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?

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?

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?

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

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?

The Butterfly Effect

The "Butterfly Effect" is the propensity of a system to be sensitive to initial conditions.Such systems over time become unpredictable,this idea gave rise to the notion of a butterfly flapping it's wings in one area of the world,causing a tornado or some such weather event to occur in another remote area of the world.

Where do these ideas of weather exist, before they find themselves funneling into man's framework, called the brain?

It was Socrates' turn to look puzzled.
"Oh, wake up. You know what chaos is. Simple deterministic dynamics leading to irregular, random-looking behavior. Butterfly effect. That stuff."
Of course, I know that," Socrates said in irritation. "No, it was the idea of dynamic logic that was puzzling me. How can logic be dynamic

In contemplating the essence of the ideas of complexity it became increasingly clear to me, that the ideas manifesting and philosophies that were looking at this, could be recognized in tell tale signs of international terrorism of the worst kind.

The final image of the twin towers in panel shown, before, such a contemplative action, spoke to such complexities. Had we been able to see what effect this action had, we might have then said look, indeed, where is it's origination. The reveberations, "symbolically," not only shook the foundation, but was started long before and continue to this day.

Whether the state of the nation or of the world community, such attempts to disrupt, left signatures with it's ideological thinking, that became the trademark of expansive and multple effects, as if, reverberating from a initial idea. Community and science spoke freely. Had we let evil loose, from such conceptualizations?

This raises a much deeper and fundamental question then, about the nature of reality that would emerge in this Third Superstring Revolution, that such conceptualization are now open and free. That questions of self organization, had fundamental thoughts governing it's growth all along.

These ideas always existed then, in the bulk, but waited, for the right channel to express themselves? Like beget's like, and manifests into form?

You see?

Plato as a City Slicker

You all know the saying of this one thing, right?



The rest of the Republic answers this challenge. It does so by way of an analogy. Socrates says that it is difficult to distinguish what is going on in the soul, but it is easier to see what is going on in the state. Thus the state will be examined by analogy to the soul. Now we would say that the state is the macrocosm (makros, "large," kosmos, "universe"), the large scale analogue, and the soul is the microcosm (mikros, "small"), the small scale analogue. When matters are sorted out for the state, then the soul can be understood in its own right.

Well wisdom is bestowed upon us all, when we consider this one thing. Is it the stuff all dreams are made up of?

Hooft, Witten and now Lauglin himself understands, that we have come face to face with a problem? By arguing "stuff", would we have divested ourselves of recognition of this Third Superstring Revolution? Of course not.:)

So instead of defining the state of the cosmo and the insignificance of the microscopic views of man's soulful journey, what value had we'd be lured in too, but by Curlies Pot of Gold?

The Republic: "You must contrive for your future rulers another and a better life than that of a ruler, and then you may have a well-ordered State; for only in the State which offers this, will they rule who are truly rich, not in silver and gold, but in virtue and wisdom, which are the true blessings of life."

I don't think so. The expansive nature of the cosmo is still very relevant to the expansiveness yet to be contained with our humble brains? Some cannot leave the four-square of earth, and wonder about the shape, representing God, yet the diversity of opinion reocgnizes that a view has formed, of a world so few recognize.

Chaotic Competition

It was always easy to focus on two points and what separate them? Quark to Quark measure, defined someway and it was not to hard to see that the space became important within those measures that we understood what this energy meant.

The emergent property, pointed us to reconsider the one dimension value to say that the mass indication could have been looking at how this formation resolved itself, that we might have called it harmonical in value?

INstead of pool balls or drunk sargeant majors, we learnt to see the concepts in another way.

Here’s an analogy to understand this: imagine that our universe is a two-dimensional pool table, which you look down on from the third spatial dimension. When the billiard balls collide on the table, they scatter into new trajectories across the surface. But we also hear the click of sound as they impact: that’s collision energy being radiated into a third dimension above and beyond the surface. In this picture, the billiard balls are like protons and neutrons, and the sound wave behaves like the graviton.