Veneziano Amplitude for Winding Strings

It seems I am caught in strange world where topological functions are happening and if such tubes could contract and then expand then what energy amplitudes on tree models would say the string should have this much energy, and then as the energy grows that the amplittude of the string is also changing? Here the loops would have varying energy determinations that would allow the loop to twist and turn?


Ramzi R. Khuri March 11 1993

String configurations with nonzero winding number describe soliton string states. We compute the Veneziano amplitude for the scattering of arbitrary winding states and show that in the large radius limit the strings always scatter trivially and with no change in the individual winding numbers of the strings. In this limit, then, these states scatter as true solitons.

In demonstration Greg Egan's site for the use of Animations this particular link was strange to me if something was considered in this link.



When you play with the coordinates you realize the energy changes that can take place in the loop. Equally important was when you observe the faces of the directions when these coordiante are selected. To me something was triggered when it was understood the the euclidean directions actually could been view from these faces, six in all if held in context of the higher dimenisons.



Unified treatment: analyticity, Regge trajectories, Veneziano amplitude, fundamental regions and Moebius transformations
Abdur Rahim Choudhary

In this paper we present a unified treatment that combines the analyticity properties of the scattering amplitudes, the threshold and asymptotic behaviors, the invariance group of Moebius transformations, the automorphic functions defined over this invariance group, the fundamental region in (Poincaré) geometry, and the generators of the invariance group as they relate to the fundamental region. Using these concepts and techniques, we provide a theoretical basis for Veneziano type amplitudes with the ghost elimination condition built in, related the Regge trajectory functions to the generators of the invariance group, constrained the values of the Regge trajectories to take only inverse integer values at the threshold, used the threshold behavior in the forward direction to deduce the Pomeranchuk trajectory as well as other relations. The enabling tool for this unified treatment came from the multi-sheet conformal mapping techniques that map the physical sheet to a fundamental region which in turn defines a Riemann surface on which a global uniformization variable for the scattering amplitude is calculated via an automorphic function, which in turn can be constructed as a quotient of two automorphic forms of the same dimension.

tracks

The Triumph of the Standard Model

The discovery of the massive top quark at Fermilab in 1994 spectacularly confirmed the predictions of the Standard Model


John Ellis

The fundamental particle interactions described by the Standard Model are the electromagnetic, weak and strong nuclear forces. It has been known from the early days of quantum physics that the electromagnetic forces between one charged particle and another are mediated by the exchange of the massless photon. Electromagnetic interactions are well described by the long-established quantum theory of electrodynamics, called QED. Meanwhile the strong nuclear interactions are described by quantum chromodynamics (QCD), and are mediated by massless bosons, called gluons. These were discovered at the DESY laboratory in Germany in 1979.

Without some acknowledgement of where we see these events significant in the early universe, it will not make much sense to anyone, if they do not recognize the microcosmic view, is very relevant to how we see the beginning of the universe?

May the strong force be with you

Particle physicists were delighted a few months ago when the Nobel Prize for Physics was awarded to David Gross, David Politzer and Frank Wilczek for their discovery of asymptotic freedom, which enabled QCD to emerge as the underlying theory of the strong interactions. Since their papers were published in 1973, and the experimental evidence for QCD has been overwhelming for a couple of decades, their prize seems a tad overdue.

The Phenix

PHENIX, the Pioneering High Energy Nuclear Interaction eXperiment, is an exploratory experiment for the investigation of high energy collisions of heavy ions and protons. PHENIX is designed specifically to measure direct probes of the collisions such as electrons, muons, and photons. The primary goal of PHENIX is to discover and study a new state of matter called the Quark-Gluon Plasma.

The Bird's eye view is really interesting once you consider the frame with which early detection system would speak to early universe formation. To me, this is a direct perspective of the spectrum's hidden aspect, from the origins of this universe to what we have around us now. From such a reductionistic valuation, how else would we be taken to such lengths of realization?

Can we see photons (particles of light) radiating directly from a Quark-Gluon Plasma? PHENIX has a preliminary measurement that confirms the presence of these direct photons. Data taken in 2004 should improve this measurement

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Fig. 2. Image showing how an 8 TeV black hole might look in the ATLAS detector (with the caveat that there are still uncertainties in the theoretical calculations).



Quark-Gluon Plasma and such early universe detection systems would make it very difficult to move the mind to consider the deepr implications of Compton scattering versus graviton scattering with the idea that such early indications from the source, would have revealled stoing gravitational tendencies from recognition of the supesymmetrical valuation of that early universe?


Nevertheless, astroparticle and collider experiments should provide useful input to the theoretical work in this area. Indeed, the signatures are expected to be spectacular, with very high multiplicity events and a large fraction of the beam energy converted into transverse energy, mostly in the form of quarks/gluons (jets) and leptons, with a production rate at the LHC rising as high as 1 Hz. An example of what a typical black-hole event would look like in the ATLAS detector is shown in figure 2.
If mini black holes can be produced in high-energy particle interactions, they may first be observed in high-energy cosmic-ray neutrino interactions in the atmosphere. Jonathan Feng of the University of California at Irvine and MIT, and Alfred Shapere of the University of Kentucky have calculated that the Auger cosmic-ray observatory, which will combine a 6000 km2 extended air-shower array backed up by fluorescence detectors trained on the sky, could record tens to hundreds of showers from black holes before the LHC turns on in 2007.

Maybe John Ellis can orientate our thinking here a bit in this regard.




John Ellis:

CLIC is based on a novel technology in which an intense low-energy electron beam is used to generate an electromagnetic wave that is used to push a lower-intensity beam to much higher energies in a relatively small distance. It seems to be the only realistic chance of colliding electrons and positrons at multi-TeV energies so, if it works, it will allay (at least for a while) some of David Gross's concerns about the prospects for future big physics projects

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Hirotaka Sugawara, former director of Japan’s KEK laboratory, also an ITRP member, described the science opportunities that a linear collider could provide.

"High energy physics has a long history of using proton and electron machines in a complementary way," Sugarawa said. "With concurrent operation, here is a remarkable opportunity to maximize the science from both a linear collider and the Large Hadron Collider. Exciting physics at the linear collider would start with the detailed study of the Higgs particle. But this would be just the beginning. We anticipate that some of the tantalizing superparticles will be within the range of discovery, opening the door to an understanding of one of the great mysteries of the universe—dark matter. We may also be able to probe extra space-time dimensions, which have so far eluded us."

Shakespearean Quandry?

e^- or not to e⁺ :)

Light-matter interaction

Low energy phenomena  Photoelectric effect
Mid-energy phenomena  Compton scattering
High energy phenomena  Pair production

Part of the realization is that if we encounter this dynamical universe with ways to intuitive glance at the interplay of this black and white, I was drawn to the idealization of the matrices, and their involvement?

Pair Production

Every known particle has an antiparticle; if they encounter one another, they will annihilate with the production of two gamma-rays. The quantum energies of the gamma rays is equal to the sum of the mass energies of the two particles (including their kinetic energies). It is also possible for a photon to give up its quantum energy to the formation of a particle-antiparticle pair in its interaction with matter.

This is very touchy area for me, but I endeavor to what Glast determinations are revealling, as we move to consider the relevance of this interactive feature of the dark matter energy, in regards to the cosmological movement revealled by the Friedmann equation.

We needed this question of Shakespeare, to move our minds to the question of the ever constant becoming, to know that it would manifest in this cyclical nature of rejuvenation. Where blackhole and gravitonic condensation, can become viable features of phase state changes, taking us back the beginning of this universe, now?

Now it's possible that those kinds of laws in physics may be incomplete. It might be that the laws change absolutely with time; that grvaity for instance varies with time and that this inverse square law has a strength which depends on how long it is since the beginning of time. In other words, it's possible that in the future we'll have more understanding of everything and physics may be completed by some kind of statement of how things started which are external tothe laws of physics.

Pg 206 and 207, of Superstrings, A Theory of Everything, by P.C.W.Davies and J. Brown

So lets cosider something else here where such dynamcial realization would point to microstate blackholes. This will follow later for consideration.

Neutrinos for Geophysics

I am always interested in seeing how the physics that has developed, could better induce minds to expand the potentials of these innovations to help the world's population in a most appropriate way.

The issues on climate and the ways in which we could measure this is far removed from the butterfly who flaps his wings, and the need for dramatic computerization functions to reveal model apprehensions of some predictable feature of that same climate. A pretty unsurmoutable problem in uncertainty? Gerard Hooft recognizes these problems, but while this uncertainty reigns alternative to using many computers to diagnosis,as in Seti and Ligo analysis.



A physicist in the US has proposed using a beam of neutrinos to measure the density of the Earth's core. Walter Winter of the Institute for Advanced Study in Princeton says that neutrinos could provide information about the Earth that is not available with other techniques (arXiv.org/abs/hep-ph/0502097).

So in this respect of information gathering, the idea here is to understand the mass density of the land mass regions to help people gather in potential spots of safety. Much like the recognition of tsunami revelations detected, so that escape from shores can be forewarn to people to move inland.

Timeline

There are reasons for this theme, that I thought most appropriate to the discussion of illusion and miracles.

In the thread previous to this one, a concept is put forward by Arkani-Hamed that focuses on the issue of the timeline from my perspective, relates to what Peter Woit speaks about here. I will try and explain, but I needed to comprehend better Peter's position.

Peter Woit:

Another way of saying it is that in the standard model you have an SU(3)xSU(2)xU(1) principal bundle, and the geometry of the fibers is tightly constrained by the gauge symmetry, which is why the theory works so beautifully.

But before addressing this a couple of things came to mind today that pointed to the need for this timeline to be addressed in a most appropriate manner that would tax the minds position it had assumed to free it to other possible realms for consideration.

So I place here two idealizations that I thought of first and by doing this help hopefully to orientate peoples minds around the string issue and it's place in the spectrum of possibilties.

The Planck Epoch



In order to further expand this conceptual frame work, I am reminded of the Glast determinations and spectrum analysis we have engaged, which has allowed a deeper look at the timeline of events. The place from that earlier time.

It was not to difficult to realize that work and place was being supplanted by a theoretical approached, so new ideas could emerge from current established views. Assumptions of theoretcial models would pushed the mind into other venues of considertaion and force upon it, the realities of acceptance.

The Pre-Big Bang Scenario in String CosmologyM. Gasperini1 and G. Veneziano

During the past thirty years, mainly thanks to accelerator experiments of higher and higher energy and precision, the standard model of particle physics has established itself as the uncontested winner in the race for a consistent description of electroweak and strong interaction phenomena at distances above 10⁻¹⁵ cm or so. There are, nonetheless, good reasons (in particular the increasing evidence for non-vanishing neutrino masses [388, 568, 569]) to believe that the standard model is not the end of the story. The surprising validity of this model at energies below 100 GeV, as well as the (in)famous Higgs mass fine-tuning problem, suggest some supersymmetric extension of the standard model (for a review see [501]) as the most likely improved description of non-gravitational phenomena over a few more decades in the ladder of scales. It is however quite likely that other questions that are left unanswered by the standard model, such as the peculiarities of fermionic masses and mixings, the family pattern, C, P, CP, B violation, etc., will only find their answers at –or around– the much higher energies at which all gauge interactions appear to unify [21]. This energy scale appears to be embarrassingly close (on a logarithmic scale) to the so-called Planck mass, MP ∼ 10¹⁹ GeV, the scale at which gravity becomes strong and needs to be quantized.

On the one hand then we see where this timeline of physics and it's approach has been and still remians consistent with established views, but we have overlayed this idealization of the spectrum with a new approach to place the established geometries toplogiies that are curently being put forward in the mathematical realms for further extension of these natural laws? So what math shall preceed these views, if we do not change the concepts we had currently established to have the mind consider other prorposals?


Drawing by Glen Edwards, Utah State University, Logan, UT

Here I will refer back to Kip Thorne and the plate for consideration about how we see this timeline further illucidated upon( I mean really)and now we place it here in context of a new approach?

Where is Gravity Stronger?

If one were to ask where this energy came from, would such a weak gravitonic scale lead us to stronger inidcations of the energies presence and becomes a trail leading us to it's source? What would gravity mean, if it was considered in context of the fifth dimension, and only became realized at this time, in the four dimensional spacetime?

So we ask the question, where is gravity stronger?

Arkani-Hamed began pondering this quandary as a Stanford University researcher and continued at Harvard. He stumbled onto the idea of extra dimensions. Imagine a piece of paper floating in space. The space is the fifth dimension. Our world, everything we can perceive, is confined to that paper. But what if there is interaction between the paper and the surrounding space?

Perhaps gravity bleeds into this fifth dimension, Arkani-Hamed theorized, or even more dimensions. But, given our four-dimensional reality, we're able to experience only the gravity left over. In other words, gravity is much stronger than we realize. Perhaps, Arkani-Hamed speculated, at super high energy levels, of an intensity never seen by humans, such as the split second after the Big Bang, gravity is like the other forces, before leaking into the fifth dimension.

Describing this conceptual breakthrough, which he backed mathematically, thus rocking modern physics, Arkani-Hamed says: "At the time, I was just in the mood for thinking about something different." As speculative as his ideas might sound, experimental verification is on the way. In three years, a massive particle accelerator in Switzerland comes on line, giving scientists a means to create super-high energy levels that will enable them to measure nature at the most fundamental scale ever. This should provide evidence confirming -- or refuting -- Arkani-Hamed's theory.

I added bold to reinforce the conceptual thinking that we are dealing with.

The Arrow of Time

Rudolf Julius Emanuel Clausius

There is but one kind of entropy change. Entropy change is due to energy dispersal to, from, or within a system (as a function of temperature.), measured by microstate change: S = k_B ln [microstates _final / microstates _initial ].

I should back up here and mentioned that Peter Woit seems to be coming out in the open and explaining somethings that have been not so clear before?

Perter Woit:

Penrose also carefully lays out areas in which his point of view differs from the general consensus of most theoretical physicists. An example is his emphasis on the importance for cosmology of understanding why the universe had such low entropy at the Big Bang

What is strange today that with this thought on the subject of entropy.

Lubos Motl:

This is what allows the early gas to clump (and seemingly create a more order state) without violating the 2nd law of thermodynamics: the gravitational entropy overcomensates the decrease of the entropy.

OK, so why was the beginning of the Universe a low-entropy state? The best explanation we have is inflation. It simply explodes the size of the Universe. During inflation, the total entropy of the Universe grows, but much more slowly than how it would grow otherwise, without inflation.

if one did not understand the early universe consideration here, and the idealization of supersymmetry, could we have found a association to low orders of entropy since this early time would have been very topologically considered and part of a continuum?

Entropy and the second law of thermodynamics

Entropy is no mystery or complicated idea. Entropy is merely the way to measure the energy that spreads out in a process (as a function of temperature). What's complicated about that? Entropy change, S, measures how much energy is spread out in a system, or how spread out is the energy of a system (both always involving T). The first example in our text was melting ice to water at 273 K where S = q/T. So, in that equation, it's easy to see that q (the enthalpy of fusion) is how much "heat" energy was spread out in the ice to change it to water. What's the big deal?

Update: Reading Peter Woit's blog today he linked Sean Carroll's "Arrow of Time article," so I thought it most apropriate to link it from here as well, since I am on the topic.


Sean Carroll:

Jennie and I do the following thought experiment -- if it weren't for inflation, what would be a "natural" state for the universe to be in? Different people have addressed this question, with different answers; Roger Penrose, for example, has suggested that it would be a lumpy universe full of black holes. Our answer is almost exactly the opposite -- the only natural state is empty space. This is basically because gravity makes everything unstable, and the entropy of any given configuration can always be increased by just expanding the universe by a huge factor. Sure, black holes will form, but they will ultimately evaporate away. If you let the universe evolve forever, it will ultimately get emptier and emptier (generically).

HIgher Dimensions Without the Geometry?

In Illusions and Miracles I became concerned with what the mind's capabilties which could encounter fifth dimensional views. That such examples were needed, and found in relation to Thomas Banchoff.

Having understood the early development from Euclidean perspective, our furthered evolutionary developement of the geometries, were gained by moving beyond the fifth postulate. I became comfortable with a dynamical realization about our universe(Omega), and about the idealization of curvature in dynamical fields of supergravity.

I made the statement that GR is reduced from the higher geometries and along with that view the understanding that things existed in earliers states of being. Robert Laughlin's views of complexity and symmetry breaking would reveal to me, that the matter states of form, were derived from "other states of existance". This is a fundamental realization of higher dimensional attributes revealled in the topologies/geometries. So from higher, and the continuity of, topological considerations to the firmly fixed realms of geometries in the forms? So from early universe to now, what views allow us to consider that symmetical breaking that has gone through phase transitions, to get from the planck epoch phase of our universe to today?

Having come in contact with a new type of thinking in the realm of the geometries, it became very important to me to understand how this could have manifested early in our historical background? I followed it through GR in order for this to make sense, I continued to move and consider the higher dimensional relevance new models might use in their move to the abstracts realms of thinking.

Here I would interject the realization of string theory, and ask why such a rejection mathematically, would dimiss the subject of strings based on this dimensional realization, and then quickly disperse, string's relevance because of the higher dimensional significance brought to bear on the attribtues of the minds capabilties? Part of the develpement of the brains compacity was the realization that such images produced(higher topological math forms), could indeed symmetryically break to forms within the world. Forms within mind, that could lead to solification in the math? When is a Pipe a Pipe?:)

This is what had troubled me most, noting Peter Woit's rejection of the value of his "anti" campaign of string theory evolution. Maybe, it was more then the idea of the subject and it's established views that he felt were as much part of the illusion as any other theory, that found itself unscientifically determined? Based on the constructs string theory developed? Maybe it was the funding biased felt towards this subject, and lack of, somewhere else. We wouldn't know this, because he had no alternative?

What Pattern Emerges?

Problem solvers have a way of getting to the heart of the issues, and unfortunately when ones engages competent minds like Peter Woit in the world? Whose sign post is,"anti-string with no explanation"? This is simple in the minds of the general public? It then becomes a rant, without a substantial basis? Why? Because he had no platform with which to refute?

So this attempt was fruitless, in wondering why strings should not be.

What I did find viable in looking for myself, is finding out where strings applicable features pervaded and what they were describing. Both bottum up and top down have to find approaches that emerge from a place that asks us to map this progress, and there is only one place that allows me to understand this operation.

The spectrum.

When you look at Glast operations this idealization of using the spectrum in cosmological discernation, helped to clarify why the move of strings to a cosmological operation platform was necessary from a experimental and scientific undertanding. Why was this move important?

It had to do with the amounts of energy needed to explore the principles of reductionism? How could we extend reductionism to a cosmological question about the origins of our beginning? There were no limitations as to the question of the energy that could be displayed for us all to wonder on that cosmological pallete, and here Relativity Ruled.

While complexity, asks us about the means of what is established in the forms, stands for us in our observations, as existing? Many people feel safe in what they can see?

I looked for comparative features. Like how ideas could emerge and as a good example of what math could issue from the minds of those whose good observation could speak about natures manfestations.

How good are the observatory minds of mathematicians? That would systematically describe for us this idealization of quantum reality and Relativity to join in a way that makes sense?

Macroscopic and microcosmo perceptions joined?

You say Time? Julian Barbour wants to do away with Time? Yet his goal is the same? He calls Time a human construct? What isn'taside from everythng else that we don't see? Science reveals a deeper truth?

Killing Time

Barbour posits that time is, in fact, an illusion - a measure imposed on the world by humanity. He explains this with the concept of a 'now', which he describes as a snapshot in time - a completely frozen, self-contained instant (much like a Polaroid photograph). Time is simply the measure of the space between two separate and unrelated 'nows.'

BarryTo offer that I am an engineer and a sculpture with a carear of problem solving. To offer that making me understand the final solution is to achieve making it clear to anyone.

I am somewhat like a philosopsher as you are, minus, the engineering, yet I am quite capable of peering past the veil that good minds construct.

In the end, what is taken with you might be the realization that of all the thought forms we have estanblished and created. The illusion that we move through, hides a deeper truth, and we were emersed within it the whole time. Science, verified the anomalies that we saw?

How much power then could we grant the mind who escapes this realization, to find that all the thoughts that have ever existed, were weighted with the gravity that held us to earth? That the forms, revealled a deeper realization of their beginnings?

As the temperature cooled, the solification was final and so was the idealization that manifested from the idea.

When is a pipe a pipe? Is a question about what supergravity reveals in the forms manifestation. Crystalization. What pattern emerges?


Betrayal of Images" by Rene Magritte. 1929 painting on which is written "This is not a Pipe"

Yet probablistic in nature, how could such things arrange themselves as they have?

There is a deeper question here about the reality. If the idea is born in mind how would it not burn up, comparative to the beginning of our universe? Yet nature has supplied a good analogy of bubbles that form, rise to the surface, and this could have been information that arose from the fifth dimension? It all arose form the mind of the subconsious? It was always closer to the source. Why Ramanujan and Einsteins note taking in the subtle realms help to spur the incubation of reality to a deepr level of questions.

People might say indeed, that this departure point from the sane world of forms, is the moving further into the illusions? But if we cannot find a way to free ourselves, then surely, one will accept the consequences of there reality, as they take it with them?:)