Showing posts with label General Relativity. Show all posts
Showing posts with label General Relativity. Show all posts

Saturday, September 15, 2012

Noncommutative standard model

In theoretical particle physics, the non-commutative Standard Model, mainly due to the French mathematician Alain Connes, uses his noncommutative geometry to devise an extension of the Standard Model to include a modified form of general relativity. This unification implies a few constraints on the parameters of the Standard Model. Under an additional assumption, known as the "big desert" hypothesis, one of these constraints determines the mass of the Higgs boson to be around 170 GeV, comfortably within the range of the Large Hadron Collider. Recent Tevatron experiments exclude a Higgs mass of 158 to 175 GeV at the 95% confidence level.[1] However, the previously computed Higgs mass was found to have an error, and more recent calculations are in line with the measured Higgs mass. [2]

Background

Current physical theory features four elementary forces: the gravitational force, the electromagnetic force, the weak force, and the strong force. Gravity has an elegant and experimentally precise theory: Einstein's general relativity. It is based on Riemannian geometry and interprets the gravitational force as curvature of space-time. Its Lagrangian formulation requires only two empirical parameters, the gravitational constant and the cosmological constant.

The other three forces also have a Lagrangian theory, called the Standard Model. Its underlying idea is that they are mediated by the exchange of spin-1 particles, the so-called gauge bosons. The one responsible for electromagnetism is the photon. The weak force is mediated by the W and Z bosons; the strong force, by gluons. The gauge Lagrangian is much more complicated than the gravitational one: at present, it involves some 30 real parameters, a number that could increase. What is more, the gauge Lagrangian must also contain a spin 0 particle, the Higgs boson, to give mass to the spin 1/2 and spin 1 particles. This particle has yet to be observed, and if it is not detected at the Large Hadron Collider in Geneva, the consistency of the Standard Model is in doubt.

Alain Connes has generalized Bernhard Riemann's geometry to noncommutative geometry. It describes spaces with curvature and uncertainty. Historically, the first example of such a geometry is quantum mechanics, which introduced Heisenberg's uncertainty relation by turning the classical observables of position and momentum into noncommuting operators. Noncommutative geometry is still sufficiently similar to Riemannian geometry that Connes was able to rederive general relativity. In doing so, he obtained the gauge Lagrangian as a companion of the gravitational one, a truly geometric unification of all four fundamental interactions. Connes has thus devised a fully geometric formulation of the Standard Model, where all the parameters are geometric invariants of a noncommutative space. A result is that parameters like the electron mass are now analogous to purely mathematical constants like pi. In 1929 Weyl wrote Einstein that any unified theory would need to include the metric tensor, a gauge field, and a matter field. Einstein considered the Einstein-Maxwell-Dirac system by 1930. He probably didn't develop it because he was unable to geometricize it. It can now be geometricized as a non-commutative geometry.

Notes

1. ^ The TEVNPH Working Group [1]
2. ^ Resilience of the Spectral Standard Model [2]

Wednesday, December 14, 2011

Explanation on Quantum Gravity in a Nutshell

Although Aristotle in general had a more empirical and experimental attitude than Plato, modern science did not come into its own until Plato's Pythagorean confidence in the mathematical nature of the world returned with Kepler, Galileo, and Newton. For instance, Aristotle, relying on a theory of opposites that is now only of historical interest, rejected Plato's attempt to match the Platonic Solids with the elements -- while Plato's expectations are realized in mineralogy and crystallography, where the Platonic Solids occur naturally.Plato and Aristotle, Up and Down-Kelley L. Ross, Ph.D.

 The goal of string theory is to explain the "?" in the above diagram.

I enjoyed the Livescribe demonstration by Clifford of  Asymptotia along with the explanation for Quantum Gravity. The two pillars for me were very emblematic with regards to "pillars of science."  This as well as the arch  is very fitting to me of what becomes self evident. If  under such an examination of the two areas Clifford is talking about,  Quantum Mechanics and General Relativity then are the attempts at unification.

The Yorck Project: 10.000 Meisterwerke der Malerei. DVD-ROM, 2002. ISBN 3936122202. Distributed by DIRECTMEDIA Publishing GmbH.

That question mark can be demonstrated above as to where in the location in Cliffords diagrams is related to the Aristotelian Arch in my view?

See:

Thursday, November 24, 2011

Relativistic Mechanical Quantities

A number of ordinary mechanical quantities take on a different form as the speed approaches the speed of light.

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Also See:

Lepton

Composition Leptons are involved in several processes such as beta decay. Elementary particle Fermionic 1st, 2nd, 3rd Electromagnetism, Gravitation, Weak l Antilepton (l) 6 (electron, electron neutrino, muon, muon neutrino, tau, tau neutrino) +1 e, 0 e, −1 e No 1⁄2
A lepton is an elementary particle and a fundamental constituent of matter.[1] The best known of all leptons is the electron which governs nearly all of chemistry as it is found in atoms and is directly tied to all chemical properties. Two main classes of leptons exist: charged leptons (also known as the electron-like leptons), and neutral leptons (better known as neutrinos). Charged leptons can combine with other particles to form various composite particles such as atoms and positronium, while neutrinos rarely interact with anything, and are consequently rarely observed.
There are six types of leptons, known as flavours, forming three generations.[2] The first generation is the electronic leptons, comprising the electron (e) and electron neutrino (ν
e
); the second is the muonic leptons, comprising the muon (μ) and muon neutrino (ν
μ
); and the third is the tauonic leptons, comprising the tau (τ) and the tau neutrino (ν
τ
). Electrons have the least mass of all the charged leptons. The heavier muons and taus will rapidly change into electrons through a process of particle decay: the transformation from a higher mass state to a lower mass state. Thus electrons are stable and the most common charged lepton in the universe, whereas muons and taus can only be produced in high energy collisions (such as those involving cosmic rays and those carried out in particle accelerators).

Leptons have various intrinsic properties, including electric charge, spin, and mass. Unlike quarks however, leptons are not subject to the strong interaction, but they are subject to the other three fundamental interactions: gravitation, electromagnetism (excluding neutrinos, which are electrically neutral), and the weak interaction. For every lepton flavor there is a corresponding type of antiparticle, known as antilepton, that differs from the lepton only in that some of its properties have equal magnitude but opposite sign. However, according to certain theories, neutrinos may be their own antiparticle, but it is not currently known whether this is the case or not.

The first charged lepton, the electron, was theorized in the mid-19th century by several scientists[3][4][5] and was discovered in 1897 by J. J. Thomson.[6] The next lepton to be observed was the muon, discovered by Carl D. Anderson in 1936, but it was erroneously classified as a meson at the time.[7] After investigation, it was realized that the muon did not have the expected properties of a meson, but rather behaved like an electron, only with higher mass. It took until 1947 for the concept of "leptons" as a family of particle to be proposed.[8] The first neutrino, the electron neutrino, was proposed by Wolfgang Pauli in 1930 to explain certain characteristics of beta decay.[8] It was first observed in the Cowan–Reines neutrino experiment conducted by Clyde Cowan and Frederick Reines in 1956.[8][9] The muon neutrino was discovered in 1962 by Leon M. Lederman, Melvin Schwartz and Jack Steinberger,[10] and the tau discovered between 1974 and 1977 by Martin Lewis Perl and his colleagues from the Stanford Linear Accelerator Center and Lawrence Berkeley National Laboratory.[11] The tau neutrino remained elusive until July 2000, when the DONUT collaboration from Fermilab announced its discovery.[12][13]

Leptons are an important part of the Standard Model. Electrons are one of the components of atoms, alongside protons and neutrons. Exotic atoms with muons and taus instead of electrons can also be synthesized, as well as lepton–antilepton particles such as positronium.

2011 Review of Particle Physics.
Please use this CITATION: K. Nakamura et al. (Particle Data Group), Journal of Physics G37, 075021 (2010) and 2011 partial update for the 2012 edition.

Sunday, November 20, 2011

Energy Boost From Shock Front

 Main Components of CNGS
A 400 GeV/c proton beam is extracted from the SPS in 10.5 microsecond short pulses of 2.4x1013 protons per pulse. The proton beam is transported through the transfer line TT41 to the CNGS target T40. The target consists of a series of graphite rods, which are cooled by a recirculated helium flow. Secondary pions and kaons of positive charge produced in the target are focused into a parallel beam by a system of two pulsed magnetic lenses, called horn and reflector. A 1 km long evacuated decay pipe allows the pions and kaons to decay into their daughter particles - of interest here is mainly the decay into muon-neutrinos and muons. The remaining hadrons (protons, pions, kaons) are absorbed in an iron beam dump with a graphite core. The muons are monitored in two sets of detectors downstream of the dump. Further downstream, the muons are absorbed in the rock while the neutrinos continue their travel towards Gran Sasso.microsecond short pulses of 2.4x1013 protons per
For me it has been an interesting journey in trying to understand the full context of a event in space sending information through out the cosmos in ways that are not limited to the matter configurations that would affect signals of those events.

In astrophysics, the most widely discussed mechanism of particle acceleration is the first-order Fermi process operating at collisionless shocks. It is based on the idea that particles undergo stochastic elastic scatterings both upstream and downstream of the shock front. This causes particles to wander across the shock repeatedly. On each crossing, they receive an energy boost as a result of the relative motion of the upstream and downstream plasmas. At non-relativistic shocks, scattering causes particles to diffuse in space, and the mechanism, termed "diffusive shock acceleration," is widely thought to be responsible for the acceleration of cosmic rays in supernova remnants. At relativistic shocks, the transport process is not spatial diffusion, but the first-order Fermi mechanism operates nevertheless (for reviews, see Kirk & Duffy 1999; Hillas 2005). In fact, the first ab initio demonstrations of this process using particle-in-cell (PIC) simulations have recently been presented for the relativistic case (Spitkovsky 2008b; Martins et al. 2009; Sironi & Spitkovsky 2009).
Several factors, such as the lifetime of the shock front or its spatial extent, can limit the energy to which particles can be accelerated in this process. However, even in the absence of these, acceleration will ultimately cease when the radiative energy losses that are inevitably associated with the scattering process overwhelm the energy gains obtained upon crossing the shock. Exactly when this happens depends on the details of the scattering process. See: RADIATIVE SIGNATURES OF RELATIVISTIC SHOCKS

So in soliton expressions while trying to find such an example here in the blog does not seem to be offering itself in the animations of the boat traveling down the channel we are so familiar with that for me this was the idea of the experimental processes unfolding at LHC. The collision point creates shock waves\particle sprays as Jets?

Soliton

Solitary wave in a laboratory wave channel.
In mathematics and physics, a soliton is a self-reinforcing solitary wave (a wave packet or pulse) that maintains its shape while it travels at constant speed. Solitons are caused by a cancellation of nonlinear and dispersive effects in the medium. (The term "dispersive effects" refers to a property of certain systems where the speed of the waves varies according to frequency.) Solitons arise as the solutions of a widespread class of weakly nonlinear dispersive partial differential equations describing physical systems. The soliton phenomenon was first described by John Scott Russell (1808–1882) who observed a solitary wave in the Union Canal in Scotland. He reproduced the phenomenon in a wave tank and named it the "Wave of Translation".

So in a sense the shock front\horn for me in respect of Gran Sasso is the idea that such a front becomes a dispersive element in medium expression of earth to know that such densities in earth have a means by which we can measure relativist interpretations as assign toward density determinations in the earth.  Yet,  there are things not held to this distinction so know that they move on past such targets so as to show cosmological considerations are just as relevant today as they are while we set up the experimental avenues toward identifying this relationship here on earth.

For more than a decade, scientists have seen evidence that the three known types of neutrinos can morph into each other. Experiments have found that muon neutrinos disappear, with some of the best measurements provided by the MINOS experiment. Scientists think that a large fraction of these muon neutrinos transform into tau neutrinos, which so far have been very hard to detect, and they suspect that a tiny fraction transform into electron neutrinos. See: Fermilab experiment weighs in on neutrino mystery

When looking out at the universe such perspective do not hold relevant for those not looking past the real toward the abstract? To understand the distance measure of binary star of Taylor and Hulse,  such signals need to be understood in relation to what is transmitted out into the cosmos? How are we measuring that distance? For some who are even more abstractedly gifted they may see the waves generated in gravitational expression. So this becomes a means which which to ask if the binary stars are getting closer then how is this distance measured? You see?

 Measurement of the neutrino velocity with the OPERA detectorin the CNGS beam

Monday, October 12, 2009

Pressure and heat melts protons and neutrons into a new state of matter - the quark gluon plasma.

Now you must know that this entry holds philosophical perspective and is the mandate of Night Light Mining Company to explore the potentials of planetary and geological data gained from scientific analysis to help the society of earth to move farther out into space, and to colonize.

Why are Planets Round?

It is always interesting to see water in space.

Image: NASA/JPL-
Planets are round because their gravitational field acts as though it originates from the center of the body and pulls everything toward it. With its large body and internal heating from radioactive elements, a planet behaves like a fluid, and over long periods of time succumbs to the gravitational pull from its center of gravity. The only way to get all the mass as close to planet's center of gravity as possible is to form a sphere. The technical name for this process is "isostatic adjustment."

With much smaller bodies, such as the 20-kilometer asteroids we have seen in recent spacecraft images, the gravitational pull is too weak to overcome the asteroid's mechanical strength. As a result, these bodies do not form spheres. Rather they maintain irregular, fragmentary shapes.

I wanted to explore the philosophical bend first, as it sets the tone for analysis not only of the potentials of planets but of what we can gained from understanding the place of values we can set around ourselves.

Two-dimensional analogy of space–time distortion. Matter changes the geometry of spacetime, this (curved) geometry being interpreted as gravity. White lines do not represent the curvature of space but instead represent the coordinate system imposed on the curved spacetime, which would be rectilinear in a flat spacetime. See: Spacetime

Be it known then, that such universality can exist in principle around this "central core" that such equatorial measures are distinctive and related to the equatorial possibility of Inverse Square Law, that as a mathematical principle, this is brought to bear on how we solidify the substance of the elemental table, that we can say, indeed, that such values can be assigned in "refractive light" to values which are built to become "round in planetary constitution."

The life cycle of a lunar impact and associated time and special scales. The LCROSS measurement methods are “layered” in response to the rapidly evolving impact environment. See: Impact:Lunar CRater Observation Satellite (LCROSS)

It becomes an evolutionary discourse then about what began from universality "in principle" can become such a state as evident in the framework of elemental consideration, that one might say indeed that it is "this constitution" that will signify the relevance to the spacetime fabric and it's settled orbit.

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Isostatic Adjustment is Why Planets are Round?

Centroids

Thursday, January 29, 2009

Formation of Gravity

Wegener proposed that the continents floated somewhat like icebergs in water. Wegener also noted that the continents move up and down to maintain equilibrium in a process called isostasy.Alfred Wegener

Just thought I would add this for consideration. Grace satellite does a wonderful job of discerning this feature? Amalgamating differing perspectives allows one to encapsulate a larger view on the reality of Earth. More then the sphere. More then, what Joseph Campbell describes:

The Power of Myth With Bill Moyers, by Joseph Campbell , Introduction that Bill Moyers writes,

"Campbell was no pessimist. He believed there is a "point of wisdom beyond the conflicts of illusion and truth by which lives can be put back together again." Finding it is the "prime question of the time." In his final years he was striving for a new synthesis of science and spirit. "The shift from a geocentric to a heliocentric world view," he wrote after the astronauts touched the moon, "seemed to have removed man from the center-and the center seemed so important...

While one can indeed approximate according to the spherical cow, in terms of events in the cosmos, I was being more specific when it comes to demonstrating a geometrical feature of the sphere in terms of the geometry of the Centroid. This feature is embedded in the validation of the sphere in regard to gravity?

Image: NASA/JPL-
Planets are round because their gravitational field acts as though it originates from the center of the body and pulls everything toward it. With its large body and internal heating from radioactive elements, a planet behaves like a fluid, and over long periods of time succumbs to the gravitational pull from its center of gravity. The only way to get all the mass as close to planet's center of gravity as possible is to form a sphere. The technical name for this process is "isostatic adjustment."

With much smaller bodies, such as the 20-kilometer asteroids we have seen in recent spacecraft images, the gravitational pull is too weak to overcome the asteroid's mechanical strength. As a result, these bodies do not form spheres. Rather they maintain irregular, fragmentary shapes.

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It was important to see how such planets form and given their "Mass and densities" which I thought to show how such a valuation could be seen in relation to the variance of gravity so it is understood.

Isostasy (Greek isos = "equal", stásis = "standstill") is a term used in geology to refer to the state of gravitational equilibrium between the earth's lithosphere and asthenosphere such that the tectonic plates "float" at an elevation which depends on their thickness and density. This concept is invoked to explain how different topographic heights can exist at the Earth's surface. When a certain area of lithosphere reaches the state of isostasy, it is said to be in isostatic equilibrium. Isostasy is not a process that upsets equilibrium, but rather one which restores it (a negative feedback). It is generally accepted that the earth is a dynamic system that responds to loads in many different ways, however isostasy provides an important 'view' of the processes that are actually happening. Nevertheless, certain areas (such as the Himalayas) are not in isostatic equilibrium, which has forced researchers to identify other reasons to explain their topographic heights (in the case of the Himalayas, by proposing that their elevation is being "propped-up" by the force of the impacting Indian plate).

In the simplest example, isostasy is the principle of buoyancy observed by Archimedes in his bath, where he saw that when an object was immersed, an amount of water equal in volume to that of the object was displaced. On a geological scale, isostasy can be observed where the Earth's strong lithosphere exerts stress on the weaker asthenosphere which, over geological time flows laterally such that the load of the lithosphere is accommodated by height adjustments.

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Such strength variances can be attributed to the height with which this measure is taken(time clocks and such) and such a validation in terms of Inverse Square Law goes to help to identify this strength and weakness, according to the nature of the mass and density of the planet.

As one of the fields which obey the general inverse square law, the gravity field can be put in the form shown below, showing that the acceleration of gravity, g, is an expression of the intensity of the gravity field.
See: Hyperphysics-Inverse Square Law-Gravity

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It is important then such a measure of the energy needed in which to overcome the pull of the earth, then was assigned it's energy value so such calculations are then validated in the escape velocity. There are other ways in which to measure spots in space when holding a bulk view of the reality in regards to gravity concentrations and it locations.

See: Hyperphysics-Gravity-Escape Velocity

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• Isostatic Adjustment is Why Planets are Round?
• Concepts of the Fifth Dimension
• Dealing With a 5D World
• Wednesday, January 23, 2008

Ueber die Hypothesen, welche der Geometrie zu Grunde liegen.

As I pounder the very basis of my thoughts about geometry based on the very fabric of our thinking minds, it has alway been a reductionist one in my mind, that the truth of the reality would a geometrical one.

The emergence of Maxwell's equations had to be included in the development of GR? Any Gaussian interpretation necessary, so that the the UV coordinates were well understood from that perspective as well. This would be inclusive in the approach to the developments of GR. As a hobbyist myself of the history of science, along with the developments of today, I might seem less then adequate in the adventure, I persevere.

On the Hypotheses which lie at the Bases of Geometry.
Bernhard Riemann
Translated by William Kingdon Clifford

[Nature, Vol. VIII. Nos. 183, 184, pp. 14--17, 36, 37.]

It is known that geometry assumes, as things given, both the notion of space and the first principles of constructions in space. She gives definitions of them which are merely nominal, while the true determinations appear in the form of axioms. The relation of these assumptions remains consequently in darkness; we neither perceive whether and how far their connection is necessary, nor a priori, whether it is possible.

From Euclid to Legendre (to name the most famous of modern reforming geometers) this darkness was cleared up neither by mathematicians nor by such philosophers as concerned themselves with it. The reason of this is doubtless that the general notion of multiply extended magnitudes (in which space-magnitudes are included) remained entirely unworked. I have in the first place, therefore, set myself the task of constructing the notion of a multiply extended magnitude out of general notions of magnitude. It will follow from this that a multiply extended magnitude is capable of different measure-relations, and consequently that space is only a particular case of a triply extended magnitude. But hence flows as a necessary consequence that the propositions of geometry cannot be derived from general notions of magnitude, but that the properties which distinguish space from other conceivable triply extended magnitudes are only to be deduced from experience. Thus arises the problem, to discover the simplest matters of fact from which the measure-relations of space may be determined; a problem which from the nature of the case is not completely determinate, since there may be several systems of matters of fact which suffice to determine the measure-relations of space - the most important system for our present purpose being that which Euclid has laid down as a foundation. These matters of fact are - like all matters of fact - not necessary, but only of empirical certainty; they are hypotheses. We may therefore investigate their probability, which within the limits of observation is of course very great, and inquire about the justice of their extension beyond the limits of observation, on the side both of the infinitely great and of the infinitely small.

For me the education comes, when I myself am lured by interest into a history spoken to by Stefan and Bee of Backreaction. The "way of thought" that preceded the advent of General Relativity.

Einstein urged astronomers to measure the effect of gravity on starlight, as in this 1913 letter to the American G.E. Hale. They could not respond until the First World War ended.

Translation of letter from Einstein's to the American G.E. Hale by Stefan of BACKREACTION

Zurich, 14 October 1913

Highly esteemed colleague,

a simple theoretical consideration makes it plausible to assume that light rays will experience a deviation in a gravitational field.

[Grav. field] [Light ray]

At the rim of the Sun, this deflection should amount to 0.84" and decrease as 1/R (R = [strike]Sonnenradius[/strike] distance from the centre of the Sun).

[Earth] [Sun]

Thus, it would be of utter interest to know up to which proximity to the Sun bright fixed stars can be seen using the strongest magnification in plain daylight (without eclipse).

Fast Forward to an Effect

Bending light around a massive object from a distant source. The orange arrows show the apparent position of the background source. The white arrows show the path of the light from the true position of the source.

The fact that this does not happen when gravitational lensing applies is due to the distinction between the straight lines imagined by Euclidean intuition and the geodesics of space-time. In fact, just as distances and lengths in special relativity can be defined in terms of the motion of electromagnetic radiation in a vacuum, so can the notion of a straight geodesic in general relativity.

To me, gravitational lensing is a cumulative affair that such a geometry borne into mind, could have passed the postulates of Euclid, and found their way to leaving a "indelible impression" that the resources of the mind in a simple system intuits.

Einstein, in the paragraph below makes this clear as he ponders his relationship with Newton and the move to thinking about Poincaré.

The move to non-euclidean geometries assumes where Euclid leaves off, the basis of Spacetime begins. So such a statement as, where there is no gravitational field, the spacetime is flat should be followed by, an euclidean, physical constant of a straight line=C?

Einstein:

I attach special importance to the view of geometry which I have just set forth, because without it I should have been unable to formulate the theory of relativity. ... In a system of reference rotating relatively to an inert system, the laws of disposition of rigid bodies do not correspond to the rules of Euclidean geometry on account of the Lorentz contraction; thus if we admit non-inert systems we must abandon Euclidean geometry. ... If we deny the relation between the body of axiomatic Euclidean geometry and the practically-rigid body of reality, we readily arrive at the following view, which was entertained by that acute and profound thinker, H. Poincare:--Euclidean geometry is distinguished above all other imaginable axiomatic geometries by its simplicity. Now since axiomatic geometry by itself contains no assertions as to the reality which can be experienced, but can do so only in combination with physical laws, it should be possible and reasonable ... to retain Euclidean geometry. For if contradictions between theory and experience manifest themselves, we should rather decide to change physical laws than to change axiomatic Euclidean geometry. If we deny the relation between the practically-rigid body and geometry, we shall indeed not easily free ourselves from the convention that Euclidean geometry is to be retained as the simplest. (33-4)

It is never easy for me to see how I could have moved from what was Euclid's postulates, to have graduated to my "sense of things" to have adopted this, "new way of seeing" that is also accumulative to the inclusion of gravity as a concept relevant to all aspects of the way in which one can see reality.

See:

• On the Hypothese at the foundations of Geometry

• Gravity and Electromagnetism?

• "The Confrontation between General Relativity and Experiment" by Clifford M. Will
• Tuesday, December 11, 2007

The Other Side of the Coin

Susan Holmes- Statistician Persi Diaconis' mechanical coin flipper.

In football's inaugural kickoff coin toss, the coin is not caught but allowed to bounce on the ground. That introduces an extra complication, one mathematicians have yet to sort out.

Persi Diaconis See here.

The Ground State

There is always an "inverse order to Gravity" that helps one see in ways that we are not accustom too. The methods of "prospective measurements" in science have taken a radical turn? Satellites as a measure, have focused our views.

While one may now look at the "sun in a different way" it had to first display itself across the "neutrino Sudbury screen" before we knew to picture the sun now in the way we do. It was progressive, in the way the sun now forms a picture of what we now know in measure.

So you try and bring it all together under this "new way of seeing" and hopefully your account of "the way reality is," is shared by others who now understand what the heck I am doing?

To get a simple physical understanding of what the acoustic oscillations are, it may be helpful to change the perspective. Normally, the common way of presenting the phenomenon has been in terms of standing waves where the analysis is done in Fourier space. But the baryon-photon fluid really is just carrying sound waves, and the dispersion relation is even pretty linear. So let’s instead think of things in terms of traveling waves in real spacehttp://72.14.253.104/search?q=cache:xLcnPGO6BDQJ:cmb.as.arizona.edu/~eisenste/acousticpeak/spherical_acoustic.ps+Fourier+space+when+I%27m+thinking+about+sound.&hl=en&ct=clnk&cd=1&gl=ca-Steward Observatory, University of Arizona
c 2005

"Uncertainty" has this way of rearing it's head once we reduce our perspective to the microscopic principals(sand), yet, on the other side of the coin, how is it that only 5% of mass determination allows us to see the universe mapped in the way it has in regards to the CMB?

There is this "entropic valuation" and with it, temperature. Some do not like the porridge "to hot or to cold," with regards to "living in a place" within the universe.

So I'll repeat the blog comment entry here in this blog so one can gather some of what I mean.

At 2:56 AM, December 11, 2007, Plato said...
As a lay person with regards to the complexity of the language(sound)and universe, it is sometimes reduced to "seeing in ways that are much easier to deal with," although of course, it may not be the same for everyone?:)

:)Something good science people "do not want to hear?"

The launching of the sound waves is very similar to dropping a rock in a pond and seeing the circular wave come off (obviously that a gravity wave, not a compressional wave, but I’m focusing on the geometry). The difference here is that the area where the “rock” entered is still the most likely region to form galaxies; the spherical shell that it produced is only carrying 5% of the mass.

Hopefully, this demystifies the effect: we’re seeing the imprint of spherical sound waves launched from the sites of dark matter overdensities in the early universe. But also I hope it makes it more clear as to why this effect is so robust: the propagation of sound in the baryon-photon plasma is very simple, and all we’re doing is measuring how far it got.

"Mapping," had to begin somewhere. Whatever that may mean,one may think of Mendeleeev or Newlands.

Generally Grouping Order increases the density of objects within a frame of reference, resulting in a more pronounced single object.

"Sand with pebbles" on a beach? It had to arise from someplace?

The other side of the Coin is?

This recording was produced by converting into audible sounds some of the radar echoes received by Huygens during the last few kilometres of its descent onto Titan. As the probe approaches the ground, both the pitch and intensity increase. Scientists will use intensity of the echoes to speculate about the nature of the surface.

and not to be undone.

Mass results in an increase in the gravitational force exerted by an object. Density fluctuations on the surface of the Earth and in the underlying mantle are thus reflected invariations in the gravity field.As the twin GRACE satellites orbit the Earth together, these gravity field variations cause infinitesimal changes in the distance between the two. These changes will be measured with unprecedented accuracy by the instruments aboard GRACE leading to a more precise rendering of the gravitational field than has ever been possible to date.

Layman pondering.

So now that you have this "comprehensive view" I have gained on the way I am seeing the universe. You can "now see" how diverse the application of sound in analogy is. It is helping me to develop the "Colour of Gravity" as a artistic endeavour. I refrain from calling it "scientific" and be labelled a crackpot.

A Synesthesic View on Life.

Who knows how I can put these things together and come up with what I do. Yet, it had not gone unnoticed that such concepts could merge into one another, and come out with some tangible result as a "artistic effort." Some may be used to the paintings of Kandinsky(abstract), yet the plethora of imaging that unfolds in the conceptual framework might have been self evident, from such a chaotic mess of the layman's view here?

Tuesday, December 04, 2007

Descriptive geometry

At this point in the development, although geometry provided a common framework for all the forces, there was still no way to complete the unification by combining quantum theory and general relativity. Since quantum theory deals with the very small and general relativity with the very large, many physicists feel that, for all practical purposes, there is no need to attempt such an ultimate unification. Others however disagree, arguing that physicists should never give up on this ultimate search, and for these the hunt for this final unification is the ‘holy grail’. Michael Atiyah

The search for this "cup that overflow" is at the heart of all who venture for the lifeblood of the mystery of life. While Atiyah speaks to a unification of Quantum theory and Relativity, it is not without a understanding on Einstein's part that having gained from Marcel Grossmann, that such a descriptive geometry could be leading Einstein to discover the very basis of General relativity?

Marcel Grossmann was a mathematician, and a friend and classmate of Albert Einstein. He became a Professor of Mathematics at the Federal Polytechnic Institute in Zurich, today the ETH Zurich, specialising in descriptive geometry.

So what use "this history" in face of the unification of the very large with the very small? How far back should one go to know that the steps previous were helping to shape perspective for the future. Allow for perspective to be changed, so that new avenues of research could spring forth

Gaspard Monge, Comte de Péluse-Portrait by Naigeon in the Musée de Beaune Born: 9 May 1746 in Beaune, Bourgogne, France
Died: 28 July 1818 in Paris, France-was a French mathematician and inventor of descriptive geometry.

Monge contributed (1770–1790) to the Memoirs of the Academy of Turin, the Mémoires des savantes étrangers of the Academy of Paris, the Mémoires of the same Academy, and the Annales de chimie, various mathematical and physical papers. Among these may be noticed the memoir "Sur la théorie des déblais et des remblais" (Mém. de l’acad. de Paris, 1781), which, while giving a remarkably elegant investigation in regard to the problem of earth-work referred to in the title, establishes in connection with it his capital discovery of the curves of curvature of a surface. Leonhard Euler, in his paper on curvature in the Berlin Memoirs for 1760, had considered, not the normals of the surface, but the normals of the plane sections through a particular normal, so that the question of the intersection of successive normals of the surface had never presented itself to him. Monge's memoir just referred to gives the ordinary differential equation of the curves of curvature, and establishes the general theory in a very satisfactory manner; but the application to the interesting particular case of the ellipsoid was first made by him in a later paper in 1795. (Monge's 1781 memoir is also the earliest known anticipation of Linear Programming type of problems, in particular of the transportation problem. Related to that, the Monge soil-transport problem leads to a weak-topology definition of a distance between distributions rediscovered many times since by such as L. V. Kantorovich, P. Levy, L. N. Wasserstein, and a number of others; and bearing their names in various combinations in various contexts.) A memoir in the volume for 1783 relates to the production of water by the combustion of hydrogen; but Monge's results had been anticipated by Henry Cavendish.

Descriptive geometry

Example of four different 2D representations of the same 3D object

Descriptive geometry is the branch of geometry which allows the representation of three-dimensional objects in two dimensions, by using a specific set of procedures. The resulting techniques are important for engineering, architecture, design and in art. [1] The theoretical basis for descriptive geometry is provided by planar geometric projections. Gaspard Monge is usually considered the "father of descriptive geometry". He first developed his techniques to solve geometric problems in 1765 while working as a draftsman for military fortifications, and later published his findings. [2]

Monge's protocols allow an imaginary object to be drawn in such a way that it may be 3-D modeled. All geometric aspects of the imaginary object are accounted for in true size/to-scale and shape, and can be imaged as seen from any position in space. All images are represented on a two-dimensional drawing surface.

Descriptive geometry uses the image-creating technique of imaginary, parallel projectors emanating from an imaginary object and intersecting an imaginary plane of projection at right angles. The cumulative points of intersections create the desired image.

So given the tools, we learnt to see how objects within a referenced space, given to such coordinates, have been defined in that same space. Where is this point with in that reference frame?

What is born within that point, that through it is emergent product. Becomes a thing of expression from nothing? It's design and all, manifested as a entropic valuation of the cooling period? Crystalline shapes born by design, and by element from whence it's motivation come? An arrow of time?

Monday, November 12, 2007

Where Spacetime is flat?

......A Condensative Result exists. Where "energy concentrates" and expresses outward.

I mean if I were to put on my eyeglasses, and these glasses were given to a way of seeing this universe, why not look at the whole universe bathed in such spacetime fabric?

This a opportunity to get "two birds" with one stone?

I was thinking of Garrett's E8 Theory article and Stefan's here.

On March 31, 2006 the high-resolution gravity field model EIGEN-GL04C has been released. This model is a combination of GRACE and LAGEOS mission plus 0.5 x 0.5 degrees gravimetry and altimetry surface data and is complete to degree and order 360 in terms of spherical harmonic coefficients.

High-resolution combination gravity models are essential for all applications where a precise knowledge of the static gravity potential and its gradients is needed in the medium and short wavelength spectrum. Typical examples are precise orbit determination of geodetic and altimeter satellites or the study of the Earth's crust and mantle mass distribution.

But, various geodetic and altimeter applications request also a pure satellite-only gravity model. As an example, the ocean dynamic topography and the derived geostrophic surface currents, both derived from altimeter measurements and an oceanic geoid, would be strongly correlated with the mean sea surface height model used to derive terrestrial gravity data for the combination model.

Therefore, the satellite-only part of EIGEN-GL04C is provided here as EIGEN-GL04S1. The contributing GRACE and Lageos data are already described in the EIGEN-GL04C description. The satellite-only model has been derived from EIGEN-GL04C by reduction of the terrestrial normal equation system and is complete up to degree and order 150.

How many really understand/see the production of gravitational waves in regards to Taylor and Hulse?

To see Stefan's correlation in terms of "wave production" is a dynamical quality to what is still be experimentally looked for by LIGO?

As scientists, do you know this?

6:41 AM, November 11, 2007
See here

Thus the binary pulsar PSR1913+16 provides a powerful test of the predictions of the behavior of time perceived by a distant observer according to Einstein's Theory of Relativity.

Since we know the theory of Relativity is about Gravity, then how is it the applications can be extended to the way we see "anew" in our world?

A sphere, our earth, not so round anymore.

Uncle has tried to correct me on "isostatic adjustment."

Derek Sears, professor of cosmochemistry at the University of Arkansas, explains. See here

Planets are round because their gravitational field acts as though it originates from the center of the body and pulls everything toward it. With its large body and internal heating from radioactive elements, a planet behaves like a fluid, and over long periods of time succumbs to the gravitational pull from its center of gravity. The only way to get all the mass as close to planet's center of gravity as possible is to form a sphere. The technical name for this process is "isostatic adjustment."

With much smaller bodies, such as the 20-kilometer asteroids we have seen in recent spacecraft images, the gravitational pull is too weak to overcome the asteroid's mechanical strength. As a result, these bodies do not form spheres. Rather they maintain irregular, fragmentary shapes. K. Shumacker. Scientific America

Do not have time to follow up at this moment.

7:02 AM, November 11, 2007
.....and here.

In context of the post and differences, I may not have pointed to the substance of the post, yet I would have dealt with my problem in seeing.

In general terms, gravitational waves are radiated by objects whose motion involves acceleration, provided that the motion is not perfectly spherically symmetric (like a spinning, expanding or contracting sphere) or cylindrically symmetric (like a spinning disk).

A simple example is the spinning dumbbell. Set upon one end, so that one side of the dumbell is on the ground and the other end is pointing up, the dumbbell will not radiate when it spins around its vertical axis but will radiate if it tumbles end-over-end. The heavier the dumbbell, and the faster it tumbles, the greater is the gravitational radiation it will give off. If we imagine an extreme case in which the two weights of the dumbbell are massive stars like neutron stars or black holes, orbiting each other quickly, then significant amounts of gravitational radiation would be given off.

Given the context of the "whole universe" what is actually pervading, if one did not include gravity?

So singularities are pointing to the beginning(i), yet, we do not know if we should just say, the Big Bang, because, one would had to have calculated the energy used and where did it come from "previous" to manifest?

So some will have this philosophical position about "nothing(?)," and "everything as already existing."

Wherever there are no gravitational waves the space time is flat. One would have to define these two variances. One from understanding the relation to "radiation" and the other "perfectly spherically symmetric."

Friday, September 28, 2007

The History of Magnetic Vision

Grossmann is getting his doctorate on a topic that is connected with non-Euclidean geometry. I don’t know what it is.
Einstein to Mileva Maric,1902

The long-distance navigational abilities of animals have fascinated humans for centuries and challenged scientists for decades. How is a butterfly with a brain weighing less than 0.02 grams able to find its way to a very specific wintering site thousands of kilometers away, even though it has never been there before? And, how does a migratory bird circumnavigate the globe with a precision unobtainable by human navigators before the emergence of GPS satellites? To answer these questions, multi-disciplinary approaches are needed. A very good example of such an approach on shorter distance navigation is the classical ongoing studies on foraging trips of Cataglyphis desert ants. My Nachwuchsgruppe intends to use mathematical modelling, physics, quantum chemistry, molecular biology, neurobiology, computer simulations and newly developed laboratory equipment in combination with behavioral experiments and analyses of field data to achieve a better understanding of the behavioral and physiological mechanisms of long distance navigation in insects and birds.

Tony Smith has some interesting information in response to a post by Clifford of Asymptotia.

Clifford writes:
This is simply fascinating. I heard about it on NPR. While it is well known that birds are sensitive to the earth’s magnetic field, and use it to navigate, apparently it’s only been recently shown that this sensitivity is connected directly to the visual system (at least in some birds). The idea seems to be that the bird has evolved a mechanism for essentially seeing the magnetic field, presumably in the sense that magnetic information is encoded in the visual field and mapped to the brain along with the usual visual data

While my post has been insulted by cutting it short(and stamping it and proclaiming irrelevance,) I'd like to think otherwise, even in face of his streamlining that Clifford likes to do. His blog, he can do what he wants of course.

In any case, it seems reasonable to agree with Buhler, who concludes in his biography of Gauss that "the oft-told story according to which Gauss wanted to decide the question [of whether space is perfectly Euclidean] by measuring a particularly large triangle is, as far as we know, a myth."

So I'll repeat the post of mine here and the part, that he has deleted. You had to know how to see the relevance of the proposition of birds in relation to the magnetic field of the earth, to know why the bird relation is so important.

On Magnetic vision
Rupert Sheldrake has had similar thoughts on this topic.

"Numerous experiments on homing have already been carried out with pigeons. Nevertheless, after nearly a century of dedicated but frustrating research, no one knows how pigeons home, and all attempts to explain their navigational ability in terms of known senses and physical forces have so far proved unsuccessful. Researchers in this field readily admit the problem. 'The amazing flexibility of homing and migrating birds has been a puzzle for years. Remove cue after cue, and yet animals still retain some backup strategy for establishing flight direction.' 'The problem of navigation remains essentially unsolved.'

Many of academics might have steered clear because of the the thoughts and subject he has about this? It seems to me that if this information is credible, then some of Rupert's work has some substance to it and hence, brings some credibility to the academic outlook?

Update: Here I am adding some thoughts in regards to Rupert Sheldrake that I was having while reading his work. He had basically himself denounced the process of birds having an physiological connection to magnetic fields because of not having any information to support the magnetic vision Clifford is talking about. So Rupert moves beyond this speculation, to create an idea about what he calls Morphic resonance with regards to animals.

So Rupert presents future data and theoretics in face of what we now know in terms of the neurological basis is experimentally being talked about in the article in question Clifford is writing about.

On How to see in the Non Euclidean Geometrical World

8.6 On Gauss's Mountains

One of the most famous stories about Gauss depicts him measuring the angles of the great triangle formed by the mountain peaks of Hohenhagen, Inselberg, and Brocken for evidence that the geometry of space is non-Euclidean. It's certainly true that Gauss acquired geodetic survey data during his ten-year involvement in mapping the Kingdom of Hanover during the years from 1818 to 1832, and this data included some large "test triangles", notably the one connecting the those three mountain peaks, which could be used to check for accumulated errors in the smaller triangles. It's also true that Gauss understood how the intrinsic curvature of the Earth's surface would theoretically result in slight discrepancies when fitting the smaller triangles inside the larger triangles, although in practice this effect is negligible, because the Earth's curvature is so slight relative to even the largest triangles that can be visually measured on the surface. Still, Gauss computed the magnitude of this effect for the large test triangles because, as he wrote to Olbers, "the honor of science demands that one understand the nature of this inequality clearly". (The government officials who commissioned Gauss to perform the survey might have recalled Napoleon's remark that Laplace as head of the Department of the Interior had "brought the theory of the infinitely small to administration".) It is sometimes said that the "inequality" which Gauss had in mind was the possible curvature of space itself, but taken in context it seems he was referring to the curvature of the Earth's surface.
See:Reflections on Relativity

As a layperson, Riemann and Gauss were instrumental for helping me see beyond what we were accustom to in Euclidean, so I find Clifford's blog post extremely interesting as well. Maybe even a biological/physiological impute into our senses as well? Who knows?:)

Einstein's youth and the compass, becomes the motivation that drives the vision of what exists beyond what was acceptable in that youth. The mystery. Creates a new method on how we view the world beyond the magnetic, to help us include the view in the gravitational one as well.

From a early age, young Albert showed great interest in the world around him. When he was five years old, his father gave him a compass, and the child was enchanted by the device and intrigued by the fact the needle followed a invisible field to point always in the direction of the north pole.Reminiscing in old age, Einstein mentioned this incident as one of the factors that perhaps motivated him years later to study the gravitational field. God's Equation, by Amir D. Aczel, Pg 14

While something could exist that is abstract, like for instance the Gaussian arc, this inclusion in the value of general relativity is well known. Mileva's response in quote above was the key for Einstein's views on developing General Relativity, and without it "electromagnetism would not, and could not" have been included geometrically in the theory of GR.

It was a succession to "Gravitational wave production" that was understood in regards to Taylor and Hulse.

The theory of relativity predicts that, as it orbits the Sun, Mercury does not exactly retrace the same path each time, but rather swings around over time. We say therefore that the perihelion -- the point on its orbit when Mercury is closest to the Sun -- advances.

I would think this penduum exercise would make a deeper impression if held in concert with the way one might have look at Mercuries orbit.

Or, binary pulsar PSR 1913+16 of Taylor and Hulse. These are macroscopic valutions in what the pendulum means. Would this not be true? See:Harmonic Oscillation

I guess not every string theorist would know this? Maybe even Bee would understand that "German" is replace by another form of seeing using abstract language, for how everything can be seen in relation to the ground state? Where there are no gravitational waves, spacetime is flat.

You had to know how such views on the navigation of the birds could have a direct link to the evolutionary output of the biology and physiology of the species. What Toposense?

Yes it's a process where the mathematical minds look at knitting and such, in such modularc forms, to have said, "hey there is a space of thinking" that we can do really fancy twists and such.

One thing us humans can certainly do is construct the monumental world reality with straight lines and such in the Euclidean view. But nature was there before we thought to change all it's curves.

But the truth is, the Earth's topography is highly variable with mountains, valleys, plains, and deep ocean trenches. As a consequence of this variable topography, the density of Earth's surface varies. These fluctuations in density cause slight variations in the gravity field, which, remarkably, GRACE can detect from space. See: The Mind Field

Look out into the wild world that nature itself presents and tell me what the ancient mind did not see. Native Americans lived closer to nature. Hopefully you'll understand why it is we must engage ourselves to experiencing the views of nature?:)

Mandalic Construction

See: The Last Mimzy

The "Ancient Medicine wheels" might have been place accordingly? Do you imagine seeing in the abstract world, the magnetic view we see of earth in it's different disguise?

So that last line about the "medicine wheels" probably caused Clifford to do what he did in regards to the post I wrote.

Yes I am creating a direct link between the Medicine Wheels and the Medicine Wheel as a Mandala constructed by early Native Americans. Where they were shamanically placed on the earth.

What is a Medicine Wheel?

The term "medicine wheel" was first applied to the Big Horn Medicine Wheel in Wyoming, the most southern one known. That site consists of a central cairn or rock pile surrounded by a circle of stone; lines of cobbles link the central cairn and the surrounding circle. The whole structure looks rather like a wagon wheel lain-out on the ground with the central cairn forming the hub, the radiating cobble lines the spokes, and the surrounding circle the rim. The "medicine" part of the name implies that it was of religious significance to Native peoples.

Figure 4 - Distribution of medicine wheel sites east of the Rockies

What was of importance is the underlying psychological patterns that exist in the forms of Mandalas. That such a thing like the Medicine wheel, would retain a impact from one's life, to another life.

There are various forms of mandalas with distinct concepts and different purposes. The individual representations range from the so-called Cosmic Mandalas, which transmit the ancient knowledge of the development of the universe and the world-systems which represents a high point among Mandalas dedicated to meditation; to the Mandalas of the Medicine Buddha which demonstrates how the Buddha-power radiates in all directions, portraying the healing power of the Buddha.

It would not be easy to understand this "seed mandala" as it makes it way into conscious recognition. It arises to awareness through the subconscious pathway during our susceptibility in dream time. This open accessibility is the understanding that there is a closer connection to the universality of being, and the realization that the degrees beyond the "emotive body" is developing the understanding of the "mental one" as well as, leading to "the spiritual one."

This comparative view is analogousness to development beyond the abstract view we see of earth in it's gravitational form.

However, the signals that scientists hope to measure with LISA and other gravitational wave detectors are best described as "sounds." If we could hear them, here are some of the possible sounds of a gravitational wave generated by the movement of a small body inspiralling into a black hole.

It would be much like a "energy packet" that would contain all that is demonstrated in "extravagant patterns." Look like a "flower in real life," or a "intricate pattern," while encouraging the person to explore these doorways and move on from.

That seed contains all of the history we have supplanted to it by how we built previously and embedded all the philosophy we had learnt from it.

The Emotional Body of the Earth

Would to me seem very emotive in terms of it's weather. How such weather patterns spread across the earth. Also, it would not seem so strange then that while we would have seen polarization aspects in the cosmos, in terms of magnetic field variances in relation to north and south, we would see "this of value" in the earth as well?

So would the earth have it's positive and negative developments in relation to aspect of it's weather? Most certainly psychological when the snows have lasted so long, one could indeed wish for warmer weather, but that's not what I mean. I mean on a physiological level, such ionic generations would indeed cause the state of the human body to react.