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Tuesday, November 30, 2004

A Classical Discription of the Quantum World?


D Orbital


Orbitals are probability diagrams. Specifically, an orbital describes a region in space where there is a 90% change of finding an electron. The electron is never restricted to an orbital as in travels around a nucleus, but it seems to keep returning to this particular region even though its behavior is random. The concept of the orbital differs from Bohr's concept of the orbit. Bohr considered an orbit to be a path that the electron always followed much like a train stays on a track. The concept of the orbital was developed in Schrodinger's work to avoid violating the Heisenberg Uncertainty Principle. In the Modern Theory of Atomic Structures a picture of an orbital is also called a Probability Diagram. By agreement among chemists, the orbital is a 90% Probability Diag ram. This idea allows the electron to be found anywhere and still indicates where the electron spends most of its time.




How would one remove the uncertainty principals from the small world but to have considered the probability density distributions? Below is a link that I saw early in my investigations that I had wondered, forced me to look at what could have been happening within the cosmo with events, that would release information into the bulk?



Electron’s probability density distribution for an atom in the state; n=4, l=4, m=0.



The star Eta Carina is ejecting a pair of huge lobes that form a "propeller" shape. Jet-like structures are emanating from the center (or "waist"), where the star (quite small on this scale) is located.

If string theory, in the Kaluza Klein tower energy determinations could have discriptively spoken to the particle natures, why was it not possible to map the nature of these particles, in gravitational information released from these cosmological events?

If information in the bulk has been released, then this information has been geometrically defined in the gravity waves that we would percieve here on earth? Ligo would have performed its ability to then map the configurations that we see happening in that same cosmos. What made this visualization interesting is if photon release was specific to electromagnetic events held to the brane, then our perception of this energy, would have been left for us to consider in those same gravitational waves?



Entanglement and the New Physics

I have to go back and look at this subject carefully to get a sense of what is going on in Lubos Blog(will supply proper link later).





It is possible to entangle two photons that have never interacted before by using two down-conversion sources and then subjecting one photon from each entangled pair to a Bell-state measurement. This causes the other two photons, which have never interacted, to become entangled.


Further Links for Consideration

The basics of two-party entanglement
---------------------------------------------


http://xxx.arxiv.org/abs/quant-ph/9511030
http://xxx.arxiv.org/abs/quant-ph/9511027
http://xxx.arxiv.org/abs/quant-ph/9604024
http://xxx.arxiv.org/abs/quant-ph/9707035
http://xxx.arxiv.org/abs/quant-ph/9709029
http://xxx.arxiv.org/abs/quant-ph/9801069
http://xxx.arxiv.org/abs/quant-ph/9811053
http://xxx.arxiv.org/abs/quant-ph/9905071


Basics of multiparty entanglement

------------------------
http://xxx.arxiv.org/abs/quant-ph/9907047
http://xxx.arxiv.org/abs/quant-ph/9908073
http://xxx.arxiv.org/abs/quant-ph/9912039
http://xxx.arxiv.org/abs/quant-ph/0005115


Basics of secret sharing

-----------------------
http://xxx.arxiv.org/abs/quant-ph/9806063







We have engineered an entangled state made of two atoms and the cavity mode. The entanglement is produced in a succession of controlled steps addresssing the particles individually. The sequence is fully programmable and could be configured to produce any quantum state. We have chosen here to prepare a triplet of entangled particles of the GHZ type. The entanglement has been demonstrated by experiments performed in two orthogonal basis. The procedure can, in principle, operate on larger numbers of particles, opening the way to new fundamental tests of quantum theory.

Test of the Quantenteleportation
over long distances in the duct system of Vienna


Working group
Quantity of experiment and the Foundations OF Physics
Professor Anton Zeilinger


Quantum physics questions the classical physical conception of the world and also the everyday life understanding, which is based on our experiences, in principle. In addition, the experimental results lead to new future technologies, which a revolutionizing of communication and computer technologies, how we know them, promise.

In order to exhaust this technical innovation potential, the project "Quantenteleportation was brought over long distances" in a co-operation between WKA and the working group by Professor Anton Zeilinger into being. In this experiment photons in the duct system "are teleportiert" of Vienna, i.e. transferred, the characteristics of a photon to another, removed far. First results are to be expected in the late summer 2002
.






Monday, November 29, 2004

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

Was the big bang really the beginning of time? Or did the universe exist before then? Such a question seemed almost blasphemous only a decade ago. Most cosmologists insisted that it simply made no sense - that to contemplate a time before the big bang was like asking for directions to a place north of the North Pole. But developments in theoretical physics, especially the rise of string theory, have changed their perspective. The pre-bang universe has become the latest frontier of cosmology.

The new willingness to consider what might have happened before the bang is the latest swing of an intellectual pendulum that has rocked back and forth for millennia. In one form or another, the issue of the ultimate beginning has engaged philosophers and theologians in nearly every culture. It is entwined with a grand set of concerns, one famously encapsulated in an 1897 painting by Paul Gauguin: D'ou venons-nous? Que sommes-nous? Ou allons-nous? "Where do we come from? What are we? Where are we going?" The piece depicts the cycle of birth, life and death - origin, identity and destiny for each individual - and these personal concerns connect directly to cosmic ones. We can trace our lineage back through the generations, back through our animal ancestors, to early forms of life and protolife, to the elements synthesized in the primordial universe, to the amorphous energy deposited in space before that. Does our family tree extend forever backward? Or do its roots terminate? Is the cosmos as impermanent as we are
?






One had to know at a deeper level how we might have engaged the cyclical universe? Could bubble nucleation fall in line with the ideas about the origins of this universe and find itself too part of this creative scenario?


Colliding branes had to have some recognition in the world that we would have considered, bubble nucleation, as manifesting itself over and over again within the confines of our own universe now? Would this have made it likely that such manifestions really go to the source of what could have begun, has always been and wil continue to evolve, in this cycle of birth death and being reborn?


Neil Turok

The Myth of the Beginning of Time

The new willingness to consider what might have happened before the big bang is the latest swing of an intellectual pendulum that has rocked back and forth for millenia. In one form or another, the issue of the ultimate beginning has engaged philosophers and theologians in nearly every culture. It is entwined witha grand set of concerns, one famosly encapsulated in a 1897 painting by Paul Gauguin: D'ou venons? Que sommes-nous? Ou allons-nous? Scientific America, The Time before Time, May 2004



Sister Wendy's American Masterpieces":

"This is Gauguin's ultimate masterpiece - if all the Gauguins in the world, except one, were to be evaporated (perish the thought!), this would be the one to preserve. He claimed that he did not think of the long title until the work was finished, but he is known to have been creative with the truth. The picture is so superbly organized into three "scoops" - a circle to right and to left, and a great oval in the center - that I cannot but believe he had his questions in mind from the start. I am often tempted to forget that these are questions, and to think that he is suggesting answers, but there are no answers here; there are three fundamental questions, posed visually.

"On the right (Where do we come from?), we see the baby, and three young women - those who are closest to that eternal mystery. In the center, Gauguin meditates on what we are. Here are two women, talking about destiny (or so he described them), a man looking puzzled and half-aggressive, and in the middle, a youth plucking the fruit of experience. This has nothing to do, I feel sure, with the Garden of Eden; it is humanity's innocent and natural desire to live and to search for more life. A child eats the fruit, overlooked by the remote presence of an idol - emblem of our need for the spiritual. There are women (one mysteriously curled up into a shell), and there are animals with whom we share the world: a goat, a cat, and kittens. In the final section (Where are we going?), a beautiful young woman broods, and an old woman prepares to die. Her pallor and gray hair tell us so, but the message is underscored by the presence of a strange white bird. I once described it as "a mutated puffin," and I do not think I can do better. It is Gauguin's symbol of the afterlife, of the unknown (just as the dog, on the far right, is his symbol of himself).

"All this is set in a paradise of tropical beauty: the Tahiti of sunlight, freedom, and color that Gauguin left everything to find. A little river runs through the woods, and behind it is a great slash of brilliant blue sea, with the misty mountains of another island rising beyond Gauguin wanted to make it absolutely clear that this picture was his testament. He seems to have concocted a story that, being ill and unappreciated (that part was true enough), he determined on suicide - the great refusal. He wrote to a friend, describing his journey into the mountains with arsenic. Then he found himself still alive, and returned to paint more masterworks. It is sad that so great an artist felt he needed to manufacture a ploy to get people to appreciate his work. I wish he could see us now, looking with awe at this supreme painting.
"


Quantum Geometricization: The Struggle



If Lorentz symmetry is broken by some mechanism originating at the Planck scale, is there any hope of detecting such an effect? Surprisingly, the answer is yes. Over the past decade Kostelecky and co-workers have been exploring how a violation of Lorentz symmetry might provide evidence for new physics arising at the Planck scale. However, rather than smash particles together at high energies to explore this, researchers are turning to ultrahigh-precision experiments at low energies to search for signs that Lorentz symmetry has been broken. The idea is that such low-energy effects are caused by corrections involving inverse powers of the Planck scale.

Possible violations of Lorentz invariance are an ideal signal of new physics because nothing in the Standard Model of particle physics permits the violation of special relativity. Therefore, no conventional process could ever mimic or cover up a genuine signal of Lorentz violation.

Since a viable theory of physics at the Planck scale remains elusive, it is difficult to make precise predictions for the small corrections that could occur due to Lorentz violation. However, we can obtain a rough estimate. The rest-mass energy of the proton, for example, is about 1 GeV, and the ratio of this energy to the Planck scale is about 1 part in 1019. If an experiment with protons is sensitive to effects at or below this level, then it is effectively probing the Planck scale.


I tend to think if one can orientate the thinking that is developing, it is not to hard to see where we might develope further perspectives, as they have been outlined in article and in articles that I have presented for consideration.

This idea of Quantum geometry being revealled in quantum geometricization is a valuable insight that Greene offers to us. Continues, to speak to Einstein revelations, much as Smolin does in his own theoretics.

"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 general relativity, this means that it too must be modified in order to reflect faithfully the new short distance physics of string theory. Whereas general relativity asserts that the curved properties of the universe are described by Reinmannian geometry, string theory asserts this is true only if we examine the fabric of the universe on large enough scales. On scales as small as planck length a new kind of geometry must emerge, one that aligns with the new physics of string theory. This new geometry is called, quantum geometry."


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

Many claim a commercialization of the work current technologies are spoken to here(?) of researchers respective corners. That piece meal information is feed to the public, does not do its justice? If such, "cut and paste" values would institute a perspective view of what has been reveallled with some consistancy, then one has done their job in getting to the source valuation and recognitions of the limitations now affecting theoretics and physic alike?

Sunday, November 28, 2004

Non Euclidean Geometry and the Universe



With Critical density ( Omega ), matter distinctions become apparent, when looking at the computerized model of Andrey Kravtsov.



Georg Friedrich Bernhard Riemann 1826 – 1866

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

To me this is one of the greatest achievements of mathematical structures that one could encounter, It revolutionize many a view, that been held to classical discriptions of reality.

In the quiet achievement of Riemann’s tutorial teacher Gauss, recognized the great potential in his student. On the curvature parameters, we recognize in Gauss’s work, what would soon became apparent? That we were being lead into another world for consideration?



So here we are, that we might in our considerations go beyond the global perspectives, to another world that Einstein would so methodically reveal in the geometry and physics, that it would include the electromagnetic considerations of Maxwell into a cohesive whole and beyond.

The intuitive development that we are lead through geometrically asks us to consider again, how Riemann moved to a positive aspect of the universe?



The activity in string theory and quantum gravity is aimed at developing a quantum theory that incorporates the physics of gravity and is valid down to the smallest length scales, where conventional quantum field theory can no longer be applied. There has been rapid progress in this area in recent years, in part due to work of Princeton faculty and students, and it continues to be a fertile source of research problems.


Friedman Equation What is pdensity.

What are the three models of geometry? k=-1, K=0, k+1

Negative curvature

Omega=the actual density to the critical density

If we triangulate Omega, the universe in which we are in, Omegam(mass)+ Omega(a vacuum), what position geometrically, would our universe hold from the coordinates given?

If such a progression is understood in the evolution of the geometry raised in non euclidean perspectives, this has in my view raised the stakes on how we percieve the dynamical valuation of a world that we were lead into from GR?

Facing the frontier of cosmological proportions, we soon meet views as demonstrated in the Solvay meetings where the thought experiments plague the relation of Quantum Mechanics. Even though Einstein held his position about the beauty of GR( it's stand alone feature) in it's own right, did not mean that the efforts to quantization had not been considered by him?

Moving to the non-euclidean realm, set up my thinking in terms of gravitational considerations. Dali's example of the tesserack reveals a deeper understanding of this progression to an non-euclidean view that Dali heightened in this aspect of religiousness and God implication, by demonstrating the Crucifixation paintng that he did. Even Escher in his realization, understood that the royal road to geometry has some road(physics) to travel before it could meet his perspective eye.

Saturday, November 27, 2004

Searching for Changes in the Fine-Structure Constant Using Atomic Clocks





Another laser beam is used to make the atoms fluoresce, and the amount of fluorescence is measured as a function of the microwave frequency to plot a "resonance curve". An ultra-precise measurement of time can be made by measuring the frequency of the peak in this resonance curve (see "Atomic clocks" by Pierre Lemonde in Physics World January 2001 pp39-44).



The reason for this post was triggered by what can be found at Lubos Motl's site One will have to watch the interaction and information that is presenting itself in the comments that come, and maybe we can build from this?

When I looked at Glast, it seemed a fine way in which to incorporate one more end of the "spectrum" to how we see the cosmo? That we had defined it over this range of possibilties? How could we move further from consideration then, and I fall short in how the probabilties of how we might percieve graviton exchange of information in the bulk could reveal more of that spectrum? A resonance curve?

If one alters their perspective in terms of resonantial features(using string theory concepts as a quantum mechanical discription of the spacetime), how would we measure these changes in planck epoch ( deeper then gamma ray detection)? Can this be done?


Variation of the Standard Two-Pin-hole "welcher-Weg" Optics Experiment






Results of different measurements of the Ft value in beta decay
George R. Welch setting up an optics experiment with graduate student Sophia Ilina
Dr. Scully and Dr. Townes, the inventor of the maser and laser (University of California, Berkeley), during the dedication of the Charles H. Townes Reading room
Assistant research scientist Daya Rathnayaka with a UHV deposition chamber


Tomorrow at 4 PM, physicist Shahriar S. Afshar, a Visiting Scientist at Harvard University's Physics Department will give a talk entitled Violation of Bohr's principle of complementarity in an optical "which-way" experiment at Texas A&M University.

Afshar has done a variation of the standard two-pin-hole "welcher-Weg" optics experiment, in which he demonstrates that wave interference is present even when one is determining through which pinhole a photon passes. This result is in direct contradiction to Neils Bohr's Principle of Complementarity, which would require in the quantum world that when one is measuring particle properties [formerly read "measuring quantum properties" -KC], all wave interference phenomena must vanish. Afshar's trick is to find the location of the minimum points of wave interference, place one or more wires at these minimum points, and observe how much light is intercepted when one is determining the pinhole through which the photons passed.

It has been widely accepted that the rival interpretations of quantum mechanics, e.g., the Copenhagen Interpretation, the Many-Worlds Interpretation, and my father John Cramer's Transactional Interpretation, cannot be distinguished or falsified by experiment, because the experimental predictions come from the formalism that all such interpretations describe. However, the Afshar Experiment demonstrates in an interaction-free way that there is a loophole in this logic: if the interpretation is inconsistent with the formalism, then it can be falsified. In particular, the Afshar Experiment falsifies the Copenhagen Interpretation, which requires the absence of interference in a particle-type measurement. It also falsifies the Many-Worlds Interpretation which tells us to expect no interference between "worlds" that are physically distinguishable, e.g., that correspond to the photon's measured passage through one pinhole or the other [the word "measured" added 4/28. -KC].

The Transactional Interpretation, on the other hand, has no problem in explaining that Afshar results. "Offer waves" from the source pass through both pinholes and interfere, creating a condition in which no transactions to the wires can form. Therefore, no photons are intercepted by wires, as Afshar observes. The quantum formalism makes the same predictions.

On this basis, it appears that two of the major interpretations of quantum mechanics have been falsified and should be relegated to the waste basket of physics history. The Transactional Interpretation, which involves a forward/back in time handshake, is one of the few (perhaps the only) interpretation(s) left standing after the Afshar test.

Yay for the home team!

(See also the Power Point presentation for my dad's Hal Clement memorial lecture at Boskone; Google also has an html cache of the Powerpoint presentation.)

LET ME KNOW if anyone reading this attends Afshar's talk or attended a similar one he gave at Harvard recently.

TRACKBACKS: My MT trackbacks don't work. One of these days I'll figure out why. But this entry has received really a lot, so here is a link to Technorati's listing of links to this post. Boingboing also blogged it, but the post has already slid off their main page.

SEE UPDATE, 5/10/04.


Friday, November 26, 2004

No Royal Road to Geometry?




All those who have written histories bring to this point their account of the development of this science. Not long after these men came Euclid, who brought together the Elements, systematizing many of the theorems of Eudoxus, perfecting many of those of Theatetus, and putting in irrefutable demonstrable form propositions that had been rather loosely established by his predecessors. He lived in the time of Ptolemy the First, for Archimedes, who lived after the time of the first Ptolemy, mentions Euclid. It is also reported that Ptolemy once asked Euclid if there was not a shorter road to geometry that through the Elements, and Euclid replied that there was no royal road to geometry. He was therefore later than Plato's group but earlier than Eratosthenes and Archimedes, for these two men were contemporaries, as Eratosthenes somewhere says. Euclid belonged to the persuasion of Plato and was at home in this philosophy; and this is why he thought the goal of the Elements as a whole to be the construction of the so-called Platonic figures. (Proclus, ed. Friedlein, p. 68, tr. Morrow)


It was interesting to me that I find some thread that has survived through the many centuries , that moves through the hands of individuals, to bring us to a interesting abstract world that few would recognize.



While Euclid is not known to have made any original discoveries, and the Elements is based on the work of his predecessors, it is assumed that some of the proofs are his own and that he is responsible for the excellent arrangement. Over a thousand editions of the work have been published since the first printed version of 1482. Euclid's other works include Data, On Divisions of Figures, Phaenomena, Optics, Surface Loci, Porisms, Conics, Book of Fallacies, and Elements of Music. Only the first four of these survive.

Of interest, is that some line of departure from the classical defintions, would have followed some road of developement, that I needed to understand how this progression became apparent. For now such links helped to stabilize this process and the essence of the departure form this classical defintion needed a culmination reached in Einstein's General Relativity. But long before this road was capture in it's essence, the predecessors in this projective road, develope conceptual realizations and moved from some point. To me, this is the fifth postulate. But before I draw attention there I wanted to show the index of this same projective geometry.

A theorem which is valid for a geometry in this sequence is automatically valid for the ones that follow. The theorems of projective geometry are automatically valid theorems of Euclidean geometry. We say that topological geometry is more abstract than projective geometry which is turn is more abstract than Euclidean geometry.

The move from the fifth postulate had Girolamo Saccheri, S.J. (1667 - 1733) ask the question?

What if the sum of the angles of a triangle were not equal to 180 degrees (or p radians)?" Suppose the sum of these angles was greater than or less than p. What would happen to the geometry we have come to depend on for so many things? What would happen to our buildings? to our technology? to our countries' boundaries?




The progression through these geometries leads to global perspectives that are not limited to the thread that moves through these cultures and civilizations. The evolution dictates that having reached Einstein GR that we understand that the world we meet is a dynamical one and with Reason, we come t recognize the Self Evident Truths.

At this point, having moved through the geometrical phases and recognitions, the physics of understanding have intertwined mathematical realms associated with Strings and loop and other means, in which to interpret that dynamical world called the Planck Length(Quantum Gravity).

Reichenbach on Helmholtz

Thursday, November 25, 2004

The Six Men and the Elephant

I'd like to embrace all those who are attempting to speak in regards to quantum gravity. This is a common poem, that reflects the efforts and differing perspectives at trying to descibe a world that is very much in the understanding below the planck epoch.

If we acknowledge the structural integrity that we assign strings and loops this then can embrace solidified positions, to the understanding that we may differ in those same positions. Logically the perspectives are even displayed very nicely in this poem? Wall, Spear, Snake, Tree, Fan, and Rope.

What taste comes to mind, and we have this same inabiltiy to express the intangible yet we have engaged mathematically something very real?





The Blind Men and the Elephant
John Godfrey Saxe (1816-1887)

It was six men of Indostan
To learning much inclined,
Who went to see the Elephant
(Though all of them were blind),
That each by observation
Might satisfy his mind.

The First approached the Elephant,
And happening to fall
Against his broad and sturdy side,
At once began to bawl:
"God bless me! but the Elephant
Is very like a WALL!"


The Second, feeling of the tusk,
Cried, "Ho, what have we here,
So very round and smooth and sharp?
To me 'tis mighty clear
This wonder of an Elephant
Is very like a SPEAR!"

The Third approached the animal,
And happening to take
The squirming trunk within his hands,
Thus boldly up and spake:
"I see," quoth he, "the Elephant
Is very like a SNAKE!"

The Fourth reached out an eager hand,
And felt about the knee
"What most this wondrous beast is like
Is mighty plain," quoth he:
"'Tis clear enough the Elephant
Is very like a TREE!"

The Fifth, who chanced to touch the ear,
Said: "E'en the blindest man
Can tell what this resembles most;
Deny the fact who can,
This marvel of an Elephant
Is very like a FAN!"

The Sixth no sooner had begun
About the beast to grope,
Than seizing on the swinging tail
That fell within his scope,
"I see," quoth he, "the Elephant
Is very like a ROPE!"

And so these men of Indostan
Disputed loud and long,
Each in his own opinion
Exceeding stiff and strong,
Though each was partly in the right,
And all were in the wrong!

Wednesday, November 24, 2004

Bubble Nucleation




Based on the no boundary proposal, I picture the origin of the universe, as like the formation of bubbles of steam in boiling water. Quantum fluctuations lead to the spontaneous creation of tiny universes, out of nothing. Most of the universes collapse to nothing, but a few that reach a critical size, will expand in an inflationary manner, and will form galaxies and stars, and maybe beings like us.

The images produce here of bubble formation are most pleasing to me, about what could have emerge from that early universe. If stringy components were evident and cosmic clumping rvealed as in previous post then how would such images lead to bubble nucleations as stringy cosmological patterns?

For such ideas to emerge in thinking there had to be a time when such conditions were conducive to bubble nucleation? Such energy considerations had to provide for these considerations to emerge so. How so?

First-order phase transitions (illustrated below) occur through the formation of bubbles of the new phase in the middle of the old phase; these bubbles then expand and collide until the old phase disappears completely and the phase transition is complete.



During a first-order phase transition, the matter fields get trapped in a `false vacuum' state from which they can only escape by nucleating bubbles of the new phase, that is, the `true vacuum' state.





G -> H -> ... -> SU(3) x SU(2) x U(1) -> SU(3) x U(1). Here, each arrow represents a symmetry breaking phase transition where matter changes form and the groups - G, H, SU(3), etc. - represent the different types of matter, specifically the symmetries that the matter exhibits and they are associated with the different fundamental forces of nature

In order for such thinking to produce the cosmos then we would have to understand its early conditions.

Physically, the effect can be interpreted as an object moving from the "false vacuum" (where = 0) to the more stable "true vacuum" (where = v). Gravitationally, it is similar to the more familiar case of moving from the hilltop to the valley. In the case of Higgs field, the transformation is accompanied with a "phase change", which endows mass to some of the particles.






The Cosmic String




It was important for me to recognize the microcosmic view, could have been united with cosmological proportions, and revealled structural integrity to the way in which the universe was formed. If such views were manifesting from planck Epoch realizations, then it really was kind of easy to see how such conceptualizations might have revealled themselves in stringy ways? I have deferred from brane considerations( this is most interestng to me of holographical proportions that such branes could intersect themselves to coordinated references?) at this point to explore this unusual unversal explanation.





This figure shows the SDSS spectrum of a quasar at a distance of 12 billion light years. The middle panel shows the complete spectrum. The upper panel is an expanded view of the region of the spectrum affected by the filaments of gas whose clumping is the focus of the present study. Each of the hundreds of dips in the spectrum corresponds to a different parcel of gas along the line of sight between the quasar and the Earth. This is schematically shown in the lower panel, which indicates a line of sight through a simulation 30 million light years across of the distribution of gas in the universe. The clumpiness of the gas is determined by, among other things, the constituents of the universe, including dark matter, dark energy, and massive neutrinos. Renyue Cen of Princeton University carried out the simulation.

A lot of times it seems the general concept is far fleeting from educated minds that in a laymen's way I wanted to put forward a generalized view from information gathered. I hope this summation is correct?












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."


Without some dynamical realization of that early universe it wouldn't make much sense not to consider the deepening revelation of how we percieve that Window on the Universe? Kip Thorne's early introspective views have become interesting ways in which to interpret that same universe, with Ligo and other means. From Wheelers day, it was important to understand this developement, along with Bells Theorem.

How could we not have considered the temeprature values of that same early universe and not wondered about the nature of supergravity associated with these energy considerations? How else might we understand resonance curve?


Tuesday, November 23, 2004

The Man Who Knew Infinity:

A Life of the Genius Ramanujan
by Robert Kanigel



Srinivas Ramanujan (1887-1920)In the past few decades, we have witnessed how Ramanujan's contributions have made such a profound impact on various branches of mathematics. The book, "The man who knew infinity", by Robert Kanigel reached out to the general public the world over by describing the fascinating life story of Ramanujan. And now, in the form of a play, the public is made aware, once again, of this wonderful story. This is a very impressive play and I had the pleasure of seeing it with Prof. George Andrews, the world's greatest authority on Ramanujan's work and on partitions.


The more I read about Ramanujan I was attracted to the idea of him being able to predict outcomes devised in some general mathematical way that seemed easy to him, but in the case of the Taxi Cab and Hardy's question, what was the nature of the taxi cab's number?

When looking through this infomration I come across interesting perspectives about such a man whose culture was far away from the society of currents math and physics. Who developed logically, through his own study. This is a intersting case to me of what could be brought to a world steep in mathematical structures. CRanks or not, whohave found joy in peering into a world that few would cosider in their day to day lives.

No account of Ramanujan is complete without the Taxi Cab episode. There is a charming scene of Hardy meeting Ramanujan in a hospital, and when Hardy mentions that he arrived by the taxi numbered 1729, Ramanujan immediately points out that 1729=10^3+9^3=12^3+1^3, the smallest positive integer that can be expressed as a sum of two cubes in two different ways. Of course, the Ramanujan taxicab equation x^3+y^3=z^3+w^3 yields Fermat's equation for cubes by setting w=0, but it is to be noted that the taxicab equation has positive integer solutions, whereas Fermat's does not.

There is something deeper here that has caught my attention. The Harmonical nature permeates my thoughts, about the extra dimensions and how we could look at the bulk?

If such thinking went beyond the two points and our focus was drawn to the space in between, what would such a nature exemplified by such harmonical attributes? Would it not have made one wonder how the world would seem in ways that our current perceptions are not accustomed too? How would Ramanujan fit here, as a emergent property of strings?

When strings vibrate in space-time, they are described by a mathematical function called the Ramanujan modular function.26 This term appears in the equation:27

[1-(D - 2)/24]
where D is the dimensionality of the space in which the strings vibrate. In order to obey special relativity and manifest co-variance), this term must equal 0, which forces D to be 26. This is the origin of the 26 dimensions in the original string theory.

In the more general Ramanujan modular function, which is used in current superstring theories, the twenty-four is replaced by the number eight, making D equal to 10.28

In other words, the mathematics require space-time to have 10 dimensions in order for the string theory to be self-consistent, but physicists still don’t know why these particular numbers have been selected.


I was interested in how this man came to think and I place this here for consideration from another poster.

Dick Well, in Ramanujans case we have some clues.

He spent his teenage years studying and mastering one book, on analytical function theory and analytical number theory (which are joined at birth). The format of the book was step by step: it started with (x-y)(x+y)=x2 - y2. You proved that and then came a slightly harder theorem of the same kind, in which the proof uses the first theorem, and so on one result building on another up to the state of the art as it was when the book was published (1880s). The book was intended to prepare or "cram" Cambridge students for the math exam known as the Tripos.

Ramanujan became not just familiar with the math in this book, it became his environment.

A recent author has suggested that math ability derives from the brain abilities used in social understanding. Think of living in a tribe or small town where "everybody knows everybody". By growing up in such an environment you know not only everyone else's name, but their preferences and personal characteristics. You are freely able to think what so-and-so and such-and-such would talk about if they had a conversation. And it is proposed that mathematicians have this same ability, only with the abstract things they think about and discuss, rather than people.

And so Ramanujan's "town" was the complex number system and the various peculiar things that could happen there. This was the focus of his imagination throughout his growing up and it is scarcely surprising that he was able to see relationships that more lazily prepared mathematicians (including great ones like Hardy) could not.

You don't have to postulate extra dimension, the depth of the human capabilities is sufficient.


As you can see Dick rejected the idea that such information could have settle in any mind, from a fifth dimensional consideration, and the extra dimensions, as he has stated. It just made sense to me, that solid things, had other information that it concealed. The harmonical nature was not only limited to the numbers and oscillations?

The Planck Epoch to now, contained interesting information. Should we find some structure to contain it all, and yet, find that this structured world is not limited to such structures alone? It was just a pattern, and one of many?


Monday, November 22, 2004

Mathematicians and Physicists Do is Perhaps Like Sculpture



"Science is that human activity in which we aim to show towards nature that respect that in a democracy we endeavor to show towards each other."

Smolin then goes on to write something interesting here. Many would have interpreted the discusion between Peter Woit's Blog and Lubos Motl's Blog, that rebels exist, but something more define I'd say in the way Smolin describes it. Arun too helps with a interesting link, that makes one wonder about the nature of numbers

But again in response to above quote, Smolin continues here below.

I must confess that I have never been able to find its source, but I have been thinking a lot about this quote recently. I hope I may be excused for using it unattributed. The stance of respect seems to me the necessary companion to the stance of the rebel, for respect signifies that we live out our lives inside an intricately structured and enormously complicated world, containing among myriads of other living creatures, many individuals like ourselves. For us human beings, the world we find ourselves in is comprised of nature, imagination and society. Science, art and politics are the ancient crafts by which we seek to understand and define our situation in these worlds. The stance of the rebel comes from the discovery that there is much in these worlds which is unacceptable. The stance of respect arises from another discovery, that to change the world requires that we acknowledge that each of our lives is but a brief moment in the vastly complicated networks of relationships that comprise our shared worlds.

It was important to me to try and find the sources of inspiration in terms of the inconsistancies of quantum mechanics and general relativity.


The first "attempt to combine the quantum theory with the theory of gravitation," which demonstrated that "in order to avoid an inconsistency between quantum mechanics and general relativity, some new features must enter physics," was made by Bronstein in 1935. That the Planck mass may be regarded as a quantum-gravitational scale was pointed out explicitly by Klein and Wheeler twenty years later. At the same time, Landau also noted that the Planck energy (mass) corresponds to an equality of gravitational and electromagnetic interactions.
Theoretical physicists are now confident that the role of the Planck values in quantum gravity, cosmology, and elementary particle theory will emerge from a unified theory of all fundamental interactions and that the Planck scales characterize the region in which the intensities of all fundamental interactions become comparable. If these expectations come true, the present report might become useful as the historical introduction for the book that it is currently impossible to write, The Small-Scale Structure of Space-Time.


Maybe the new book should be written by Lubos?



Sunday, November 21, 2004

Quantum Gravity

Here is one of two methods that help explain. The next post will follow tomorrow if I have time. The complexity of the pictures involved is linked down below in Fig 15-17. This will give some generalizations that I had been looking too, to comprehend the model of strings and its geometrical discriptions.

Continuity



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.

Such transformations of ideally elastic objects are subject only to the condition that, for surfaces, nearby points remain close together in the transforming process. This condition effectively outlaws transformations that involve cutting and gluing. For instance a doughnut and a coffee cup are topologically equivalent. One can be transformed continuously into the other. The hole in the doughnut will be preserved as the hole in the handle of the coffee cup.











Topology becomes an important tool in superstring when it is treated as quantum mechanical object. This branch of mathematics is concerned with smooth, gradual, continuous change of geometric shape. For example, a square can be continuously deformed into a circle by pushing in the corners and rounding the sides. The essential rule is that no new hole can be created in the new form by tearing. Some topological equivalent objects are shown in Figure 15-17.

Unfortunately I lost the link to this quote and if someone could remember seeing this, I hope you will let me know.

We expect that the divergences of quantum gravity would similarly be resolved by introducing the correct short-distance description that captures the new physics. Although years of effort have been devoted to finding such a description, only one candidate has emerged to describe the new short-distance physics: superstrings. Vibrational modes

This theory requires radically new thinking. In superstring theory, the graviton (the carrier of the force of gravity) and all other elementary particles are vibrational modes of a string (figure 1). The typical string size is the Planck length, which means that, at the length scales probed by current experiments, the string appears point-like.

The jump from conventional field theories of point-like objects to a theory of one-dimensional objects has striking implications. The vibration spectrum of the string contains a massless spin-2 particle: the graviton. Its long wavelength interactions are described by Einstein's theory of General Relativity. Thus General Relativity may be viewed as a prediction of string theory!


This highlighted print tells us a lot, about the higher dimensional values assigned to spacetime as being a result. If we were to entertain the holographical consideration of these higher spaces manifesting into the spacetime curvature, that we have come to know and love, then we have indeed not only used Klein to travel to the fifth dimension but have come back home, to what GR represents for us a sa tangible?

Is Line , Hook and Sinker, Dimensionally Leading to Soul Food?

Oskar Klein (left) proposed in the 1920s that hidden spatial dimensions might influence observed physics. He poses with physicists George Uhlenbeck (middle) and Samuel Goudsmit in 1926 at the University of Leiden, the Netherlands.

AIP Emilio Segrè Visual Archives

I think sometimes the road begun existed before many of our own perspectives were added for considerations, so although we find that Einstein argue the simplicity and beauty of GR as it is, and rejected the quantum mechanical nature of the world, he did not reject the extensions of his thoughts to lead to other things. Some might of called this a mistake as well?

Kaluza and Klein showed in the 1920s that Maxwell's equations can be derived by extending general relativity into five dimensions. This strategy of using higher dimensions to unify different forces is an active area of research in particle physics.

General consistancy of mathematics and numerical correlation, that unite, seem very plausible tools for recognition? Even if the mathematician, has divorced himself from the real world and said, it fits? Do they not become the Lewis Carroll's and paint pretty pictures for us of a implausible world when they move into this abstract world of mathematics, without joining the physics? Einstein and Kaluza did this for us? There mathematics worked, and why not the Kaluza's consideration to extra dimensions?

Let there be light! How could we not see that if the extra dimension was added how relevant might such unification have spoken to electromagnetism and gravity?

Kaluza-Klein theory is a model which unifies classical gravity and electromagnetism. It was discovered by the mathematician Theodor Kaluza that if general relativity is extended to a five-dimensional spacetime, the equations can be separated out into ordinary four-dimensional gravitation plus an extra set, which is equivalent to Maxwell's equations for the electromagnetic field, plus an extra scalar field known as the "dilaton"

Thank you Wikipedia.

Einstein's special relativity was developed along Kant's line of thinking: things depend on the frame from which you make observations. However, there is one big difference. Instead of the absolute frame, Einstein introduced an extra dimension. Let us illustrate this using a CocaCola can. It appears like a circle if you look at it from the top, while it appears as a rectangle from the side. The real thing is a three-dimensional circular cylinder. While Kant was obsessed with the absoluteness of the real thing, Einstein was able to observe the importance of the extra dimension


Saturday, November 20, 2004

Fool's Gold



Ludwig Boltzmann
(1844-1906)

In 1877 Boltzmann used statistical ideas to gain valuable insight into the meaning of entropy. He realized that entropy could be thought of as a measure of disorder, and that the second law of thermodynamics expressed the fact that disorder tends to increase. You have probably noticed this tendency in everyday life! However, you might also think that you have the power to step in, rearrange things a bit, and restore order. For example, you might decide to tidy up your wardrobe. Would this lead to a decrease in disorder, and hence a decrease in entropy? Actually, it would not. This is because there are inevitable side-effects: whilst sorting out your clothes, you will be breathing, metabolizing and warming your surroundings. When everything has been taken into account, the total disorder (as measured by the entropy) will have increased, in spite of the admirable state of order in your wardrobe. The second law of thermodynamics is relentless. The total entropy and the total disorder are overwhelmingly unlikely to decrease



However, don't be fooled! The charm of the golden number tends to attract kooks and the gullible - hence the term "fool's gold". You have to be careful about anything you read about this number. In particular, if you think ancient Greeks ran around in togas philosophizing about the "golden ratio" and calling it "Phi", you're wrong. This number was named Phi after Phidias only in 1914, in a book called _The Curves of Life_ by the artist Theodore Cook. And, it was Cook who first started calling 1.618...the golden ratio. Before him, 0.618... was called the golden ratio! Cook dubbed this number "phi", the lower-case baby brother of Phi.

How much wiser are we with the understanding that Curlies Gold told us much about what to look for in that One Thing?



The result is that the pinball follows a random path, deflecting off one pin in each of the four rows of pins, and ending up in one of the cups at the bottom. The various possible paths are shown by the gray lines and one particular path is shown by the red line. We will describe this path using the notation "LRLL" meaning "deflection to the left around the first pin, then deflection right around the pin in the second row, then deflection left around the third and fourth pins".


So, what is the value of PI, if a "point" on the brane holds previous information about the solid things we see in our universe now? Have we recognized the momentum states, represented by the KK Tower and the value of 1R as it arises from the planck epoch?

The statistical sense of Maxwell distribution can be demonstrated with the aid of Galton board which consists of the wood board with many nails as shown in animation. Above the board the funnel is situated in which the particles of the sand or corns can be poured. If we drop one particle into this funnel, then it will fall colliding many nails and will deviate from the center of the board by chaotic way. If we pour the particles continuously, then the most of them will agglomerate in the center of the board and some amount will appear apart the center. After some period of time the certain statistical distribution of the number of particles on the width of the board will appear. This distribution is called normal Gauss distribution (1777-1855) and described by the following expression:





Predictability with Numbers in Resonantial Features

Butterflies can cause hurricanes, according to the classical theory of chaos. But what happens when chaos encounters the quantum world?


Manjul Bhargava: An Artist of Music and Math




So where has Alice Gone?

With some certainty I understood that gamma ray detection woud have easily directed our perspective of information of cosmological events, but imagine, if we are faced with so much information, how we would resolve all possible outcomes?





Classically the world of computerization would rest easy knowing that it has been modelled on the perspective of gamma ray detection, but if we raised the question of Gerard t'Hooft's thinking now, could we ever assign computerization, to quantum mechanical realities of strings? We would have then mastered the realm of unpredictability?