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Showing posts with label Mandelstam. Show all posts
Showing posts with label Mandelstam. Show all posts

Saturday, July 12, 2008

The Geologist and the Mathematician

In an ordinary 2-sphere, any loop can be continuously tightened to a point on the surface. Does this condition characterize the 2-sphere? The answer is yes, and it has been known for a long time. The Poincaré conjecture asks the same question for the 3-sphere, which is more difficult to visualize.

On December 22, 2006, the journal Science honored Perelman's proof of the Poincaré conjecture as the scientific "Breakthrough of the Year," the first time this had been bestowed in the area of mathematics


I have been following the Poincaré work under the heading of the Poincaré Conjecture. It would serve to point out any relation that would be mathematically inclined to deserve a philosophically jaunt into the "derivation of a mind in comparative views" that one might come to some conclusion about the nature of the world, that we would see it differences, and know that is arose from such philosophical debate.

Poincaré, almost a hundred years ago, knew that a two dimensional sphere is essentially characterized by this property of simple connectivity, and asked the corresponding question for the three dimensional sphere (the set of points in four dimensional space at unit distance from the origin). This question turned out to be extraordinarily difficult, and mathematicians have been struggling with it ever since.


Previous links in label index on right and relative associative posts point out the basis of the Poincaré Conjecture and it's consequent in developmental attempts to deduction about the nature of the world in an mathematical abstract sense?

Jules Henri Poincare (1854-1912)

The scientist does not study nature because it is useful. He studies it because he delights in it, and he delights in it because it is beautiful.


HENRI POINCARE

Mathematics and Science:Last Essays

8 Last Essays

But it is exactly because all things tend toward death that life is
an exception which it is necessary to explain.

Let rolling pebbles be left subject to chance on the side of a
mountain, and they will all end by falling into the valley. If we
find one of them at the foot, it will be a commonplace effect which
will teach us nothing about the previous history of the pebble;
we will not be able to know its original position on the mountain.
But if, by accident, we find a stone near the summit, we can assert
that it has always been there, since, if it had been on the slope, it
would have rolled to the very bottom. And we will make this
assertion with the greater certainty, the more exceptional the event
is and the greater the chances were that the situation would not
have occurred.


How simple such a view that one would speak about the complexity of the world in it's relations. To know that any resting place on the mountain could have it's descendants resting in some place called such a valley?

Stratification and Mind Maps

Pascal's Triangle

By which path, and left to some "Pascalian idea" about comparing some such mountains in abstraction to such a view, we are left to "numbered pathways" by such a design that we can call it "a resting" by nature selection of all probable pathways?


Diagram 6. Khu Shijiei triangle, depth 8, 1303.
The so called 'Pascal' triangle was known in China as early as 1261. In '1261 the triangle appears to a depth of six in Yang Hui and to a depth of eight in Zhu Shijiei (as in diagram 6) in 1303. Yang Hui attributes the triangle to Jia Xian, who lived in the eleventh century' (Stillwell, 1989, p136). They used it as we do, as a means of generating the binomial coefficients.

It wasn't until the eleventh century that a method for solving quadratic and cubic equations was recorded, although they seemed to have existed since the first millennium. At this time Jia Xian 'generalised the square and cube root procedures to higher roots by using the array of numbers known today as the Pascal triangle and also extended and improved the method into one useable for solving polynomial equations of any degree' (Katz, 1993, p191.)



Even the wisest of us does not realize what Boltzmann in his expressions would leave for us that such expression would leave to chance such pebbles in that valley for such considerations, that we might call this pebble, "some topological form," left to the preponderance for us in our descriptions to what nature shall reveal in those same valleys?

The Topography of Energy Resting in the Valleys

The theory of strings predicts that the universe might occupy one random "valley" out of a virtually infinite selection of valleys in a vast landscape of possibilities

Most certainly it should be understood that the "valley and the pebble" are two separate things, and yet, can we not say that the pebble is an artifact of the energy in expression that eventually lies resting in one of the possible pathways to that energy at rest.

The mountain, "as a stratification" exists.



Here in mind then, such rooms are created.

The ancients would have us believe in mind, that such "high mountain views do exist." Your "Olympus," or the "Fields of Elysium." Today, are these not to be considered in such a way? Such a view is part and parcel of our aspirate. The decomposable limits will be self evident in what shall rest in the valleys of our views?

Such elevations are a closer to a decomposable limit of the energy in my views. The sun shall shine, and the matter will be describe in such a view. Here we have reverted to such a view that is closer to the understanding, that such particle disseminations are the pebbles, and that such expressions, have been pushed back our views on the nature of the cosmos. Regardless of what the LHC does not represent, or does, in minds with regards to the BIG Bang? The push back to micros perspective views, allow us to introduce examples of this analogy, as artifacts of our considerations, and these hold in my view, a description closer to the source of that energy in expression.

To be bold here means to push on, in face of what the limitations imposed by such statements of Lee Smolin as a statement a book represents, and subsequent desires now taken by Hooft, in PI's Status of research and development.

It means to continue in face of the Witten's tiring of abstraction of the landscape. It means to go past the "intellectual defeatism" expressed by a Woitian design held of that mathematical world.

Thursday, July 10, 2008

Stanley Mandelstam



Research Interests

My research concerns string theory. At present I am interested in finding an explicit expression for the n-loop superstring amplitude and proving that it is finite. My field of research is particle theory, more specifically string theory. I am also interested in the recent results of Seiberg and Witten in supersymmetric field theories.

Current Projects

My present research concerns the problem of topology changing in string theory. It is currently believed that one has to sum over all string backgrounds and all topologies in doing the functional integral. I suspect that certain singular string backgrounds may be equivalent to topology changes, and that it is consequently only necessary to sum over string backgrounds. As a start I am investigating topology changes in two-dimensional target spaces. I am also interested in Seiberg-Witten invariants. Although much has been learned, some basic questions remain, and I hope to be able at least to understand the simpler of these questions.
http://www.physics.berkeley.edu/research/faculty/mandelstam.html



Stanley Mandelstam (b. 1928, Johannesburg) is a South African-born theoretical physicist. He introduced the relativistically invariant Mandelstam variables into particle physics in 1958 as a convenient coordinate system for formulating his double dispersion relations. The double dispersion relations were a central tool in the bootstrap program which sought to formulate a consistent theory of infinitely many particle types of increasing spin.

Mandelstam, along with Tullio Regge, was responsible for the Regge theory of strong interaction phenomenology. He reinterpreted the analytic growth rate of the scattering amplitude as a function of the cosine of the scattering angle as the power law for the falloff of scattering amplitudes at high energy. Along with the double dispersion relation, Regge theory allowed theorists to find sufficient analytic constraints on scattering amplitudes of bound states to formulate a theory in which there are infintely many particle types, none of which are fundamental.

After Veneziano constructed the first tree-level scattering amplitude describing infinitely many particle types, what was recognized almost immediately as a string scattering amplitude, Mandelstam continued to make crucial contributions. He interpreted the Virasoro algebra discovered in consistency conditions as a geometrical symmetry of a world-sheet conformal field theory, formulating string theory in terms of two dimensional quantum field theory. He used the conformal invariance to calculate tree level string amplitudes on many worldsheet domains. Mandelstam was the first to explicitly construct the fermion scattering amplitudes in the Ramond and Neveu-Schwarz sectors of superstring theory, and later gave arguments for the finiteness of string perturbation theory.

In quantum field theory, Mandelstam and independently Sidney Coleman extended work of Tony Skyrme to show that the two dimensional quantum Sine-Gordon model is equivalently described by a thirring model whose fermions are the kinks. He also demonstrated that the 4d N=4 supersymmetric gauge theory is power counting finite, proving that this theory is scale invariant to all orders of perturbation theory, the first example of a field theory where all the infinities in feynman diagrams cancel.

Among his students at Berkeley are Joseph Polchinski and Charles Thorn.

Education: Witwatersrand (BSc, 1952); Trinity College, Cambridge (BA, 1954); Birmingham University (PhD, 1956).

Wednesday, June 06, 2007

The Cosmic Landscape

I noticed a few blogs mentioning the landscape.

Asymptotia(Clifford Johnson), The Reference Frame(Lubos Motl), and Not Even Wrong (Peter Woit's) blog.

The Cosmic Landscape:String Theory and the Illusion of Intelligent Design by Leonard Susskind

After reading Susskind's book in regards to the landscape issue, I was intrigued by the First Three Microseconds previous as it helped iilucidate some of this information for me. As well as giving me some indications from the blogs mentioned and the topic therein.

What struck me a quite profound in reading Susskind's book, was that what was to all appearances a troubling issue with "eyesight," in regards to Peter Woits idea of intelligent design attributed to the landscape of string theory, that Susskind, was actually answering him by pronoucing the title of this book of his. It's obvious, he has been watching the discussions.

Now what was profound, was that the idea of the landscape was a mathematical construct. If you were so concerned about the idea of the landscape, then why would anyone with "math skills" reject the landscape? If the day is announcing itself in blog voices and now say hmmm.... with interest, I see that it is becoming more acceptable?

If you did not see the "hills and valleys" for what they were, then why would you reject what was leading in terms of the finiteness of Mandelstam, and then say, there was no more future in regards to where math had left off?

This is Lee Smolin's downfall I think when discussing the issue of Polchinski's concepts, reitereated with regards to Lee's book, and the "ventures of mathematics" as it has been spelted out and had pointed towards the landscape issues.

This is where Peter Woit made his mistake as well.

I accept that a lot of people don't like it. But that's not the point in terms of mathematical development, as it had been argued by Polchinski, against his reading and comments in regards to Lee Smolin's book.

See:The First Three Microseconds

This infomration has lead me to insights about the landscape that had missed most people, even those who are well educated. My point above is in regards to Mandelstam, and the arguments against Lee by Jacques distiller, was important from this aspect.

Reject the notion of the topological figures in relation to the landscape issue, and what is left? Yes, Lee's and Peter Woits ideas about the landscape, which is not finished. Which is leading with concepts, by mathematical deduction.

Can't always answer in post responses, but please let me know that you are visiting? :)

My son and I are starting our foundation. I write when I can, but read in the hours without our electricity and by battery alone.

Thursday, April 12, 2007

The CrossOver Point within the Perfect Fluid?

I had been following this research because of what I had been trying to understand when we take our understanding down to a certain level. That level is within the context of us probing the collision process for evidence of "some new physics" that we had not seen before.

Evidence for Neutrino Oscillations from the LSND Experiment
One of the only ways to probe small neutrino masses is to search for neutrino oscillations, where a neutrino of one type (e.g. numubar ) spontaneously transforms into a neutrino of another type (e.g. nuebar ) For this phenomenon to occur, neutrinos must be massive and the apparent conservation law of lepton families must be violated. The probability for 2-flavor neutrino oscillations can then be expressed as P=sin2(2theta) sin2(1.27 m2L/E) , where theta is the mixing angle, m2 is the difference in neutrino masses squared in eV2, L is the neutrino distance in meters, and E is the neutrino energy in MeV. In 1995 the LSND experiment [1] published data showing candidate events that are consistent with numubar->nuebar oscillations. [2] Additional data are reported here that provide stronger evidence for numubar->nuebar oscillations [3] as well as evidence for numu->nue oscillations. [4] The two oscillation searches have completely different backgrounds and systematics from each other.


What valuation of this process allows us to think that while speaking to "probing this perfect fluid" that we had not discovered some mechanism within it, that allows us to see Coleman Mandula effects being behind, as a geometrical unfoldment from one state into another?

If we had looked at the Genus 1 figure then what avenue would help us discern what could come from the string theory landscape and the "potential hill" discerned from the blackhole horizon? What tunnelling effect could go past the hill climbers and valley crossers to know that you could cut "right through the hill?"

MiniBooNE opens the box

BATAVIA, IllinoisScientists of the MiniBooNE1 experiment at the Department of Energy's Fermilab2 today (April 11) announced their first findings. The MiniBooNE results resolve questions raised by observations of the LSND3 experiment in the 1990s that appeared to contradict findings of other neutrino experiments worldwide. MiniBooNE researchers showed conclusively that the LSND results could not be due to simple neutrino oscillation, a phenomenon in which one type of neutrino transforms into another type and back again.

The announcement significantly clarifies the overall picture of how neutrinos behave.


So while I am looking for some indications as I did in the strangelet case, as, evidence of this crossover, this had to have some relation to how we seen the neutrinos in development. This was part of the development as we learnt of the history of John Bahcall.

John Bahcall 1934 to 2005 See also "John Bahcall and the Neutrinos"


Plato Apr 11th, 2007 at 8:47 pm

the quark-gluon plasma behaves according to hydrodynamic calculations in which the matter is like a liquid that flows with no viscosity whatsoever.” See here

No cross over point? What role would Navier Stokes play in this?
See here

This does not minimize the work we see of Gran Sasso in relation to the LHC project.

Honestly, I do not know how someone who could work on the project, could not know what they were working on? It as if the "little parts" of the LHC project only cater to the worker Bees working just aspects of the project and their specializations.

Whilst now, you go way up and overlook this project. To see the whole context measured within that "one tiny big bang moment." Trust me when I say, we shall not minimize the effect of calling the collision process as "one tiny moment," for you may never see the whole context of this project being developed for this "one thing."

I did not realize the shortcomings that scientists place on themselves when they do specialize. I just assumed they would know as much as I did and see the whole project? I do not say this unkindly, just that it is a shock to me that one could work the string theory models and not realize what they are working on. I have heard even Jacques say there is no connection and listening to Peter Woit, I was equally dismayed that he did not realize what the string theory model was actually doing as it found it's correlation in the developing views of how we look at the moments of creation.

Bigger is better if you’re searching for smaller

Neutrinos may be in CERN's Future

The next step will again be taken in Japan, with the new J-PARC accelerator starting in 2009 to send neutrinos almost 300 km, again to the Super-Kamiokande experiment, to probe the third neutrino mixing angle that has not yet been detected in either atmospheric or solar neutrino experiments. This may also be probed in a new experiment being proposed for the Fermilab NuMI beam. One of the ideas proposed at CERN is to probe this angle with an underwater experiment moored in the Gulf of Taranto off the coast of Italy, viewing neutrinos in a modified version of CERN's current Gran Sasso beam.
See "CERN and Future Experiments"

Plato Apr 12th, 2007 at 7:31 am

I think my comment on previous post of looking for the perfect fluid should have been here.

Also I do not think this changes how we look at string theory as a model probing the perfect fluid, and "the understanding" of developing a mechanism for this "cross over point?"

Topologically, how would this have been revealed in the string theory landscape??
See here and know that Clifford again deleted the short little post above. The point is I think for some reason once I mention string theory or evn M theory in relation to what is transpiring in the views of model development he doe not like this and would be support by Jacques as well.

That would be my job to convince them and anyone else that hold their views that taking our view to the microseconds, there is a definite relation to the timeline whether you agree with this or not. By introducing "the point of the cross over" you in effect have taken the model and presented it as part of the mechanism for this universe and effectively given new meaning to the "string theory landscape."

You may want it to be "background independent" like Lee wants it to be, but if you view the background as a oscillatory one, then any idea as configured to the mass of any particle, then you have define this particle as a energy relation? So Lee does not like the oscillatory universe?

See "Finiteness of String Theory and Mandelstam"

It is contained "within the moment" of the creation of this universe, yet, we do not know what design this particle is to be in context of the microscopic view of geometrical topologically finishes? As the Genus 1 figure and as an expression of this universe? You had to know what was lying in those valleys, and the potentials of expression, and I relay that in the blackhole horizon as a potential hill.

The time has come for some changes in this blog and I have been thinking about moving on. While a layman, I do not like to be treated like a fool. Maybe not educated fully and with some work to do, but never as a fool.

Wednesday, April 04, 2007

Finiteness in String Theory Landscape

Quantum Effect, however allow a manifold to change state abruptly at some point-to tunnel through the intervening ridge to a nearby lower valley.
Please take note of the underlined.

Well after some thought here in terms of the landscape, it was important from what I understood, that finiteness be explained in the String Theory landscape. That there were markers with which to measure this progress?

A sphere with three handles (and three holes), i.e., a genus-3 torus. See Finiteness of String Theory and Mandelstam

There is a conversation going on at Cosmic Variance that is continuing with the ongoing debate String Theory is Losing the Public Debate. Well from the technical aspects that is foolish.



As a lay person following the debate on the issue of Finiteness in String Theory landscape was the point technically reached that I was referring too.

David has been careful to lead us through this and as a layman I am watching the way he is describing, so I am learning, as I learnt in other debates.

I hope Jacques that you would encourage David instead of express the futility of such an debate, I have learnt as so many others that you have to "talk past a certain point" if you can no longer get the subject moving beyond the ole rhetoric.

So while learning the difference between the "Fitness landscape" and the "String theory landscape, I learnt the difference is the "finiteness issue in the String theory Landscape?" This then been carried to the issue of Mandelstam and the triple torus?

So this in itself was what allowed us to say that the string theory landscape was indeed working toward the issue of Finiteness with which many have found to be a problem.


See here

Sometimes I wonder why I care so much about working this process and I can only conclude that having my own motivations, and seeing where we had been lead to a point, I had see for myself where the limits of the discussion or debate was being left off.

I learnt to move this forward in face of the points reached. In terms of the same ole rhetoric supplied by Peter Woit. I found that if I wanted to learn anything further in regards to string theory I had to move beyond his arguments confronted, and I have even stopped listening to him. Why would you continue to do research, when a forgone conclusion had been adopted? It's easy, just adopt his point of view and why comment any further unless you had some ulterior motive? Some important information that you could discredit the string theory model itself?

Then it would all be done an dover with and we would have no need further for their services.

Mandelstam held within context of the String landscape

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. See Blackhole Horizon, "as a Hill?"

So for me having markers in place seems critical so I can progress from where future points being talked. I continue to learn from Lee Smolin and why it was important to differentiate between the String theory Landscape and the Fitness Landscape that he is extolling.

Now what does this mean and I needed the article from George Musser's editorial position with the Scientific America magazine to further what I had found. Who said a good magazine, holding a independent position, one way or the other, could not report "bias free" without interjecting it's thought to further embed in consciousness, that a perceived condition exists? That string theory is dead? No, that string theory is loosing ground in a debate? Hardly :)

Considering it's source, I would think about shifting the need for consultation to incentives to post docs, and then maybe Lee Smolin could come in and support that position and then it seems, the debate is going in their direction? Talking about getting away form the essence of the debate on string theory loosing ground. This is a smoke screen being put up when the issue technically were getting close, now required some kind of diversion tactic, of course bas don the same issue with which they perceive string theory is being supported by special interest, and then moving the perception to who should be hired and preferential treatment?

Wednesday, March 14, 2007

IN Search of Mandelstam's Holy Grail



There are two posts that reflect the purpose of this post today. One is Clifford's linked through Lee Smolin's comment and the other, at Backreaction. Good Physics is Conflict

A lot of you may never understand the significance of the mystery that follows the thinking of the Holy Grail. Yet is it more the knowledge that can be gained from all soul's day, that on this occasion we may have called it Halloween.

We celebrated the past, in the living of today? You philosophize, while you become the thoughts of models created by science leaders shared? I do not think any have a "personality disorder" like I do:)

Lee Smolin:
Here is an example of the kind of question I found I needed a book to explore: what to think of the problems that arise from the need for higher dimensions in string theory, such as the problem of moduli stabilization and the vast number of static solutions. To approach this I read books on the early history of GR and unified field theories and learned that higher dimensional compactifications were explored many times between 1914 and 1984 and that close to the beginning these problems were appreciated and discussed by Einstein and others. I weave this story into my book because I find it useful when trying to judge how serious the present issues in string theory are to know how Einstein and many others struggled with the same issues over decades.


So of course when we think of the persons of science who walked before us (shoulders of giants), what are their whole stories, but what is evidenced to us as we read those words? So you compile your data accordingly, and from it, we say at certain spots, how are we to react to the challenge now facing us?



Stanley Mandelstam, Professor Emeritus, Particle Theory

My present research concerns the problem of topology changing in string theory. It is currently believed that one has to sum over all string backgrounds and all topologies in doing the functional integral. I suspect that certain singular string backgrounds may be equivalent to topology changes, and that it is consequently only necessary to sum over string backgrounds. As a start I am investigating topology changes in two-dimensional target spaces. I am also interested in Seiberg-Witten invariants. Although much has been learned, some basic questions remain, and I hope to be able at least to understand the simpler of these questionsStanley Mandelstam-Professor Emeritus Particle Theory


As a lay person watching the debate it is difficult for me to discern the basis of these arguments. But I strive to go past what you think is surface in conduct in science's response, as some may show of themself in a reactionary pose. Should we all be so perfect, that the human condition is not also the example by which we shall progress in science?

Dealing in the Abstract



A sphere with three handles (and three holes), i.e., a genus-3 torus.

Of course the thinking may seem so detached from reality that one asks for some reason with which to believe anything. It required, that the history of this approached dust off models in glass cabinets, that were our early descendants of the museum today.

Sylvester's models lay hidden away for a long time, but recently the Mathematical Institute received a donation to rescue some of them. Four of these were carefully restored by Catherine Kimber of the Ashmolean Museum and now sit in an illuminated glass cabinet in the Institute Common Room.




How many of you know how to work in such abstract spaces, and know that what you are talking about has it's relationships in the physics of today? Or that, what satellites we use in measure of, have some correlation to how one may have seen "UV coordinates supplied by Gauss?"

Wednesday, December 13, 2006

Visual Abstraction to Equations

Sylvester's models lay hidden away for a long time, but recently the Mathematical Institute received a donation to rescue some of them. Four of these were carefully restored by Catherine Kimber of the Ashmolean Museum and now sit in an illuminated glass cabinet in the Institute Common Room.


Some of you might have noticed the reference to the Ashmolean Museum?


Photo by Graham Challifour. Reproduced from Critchlow, 1979, p. 132.


It seems only the good scientist John Baez had epitomes the construction of the Platonic solids? A revision then, of the "time line of history" and the correction he himself had to make? Let's not be to arrogant to know that once we understand more and look at "the anomalies" it forces us to revise our assessments.

The Art form

I relayed this image and quote below on Clifford's site to encourage the thinking of young people into an art form that is truly amazing to me. Yes I get excited about it after having learnt of Gauss and Reimann's exceptional abilities to move into the non euclidean world.

Some think me a crackpot here? If you did not follow the history then how would you know to also include the "physics of approach," as well? Also, some might ask what use "this ability to see the visual abstraction" and I think this art form is in a way destined, to what was kept in glass cabinets and such, even while the glass cabinet in analogy is held in the brain/space of them) who have developed such artistic abilities.

It's as if you move past the layers of the evolution of the human being(brain casings) and it evolution and the field that surrounds them. Having accomplished the intellect( your equations and such), has now moved into the world of imagery. Closet to this is the emotive field which circumvents our perspective on the greater potential of the world in the amazing thought forms of imagery. This move outward, varies for each of us from time to time. Some who are focused in which ever area can move beyond them. This paragraph just written is what would be considered crackpot(I dislike that word)because of the long years of research I had gone through to arrive at this point.

Of course, those views above are different.

Mapping



Is it illusionary or delusional, and having looked at the Clebsch's Diagonal Surface below, how is it that "abstraction" written?



The enthusiasm that characterized such collections was captured by Francis Bacon [1, p. 247], who ironically advised "learned gentlemen" of the era to assemble within "a small compass a model of the universal made private", building

... a goodly, huge cabinet, wherein whatsoever the hand of man by exquisite art or engine has made rare in stuff, form or motion; whatsoever singularity, chance, and the shuffle of things hath produced; whatsoever Nature has wrought in things that want life and may be kept; shall be sorted and included.


There is no doubt that the long road to understanding science is the prerequisite to mapping the images from an equation's signs and symbols. While not sitting in the classroom of the teachers it was necessary to try and move into the fifth dimensional referencing of our computer screen to see what is being extolled here not just in image development, but of what the physics is doing in relation.

In 1849 already, the British mathematicians Salmon ([Sal49]) and Cayley ([Cay49]) published the results of their correspondence on the number of straight lines on a smooth cubic surface. In a letter, Cayley had told Salmon, that their could only exist a finite number - and Salmon answered, that the number should be exactly 27



So of course to be the historical journey was established like most things, Mandelstam current and what is happening there as an interlude, as well as helping to establish some understanding of the abstractions that had been developed.



But yes, before moving to current day imagery and abstraction, I had to understand how these developments were being tackled in today's theoretical sciences.

Saturday, December 02, 2006

Finiteness of String Theory and Mandelstam



It might be that the laws change absolutely with time; that gravity 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 to the laws of physics. Richard Feynman



I was lead into this subject of Quantum Gravity, by Lee Smolin's book called, "Three Roads to Quantum Gravity." As a lay person reading what our scientist's have to say, I have a vested interest in what can start one off and find, that changes are being made to the synopsis first written. Did I understand his position correctly from the very beginning? I'll have to go back over my notes.

But with this format now I have the opportunity to...ahem... get it..directly from the horses mouth(no disrespect intended and written based on knowing how to read horses). As I said, I tried early on to see how the situation of string theory could be refuted. I "instigated" as a comparative front for Lubos Motl and Peter Woit to speak from each of their positions. I had to disregard "the tones" set by either, as to the nature of whose what and how ignorant one might be, and comparatively, one might be to intelligent design? To get "some evidence" of why string theory might not be such a good idea?

Now I believe this is a more "civil situation" that such a format has been proposed and that Lee Smolin can speak directly. As well as, "further information" supplied to counter arguments to Lee's position.


A sphere with three handles (and three holes), i.e., a genus-3 torus.


Jacques Distler :
This is false. The proof of finiteness, to all orders, is in quite solid shape. Explicit formulæ are currently known only up to 3-loop order, and the methods used to write down those formulæ clearly don’t generalize beyond 3 loops.

What’s certainly not clear (since you asked a very technical question, you will forgive me if my response is rather technical) is that, beyond 3 loops, the superstring measure over supermoduli space can be “pushed forward” to a measure over the moduli space of ordinary Riemann surfaces. It was a nontrivial (and, to many of us, somewhat surprising) result of d’Hoker and Phong that this does hold true at genus-2 and -3.


Just a reminder about my skills. While I do things like carpetry, plumbing, electrical, I do not call myself a Carpenter, a Plumber or a Electrician. Nor shall I ah-spire to be more then I'm not, as I am to old this time around.

Greg Kuperberg:
The string theorists are physicists and this is their intuition. Do you want physical intuition or not?

Okay, Smolin is also a physicist and his intuition is radically different from that of the strings theorists. So who is right?


Yet, least I not read these things, can I not decipher "the jest" while it not being to technical? Shall I call it a Physicists intuition or I will only call my intuition what it is?

Jacques Distler:
When most people (at least, most quantum field theorists) use the term “finiteness,” they are referring to UV finiteness.


While the things above talked about from Jacques are served by hindsight, "the jest" follows what comes after this point.

The Jest of the Problem?

My present research concerns the problem of topology changing in string theory. It is currently believed that one has to sum over all string backgrounds and all topologies in doing the functional integral. I suspect that certain singular string backgrounds may be equivalent to topology changes, and that it is consequently only necessary to sum over string backgrounds. As a start I am investigating topology changes in two-dimensional target spaces. I am also interested in Seiberg-Witten invariants. Although much has been learned, some basic questions remain, and I hope to be able at least to understand the simpler of these questionsStanley Mandelstam-Professor Emeritus Particle Theory


Gina has asked questions in context of "academic excellence" in relation to what is being seen in relation to string theory. Of course we thank Clifford for providing the format for that discussion.

The Trouble With Physics,” by Lee Smolin, Index page 382, Mandelstam, Stanley, and string theory finiteness, pages 117,187, 278-79, 280, 281, 367n14,15

For reference above.

Gina:
I raised 16 points that I felt Lee’s arguments were not correct or problematic. This is an academic discussion and not a public criticism, and I truly think that such critique can be useful, even if I am wrong on all the 16 points.

Three of my 16 points were on more technical issues, but I feel that I can understand Lee’s logical argument even without understanding the precise technical nature of “finiteness of string theory” (I do have a vague impression of what it is.) I think that my interpretation of this issue is reasonable and my critique stands.


I find this interesting based on what information has been selected to counter the arguments that Lee Smolin used to support his contentions about what is being defined in string theory.


Stanley Mandelstam Professor Emeritus Research: Particle Physics
My research concerns string theory. At present I am interested in finding an explicit expression for the n-loop superstring amplitude and proving that it is finite. My field of research is particle theory, more specifically string theory. I am also interested in the recent results of Seiberg and Witten in supersymmetric field theories.


So of course, here, I am drawn to the content of his book and what is the basis of his argument from those four pages. I hope my explanation so far summarizes adequately. For the lay person, this information is leading perspective as to the basis of the argument.

Lee Smolin:
Perturbative finiteness is a major element of the claim of string theory as a potential theory of nature. If it is not true then the case for string theory being a theory of nature would not be very strong.

-Perturbative finiteness has not been proven. There is evidence for it, but that evidence is partial. There is a complete proof only to genus two, which is the second non-trivial term in an infinite power series, each term of which has to be finite. The obstacles to a complete proof are technical and formidable; otherwise we would certainly have either a proof or a counterexample by now. There is some progress in an alternative formulation, which has not yet been shown to be equivalent to the standard definition of string theory.

-This is not an issue of theoretical physicists rigor vrs mathematical rigor. There is no proof at either level. There is an intuitive argument, but that is far from persuasive as the issue is what happens at the boundaries of super-moduli space where the assumption of that argument breaks down. In the formulation in which there is a genus two result it is not clear if there is an unambiguous definition of the higher order terms.

Is string theory in fact perturbatively finite? Many experts think so. I worry that if there were a clear way to a proof it would have been found and published, so I find it difficult to have a strong expectation, either way, on this issue.


It should be known here and here that all along I have been reacting to Lee Smolin's new book. The title itself should have given this away?

The explanation of scientific development in terms of paradigms was not only novel but radical too, insofar as it gives a naturalistic explanation of belief-change. Thomas Kuhn


So of course knowing the basis of my thought development is a "good idea" as the links show what spending our dollars can do, having bought what our good scientist Lee Smolin has written.

There is a little "tit for tat" going on right now, but I think the point has been made sufficiently clear as to where Gina's thoughts in regards to the points on Finiteness is being made beyond 2?

In these lectures, recent progress on multiloop superstring perturbation theory is reviewed. A construction from first principles is given for an unambiguous and slice-independent two-loop superstring measure on moduli space for even spin structure. A consistent choice of moduli, invariant under local worldsheet supersymmetry is made in terms of the super-period matrix. A variety of subtle new contributions arising from a careful gauge fixing procedure are taken into account.


Yes I think I have to wait now to see if the discussion can now move beyond the first three points raised? Hopefully Lee will respond soon?

How do you fight sociology

Because this by any of the leaders of string theory. it was left to someone like me, as a quasi "insider" who had the technical knowledge but not the sociological commitment, to take on that responsibility. And I had done so because of my own interest in string theory, which I was working on almost exclusively at the time. Nevertheless, some string theorists regarded the review as a hostile act.

The trouble with Physics, by Lee Smolin, Page 281


I have discovered one of Lee Smolin's objection to a string theorist. They are only craftsman, and not seers.