Rayleigh Scattering

Over top of this whole post, I have wrapped it in context as if the fifth dimension. It is being expresed as part of a larger understanding of how such grvatons in their congergations might have been percieved? Yet Lubos cautions this perspective. I don't understand why.

Aaron Bergman on Dec 10th, 2005 at 1:46 am

The S-matrix is contact with (hypothetical) experiments. Most of the things we compute in QFT are S-matrix elements. The fact that we’re not really living in a region with free |in> and |out> states doesn’t stop us from figuring out what happens in a collider.

Some now looking at the relation to what can be constitued to interactions between the nature of the Sun such relation woud have spelt opportunities of what John Ellis might have expressed in the Pierre Auger experiments? NON?

As I read about this particular subject of the S-matrix I choose this particluar subject to get my head around it, and still, might have been lacking in moving through this subject. But something triggered in my mind to a previous question raised, that I thought I would bring forward here.

Of course I am thinking about the calorimeters used in Glast and the cosmological depth, as well, in the LHC where the quantum nature is expressed as well. These cannot be taken together?

Gavin Polhemus on Nov 23rd, 2005 at 6:24 pm
When you look at a rainbow you see the arcs of color, often against a dark backdrop of clouds. You also see the grayish mist of the falling rain. Where does the mist appear brighter?

a) inside the rainbow
b) outside the rainbow
c) the brightness is the same inside and outside
d) it varies



While I am talking about "Heaven's ephemeral qualites" in the pictured link, there was also a link attached to it as well in that post. It would help explain this process in context of Gavin's question. I'm definitely listening, and the information is coming from various sources. You see this, as I bring those sources together here.

Lubos Motl:

String theory allows us to calculate the S-matrix (another example that we do call an "observable") for all particles in the spectrum which includes the scattering of gravitons. We don't have to insert our knowledge about the problematic "bulk" observables: string theory automatically tells us not only the right answers but also the right questions. "It is the S-matrix you should calculate, silly," she says. It also tells us what are the corresponding evolution observables for anti de Sitter space.

Someone may therefore convince you that the S-matrix is the only meaningful observable that has any physical meaning in a quantum theory of gravity. This sentence is both deep, if an appropriate interpretation is adopted, as well as discouraging.

What is most troubling then is that a simpe picture of the lensing that can occur in the the gravitational perspective, might have been enlisted in how we see this light travel through to the CSL lensing that is being spoken too?

Simulating the joint evolution of quasars, galaxies and their large-scale distribution

The cold dark matter model has become the leading theoretical paradigm for the formation of structure in the Universe. Together with the theory of cosmic inflation, this model makes a clear prediction for the initial conditions for structure formation and predicts that structures grow hierarchically through gravitational instability. Testing this model requires that the precise measurements delivered by galaxy surveys can be compared to robust and equally precise theoretical calculations. Here we present a novel framework for the quantitative physical interpretation of such surveys. This combines the largest simulation of the growth of dark matter structure ever carried out with new techniques for following the formation and evolution of the visible components. We show that baryon-induced features in the initial conditions of the Universe are reflected in distorted form in the low-redshift galaxy distribution, an effect that can be used to constrain the nature of dark energy with next generation surveys.

The poster shows a projected density field for a 15 Mpc/h thick slice of the redshift z=0 output. The overlaid panels zoom in by factors of 4 in each case, enlarging the regions indicated by the white squares. Yardsticks are included as well. The postscript file has been produced for A0 format. Beware of it's huge size!

Now Lubos mentions the bulk relation here, and I wonder why such a take on a gathering of graviton perceptions would not help to see Heaven's ephemeral qualites as consequences of the pathways this light can take?

Mine is a simple way in which to understand such graviton scattering which might have "some reasoning?" behind it that would have said the blackhole concentration of such a photon persepctive woud have held greater consequence to the blackhole position in the universe? non?

Rayleigh scattering using the S-matrix

For the example of sunlight shining on the atmosphere, the S-matrix predicts that shorter-wavelength light (blue end of the spectrum) will scatter at larger angles than longer-wavelength light (red end of the spectrum). And this is exactly what we see! Let me go through it. It helps to have a globe handy, perhaps using a pencil or straight piece of wire to simulate an incoming ray of sunlight; imagine a very thin layer over the surface which is the atmosphere. A small scattering angle means the light continues on nearly in the direction it started out in, while a large angle means close to perpendicular to the incoming direction.

Laughlin, Reductionism, Emergence

I am still operating from the idea of Xtra-Dimensions. What motivating force would have brought such a quantum gravity group together and the aspect it might have spoken from? What mysterious forces motivates all these ladies/ gentlemen?

Everyone knows that human societies organize themselves. But it is also true that nature organizes itself, and that the principles by which it does this is what modern science, and especially modern physics, is all about. The purpose of my talk today is to explain this idea.

Can I hardly leave this post written below in my linked coment without some further explanantion?

Sean:

You have to be careful about words like “emergent,” because it has pre-existing connotations that may or may not be relevant to how the theory ends up actually working.

You know for me it became the quest to understand what the basis of reality was. So if one is given perspective to think about from different angles, then the very idea of a "emergent process unfolding from the quantum gravity regimes", then it would have been a truly ground breaking acknowledgement of what the basis of reality really is?

Plato:

I would have thought the modifications to GR might have signalled some truth to what was emergent(although this would ask us what that quantum geometry is?) from a condense matter perspective, as Witten saids below.

I also heard Robert Laughlin say, it didn’t matter if you use bricks or sargeant majors?

I had trouble with this ,and looking at CFT on the horizon, it made me think of string as a fifth dimensional component within the blackhole. Is this wrong and misleading, not to have looked at the spacetime fabric a a graviton constituent since these modifications were made to GR?

My thoughts were developing in perspectve as I did my own research, so all of a sudden the basis of the views that I was capturing started to make sense. What were people doing with the very ideaas of this theory of everything?


Witten:

One thing I can tell you, though, is that most string theorist’s suspect that spacetime is a emergent Phenomena in the language of condensed matter physics.

The Elephant?

Now having given the poem there for Sean's introduction to Mind and the poetry, we are given a sense of what the historical issues plaguing the ideas of quantum gravity? Filled with the perplex of citizens of a town? To have the proverb, this hinduist portrayal, Sufi expressed, as a lessson in our attempts to understand. It was not me, who first used John Saxes poem in the Physics realms, so do you know who this was?




So now we have this condense matter approach to consider? I wonder how well it will do when people share perspective about "this approach" to have taken a strong stance against Robert Laughlin's theory of everything? Where are you Peter Woit? What is your way, that you should be so different from what Lubos is saying below?


Lubos Motl:

All of us agree that some important features of physical phenomena do not depend on the details of underlying physics; many of these phenomena are emergent in character; it is not too important or useful to know quarks or strings in order to study most of the crucial concepts in biology, climate, physics of water, or quantum computing. If Laughlin thinks that other physicists do not realize this fact, then he is fighting a strawman. Most physicists realize these things - and many fundamental physicists actually use very similar mathematical techniques as Laughlin does in his "emergent" approach.

So is there a consensus on how the science of our day recogizes the work that is trying to make iself known, as the truth and the light of the way? What does the elephant represent?

Robert Laughlin:

Likewise, if the very fabric of the Universe is in a quantum-critical state, then the "stuff" that underlies reality is totally irrelevant-it could be anything, says Laughlin. Even if the string theorists show that strings can give rise to the matter and natural laws we know, they won't have proved that strings are the answer-merely one of the infinite number of possible answers. It could as well be pool balls or Lego bricks or drunk sergeant majors.

How far in depth shall our abstract views look, as one uses the math to gaze into the "blackhole of oblivion" and wonder? What constitues the very nature from that very horizon. How shall Robert Laughlin speak on it? How shall he speak about the trigger?

Satellites Can Glide But Bee's Can't?

I just wanted to clarify my statements in regards to the association I made In Bumble Bee Rotations.

If you understood the "easiest route/shortest distance" in which to travel, how can a satellite be propelled along pathways, with the least resistance? You had to be able to see properly, and in a abstract sense?



If you understood "tubes" as possible routes, then how would such energies be revealled as such cosmic strings crossed the universe? In the early cosmological design one would understand Andrey's computerized model settings as the earlier face of supersymmetrical valuations. This had to arise from the planck epoch?

If you held such views in relation to the principals inherent in the lessons provided by Wayne Hu below, then you get some idea of what happens when the simplification takes hold of one's mind, and one sees the landscape not as some fictional entry to pet peeves and name calling.

I have assigned simplification by providing data to show how ideas of those xtra dimensions would have permitted the photons pathways easy traversables, while CSL patterns can be established?

You choose how and which side you want to focus on in looking at those langrange points? Easiest routes to langrange point considerations. While you consider this, think about the lensing that occurs.

The figure to the right
{above here} shows the equivalent of a Feynman diagram in a string theory. String theorists hope that since this reaction is no longer confined to a single point it may be possible to unify all four fundamental interactions.

Neural Correlate Speculation

Neural correlates in my speculations, but once the patterns had been established, it made sense to me that lumiousity would have highlighted the rasiets pathways of expression. As if enlightenment would have taken hold, fromthe first elements of the universe in expression would have been seen as these CSL cosmic strings? Just a thought in passing:)

Xtra dimensions

In the Beginning.....

The field of cosmology has experienced an explosion of activity since the discovery of ripples in the energy of the primordial light of the big bang. Cosmology is the study of the origin, evolution, and fate of objects in the observable universe. These include galaxies like our Milky Way, a vast collection of stars spanning many thousands of light years. The key to the birth and evolution of such objects lies in the primordial ripples observed through light shining through from the early universe.

Having learnt from Wayne Hu and his CMB info study, it help me see where the hills and Valleys might have attained some recognition in how one landscape might have been seen in relation to Wayne Hu's.

Cosmologists actually run computer simulations to track how matter collects into valleys. For example, here is a simulation running forward in time which shows how particles collect and enhance small initially small wrinkles

Thank you Wayne Hu to opening the doors to the realizations that I had formed in the ideas of the supersymmetrical Universe. Little did you know that Andrey's picture would set the course for how I saw the Cosmic string arise from such a background.



Develope our views into the CSL Pictures here. I wanted to take this time to thank Lubos Motl for his continued efforts in this direction.

CSL-1 cosmic string gravitational lens and 2 more, with many views of the Capodimonte Deep Field OACDF2 with subtle background features, similar to recent Millennium Simulation of evolution of structure in our Universe. Identical stereo pairs are introduced.

So to then, if such a trail leads us to what that geometical propensity is, how so from such a tale of quantum gravity? It had to lead from something, so from the beginning.......? :)

Modification To GR

Sean Carroll:

Why three dimensions of space just aren't enough?

What does General Relativity say in terms of a simple word to describe it? "Gravity?"

“This is what’s happening all the time within us, we have these little lava lamps,” said Frank Wilczek in his Nobel lecture in 2004 when he showed this QCD animation created by Derek Leinweber. The animation illustrates the fluctuations of the quark and gluon fields over time, revealing a lumpy structure that Leinweber dubbed the QCD lava lamp.

So modifications to Gr bring perspective to lead us to other views in terms of xtra-dimensional analysis(degrees of freedom at a gluonic level)? Can I say this in regard to such things as xtra dimensional analysis?

Of course mine is a generalization spoken from the idea of what Eric Aldeberger might find, but this did not limit the scope of vision that would have moved us beyond the fifth postulate. Non euclidean geometries, were very hepful here and so too, hyperdimensional thinking?

Relativistic Jets: The Common Physics of AGN, Microquasars and Gamma-Ray Bursts

Reimann then thought there would come a time to see such thinking expressed beyond just the positive expressions in spherical relations? Jets, in relation, to Anti-matter creation? A whole new abstract way of thinking in the mathematical realms?

So what had radiation and CFT showed us from Bekenstein bound, as we peered into the inside of the blackhole construction? What geoemtries existed? Was there a emergent geometric principal. Of course, that is in question, and the degrees of freedom would spell the depths to what we were able to see? That did not stop us from talking about the substance of quantum Geometry as Greene explained to us.

What value did the temperatures play in our assessment of the internal dynamics of what would have happpened from a the grvaiational collapse generated and the radiation, that would hav been emitted. Acoustic radiation helps to a degree.

Thank you Smolin for such a responsible attitude of the science position of Glast, but it now has to induce new insight by adopting other theoretical positions?

Religious Convictions and Belief

I as a layman do operate from a biased position, and one that would have asked for a better respect of the scientific procedure, as Peter Woit and those of science would ask us as layman in our demonstrations.

Would I accept the responsibilty of Sean atheistic valuations, in our determinations of what we can be held accounatble as to the repercussions of our very actions. In our thoughts, that would ripple ever wider, as a consequence of our choices?

Yes I think deeply about these things, and they are far distant from the responsibilities of science, but I needed to show this, so it is understood that I accept that responsibility, even though I too might have had a belief about God and and our roles in choosing to evolve?

I quickly generalized Relativity above, and so too, did my journey to have been thinking about a simplification in general conceptualizations of those extra dimensions.

Was it wrong to do so in light of the need for sound thinking right now? I have to apologize for that too, as this is biased in my views from such a simplifcation.

There is a result in thinking about the measure of those extra dimensions, and what had been missing from the initial energy determinations calculated. Where is that missing energy?

Did such a simple logic not recognize that associated in this energy valuation, to reductionist principles, that this would be sent off into some other dimensional recognition of the values of that energy along side of modification to General relativity?

There had to be a consistancy lead from to incorporate such thinking to simplfications in general concepts and views I have about the psychological prospects of causes of our thought processes. To have ramifications beyond the border of our own brains. But this is just me right now. So I don't want to mislead anyone.

Further Speculations

Sometimes I can't but help think that we currently in a blackhole that driven to expansitory values and curent CMB temepratures made me think, that if we saw the expansion process as inhernet in this universe, then why is it not that we see we are in such a Blackhole? Is this wrong?

Then what value these Suns that still burn within this context, and such distance between the objects of space seen in a cosmological distance? More speculation that I send such thoughts of mine to the beginings of the universe and what interactive features sent this universe into it's expansion process? What stage are we atthen, to have been held at a certain process in the blackholes status, to have thought about the big crunch signal by the very initial response and distance of the schwarzchild radius that preceded this expansive view?

Inverse Square law, to explain the value of these determinations, as to what would exist on our horizon?

Forgive me as I lost myself in such thoughts.

Color Glass Condensate

A Second Chance?

Just so that I undertsood this part, intuitive recognition and short requirements previews, had me wonder about how I am proceeding? If as a layman I could not voice what was inherent in the process, did I lack sufficient credibility?

I understand that.

I once heard that a mechanic will on the sake of profession and support of colleagues, not tolerate opinion about another of profession without having the sufficient rank. "So and so did this and," I understand that too.



I know we are talking about the valuation of supersymmetry? Had we not recognized the value it serves in experimental process? Then how would such relations not have been embedded in "thought processes" which serve to catelyst thinking to ideas about "communication viabilties?" A gravitational wave generated that would tell us something about how this early geoemtrical design was initiated?

What made one not think that such phenomena would not have been incurred in galaxy rotational designs, that lead to states of consideration held in the Crab Cake design of Cosmic Variance, to not have seen the uses of early universe design as feasible structures within the context of the global universe?

On Physics Watch

Kapusta points out that the condensation temperature would be well below the cosmic background temperature, so it would be quite a feat to make this superfluid. However, Kapusta also notes that a sufficiently advanced civilization might use pulses of neutrino superfluid for long-distance communications.

So what value does such thinking take hold of our imagnation not to have understood that if saw in a particle collisions in landscape design and relevance, then what made such landscape possibilites seen from a particluar light called supersymmetry?

This was a guiding principal was it not that had accomplished soemthing tangible in what began as a theoretcial idealization, and moved through thinking and design to have culminated in further thought patterns? It moved from the concrete?:)

So what is a color glass condensate? According to Einstein's special theory of relativity, when a nucleus travels at near-light (relativistic) speed, it flattens like a pancake in its direction of motion. Also, the high energy of an accelerated nucleus may cause it to spawn a large number of gluons, the particles that hold together its quarks. These factors--relativistic effects and the proliferation of gluons--may transform a spherelike nucleus into a flattened "wall" made mostly of gluons. This wall, 50-1000 times more dense than ordinary nuclei, is the CGC (see Brookhaven page for a letter-by-letter explanation of the CGC's name). How does the gluon glass relate to the much sought quark-gluon plasma? The QGP might get formed when two CGC's collide.

http://www.aip.org/pnu/2004/669.html

Bumblebee Wing Rotations and Dancing

The Bumble Be, Mentality

So what is the Gluon that binds?:)

For introduction sake, I might have deviated from Sean Carroll's ideas about the, "what science doesn't know" and traded it for mechanical systems interpretations, and the way we can write comprehension forms from such patterns inherent?

It always comes down to the lesson of a Beautiful mind? It's struggle for freedom from the illusions that we might perpetuate. The escape from, those delusions, to concrete analysis of such systemic thought patterns within human nature. The triumph and freedom, to overcome all odds?

If we thought of Belt rotations and Greg Egan, it wouldn't be to hard to place some perspective on how Sean might have intepreted the "wing rotation of slowed photography," and said, "hey, here is this pattern, and something a string theorist could hang their hat on?"

Satisfactory conclusion to rotations, that equatively reach across and touch us like E=mc² does, then what's the point of concluding any thoughts if this consistancy can't be accomplished? So herein lies my inexperience, and the last recursive thought of, "okay, what science doesn't know, I scream?" :) Was it emotive enough to make my point?

And so in reference to string theory work, I couldn't help but think of the rotations, waiters and table trays and such. But it also made me think of the inroads to observation of nature and flight? Wilbur and Orville Wright as well?

But looking deeper, and from what one could gain from such observations, did I miss Sean's point?


Kosmopolis 05

Marc D. Hauser:

We know that that kind of information is encoded in the signal because people in Denmark have created a robotic honey bee that you can plop in the middle of a colony, programmed to dance in a certain way, and the hive members will actually follow the information precisely to that location. Researchers have been able to understand the information processing system to this level, and consequently, can actually transmit it through the robot to other members of the hive.

But it's more then the honey bee mentality. It's about communications systems we use to explain? So am I going to get Sean's goat on this one, and reverberate something he does not like? :)

But we know relatively little about how the circuitry of the brain represents the consonants and vowels. The chasm between the neurosciences today and understanding representations like language is very wide. It's a delusion that we are going to get close to that any time soon. We've gotten almost nowhere in how the bee's brain represents the simplicity of the dance language. Although any good biologist, after several hours of observation, can predict accurately where the bee is going, we currently have no understanding of how the brain actually performs that computation.

So I have in essence percieved the "Bee HIve Mentality of string theory" as a underlying causation, that if held too, becomes, "how little we really know." What ha/ormonial( I like to play with words?) factor, drives that body/system?

I bet that sounds like chalk board screeching to him:) Yes I gave the anti-string/M theorist more ammunition.

I also opened the door to another thought of mine. About the uses of, "Math and the foundations." But this is just me, trying to break down the reistance to mathematical prowness, that any other mathematician might try and hide, as a model of strng theory/M intepretation.

You can't just sweep it under the rug kind of thing and say what science doesn't know. Has yet to be proved?:) Oops, I extended the board screeching to include, the extension of, and Modifications to GR. I can't help it. The power of the "force" is really string?

The Cosmological Constant and the Vacuum Energy



Jacque Distler:

The cosmological constant is not “predicted” to be Planck scale, simply because, in a QFT context, it is not predicted at all. It is a renormalized coupling and can have any value whatsoever.

What is true is that, in order to achieve the observed value at low energies, the bare value (at the cutoff scale, which we might take to be the Planck scale) must be fine-tuned to enormous accuracy.

But that’s not the same thing at all as saying that the value of the cosmological constant is predicted, and that the prediction comes out wrong.

Jacques Distler has volunteered(?) for the sake of people like myself by opening the doors to clarity issues around the interrpetation of the cosmological constant.

So this leads to the second part of Sean's post that gets me to thinking about how perception might have been revealled in the dynamics scenario of Omega (w) and how we see that the background as a "energy density," can ever be seen as zero? That such a valuation would limit one to thinking that such a dynamical universe had to explain the nature of the curvature parameters beyond, what was comsologically understood?

The Friedmann equation which models the expanding universe has a parameter k called the curvature parameter which is indicative of the rate of expansion and whether or not that expansion rate is increasing or decreasing. If k=0 then the density is equal to a critical value at which the universe will expand forever at a decreasing rate. This is often referred to as the Einstein-de Sitter universe in recognition of their work in modeling it. This k=0 condition can be used to express the critical density in terms of the present value of the Hubble parameter.

For k>0 the density is high enough that the gravitational attraction will eventually stop the expansion and it will collapse backward to a "big crunch". This kind of universe is described as being a closed universe, or a gravitationally bound universe. For k<0 the universe expands forever, there not being sufficient density for gravitational attraction to stop the expansion.

Plato:

So on a csomological level we get this sense of curvature and here to further exploit this understanding the means to such equations supplied for this endeavor.

Now for the vacuum to be define here in a planck scale valuation, it was not important for me, (okay maybe it is needed) to see the positive and negative effect of what and how the universe was doing at any particular stage. I always saw it as expanding, yet within the confines of the universe, it had the capability of doing galaxy dynamics, that would lead to greater intensities, expansive and contraction features, when we looked at the energy and matter cyclical valutions, in a geometrical sense, wrapped as "global" cosmological constant.

Bumble Bee Economics

See what happens when the creative juices are added to imagery and analogy gives insight from another perspectve?



Ed Hessler added this to the comment section of Cosmic Variance.

General Relativity

I took GR because I thought Neil Turok was dreeeamy.

Well I dunno? He certainly got me thinking about brane world collisions, along with steinhardt, that’s for sure. We are most certainly dealing with a cosmological placement here with General relativity, but has been extended, as we look at string/M theoretical successes.



You had to make "certain assumptions I know" in order to get here in the picture, and you had to have some inkling of what gravitational waves were and how they were transmitted.

Completed 720 degree rotations, as "tidbits" of the process which are given to us from a cosmological standpoint.


So what is transmitted in the bulk in terms of "gravitational lensing" has some relation, to what we see in the picture above. Look at the placement of the gravitons in bulk perspective and how they are concentrated on and around the brane.

So it is not without reason that we see bulk perspective as a extension and not scientifically up to the challenege because Peter Woit say so?

Modifications to General Relativity

So "six weeks" we should have known something by now with respect to below statements? Jo-Anne, of cosmic varaince selected this answer next to the Pioneer Anomalie.

Eric Adelberger on Aug 12th, 2005 at 2:37 pm

Please don’t get too excited yet about rumors concerning the Eot-Wash test of the 1/r^2 law. We can exclude gravitational strength (|alpha|=1) Yukawa violations of the 1/r^2 law for lambda>80 microns at 95% confidence. It is true that we are seeing an anomaly at shorter length scales but we have to show first that the anomaly is not some experimental artifact. Then, if it holds up, we have to check if the anomaly is due to new fundamental physics or to some subtle electromagnetic effect that penetrates our conducting shield. We are now checking for experimental artifacts by making a small change to our apparatus that causes a big change in the Newtonian signal but should have essentially no effect on a short-range anomaly. Then we will replace our molybdenum detector ring with an aluminum one. This will reduce any signal from interactions coupled to mass, but will have little effect on subtle electromagnetic backgrounds. These experiments are tricky and measure very small forces. It takes time to get them right. We will not be able to say anything definite about the anomaly for several months at least.

As stated maybe this "anomalie" might be significant and for scientists it is necessary such a quirk of nature be seen and understood. I relayed Einstein's early youth and the compass for a more introspective feature that such anomalies present.

The Eotwash Group is a sign of relief, for the speculative signs attributed from other scientists, made this topic of extra-dimensions unbearable and unfit for the general outlay for scientists who did not understand this themselves.

Deviations from Newton's law seen?

So what does Lubos have to say about this in his column?

Lubos Motl:

The most careful and respected experimental group in its field which resides at University of Washington - Eric Adelberger et al. - seems to have detected deviations from Newton's gravitational law at distances slightly below 100 microns at the "4 sigma" confidence level. Because they are so careful and the implied assertion would be revolutionary (or, alternatively, looking spectacularly dumb), they intend to increase the effect to "8 sigma" or so and construct different and complementary experiments to test the same effect which could take a year or two (or more...) before the paper is published. You know, there are many things such as the van der Waals forces and other, possibly unexpected, condensed-matter related effects that become important at the multi-micron scales and should be separated from the rest.

On Relativity again

According to General Relativity, the key qualities of strong sources of gravitational waves are that they be non-spherical, dynamic (i.e. change their behavior with time), and possess large amounts of mass moving at high velocities. So prime suspects should exhibit one or more of the following characteristics.

1. Spinning

2. Mass tranfer

3. Collpase

4. Explosion

5. Collision

As to “online resources” for General Relativity, is there one preference if you do not have access to the Hartle book or the other?

Lecture Notes on General Relativity, by Sean Carroll

Preface
These lectures represent an introductory graduate course in general relativity, both its foundations and applications. They are a lightly edited version of notes I handed out while teaching Physics 8.962, the graduate course in GR at MIT, during the Spring of 1996. Although they are appropriately called \lecture notes”, the level of detail is fairly high, either including all necessary steps or leaving gaps that can readily be filled in by the reader. Nevertheless, there are various ways in which these notes differ from a textbook; most importantly, they are not organized into short sections that can be approached in various orders, but are meant to be gone through from start to finish. A special effort has been made to maintain a conversational tone, in an attempt to go slightly beyond the bare results themselves and into the context in which they belong

Or a link to this one for a historical look?

Relativity
The Special and General Theory

What First principle was-- was it the geometry

I thought I would contrast this quote of Dirac's with the one of Feynman's.

You see the very idea of a constancy that spread through all Maxwell's equations was a necessary one which allowed Einstein to move into positive and negative valuations within the geometries? So did Dirac know how this was to be approached?

Dirac:

When one is doing mathematical work, there are essentially two different ways of thinking about the subject: the algebraic way, and the geometric way. With the algebraic way, one is all the time writing down equations and following rules of deduction, and interpreting these equations to get more equations. With the geometric way, one is thinking in terms of pictures; pictures which one imagines in space in some way, and one just tries to get a feeling for the relationships between the quantities occurring in those pictures. Now, a good mathematician has to be a master of both ways of those ways of thinking, but even so, he will have a preference for one or the other; I don't think he can avoid it. In my own case, my own preference is especially for the geometrical way.

Feynman:

‘Maxwell discussed … in terms of a model in which the vacuum was like an elastic … what counts are the equations themselves and not the model used to get them. We may only question whether the equations are true or false … If we take away the model he used to build it, Maxwell’s beautiful edifice stands…’ – Richard P. Feynman, Feynman Lectures on Physics, v3, c18, p2.

Paul Dirac Talk: Projective Geometry, Origin of Quantum Equations Audio recording made by John B. Hart, Boston University, October 30, 1972

The quote below is in response to Dirac's comments

[ROGER PENROSE]

"One particular thing that struck me... [LAUGHTER]...is the fact that he found it necessary to translate all the results that he had achieved with such methods into algebraic notation. It struck me particularly, because remember I am told of Newton, when he wrote up his work, it was always exactly the opposite, in that he obtained so much of his results, so many of his results using analytical techniques and because of the general way in which things at that time had to be explained to people, he found it necessary to translate his results into the language of geometry, so his contemporaries could understand him. Well, I guess geometry… [INAUDIBLE] not quite the same topic as to whether one thinks theoretically or analytically, algebraically perhaps. This rule is perhaps touched upon at the beginning of Professor Dirac's talk, and I think it is a very interesting topic."

So the question might have been, how this was viewed and what the result was through such a axiomization? What was the first principe here? Was there one that became the guiding principal?

I mentioned the compass for Einstein, as a modelled perception that grew into the later years, but here, we might have seen the beginnings Feynmans toys model for such geometries?

Foundations of Mathematic

Mathematics, rightly viewed, possesses not only truth, but supreme beautya beauty cold and austere, like that of sculpture, without appeal to any part of our weaker nature, without the gorgeous trappings of painting or music, yet sublimely pure, and capable of a stern perfection such as only the greatest art can show. The true spirit of delight, the exaltation, the sense of being more than Man, which is the touchstone of the highest excellence, is to be found in mathematics as surely as in poetry.

--BERTRAND RUSSELL, Study of Mathematics

In a Question below, is it worth it, to look at the context of what groups who gather might spark to the rest of society(click on it)? Look at what it has done for myself, and the reasons why such inductive/deductive features seem to be a part of the origins of cognitive functions that mathematically display itself?

Is there a theme in this regard through my blog that I had questioned earlier and links brought forth to raise awareness of what might have been implied in that true "consciousness sense" about the very nature of our involvement in the nature of reality?

But then too, awareness, about the death of such sensations. This is most troubling to me, if such model consumptions had made this impression then what had happened to the views as they exploded into the other realms? Other Realms? Why would I introduce Thales as a culminative vision about what could emerge and the father of geometry? Models make our view culmnative and increase the vision capabilites. Is there no one here that see differently after they had crossed a page to find that in our new tomorrows we see reality a little different now?

You have been touched at a most deep level, that goes beyond the death of such sensations as Toposense, or momentums of curvatures. A microscopic eye now, to the quantum nature, right next to your reading from this screen. It's in the air all around you, this potential? :)

Plato:

Mathematics(logic?) and experiment?

I respond in that thread, and although it would seems disjointed from the rest of the commentaries, I thought I was talking directly to Sean's opening post. So I have linked the post on the very title as I have done with previous entires, as they have been setting the pace for my thinking about what views they share and what safety net is placed out there for us lay readers.

Would this impede my question as to the relation of philosphy in Sean's opening statement, to find that it had found a trail that leads to reasons why funding and perspective on it, should be thought about most carefully. Held in the esteem, with which one's adventures in physics and mathematics might have benefited society?

I understand this need for determination, and as well, the need to reaffirm what philosophy might hold in regards to truly active memebers of the science community and the projects they are engaged in. Would they have a distain for the philosophy of mathematics?

I left a question mark out there, and this question although never answered did see some slight comment in relation to the philosophy that where such logic might have gained in relation, being mentioned. I'll have to explain this some more so you understand that I am working hard to make sense of what is out there and viewed, whether in the tabloids, or what ever generalizations made by mathematicians, or the physicist who looks that little bit further.

Shall I quickly respond to the thread commetary or should I continue? I thnk it important that I respond to the comments rasied but I'll do this after by highlighting the area that spoke to me in relation to this train of thought.

I linked a quote from Plato on the idea of philosophy in my comment. I wil be moving from that position.

Philosophy of Mathematics

Foundations Study Guide: Philosophy of Mathematics by David S. Ross, Ph.D.
The philosophy of mathematics is the philosophical study of the concepts and methods of mathematics. It is concerned with the nature of numbers, geometric objects, and other mathematical concepts; it is concerned with their cognitive origins and with their application to reality. It addresses the validation of methods of mathematical inference. In particular, it deals with the logical problems associated with mathematical infinitude.

Among the sciences, mathematics has a unique relation to philosophy. Since antiquity, philosophers have envied it as the model of logical perfection, because of the clarity of its concepts and the certainty of its conclusions, and have therefore devoted much effort to explaining the nature of mathematics.

You have to understand that although I am deficient in the math skills many have, it is not without effort that I am enaging myself in what appears to be beautiful and simplistic design when completed as a model. When we look at what the Wunderkammern had to offer in a revitalizing and dusting off of, models that were concretized for us. Did they lanquish until they were refurbished to the museums of time, so that we may again look at what mathematics has accomplished for us. In ways, that are very abstract and beautiful? What then exist as you gazed into the magnetic field, the dynamcis of brane held issues and the exemplification of design in those branes? It had to follow consistent and progressive developement in the physics of.



The Unreasonable Effectiveness of Mathematics in the Natural Sciences by Eugene Wigner

The great mathematician fully, almost ruthlessly, exploits the domain of permissible reasoning and skirts the impermissible. That his recklessness does not lead him into a morass of contradictions is a miracle in itself: certainly it is hard to believe that our reasoning power was brought, by Darwin's process of natural selection, to the perfection which it seems to possess. However, this is not our present subject. The principal point which will have to be recalled later is that the mathematician could formulate only a handful of interesting theorems without defining concepts beyond those contained in the axioms and that the concepts outside those contained in the axioms are defined with a view of permitting ingenious logical operations which appeal to our aesthetic sense both as operations and also in their results of great generality and simplicity.

[3 M. Polanyi, in his Personal Knowledge (Chicago: University of Chicago
Press, 1958), says: "All these difficulties are but consequences of our
refusal to see that mathematics cannot be defined without acknowledging
its most obvious feature: namely, that it is interesting" (p 188).]

Social constructivism or social realism

Now here is the part, that while I saw the devloping nature of the tread of thinking and comments how would I answer and stay in tune? I previously spoke of John Nash and the inherent nature of mathematics as it could pierce the bargaining process, that to have this moved t a dynamcial social and constructive pallette developed in the ongoing relations of nations, why would such a scoial construct not be recognized as to the direction and strength of what mathematics might mean from a cognitive and developing brain that we have.

This theory sees mathematics primarily as a social construct, as a product of culture, subject to correction and change. Like the other sciences, mathematics is viewed as an empirical endeavor whose results are constantly compared to 'reality' and may be discarded if they don't agree with observation or prove pointless. The direction of mathematical research is dictated by the fashions of the social group performing it or by the needs of the society financing it. However, although such external forces may change the direction of some mathematical research, there are strong internal constraints (the mathematical traditions, methods, problems, meanings and values into which mathematicians are enculturated) that work to conserve the historically defined discipline.

This runs counter to the traditional beliefs of working mathematicians, that mathematics is somehow pure or objective. But social constructivists argue that mathematics is in fact grounded by much uncertainty: as mathematical practice evolves, the status of previous mathematics is cast into doubt, and is corrected to the degree it is required or desired by the current Mathematical Community. This can be seen in the development of analysis from reexamination of the calculus of Leibniz and Newton. They argue further that finished mathematics is often accorded too much status, and folk mathematics not enough, due to an over-belief in axiomatic proof and peer review as practices.

This gets very comlicated for me. Yet I recognize the inhernet pattern at the basis of these negotiatons and the games involved. More to follow, and short on time.

Aristotle and the Logic of the Natural World

Aristotle's logic, especially his theory of the syllogism, has had an unparalleled influence on the history of Western thought. It did not always hold this position: in the Hellenistic period, Stoic logic, and in particular the work of Chrysippus, was much more celebrated. However, in later antiquity, following the work of Aristotelian Commentators, Aristotle's logic became dominant, and Aristotelian logic was what was transmitted to the Arabic and the Latin medieval traditions, while the works of Chrysippus have not survived.

First and formost one should be drawn to the very highlighted statement emblazoned at the top of this blog.

PLato saids,"Look to the perfection of the heavens for truth," while Aristotle saids "look around you at what is, if you would know the truth"

I have to move quick forward here and reveal why the thinking is quite intense in terms of what such logic would have been revealling by "looking around you at what is." While I recognize this basis implanted in the natural world, such divisions arises from what had already existed. What we could accesss, as tangible realities of the ideas around us. "From whence they come?"

So maybe a list of the maths involved so far? If we can wrap these maths then what had we done from the perspective of the natural world? Would such creation of a new math help here?:) I have an idea, but all that thngs that currently exist and that will exist are already here. We just have to access them right? So what would support such adventures froma philosophy that had endured to realites of the natural process from the logic of a math? What math would this be?:)

Algebra

Geometry

Trigonometry

Calculus (single variable)

Analytic Geometry

Linear Algebra

Ordinary Differential Equations

Partial Differential Equations

Methods of approximation

Probability and statistics

Real analysis

Complex analysis

Group theory

Differential geometry

Lie groups

Differential forms

Homology

Cohomology

Homotopy

Fiber bundles

Characteristic classes

Index theorems

Supersymmetry and supergravity

K-theory

Noncommutative geometry (NCG for short)

So the idea is that Plato and Aristotle stand together, as a basis of what is happening in our world now. Between those of science and the resulting needs for experimentation. The roads to lead from the underlying avenues of philosophical thought, that would include math develoepment.

Now how is this possible you ask? How is it possible such logic coud have been so revealling of nature that we would strive to find it's meaning in patterns underlying the nature of this reality, are actually abstract rules of engagement, that had been developed through philosophical thought? How so?

If we look at the number of mayh creations what uses are these when moved into the basis is of the natural world? Would you not think these modes of thinking would be tempered by such logic, that math would find it's birthing as to the need for such expressions from this natural world?

So part of the realization is that the creation of the math had to have already existed in the forms of natures response, and that such access gained to these ideas, are worth noting as a means to what already existed in nature. That is my logic:)

Experimentation

So is there a method to the madness of all these tidbits of information that would wrap all of this in a easy way to divine the logic of the natural world? Is it beyond comprehension? I don't believe so, or why would I waste my time as a lay person, to move into this world of a higher standard of abstract thought and developing sciences, to wonder about the origins of the nature of this reality and the cosmolgical equivalent of asking what happened in that beginning of creation?

Would it be so subtle that such logic woud have been driven to ask where this beginning was, and what roads had currently lead all these minds to this very question.

Some act very safe, and walk safe ground, by what methods are currently tangible in our assessments, while other are quite adventurous. Some ask, that you stay in line, with current experimentation or suffer the wrath of deriving illusionary tales of ideas, that had not matured yet, as to the feasibility to what will express this logic of the natural world.


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

So mine is a simple philosophy, that holds complex variables. A simple painting, that holds a thuosand words?:) To me Math is like that, yet I am deficient in all the logic it had to bear down on the natural processes in this world. While my collegues are simple folk, I recognized the diversity of that group that Lubos and Clifford belong too. This is the origins of my statement. I understand as well, about the crackpostism that follows aether rejuvenation, yet I see the graviton as a member of that spacetime fabric.

Is this enough to speak on the creation and fabrications we like to embue to that natural world? Is it enough to understand these concepts, and find such roads leading too, are the very fringes of what is known and came from a brighter light that shines from behind us, to those shadows on the wall?