagel

Richard Feynman developed the path integral formulation of quantum mechanics in 1948 (some preliminaries were worked out earlier, in the course of his doctoral thesis work with John Archibald Wheeler) as a description of quantum theory corresponding to the action principle of classical mechanics. It replaces the classical notion of a single, unique history for a system with a sum, or functional integral, over an infinity of possible histories to compute a quantum amplitude.

I do not know if I have fallen astray from the interesting perspective strings has alloted to us, in the way in which we have always percieve the quantum mechanical discription based on some,” sum over history” of all interactions.

Under the heading of “Time and the Quantum,” Pg 189 Fabric of the Cosmo, by Brian Greene a interesting statement of historical proportions that askes questions about the nature of the way in which we percieve same. A better indication of the Full Monty, is demonstrated as well?:)

The beam splitter is not a labratory variety, either, but is a intervening galaxy whose gravitatinal pull can act like a lens that focuses passing photons and directs them to earth,as in Figure 7.3. Although no one has yet carried out this experiment, in principle, if enough photons from the quasar are collected, they should fill out an interference pattern on a long-exposure photographic plate, just as in the labratory beam-splitter experiment. But if we put another photon detector near te end of one route or the other, it which provide which path information for the phtons, thereby destroying the interference pattern.

I have shown, where this extra dimension was added by Kaluza in 1919, and unless I am quoting the references to Kaku wrong, then such considerations would to me, have changed the way in which we would percieve all these interactions? Something then has happened to the spacetime fabric and how all these interactions would be conceptually addressed? Hence the reference to what String Theorists have done, by changing the disciption to one of strings?

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 gravity 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.

It has been relatively quiet here in the GP-B Mission Operations Center, since the strong solar flares and geomagnetic storm three weeks ago. Our team continues to adjust the flow rate of the excess helium from the Dewar during the present a 6-week “hot” season, where the spacecraft is continually in sunlight throughout each orbit. (See last week’s highlights for a discussion of the spacecraft’s seasons.)

Immediately to me, the instantaneous feature of photon expression would have detailed a topological value, where such gravitation/photon would demonstrated of itself a continuity of expression? If such geometrical tendencies would have considered the dynamical relationship of the orbital on cosmological correlations then such energy perceptions would have immediately painted a portrait for us, of what has existed in the past, what continues to exist, and what will exist in the future?

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Strings Change Quantum Mechanical Discription of the World?

Posted on December 7, 2004 by PlatoHagel

Often times harmonical oscillators can disguise themselves in dialogue, and opposition, and bring about a “signatured state” of recognition? Have they become entangled? Have they defined themselves in terms of new elemental features of existance?

Has strings presented itself as a new issue in entanglement and the “new physics,” it would represent?

Physicists have succeeded in entangling five photons for the first time. Although four photons have been entangled before, five is the minimum number needed for universal error correction in quantum computation. Moreover, the same team has demonstrated a process called “open-destination teleportation” for the first time (Z Zhao et al. 2004 Nature 430 54). The results represent a major breakthrough in efforts to exploit the laws of quantum mechanics in quantum information processing.

By taking advantage of quantum phenomena such as entanglement, teleportation and superposition, a quantum computer could, in principle, outperform a classical computer in certain computational tasks. Entanglement allows particles to have a much closer relationship than is possible in classical physics. For example, two photons can be entangled such that if one is horizontally polarized, the other is always vertically polarized, and vice versa, no matter how far apart they are. In quantum teleportation, complete information about the quantum state of a particle is instantaneously transferred by the sender, who is usually called Alice, to a receiver called Bob. Quantum superposition, meanwhile, allows a particle to be in two or more quantum states at the same time

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