Torsors Made Easy

John Baez:

In Newtonian mechanics, we can only measure energy differences, not energies themselves. The reason is that we can add any real number to our definition of energy without changing any of the physics. This means it doesn't make much sense to ask what the energy of a system is - we can answer this question only after picking an arbitrary convention about what counts as "zero energy". What makes more sense is to talk about the difference between the energy of a system in one state and the energy of that system in some other state.

We can express this in terms of torsors as follows: energy differences lie in the group of real numbers R, but energies themselves do not: they lie in an "R-torsor".

In quantum mechanics, we can only measure relative phases, not phases themselves. The reason is that we can multiply the phase of a quantum state by any unit complex number without changing any of the physics. So, it doesn't make much sense to ask what the phase of a quantum state is - we can answer this question only after picking an arbitrary convention. What makes sense more sense is to talk about the relative phase between two states that differ only by a phase.

We can express this in terms of torsors as follows: relative phases lie in the group of unit complex numbers, which is called U(1), but phases themselves do not: they lie in a "U(1)-torsor".

Deep Impact craters on the moon.

What do they reveal about the moon's geological structure?


The colors in this image can be used to ascertain compositional properties of the materials making up the deep strata of these two regions.

One day I'd like to think we will be precise enough to ascertain all geological structure of the planets by info that we don't have just yet in terms of gravitational perspective? Maybe we can insert in between space of Mendeelev's model one day?

These are good indicators to help us see the nature of the planets organization constituents, as fundamental characters, of that same planet?



Studying gravitational models also help in this direction. The unique character is amazing once we thought the sphere on whch we live was to be so round, when in fact, from that same gravitational perspective, this is just not so.:)

Lee Smolin's Case for Background Independence

While we were privy to the debate between Susskind and Smolin in a previous post, the origins and definitions have been drawn from the deeper requirements of an ideology.

Where do these begin, and we find the inner compulsion of a scientist to find the means and defintions to extend the basis of our perceptions on a basis that both agree.

Lubos reaffirms this many times, and is in concert, as many in string theory continue to hold to what this desire should be.

Lubos saids:

Some of Lee's points can be agreed with, for example:

It is desirable to find a background independent formulation of string/M-theory

Such a formulation would likely to answer the questions whether the landscape approach to string/M-theory is correct; why it's not; what it should be replaced with.

This post represents a becoming. From those deeper levels, such a stage must be set?

Good for Lee Smolin, and the work he has been doing for laying a foundation, that all see, must reside to an synoptic closure, before such progressions become. If it got Lee smolin and others thinking, then, it served it's purpose, and those who say, a waste of time, would have undertsood then, Lee Smolin would not be where he is today on the pdf file here written.

So has Lubos has then directed our perspective in relation to how Lee Smolin sees the issues, and we have found the direct relationship and difference between how M Theory apporaches and How LQG does.

Lubos Motl saids:

An attempt to revive Mach's principle means to argue that the gravitational waves do not exist. It is a struggle to return us not only before General Relativity; it is a program to return the humankind to the pre-Newtonian era and the dark Middle Ages. Some people may be permanently impressed by Mach's principle and some people may find it shallow after a closer scrutiny. These two groups may be composed of equally nice people. But the difference is that the critics of Mach's principle have a good physical intuition; its advocates are philosophers who are unable to think analytically and quantitatively and they prefer to insist on prejudices that can be shown flawed by a five-minute-long quantitative argument.

There are catelysts all around, that ask for this deeper resolve to come forth. Asking for greater potentials in our visionistic qualities, to understand, that we can see this world very much differently? What pathway had been established then that Lee Smoln would attack this from another perspective held within the ideas of Special Relativity, that holds the idealization before the roads to gravitational understanding had been theoretically proven by Einstein.

Lubos Said:>

OK, let me start with the questions about relationism and Mach's principle. I highly recommend you the second popular book by Brian Greene, "The Fabric of the Cosmos", where the relative vs. absolute debate is covered in the first chapters. And the presentation is very nice.

How often the debate on such levels of what seems has been lacking in string/M theory that such voices extolled would relinquish it to paths unexperimentally challenged? They would have missed the opportunity ofsuch a debate brought forth from the Dialogos of Eide.

It is a strong statement which arises from the Platonic school, that such a discussion would reveal, that what is in the Heaven of ideas, could descend to minds and those who ask, those who embroil themselves, to questions of what it is, that makes the ideas of reality, a part of the natural world.

Lee Smolin:

The aim of this paper is to explain carefully the arguments behind the assertion that the correct quantum theory of gravity must be background independent. We begin by recounting how the debate over whether quantum gravity must be background independent is a continuation of a long-standing argument in the history of physics and philosophy over whether space and time are relational or absolute. This leads to a careful statement of what physicists mean when we speak of background independence. Given this we can characterize the precise sense in which general relativity is a background independent theory. The leading background independent approaches to quantum gravity are then discussed, including causal set models, loop quantum gravity and dynamical triangulations and their main achievements are summarized along with the problems that remain open. Some first attempts to cast string/M theory into a background independent formulation are also mentioned.

The relational/absolute debate has implications also for other issues such as unification and how the parameters of the standard models of physics and cosmology are to be explained. The recent issues concerning the string theory landscape are reviewed and it is argued that they can only be resolved within the context of a background independent formulation. Finally, we review some recent proposals to make quantum theory more relational.

Kilometric Radiation?

So we use physics in ways to change the way we see? Here are some examles from the Cassini Project and Wikipedia.

Cassini Plasma Spectrometer (CAPS)
The Cassini Plasma Spectrometer (CAPS) is a direct sensing instrument that measures the energy and electrical charge of particles such as electrons and protons that the instrument encounters. CAPS will measure the molecules originating from Saturn's ionosphere and also determine the configuration of Saturn's magnetic field. CAPS will also investigate plasma in these areas as well as the solar wind within Saturn's magnetosphere.[1]

Cosmic Dust Analyzer (CDA)

The Cosmic Dust Analyzer (CDA) is a direct sensing instrument that measures the size, speed, and direction of tiny dust grains near Saturn. Some of these particles are orbiting Saturn, while others may come from other solar systems. The Cosmic Dust Analyzer onboard the Cassini orbiter is ultimately designed to help discover more about these mysterious particles, and significantly add to the knowledge of the materials in other celestial bodies and potentially more about the origins of the universe.[2]

Composite Infrared Spectrometer (CIRS)

The Composite Infrared Spectrometer (CIRS) is a remote sensing instrument that measures the infrared light coming from an object (such as an atmosphere or moon surface) to learn more about its temperature and what it's made of. Throughout the Cassini-Huygens mission, CIRS will measure infrared emissions from atmospheres, rings and surfaces in the vast Saturn system to determine their composition, temperatures and thermal properties. It will map the atmosphere of Saturn in three dimensions to determine temperature and pressure profiles with altitude, gas composition, and the distribution of aerosols and clouds. This instrument will also measure thermal characteristics and the composition of satellite surfaces and rings.[3]

Ion and Neutral Mass Spectrometer (INMS)

The Ion and Neutral Mass Spectrometer (INMS) is a direct sensing instrument that analyzes charged particles (like protons and heavier ions) and neutral particles (like atoms) near Titan and Saturn to learn more about their atmospheres. INMS is intended also to measure the positive ion and neutral environments of Saturn's icy satellites and rings.[4]

Imaging Science Subsystem (ISS)

The Imaging Science Subsystem (ISS) is a remote sensing instrument that captures images in visible light, and some in infrared and ultraviolet light. The ISS has a camera that can take a broad, wide-angle picture and a camera that can record small areas in fine detail. Scientists anticipate that Cassini scientists will be able to use ISS to return hundreds of thousands of images of Saturn and its rings and moons. ISS includes two cameras; a Wide Angle Camera (WAC) and a Narrow Angle Camera (NAC). Each uses a sensitive charge-coupled device (CCD) as its detector. Each CCD consists of a 1,024 square array of pixels, 12 μm on a side. The camera's system allows for many data collection modes, including on-chip data compression. Both cameras are fitted with spectral filters that rotate on a wheel—to view different bands within the electromagnetic spectrum ranging from 0.2 to 1.1 μm.[5]

Dual Technique Magnetometer (MAG)

The Dual Technique Magnetometer (MAG) is a direct sensing instrument that measures the strength and direction of the magnetic field around Saturn. The magnetic fields are generated partly by the intensely hot molten core at Saturn's center. Measuring the magnetic field is one of the ways to probe the core, even though it is far too hot and deep to actually visit. MAG's goals are to develop a three-dimensional model of Saturn's magnetosphere, as well as determine the magnetic state of Titan and its atmosphere, and the icy satellites and their role in the magnetosphere of Saturn.[6]

Magnetospheric Imaging Instrument (MIMI)

The Magnetospheric Imaging Instrument (MIMI) is both a direct and remote sensing instrument that produces images and other data about the particles trapped in Saturn's huge magnetic field, or magnetosphere. This information will be used to study the overall configuration and dynamics of the magnetosphere and its interactions with the solar wind, Saturn's atmosphere, Titan, rings, and icy satellites.[7]

Radio Detection and Ranging Instrument (RADAR)

The Radio Detection and Ranging Instrument (RADAR) is a remote active and remote passive sensing instrument that will produce maps of Titan's surface and measures the height of surface objects (like mountains and canyons) by bouncing radio signals off of Titan's surface and timing their return. Radio waves can penetrate the thick veil of haze surrounding Titan. In addition to bouncing radio waves, the RADAR instrument will listen for radio waves that Saturn or its moons may be producing.[8]

Radio and Plasma Wave Science instrument (RPWS)

The Radio and Plasma Wave Science instrument (RPWS) is a direct and remote sensing instrument that receives and measures the radio signals coming from Saturn, including the radio waves given off by the interaction of the solar wind with Saturn and Titan. The major functions of the RPWS are to measure the electric and magnetic wave fields in the interplanetary medium and planetary magnetospheres. The instrument will also determine the electron density and temperature near Titan and in some regions of Saturn's magnetosphere. RPWS studies the configuration of Saturn's magnetic field and its relationship to Saturn Kilometric Radiation (SKR), as well as monitoring and mapping Saturn's ionosphere, plasma, and lightning from Saturn's (and possibly Titan's) atmosphere.[9]

Radio Science Subsystem (RSS)

The Radio Science Subsystem (RSS) is a remote sensing instrument that uses radio antennas on Earth to observe the way radio signals from the spacecraft change as they are sent through objects, such as Titan's atmosphere or Saturn's rings, or even behind the sun. The RSS also studies the compositions, pressures and temperatures of atmospheres and ionospheres, radial structure and particle size distribution within rings, body and system masses and gravitational waves. The instrument uses the spacecraft X-band communication link as well as S-band downlink and Ka-band uplink and downlink.[10]

Ultraviolet Imaging Spectrograph (UVIS)

The Ultraviolet Imaging Spectrograph (UVIS) is a remote sensing instrument that captures images of the ultraviolet light reflected off an object, such as the clouds of Saturn and/or its rings, to learn more about their structure and composition. Designed to measure ultraviolet light over wavelengths from 55.8 to 190 nm, this instrument is also a valuable tool to help determine the composition, distribution, aerosol particle content and temperatures of their atmospheres. This sensitive instrument is different from other types of spectrometers because it can take both spectral and spatial readings. It is particularly adept at determining the composition of gases. Spatial observations take a wide-by-narrow view, only one pixel tall and 60 pixels across. The spectral dimension is 1,024 pixels per spatial pixel. Additionally, it is capable of taking so many images that it can create movies to show the ways in which this material is moved around by other forces.[11]

Visible and Infrared Mapping Spectrometer (VIMS)

The Visible and Infrared Mapping Spectrometer (VIMS) is a remote sensing instrument that is actually made up of two cameras in one: one is used to measure visible wavelengths, the other infrared. VIMS captures images using visible and infrared light to learn more about the composition of moon surfaces, the rings, and the atmospheres of Saturn and Titan. VIMS also observes the sunlight and starlight that passes through the rings to learn more about ring structure. VIMS is designed to measure reflected and emitted radiation from atmospheres, rings and surfaces over wavelengths from 0.35 to 5.1 mm. It will also help determine the compositions, temperatures and structures of these objects. With VIMS, scientists also plan to perform long-term studies of cloud movement and morphology in the Saturn system, to determine the planet's weather patterns.[12]

So how does String/M theory change the way we see?

The calorimeter design for GLAST produces flashes of light that are used to determine how much energy is in each gamma-ray. A calorimeter ("calorie-meter") is a device that measures the energy (heat: calor) of a particle when it is totally absorbed.

Smolin added his contribution to the string theory discussion on the new Cosmicvariance.com site that has been created by a group of people that offer perspective. In this case Sean Carroll posted a thread on Two Cheers for String theory, provoked some iteresting responses by minds who are at the forefront of these conversations.

I responded to this becuase I had been following both avenues Smolin spoke too, so I'll put my comment here as well.

This topic thread was develope from my reactions based on those who call people who are trying hard to integrate views of the natural world with the physics ideology of the topic of Strings?M theory, these fellows present. If they can not show us these new views as Smolin offers for inspection then what use the models and theories if no onne wants to se these work in the world we undrstand well by seeing around us?

While some people are looking for consistant means of determinations, others apply "conceptual situations" and bring forth comprehension of a kind. Now to this degree, that "gluonic perception is being adjusted" to see these values. The Smolins and others understood well the limitation of these views? Are there any?

Radio sounds from the source

All of the structures we observe in Saturn's radio spectrum are giving us clues about what might be going on in the source of the radio emissions above Saturn's auroras," said Dr. Bill Kurth, deputy principal investigator for the instrument. He is with the University of Iowa, Iowa City. Kurth made the discovery along with Principal Investigator Don Gurnett, a professor at the University. "We believe that the changing frequencies are related to tiny radio sources moving up and down along Saturn's magnetic field lines."

Has Sound, Changed the way we See?

Most of us understand the the aurora display do we not, and the resulting interactive play between the sun and the earth? The Auger experiment previously talked about and spoken too, by John Ellis, is a fine example of the diversity of interative features we can hope to see, as we examine the particle nature apart from the LHC rules of energy engagement, above and beyond the limits that have been imposed on us earthlings:)


The Fly's Eye and the Oh My God Particle

While the topic is produced for this conversation seems disjointed, the ideology of the string theorist is held to a boundry of thinking in my eyes that such a membrane( here I could link a toy model for comparison), and defined in this bubble context, as rudimentry as it appears in my mind's eye, it follows the developemental processes we see from the eulicidation Einstein offered us by joining Maxwell into the process unfolding in nature and to see the effect of any bulk production as a necessary step beyond the boudaries of this bubble?


Now in contrast I see the soapy bubble and light refraction dispalyed in such a lovely continuous flow over it's surface, that to me, it does not make sense if such auroric dispalyes are not to give us new ideas about the interactive feature of the sun with earth? Conceptually, thes ideas of hitting metal plates and such present new ideas in how dispersion across that plate could represent other ideas. What are those. Wel that's what I am trying to do is free the mind from th econstraints we had put on it in sucha strick language accompany those that step ahead of us in their own specualtions educationally followed doctrine. What new light and thinking patterns follow these people?

The auroral ionosphere is a natural emitter of radio waves, and many of these emissions are observable at ground level. Several types of radio emissions have been well documented using a variety of ground-based, stepped-frequency receivers (see reviews by LaBelle [1989] and LaBelle and Weatherwax, [1992]). In particular, auroral roar is a relatively narrowband emission at roughly 2 and 3 times the local electron cyclotron frequency ( ) [Kellogg and Monson, 1979; Kellogg and Monson, 1984; Weatherwax et al., 1993, 1995]. Much effort has been made in characterizing the seasonal, diurnal, and spectral characteristics of auroral roar to aid in determining its generation mechanism [e.g., Weatherwax et al., 1995.

See also:

http://www-pw.physics.uiowa.edu/plasma-wave/tutorial/examples.html

News articles shamelessy borrowed:

Space Music

The Musical Sounds of Space

'Sun Rings' Shares the Music of
Space

Quartet, Choir Debut NASA's 'Space Music'

Out of This World

Music of the Stars

Music of the Spheres

NASA Music Out of This World

Sun Rings

Turning Sounds From Space Into a Symphony

Science and Music Merge for Fall Concert

UI Space Physicist's Sounds of Space Inspire Work of Art

Themis

THEMIS's ground network of all sky imagers will have the density and time resolution to detect auroral onset within 10s and 0.5 degrees of longitude. The University of Calgary will deploy 16 imagers across Canada, combined with imagers in Alaska the THEMIS array will consist of 20 ground-based observatories (GBOs). Each GBO will consist of a white light all sky camera and a host of support equipment such as a computer, GPS antenna, and a satellite dish (in the event that an internet connection is not available at the site). [more information on GBOs]

It is always important to move the mind to encompass greater potentials, even within the confines of the physics we understand, and move this, to the natural world we see, while we witness it's glory.

Astronaut's view of the Aurora Australis, or southern lights, from aboard Space Shuttle Discovery 1991 (Courtesy: NASA)

Those more adventourous, and with better visonistic qualities , and those having consumed models of apprehension, might be able to talk about these things in ways that we are not accustomed too?

Like learning a new language, and conceptual framework, that loosens those things we hold so tight, that no room is granted for the neurons to fire new pathways?

The Black Hole Final State

Mathematics is not the rigid and rigidity-producing schema that the layman thinks it is; rather, in it we find ourselves at that meeting point of constraint and freedom that is the very essence of human nature.

- Hermann Weyl

It was a nice vacation and now being back, I see Lubos is clarifying some issues here for us to consider.

"Lubos Motl:

However, Hawking's semiclassical calculation leads to an exactly (piecewise) thermal final state. Such a mixed state in the far future violates unitarity - pure states cannot evolve into mixed states unitarily - and it destroys the initial information about the collapsed objects which is why we call it "information loss puzzle". A tension with quantum mechanics emerges.

The Gepner point demonstrates greater potential recognition of the brane world understandings and two dimensional views from a five dimenisonal developmentment for those who do not like such abstract adventures P.P. Cook helps to enlighten us on this subject.

So have I done justice to the developing perspective, that we are now ready to take what what demonstrated, and move it to a greater format for those who will lead us laymen through the world of the abstract mathematics? To help us enjoy what was mathematically unenduring for those not gifted to see the B field manifestaion, is a continuance of what we like to engage at higher dimensional perspectives. And really, it is all about imagery is it not?




Lee Smolin:

It was worry about the possibility that string theory would lead to the present situation, which Susskind has so ably described in his recent papers, that led me to invent the Cosmological Natural Selection [CNS] idea and to write my first book. My motive, then as now, is to prevent a split in the community of theoretical physicists in which different groups of smart people believe different things, with no recourse to come to consensus by rational argument from the evidence.

You must understand the state of thinking and dualistic nature that continues to force minds to engage the process, and this quest for wholeness, between two thoughts that are part and parcel of the same thing? Relativity and Quantum Nature. The larger circle is RElativity, and the smaller, the quantum nature. LQG and STring work from their respective positions.

So do we select the basis for this model, and find that LQG and Strings are formulated on principals embedded in association with the blackhole topic? This throws light back again on a topic that has been shared more then once by such trends in thinking as Lubos exemplfies for us, and again directs our thoughts towards Lenny Susskind and Lee Smolin, in contrast to each other.

I see people are teaming up appropriately, such as Cosmic Variance, and this of course has already been lead by Lubos and Peter's contrast to each other. Whether some like to speculate on co-joining for such comparsions on the validity of strings, versus no strings approach, as resolutions, had already been developed while we see this new means to develope, much as Brain Greene and others in ISCAP foundations principals.

So of course onward and forward, we push the topic and the expertise for the layperson like me, that we see and continue to find, developmental processes appropriately gathering for future thoughts shared? Again too, we see Quantum Diaries has indeed served it's purpose more then once in what John Ellis and other's have shared, have open the doorway to how we see such developmental attitudes expanding in contrast to the larger circle of possibilties.

See John's latest entree and for me, hitting big objects and particle collisions still open the mind for the natural cosmic interactive processes ongoing in nature around us.

Anyway back to the title of this post. I have some thinking here to do.

Gary T. Horowitz1 and Juan Maldacena,2

The purpose of this note is to provide a possible answer to this question. Rather than the radical modification of quantum mechanics required for pure states to evolve into mixed states, we adopt a more mild modification. We propose that at the black hole singularity one needs to impose a unique final state boundary condition. More precisely, we have a unique final wavefunction for the interior of the black hole. Modifications of quantum mechanics where one imposes final state boundary conditions were considered in [6,7,8,9]. Here we are putting a final state boundary condition on part of the system, the interior of the black hole. This final boundary condition makes sure that no information is “absorbed” by the singularity.

If indeed we started to think about the point on the brane then what kind of simplification can be drawn so that those less enclined to such abstract thinking could find a greater potential to that dimensionnal thinking?

(a) Compactifying a 3-D universe with two space dimensions and one time dimension. This is a simplification of the 5-D space­time considered by Theodor Kaluza and Oskar Klein. (b) The Lorentz symmetry of the large dimension is broken by the compactification and all that remains is 2-D space plus the U(1) symmetry represented by the arrow. (c) On large scales we see only a 2-D universe (one space plus one time dimension) with the "internal" U(1) symmetry of electromagnetism.

Here such thoughts begin to form around the idealization of computer graphics imagery developed and leading in this idealization of this two dimensional screen. We see where the likes of Thomas Banchoff demonstrate where such new roads to the developing insight ot this imagery can be seen in Smolins views of the Bekenstein Bound, that we we now understand a greater potential exists in how we view the screen, and what is being described in the blackhole horizon?



Let me show this image again, for greater clarity of what I mean.

Liminocentric Structures: Which Circle do you Belong Too?

If conceived as a series of ever-wider experiential contexts, nested one within the other like a set of Chinese boxes, consciousness can be thought of as wrapping back around on itself in such a way that the outermost 'context' is indistinguishable from the innermost 'content' - a structure for which we coined the term 'liminocentric'.

As most know "Liminocentric structure" will have been defined here then? I like to think this goes back much further in our natures, and to recognize this pattern, much as Brian Greene might have spoken too, in article above one would have ot venture into it to understand.



Then why would I inject past historical views here to current research? It is a issue of wholeness and bringing resolution to the camps of LQG and Strings. If you look at the circle here in an expansitory view. The circle as a point, deals with particle reductionistic principals as well as dealing with General Relativity on a cosmological scale. They both deal with gravity from their respective positions. What are their strengths and weaknesses?

I will be away for about two weeks and a much needed break, so I hope people will explore this avenue, for it is the basis of my research in understanding this interchange between, depending on which circle you belong, two ends that need to come together and in this regard, LQG and String theory might have found this unification, but from which different ends?



There is no end, and it is continous by nature?

One harmonious possibility is that string enthusiasts and loop quantum gravity aficionados are actually constructing the same theory, but from vastly different starting points. That each theory involves loops-in string theory, these are string loops; in loop quantum grvaity, they're harder to describe nonmathmatically, but. roughly speaking, they'r elementray loops of space-suggests there might be a connection. This possibility is further supported by the fact that on a few problems accessible to both, sucha s blackhole entrophy, the two theroies agree fully. And on the question of spacetime's constittuents, both theories suggest that there is some kind of atomized structure. Page 490, Fabric of the Cosmos by Brian Greene

To me this connection lies in how we interpret the circle and this variation in between them, is a powerful topological structure form that is understood as we see the question of which circle is which? From which space quantum mechanically to cosmologicazlly. In terms of that atomized look, to the nature of relativity through that cosmo.

The last departing statement in Brian Greene's book sets the stage for how the string community has to orientate its view from one perspective, while LQG needs to orientate theirs. This is used, to point to ISCAP and the introduction Brian Green gives us.

Look at Page 493 of his book, and then look here.

The goal of ISCAP is to bring together theoretical physicists, astrophysicists, and observational astronomers to address key problems in particle physics and cosmology that require a broad confluence of expertise and perspective.

Even the good intention would have failed to see this connection between both camps, but I see that having it explained as such here, I hope to point to something much deeper in our psyche that warrents the orientation to mathematcial structures that underlies our consciousness. As subjective a view as it might seem to some, there are reasons that I support such views, and without hurting the purity of the direct mathematical relations, I needed to bring the article and title of this entry forward for consideration. It is a necessary part of wholeness that the dicrete natures and the wonderful views of continuity would share some relationship even in the bulk of our considerations?

Which Circle do you belong too? You are one, and the same are you not?:)



"Nothing to me would be more poetic; no outcome would be more graceful ... than for us to confirm our theories of the ultramicroscopic makeup of spacetime and matter by turning our giant telescopes skyward and gazing at the stars," Greene said.


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

"But now, almost a century after Einstein's tour-de-force, string theory gives us a quantum-mechanical discription of gravity that, by necessity, modifies general relativity when distances involved become as short as the Planck length. Since Reinmannian geometry is the mathetical core of genral relativity, this means that it too must be modified in order to reflect faithfully the new short distance physics of string theory. Whereas general relativity asserts that the curved properties of the universe are described by Reinmannian geometry, string theory asserts this is true only if we examine the fabric of the universe on large enough scales. On scales as small as planck length a new kind of geometry must emerge, one that aligns with the new physics of string theory. This new geometry is called, quantum geometry."

B Field Manifestations

Ah what the heck......I'll bite....let the skeptics converge in a harmonic convergence:)

Nigel Hitching

Sylvester Surfaces and the B field?

Are you a "gold fish" or a "Ant world person?" Are you a pigeon? Have you sent your vision into the things of nature, to explore it's potential in other ways?



Figure 2. Clebsch's Diagonal Surface: Wonderful

Rupert SheldarkeThe morphic fields of mental activity are not confined to the insides of our heads. They extend far beyond our brain though intention and attention. We are already familiar with the idea of fields extending beyond the material objects in which they are rooted: for example magnetic fields extend beyond the surfaces of magnets; the earth’s gravitational field extends far beyond the surface of the earth, keeping the moon in its orbit; and the fields of a cell phone stretch out far beyond the phone itself. Likewise the fields of our minds extend far beyond our brains.

The Faraday's, the Gauss's, the Reimanns learnt to see in other ways? Does this imply some spooky valuation beyond the confines of the brain's home?

"The gravitons behave like sound in a metal sheet," says Dvali. "Hitting the sheet with a hammer creates a sound wave that travels along its surface. But the sound propagation is not exactly two-dimensional as part of the energy is lost into the surrounding air. Near the hammer, the loss of energy is small, but further away, it's more significant."

So is it just a brain thingy, or is this "field real?" Some were not so unintelligent to "refute the aether" at one time. For we now understand what exists in the real spacetime valuations, beyond what is held to the brane, and see bulk manifestation, as real and populated. AS a extension, beyond those surfaces.

The Sound of Billiard Balls

Savas Dimopoulos:

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

Are we execising the brains ability to get this toposense and geoemtrical revelation beyond straight lines and distances between points?

So what is a chaldni plate?:) helps you to see how sound is of value beyond the confines Faradays magnetic field lines, as real effects of that same magnet, and resonant coupling points. Exercising the potential of banging metal, helps the mind point to other places too. Playing pool, does too?:)

Expansitory Valuation of a Circle with Gravity?

If conceived as a series of ever-wider experiential contexts, nested one within the other like a set of Chinese boxes, consciousness can be thought of as wrapping back around on itself in such a way that the outermost 'context' is indistinguishable from the innermost 'content' - a structure for which we coined the term 'liminocentric'.

Now I refer to this often, because of this connection between inner content and outer context. I know it deals with a consciousness and subjective valuation, but it seems very important when you think of what could happen between the compactification of the sun or earth and its size, once dealt to a blackhole?

In this setting of the spherical mass M, we define the value rS = 2M as the Schwarzschild radius of the mass. If the mass has a radius less than rS, then it is called a black hole. In that case, the surface r =rS is called the event horizon of the black hole.

Sometimes the determination of this value has to be seen in light of how we see the gravitational properties of the energy. Windings then, come of value in KK tower representations, and hence images of circles joining other circles can represented in a tree?

It's trunk and branches. Although this imagery is a little different, the base of the larger circle has pointed in the right direction, if we think of flat euclidean space, where no gravity potential can exist? Although we like to think there is never this abscence of harmonic oscillation, it would have to be assumed that it had always existed and can never really be zero?

Had I then complicated the ideal of this circle by recognizing this value from the ground up, had I lost sight of it's root system, and how well it is buried in the earth. How shall I explain this, but as a inverse function of growth? This is not possible. So we see where the seeding had the potential to rise from the earth in one form, and proceed to move into the air, as a phase from it's early unverse beginnings?

So where does this motivation then exist in the design?

A circle of radius r has a curvature of size 1/r. Therefore, small circles have large curvature and large circles have small curvature. The curvature of a line is 0. In general, an object with zero curvature is "flat."

See LIminocentric structure here for a deeper explanation. Greene's emphasis helps in other aspects as well. How can a six foot man exist in such a tiny circle?:)

The familiar extended dimensions, therefore, may very well also be in the shape of circles and hence subject to the R and 1/R physical identification of string theory. To put some rough numbers in, if the familiar dimensions are circular then their radii must be about as large as 15 billion light-years, which is about ten trillion trillion trillion trillion trillion (R= 1061) times the Planck length, and growing as the universe explands. If string theory is right, this is physically identical to the familiar dimensions being circular with incredibly tiny radii of about 1/R=1/1061=10-61 times the Planck length! There are our well-known familiar dimensions in an alternate description provided by string theory. [Greene's emphasis]. In fact, in the reciprocal language, these tiny circles are getting ever smaller as time goes by, since as R grows, 1/R shrinks. Now we seem to have really gone off the deep end. How can this possibly be true? How can a six-foot tall human being 'fit' inside such an unbelievably microscopic universe? How can a speck of a universe be physically identical to the great expanse we view in the heavens above? (Greene, The Elegant Universe, pages 248-249)

So in the one sense(or topo-sense) I see similarities between planes and cyliners and they are isometrically equivalent, and then ideas of topological design spoken of, in the idea of the coffee cup becoming a donut, and all of a sudden this kind of geometry had taken a turn for perspective that deals with other things then I am normally accustom too.

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.



But taken to the tree level(potato plant):) and interactive features of windings how shall we interpret such energies, but by those same windings? That the seed of the plant held a greater design for growth, yet it is in the seed this plant and it's energy contained that it's futre is realized. I know this plant thingy is a bad analogy for how such circle and the arrow of time. Would a flower be better? How does anything loop back onto itself and replay this universe all over again?

Physics at this high energy scale describes the universe as it existed during the first moments of the Big Bang. These high energy scales are completely beyond the range which can be created in the particle accelerators we currently have (or will have in the foreseeable future.) Most of the physical theories that we use to understand the universe that we live in also break down at the Planck scale. However, string theory shows unique promise in being able to describe the physics of the Planck scale and the Big Bang.

So when you read Lubos's entry here in Nasa's Collider you have to wonder? How on a physical level, the circle implied( our universe now after the first three minutes) could have ever recieved the connotation of it's valuation in a collision as large as we see in that situation? But you have to understand this connection between Gia and the "plate he hits", or the mirror moon measures and of course, there are simultaneous question about dimensional perspectve and compacted circles that raised the undertanding beyond current standards in our everyday world. Much like understanding strong curvature in a circle. How far can this be taken?

You would not think this post here would have ever had anything to do with Lubos simple statement about Nasa'a Collider, but it does?:) I guess it depends on which circle you belong too?

Anomalistic Features of Gold Fish and Ant World?

I was reading Mark Trodden's blog called, "Orange Quark" for reading, and he pointed out the following article. In Praise of Hard Questions, by Tom Siegfried

Geometric basis underlying science? I see this tendency of many to the Halls of records, museums, and whatever you like, to keep current for all us folks outside academia.

These are important historical correlations to draw from. These are wonderful connections to the fathers/mothers of science. Distinctive historical figures who embue science with their particular inflections and bend.

Should we dismiss the motivations of those who are driven by "anomalistic behaviors"? Remember Einstein in his youth and the compass? What are we ignorant of in such a case?

We know well, that such measures, if not supported, cannot be easily removed from the memories. Can be relinguished to subjective interpretations. Should not be ruled inadmissable:)Yet, it can drive the motvation of youth in that case t hard and fsat rules of order?

Had there ever been a time where a scientist had seen something that ran contrary to everything they know? It had to be at the front line, or how would anomalistic valuation had ver been entertained? Had been seen by a reputable scientist and held in the idealization of the Einstein who at his time, "lacked comprehension" but was moved.

Here I point out David Gross's statement and context supplied by Tom Siegfried .

Science's greatest advances occur on the frontiers, at the interface between ignorance and knowledge, where the most profound questions are posed. There's no better way to assess the current condition of science than listing the questions that science cannot answer. "Science," Gross declares, "is shaped by ignorance."

Yes I think we all understand.

So indeed we see then that all the forebears of our science then had something in common as they sought to geometrically express the abstract, and in my line of thinking, runs the Wunderkammer models. These are hard and concrete models in glass cases.

Maxwell understood this in Gauss and Faraday, and Einstein, understood this in Riemann? Sachherri elucidating beyond the limits of Euclids postulates 1-4, paved the way for a new dynamcial world? So how strange indeed that Sean Carroll would give us a sixty second explanation on extra dimensions. Have we eluded to an "aspect of mind" in abstraction?

Extra dimensions sound like science fiction, but they could be part of the real world. And if so, they might help explain mysteries like why the universe is expanding faster than expected, and why gravity is weaker than the other forces of nature.
Three dimensions are all we see -- how could there be any more? Einstein's general theory of relativity tells us that space can expand, contract, and bend. If one direction were to contract down to an extremely tiny size, much smaller than an atom, it would be hidden from our view. If we could see on small enough scales, that hidden dimension might become visible.

Sean, what shall you say to Peter Woit, who might say to you. "We are not Ants?"

So this sixty second explanation now presents itself, for the "mantra induced introspection" that one wonders, what the heck might Sean be talking about? Is there a world somewhere that that exists much like "ant world" in which we take part in?

How strange indeed then that the mind has been taken to Ant World, so that we may see, the angles of perception greatly ehanced for us? Where in the real world, walking straight lines is a "balancing act" when we engage the dynamcial qualites of science, that although engineered, also speak to the dynamcial relation underlying our everyday world.

So how shall such analogies then prepare us for the hard questions of science? Can we see now where such abstractions has moved science and the road shall lead us through to the idea of KLein's Ordering of Geometeries? Have we entered a new dynamcial realm of ant world, and together with Michio Kaku, created the new animated "goldfish world" as well, who see very much different then we see from the bridge?

Who is it that now sees and send our minds into "ants and goldfish?"